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CHAPTER12.

THE MAINTENANCE OF BLOOD PRESSURE.

The systolic blood pressure is equivalent to the product of R . l . PR , and this means thatsystolic pressure will fluctuate when any one of these variables is changed unless there is asimultaneous alteration of one or both of the others in the opposite direction.In this sense theblood pressure is fixed by the balance struck between its constituents.Now the significance ofthe level of the blood pressure also depends upon this balance, in the sense that a rise in say thevalue of `R' has a quite different implication for the circulation, from a rise in `lPR'.In the firstinstance, the circulation is contracting in volume and becoming concentrated into the centralvessels, while in the second, the circulatory volume is expanding into the capillary bed, yet thefinal systolic blood pressure may be the same in each case. On the other hand, either change islikely to be reflected in alteration in stroke volume and / or average mean linear velocity of theblood, and of the mean linear velocity at the end of diastole.Variations of pulse pressure and ofdiastolic blood pressure will accompany these changes, and will be of different magnitude anddirection in each example.It is the purpose of this chapter to attempt to coordinate all of thevarious factors which together produce the level of blood pressures for any particular individual,and the implications these factors may have for that individual's present and future function.

The combination of energy sources available in the effector cells at systole is proportional to' 'and includes stored energy, accumulated energy, and developed energy, each equivalent tothe factor 'l', as well as a factor representing kinetic energy, and proportional to 'PR', whichmoves fluid and energy to tissue fluid from the combined energy available. The total energy isthen or systolic blood pressure, and can be represented as the product of pulse rate,stroke volume and lactate concentration, which between them maintain the combined energysource available for cell work.

Difficulty arises in maintaining blood pressure if 'l' is restricted and is then diminished,indicating a fall in stroke volume, lactate concentration, and/or pulse rate, each of which isnecessary to maintain the required cell energy level. Lactate concentration is proportional to cellenergy level at diastole, remaining from the previous ventricular beat, against which bloodvolume equivalent to stroke volume must be contributed to circulating blood volume. Strokevolume depends on cell length and cell strength, or 'l' and ' ', and can only increase if thesefactors are varied. Increase in stroke volume readily increases blood pressure if the otherparameters are unaltered. But if for some reason such an increase is impossible, pressure canonly rise if lactate concentration or pulse rate is increased instead. Increase in pulse rate whenstroke volume is limited may decrease its value even further, and any pressure increase thendepends on increased circulating lactate. The level of blood pressure depends on a three waybalance between stroke volume, lactate concentration , and pulse rate, and is regulated by mutualalteration of these values.

The requirements of different parts of the circulation vary widely from one another, both asregards total requirements over a set period, and also with respect to sudden change and rapid

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increase in demand. Some areas require a constant flow at constant pressure with little variationin metabolic activity over long periods of time, while others are subject to rapid surges in activitywhich place large demands on the local circulation, and also on the circulation as a whole. Thecirculation of the central nervous system is an example of the first type, while rapid contractionsof muscle groups during physical activity is an example of the second. The circulation must beso adjusted that both areas are adequately supplied at the same time. While variation in pressureand flow rates may be tolerated, and may even be desirable for repeated muscular contractions,the same variations could lead to interference with function in the central nervoussystem.Conditions of constant supply are so important in the latter case that an elaborate systemof homeostatic mechanisms is provided to ensure such a supply, and the conditions that thesemechanisms set, then have to be accepted by the other parts of the circulation in turn. The carotidsinus and carotid body have this type of function.

Wide variations of blood pressure are therefore undesirable in the circulation as a whole, quiteapart from the excessive strain which might be placed upon blood vessels that are not adaptedfor such variations. There is a considerable literature covering the vascular lesions which arelikely to occur when blood pressure is artificially raised (c.f. Goldby, 1974). On the other handsudden rises in arterial pressure occur normally at or before the commencement of muscularactivity, with emotional stress, and so on. Why does damage occur in some instances and not inothers?

Whatever the reason may be, consideration of this question must be deferred for the moment. Inthe meantime it is sufficient to accept that while variations of the order of 100% or more canoccur under physiological conditions, such changes are of a temporary nature, associated withemergency or stressful conditions, and in the normal subject, return rapidly to a normal level assoon as, or soon after, the emergency is over. Indeed, the time it takes for this to occur may beused as an indication of the `normality' or otherwise of the response.

During consideration of the energy equivalents in the circulatory model, it was stated that theenergy developed by the ventricle per beat was proportional to the product of peak arterialsystolic pressure and the circulatory volume, i.e. APs . Vs , modified by the ratio VPp / DPs(which sets the conditions for contraction of the ventricular muscle, VPp being the fillingpressure for the ventricle, and DPs being the after load, and consisting of the product of EDPland the contractility factor, ̀ 8'). The external cardiac work which this energy performs, is givenby the product of stroke volume, Q, and peak arterial systolic pressure, APs. It will be apparentthat this work can be represented by different values of `Q' and `APs' so long as they arereciprocally related and their product remains the same. Nevertheless the significance for themechanics of the circulation of any variations of `Q' and `APs' can be very great indeed. Themechanical efficiency of the ventricular contraction depends to a very great degree on the valueof ̀ Q', and in a previous chapter it was argued that the value of ̀ Q' was determined by metabolicconditions in the active tissues, and particularly by the ratio of the partial pressure of carbondioxide to that of oxygen, and the partial pressure of oxygen which was optimal for the activityof the oxidative enzymes in those tissues. These factors must be of considerable importance indetermining ̀ APs' as well as ̀ Q', and by inference, the values of ̀ R' and possibly of ̀ lPR' as well.It is necessary to consider the relationships between these variables in further detail.

If the work done by the ventricular muscle per beat is given by Q . APs , this can be written asQ . R . lPR , giving three variables, any one of which can alter the ventricular work, or if the

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latter is to remain constant, then one or both of the remaining two variables in the expression.There are in fact four variables, but it is convenient to treat `lPR' as a single variable in anargument in which `l' is assumed not to vary significantly.This may not always be the case; `l'can vary for instance if ligatures are placed on the limbs, and it can also vary if there is vascularocclusion, either temporary or permanent, from intense vasoconstriction or vascular damage. Atthe same time it should be borne in mind that any variation in the value of `l' would affect notonly the value of `lPR', but also the values of `Q' and `R' in equal degree, because each of thesevariables has `l' as one of its factors. In order to keep the argument as simple as possible, the likelihood of such events is ignored forthe present, though they must be addressed later in the chapter on adaptation to stress. (Theproduct `lPR' can be regarded as indicating the momentum given to each ml. of stroke volumeby ventricular contraction, and it therefore represents the `force of ventricular contraction'.)

For a given value of ventricular work per beat then, there is a three way balance which has to beachieved, and the ratios between each of the variables has some particular significance for thecirculation, as also have their products. In order to demonstrate this, the variables, their ratiosand their products, can best be illustrated in a triangular diagram as in Figures 14.1 and 14.2 .

In this equilateral triangle, the angles have been labelled `Q',`R', and `lPR'. Perpendicularsbisecting each angle will also bisect the opposite side of the triangle, and these lines will allintersect at a point in its centre. An imaginary line passing through this intersectionperpendicular to the plane of the triangle, allows the plane to be moved either forwards orbackwards along its length.The product of Q . R . lPR is the work done by the ventricle per beat.It can be imagined that moving the plane of the triangle forwards represents an increase in thevalues of `Q', `R', and `lPR', so that ventricular work is increased, and moving the planebackwards represents a decrease in these values, and a decrease in work done. For a particularwork load, it is of course possible to have different combinations of variables as alreadymentioned, and this can be represented by tilting the plane of the triangle so that it is no longerperpendicular to the imaginary line passing through its centre, though it is still possible for thetriangle to move forwards or backwards along it as before, representing changes in ventricularwork. This diagram allows one to estimate fairly readily what is likely to happen to theremaining variables should one or more of them, and/or the ventricular work load, be subject toalteration. Some examples may help to illustrate this.

a. Suppose in a particular case that `Q' and `R' remain constant, while `lPR' is allowed to vary.The triangle is then able to rotate about the axis `QR', and the work done must vary as thevariation in `lPR', and in the same direction. This requires that all of the variables in thecirculation will alter excepting only those which involve `Q' and `R' solely. i.e. the ratio of Q/R(or momentum / systolic pressure), and the product `QR' (R.V . v/lPR) will remain constant,while those involving `Q' and `lPR' plus those involving `R' and `lPR' (momentum in thecirculation and energy produced by the ventricle per beat, plus systolic pressure and energyproduced) will vary as `lPR' varies.b. If on the other hand, `Q' and the ventricular work both remain constant, while `R' and `lPR'are allowed to vary,. their variations will be of the same degree but in opposite directions as thetriangle rotates about the axis bisecting the angle at ̀ Q', but in this case the values of all the othervariables except ̀ Q' and the ventricular work will also vary, and the extent and direction of thesevariations can be readily estimated from the changes in `R' and `lPR'.

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A case of particular interest for the present discussion is similar to example b., but with ̀ lPR' andthe ventricular work remaining constant. Remembering that the square of `lPR' is an indicationof the energy release by the ventricle in unit time, this parameter will also be constant, and sowill the mechanical efficiency, unless it is modified by the ratio Vpp/DPs. The variablesinvolved in determining ventricular work which are still free to vary are ̀ Q' and ̀ R'. The productQ . R (or Q/V times R.Vs, or ventricular filling) is related to v/lPR, or the circulatory efficiency,while the ratio Q/R is largely determined by the oxidative capacity of the active tissues, whichis given by the ratio of partial pressure of carbon dioxide to the partial pressure of oxygenprevailing when oxidative conditions are optimal. This ratio of Q/R or , will nowbe referred to as the metabolic index because of its great importance in balancing theapportioning of ventricular work between potential and kinetic energy. If `Q' and `R' are eachmultiplied by ̀ lPR', the results are Q . lPR = v . V which is equivalent to the momentum of bloodin the circulation, and R . lPR = APs, so the ratio becomes `momentum' / systolic pressure. The importance of the metabolic ratio in determining arterial pressure when the work of theventricle remains constant, will be immediately apparent. The ratios of the other variables, i.e. R/lPR, and Q/lPR, are also of great interest. R/lPR, or the circulatory index has already been mentioned as determining the distribution ofblood in the circulation between the great vessels and the capillary circulation. If bothnumerator and denominator are multiplied by `lPR' , this will give a ratio of arterial pressure /energy released per unit time. Q/lPR in the same way is the ratio of momentum / energy releasedper unit time, and will now be called the `kinetic index', indicating the importance of `Q' indetermining the efficiency of the ventricular contraction. The products Q . lPR , and R . lPR,represent momentum and arterial systolic pressure respectively. In the present example if `R'goes up `Q' must be reduced, so that `momentum' is reduced and arterial pressure is increasedwith respect to energy released. The kinetic index is reduced, but efficiency is maintained by theincrease in ̀ R' and hence of the diastolic pressure, and the ratio DPs/VPp, the effect of which hasalready been emphasised in a previous chapter.On the other hand a fall in momentum means afall in average mean linear velocity,`v', and an increased average mean circulation time (CT).These examples are of course simplified `special cases' insofar as only two variables have beenfree to alter (and then only in a rigidly defined way) on each occasion.

But the triangle representing the variables involved in determining ventricular work could in factrotate about any axis allowing all three variables and the cardiac work to change simultaneously.Although the outcome would be more complicated, the final parameters would still bepredictable in terms of ̀ Q',`R', and ̀ lPR', and the metabolic, circulatory, and kinetic indices stillhave the same significance for circulatory function and the maintenance of blood pressure.Because of the importance which is attached to these various indices in determining the balanceof variables which control blood pressure, a summary of the significance of each of them is givenbelow.

Every individual organism exists in a particular external environment, which while it must bereasonably similar for all members of that species, yet is not rigidly the same for each at anyparticular time. In order to maintain a relatively independent existence, each member must beable to modify and adapt its activity in accordance with changes in the external environmentalconditions.The result of these adaptations is to maintain a relatively constant and satisfactoryinternal environment for the continued function of its constituent cells. The ultimate activitieswhich maintain the requisite boundary conditions between internal and external environments,

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are set by the properties and function of the integument (i.e., the skin and its appendages), andthe energy balance which is required to maintain these conditions. In general terms this energybalance is achieved by changing the linear velocity of the circulating blood. Such changes inlinear velocity of blood flow, are of particular importance in the regulation of body temperaturewith respect to that of the external environment, and in the transfer of heat from one area of thebody to another, and to relate heat production from metabolism and activity, to the amount ofheat lost to the external environment. This function is intimitately associated with the force ofventricular contraction, or ̀ lPR', and this factor in the production of ventricular work or energy,is then that which is required to maintain the internal environment, including the volume andenergy given to the fluid in the extra-vascular space.

The stroke volume, or `Q', is representative of the energy which has to be provided bycontraction of the ventricle to maintain the circulation to the `effector organs' (the nervoussystem, voluntary muscles, and glands) which predominantly require carbohydrate as themetabolic substrate for energy production. The oxidation of carbohydrate to carbon dioxide andwater, requires an equivalent amount of oxygen consumption for the amount of carbon dioxideproduced, so that [ ] and [ ] can be maintained at a fixed ratio in the active tissues, whilethe product of the two , , is proportional to the ratio Q/Vs, or circulatory ratio.Increase in the activity of these organs is indicated by an increase in stroke volume, and also byan increase in systemic blood volume, so that the energy requirement for the `effector' organscan be represented by changes in stroke volume with respect to the total energy output of theventricle per beat.

The remaining factor which determines the energy output of the ventricle, `R', is indicative ofthe energy requirement for circulation through the `core' organs (including the heart, kidneys,liver and digestive tract) which are responsible for much of the ̀ basal metabolic rate' which hasto be maintained even when the `effector organs' are relatively quiescent, and energyrequirements for maintenance of the internal environment are minimal. Unless ̀ R' is maintainedunder these circumstances, energy production by the ventricle would soon be reduced to a levelwhere the circulation could well cease altogether, and this emphasises the importance of `R' inmaintaining circulatory efficiency during periods of inactivity, and in particular during sleep.It has already been claimed that the value of `R' is proportional to ` , so that themaintenance of these parameters is important for the survival of the individual at such times.Even an adequate partial pressure of oxygen may be insufficient to assure survival if the ̀ averagemean' length of the circulation, or `l', is reduced, or the `apparent viscosity' of the blood isinadequate to maintain the value of `R'. These problems associated with inactive and quiescentstates especially if associated with periods of apnoea, accentuate the hazards which can beassociated with sleep.

An immediate objection to the relationship which has been suggested between the relative valueof `R' and the proportion of circulatory energy supplied to the `core' organs, is related to thepartial pressure of oxygen which is a key factor in determining the value of `R'. As [ ]increases in the ̀ effector' organs when oxidative activity of the respiratory enzymes is reduced,arteriolar constriction results, and the circulation through these organs is reduced. Any increasein the relative circulatory energy and volume supplied to the `core' organs, would require thatsimilar vasoconstrictor activity does not happen in these latter organs to the same degree.

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Furthermore, continued metabolic activity in the `core' organs, should still produce carbondioxide and so help to maintain stroke volume and circulatory length, and reduce the relativeincrease in `R'. The answers to these objections lie partly in the anatomical and physiologicalpeculiarities of the circulation in the `core' organs, and partly in the metabolic substrate whichthey require for energy production; and each of these features requires some further elucidation.

The term `core organs' is of necessity somewhat imprecise, but the main area of the `core'circulation includes the heart, kidneys, liver, and the gastro-intestinal tract (at least in the post-absorptive state) together with the uterus , especially during pregnancy; i.e., the coronary, portal,genital, and renal circulations.

Because the heart is required to contract regularly on a continuing basis for the life of theindividual, it uses oxygen at a rate consistent with its energy production, and this has alreadybeen considered in previous text. The result is that the oxygen partial pressure in cardiac tissueis maintained below the level which would be present if the muscle remained quiescent, and[ ] in cardiac muscle may remain consistently less than that which inhibits the respiratoryenzymes in inactive voluntary muscle. Any general increase in ̀ R' for the whole circulation, doesnot then restrict coronary flow to the same extent as that in the `effector' organs, and so as `R'increases, the coronary circulation is maintained commensurate with the work the heartperforms.

With the liver the situation depends more on the anatomical features of the hepatic circulation.Because the liver is supplied with a mixture of arterial and portal vein blood, [ ] in the livercells can be maintained at a consistently lower level than that present in the inactive `effectororgans', and the liver circulation is less likely to be affected by an increase in [ ] in moreperipheral areas. Although details of the controlling mechanisms which vary the proportions ofarterial and portal vein blood, and so of the [ ] supplied to the liver cells are not known, thereis scope for considerable variation in this level, while the proportion of portal vein blood comingfrom the splenic vein, may also have some effect in controlling oxygen levels in the hepaticblood supply. The kidney enjoys considerable autonomy in the regulation of its circulation, and this will beexplored more fully in a later section. Although [ ] in the cells of the renal tubules may affectrenal blood flow, there are a number of other considerations which together tend to stabilise andmaintain the renal circulation in the presence of great variations in circulatory conditions, so thatat rest, a large part of the cardiac output is directed into the renal circulation, and the energyassociated with it maintains renal function at a high level.Changes in [ ] in the more peripheral`effector organs', while they affect the volume and energy levels of blood supplied to theseorgans, also alter the circulation to `core' organs in a reciprocal fashion.

The preferred metabolic substrate for energy production by the `core' organs are lipids orintermediate metabolites of fatty acid metabolism, while the effector organs are primarilydependent on glycolysis or the oxidation of the end products of glycolysis to fuel their activity.The significance of this difference in metabolic preference lies in the end products of metabolismwhich each produces. For each molecule of oxygen used to oxidise carbohydrate, one moleculeof carbon dioxide is produced. When fat is oxidised, only some of the oxygen used appears as

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carbon dioxide, while the remainder is used to oxidise hydrogen with the production of water.The amount of carbon dioxide produced for a given amount of oxygen used is different in eachcase, and the ratio of in the active tissue is also likely to be different. Because

is proportional to Q/R, any increase in this ratio reflects an increase in the ratioof stroke volume with respect to resistance per unit velocity per ml. of systemic blood volume,while any decrease in the ratio has the opposite effect. As the ratio of carbohydrate / fatmetabolism is varied there is a corresponding shift in the ratio of Q/R, or circulatory volume andenergy directed to the effector organs / circulatory volume and energy directed towards the coreorgans. A satisfactory balance between ̀ Q' and ̀ R' is considered to reflect a similar satisfactorybalance between fat and carbohydrate metabolism. Distortion of these ratios is then likely toresult in alteration of the circulatory balance between the effector and core organs, and to bereflected in the balance between stroke volume, systolic arterial blood pressure , circulatorylength, and pulse rate.

