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Cardiac-coronary interactions in humans: Mechanistic insights from waveintensity analysis

Rolandi, M.C.

Publication date2014

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Citation for published version (APA):Rolandi, M. C. (2014). Cardiac-coronary interactions in humans: Mechanistic insights fromwave intensity analysis.

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General Introduction

Chapter 1

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The heart is responsible for the blood supply throughout the coronary and systemic circulation. In order to maintain its pumping function, the heart muscle needs nutrients and oxygen, which are supplied via a dedicated vascular system. Two main arteries emanate from the aortic valve area and run initially at the base of the heart providing the appearance of a crown or corona which gives rise to the name of the vascular system of the heart: the coronary circulation. In this introduction, the basics of blood flow in the coronary arteries will be described at three different conceptual levels: 1) averaged over the heart beat 2) time-varying throughout the heart beat and 3) as waves traveling along the vessels wall. Coronary flow refers in general to blood flow trough large coronary arteries and is simply expressed as the amount of blood passing a cross-section per unit time. Coronary perfusion is defined as the amount of blood that enters and leaves the coronary microcirculation , in terms of a unit volume of tissue per unit time. Only when averaged over time, the product of flow through a coronary artery and the weight of the tissue that depends on it equal to perfusion. Resting coronary blood flow is in the range of 225-250 ml/min, about 4-5% of the cardiac output. Assuming a normal adult heart weight of about 280g, this is equivalent to a perfusion of 75ml/min per 100g of tissue.Because of conservation of mass, inflow and outflow of a perfusion territory must be equal when averaged over time. However, this equality does not hold true for instantaneous flow because of the microvascular compliance. The most elementary observation illustrative of the conceptual difference between perfusion and flow is the salient difference between the flow signals in coronary arteries and veins, which are out of phas, i.e. when arterial flow is high (diastole) venous flow is low and when arterial flow is low (systole) venous flow is high. The coronary arterial flow variations throughout the cardiac cycle will be discussed in the second part of this introduction and forms the main focus of this thesis.Finally, in the third part of this introduction the hemodynamic signals will be conceptually unified into a collection of waves traveling along the vessels ans described at different characteristic moments within the cardiac cycle. This concept opened a new form of analysis to understand coronary hemodynamics.

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1PHYSIOLOGY OF THE HUMAN CORONARY CIRCULATIONBranching and basic functions of the coronary circulation

The two arteries branching from aortic ostia near the sinus of Valsalva are denoted as left and right coronary artery (RCA). The RCA supplies predominantly the right ventricle and - to a varying degree and dependent on species - also a substantial portion of the left ventricular free wall. The stem of the left coronary artery is only a few millimeters long and branches rapidly into two major branches, the left anterior descending artery (LAD) and the left circumflex coronary artery (LCx) . The position and branching of LAD and LCx are clear from the image depicted in the left panel of Fig. 1, which was obtained after the reconstruction of fluorescent vascular cast images obtained by an imaging cryomicrotome [1]. The LAD runs from the base of the heart to the apex in a groove between the surface of the free walls of left and right ventricle. The LCx runs in the groove between left ventricle (LV) and atria at the base of the heart. The LAD supplies a portion of the LV free wall but also part of the septum, the wall separating the LV and RV. The LCx supplies mainly a large portion of the LV free wall. LAD and LCx branch further over the surface of the heart, the epicardium, where they branch into many smaller arteries penetrating the heart muscle and from the epicardium to distribute the blood flow over the ventricular wall (Fig. 1, right)[2-3].

The different branches and vascular segments can be characterized and distinguished based on function and dimensions. Arteries with diameter larger than 400 μm are defined as large or conduit arteries, with diameter between 100 and 400 μm as small arteries and with diameter smaller than 100 μm as arterioles. The function of the large arteries is mainly to distribute the blood over the myocardium with minimal pressure loss. They contribute to less than 5% of

Figure 1: View of the coronary vessels of a pig heart. Left: Anterior view of the heart. The left main coronary artery splits into the left circumflex artery (LCX) that runs through the left atrioventricular sulcus and the left anterior descending artery (LAD) that runs down the anterior interventricular groove. The right coronary artery (RCA) follows the atrioventricular sulcus. Right: Cross-section of the heart. Showing how the epicardial vessels branch into many smaller arteries within the myocardial wall. [Courtesy of dr. Jeroen van den Wijngaard AMC].

