1

Chapter 1

INTRODUCTION TO CIRCULATORY AND RESPIRATORY SYSTEM

MODELING

Gianfranco Ferrari, Marek Darowski, Tomasz Gólczewski, Krystyna Górczyńska, Maciej

Kozarski

ABSTRACT

This chapter is focused on circulatory and respiratory system modeling. It includes a brief history

of circulatory and respiratory system modeling development and a short description of the state

of art. In the chapter also basic classification of mechanical circulatory and respiratory assistance

is presented. The last part of the chapter deals with innovative approaches to modeling of both

circulatory and respiratory system which concern hybrid models and virtual organs. Hybrid

modeling consists in merging numerical and physical models or devices exchanging data among

them in real time. In this way it is possible to use the best features of numerical models

(accuracy, flexibility, low cost) without loosing the possibility of testing physical devices. Hybrid

approach is extremely useful for testing mechanical heart and lung assist devices. The idea of

virtual organs is applied to the respiratory system and is created to analyze a whole class of

problems which are not known or clearly defined before creation of a virtual organ.

1.1. INTRODUCTION

A model is a set of equations representing some aspects of a physical phenomenon. The models

representing biological systems are a special class of models that however obey to the general

principles underlying the development of any model. The difference lies in the complexity of

biological systems. In fact, for any model and especially for models of biological systems, the

key point is the amount and type of necessary simplifications. As a matter of fact any model is a

simplified representation of a real phenomenon. It is important is to know exactly the impact of

the simplification on the comprehensive system and which aspects of its behavior can be taken

into account by the model. These considerations are critical when models represent complex

biological systems where, as for example in the case of the circulatory or respiratory systems,

there are several subsystems operating concurrently. It is then evidently fundamental to separate

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the effects of the different subsystems to achieve the necessary simplification but it is necessary

as well to develop the models preserving the possibility to take into account the interactions

among the different subsystems and the circulatory and respiratory mechanical support when it is

present.

1.2. MECHANICAL CIRCULATORY ASSISTANCE (MCA)

Krystyna Górczyńska

This paragraph does not pretend to give an exhaustive description of mechanical circulatory

assistance but rather to evidence, after some brief historical remarks, the features that may be

relevant for modeling.

The MCA can be used as a bridge to recovery when the heart inefficiency is reversible or as a

bridge to transplant when waiting for a donor’s heart. In the cases of the end-stage heart failure

only a total artificial heart can be taken into account [1],[2].

The patient’s heart condition, as well as the type of his heart disease, impose the choice of the

assist device to be used. For example, the IABP is widely used for assistance in the case of left

ventricular failure (e.g. induced by the coronary dysfunction) to unload the ventricle. On the

contrary, the main goal of the parallel LVAD assistance is to discharge pulmonary stagnation by

creating a bypass of the inefficient left ventricle to shift a volume of blood from the left atrium to

the aorta.

Thus, the MCA can be mainly used:

- in the case of heart infarction to decrease cardiac work by unloading the inefficient

ventricle during the systole and to improve its coronary perfusion during the diastole,

- to stabilize patient’s hemodynamic conditions in pre-operation stages,

- in post-operation stages (e.g. after coronary bypasses, heart valves grafts) to enable

disconnecting the patient from the cardio-pulmonary bypass,

- in the case of sudden (e.g. post-operation) ventricular insufficiency.

Historically, roller (peristaltic) pumps were the first step in MCA development. They are a

typical extra-corporeal device due to their relatively large dimensions and weight. They have

been used in heart-lung machines during surgical operations. Roller pumps were in a sense the

forerunners of MCA as it is known nowadays.

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The next step was the development of rotary blood pumps (axial, radial, diagonal) [3],[4] that are

characterized by smaller dimensions and invasiveness. The rotary blood pumps, similarly to other

continuous-flow pumps do not need any additional heart valves. The miniature axial flow pump

developed at the Baylor School of Medicine (Houston, Texas) [5],[6],[7] has a weight of 94 g

only.

Advantages of rotary pumps are: small hemolysis and ability of appliance for a couple of days,

small dimensions and small filling volume. The main disadvantage is necessity of limiting its

rotational speed because of stress and cavitation [8].

The applied methods of assistance differ in a goal (recovery, bridge to transplant) and mode of its

usage (pulsatile, continuous flow) and connection to the circulatory system (“in series”, parallel)

as well as an extent of invasiveness of the surgical intervention.

The development of total artificial heart was parallel to MCA development. However some of the

technical solutions were adopted in both MCA and total artificial heart [8],[9].

A simple definition of mechanical circulatory assistance (MCA) can be given from strictly

engineering point of view: in the case of heart failure one or both ventricles may become no more

able to transfer to the circulatory system the energy necessary for organ perfusion. The role of the

MCA is delivering to the circulatory system the energy difference between the energy demand

and its supply produced by the failing ventricle.