To return to the prime functions which have to be satisfied by the efficient circulation. It mustfirst be of sufficient size to provide for the metabolic needs of the tissues.The blood must thenbe distributed according to the different requirements of the individual organs and tissues.Finally it must maintain efficiency of energy production and usage for the whole of the life spanof the individual.The work done is directed towards these needs, and the balance maintainedbetween the factors involved in ventricular work, has a major part to play in accomplishing itsprime functions in an adequate way. The factors involved in the production of ventricular workare ̀ Q', the stroke volume, ̀ R', the resistance offered by the circulation per unit velocity of bloodflow for each ml. of blood in the systemic circulation, and `lPR', the product of average meanlength of the circulation and the pulse rate. From what has already been examined in previouschapters, it can be stated that `Q' is an indicator of kinetic work done by the ventricle per beat,and also of the efficiency of the ventricular muscle. `R' is an indicator of potential energyproduction, and at the same time it tends to increase efficiency by limiting energy expenditurefor the amount of work performed. The force of ventricular contraction and the total energyreleased by the ventricular muscle per beat is varied as the variation in `lPR', (and lPR squared,which represents the power developed). It also indicates the level of energy directed towardsmaintaining the internal environment, represented by the extra-vascular fluid.

The ratios of these three variables govern the activities of the circulation which have beenoutlined above. Perhaps the most important of these ratios is the `metabolic' index, or ratio of`Q/R'. This is an indicator of the ratio of ` ' maintained in the active tissues whenconsidered as a whole, and the index controls the circulation according to metabolic requirement.The metabolic index can also be represented as the ratio of `Vv/AP', or momentum of blood inthe circulation, and the systolic pressure, or again the momentum of blood at diastole/ diastolicblood pressure.The metabolic index indicates the amount of, and conditions required for,oxidation in the tissues. It also probably determines the rate and amount of gluconeogenesis inthe liver by alterations of `EDP' in the right ventricle, through the secondary effect of `[ ]'on diaphragmatic tone, and thereby pericardial restriction on ventricular filling.

The circulatory (vascular) index is the ratio `R/lPR' , and it indicates the distribution of bloodbetween the great vessels on the one hand, and the capillary or peripheral circulation on theother. A rise in the value of the index indicates that a greater proportion of the circulating blood

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is contained in the arterial system than is the case when the value of the index falls. It can alsobe indicated by the ratio AP/ , so that an increase in the value of the index indicates a riseof systemic arterial pressure with respect to the energy output by the ventricle, and this hassignificant consequences for the strain put on the arteries by such an increase. A fall in the valueof the index on the other hand indicates a fall in arterial pressure with respect to ventricularenergy release, a redistribution of blood away from the great vessels and into the capillary bed,and a reduced strain on the arterial system.In other words, when the value of the ratio falls witha relative increase of `lPR' with respect to `R', the circulation expands, compared withcontraction of the circulation when the ratio rises. A simple clinical estimation of the degree ofarterial wall stress can be made from the ratio of `APs/PR'. This ratio is proportional to `R.l',which is proportional to `l.l /a' , or `R.Vs.[ ]'. It represents the product of `vascular filling'and the partial pressure of oxygen required in the tissues for oxidation reactions to occur in amanner which is satisfactory both for completeness and rate. The ratio `APs/PR' is an index ofarterial wall stress, especially for the elastic (non-contracting) arteries. In large part it representsthe square of the ratio between vascular length and vascular radius, over the whole of thesystemic circulation. If the ratio of arterial volume at diastole / systemic blood volume, isproportional to ̀ R / lPR' , then arterial volume is proportional to ̀ R.Vs / lPR', or ̀ R.a/PR', whichreduces to `l. /PR'. With animals of different sizes therefore, `l' and `PR' are reciprocallyrelated, the pulse rate slowing as the vascular length increases. While arterial wall stress dependson the ratio of vascular length / vascular radius, this ratio tends to be the same for all species.Arterial volume on the other hand is the product of vascular length and vascular radius squared,so that arterial volume increases at a greater rate than vascular length.

Increased arterial volume in larger animals therefore requires the ratio of length over pulse rateto be increased progressively with overall size, and this is reflected in a slower pulse rate in thelarger species.

The kinetic index is the ratio ̀ Q/lPR' , which by expansion becomes momentum/energy releasedwhen applied to the whole circulation.It is a measure of the energy required to maintain a givenlevel of momentum in the whole of the blood in that half of the circulation supplied by theventricle. As such it is inversely proportional to ̀ ' , the contractility factor, which increases as the kineticindex falls, because of the direct relationship between ` ' and `lPR/LTDTR', outlined in aprevious chapter.Any tendency for the kinetic index to raise ventricular efficiency is countered,at least in part, by an opposite shift in the contractility factor, mainly by an increase in theshortening velocity of muscle contraction as stroke volume increases. On the other hand anincrease in the value of ̀ lPR', decreases the kinetic index, but increases ̀ ' , so that any changein diastolic pressure by a change in `EDP' and/or `R', is immediately countered by a change in`lPR'. The level of diastolic blood pressure then tends to be preserved, in spite of changes toother parameters, which might be expected to alter it to a greater extent. `Q /Vs' is also anindicator of the relative volume of blood in the systemic circulation which is contained in thevenous system (as opposed to ̀ R /lPR' which indicates the proportion of the systemic circulationcontained within the arterial system).

The energy equivalent for pulse rate may be derived from the momentum of venous bloodpresented to the heart. Venous volume is proportional to ̀ Q', and pulse rate is proportional to thelinear velocity of venous blood entering the ventricle. The product of venous volume and venous

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linear velocity is momentum, and proportional to venous return, or `Q.PR', and the ratio ofvenous volume and systemic blood volume is `Q/Vs'. In the `effector' cells, the energy for fluidexchange is proportional to ̀ v', and the cell volume and energy ̀ store' is proportional to ̀ R'. Theratio between the two is `v/R', or `Q/[ ]', and this is the rate at which energy is liberated, or

`PR'. Pulse rate becomes related to ̀ v/R', ̀ ', or ̀ '. The energy equivalent for`l.PR' is `R.Vs/[ ]', or `Q.Vs', because `Q' is proportional to `R/[ ]', and `Q' and `R' areproportional to each other for a constant value of `[ ]'.

Before leaving the triangular diagram representing ventricular work, it is interesting to considerthe products of each pair of variables. `Q . R . lPR' is ventricular work per beat; `R . lPR' issystolic pressure; `Q . lPR' is equivalent to momentum of blood in that particular circulationwhich is also equivalent to the ratio ̀ PP.RV/AP'; ̀ Q . R' is proportional to ̀ R.V . v/lPR' (whichis proportional to efficiency of the peripheral circulation for a given level of vascular filling, andwhen the efficiency is `normal' , to ventricular filling). Another illuminating procedure is toconsider each of the axes bisecting each angle. For example, the axis bisecting the angle at ̀ lPR',or `metabolic axis', can be used to illustrate what happens if `Q' and `R' are varied while `lPR'and ventricular work remain constant. If is increased, this means a relative increasein `Q', and an equal and opposite fall in `R', and the balance of these two about this axisdetermines :-1. The size of the stroke volume2. The size of the resistance per unit velocity3. Helps determine the distribution of circulatory volume between central and peripheral regions.4. Determines the diastolic pressure necessary to maintain ventricular efficiency.5. Helps determine the ratio `PP/AP' which is equivalent to the cardiac output in unit time (fora circulation of constant length and blood viscosity).6. Helps determine the efficiency of the peripheral circulation i.e. `v/lPR'.

Similarly, the axis bisecting `Q' or `circulatory axis';1. Determines the balance between `R and lPR', the distribution and volume of the circulation.2. Is important for estimating the probability of vascular damage, and to preserve vascular health.3. Helps determine momentum and ventricular efficiency when `Q' is constant.4. Helps determine the amount of energy produced by ventricular contraction per beat.

Finally the R axis bisecting the angle at `R' , or kinetic axis;1. Determines the ratio of stroke volume and energy output of the ventricle per beat.2. Helps determine the ratio `Q/R' and hence3. Helps determine the size and `type' of change in arterial pressure.4. Helps determine the value of the contractility component. There are other changes which can be inferred from this diagram, but the above examples aresufficient to illustrate the uses to which it may be put.

To return once more to the main purpose of this chapter in considering the maintenance of bloodpressure, it is now necessary to assess the importance of each of the factors which contribute tothe final value. For systolic pressure this reduces to the value of `R', and the value of `lPR'. Inthe final outcome `R' depends on the metabolic index, or the ability of the tissues to utiliseoxygen at a minimal partial pressure. The capacity to utilise oxygen at this pressure is reflected

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in the ability to produce carbon dioxide and to keep the level of unmetabolised lactate at asatisfactory level. The consequences of inability to achieve an adequate balance, or of anunacceptably high level of oxygen to produce adequate oxygen usage, are ischaemia, or localimpairment of blood flow from vasoconstriction, a fall in stroke volume, an increase in end-diastolic pressure in the ventricles, reduced gluconeogenesis in the liver, a rise in blood lactateand blood pressure, a relocation of blood to the central areas of the circulation with increasedarterial and venous volume, transfer of blood to the pulmonary circulation, a change in thecontractility component, and so on until most areas of the body are affected in some way. Underphysiological conditions these are temporary phenomena, and subside when the situationchanges, or the stress which produced it in the first place has been removed. But the situation foreach individual will vary with time, with the state of physical fitness, with the genetic makeupof each person, with age and external constraints such as temperature, or other climatic stress.If for some reason it is impossible for the individual to maintain an adequate level of oxidisingability in the tissues, then a more permanent elevation of blood pressure may result.

The present concern is rather with the mechanisms which determine the blood pressure at anyparticular time, and the importance of the metabolic factors which control `R' have beenconsidered. The level of `lPR' is of equal importance, not only because most physiologicalincreases of blood pressure are brought about by changes in `lPR', but also because the ratio of`R' and `lPR' is of vital importance in determining the stress on individual blood vessels, whichif not controlled, can result in life threatening episodes.

The pulse rate is determined in the first instance, by spontaneous rhythmical discharges of thecell membranes of certain specialised cells in the sino-atrial node of the right atrium. Themechanics involved in the build up and discharge of these electrical potentials, are at this stage,beyond the scope of the present chapter, except to note that the process is subject to the sameinfluences as other active cells; such as the nutrition, nerve supply, temperature, the level ofcatecholamines and the ionic environment.

Initiation of cardiac contraction originates in the sino-auricular node with rhythmical andapparently spontaneous cell discharge of energy and fluid, associated with cell membranedepolarisation, which spreads to all other cardiac cells in an `all-or-none' fashion. There is apresumption of a steady build up of free energy within the cell which reaches a level where cellmembrane polarisation (i.e., [ ]) is overcome, and fluid, ions, and energy are able to escapeto the extra-vascular fluid. Following the discharge with breakdown of high energy phosphatebonds, inorganic phosphate is available to stimulate or facilitate glycolysis, and production ofpyruvate which may then be oxidised to carbon dioxide and energy. Some of the energy is usedto produce more high energy phosphate bonds, restore cell membrane polarity, and build up freeenergy once more, until it eventually overcomes the cell polarity again, allowing rhythmicaldepolarisation to continue.

The ratio of free energy/ circulatory length determines the rate of discharge of the pace makercell, which can be varied by altering circulatory length, and the permeability of the cellmembrane by gas concentrations or neuro-transmitter substances.

Necessary conditions for pacemaker activity are1. `Free energy' build up continuing at a steady rate which is greater than the rate of transfer of

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energy to the energy store (oxidation greater than lactate accumulation).2. Increase of carbon dioxide concentration at a greater rate than that of oxygen, or rate of activepermeability compared with passive permeability.3. Maintenance of sufficient momentum in the extra-vascular fluid to re-expand the pacemakercells after each beat.4. A relatively low capacity of the cell to maintain the energy store(i.e., in cells), or carbondioxide concentration and oxidation dominate over oxygen concentration and oxidativephosphorylation. (If glycolysis increases cell length compared with cell strength, there is anincrease in the ratio of lactate concentration compared with that of carbon dioxide, increasedenergy store, and reduced pulse rate. If glycolysis is decreased, lactate is reduced comparedwith carbon dioxide, reduced cell energy store, and increased pulse rate.) Both pulse rate andenergy store may be influenced by introduction of excess lactate from effector cells, to increasethe inotropic state.

Pacemaker activity depends on the dominance of oxidation compared with oxidativephosphorylation in the pacemaker cells, and ectopic beats may have a similar origin, as well assome other arrhythmias, where there is not sufficient lactate available to slow the discharge rateof the appropriate cells.

Pulse rate equivalents may be derived as follows:Stroke volume, `Q', is proportional to `V venous', and pulse rate is proportional to `v venous',the linear velocity of venous blood. The venous return is proportional to `Q.PR', and `Q/Vs' isproportional to `V venous/Vs'.

In the `effector cells', the volume of fluid exchanged, `Q', as a ratio with cell volume,`[ ]', isproportional to the liberation of energy, or `PR', so that `PR' is proportional to `Q'/`[ ]', or`l. /[ ]'. Alternatively, the energy of fluid exchange, or `v' as a ratio with the cell `energystore' or `R', is proportional to pulse rate, while `l.PR' is proportional to `R.Vs/[ ]', or `Q.Vs'.Providing `[ ]' remains constant, `Q' is equivalent to `R', or `Q' is `R/[ ]'. The stability ofthese relationships depends on an unchanging level of oxygen concentration. The arterial bloodvolume is proportional to `[ ]', and venous blood volume to `Q', or `l. ', and the ratio of thetwo, `venous volume'/`arterial volume' is `l. /[ ]' or proportional to pulse rate, while for agiven value for `[ ]', systolic pressure is proportional to circulatory momentum.

These things having been said, and the importance of the various factors acknowledged, thefactor which is generally accepted as having most influence is the level of vagal tone which thatnerve exerts upon the activity of the node itself. Although the importance of the cardio-accelerator fibres of the sympathetic nervous system must be accepted, it is variations of vagaltone which generally sets the cardiac rate. What this rate will be is largely determined by theflood of afferent nerve impulses from many areas of the body which can influence pulse rate, andthe final rate is determined by the final sum of excitatory and inhibitory impulses which reachthe medullary nuclei. Of these the ones with greatest influence are those from the great vessels, particularly the aorticarch, carotid sinuses, and probably lungs, great veins, heart wall, and pericardium. But it is thosewhich are directly responding to conditions within the vascular system, or the tension in the

12

walls of those vessels, which are of immediate concern. Of these the cardio-depressor nervefrom the arch of the aorta, together with the nerves from the carotid sinus and carotid body havemost effect on heart rate.Those from the other areas mentioned are perhaps of less importance.The possibility of cardio accelerator fibres from the great veins has been rejected for the presentin favour of nerve endings with similar function in the pericardium and walls of the heart. Ifanything, raised pressure in the great veins appears to result in cardiac slowing rather thanacceleration. The point to be made is that distention of the aorta results in reflex cardiacslowing, an observation which is the basis of "Marey's Law"; the only query to be made iswhether the adequate stimulus for this slowing is distention of the vessel wall rather than theactual level of blood pressure. The importance of this query will be clear to the reader who haspersisted to this stage, because the importance of recognising the factor which is bringing aboutthe pressure rise has already been stressed. The level of systolic pressure is determined by theproduct of `R.l.PR', but the distention of the vessels depends on the ratio `R/lPR' which isproportional to the ratio of diastolic arterial volume / volume of the systemic vascular system.Though the arterial pressure may be the same, the individual with a raised value of ̀ R' comparedwith ̀ lPR', has more arterial distention than one with a raised value of ̀ lPR' compared with thatof `R'. In the view of the author, the latter is likely to suffer less depression of pulse rate fromvagal reflexes than the former. Furthermore, the greater the depression of pulse rate associatedwith a particular blood pressure reading, the greater the degree of arterial distention, the greaterrestriction of capillary circulation, and the greater the possibility of vascular accident anddamage which will be present. This is the basis for the description of the `quality' of bloodpressure elevation which will be mentioned in a later chapter.

While the vagal outflow represents the effects of a large array of afferent impulses which eachhave their own input for the regulation of the pulse rate, one must not lose sight of the fact thatthese are regulatory only in their activity, and have no part in the initiation of cell depolarisation,which remains an inherent property of the pacemaker cells.Under most circumstances these cellsare situated in the sino-auricular node, though the pacemaker activity can extend to other areasof junctional tissue, or even to irritable foci in cardiac muscle itself should the nutrition oroxygen supply or other environmental or noxious influences disturb their functionsufficiently.This presupposes that similar environmental changes (e.g., ionic or pH ortemperature variations) will each have their own effect upon the depolarisation of the cellmembranes of the pacemaker cells which initiate excitation of the surrounding cells andultimately the whole remaining cardiac muscle. For the most part, as stated earlier, considerationof these influences are beyond the scope of this examination, but mention has already been madeof the physical factors associated with and determining the distribution of fluid between the cellsand the extra-vascular fluid, namely the values of `R' and `lPR', which also determine the levelof systolic blood pressure. The possibility exists, that variation of the rate at which fluid entersand leaves the cells, might have its own regulatory influence on the movement of ions across thecell membrane, thereby affecting the rate of polarisation and discharge of the pacemaker cells.Variations in the values of ̀ R' and ̀ lPR' might thereby provide a ̀ feedback' mechanism with itsown regulatory effect upon the pulse rate, or even have a vital part in the initiation andmaintenance of the rhythmical discharges upon which all cardiac activity ultimately depends.