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the total coronary resistance. The small arteries distribute flow from the larger the arteries to the arterioles but also contribute to the control of blood flow since their resistance forms a substantial part of total coronary resistance. Hence, all arteries smaller than 400 μm are referred to as resistance arteries. Resistance arteries can control blood flow by changing their tone, i.e. altering the diameter as result of activation of smooth muscle cells in their walls [4]. The arterioles can be subdivided into large arterioles with diameter ~100 μm, small arterioles with diameter ~75 μm and terminal arterioles with diameter between 10 and 50 μm. The role of the arterioles is to lead the blood flow to the capillary bed and most importantly to control blood flow in relation to the oxygen consumption of the tissue at the local level. The capillary bed forms an interconnected network of small vessels with diameter as large as a red blood cell. The thin and semipermeable membrane of these vessels allows the exchange of oxygen, electrolytes and nutrients within the blood with the CO2 and metabolites of the cells. Blood from the capillary bed is drained into the venules and is then directed via the transmural veins to the epicardial veins.The continuous pressure drop between the upstream arterial and downstream venous ends of the coronary circulation reflects the distribution of resistance over the different vessel types as depicted in Fig. 2. The difference in distribution of pressure drop between control condition and at dipyridamole-induced vasodilation demonstrates which vessel types are involved in the control of coronary blood flow.

These measurements where obtained in a beating cat heart with a controlled pressure needle impaled into the epicardial vessels and moving with the epicardium

Figure 2: Pressure distribution over the different sizes of coronary vessels at control condition and during dipyridamole infusion. The gradual decrease in pressure indicates that all vessels with diameter smaller than 400 μm take part in the control of coronary resistance. (Adapted from [5]).

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Table 1: Estimate of coronary volume distribution

Pressure(mmHg)

Volume*(ml)

Distensibility(10-3/ mmHg)

Compliance*(ml/mmHg)

Arteries (>200µm) 100 1.6 1.4 0.002

Small arteries 35 2.7 4.5 0.013

Capillaries 20 6.3 5.5 0.035

Small veins 12 5.4 8 0.043

Large veins 8 3.2 14 0.045

Total 19.2 0.138

Intramyocardial 14.4 0.091

Adapted from [6]. * values for 100g of LV tissue.

[5]. The method did not allow the measurement of pressure in arterioles and venules and from this figure, pressures in these vessels can only be inferred. Under normal functional conditions, pressure in the coronary system starts to decrease in arteries with a diameter of 300 µm and is reduced to a venous level in the veins of 100 µm and larger. However, when dilation of resistance vessels to control blood flow is mimicked by administration of dipyridamole, the pressure starts to drop in vessels of 400 µm diameter and remains at a lower level over the arterial diameter range, indicating that diameter variations in these vessels affect coronary resistance and may contribute to the control of flow. The absence of a pressure drop between small and larger veins indicates a very low resistance in the outflow pathways of the coronary circulation under control conditions. However, with arterial vasodilation, the relative contribution of venous resistance to total coronary resistance increases, such that pressure rises about five fold in the small veins. Capillary pressure was not measured and therefore, it is not clear from these measurements how much capillary pressure in the coronary circulation rises during coronary arterial vasodilation. The distribution of pressure and volume over different vascular compartments as well as related physical properties such as distensibility and compliance are indicated in Table 1, which was collected from different studies by Spaan in 1985 [6]. In contrast to the systemic circulation, where most blood volume is within the smaller veins, most volume in the coronary system is within the capillary network, reflecting the high capillary density in the myocardium. It is important to recognize that the diameters of the different vessel types are not only dependent on smooth muscle cell control, which is absent in capillaries, but also on distending pressure, since all vessels are elastic. This is expressed by the distensibility, which is highly non-linear, since vessels become stiffer at higher pressure. Distensibility in capillaries and veins is higher than in arteries. Since vasodilatation elevates pressure in the capillaries and veins one may expect that it increases blood volume and decreases distensibility in these compartments. For the functional relation between time-varying pressure and flow in the different compartments their compliance is of importance. Compliance is the product of distensibility and volume and hence, most of the coronary compliance is located in capillaries and downstream of that. The distribution of these physical quantities illustrates that describing

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the coronary circulation in a quantitative way is complicated, since the different compartments play a different role where resistance and compliance are dependent on perfusion condition.