Of course, the problem is not only an engineering one - the role of the MCA is more complex as

it interacts with a biological system. Nevertheless, the above simple statement leads to the

effective synthesis of one of the main goals of MCA; its importance changes in relation to the

aim of the assistance. If the MCA is used as a bridge to transplant or long term implant, the

sufficient energy transfer to the load is of a primary importance to fulfill the minimal

requirements for patient’s wellbeing. The assistance can be also applied for heart recovery. The

mechanical support consists in this case in inserting an additional pump into the circulatory

system to unload the insufficient heart and to improve hemodynamic parameters of the patient,

promoting in this way heart recovery. The energy transfer to the load is still fundamental and the

assistance should be managed to create the best conditions for heart recovery. Then, beyond the

relation between MCA and the arterial load, other variables such as coronary perfusion should be

taken into account. MCA can be inserted into the circulatory system “in series” or in parallel and

the generated flow can be pulsatile or non pulsatile [10]. This is not the place to add further

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contributions to the debate concerning features of different types of MCA; what is important is to

be aware that different insertions and different flow types imply different solutions for modeling

the device and heart-MCA interaction as it will be shown in the examples in chapter 4. It should

be mentioned that flow pulsatility implies often but not always the presence of mechanical heart

valves that, in the simplest version, can be modeled as ideal diodes.

It is worthwhile to give a short classification of MCA in relation to its insertion place into the

circulatory system:

1. “In series” assistance:

• Left Ventricular Assist Device (LVAD).

• Rotary pumps.

• Centrifugal pumps.

• Axial flow pumps.

• Intra-Aortic Balloon Pump (IABP).

• Para-aortic counterpulsation.

• External counterpulsation - a non-invasive method based on sequential

compression of a vascular bed by cuffs placed on the legs [11],[12],[13],[14],[15].

2. Parallel assistance:

• Left Ventricular Assist Device (LVAD).

• Bi-Ventricular Assist Device (BVAD) – simultaneous assistance of the left and

right ventricle.

• Roller pumps.

• Rotary pumps.

“In series” assistance connection includes several devices, pulsatile or non pulsatile. One of the

most representative is IABP [16],[17],[18],[19],[20],[21],[22] a simple to apply and rather

effective device; it is widely used for assistance in the case of left ventricular failure induced by

e.g. coronary dysfunction. An example of IABP modeling will be presented in Chapter 4, so a

short description of this device action is needed. In the IABP, the role of the pump actuator is

played by the balloon inserted into the descending aorta through the femoral artery. The balloon,

connected to the driving unit by the catheter, is periodically filled with gas and emptied,

according to the heart rate (HR) and systole-to-diastole ratio (S/D) of the patient. The goal of the

IABP assistance is heart muscle’s recovery by its unloading, due to systolic aortic pressure

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decrease, and better perfusion, by the diastolic aortic pressure increase - diastolic augmentation

(Figure 1). The increased coronary flow attained in this way can rise the ventricular contractility

finally resulting in the improvement of general hemodynamic conditions [16].

Figure 1 : IABP assistance. Pas – aortic pressure (from „Biocybernetyka i Inżynieria Biomedyczna 2000”, Vol. 3. Copyright by EXIT , 2001, reproduced by permission).

The IABP assistance effectiveness is dependent, besides initial circulatory and ventricular

conditions, on the balloon emptying and filling velocity as well as on time delay of the balloon

inflation and deflation (in relation to the QRS complex of the patient’s ECG) [23], on the balloon

shape, volume and position in the aorta, on the sort of gas filling the balloon and finally on the

posture [24]. Characteristic for the balloon assistance is the systolic aortic pressure and end-

diastolic pressure (EDP) decrease and the diastolic augmentation.

Another device that will be modeled in Chapters 4 and 8 is parallel, pulsatile LVAD. This device,

important for historical and practical reasons, deserves some comments.

In the case of blood stagnation in the pulmonary system, usually caused by left ventricular

inefficiency, the parallel assistance can be applied. Independently of the structure of the assist

device pumping unit, the role of such assistance is mainly to shift a volume of blood from the left

atrium to the aorta, (Figure 2), to create so called bypass of the insufficient left ventricle. When

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the heart is assisted by the LVAD applied as a bridge to recovery, the artificial ventricle only

partially takes over the pumping function of the native ventricle [25],[26]. The LVAD action in

that case should be synchronous with the ECG signal and in general carried out on the principle

of counterpulsation; owing to such kind of assistance, harmful stagnation in the pulmonary

circulation can be discharged bringing about the arterial pulmonary and left atrial pressure drop

along with significant rise in the ventricular and arterial pressure and in total cardiac output.

Figure 2 : Block diagram of the parallel ventricular assistance (LVAD): LA – left atrium, LV – left ventricle, ALV – artificial left ventricle, ECU - electronic control system, PDU – pneumatic

drive unit, P± - control pressure (from „Biocybernetyka i Inżynieria Biomedyczna 2000”, Vol. 3. Copyright by EXIT , 2001, reproduced by permission).