The electrical and mechanical activities of the heart are intimately connected so that one rarelypersists in the absence of the other. While the arrested heart can, at least on some occasions, berestarted by an outside electrical stimulus, the opposite is also sometimes true, and provision of

13

some circulation by cardiac massage may also sometimes again induce electrical activity, andthereby produce a self-sustaining circulation once more. In other words there is some a priorievidence that the mechanical and electrical activities of cardiac function may be mutuallyinterdependent. Once regular polarisation and depolarisation have become established, andassociated mechanical contractions with changes in linear velocity are occurring, the two mayreinforce each other, as a result of rhythmical changes in cell volume, and ionic exchanges acrossthe cell membrane. The electrical activity is then also subject to nervous outflows from both thevagus and sympathetic (cardio-accelerator) nerves, and to alterations in hormone concentrationsand neuro-transmitters, which in turn are affected by peripheral afferents from muscles, the greatvessels, carotid body etc., and also from centres in the spinal cord, medulla, hypothalamus, andeven higher centres. This variability in the sources of afferent stimuli, gives great flexibility tothe pulse rate, and to the power output of the ventricle, although the underlying mechanism formaintenance of pulse rate remains the cyclical exchange of fluid and ions across the cellmembrane.

The fluid and ionic exchange, while they might progress at equivalent rates, do not necessarilyreach their maximal values at the same time. While for most cells the fluid exchange has adominant role, reaching its maximal value and then diminishing again before the potential acrossthe cell membrane has reached a level which will initiate spontaneous depolarisation, it wouldappear that in the pacemaker cells the ionic exchange assumes a more prominent role, reachingan electrical potential which is able to overcome the electrical resistance of the cell membrane,and so produce a wave of depolarisation which spreads to neighbouring cells before the cellvolume has reached its maximum. The point at which depolarisation begins may be varied bythe nervous and other influences which have already been mentioned.

The relationship between cell volume and cellular activity and irritability, may have widerimplications. With fertilisation of the ovum, there begins a period of intense activity, governedin large part by the genetic makeup, but requiring development of considerable energy, withsynthesis of protoplasm, increased cellular volume, and at a certain critical point, leading to celldivision, with ever increasing volume of each cell, and of the cellular mass. If, as seems likely,energy developed by the mature organism can be expressed in terms of the concentration of`lactate', ̀ carbon dioxide', and ̀ oxygen' persisting within the active cells, these parameters maywell be associated with initial energy production in the embryo, and [lactate], [ ], and [ ]assume vital functions in cell division. Should [lactate] lead to continuously increased cellenergy and cell division, controlled cell differentiation may involve [ ], favouring particularspecific chemical reactions with appearance of organiser substances, as well as arrangement ofmolecules in specific patterns on the template of D N A, and the genome. The stability of cellsize, shape, and general uniformity in the developed tissues, may then result from the constantvalue of oxygen concentration which appears as the levels of `lactate', `carbon dioxide', and`oxygen' assume a `balance' regulating energy content and exchange, with development of thecirculation. The development of living tissue, as well as its function after development, dependsultimately on the supply and application of energy. If the representation of energy associatedwith function can be reduced to the ratios of concentrations of oxygen, carbon dioxide, andlactate available at any particular time, then energy for development, growth, and differentiationof tissues, is probably derived from concentrations involving the same parameters which initiateand maintain the circulation; i.e., the relative concentrations of the metabolic gases, oxygen andcarbon dioxide, and the concentration of metabolic substrate available.

14

In developing tissue, the substrate for energy development would appear to be lactate and/orpyruvate from glucose, and the relative levels of glycolysis and oxidation which are involved inproducing them. The critical parameter for stability of cell size and energy content, is `[ ]'which regulates cell size in the resting state, and opposes cell differentiation when the celldivides, so that it regulates uniformity of cell size and shape in the resulting tissue cells. Bycontinuously increasing cell energy content ̀ lactate concentration' may lead to cell division, butwithout `controlled' differentiation, which could require particular specific chemical reactionsto be favoured, with production of `organisers', as well as arrangement of molecules in patternson the template offered by D N A and the genome. This organisation becomes a function of`[ ]' indicating the amount of oxidation activity, and limiting lactate concentration comparedwith that of oxygen and carbon dioxide. In general terms lactate may regulate continualmultiplication of tissue cells, and tissue growth, while carbon dioxide may regulate theproduction of organisers, and the differentiation of emerging tissues and organs in accordancewith the genetic pattern, through its moderating influence on oxidation / reduction reactions, pH,etc. Uniformity of cell size and function in the new tissue is obtained through oxygenconcentration. Development may be as set out in the genetic pattern, but the required energy forthis development, results from the relative concentrations of the metabolic gases and the requiredsubstrate.

At some point associated with differentiation of tissues, cell growth slows, and it then becomesassociated with developing circulation, and rhythmical volume changes in the cells resulting incardio-vascular activity. Just what initiates this rhythmical volume change is not clear, butpresumably genetic control which slows the rate of cell division, allows the volume of some cellsto increase until depolarisation becomes inevitable with increasing ionic exchange. Increasingthe cell volume beyond the threshold for depolarisation to commence, then gives such a cell a`pacemaker' function, allowing spread of the depolarising wave to the other cells in the area. Inother cells, the volume changes, and changes in ionic concentrations, never reach a levelsufficient to produce depolarisation spontaneously, and such depolarisation if it occurs, has tobe induced by spread from nearby cells. If these assumptions are justified, it would appear1. Cell polarisation and cell volume changes are in some way associated phenomena.2. In ̀ pacemaker' cells depolarisation occurs before cell volume reaches its potential maximum(when for example fluid enters the cell during the cardiac cycle, as the momentum of the extra-vascular fluid alters).3. Alterations in cellular volume also have an effect in determining when spontaneousdepolarisation will occur. As cell volume increases relative to the volume of the extra-vascularfluid, the cells become more `irritable', and are more easily depolarised, so the latter may thenoccur spontaneously in areas where it is usually induced from other cells.

If cell volume is related to `R', then as `R' increases relative to `lPR', the rate of the regularcellular depolarisation in the pacemaker should also increase.This would increase pulse rate,arterial pressure, and produce a further increase in `R', involving a continuous increase in cellvolume and cardiac work. Some mechanism to slow down this cycle would seem to be desirable,and it is provided by the vagus nerve exhibiting continuous `vagal tone', changing thecharacteristics of the cell membranes in the pacemaker, and altering the conditions necessary forspontaneous depolarisation. Vagal tone is provided by the nervous reflexes outlined, and themost important afferents in this regard are those which reflect increasing strain in the elasticarteries as detected in the carotid sinus, and those from the arch of the aorta, and referred to as

15

the `cardio-depressor' nerve. The increase in irritability with increasing cell volume is perhapsbest observed in the nervous system, where increased fluid content of nerve cells can result inspontaneous bursts of cerebral motor activity, appearing as fits or seizures, especially when `R'is increased as in vascular hypertension, or other causes of cerebral oedema. So far as possible,nerve cells need to be isolated from random alterations in cell volume and irritability, and thisis achieved by enclosing the central nervous system within the cranium.

Although the preceding section suggests a possible way in which the basic regulation of pulserate may be initiated, there remains one last factor in determining cardio-vascular activity whichstill has to be considered. This factor is the value of `l', or average mean length of the systemiccirculation.

The concept of any increase in ̀ vascular length' immediately suggests an increase in vascularityof the more peripheral tissues supplied by the systemic circulation. When the average meanlength of the circulation is increased, this in turn implies both increased activity in those tissues(mostly muscle and skin) and an increase in the number of functional capillaries supplying theregion, so that an increased proportion of the cardiac output is transferred from `central' areasto more `peripheral' areas.

Each of the three parameters which have been considered to be of importance in determiningventricular work, produces its own characteristic effect on overall circulatory length, which canbe in response to change in either the physical, chemical, or mechanical conditions to which thatparticular section of the circulation is subjected at any time. For example, the amount of energyin the form of heat, which has to be provided at the skin surface to maintain internal bodytemperature in the face of changes in the temperature of the external environment so that bodyheat is either lost or retained as may be appropriate, is determined by changes in the skincirculation. The vascularity of a particular region of skin can be increased by direct applicationof heat, just as it may be decreased by direct application of cold. The physical length of the bloodvessels is varied in response to the physical variations in temperature to which the area issubjected.

The length of the circulation in active voluntary muscle, on the other hand, varies according tothe level of activity of the muscle, and is predominantly altered by changes in chemicalconcentrations in the area, either of chemical neuro-transmitters, or of the products of subsequentmetabolism.

This increase in vascularity and blood flow, in active muscle for example, can be very rapid, andprecedes any increased metabolic activity, seeming to occur almost instantaneously withmuscular contraction (see Benegard and Shepherd, 1967; Corcondilas, Koroxenidis, andShepherd, 1964). It would therefore seem to be initiated either directly or indirectly by theevents which lead to muscle contraction as a local event. In other words, it seems to be closelyrelated to the time frame for the activity of the neuro-muscular transmitter, acetyl choline. (Itmay not be a direct effect, but as any intermediate steps between the initiation of musclecontraction and increased vascular activity are unknown at present, there is little point in furtherspeculation). The salient fact is that an increased vascular length, and increased muscular activityseem to take place before the subsequent metabolic changes which follow muscular contraction.This increase in the value of `l' has very great significance for cardiac work and for bloodpressure maintenance. Increase in ̀ l' means increased ̀ APs', even before any metabolic activity

16

occurs. The later local increase in lactate concentration from glycolysis has the effect ofprolonging and maintaining increased vascular length until lactate concentration returns to itsresting level. The value of ̀ l' may then be set by the relative amount of activity of the ̀ peripheral'tissues compared with that of the vital `central' organs. In these latter organs, where excesslactate production is not such a characteristic feature of metabolism, increase in vascular lengthis more directly influenced by mechanical stretching of the vessels following distention ofhollow organs such as the heart and alimentary tract as part of their functional activity. Wherethe increase in functional length is not associated with a commensurate increase in carbondioxide production (and stroke volume) it results in a relatively greater increase in the value of`R', with oxidation of lipid rather than oxidation of carbohydrate becoming responsible for theincreased energy produced, and resulting in higher pressure rather than increased volume flow.In a similar fashion, unless increase in the functional length of the vascular system, representedas ̀ l', is accompanied by a commensurate increase in the linear velocity of blood flow, the pulserate will be reduced. Under those circumstances where a reasonably steady linear velocity offlow is able to maintain a constant internal environment, increasing the length of the circulationwill then result in a reciprocal reduction in pulse rate.

Although it has a separate circulation, the length of the circulation in the lung is also subject tochange by distention of the air sacs during respiration. The ultimate determination of `l' , thecirculatory length, is the sum of the effects produced in the three main sections of the systemiccirculation, which each have the capacity to lead to variations in its value, depending onvariations in functional activity in each area. It is the balance achieved between these activities, and the demands which they make upon ventricular energy production which determine therelative levels of `Q',`R', and `l.PR', and secondarily, of linear velocity, systolic arterial bloodpressure, blood volume and so on.

Because ̀ l', the circulatory length, is a common factor in each of the following, the significancethat it then has for stroke volume,`Q', the systemic blood volume,`Vs', resistance per unitvelocity for each unit volume of blood in the systemic circulation,`R', or for ventricular energyoutput (proportional to ̀ lPR') is modified by the ratio of gas partial pressures, . Thisratio is in turn dependent on the oxidising capacity of the active tissues; lowered oxidisingcapacity resulting in a lowered ratio, and increased oxidising capacity resulting in an increasedratio. It is in determining the ultimate value of the ratio , that the effect ofadministering lactate becomes significant. While the oxidising capacity of the active tissues is`adequate', administered lactate is not vasoactive. Nevertheless it has one significant effect,insofar as it appears to reduce the `toxic' effects of oxygen (Felig and Lee, 1965).

When living organisms are exposed to concentrations of oxygen greater than those to which theyare adapted, a variety of `toxic' effects may be seen. Although oxygen is universally toxic toliving cells, there are differences between cells of different tissues, depending on the specialdefence mechanisms which they are able to develop. Such defences may include oxidation-reduction buffering systems present in the cell, and in this regard glutathione is especiallyimportant. The oxygen supply and rate of oxygen consumption are important factors indetermining the oxygen tension, and resulting toxicity. Oxygen is a potent enzyme inhibitor, andenzymes can be inactivated when [ ] is sufficiently increased, and there is evidence thatincreased oxygen tension produces altered cell metabolism, passing eventually to disturbed cellfunction, and oxygen poisoning (see Haugaard, 1968 ; Balentine, "Oxygen and Physiological

17

Function", ed. Jobsis, F., 1974).

Enzymes inhibited by oxygen as set out by Haugaard (1968) are: 1. Oxidation of sulphydryl-containing co-enzymes such as lipoic acid and co-enzyme A. 2. Inactivation of enzymes withsulphydryl groups essential for their activity. 3. Inhibition of iron and -SH containing flavo-proteins. 4. Damage to cellular membranes by lipid peroxidation. 5. Oxidation of glutathione,ascorbic acid etc.

In the intact animal intra-cellular metabolic changes occur before any signs of oxygen toxicity. For example, pyridine nucleotides are oxidised in animals exposed to elevated oxygen tension,so that glycolysis and energy transfer are all involved. The presence of oxidation-reductionbuffering systems present in the cells and involving glutathione always cause some delay in theeffects occurring. The observation of Felig and Lee (1965), that administration of sodium lactate,but not sodium pyruvate or sodium bicarbonate, resulted in significant protection of rats againstoxygen toxicity during breathing of oxygen at one atmosphere pressure, has considerablesignificance .

The above observation could mean that oxygen concentration can be increased without furtherdiminishing the activity of oxidative enzymes, provided there is an increased substrate consistingof lactate available. Administering lactate to a subject at rest (so that no great alteration of theaverage mean length of the circulation occurs through activity) can then have an effect on bloodpressure, depending on whether the lactate is readily oxidised to carbon dioxide, or whether anincreased value of oxygen concentration is necessary to achieve oxidation. In the first case, readyoxidation to carbon dioxide means an increase in the ratio of , so that there is anincrease in stroke volume compared with ̀ R', and a fall in blood pressure (and a fall in pulse rateif the cardiac output remains constant). In the second case, if an increase in [ ] is necessary toremove the added lactate by oxidative phosphorylation, then the ratio will fall witha reduction of ̀ Q' with respect to ̀ R', and a rise in systolic pressure, though in this case there willbe little alteration of pulse rate.While the increase in [ ] is reflected in an increased value of`R' relative to ̀ Q', this increase can only occur if there is a local increase in both [ ] necessaryfor oxidation at an adequate level, and the concentration of the substrate [lactate] required toallow maintenance of [ ], and of the length of the circulation in the local area. Therelationship between these two concentrations ( ) then produces relatively slow andprolonged changes in blood pressure, which are probably mediated by the relative amounts ofvaso-active enzymes or other materials liberated. The type of vaso-active enzymes envisaged areof the ̀ kinin' type producing vaso-dilatation, and of the ̀ renin' type producing constriction. Thereis increasing evidence of the presence of both types of enzymes in peripheral ̀ active' tissues, e.g.salivary glands, as well as in the cells of the macula densa or juxta-glomerular apparatus of thenephron in the kidney. In the latter case, evidence may be produced to support the view thatvariations of the ratio ̀ oxygen utilisation / oxygen concentration', influences the relative amountsof vaso-constrictor `renin type' , and vaso-dilator `kallikrein type' enzymes produced andsecreted, and the effects they produce on glomerular function through the relative effects onglomerular blood vessels.

It seems possible that a similar ratio of oxygen consumption /oxygen concentration could be

18

effective in determining the relative production of vaso-constricting and/or vaso-dilatinghormones in other active tissues. Considered in this light, the relative concentrations of oxygenand lactate can be regarded as constituting a `switching mechanism' which determines therelative values of `Q' and `R', through the metabolic activity of the oxidising enzymes. Such aswitching mechanism would favour an increase in stroke volume, and an increased concentrationof carbon dioxide when this oxidising activity is high, as opposed to an increase in oxygenconcentration and `R' when the activity is reduced for a particular value of `l', and of relativetissue activity.

More recent reports (Brennan, Troy, and Ballermann, 1989; also Pisano and Austen, 1989?)suggest that the vaso-active agents may be produced by vascular endothelial cells. The activevaso-dilating substance affecting smooth muscle may be nitric oxide (E-NO) produced inresponse to acetyl choline, kallikrein-bradykinin, or a fall in oxygen concentration. ̀ Endothelin',which may be more prolonged in its activity than the `renin-angiotensin' mechanism, is thesubstance which brings about vaso-constriction in response to vessel wall stretching orepinephrine. These substances which are both produced in the same cell, have their effects byinfluencing phosphorylation of light myosin chains in smooth muscle. Just what the chain ofevents might be must be left open for the present. This account simply suggests the type of`trigger control' which could be the activating mechanism.

In the absence of increased lactate concentration (and no increase in `l' because there is noincreased tissue activity), increasing oxygen concentration simply inhibits oxidising enzymesand results in diminished carbon dioxide production and stroke volume, while vascular fillingis only changed by variation of viscosity, if `l' is unaltered. At the same time `R' is increasedcompared with `Vs' so that the circulation in the area is `shut down'. A certain minimumconcentration of lactate is necessary to maintain [ ], `Q', `Vs', and hence `l' in the localcirculation.Maintenance of carbon dioxide production then depends on both the partial pressureof oxygen and the concentration of substrate [lactate].

In this suggested model, although ̀ l' is increased by the initial activation of muscle, the increasein circulatory length needs increased provision of lactate if it is to be maintained. Lactateconcentration is perceived as having a secondary effect on the value of ̀ R', through its effect oncirculatory length, but only in the presence of a sufficient oxygen and carbon dioxideconcentration. If the oxygen concentration is not sufficient, there will be a fall in ̀ R', but the circulation cannotbe sustained if carbon dioxide concentration and stroke volume is reduced as oxidation ceasesfrom ischaemia associated with relative change in oxygen concentration.