Autoregulation of coronary blood flow

The heart has to adjust its systemic output to the metabolic needs of the body. The mechanical work of the myocytes will increase with exercise requiring a higher coronary blood flow to provide oxygen and nutrients. When the supply of coronary blood flow does not match the oxygen demand of the myocardium, oxygen shortage of the tissue will result, which is known as ischemia. Severe ischemia can cause irreversible damage to the heart muscle that may ultimately lead to myocardial infarction. Coronary blood flow is mainly controlled at the local level by a process called autoregulation. Autoregulation is the intrinsic tendency of the vasculature to maintain blood flow well matched to cardiac metabolism despite changes in perfusion pressure as depicted in Fig. 3 [7]. The plateau in the autoregulation curve obtained at constant cardiac work implies that coronary resistance is changing with perfusion pressure [8]. The autoregulatory plateau shifts upward with elevated cardiac metabolism, i.e. at constant coronary pressure, coronary resistance decreases to accommodate the increased myocardial oxygen demand by a higher blood supply. During maximal vasodilation, the microvascular resistance is at its lowest level i.e. without control of smooth muscle tone. As shown in Figure 3, the coronary flow-perfusion pressure relation at maximum vasodilation is incremental linear because there is a residual pressure when flow is zero.

Figure 3: Coronary flow as function of perfusion pressure with and without tone control. At rest, flow is maintained constant over a large range of pressures by a parallel change of resistance. The dashed line indicates autoregulation at a higher oxygen consumption (MVO2). At maximal vasodilation, there is no control and coronary flow has an incremental linear dependence on perfusion pressure. Pzf is the zero-flow pressure.

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1Alterations due to coronary artery diseases Coronary artery disease is often equated with the presence of atherosclerotic plaque since this is the principal cause of vessel narrowing. It is a chronic inflammatory response resulting in the accumulation of lipids and fibrous material in the arterial wall. This accumulation may form multiple plaques that decrease the lumen and can result in an insufficient blood supply to the cardiac muscle.

Stenosis and its pressure dropAn abnormal narrowing of the epicardial segment of a coronary artery is called a coronary stenosis. A coronary stenosis adds a resistance to the epicardial compartment and thereby reduces the perfusion pressure for the tissue dependent on this artery. Frictional and inertial energy losses associated with fluid dynamics across the stenosis are at the origin of the pressure loss. Frictional losses occur in all vessels but are minimal in unobstructed conduit arteries. In the stenotic region these frictional losses become notable since, according to Poiseuille’s law, the resistance of a tube is inversely related to the 4th power of diameter. However, in the stenosis, flow velocity is higher than in the non-diseased part since the same amount of blood has to pass through a smaller cross-section in the same

Figure 5: Coronary pressure-flow relation with and without a stenosis. S2 is a more severe stenosis than S1. The effect of the stenosis is seen in particular at vasodilation, because the resistance vessels cannot dilate enough to compensate for the stenosis pressure drop. Pzf is the zero-flow pressure. (Figure from [16] ).

Figure 4: Representation of a stenosis. The converging part is characterized by an accelerated flow. The diverging part is characterized by flow separation and deceleration of flow. (Figure from [9]).

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amount of time. Therefore, blood is accelerated at the entrance of the stenosis and its kinetic energy increases at the expense of potential energy. The drop of pressure related to blood acceleration between stenosis entrance and reduced cross-sectional diameter in the stenosis is described by Bernoulli’s law. In theory, kinetic energy is converted back to pressure at the exit of the stenosis, since blood flow decelerates at that point. However, at the exit the flow field is characterized by flow separation and recirculation eddies, leading to significant energy losses limiting the pressure recovery. One therefore refers to exit losses when indicating the pressure loss over the stenosis related to Bernoulli’s law. The combination of viscous losses and exit losses is illustrated in Fig. 4 [9].

The total pressure drop (ΔP) across the stenosis can be described as the sum of pressure drop due to friction, linearly dependent on the flow (Q), and due to convective acceleration, related to the square of Q:

(1)

The constants ‘a’ and ‘b’ depend on the shape parameters of the stenosis (Fig. 4) such as length L, proximal and minimal diameters, D0 and Ds, blood viscosity µ and density ρ [9-11].