There are then two factors regulating the circulatory length in voluntary muscle. The firstis a local factor, initiated by the commencement of activity (possibly acetyl choline release),which might be called ̀ activation dilatation'.The second or ̀ metabolic dilatation', is maintainedby continuing metabolic activity, and depends on the relative levels of lactate, carbon dioxide,and oxygen concentrations, and liberation of vaso-active enzymes, peptides, or other substances.That a combination of substances might be responsible for vasodilatation occurring withmuscular activity was suggested by Haddy and Scott (1968) in their review of the field. Thefunctional length of the circulation,`l', is then considered to be greatly dependent on lactateconcentration. While other metabolites and ions may of course be involved, lactate concentrationis taken to be representative of these products of metabolism also.Control of lactate

19

concentration then becomes a basic homeostatic mechanism which controls the functional size(length) of the circulation, while the concentrations of oxygen and carbon dioxide control thefunctional cross-sectional area of the blood vessels. Together they control circulatory volume(l.a), `R' (l.n/a), and arterial pressure ( ) for a given pulse rate. It must be remembered that other things (e.g., circulatory length) being equal, `Q' and `R' arereciprocally related, and that a rise in the value of `R' means a fall in the value of `Q'. This is ofparticular significance when considering the maintenance of diastolic blood pressure. Diastolicblood pressure is subject to the same variables as systolic pressure, but has the further variableof `vd/v', which in fact determines the ratio `DPs/APs'. While `vd' is determined by the flowconditions in the circulation at the end of diastole, `v' is closely related to the pulse pressure,which itself is determined by flow conditions throughout the cardiac cycle. The pulse pressurecan be represented as `lPR . Dv/2' , or if one wishes to relate its value to that of the systolicpressure, as `AP . Dv/2R', while `DP/AP' is `vd/v' , and the ratio `PP/DP' equals `, so that the relationships between systolic arterial pressure, diastolic pressure, and pulsepressure, essentially depend on values of ̀ R',`v' and ̀ vd'. At the same time diastolic pressure canbe represented as ̀ EDP . ̀ ', and while ̀ R' is the reflection of the ratio ̀ EDP/LTDTR', ̀ ' canbe represented as

(or EDP )where `LTDTR' is the ratio of `initial fibre length / time taken to develop unit tension ofisometric contraction'. `R' is shown as related to `EDP', and ` ' as related to `lPR'. An increasein diastolic pressure from a rise in the value of `R', results in an increase in `EDP', while anincrease in `lPR' will result in a rise in the value of ` '. In this instance an increase in `lPR'which increases the level of diastolic pressure can also bring about an increase in efficiency ofventricular contraction without any increase in `EDP'. This is the situation which occurs at theonset of exercise, when both pulse rate and blood pressure can rise with an increase in cardiacefficiency, and an expansion of the circulation into the capillary bed, while the volume of thesystemic circulation is expanded with blood from the pulmonary circulation, and `EDP' slowlyfalls as more carbon dioxide is produced in the active tissues.Under these circumstances thediastolic volume of the heart may actually decrease in size, as efficiency increases.

This increase in efficiency is accompanied not only by a fall in `EDP', but also with a probablerise in liver temperature, and increased gluconeogenesis, up to the capacity of the peripheraltissues to use oxygen at the available partial pressure, for efficient conversion to carbon dioxide.

In summary, the main determinant of arterial pressure is the metabolic activity which determinesstroke volume and resistance per unit velocity, which have a reciprocal relationship with eachother. This ratio is determined by the capacity of the tissues to use oxygen at a particularpressure in an optimal way with production of carbon dioxide, and a limitation of the amount oflactate available for oxidation. A rising level of lactate is an indication of the inability of thetissues to accomplish oxidation satisfactorily, without an increase in the partial pressure ofoxygen supplied, and this in turn leads to an increase in `R' with slowed capillary flow, anincrease in blood pressure, a fall in stroke volume, and requiring an increase in pulse rate, if

20

excessive vascular strain is to be avoided. If on the other hand increased blood pressure happensas the result of an increase in pulse rate, stroke volume is likely to be unaltered, and anyexcessive strain on the arterial system is largely avoided. The rise in blood pressure is the normalresponse to the commencement of physical exercise. The adjustment of pulse pressure anddiastolic blood pressure occurs in response to changes in velocity and resistance per unit velocityof blood, according to readily definable formulae.

The blood pressure required for a particular individual under a given set of circumstances isdetermined in the first instance by the diastolic pressure needed to maintain ventricularefficiency in the face of the ventricular stroke volume set by the metabolic activity ([ ] in thetissues) of the individual overall. On top of this is the circulatory momentum required tomaintain the product ` ' (which is equivalent to the ratio Q / Vs ) at a constant value,or nearly so, in the tissues generally. This momentum in the extravascular fluid is equivalent to`v/R' or the ratio of `PPs/APs', where `APs' is also equal to `DPs' plus `PPs'. These values arefurther defined by the metabolic index `Q/R' (equivalent to the ratio ) which isdetermined by the partial pressure of oxygen required to produce the required amount or partialpressure of carbon dioxide necessary to maintain stroke volume for a given state of tissueactivity. The partial pressure of oxygen determines the value of ̀ R', and, together with ̀ l.PR', and`Q', the momentum in the extra-vascular compartment, and the levels of the various componentsof the blood pressure.

Three factors finally determine the current level of blood pressure maintained at any time. Ofthese the oxidative capacity of the respiratory enzymes must be regarded as of the greatestimportance, but its effects are modified by the level of lactate concentration associated with it,which is able to vary the inhibitory effects of raised oxygen concentration on respiratoryenzymes, and so the cell volume and `[ ]' which can be tolerated, and still allow oxidation tocontinue.The relative permeability of the cell membrane not only affects these levels but isinfluenced by each of them in turn, so that the overall result is to vary the level of energycontained within the cell which derived originally from momentum in the extra-vascularcirculation as well as cell metabolism, and which should therefore be available to return kineticenergy to the extra-cellular fluid under appropriate conditions. Change in the permeability of thecell membrane will require a change in linear velocity of blood flow (and so of extra-vascularvolume) in order to maintain the same fluid and energy exchange across this barrier, while thealtered value of `[ ]' and associated cell volume increases the value of `R', and so the energylevel present in the cell at any particular time. More energy is then required to move fluid andenergy into the cell, while a smaller proportion per beat of the total cell energy is returned to theextra-vascular fluid (and eventually to the venous return) from the energy ̀ store' within the cell. The result is that a greater amount of total energy is required to be maintained within the extra-vascular compartment at any particular time, because of the increase in momentum needed toinject fluid and contained material for cellular nutrition, and of the increase in intra-cellularvolume and energy (represented as `R' ) retained from beat to beat because of the increased`[ ]' and the resultant change in permeability of the cell wall. The increase in `R' and `lPR'together indicate an increase in systolic blood pressure in order to provide the same flow of fluidand energy into and out of the cell, in the face of the increased energy `store' which the cellcontains, and which resists the storage of further energy with each beat. The adjustments of

21

`[ ]', lactate concentration, and cell permeability which are necessary to control this energyexchange, determine the current level of systolic blood pressure required to be maintained.

The adjustment of lactate concentration to maintain circulatory length must also vary linearvelocity (and so extra-vascular volume) if the pulse rate remains constant. The mechanismswhich lead to either variation or stability of blood lactate concentration in response to changein circulatory length occurring through heat production and elimination from the extra-vascularcompartment, or through distention of hollow organs, together with the regulation of glycolysiswithin the effector organs or the liver, all have very significant effects on circulatory activity.In general, these mechanisms involve glycolysis in the ̀ effector' organs as part of their cycle ofenergy production, glycolysis elsewhere in the body where the underlying significance is lessclear, and glyconeogenesis from lactate in the core organs requiring the input of energyessentially from fat metabolism. While details of these mechanisms are by no means clear, it ispossible to consider the results which are likely to occur when lactate levels are varied, eitherappropriately to regulate circulatory response to some imposed `stress', or possiblyinappropriately when circulatory length and/or lactate level is either excessive, or reduced belowthe level which is required for optimal circulatory function. It is also important to recognise that the production of lactate as a result of glycolysis, involvesthe release of energy which has further significance for the energy balance between the cells andthe circulation. Some syndromes involving changes in either circulatory length or variations inmetabolic gas concentrations are briefly considered in later chapters.

While the gas concentrations in the active tissues are crucial in determining the level of bloodpressure, these gas concentrations also have a close relationship with the relative volumes in thethree main fluid compartments of the body. As the intra-cellular fluid volume, `Vc', isproportional to `R' at systole, and the extra-vascular fluid volume, `Vx', is proportional to `lPR'at diastole, then the product ̀ R.lPR' (or ̀ APs') is proportional to both the intra-cellular and extra-vascular fluid volumes. On the other hand, the intra-vascular volume is proportional to ̀ Vs', withappropriate change in the stroke volume. This implies that if the division of body fluid volumesis directed towards increasing the volume of the intra-vascular compartment rather than vascularfilling, then the current blood pressure will be reduced , while when body fluid is concentratedwithin the cells and extra-vascular compartments rather than the intra-vascular compartment, thearterial blood pressure is then increased. Blood pressure levels consequently are largelyregulated in parallel with the distribution of fluid within the body. A relative comparison of thesize of each of these fluid compartments can be obtained by estimating `APs / lPR : PPs / lPR: Q.PR/ lPR(i.e, Vs)' as being in the same proportions as `Vc : Vx : Vs', or `R : v : :: Vc :Vx : Vs'; and the activity of the ventricular contraction in maintaining body fluid distribution willthen be in proportion to the levels of these three variables which determine the amount of workwhich is performed by the ventricle per beat. The level of each variable is adjusted to maintainthe optimal conditions of strength, and circulatory momentum, and in turn the volume and linearvelocity of moving fluid, which is most appropriate for a particular activity, and the requiredenergy level is obtained by suitable alteration of ventricular size and shape to determineventricular filling.

Vascular filling is the energy required to distend the vascular system and allow the requiredvolume flow in spite of the constricting effect of oxygen partial pressure affecting the vesselsof the arterial system. Vascular filling restricts the increase in linear velocity of flow which

22

would otherwise follow vasoconstriction by increasing vascular volume instead. It can berepresented as proportional to `R.Vs', or [lactate]. , which is equivalent to` ',

or ̀ ', the energy developed in the cells / constricting force on the blood vessels, or ̀ l.Q'.

Vascular filling arises because of :- 1. the energy store persisting in the body fluid compartments at diastole and proportional to[lactate].2. blood viscosity proportional to ` '.3. `cell strength' , or the concentration of stored energy in the cell , ` ' `Vs'i.e., vascular filling is the energy represented by `PR.R/Vs', or osmotic pressure exerted by theplasma proteins times oxygen concentration.

The energy store at diastole is proportional to lactate concentration, and the resistance to beovercome is `[lactate]. viscosity' `R', while `cell strength' represents the energy required tomove blood against this resistance, so that `R.Vs' represents vascular filling. Vascular fillingovercomes the plasma osmotic pressure and passive permeability of the capillary membrane toproduce tissue fluid , and maintain the balance of energy between blood and tissue fluid.

The significance of vascular filling is that it allows an increase in the diameter of blood vessels,and an increase in volume flow as well as circulatory length, so that when filling is increasedvolume flow is also increased. When blood viscosity is increased, vascular volume is increasedas a result, while stroke volume increases as the product of vascular volume and circulatorylength. The ratio `Q/Vs' is increased as `l' increases, with increased ventricularefficiency.Increased vascular filling and associated vascular volume then allows increasedvolume flow as well as increased circulatory length, with greater stroke volume as vasculardiameter increases as well as vascular length. In this way increased vascular filling can alsoincrease ventricular output and volume flow as well as ventricular efficiency, but only providingcirculatory length increases faster then oxygen concentration, allowing viscosity and vascularvolume (i.e., ` ' and so stroke volume) to increase compared with `R', and so [lactate] tobecome reduced compared with circulating volume. This can only occur if cell activepermeability is increased as well as the cell energy store, so that stroke volume increases as wellas circulatory length, but at a faster rate.

When vascular filling (represented as R.Vs) is increased, there is some constraint placed uponthe maintenance of systemic blood volume, which tends to be reduced as `[lactate]' (i.e., R/Vs)increases because of the associated reduction in the cross sectional area of the vascular bed(represented as ` '). If such a reduction occurs, systemic blood volume will be reduced,and `vascular filling' returns to its original value, unless the circulatory length and/or apparentviscosity are increased ( is increased). As `Vs' is reduced, the stroke volume,`Q' will bereduced also. The increased vascular filling needs to be maintained so that right ventricularfilling (Q.R) is also maintained. There are two mechanisms which can act to maintain vascularvolume under these circumstances. 1. Any rise in oxygen partial pressure which is involved in the regulation of arteriolarconstriction and therefore of the value of `R', also decreases capillary permeability, and altersthe relative values of intra-vascular and extra-vascular volumes, so that systemic vascularvolume is maintained more readily.

23

2. An increase in the production of circulatory protein, which probably results from changes ingluconeogenesis in the liver, following liver temperature adjustments when end-diastolicpressure is varied in the ventricles (see Chap.8,10). These mechanisms together prevent thereduction of ̀ Vs' below a critical level for maintenance of stroke volume.If by these means, ̀ Vs'can be maintained at a relatively constant value, vascular filling then becomes a function of thevalue of `R' (or apparent viscosity, vascular length, and tissue oxygen concentration) and theosmotic pressure exerted by the plasma proteins. If `Vs' remains at a fairly constant value, thenchanges in `Vx' and `Vc' must depend on variations of `R' and/or `lPR', i.e., of systolic arterialpressure.

The vascular filling, `R.Vs', may be represented as indicating the level of residual momentumwhich needs to be maintained in the extra-vascular compartment to ensure that sufficientmomentum is contributed to the venous system with the stroke volume for provision of adequatevenous return and cardiac filling. The `balance' between `R' and `Vs' indicates the relativevolumes of the cellular and intra-vascular compartments, and the energy which needs to beavailable in the cells for an adequate return of kinetic energy to the venous system. If thisbalance is upset, for example, by increase in the value of ̀ R' and ̀ [ ]', maintenance of the samevalue of vascular filling, `R.Vs', would imply a smaller value of `Vs', and so restriction of thecirculation, unless the overall vascular filling increases to maintain the vascular volume, `Vs'.Any change of vascular filling implies a considerable alteration in the level of energy availablewithin the extra-vascular compartment, if `Vs' (and the venous return and cardiac output) is tobe kept from falling below an adequate minimal level.While `R.Vs' is equivalent to themomentum required to be present to maintain equilibrium between compartments, and `v/R' isthe momentum required for a constant value of ̀ R.Vs' to maintain the balance between ̀ Vx' and`Vc' (the relative volumes of the extra-vascular and intra-cellular compartments), any alterationof `R.Vs' requires a change also in the energy level of `Vx' to maintain the balance with theincreased value of ̀ R'; i.e., ̀ Vc'. The energy required in the extra-vascular circulation (and whichmust be supplemented by ventricular contraction at each beat) is proportional to ̀ Vs.APs', whichmust then be proportional, not only to ̀ R.Vs', but to an additional factor of ̀ lPR' which increasesproportionally with `R' (as v/R increases) so that for `Vs' to remain constant, requires that theenergy available in `Vx' must increase by a factor of `R squared'. `lPR squared'. This increaseis reflected in changes in arterial blood pressure, because the ratio of `v/R' is proportional to`PPs/APs' (D.v.lPR/2.R.lPR), and the ratio of `Vx/Vs' at a given value of `R.Vs' is proportionalto `APs'.The energy increase required to maintain a constant value of `Vs', is then proportionalto ̀ Pps/ . This relationship between pulse pressure and arterial pressure may frequently beobserved in clinical hypertension, and indicates the increased difficulty in maintaining anadequate circulation, because of altered conditions for `storage' of kinetic energy in the extra-vascular compartment which is a feature of the condition.

If `Vs.R' is proportional to momentum required to be maintained in the extra-vascularcirculation, then `Q.R' is proportional to the momentum which is needed to maintain adequateventricular filling, and is required to be proportional to the momentum which has to be providedto the venous circulation per beat to maintain the venous return. In the provision of thismomentum, `Q' is the volume added to the venous circulation per beat, and `R' is proportionalto the momentum per ml. required to be given to `Q', in order to maintain ventricular fillingagainst a particular level of end-diastolic pressure in the ventricle.

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The capacity for work by the heart, and the effector organs, requires careful adjustment of thestrength or accumulated energy needed for continuing optimal performance, which becomes acritical factor in physical activity.

Blood Pressure Maintenance in the Pulmonary Circulation.There are fundamental differences between the two circulations in the manner in which eachmaintains the level of blood pressure. In the systemic circulation, prominence has been givento the importance of systolic pressure in determining the distribution of fluid between the mainbody compartments and the exchanges which take place between them. The level of arterialblood pressure has been related to, and largely results from, the level of metabolic activity in theperipheral tissues, depending upon the partial pressure of oxygen which has to be maintainedtherein for oxygenation to proceed in an adequate fashion, in order to limit the accumulation ofanaerobic metabolites.

The pulmonary circulation does not have to support an extra-vascular circulation in the samefashion, very little fluid escaping from the blood vessels under usual circumstances, while thedisparity between blood pressure at diastole, and the osmotic pressure exerted by the plasmaproteins, ensures the rapid reabsorption of any fluid which might escape into the alveoli. At thesame time the partial pressures of oxygen and carbon dioxide, which are regarded as of suchimportance in regulating blood flow in the systemic circulation, are largely regulated in the lungsby respiratory activity, which negates any local effect on the small vessels that changes in gasconcentrations might otherwise exert. Nevertheless, when there are marked alterations in thepartial pressures of gases in the inspired air, alterations in the resistance of pulmonary vesselsdo occur, but these are in the opposite direction to those found in the systemic circulation.Decreased oxygen concentration in the inspired air, for example, leads to vasoconstriction in thelung vessels, but may result in vasodilatation in the systemic circulation. The factors controllingblood pressure maintenance in the pulmonary circulation must be sought elsewhere.

A possible clue might lie in the different functions which have been allotted to the systolic anddiastolic blood pressures in circulatory activity. While systolic pressure is a measure of the"power" which the cardiac muscle must develop in order to regulate fluid distribution andcirculatory energy in the extra-vascular regions, diastolic pressure has a greater role inmaintaining ventricular efficiency, by regulating the conditions under which the ventriclecontracts, and the energy remaining in the circulation at diastole. In the absence of anysignificant extra-vascular circulation, power development is of less importance for thepulmonary circulation. Maintenance of ventricular efficiency, on the other hand, is essential, andin this area, close control of diastolic blood pressure is a prime consideration for the pulmonarycircuit. Blood pressure levels in the lungs are then likely to be set by the pulmonary diastolicblood pressure which is required to maintain right ventricular efficiency.

The other factors in the efficiency formula, in addition to the pulmonary diastolic blood pressure,are `Q', the stroke volume; `Vp', the volume of the pulmonary circulation; and `VPs', theeffective venous pressure for right ventricular filling. Each of these (with the exception ofpulmonary diastolic blood pressure) is either determined or greatly influenced by, events in thesystemic circulation, and any adjustment required to maintain ventricular efficiency can only bemade by adjustment to the level of pulmonary diastolic blood pressure, which is therefore theimportant parameter for maintaining the pulmonary circulation.

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The mechanics involved in the regulation of pulmonary diastolic blood pressure, would seem tobe those involved in determining the distribution of blood volumes between the two circulations(see Chapter 8). If, for any reason, stroke volume is reduced, a compensatory fall of circulatingblood volume may occur by transfer of blood to the pulmonary circulation. Right ventricularefficiency is maintained by a rise in pulmonary diastolic blood pressure, which occurs as a resultof change in the "shape" of the cavity of the ventricle as its diastolic filling increases, becauseof the shortening of the internal radius of the cavity as it changes shape from a crescentic to amore globular form (see Chap.7). As the internal radius diminishes, the pressure transmitted tothe fluid contents of the cavity increases for a given force of contraction of the muscle fibres, asrequired by LaPlace's Law (wall tension depends on the ratio of the internal radius of the cavityto wall thickness, and also on the integrated cavity pressure during systole). For a given walltension or force of contraction, the cavity pressure developed during the isometric phase(diastolic pressure) will be greater if the ratio of the internal radius of the cavity to wall thicknessis reduced. This allows variations of diastolic blood pressure to be developed for the same forceof contraction by variation of the shape of the internal cavity of the right ventricle, and itsrelationship to wall thickness. This relationship can be approached from an alternative point ofview, such as that expressed as `the energy transfer factor'( PR), which when divided by'LTDTR" gives the `contractility factor'( or ) which has already been considered in somedetail. The `energy transfer factor' (vd . lpPR / v) has the equivalent value `DP.lpPR/AP' , andrelates the values of `DP' and `AP' for a given value of `lpPR'. In this relationship for the rightventricle, ̀ lp' is the average mean length of the pulmonary circulation, which of course must varywith each respiration.Changes in pulse rate may also occur with respiratory movements (sinusarrhythmia) through alterations in vagal tone, and the variations in `lpPR' which result, musthave their own effects on the "energy transfer factor".These relationships between them, fix thevalues of both diastolic and systolic pressure for the pulmonary circulation. A major differencein the maintenance of blood pressure in the two circulations is that in the systemic circulation,the systolic blood pressure is determined by metabolic considerations, and the diastolic bloodpressure is then adjusted to preserve ventricular efficiency, while in the pulmonary circulation,diastolic blood pressure is determined by the conditions in the pulmonary circulation imposedby the demands of the systemic circulation on the parameters which determine ventricularefficiency Carried a step further, in the systemic circulation, blood pressure maintenance is setby the average mean linear velocity of circulating blood required to maintain the distribution offluid within the body; while in the pulmonary circulation, blood pressure maintenance dependson the average mean linear velocity at diastole, required to maintain right ventricular efficiency. In practice this means that in the systemic circulation, the greatest variations of blood pressureare in the values of systolic pressure, while in the pulmonary circulation the greatest variationsof blood pressure are in the values of diastolic pressure. The pulmonary systolic blood pressureon the other hand does not show such great variations, and therefore is less likely to producepressure levels in the capillaries which would exceed the osmotic pressure of the plasma, leadingto pulmonary oedema.

There are several features of the pulmonary circulation which it would be convenient to considerat this time. It has already been mentioned that there is virtually no extra-vascular circulation inthe lungs, although sufficient fluid enters the alveoli to saturate the gases therein with watervapour, but any excess is normally reabsorbed rapidly.The passage of fluid from the blood to thealveoli is resisted by the algebraic sum of the osmotic pressure exerted by the plasma proteins,

26

and the pressure differential between the gases distending the alveoli and the bloodvessels.Because the extra-vascular circulation is absent in the lungs, ̀ Rp', the resistance per unitvelocity offered to each ml. of blood in the pulmonary circulation, and `vp', the average meanlinear velocity of the pulmonary blood flow, are both greater than the equivalent resting valuesin the systemic circulation, and the `peripheral resistance' (Rp.vp), is some three or four timesgreater.This results from the increased peripheral resistance which occurs when the blood is allconfined to passing through the small blood vessels (capillaries) in the lungs, while in thesystemic circulation, the extra-vascular fluid ̀ by-passes' the capillary network, and then re-entersthe venous system, with a considerable overall saving in energy expenditure in overcoming theresistance offered by the small vessels.(Estimation of values for ̀ v' and ̀ R' can be obtained fromapplication of the formulae `AP = R.l.PR', and `D.V.v squared = Q.PP' for each circulation.Taking `APs' as 120 mm.Hg., and `APp' as 40 mm.Hg., `PPs' as 40 mm.Hg, and `PPp' as 30mm.Hg., while the average mean length of the systemic circulation is about 73 cm. and thepulmonary circulation about 18 cm., this gives `vp/vs' at about 2.45, and `Rp/Rs' at about 1.35. The peripheral resistance in the pulmonary circuit is then about 3.3 times that in the systemiccircuit per ml. of blood in each.)

The energy given to each ml. of blood in the pulmonary circulation per beat is then greater thanthat required in the systemic circulation, because of the `storage' of momentum in the extra-vascular circulation from one beat to the next. Without this `store' of energy, the energy whichwould be dissipated per beat in the systemic circulation, would be of the order of three times thatwhich is normally required, which would have a marked influence on ventricular energyproduction and efficiency. While the ratio, `R/lPR', and value of `Q', have no significance asindicators of relative volumes between fluid compartments in the pulmonary circulation, therelative increase in the value of each, means that the arterial and venous volumes in the lungsare relatively greater compared with the total volume of the pulmonary circulation, so that thesevessels remain comparable in size with the aorta and venae cavae.

In the systemic circulation `R' is diminished by the passage of fluid to the extra-vascular space,with little loss of momentum which is later transferred back into the venous blood, so that thefinal values of `R' and `v' depend on the partial pressures of the respiratory gases ( ),and `lPR'.

In the pulmonary circulation ̀ R' is partly controlled by the alteration of viscosity of blood in theright side of the heart, which varies with the oxygen saturation of haemoglobin.It is greater inpulmonary arterial blood than in pulmonary venous blood because of the gas exchange whichoccurs in the lungs. Resistance to flow is also altered by the air pressure in the alveoli, which inturn is regulated by the tone of the bronchiolar muscle, and this also influences linear velocityof blood flow. Constriction of the bronchioles, by delaying expiration and increasing alveolarpressure, may increase `Rp' and diminish `vp', and the reverse situation also probably occurs.While flow through the pulmonary circulation may be varied by air pressure in the alveoli, whichvaries with respiration and the tone of the bronchiolar muscles, i.e., partly by ̀ [ ]' and ̀ [ ]'affecting respiratory activity, and blood viscosity, and partly through the vagal outflow, reflexlyaffecting the pulse rate and reflecting other afferent stimuli; it is also influenced by changes intone in the pulmonary arterioles. Most of the energy in the pulmonary circulation is used anddissipated with each beat in filling the left ventricle, while energy in the systemic circulationmay be stored from one beat to the next in the extra-vascular compartment, so that much less

27

energy is used pro rata compared with the pulmonary circulation. Flow energy to fill the leftventricle must come from right ventricular contraction by way of the arteries, capillaries andveins, by a completely intra-vascular route.

Energy to fill the right ventricle is in large part transmitted from the extra-vascular compartmentto the veins. If it all came directly via the capillaries to the veins, more energy would need to beprovided per beat to maintain ventricular filling. By providing a higher energy level per ml. toa smaller total circulatory volume, the pulmonary circulation acts as an energy booster, to ensureleft ventricular filling at a higher linear velocity and a relatively lower venous pressure, therebyenabling the left ventricle to perform the same work for less energy output per beat, andrequiring less energy to produce a self-sustaining circulation.The important functional features of the pulmonary circulation involve:-1. The main function is to provide the opportunity for gas exchange with the atmosphere andinspired gases, with all the important implications of this exchange concerning pH adjustment,and other ionic variations.2. By increasing the linear velocity of flow as an aid to left ventricular filling, right ventricularcontraction improves the efficiency of the left ventricle, reducing the work required to supplyblood at high linear velocity but lower pressure for left ventricular filling. If this blood had laterto be directly supplied with energy by the left ventricular contraction, a greater amount of energywould be required. By confining the energy increase to a smaller volume of blood in thepulmonary circulation, the system becomes more efficient.3. Because of the variability of ̀ energy transfer' which can be provided by alteration of "shape"of the right ventricular cavity (LaPlace's Law), the output of energy of the right ventricle is ableto vary independently of the filling(i.e.,venous) pressure. An illustration of this can be seen inthe results of Expt. 1. (Chap.4).4. Because the increased linear velocity of blood flow provided by the right ventricularcontraction, only affects a relatively small amount of the circulating blood (about 1/6 to 1/8), thisarrangement allows a considerable saving in the energy required to produce a self-sustainingcirculation. 5. Blood pressure in the pulmonary circulation is provided through variation of the diastolicblood pressure, from altered energy transfer, rather than through variation of systolic bloodpressure by change of diastolic length of fibres, and/or changes in the contractility factor, of thekind which occur in the left ventricle and systemic circulation. Such changes in pulmonarydiastolic pressure do not threaten to produce pulmonary oedema, in the same way as changes insystolic pressure might do. The role of vascular filling in the maintenance of systolic blood pressure.The energy equivalent of systolic arterial pressure has been given as ̀ R.l.PR', and if the variableswhich regulate the value of `R' are substituted in this expression, it becomes proportional to`l. .l.PR /a' , or `R.V.PR/a' , or `R.V.PR.[ ]'. While the significance of `PR' and `[ ]' havealready been explored, at least in some degree, it is now necessary to consider the degree ofvascular filling (R.V) and its intimate relationship with the average mean length of thecirculation (l).

Vascular filling has been represented as varying with the square of the vascular length, and withthe ̀ apparent viscosity' of the blood. At the same time it is also an expression of the state of fluidand electrolyte balance between the intra-cellular (R) and intra-vascular (V) compartments ofthe body, and it is now necessary to examine the mechanisms by which the appropriate amounts

28

of fluid and electrolyte are maintained in the body, and varied as required.

While an adequate intake of water and the other necessary constituents is obviously a pre-requisite, regulation of the amount remaining in the body at any time, and under any particularcircumstances, really depends on the rate at which the substances involved are lost by excretion,or otherwise disposed of during the metabolic process. Necessary losses of fluid from the lungsand bowel are part of normal physiological activity, and other losses in secretions, such as tears,nasal secretions, and saliva also occur to some extent. The main areas of loss however, are fromthe skin and in the urine. Such losses vary, both with internal and external environmentalconditions, and although no comprehensive or detailed account of the intricate variations andadaptations to these altered circumstances, which together constitute the physiology of fluid andelectrolyte balance will be attempted, some understanding of the circulatory limitations whichare imposed on these necessary changes, should be outlined.

For the most part regulation of the overall volumes and concentrations of solutes within the body(as opposed to the relative distribution of fluid volumes between the several compartments) isthe function of the kidney, though skin losses also have a part in modifying this activity. Thisis particularly so because loss of fluid from the skin has become adapted to serve temperatureregulatory activity, a function which is equally important with fluid balance in maintainingnormal cellular function. An account of the control of circulatory and excretory activity in thekidney, which in turn regulates the volumes of fluid remaining within the body compartments,and eventually the degree of circulatory filling, and circulatory length is also desirable, and willbe attempted in a later section. Circulatory length, together with the gas concentrations in thetissues and the pulse rate, ultimately decide the prevailing systolic blood pressure.

The reason for introducing these considerations at this stage, is that variations in the level of theions in the cell environment may in turn influence the fluid exchange between the cells andextra-vascular fluid, together with the rate of polarisation and the level of `irritability' of thecells. In addition the amount of energy which is required to maintain the balance of volumesbetween the fluid compartments, and ultimately vascular filling, blood pressure, and the energyoutput of the left ventricle per beat, arterial filling, and arterial vascular stress may all be affectedin some degree. What is suggested is a possible link between electrolyte balance, e.g., [potassium ion] andvascular disorder, which while it will not be pursued here, could well repay future consideration.The circulatory energy which is required to be maintained per beat is proportional to ̀ R.V.lPR',or ` '. This energy is present in the extra-vascular compartment, and is in turnproportional to the extra-vascular volume. Only a small portion of the energy is `used' orotherwise dissipated per beat. This fraction is proportional to the ratio `Q/Vs' , the remainder atdiastole constituting the store of momentum which has been designated the `flywheel effect' inprevious text. During systole, the energy is augmented through ventricular output by an amountproportional to ̀ Q.R.lPR', which expands both the extra-vascular volume, and its energy contentagain to its original level, before energy is dissipated once more in transfers to increase cellvolume and intra-vascular volume (venous volume and kinetic energy). Any expansion ofcirculatory length then has the potential to increase intra-vascular volume (provided the crosssectional area of the vascular bed remains unaltered) in direct proportion to the increased length,but it will also expand vascular filling proportionally as length squared, and extra-vascularvolume and energy required as length cubed. But should vascular volume simply be maintained

29

by an increase in length to compensate for a reduction in ̀ a' (increase in [ ]), ̀ vascular filling'is still increased as length squared, and extra-vascular volume as length cubed, while the intra-cellular volume also increases as length squared, because of the increase produced in `R' asvascular filling increases. A tremendous increase in the energy required in the extra-vascularcompartment becomes necessary simply to maintain the status quo for the intra-vascular volumeand associated stroke volume. Finally, if intra-vascular volume is reduced by a reduction in thearea of the vascular bed (in spite of the circulatory length being maintained at its original value),the extra-vascular volume and energy content is unchanged, but `R' is increased and intra-cellular volume is also increased, although vascular filling is unchanged. The reduction ofvascular volume has the result of producing a reduced stroke volume of an even greater degree,while the increase in `R' means that the diastolic pressure necessary to preserve ventricularefficiency is also increased as well as systolic pressure.

The "ideal" situation is that `a' and `l' should increase or decrease at the same rate, so thatalthough vascular filling increases at the same rate as `l', the value of `R' is unchanged because[ ] falls as `a' increases.The stored energy which is retained in the extra-vascular compartment at diastole (and whichis subsequently available to increase velocity in the venous return), can be regarded as a measureof residual energy times the `flywheel effect' of the stored momentum, and is therefore definedby the product of `lPR' and `R', or 'the systolic arterial pressure'. This is regarded as indicatingthe "notional efficiency" of the circulation times `diastolic arterial pressure', and is equivalentto ` .v', the product of the gas concentrations which are maintained in the activetissues, times diastolic pressure.(Alternatively, it may represent `[lactate] times l.PR.Vs', or`R/Vs . l.PR.Vs.'). Provided `Q/Vs' is maintained constant, the amount of the gas exchange is afunction of the pulse rate, which, apart from the influence of the reflexes which have a large partin controlling it, is initiated by the fluid volume changes, and the ionic concentrations in itsimmediate environment (see above).

Because `EDP' is proportional to `R . LTDTR' , `Q . R' is proportional to `Q . EDP / LTDTR' In the extra-vascular circulation, the energy supplied by each ventricular contraction isproportional to ̀ Q.R.lPR' per beat, while the ̀ energy store', or energy required to be maintainedin the extra-vascular fluid is proportional to `R.Vs.lPR', which is equal to `Vx.OPP/ ' (or theenergy required to balance the reabsorptive force applied to the extra-vascular fluid by theosmotic pressure exerted by the plasma proteins and ).

The ratio of `Vx/ ' is then proportional to `APs/OPP'. The momentum supplied to the extra-vascular fluid per beat is proportional to `D.Q.lPR/OPP' , or its equivalent value `D.Vs.v/OPP'. The momentum required to be present is `D.V.lPR/OPP' , and represents the `stored'momentum which maintains the balance between `Vx', `Vc', and `Vs'. (The density of plasma,`D', is proportional to the concentration of plasma proteins, and therefore closely related to theosmotic pressure while the permeability of the capillaries remains unchanged.)

Of the energy supplied to the extra-vascular fluid per beat, (R.Q.lPR/OPP. or v) , thedistribution between the cells and the intravascular circulation will be according to the ratio of`R/Vs' , so the portion the cells receive will be proportional to `R.lPR/v' of `OPP.v/ ', or `R

30

/ times ' , or ̀ R'. The distribution between the cells and extra-vascular fluid is howeverproportional to `v/R', which is representative of the momentum available, or `PPs/APs', for aparticular value of vascular filling. The energy received by the intra-vascular circulation fromthe extra-vascular circulation will be ̀ Q.OPP/Q.R.lPR' (or ̀ OPP/APs') of ̀ Q.R.vx' , the energyavailable, which is equivalent to `Q.vx'. The distribution between the volume of the cells, `Vc',and the volume of the intra-vascular compartment ̀ Vs', is `Vx/Vc' times `Vs/Vx' , or `PPs/APs'times `Q.vx' or `Q.R.vx / OPP', equivalent to the stroke volume, `Q'. The energy exchange willthen be `Vx/Vc' of energy available times `Vs/Vx' of energy available , or `Q.vx.R' isproportional to ̀ Q.OPP', i.e., requires the volume exchanged to be proportional to ̀ Q', or strokevolume. An increase in vascular filling (and so of energy `store') requires `stored' energy toincrease as `APs2', while the energy released from the `store' per beat increases as `PPs'increases.

In order that the intra-vascular circulation should receive the required momentum ,`Q.R', thecells must receive energy proportional to `R', (OPP/vx), while the intra-vascular circulation isprovided with energy proportional to `Q.OPP'. For any fixed value of energy available(OPP.Vx), if `R' is increased, `vx' will decrease, and `Vs' will decrease, unless the energysupplied by ventricular contraction is increased in order to boost the amount of energy availablein the extra-vascular compartment, and this boost needs to be proportional to `APs2'.L (i.e.,APs.R.v, including peripheral resistance). The energy store is then proportional to ̀ APs2', whilethe energy released to the extra-vascular circulation is proportional to ̀ PPs', and this representsthe energy available to maintain `R.Vs' and `R.Q' at the required levels.