Physiological implication of a coronary stenosisWhen at rest, under normal workload of the heart, the presence of a moderate stenosis does not result in an inadequate blood supply, since the resistance vessels dilate by means of local flow control to compensate for the stenosis induced pressure drop. However, with exercise, the demand for flow may reach a level that cannot be achieved by further vasodilatation, since this mechanism is already exhausted at baseline workload of the heart. At maximal vasodilation, the stenosis leads to a nonlinear hyperemic pressure-flow relation such that at the same pressure the increase in flow is limited compared to a normal vessel (Fig. 5) [12-14]. The ratio between maximal flow and the level with autoregulation is called the coronary flow reserve and can be used as a diagnostic index [15].

PULSATILITY OF THE CORONARY HEMODYNAMIC SIGNALS AND CARDIAC-CORONARY INTERACTION

Coronary arterial flow during the cardiac cycle

The intramural coronary blood vessels are embedded in the myocardium, where the interaction of blood pressure, vessel elasticity, smooth muscle tone and cardiac mechanics leads to a complex blood flow pattern [17]. Figure 6 shows the typical coronary arterial flow waveform in relation to cardiac mechanics displayed as left ventricular pressure. When the heart contracts in systole the flow velocity in arteries is minimal while the major contribution to coronary flow is

ΔPstenosis = aQ + bQ2

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Figure 6: Coronary recordings from an angiographically normal LCx in relation to cardiac mechanics. Blood flow velocity U is minimal in systole when left ventricular pressure (PLV) is higher, while the majority of perfusion occurs during diastole despite a lower input pressure (Pa), when PLV is minimal.

Figure 7: Parameters affecting coronary pressure and flow velocity waveforms. SV: stroke volume; CO: Cardiac output; MVO2: myocardial oxygen consumption. Three major factors are responsible for the intracoronary pressure and flow velocity profile. 1) Systemic circulation, since aortic pressure is the input pressure in an undiseased coronary artery. 2) Cardiac mechanics, since during each contraction, the myocardium impedes its own perfusion that therefore occurs mainly during diastole when the heart relaxes. 3) The status of the microcirculation, since the more dilated the microvessels are, the lower is the resistance to flow.

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during diastole. Note that the mean systolic flow is lower than mean diastolic flow despite the higher input pressure during systole.

This interaction between cardiac contraction and coronary flow has been the subject of great interest for coronary physiologists. Before summarizing the major determinants of coronary flow, first a short history is presented of the development of concepts on cardiac-coronary interaction responsible for the pulsatility of coronary arterial flow.

Effect of left ventricular contraction on coronary perfusion

The first observations that coronary arterial inflow is impeded during cardiac contraction was by Scaramucci [18] in 1695. The relation between cardiac contraction and coronary flow has been studied since then. Since it is the most frequently studied signal, the developed concepts on the interaction between cardiac contraction and coronary blood flow on the one hand and myocardial perfusion on the other hand are often based on the coronary arterial flow signal alone. Ignoring intramural compliance, it has often been concluded that coronary perfusion follows the coronary arterial flow signal and hence is high in diastole and low or absent in systole. This has led to concepts of a high systolic and low diastolic resistance of the microcirculation [19-20] switching on and off during the cardiac cycle. Interestingly, some reports on venous outflow suggest that cardiac contraction promotes coronary venous blood flow [21]. An alternative concept was developed, the waterfall model [22], explaining the reduced coronary in-flow by the increase in resistance from the collapse of intramural vessels. However, these models ignored a dynamic component of flow resulting from the periodic loading and unloading of intramural compliance by cardiac contraction [23]. Hence, arterial flow is not only the result of arterial pressure and total coronary resistance but also of periodic changes of intramural volume that reduces systolic arterial flow and enhances systolic venous flow. These respective negative and positive flow contributions are compensated in diastole, by enhancing arterial and reducing venous flow. The changes in vessel volumes within the cardiac cycle were later shown to follow the same dependence on the elastance [24] that was proposed to describe the pump function of the left ventricle a decade earlier [25]. This concept emphasizes the effect of time-varying ventricular stiffness on coronary blood volume which is assumed to be independent of ventricular pressure. However more recent studies again suggested that ventricular pressure and myocardial contraction also have an effect on coronary flow pulsatility[26-27].