While `R.Q' represents the momentum needed to ensure ventricular filling, and therefore theminimum momentum returned to the venous system from the extra-vascular circulation witheach beat, the momentum given to the blood by each ventricular contraction, must be `Q.D.v' .This means that the momentum in the extra-vascular fluid must be increased by this amount (ora very significant portion of it) with each beat. The momentum present in the extra-vascularcirculation is proportional to `v/R', which also represents the relative distribution of fluid andenergy between the extra-vascular fluid,`Vx', and the intra-cellular compartment ,`Vc'. Themomentum which is available for transfer to the cells with fluid exchange must then beproportional to `D.v.Q.R/v.D', or `Q.R' per beat, while the fluid and momentum transferred tothe veins and intra-vascular circulation, must be at least equivalent to `Q.R' . The momentumcontributed to the circulation with each beat is proportional to `v.D.Q', while the momentumreturned to the veins is proportional to `Q.R', and to maintain the appropriate balance betweenthe three fluid compartments, ̀ D.v' must vary as ̀ R squared'. This means that when ̀ R' increases,the momentum supplied to the extra-vascular compartment must vary as `R2', and requires thatthe kinetic energy, represented by `v' , and pulse pressure, should increase proportionally aspotential energy squared (APs2/l.PR). Any increase in the value of ̀ R' therefore requires a veryconsiderable increase in kinetic energy compared with potential energy, in order to maintainfluid exchange (proportional to `Q') with the cells on the one hand, and the intra-vascularcirculation on the other.

Control of ̀ R' within strict limits is necessary for maintenance of ̀ normal' systemic arterial bloodpressure. The exchange of fluid and energy between the cells and the extra-vascular fluid isdirectly proportional to the stroke volume,`Q', while the momentum necessary to accomplish thisexchange is directly proportional to ̀ Q.D.v', and the momentum which is required to be provided

31

to the venous return per beat in order to produce ventricular filling sufficient to maintain systolicmomentum when the ventricle contracts again, is ̀ Q.R'. This represents the significance for thecirculation of the relative values of `R', `Q', and `v'. Because `l' is a factor in the value of eachof `R', `Q', and `v' (which is proportional to .), `l squared / Vs' , or the lactateconcentration in the cells, is a critical part of this relationship , and is therefore critical formaintenance of arterial blood pressure. Because blood pressure depends on the fluid and energyexchange between the vascular system, the ̀ internal environment' and the cells, it finally dependson the oxidative enzymes within the cells, which by their activity , control the levels of `[ ]',`[ ]', and lactate concentration, and ultimately the pulse rate as well. The ratio of volume offluid exchange with cell volume is proportional to the rate of breakdown of pyrophosphate toprovide the necessary energy. Pulse rate then becomes proportional to ` ', and if ` ' isproportional to `[ ]', the gas concentrations, ` ', and `l', the circulatory length,determine the pulse rate, and rate of energy release in the cell. `PPs/APs2' is then proportionalto `energy released per beat' / amount of energy required to be available in the extra-vascularcompartment, or `energy store' needed to maintain adequate ventricular filling. When `R'increases, so does the `storage' of energy in the extra-vascular compartment and in the cells,equivalent in magnitude to ̀ APs2', while the average mean linear velocity of blood,`v', also needsto increase by an amount of similar magnitude in order to maintain the momentum of venousreturn equivalent to `Q.R', which is that required to maintain ventricular filling for an adequatecirculation, by increase in average mean linear velocity ,`v', and the force of ventricularcontraction, `lPR', (i.e., `PPs').

The necessity for average mean linear velocity of flow to vary proportionally with `R2', mustfollow from the necessity to maintain the circulatory ratio and circulatory volume within fairlystrict limits. Q 2PP . R2 Q . lPR 2PP.lPR.R2

If --- = --------- then --------- = ---------- Vs D . APs2 Vs D . APs2

v 2PP . lPR or -- = ----------- R2 D . APs2

The density of blood ,`D', is closely related to the protein concentration of plasma, and so to theosmotic pressure it exerts for a given ̀ [ ]' . The ratio ̀ v.lPR/D' becomes related to ̀ Vx', so thatfor a given value of `Vx',

v 2PP --- is proportional to --- R2 APs2 . Because ̀ Vx' varies as ̀ v', any increase in ̀ Vx' produces a similar increase in ̀ v', while the ratioof `Vx/Vs' is proportional to `APs/Q' . This means that for `Vs' to be maintained at a particularvalue, `Q.Vx/APs' must also be maintained, and so `Vx' must increase as `APs/Q' in order topreserve `Vs' at an adequate level. To preserve the fluid exchange between cells and extra-

32

vascular fluid requires `v' to increase as ` ', and `PPs' to increase proportionally as ' ',while the volume of extra-vascular fluid, ̀ Vx', must be further increased as ̀ APs/Q' to preserve`Vs'; `v' must therefore increase as `R2', i.e., `2PP' must increase as `APs2' in order to preservean adequate circulatory volume , venous return, and stroke volume. Any increase in venousreturn is a function of energy distribution in the extra-vascular circulation, and depends directlyupon the values of stroke volume and resistance per unit velocity for each unit of circulatoryvolume.

But if `Q' is proportional to `[ ].l' , and `R' is proportional to ` ', the venous returndepends directly on the product of ̀ ', and on ̀ R.Vs', or vascular filling. This impliesa possible relationship with vascular length and lactate concentration maintained in the tissues, and with ̀ apparent viscosity' of the blood. In other words, venous return is directly determinedby oxidative metabolism and the metabolic substrate in the active tissues, so that the amount ofvenous return will be influenced by whether carbohydrate or fat is the main oxidative substrate.

The reason the energy requirement in the extra-vascular circulation increases dramatically when`R' has been increased, is the result of a double effect. Energy is not only required to increasethe cell volume above its previous level, but because this increase in volume is associated witha rise in `[ ]', which has an independent effect on cell membrane permeability, it requires afurther increase in energy to overcome the permeability change. The amount of energy requiredto produce a sufficient alteration in momentum by increasing linear velocity, `v', or pulsepressure, then has to be varied as `R2' or `APs2'.

The necessity to maintain equivalent amounts of potential energy on either side of the cellmembrane, presupposes the continual presence of a sufficient quantity of energy not only tomaintain the energy balance, but also sufficient to transfer additional fluid and energy fromtissue fluid into the cell at systole, as the result of extra momentum becoming available at thecell surface from ventricular contraction, and an equivalent amount of fluid and energy leavingthe cell at diastole. The balanced amount of persistent energy at the cell surface then ensures thatthe fluid and energy exchange with each beat is also balanced. If the energy store in the cell atsystole is equivalent to `R', the total store of energy present at the cell/extra-cellular boundarymust be at least equivalent to ̀ R', and it must also include a factor for the stored energy presentin tissue fluid (i.e.,`v.l.PR.vx.). The equivalent energy will be proportional to `Vx.R. ' or`v.R. ', the amount of the total peripheral resistance, and this is provided by potential energyequivalent to ` .R.vx ' or `v.l.PR ' (the pulse pressure) and volume of tissue fluid, or `v'.Following each contraction the stored energy falls from `R' to `R/Vs', and the total energy fallsfrom `v.l.PR.v' to `l.PR.v', and the total energy from PPs.v to PPs, or by a factor of `v'. If thepersisting energy is `R/Vs', or [lactate], it must be increased by `Vs' at systole (or `Q' ,because momentum is also increased by `l' above the diastolic level, and the total increase is `R.Vs' from ventricular systole, which is dissipated before diastole, and must be replaced by celloxidative metabolism proportional to `l. . '). The persisting potential energy from beatto beat is represented by the concentration of cell lactate times oxygen concentration( , or R / vx ) which is elevated by the momentum in the extra-vascular compartment(v . vx) to produce energy proportional to the peripheral resistance (R.v) or stored energy in thecells at systole, times cell energy exchange. As a result of these energy transfers, momentum

33

in the extra-vascular compartment is diminished, and is replaced by kinetic energy from the cells( l.PR . vx , the extra-vascular fluid volume at diastole times its linear velocity of flow, or cell`free energy' times the linear velocity given to fluid leaving the cell)

The energy provided to the extra-vascular fluid at systole is R.vx, which is equivalent to`Vx.pulse pressure', but by diastole the energy is equivalent to R / Vs times PR.l.vx.l or v.l.PR,and the ratio between them is ̀ v' and proportional to energy exchange. The reduction in energyproportional to cell energy exchange is dissipated in two ways; by reduction in volume of theextra-vascular fluid proportional to `l ', as linear velocity slows in the circulation, and bycontribution of energy proportional to ̀ R.vx' to the intra-vascular compartment. The relationshipbetween `R' and `[lactate] times ' depends on `vx' , or the ratio between . Diastolic energy in the cell may be represented as `R / vx', `R.l / PR', or . Energy

equivalent to ̀ remains present at diastole, after transfer of energy equivalent to ̀ Vs. lPR'

(i.e., or Q.PR), back to the extra-vascular fluid, where it eventually gives rise to the venousreturn. The persistence of potential energy at the cell / extravascular fluid interface throughoutthe cardiac cycle, limits the extrusion of fluid from the cell at diastole, and this suggests that itis equivalent to the concentration of an intermediate metabolite, probably the concentration oflactate. Assuming this to be so, energy equivalent to [lactate] is distributed equally on eachside of the cell membrane, and regulates the passage of fluid and energy into and out of the cellwith fluctuating energy levels, and cell permeability.

(The concentration of lactate only remains closely related to ` ' while there is parity betweenthe concentrations of oxygen and carbon dioxide in the `effector cells', and the ratio between`active' and `passive' permeability. Should the ratio of gas concentrations vary, then[lactate]. increases or decreases with respect to ` ', depending on the pulse rate , and any

alteration of this ratio can be expressed as `APs/ `. The latter expression can be used asan indication of the relative levels of `active' and `passive' permeability of `effector cells', andthe relative levels of the concentrations of respiratory gases.)

This implies that any increase in `Vs' or `vx' may well be associated with increased capillarypermeability, while a reduced value of `vx' or `Vs' may be associated with reduced capillarypermeability, but the associated changes are dependent upon changes in the oxygenconcentration required for adequate oxidising reactions in the active tissues. This situation needsto be contrasted with that seen in e.g. "surgical shock", where a diminished value of `Vs' isassociated with increased capillary permeability, because of an inadequate partial pressure ofoxygen in the active tissues, which results when both ̀ Vs' and ̀ Q' (and ̀ lPR') are allowed to fallbelow the critical levels necessary to provide an adequate oxygen supply (see Chap.13). (Thesignificance of these mechanisms for the excretion of sodium, and therefore for the regulationof the overall volume of extra-cellular fluid will be considered again in a later chapter).

When the length of the circulation changes, a further variable is introduced requiring alterationof the energy available to the peripheral circulation, and the exchange of energy and fluid withthe tissue cells, if the arterial blood pressure is to be maintained at the same level as previously.In general terms, as the circulatory length increases, so does the required level of `capillary

34

filling' (Q.R.) , together with the fluid and energy exchange with the extra-vascular fluid. Theresult in turn is a greater overall fluid and energy exchange with the intra-cellular compartment.

These alterations in the energy levels and volumes of the extra-vascular and intra-cellularcompartments are associated with corresponding changes in the intra-vascular compartment,involving both potential and kinetic energy. The changes are reflected in altered volume flow,and the level of arterial pressure and altered cardiac activity which result.

In the triangular diagram representing cardiac activity which was presented earlier in the chapter,`l.PR' has been considered as a single variable on the presumption of a constant value for ̀ l' withthe individual remaining in a `basal' state. But if, as the result of some stimulus, this basal stateis converted into a more active one, the situation is altered, particularly for the active or ̀ effector'cells, where the energy requirements are increased. This may not be of great immediatesignificance for cardiac function, where the force of ventricular contraction remains proportionalto `l.PR', which may be changed by alteration of either `l' or `PR', but only if the product `l.PR'is also altered.

At the periphery this equivalence no longer holds. When fluid and energy is exchanged between`compartments', changes in pulse rate reflect alteration in the speed at which the exchange takesplace, while any alteration in circulatory length, reflects the amount of the transfer which occursat each beat. The product `l.PR' represents both the amount of fluid and energy transferred ateach beat, and the speed with which it occurs, and the result will be different if one parameteris varied rather than the other.

When considering the energy (and fluid) balance of the individual cells therefore, there are fivevariables, and the influence of each may be illustrated using a different diagram from that usedearlier to represent cardiac (ventricular) activity. (Fig.21)

In the revised diagram, `Q' and `R' are replaced by `[ ]' and `[ ]' (whose product isequivalent to Q/Vs, or `l') , while the product `l.PR', representing the force of ventricularcontraction, is replaced by two variables, `l', representing the `length' of the cell related to theamount of ATP available for performance of external work, and `vx' or linear velocity of extra-cellular fluid, and representing the permeability status of the cell. The product of `l` and `vx' is`PR', and the product of all four of the above (i.e., ` ) is proportional to `l.PR' ,or the `free energy' level within the cell, representing the fifth variable. The cell energy levelmay be elevated by an amount related to the momentum present in the extra-cellular fluid atsystole, after which it falls again when fluid and energy is lost from the cell , despite theproduction of further energy from glycolysis and/or oxidation to preserve cell `free energy'proportional to `l.PR' . The energy present on each side of the cell membrane at systole is`R.lPR', or `APs', and the overall energy equivalent is ` ' which is supplied by the pulsepressure `v.lPR' (or ` ' because across the cell membrane) and cell `energyexchange or v' . At diastole the stored energy present on each side of the cell membrane is` ' inside the cell (where it is still elevated by the oxygen concentration) but equivalentto ` ' in extra-vascular fluid, which is the concentration of lactate in the system. The

energy passing to the extra-cellular fluid as cell permeability alters is `v' or /vx, and thisenergy then passes to the intra-vascular circulation, and venous return as venous momentum.

35

The diagram representing cell energy , illustrates three levels of energy where (a) is the freeenergy generated within the cell; (b) is the energy present at the cell membrane at systole,where the free energy is elevated to be equivalent to the factor ̀ R' (cell energy storage); and (c)is free energy elevated by the factors ` ' and ` , which is the energy store at diastole(which must be balanced by a similar factor in the extra-cellular fluid , opposing loss of fluid andenergy from the cell), requiring total energy proportional to lactate concentration, which mustbe present continuously to maintain circulatory function. Variation of tissue lactate level mustthen have great significance for circulatory function , which is reflected in ̀ lactate tolerance'. If`R/vx ' is taken as equivalent to the lactate concentration times oxygen concentration ( ),the work done by the ventricle per beat which was previously represented as `Q.R.lPR' is nowequivalent to ` ', and ` or R.v/Vs ' represents the fraction ofventricular work per beat which remains after provision for the ̀ apparent viscosity' of the blood,(equivalent to Vs). The internal resistance to flow offered by the blood depends not only on the ̀ apparent viscosity'but also on the distance the blood has to move, or`l', so the total internal resistance is equivalentto `l. '.and the residual energy is then `Q.R' . This extra factor involving circulatory length isalso the distance the ventricle has to move blood each time it contracts, so the work performedby the ventricle per beat is proportional to ̀ force times distance' or ̀ l.PR.l', while the momentumequivalent which has to be provided to overcome the resistance offered by the circulationbecomes `internal resistance offered by the blood' times `circulatory length' , or `l. '.`l', whichis equivalent to `R.Vs' (vascular filling). Because blood viscosity is directly related to carbondioxide concentration, internal resistance to flow is related to stroke volume and systemic bloodvolume, and both internal resistance, and pulse rate, can be expressed in terms of circulatorylength, and the gas concentrations.

Vascular filling represents the force which must be provided at the cell surface before therequired quantity of fluid can enter the cell from the extra-vascular fluid. It is also the forcewhich fluid within the cell must have before there can be any transfer from the interior of the cellback to the extra-cellular fluid. The motive force to transfer fluid into the cell results from thelinear velocity of blood,`v', provided from the energy of ventricular contraction, `v.R.Vs'. Toprovide for minimal energy necessary to move fluid through blood vessels, `v' needs to beproportional to ̀ R.Vs', and to ̀ R2'; and ̀ V2' also remains proportional to ̀ v', and this relationshipis that which regulates blood volume, but as with lactate concentration, the relationship of `v'with ̀ only holds exactly when ̀ [ and the ratio ̀ R / PR' remains constant; otherwise therelationship varies as ̀ vx'. The linear velocity, ̀ v', increases the stored energy within the cell bya factor ̀ R', while an additional amount equivalent to ̀ R' is expended to overcome the resistancewhich measures ̀ permeability' of the cell membrane (equivalent to the reciprocal of ) , andto overcome increased energy production within the cell from glycolysis (equivalent to ̀ l. .vx').These latter two factors produce `R', which together with the increase in `stored energy' (whichis also `R') requires `v' to be equivalent to `R2' for energy transfer to be completed, but withoutalteration of the linear velocity of extra-cellular fluid, or `vx'. While `permeability' is related tothe oxygen partial pressure, energy is also required to overcome the cell generated energy, or `l

', and the product of these two is `l [ ]' or `R'.

36

Because circulatory energy arises from two sources, the `effector cells' and myocardial cells,both have to be allowed for in the transfer of energy in each area. For ventricular contraction,momentum from the venous return (provided from the effector cells, and equivalent to `Q.PR')is needed to maintain ventricular output, while the momentum equivalent `R.Vs'(i.e.,[lactate].PR) is required at the cell surface before adequate energy exchange is possible.