Determinants of intracoronary signals The shape of coronary pressure and flow velocity waveforms is therefore the results of a complex interaction between cardiac mechanics, coronary microcirculation and systemic circulation (Fig. 7). Although the heart is the source of its own perfusion pressure, myocardial contraction effectively compresses its own vasculature. Therefore, the profile of blood flow through the coronary arteries

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depends on both the perfusion pressure [28] in the aorta and the extravascular compression exerted by the contracting left ventricle [29]. Additionally, the smooth muscle tone of the small vessels in the microcirculation will also affect the flow velocity in the epicardial coronary vessels, altering the flow velocity via changes in the resistance vessel diameters.

Figure 8: Effect of ageing and pressure on pulse wave velocity (PWV) in the systemic circulation. Wave speed is depicted for a wide range of patients of different age. For each age group, wave speed was assessed at different pressures, showing the increase of wave speed with age and transmural pressure. (Adapted from [32]).The compliance of the vessel can also be changed transiently, by altering the transmural pressure of the vessel. An increase in transmural pressure will decrease the compliance of the vessel and thus increase wave speed [33] (Figure 8).

Figure 9: Wave speed estimation in the aorta from the PU-loop. The slope of the plot at the beginning of systole represents the density of blood times wave speed. (Figure from [35]).

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WAVES AND WAVE INTENSITY ANALYSIS

The dynamic pressure and flow velocity waveforms are generated by contraction and relaxation of the heart and propagate trough the entire cardiovascular system.

Wave speed

Due to the elasticity of the arterial wall, locally induced changes in pressure and flow are not transmitted instantaneously to the periphery but propagate as waves through the arterial tree at a certain speed (c) also known as pulse wave velocity. The wave speed in the arteries is linked to the elastic modulus of the wall via the Moens-Korteweg equation: (2)

Where Einc is the incremental elastic modulus, h is the wall thickness, D is the lumen diameter and ρ is the blood density. This equation can be rewritten for an elastic tube of unit length to relate wave speed to the compliance ΔV/ΔP as described by the Bramwell-Hill equation [30]:

(3)

where V is artery volume, ΔV is change in volume, and ΔP is the change in pressure. The compliance of the vessel can be irreversibly altered by changes in the vessels amount of collagen and elastin, resulting in a relation of wave speed with age (Fig. 8) [31-32].

The compliance of the vessel can also be transiently changed altering the transmural pressure of the vessel. An increase in transmural pressure will decrease the compliance of the vessel and thus increase wave speed [33] (Fig. 8).

Measurement of wave speed by the foot-to-foot methodThe time-delay method is the most direct way to estimate wave speed. It is based on the time it takes for the wave to travel between two sites a known distance apart using a fiducial point on the respective pressure waveforms. The foot of the pressure waveform is the most frequently used fiducial point, giving to this method the name “foot-to-foot” method. It is the most commonly used method to estimate wave speed over a long distance, but it is important to notice that this method results in an average speed for the entire path traveled by the wave. Along this path, the wave can travel through vessels of different stiffness, for example from the arm to the ankle [34].

Measurement of wave speed by the PU-loopWave speed can also be determined locally by simultaneous measurements of pressure (P) and flow velocity (U). Assessment of wave speed using the PU-loop originated from the observation that in the presence of waves travelling only in one direction, P and U are linearly related and the slope of the P-U plot equals the wave speed times the density of blood [35]. In systemic arteries, such a

c =1 ∆P

Vρ ∆V

c =h∙EincD∙ρ

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1unidirectional wave period occurs at the beginning of systole when reflected waves are absent (Figure 9). However, in coronary arteries, forward and backward waves are simultaneously generated during both contraction and relaxation phases of the cardiac cycle, preventing the application of this method.

Estimation of wave speed by the single point techniqueMore recently, another technique has been developed to estimate local wave speed from simultaneous pressure and flow velocity: the ‘sum-of-squares’ or ‘single-point’ technique (SPc) [36]. This method does not rely on a unidirectional wave period and is derived from changes in pressure P and flow velocity U over the entire cardiac cycle:

(4)

where ρ is the blood density.In the aorta, local wave speed assessed by SPc yielded similar results as the foot-to-foot method. Its use was also extended to assess local wave speed in human coronary arteries but without previously direct validation. The application of SPc in the coronary vessels was later on challenged by Kolyva et al [37].SPc resulted in counter intuitive results such as a decrease in wave speed downstream of a stenosis when increasing pressure after stenting. Moreover, it was found that hyperemia following microvascular dilatation had an effect on wave speed in the larger coronary artery, which was highly unlikely.