Energy required to maintain the circulation of fluid then arises from two sources. In the ̀ effectorcells' glycolysis produces pyruvate and anaerobic energy, and part of the pyruvate is thenoxidised to carbon dioxide producing aerobic energy, while the remaining pyruvate is convertedto lactate, which in association with oxygen partial pressure in the cells, determines the level ofstored energy, and influences the toxic effects of oxygen for respiratory enzymes. The energyrequired to transfer energy into the cell with a given level of permeability is ̀ ', or

` ', which allows for the increase in linear velocity given to blood by ventricularcontraction, and proportional to `l', so that energy increases to . For energy to leave thecell, the necessary energy is 'free energy' times [lactate] times cell volume, or l.PR.l. ,

equivalent to in the cell , and 'v' in tissue fluid, which is the energy exchange. Cell 'freeenergy' which is able to change cell shape i.e., length or 'L', and cross sectional area, or ' ',isprovided from glycolysis, while a factor representing 'cell strength' or ' ', comes from energyfrom oxidation by way of the 'Kreb's' cycle. This provides 'free energy' 'l.PR', and with energyfrom stroke volume 'Q', allows energy to pass to tissue fluid at systole l.PR .Q/ , or

at systole. At diastole, energy represented by length has been dissipated leavingmomentum , with the energy already in tissue fluid , i.e., [lactate] and strength fromtissue cells, or ' ', and 'R', gives total energy or power remaining at diastole. Atsystole the energy is proportional to pulse pressure before dissipation of energy 'l' representedby reduced volume of Vx (from v to l.PR). Unless cell energy is regularly replaced in this way(by stroke volume from ventricular contraction and energy from glycolysis 'l. .vx' to providethe energy exchange 'v', the cell energy store declines, and with it the capacity for externalwork A disparity occurs between the oxidative energy produced within the cell ( and the energy contributed by the ventricle to the circulation per beat, which is proportional to` ', and the ratio between them is equivalent to the apparent viscosity, or` '. The extra energy which contributes a factor equivalent to ` ', would seem to be thatprovided by glycolysis (equivalent to that provided by oxidation of pyruvate), andproportional to . In effect there seems to be a shortfall in the amount of carbon dioxide provided by oxidation toensure kinetic energy in sufficient amount to maintain the circulation of blood, and additionalcarbon dioxide needs to be provided from glycolysis to overcome the deficiency. Restrictedcarbon dioxide from oxidation allows increased glycolysis, while reduced glycolysis increasesoxidation (Pasteur and Crabtree effects) and carbon dioxide concentration then approaches aconstant value as a result, overcoming the 'bottlenecks' in kinetic energy which might otherwiseappear. Examples are the increase in flow energy following effector cell depolarisation withcommencing activity (Corcondilas et al.1964 ), and energy proportional to 'Q.vx' to maintainthe energy balance between the fluid compartments of the body at all times (i.e., 'L' for cells, 'vx'

37

for tissue fluid, and ' ' for the intravascular compartment). Each of these activities requireenergy proportional to carbon dioxide concentration in each of three dimensions in the ventricle,or ' ' overall for each ventricular contraction provided by glycolysis as well as ' 'from ventricular contraction (and oxidation), or energy overall of ' ' provided by eachventricular beat A fixed proportion of this energy ( ) is provided by glycolysis comparedwith ' ' from oxidation. When carbon dioxide from oxidation is reduced it is immediatelyboosted by carbon dioxide from glycolysis, and when glycolysis is limited, carbon dioxide fromoxidation maintains the concentration in the circulation. Glycolysis provides a fixed proportionof circulatory energy, represented as 'pulse rate' with each ventricular beat.

This suggests that the amount of oxidation in ̀ effector' cells is related to the ̀ apparent viscosity'of the blood, which is in turn varied with the oxygen saturation of haemoglobin as blood changesfrom the arterial to venous state. The energy provided by oxidation in `effector cells' thenbecomes available to overcome the change in internal resistance to flow of venous blood, andassist the ̀ venous return' by an appropriate amount. The energy available in the cells is elevatedto ` ', which balances that available to the circulation from the ventricle). Inthis way each organ or group of cells is able to regulate its own `venous return' through theenergy provided first by glycolysis, and then by oxidation to maintain the resting level of highenergy level phosphate bonds which constitute its energy `store'.

The work of the ventricle per beat is proportional to ( .PR) and also depends on the loading setby the total energy exchange with the cells per beat, and the momentum needed to allow thisexchange, all of which is an additional factor to the momentum equivalent (R.Vs) which isrequired before any movement can occur. The total of the cellular energy exchange depends onthe product (passive times active permeability) and the work done depends on the amount of theenergy exchanges, the force of contraction, and the distance the fluid moves (equal to `l'). Themomentum equivalent required then depends on the ease with which fluid and energy enter andleave the cell, and the distance the fluid moves i.e., ` ', or `l' which when multiplied

by ̀ .PR', gives that fraction of the energy per beat which remains after the internal resistanceof the blood represented by the `apparent viscosity' or ` ' has been allowed for.

The total energy which has to be available to overcome resistance in the circulating fluid, hasthe momentum equivalent ̀ R.Vs' ( ) or vascular filling. Once this energy has been provided,the remainder of the energy produced by ventricular contraction is available to move fluid, withassociated kinetic energy of flow, between the fluid compartments. Fluid movement involvesflow to and from the capillaries, between the intra-vascular and extra-vascular compartments,and from the extra-vascular fluid to and from the cells. As previously mentioned, this energy hasto move a volume of fluid at an adequate speed in order to accomplish the transfer, and these twoelements need to be represented in the algebraic model involving the energy variables presentin the system.

As illustrated in Fig.23 the variables are the gas concentrations present locally, `[ ]' and`[ ]', the product of which is equivalent to the `circulatory ratio', or `Q/Vs', which has to bemaintained at a relatively stable value to maintain normal circulatory function. The other

38

variables are linear velocity of extra-cellular fluid, and the length of the circulation, and theproduct of these four gives `l.PR' , or force of ventricular contraction. It is proposed that ̀ R /vx'in the polarised cell is proportional to ̀ lactate concentration' times oxygen concentration, so that` / PR ' can be represented as [lactate]. in the diagram. The product of all four variablesis ` ', which is equivalent to the remaining `free' energy at the cell level after theventricular work per beat has provided the energy equivalent for external work, as well as theenergy store at diastole, and the extrusion of fluid and energy to the extra-cellular fluid,necessary to maintain momentum in the venous return .

Because ventricular work includes a factor or fraction, by which it must be increased above thecellular energy produced by oxidative metabolism alone in order to overcome the viscosity orinternal resistance to flow of blood, the cellular energy produced by oxidation must be increasedby a similar fraction, to achieve `energy balance' between the two systems. The energy level inthe cell is elevated by glycolysis, which also provides the lactate concentration necessary foroxidation to proceed.

If the glycolytic energy is equivalent to that necessary to overcome internal resistance to bloodflow, it implies a possible relationship between regulation of glycolysis in the cell, and theapparent viscosity of the blood, which is altered as the oxygen saturation of the blood changes.In other words there is a possible regulation of glycolysis associated with variation of the oxygenconcentration in the blood, leading in turn to alteration of the oxygen concentration in the cellsof `effector' organs, occurring in the following fashion. As the oxygen concentration in the tissues diminishes, and oxygen usage increases, the currentlevel of lactate concentration must also be reduced as the amount of high energy phosphatebonds constituting the `energy store' increases. When the lactate level diminishes sufficiently,the level of high energy phosphate bonds has increased to a satisfactory level (having regard tothe amount of inorganic phosphate available to produce them) and as a result of theunavailability of inorganic phosphate, oxidation diminishes, and the oxygen concentrationincreases once more. Depolarisation of the cell is followed by breaking of the high energy bonds to fuel cell activity,releasing inorganic phosphate, which immediately becomes available for glycolysis and furtherlactate production, with liberation of energy as a result.In this way a relationship is developed between the energy produced by glycolysis, oxygenconcentration, oxygen usage, and the lactate concentration in the tissues. If lactate concentrationis related to circulatory length,`l', and also to the cell oxygen concentration, lactate concentrationmust be related to ` ', or the stored energy remaining within the cell after depolarisation,elevated by a further fraction equivalent to before depolarisation occurs. Furthermore, inorder to retain this stored cell energy, there must be a similar energy level maintained on theother side of the cell membrane to prevent the escape of further fluid and energy, and this mustalso be related to lactate concentration, and the total energy present becomes proportional to

, or inside the polarised cell, and R / Vs in the tissue fluid. It appears that theconcentration of lactate regulates the amount of energy present on each side of the cellmembrane, and the ease with which fluid and energy pass across it after depolarisation, and theamount of energy then remaining within the cell. Because it controls fluid extrusion from thecells, which is reduced as lactate concentration increases, an increase in energy level is necessaryat systole to maintain tissue perfusion for a particular level of ventricular filling, and maintain

39

the momentum of extra-vascular fluid, or ̀ '. Blood pressure level should rise as lactateconcentration increases, unless there is some adaptation to prevent it

With the pulse wave at systole, the cell energy level represented by lactate concentration, isincreased by energy proportional to cardiac output to become , or `/ l ', while the diastolic value becomes `lactate concentration times cell free energy' (

, or ). The ratio between systolic energy and diastolic energy is then `Q / l'or `Vs', or proportional to the systemic blood volume, `Vs', and represented by ` ' , or theconcentration of carbon dioxide present. For this reason, sensitive individuals may suffer anincrease in blood pressure following lactate administration, when tissue perfusion issimultaneously reduced. When pulse rate (and tissue perfusion) is already increased as well asblood pressure, to produce ̀ labile hypertension', administration of lactate may reduce perfusionand pulse rate (i.e., , and ) and reduce blood pressure. However if tissue perfusion is alreadythreatened, further lactate increases `R' and reduces `PR', and accentuates the situation.Insufficient lactate concentration on the other hand, allows increased perfusion (i.e., Vs, PR, and ) but reduces external work capacity ` '. By controlling the ratio of ` ' in this way,regulation of lactate concentration becomes essential for adequate circulatory performance.Alteration of lactate concentration becomes associated with much cardio-vascular disturbance.Factors regulating lactate concentration include the following:-1. The oxidising capacity of the respiratory enzymes.2. Disturbances with glyconeogenesis, and fat metabolism (e.g., altered regulation of livertemperature leading to disturbed balance between tissue perfusion, and effector cell workcapacity)Disorders involving these two factors are likely to be found in life threatening conditionsinvolving circulatory dysfunction, and some of these states are considered in later chapters.3. Reduction of `active permeability' and increase in `passive permeability' of cells areassociated with increased lactate concentration, and may increase efficiency for performance ofexternal work, but only by reducing tissue oxidation compared with oxidative phosphorylationand glycolysis, with reduced tissue perfusion and increased tissue ischaemia which becomesprogressively more extreme. Because an adequate concentration of lactate is necessary to maintain the energy stored at celllevel both inside and outside the cell, without this supply of lactate, the circulation would ceaseas the energy store becomes exhausted. The energy stored to maintain external work capacity,and energy required for tissue perfusion are inversely related to each other ; too much storedenergy leads to impaired tissue perfusion, and vice versa. Regulation of the balance betweenthem depends to a large extent on the lactate concentration, with the associated factors ofoxidative capacity of the respiratory enzymes, the permeability of cell membranes, together withthe level of gluconeogenesis. Lactate concentration is proportional to .The concentrationof lactate while there is parity between oxygen and carbon dioxide concentrations, andactive and passive permeability are roughly comparable. Should the gas ratio alter, [lactate]becomes either greater or less compared with ̀ ', and the ratio between ̀ R.' and [lactate] thenbecomes an indication of relative cell permeability. and of cell `strength'.

If as a result of any variation , the oxygen saturation of the venous blood also varies, the apparentviscosity, ̀ ', of venous blood will alter, and so become related to the glycolytic reaction in the

40

cells, depending on the ratio between ̀ [ ] blood', and ̀ [ ]cells'. The lactate level in the cellsis related to the partial pressure of oxygen which is maintained there, decreasing when the ̀ [ ]'falls, and increasing again as `[ ]' rises (Pasteur and Crabtree effects). For a given linearvelocity of blood flow ( , and PR), `[lactate]' is also inversely related to oxygensaturation of the blood, so that `[lactate]' tends to be increased when the ratio`[ ]cells'/`[ ]blood' is increased, and linear velocity reduced.

In the intra-vascular circulation, the energy needed to accomplish fluid transfer into the cells,will be reduced by the fraction ` ', when the viscosity of the extra-vascular fluid is diminishedwith respect to that of blood, unless the energy within the cell is increased by the same fraction,` ', equivalent to the elevating fraction of oxidative energy released. The energy required fora fluid volume, ̀ Q', to enter the cell, is then proportional to ̀ ', but this must be elevatedby the fraction,` ', if the energy within the cell has been augmented by a similar fraction ` ',equivalent to the oxidative energy released. While the energy needed to propel `Q' into the cellis proportional to ̀ ', this will need to be increased by a fraction equivalent to ` ', fromoxidation of pyruvate following glycolysis, and energy `storage' then becomes` '. The work which the cell can do is proportional to ̀ l.PR.l', and must also be

elevated by the product `l ', or internal resistance to flow, to become ` '. The ratiobetween `energy store' and work capability becomes ` R / PR. ', or `Q/Vs .R/l.PR', and these ratios determine the linear velocity of venous blood entering the ventricle, forstable values of `Q', `Vs', and `PR'. The linear velocity of venous blood is regulated by the`apparent viscosity' of venous blood, and the oxygen concentration in the ̀ effector cells', and theviscosity is overcome by oxidation following glycolysis in the cells, which is proportional to ̀ '.The significance of this energy relationship will be shown in later text, to be important incontrolling the rate at which fluid is expelled from the ̀ effector cell' following depolarisation ofthe cell membrane.

What this means is that when fluid leaves the blood stream, ̀ ' is no longer a factor influencingits dynamics except to balance the energy available in the cells. Because ` ' is relativelyconstant while the blood is fully oxygenated, and travelling at a relatively greater velocity, it canbe treated as a constant in the calculations involving fluid movement, until the fluid reaches theextra-vascular compartment. In the capillaries the oxygen partial pressure begins to fall belowthat in the arterial blood, while the carbon dioxide partial pressure is increasing in the relativesense. At this stage ` ' in the blood within the capillaries begins to vary, changing the internalresistance offered by the venous blood, though there will be little effect on either the value of`R' or `R/ ' in the arterial blood, or affecting the movement of fluid from this source, until itreaches the extra-vascular fluid, and the interface between this fluid and the tissuecells.Nevertheless, to allow for any alteration where the variability of ` ' may be a factor, `R'can be replaced by `l.[ ]' in the calculations involving cell permeability, as well as in thecalculations of momentum and linear velocity which involve the ̀ momentum equivalent', whichmust be included in the energy necessary to overcome resistance and inertia to fluid movement.For example, the momentum in extra-vascular fluid has been calculated as `v.R.Vs'/`R' (or`v.Vs') which still has the same value, although the correct ratios might then be ̀ v.Vs.R/ ' times

41

` /R' , but in calculating the linear velocity of the extra-vascular fluid (`vx') `OPP' would beproportional to `vx.R', and `vx' proportional to `OPP/R' . (The effect of the elimination of ` 'will be evident in the diagram showing the energy relationships within the cells between`[ ]',`[ ]', `l', and `vx', where the production of energy by oxidation only has beenillustrated (Fig.23 ) . While `v' remains proportional to `Q.l.PR/Vs', `vx' appears to becomeproportional to `OPP. /R', and the ratio between `v' and `vx' would then be proportional to`( )[ '. Energy equivalent to ` ' needs to be contributed by respiratory oxidative

enzymes, to allow `v/vx' to become proportional to `( [ '). In the `lactate tolerance test',when [lactate] is artificially increased, the effect depends on changes to the ratio `vx/v', andwhether the increase in `l' is accompanied by a decrease in `[ ]' (so that `Q' and `Vs' are ableto increase) or by maintenance of `[ ]', so that `l.[ ]' is able to increase, with resultantincrease in `APs'. The result of increasing lactate concentration without altering the rate ofglycolysis, depends essentially on the oxygen concentration and the associated activity of the celloxidising (i.e, respiratory) enzymes. The relationship between glycolytic energy production, thecell energy level, and energy exchange with extra-vascular fluid, can be indicated by the energyrequired to overcome internal resistance to flow in venous blood. Glycolysis produces energyequivalent to that needed to overcome this internal resistance, (i.e., ̀ l .vx'). At the same timeit produces pyruvate, which may be converted to lactate, and in turn become a factor forincreased oxidative energy also proportional to ̀ l. ', through its facilitating effect overcomingthe inhibition of oxidative enzymes by oxygen. The extra energy is then proportional to ` ', of which `l. ' overcomes viscosity of venousblood, while `l. ' is the factor increasing the cell energy store which becomes related to`vascular filling', `internal resistance to blood flow', and `passive permeability'; i.e., `R.Vs' . `l. ' . `[ ]', or ` .[ ]'. Lactate concentration regulates the amount of oxidative energy which becomes available byfacilitating oxidation through respiratory enzymes; oxygen concentration regulates theaccumulation of cell energy, and the value of `R'; while carbon dioxide concentration regulates`active permeability' from the cell, stroke volume and energy exchange, and inhibits furtherglycolysis as the concentration of the gas rises. Oxidation energy increases by a factor equivalentto glycolytic energy, and the energy in the system increases by a factor equivalent to ̀ l2.n2', andafter overcoming the internal resistance to flow, produces an increase in ̀ energy store' equivalentto `l .[ ]', or `R'. This is a factor by which residual momentum (`R.Vs') has to be elevated

to give the total energy store proportional to `R2.Vs', ( at systole) after including theeffects of permeability, momentum, and the application of metabolic energy.

A number of other energy equivalents depend on these parameters; e.g., ̀ PR.[ ]' is equivalent

to `R.l.PR/ ', or systolic pressure /vascular filling, which may be expressed as `l.PR/Vs,',providing a relationship between intra-vascular and extra-vascular volume for a given value ofosmotic pressure exerted by the plasma proteins. The product of `[lactate].R' is equivalent to` (capillary filling/linear velocity of tissue fluid' or `Q.R./.vx)'. Combining theseequivalents gives a relationship between `capillary filling', the relative volumes of the intra-vascular and extra-vascular compartments, and the work of the ventricle per beat. Thesevariables can be combined in an alternative fashion to represent `passive' and `active'

42

permeability, and the relationship which they have to ventricular energy output per beat. Theproduct of `[ ].[lactate]' is proportional to `passive permeability' of the tissue cells, whichdepends directly on ̀ [ ]', but also on ̀ [lactate]' and contributes to the accumulation of fluid andenergy within the cells. The product `[ ].PR' is equivalent to `Q.l.PR/l2', or `momentum inthe circulation'/`length squared', which is proportional to ` ' .

`Q/[lactate]' represents ̀ active permeability', and the product of active and passive permeabilityis `Q.[ ]' (which when multiplied by ` .PR' gives the `ventricular work per beat / ' asbefore). Because ̀ Q.[ ]' is equivalent to ̀ [ .l' , it represents the proportion of energyper beat which is either transferred into the cells and then returned again to the extra-vascularfluid, or transferred directly to the venous return. This amount of energy , equivalent to ̀ Q.l/Vs'needs to be supplied for each unit of the `momentum equivalent' proportional to `R.Vs' ( )before the movement can occur, and the speed of fluid movement depends on the pulse rate, or`PR'. The product of these three is again ` .PR.Q/Vs', or work performed per beat; and`Q.l/Vs' is the fraction of ventricular work needed to accomplish this fluid transfer, and isequivalent in value to `R'. The provision of extra energy equivalent to ̀ ' (by oxidation following the glycolytic reaction)to fluid leaving the cell, and returning to the extra-cellular fluid and intra-vascular circulation,ensures maintenance of ̀ venous return' determined in the first place by the energy which has tobe replaced, and the amount of glycolysis which is initiated as a result.

The fluid exchanged with the cells per beat is then proportional to `l' , the circulatory length,which represents the amount of the transfer, so that `l' must vary with changing activity andmetabolic needs of the individual cells.(Because ̀ Q' is equivalent to ̀ .l', the fluid exchangeis proportional to `Q', which is `l' modified by ̀ [ ]'). The relationship of ̀ v/PR' will dependon the fluid exchange (because `v/l.PR' is the circulatory ratio). The importance of thecirculatory ratio for normal circulatory function has been mentioned in Chapter 5. , while therelationship of linear velocity of flow of venous blood with pulse rate is regulated by a nervousreflex from receptors in or near the pericardial surface of the heart. By regulating the ratio `vvenous/PR', this reflex must at the same time influence the exchange of fluid between the cellsand the extra-vascular fluid.

The product of passive and active permeability can also be represented as `Q.R/l. ' ( orventricular filling/internal resistance offered to blood flow) which is in turn related to theperipheral fluid exchange, or `R'. Put as simply as possible, the relative increase in bloodviscosity seems to be directly proportional to the amount of energy available from oxidation ofpyruvate following glycolysis, to provide fluid and energy outflow from the cell, and the alteredgas ratio which results; or in other words, the relative levels of changing cell permeabilityappearing during the cardiac cycle, and resulting in altered flow energy available to venousblood.

Energy from glycolysis within the cells, replaces the kinetic energy passing from cell to bloodwith the energy and fluid exchange, while energy made available by oxidation, increases `freeenergy' in the cell and allows re-expansion of the cell volume, and re-establishment of the storeof A.T.P. which had previously been reduced to perform the mechanical work associated with

43

contraction. The amount of energy released by glycolysis, is closely related to blood viscosity through theamount of oxygen usage, and the production of carbon dioxide which it allows through theavailability of oxidative substrate (pyruvate or lactate equivalent) and the oxygen consumptionnecessary to produce carbon dioxide, and maintain the permeability balance between ̀ [ ]' and`[ ]' for a given circulatory length, `l', and the circulatory velocity, and circulation time,present in circulating blood.

The energy from oxidation of pyruvate following glycolysis, in this way affects the apparentviscosity of blood (particularly in the veins) and regulates the linear velocity, `vx', with whichfluid leaves the cell and extra-vascular fluid. As it enters the venous blood under the influenceof osmotic pressure of the plasma (equivalent to `l.PR' , `vx.R' , or `vd' at diastole), it is able toinfluence the final velocity of venous blood entering the ventricle, or ̀ v venous' ( `l / ).

The ratio of muscular work capacity, and fluid exchange with the cells, is regulated by theamount of glycolysis compared with the amount of oxidation.Excess glycolysis leads to excesslactate, which then has to be removed from the circulation by glyconeogenesis in the `core'organs. Increased oxidative capacity reduces the amount of lactate, and leads to a reduction inexternal work capacity, and the cell `energy store'. In effect, there is increased `passivepermeability' with excess lactate, while if insufficient lactate is available, it leads to increased`active permeability'.An increased ̀ energy store' leads to increased work capacity, and increasedblood pressure, while a reduced ̀ energy store' can result in reduced ̀ work capacity', and possiblyreduced blood pressure, with increasing `quiescence' of the cells. Increased energy store mayproduce ̀ hypertension', while a reduced energy store may result from an asthma attack. Each ofthese states may be predisposed by genetic factors which determine the relative levels ofpermeability, so that the likelihood of development of ̀ essential hypertension' is increased withany increased tendency to greater passive permeability and increased energy store, while agreater possibility of increased active permeability results in a predisposition to asthma attack(especially when cell permeability is further altered by environmental conditions such as thepresence of histamine like substances and allergens. see Fig. 26.) In summary, passive permeability is related to both `[ ]' and `[lactate]'. Taking voluntarymuscle as a tissue typical of `effector organs' , while `[ ]' has a direct effect on membranepermeability, [lactate] increases the production of `high energy level' phosphate bonds, andassists muscle relaxation, allowing muscle cells to enlarge as they relax. At the same timeincreased [lactate] leads to lower [ ], and the final effect of passive permeability is set by theproduct of [ ].[lactate]. As a further effect increased ̀ [lactate]' decreases ̀ active permeability'by increasing the energy available for, and the rate of polarisation of the cell membrane in therecovery phase, so reducing its permeability, while increased utilisation of lactate, leads toincreased `[ ]' and stroke volume. `Active permeability' then becomes proportional to`Q/[lactate]'. Because of this effect on active permeability, excessive accumulation of lactatemust eventually produce muscle fatigue.

The effect of increased lactate concentration is to increase `energy storage' in the cells byincreasing high energy phosphate bonds, and at the same time increased `[ ]' leads to anincreased cell volume. There is then greater potential for increased or stronger muscle

44

contraction when the cell depolarises, but this depends to some extent on the frequency withwhich depolarisation occurs. In cardiac muscle the frequency of depolarisation depends on thepulse rate. It is for this reason that `l.PR' indicates the force of ventricular contraction, `l'increasing with the rate at which high energy phosphate bonds accumulate with consequentincrease in the total energy in the system, while `PR' indicates the frequency with which thebonds are broken down to fill the deficiency in energy available from oxidation, and release theextra energy needed to perform external work, following more frequent depolarisation in cardiacmuscle.

The energy made available to the circulation by the ventricle per beat is equivalent to` PR ', and is a combination of three factors.1. `l.PR' which represents the force of ventricular contraction.2. `l. ', or the internal resistance offered by the viscosity of the blood .3. ̀ ', or the energy ̀ accumulated' in the circulation with each beat, and either ̀ stored'in the cells temporarily, to be later released when the cell membrane depolarises, or madedirectly available to give momentum to the venous return.The total energy produced isproportional to `l cubed' or `[lactate].l. '(stored energy after depolarisation times glycolyticenergy), which is then elevated by a fraction representing energy from oxidation, and equivalentto ` ', and `l.PR'.

The manner in which this energy is apportioned between these two areas is related to the balanceachieved between `[ ]' and `[ ]' by metabolic activity. For a particular amount of energyprovided for this purpose by the ventricular contraction, `Q.[ ]' may be dominated by anincreased value of `Q', and reduced `[ ]', so that less energy is retained in the cells, and moreenergy remains in the extra-vascular circulation, with increased `vx' rather than `Vx', and lessretained energy to the next beat. On the other hand if there is increased ̀ [ ].l. ', while ̀ [ ]'and stroke volume is relatively smaller, there will result a greater amount of energy retained inthe cells, and a higher level of arterial systolic pressure, compared with the energy transmittedto the venous blood. When `[ ]' increases, much more energy is required to be retainedcompared with that used to move venous blood, while the production of greater `[ ]' leadsto much less retained energy compared with that producing increased ̀ venous return', and thereresults a greater venous return for a particular energy production by the ventricle.This is reflectedin the ratio `APs/PR' or `R.l' (R.Vs.[ ]), which is the product of `l. ' (internal resistance toblood flow) and `l.[ ]' (representing [lactate] or energy `storage' in the cells with increasing`passive permeability).

The energy factor required to produce the venous return is equivalent to `Q.[ ]', so that for agiven stroke volume, the energy increases as `[ ]', with more energy accumulating as `stored'energy in the cells. This `stored energy can be released by changing cell permeability, e.g., bydepolarisation of the cell membrane. The energy is then available to perform external work. If`[ ]' is maintained at a low level, the energy factor then varies as `Q', and the total energysupplied for maintaining the venous return is much less. At the same time the energy availablefor external work remains at a smaller fraction of the possible level, and depends on the value

45

of `l', which increases proportionally for each of the factors `l.PR',`l ', and `l.[ ].[ ]', so

the total energy developed depends on ` / Q ' or `[lactate]', the mechanical efficiency of thecirculation decreasing as lactate is metabolised to increase `[ ]' compared with `[ ]'. Thismeans that the necessary energy to maintain the circulation is determined by the oxidising abilityof the respiratory enzymes.

For the most `efficient' state, energy per beat must contribute to both venous return andcirculatory efficiency by maintaining the stroke volume, but must also produce sufficient`accumulated energy' in the active cells at any particular time to allow an equivalent productionof external work when required. The apportioning of energy between the two areas depends onthe ratio ` ', while the total of each depends on the circulatory length.The system islimited by the levels of `[ ]' and `[ ]' which can be tolerated, and the optimal level of`[lactate]' is obtained when `[ ]' and `[ ]' are correctly balanced.

The differences between energy applications which follow increases in and those associatedwith increased are very great and have given rise to the concepts of 'inotropic state' and'active state'. Inotropic state indicates the increase in stored/accumulated energy in active cellsassociated with increasing multiples of oxygen concentration, while active state results fromincreased multiples of carbon dioxide compared with those of oxygen concentration. Inotropicstate and increased cell length is indicative of increasing efficiency in the use of energy whichaccumulates with little development of heat but with increasing glycolysis. With active statethere is increased oxidative energy with much heat development, increased cell strength ascarbon dioxide accumulates, but gradual loss of cell energy store so that work capacity falls ascirculatory energy increases and dissipates heat to the atmosphere or surrounding environment(with diminished cell length, but reduced cell diameter and volume. Inotropic state (withincreased glycolysis as oxygen and lactate concentrations increase), conserves stored energywhile inhibiting oxidation to produce carbon dioxide. Active state reduces oxygen concentration,but increases oxidation with carbon dioxide and heat production, circulating blood volume, andcell strength.

The ratio of active state / inotropic state is proportional to or ' ', and isconstantly being adjusted in line with required activity. and whether a short maximal effort withincreased blood volume is required, or a steady continuous work capacity at a more economicalenergy level. Active state increases those parameters representing increased multiples of carbondioxide concentration compared with multiples of oxygen concentration, while inotropic statepreserves those which have increased multiples of oxygen concentrations to make up energyoutput. The ratio between them is related to vx and to contractility of muscle fibres, indicatingthe rate at which energy leaves the cells compared with muscle shortening. When this balance is upset, conversion of pyruvate to carbon dioxide and water is alsoaltered, resulting in a level of `[lactate]' which is either higher or lower than is desirable. If therelative level of `[lactate]' is too high it results in too much energy `storage' in the cells , and isaccompanied by increased blood pressure, while a level of [lactate] which is less than desirableresults in too low an energy `storage' level in the cells, and inability to accomplish an adequatework load. Changing levels of `[lactate]' may result not only from an altered rate of glycolysis,and the oxidising capacity of the respiratory enzymes, but also from associated changes to

46

glyconeogenesis in the `core' organs which might follow. The relative rates of glycolysis, andoxidative metabolism of the lactate produced, become important regulators of cell function,which would appear to be related to apparent viscosity of blood (particularly the level of oxygensaturation of venous blood ). These rates would appear to be related to the `Pasteur' and`Crabtree' effects, where oxidation inhibits fermentation, and glycolysis in turn inhibitsoxidation. The mutual inhibition probably involves competition for inorganic phosphate, whichbecomes available when high energy phosphate bonds are disrupted, e.g., associated with musclecontraction. Whether glycolysis is greater than oxidative metabolism depends on the oxygenconcentration in the tissues.If the level is high, lactate production is increased, while if it is low,lactate production is reduced. The glycolytic/oxidative ratio depends on the ratio of`[lactate]/[ ]' in the tissues, and also the ratio of ̀ [ ]cells / [ ]blood'. The ̀ stored' energyprovided in the cells is then proportional to `[lactate].l. .[ ]cells/[ ]blood' or

`[ ]cells. ', or ` ', where 'R' represents cell energy store, and 'R' is also peripheralresistance An outline of the energy generation and exchange in the cells of the myocardium using ‘lactateas fuel, in terms of the ‘circulatory model’.The transfer of energy between the cells and the extra-vascular fluid depends on the energyavailable to the extra-vascular fluid as well as the energy liberated by cellular activity. Theenergy available to the extra-vascular compartment, depends on the external work performed bythe myocardium per beat ( .PR), as well as the energy equivalent needed to overcome theinternal resistance of the blood (l. ), so the total energy release is equivalent to ` ' , andthe energy per beat to maintain the energy exchange with the cells after allowing for the bloodviscosity, ` ', is ` .PR' .The exchange between the cells and extra-vascular fluidmay then only occur because of variation in the concentration of oxygen and carbon dioxide.While the product of these concentrations must be kept fairly constant to maintain the ratio of`Q/Vs' (the circulatory ratio), variation of the ratio [ ]/[ ] results in changes in `activepermeability' with respect to `passive permeability', and so regulates the fluid and energyexchange between the two compartments at an individual cell level. The changes in permeabilityare reflected in changes in the linear velocity of flow of fluid in the vascular system (i.e., `v') ,compared with changes in the linear velocity of extra-vascular fluid (i.e., ̀ vx'), so that fluid andenergy exchange depend on [ ]/[ ] in individual cells, and this is reflected in changes inthe general level of the ratio `vx/v', governing the movement of fluid within the body.

While ̀ v' is proportional to ̀ .l.PR', ̀ vx' can be represented as equivalent to ̀ PR/l', andthe ratio `v/vx' is then proportional to `R.l'. `Passive permeability' is regarded as beingproportional to `[ ].[lactate]', while `active permeability' can be represented as proportionalto `[ ].l/[lactate]', and the product `active times passive' permeability is proportional to` ', or ̀ length times circulatory ratio', which then becomes a significant factor in theamount of ventricular energy which must be supplied per beat. For optimum function` ' needs to be equivalent in value to that of `R'. The force of contraction is ̀ l.PR', and the ̀ internal work' required to overcome the resistance ofthe blood is proportional to `l. '. These three factors then account for the total energy ofventricular contraction per beat, ̀ [ ].[ ].l'.`l '.`l.PR'. Of this total , ̀ ' is blood viscosity,

47

`[ ].[ ].l.l ' is the energy to effect the cellular fluid exchange (equivalent to `R.Q') and

` ' represents the external work done per beat.

For the estimation of `vx', the following are considered to be significant factors.1. The effect of gas concentrations on the permeability of cell membranes.2. The effect of ` ' (i.e., lactate concentration. Q) on the amount of energy which isaccumulated within the cell as high energy phosphate bonds.3. The effect of ̀ pulse rate' on the rate of energy release in the cell by breakdown of high energyphosphate bonds, the speed with which this energy leaves the cell, and the volume of fluidconsequently transferred out of the cell per beat.

Depending on the relative effects of these three factors, energy may accumulate within the cellas high energy phosphate bonds, it may be lost to the cell to maintain `vx', or it may performmechanical work by approximating the ends of the myofibrils. The latter two effects may varywith respect to each other for a given amount of energy accumulated within the cell. This energythen appears either as mechanical work, or as energy of motion associated with movement offluid out of the cell at a particular rate for a given volume.

The function of the cell may then be varied as the gas concentrations vary, while the linearvelocity of flow in the extra-vascular fluid, together with the volume which is moved, requiresutilisation of energy.The quantity of energy will be regulated by the speed of contraction (andtherefore the pulse rate) while the remaining energy is available to perform mechanical work.

The product `[ ].[lactate]' is a `measure' of passive permeability, and the accumulation ofenergy within the cell, because the oxidative phosphorylation requiring lactate results in theaccumulation of high energy phosphate bonds, while greater oxygen concentration leads toincreased cellular volume.`Active permeability' can be represented by `[ ].l / [lactate]' which increases as strokevolume increases and is diminished by increasing lactate concentration. It therefore depends onthe rate of metabolism of lactate to produce carbon dioxide and water, and this reaction reduces[ ] as well as [lactate], while converting the energy produced to high energy phosphate bonds,which then assist in muscle relaxation.

With ̀ depolarisation' of the cell membrane when the cell is stimulated above its threshold, thereis a sudden increase in `active permeability' , and loss of fluid and energy from the cell. Theamount of fluid which is lost will depend on the change in permeability, and the rate or linearvelocity at which the fluid moves, and this will depend on the pulse rate, which is associatedwith the rate of breakdown of high energy level phosphate bonds.When the rate of breakdownis higher, the linear velocity of fluid leaving the cell is increased, resulting in increased valuesfor ̀ vx', ̀ Vs', and ̀ Q.PR', while any increase in ̀ l' resists and slows down the rate of breakdownof high energy level phosphate bonds, by the reverse process of producing more of them. `vx'is proportional to `OPP / R' which may be expressed as `PR / l.', or the ratio of the pulse rate /circulatory length.

The relationship of `[ ]' and `[ ]' , and the relative rates of accumulation of high energy

48

phosphate bonds and their breakdown, depends on the level of ̀ [ ]' , which is itself dependenton `[lactate]' .It is the relative levels of `[ ]' and `[lactate]' which regulate `[ ]' and `l.PR',depending upon the activity of the respiratory enzymes.For these reasons, the levels of `[ ]'and `[lactate]' maintained in the tissues, and the balance between them, become the essentialparameters in the regulation of arterial blood pressure.

The hydraulic system which the circulation of body fluid represents is regulated by twoprinciples.1. The necessity to maintain oxygen partial pressure and the `passive permeability' of cellmembranes at a relatively constant level.2. Frequent or continual adjustments in `active permeability', blood viscosity, and length ofblood vessels, with changing carbon dioxide and lactate levels to regulate volume and velocityor momentum of moving fluid.3. Various combinations of circulatory length and viscosity represent fluid volume and energytransfers within the system, by altering membrane permeability, and the amount and rate oftransfer of fluid volume.

The parameters involved in regulation of the circulation, may all be expressed in terms of ̀ l' and` ', each of which may be varied over a comparatively wide range, so long as oxygenconcentration is kept relatively stable through appropriate variation in the other factors, ` ' or`l'.Some examples of relevant parameters in terms of `l', ` ', and `[ ]' are set out below.

`[ ]' is equivalent to arterial volume,`[ ].l' (i.e., `Q') is equivalent to venous volume,`l/[ ]' (i.e., `Vs') is equivalent to systemic volume,`l.[ ]' is stroke volume,`R' (or `l.[ ') is proportional to cell volume and energy level at systole

`l.PR' (or ` ) is diastolic linear velocity, or `Q . Vs' . `l. /[ ]' represents pulse rate,

` ' is `average mean' linear velocity of flow, etc.`l. /[ ]' is pulse rate, or `venous/arterial' volume.The equivalence between `R2' and `v' which is required to preserve adequate function,

is only possible while `[ ]' can be represented as `constant' in value.