Wave reflection and wave components

Any discontinuity of the arterial tree generates a reflection of waves due to the change in the transmission properties at such a point. Stenoses or aneurysms are good examples of elastic and geometric discontinuity of the vessels wall. Reflections are also generated at arterial bifurcations when the impedances of the branches do not match the impedance of the mother segment. The measured signals are therefore the sum of two components arriving at the site of measurement: a forward and a backward component [38]. In the systemic circulation, forward components originate in the left ventricular cavity and backward components originate from reflections in the systemic periphery. In the aorta, the principal site of reflection is in the distal abdominal aorta [39-40]. The time in which a reflected wave returns to the heart depends on the length of the system and on the wave speed. The branching patterns in the coronary circulation are ideally matched so that reflections at a bifurcation are likely to be minimal [41]. However, the measured signals are still the result of two components. In the coronary circulation, the forward component originates in the left ventricular cavity and reaches the coronary arteries via the proximal aorta, while the backward component originates in the microcirculation. Figure 10 shows an example of the coronary pressure and flow velocity with their respective forward (P+ and U+) and backward (P- and U-) components.

SPc =1 ∑dP2

ρ ∑dU2

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Wave Intensity analysis

Wave Intensity Analysis (WIA) is a method for the assessment of traveling waves in the cardiovascular system. It is based on the method of characteristics, a technique widely used in gas dynamics that was further extended to elastic arteries by Parker and Jones [42].It is a time-domain method and assumes that every waveform can be reconstructed by the superposition of infinitesimal wavefronts. No assumption regarding the periodicity of the measured signals or the linearity of the system under investigation is necessary.Net wave intensity (dI) is defined as the amount of energy carried by traveling wavefronts per cross-sectional area of a vessel and is determined as the product of changes in pressure and velocity at a single location [43]:

dI=dP∙dU (5)

where dP and dU are the incremental changes in measured pressure and flow velocity between successive time intervals.P and U are not always changing in the same direction within the cardiac cycle. The changes of sign of dI result in a series of positive and negative waves, which define the major components responsible for the measured signals in the time domain. When P and U are changing in the same direction, dI is positive and the wave is defined as forward traveling; when P and U have an opposite change, dI is negative and the wave is defined as backward traveling. Another distinction is based on the effect of pressure: if the wave corresponds to an increase in pressure it is defined as compression wave; if it corresponds to a decrease in pressure, it is defined as an expansion wave. Thus, four types of waves can be defined [44]: Forward compression wave (FCW), forward expansion wave (FEW), backward compression wave (BCW) and backward expansion wave (BEW). It is important to note that, as the measured pressure and flow velocity represent the summation of forward and backward contributions, the same applies for wave intensity. The wave intensity derived from the measured pressure and velocity at a single location is the sum of the separate contributions of the forward and backward traveling waves arriving at the site of measurement [45]:

dI = dI+ + dl- (6)

where dl- represents the forward contribution and dl+ represents the backward contribution.Mathematical equations have been developed to separate the net dI into the forward and backward components [42]:

dI± = ± (dP ± ρcdU)2 (7)

This separation of contributions to the net wave intensity is therefore only possible when the wave speed c is known.

14ρc

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Figure 10: Top: Measured (thick line) intracoronary pressure (left) and flow velocity (right) with the corresponding forward (solid) and backward (dashed) components. Both components sum up to form the measured signal. Bottom: representation of a vessel where the forward (solid arrow) and backward (dashed arrow) components of measured signals arrive to the site of measurement (black dot).

Figure 11: Aortic wave intensity analysis. FCW: Forward compression wave; FEW: Forward expansion wave; BCW: Backward compression wave. FCW and FEW are generated from the left ventricle during contraction and relaxation, respectively. BCW is caused by reflections. (Adapted from [46]).

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A problem with this definition of wave intensity is that its value depends upon the sampling time. Doubling the sampling time will double the value of dP and dU increasing the magnitude of dI. This problem can be eliminated normalizing dP and dU by the sampling time. Therefore eq.5 and eq.7 become:

(8)

dI± = ± (9)

and dI is then expressed in W∙m-2∙s-2.

In wave intensity analysis, several parameters can characterize a wave. The simplest is the magnitude of the wave that is given by the peak of dI. However a weaker wave but with a longer duration can be as important as a stronger but shorter wave. Therefore it is useful to characterize a wave by the integral of dI between the start and the end of the wave: the wave energy, with units J∙m-2∙s-2.

Waves in the aorta and coronary arteries

In the aorta, forward waves are generated by contraction and relaxation of the left ventricle while backward waves result from reflections distal in the aorta (Figure 11). The coronary circulation is different from the systemic circulation in terms of wave generation and reflection. Due to its specific branching pattern reflections are minimal in the coronary circulation, yet there are four major waves (Figure 12). The forward coronary waves are coming from the aorta, while the backward waves are generated in the microcirculation by the contracting and relaxing myocardium. The typical coronary wave intensity pattern shows a compression wave (BCW) propagating from the microcirculation at the start of cardiac contraction, generated by the compression of the intramural vessels. When the aortic valve opens wave energy exits the ventricle and enters the coronary artery via the aorta: that is a forward compression wave (FCW). With the onset of cardiac relaxation, an aortic-originating wave appears as pressure decreases: a forward expansion wave (FEW). Finally, the release of the compression of the intramyocardial vessels during ventricular relaxation generates a backward expansion (suction) wave (BEW) that accelerates flow into the coronary artery. This last wave is hence associated with coronary perfusion.Because of its capacity to distinguish the origin of the coronary pressure and flow velocity profile, the application of WIA to the coronary circulation has provided a valuable tool for studying the interaction between cardiac mechanics, dynamics of the coronary circulation and systemic hemodynamics.The first application of WIA in the coronary system was performed in open-chest dogs about ten years ago [47]. Its application in humans has been described some time later [48], but it is only very recently that it has been fully applied in the human coronary arteries as a tool for deeper understanding of coronary physiology [49-52].

dP dUdt dt

dl = ∙

ρc±dP dU1 2

dt dt4ρc( )

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Figure 13: General overview of the principal chapters of the thesis. Chapter 2 checks the validity of the single point technique (SPc) to assess wave speed in the coronary artery at rest and maximum hyperemia. Chapters 3, 4, 5 and 6 describe the effect on cardiac coronary interactions of different types of diseases or interventions.

Figure 12: Typical coronary wave intensity pattern. Pa: aortic pressure; PLV: left ventricular pressure; Pd: coronary pressure; U: coronary flow velocity; FCW: Forward compression wave; FEW: Forward expansion wave; BCW: Backward compression wave; BEW: Backward expansion wave. FCW and FEW are generated from the left ventricle during contraction and relaxation respectively. BCW and BEW are generated by the compression and relaxation of the microcirculation

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AIM AND OVERVIEW OF THE THESIS

Despite the many different forms of coronary diseases, the coronary circulation still remains poorly understood. The reason for this is that clinical work has largely focused on diseased vessels with an approach based on means per beat analyses rather than on the dynamics of coronary flow. This thesis aims to give a better understanding of these dynamics using wave intensity analysis, discerning the complex interaction of cardiac mechanics and myocardial perfusion under different conditions (see Figure 13 for a schematic overview of thesis chapters).To fully apply wave intensity analysis, wave speed needs to be known. This was a limitation for the application of wave intensity analysis in the coronary arteries, since no method to estimate wave speed in these vessels was previously validated. In Chapter 2, we confirm the single point technique as a valid method to estimate wave speed in normal coronary arteries at rest and we propose an approach to extend its use to maximum hyperemia.In the next chapters, we used wave intensity analysis to study the effect of different interventions or diseases on cardiac-coronary interaction.In Chapter 3, we investigate the consequence of an abrupt increase in intrathoracic pressure on coronary hemodynamics in undiseased vessels. In the catheterization laboratory, this increase in intrathoracic pressure was induced by having the patients perform a Valsalva maneuver. Chapter 4 focuses on the consequences of an aortic valve stenosis on coronary flow dynamics. Here we try to understand the reasons behind angina symptoms despite unobstructed coronary arteries. Moreover, the acute effect of treatment by transcatheter aortic valve implantation has been investigated. In Chapter 5 we propose some mechanistic explanation for the warm-up phenomenon in patients with coronary artery disease. This could explain the decrease of angina symptoms during repeated exercise. In Chapter 6 we compare the effect on coronary flow dynamics induced by right atrial pacing with that of exercise, which has a profound influence not only on cardiac mechanics, but also on the systemic circulation. A general discussion of our findings is presented in Chapter 7.

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