Some of the assist devices available on the market for heart recovery or as a bridge to

transplant, are extracorporeal, some – implantable [8],[27],[28],[29],[30],[31].

In the case of inefficiency of both ventricles, biventricular assistance (BVAD) can be applied

using two identical LVAD and RVAD diaphragm pumps [32],[33], rotary pumps [34],[35] or e.g.

a combination of the para-aortic left heart-assist pump connected to the aorta and the IABP

inserted into the pulmonary artery [36].

Pulsatile flow assistance was the first type of assistance to be developed and clinically used. It is

essentially based on a chamber separated from the remaining part of the circulatory system by

means of artificial valves. In the assist devices, the energy can be transferred to the blood in

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different ways: pneumatically, electromechanically, electromagnetically. The flow pulsatility is

determined, together with the artificial heart valves, by a moving piston or diaphragm that creates

the conditions for filling and ejection of the assist ventricle.

1.3. MECHANICAL RESPIRATORY ASSISTANCE

Marek Darowski, Tomasz Gólczewski

The International Standards Organization Committee is still working on standards for ventilator

mode nomenclature, but recent publications allow us to present how to distinguish basic modes of

ventilation [37],[38].

The classification of ventilation modes is based on the following criteria:

1) what is the independent variable (pressure or volume) during ventilation, that can be

controlled by an anesthesiologist;

2) how breaths (mandatory or/and spontaneous) are sequenced, triggered and cycled.

According to the 1st criterion we have:

a) pressure controlled modes: artificial pressure controlled ventilation (PCV), continuous

positive airway pressure (CPAP), pressure-support ventilation (PSV), proportional-assist

ventilation (PAV) and neurally adjusted ventilatory support;

b) volume controlled modes, e.g. artificial volume controlled ventilation (VCV),

characterized by a mandatory tidal volume delivered by a ventilator to the lungs,

independent of changes in lungs mechanics and patient’s inspiratory effort as well as

chosen inspiratory flow patterns (constant, ascending/descending ramps or sinusoidal),

According to the criterion 2 we have:

a) continuous mandatory ventilation with all mandatory breath, from a ventilator,

b) continuous spontaneous ventilation, with all spontaneous breaths, when inspiratory

periods are triggered and cycled by a patients,

c) intermittent mandatory ventilation, when ventilatory assistance consists of spontaneous

and mandatory breaths.

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During ventilatory support, the lungs and a ventilator create one mechanical system in which

interaction between variables values (airway and alveolar pressure, inspiratory and expiratory

flow, tidal volume) depends on the respiratory system mechanical properties (e.g. airways

resistance, and the lungs/thorax compliance), the mode of ventilation applied, and ventilatory

parameters settings.

VCV always gives the required minute ventilation. However, also PCV may provide a desired

ventilation in steady state conditions, i.e. when the lungs mechanisms do not change. On the other

hand, PCV is associated with a decelerating inspiratory flow, which is supposed to be responsible

for a better gas exchange1. However, in most of the modern respirators a decelerating inspiratory

flow pattern is also available during VCV [39],[40],[41],[42]. It implies that the discussion on

optimal control variables may concern not a specific mode of the artificial ventilation (PCV or

VCV) but rather the inspiratory pressure or flow pattern itself [43],[44]. The pattern may be

expected to influence both pressure and ventilation distributions in the lungs, in particular in

cases of lung pathology, which is often manifested by differences in lung mechanics between left

and right lobes.

VCV always gives a preset tidal volume VT because the airflow rate is the independent (control)

variable. However, the airway and alveolar pressures cannot be predetermined because they

depend on the lung compliance and airway resistance (Raw) (Figure 3a). In PCV, the airway

pressure is the control variable but VT changes according to the lung mechanics properties

(Figure 3b). Thus, either the pressures or VT is behind the control.

For the above reasons, in VCV there is a risk of:

• barotrauma when the pressures increase too much because of the lungs compliance smaller than

the expected,

• volutrauma of one lung in asymmetric pathologies, e.g. when airways of the other lung are

obstructed (the whole VT is loaded into the healthy lung).

In PCV, there is a risk of:

• hyperventilation (volutrauma) if the lungs compliance is greater than the expected,

• hypoventilation if the compliance is smaller or Raw is greater than the expected.

1 An example of the use of a virtual respiratory system in investigation of inspiratory pattern influence on gas exchange and blood oxygenation is presented in the Chapter 6.5

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Figure 3 : The difference between power controlled ventilation (PoCV) and volume (VCV) or pressure (PCV) controlled ventilation from the cybernetic point of view.

R – respirator, RS – respiratory system, P – pressure, Q – airflow, VT - tidal volume, Po - power.

a) Q and VT are preset but P is uncontrolled in VCV.

b) P is preset but Q and VT are uncontrolled in PCV: their values depend on RS properties and may be dangerous for RS.

c) It depends on RS properties how quickly P increases. For example, as an increase of P causes a decrease of Q to maintain Po=Q*P preset, there is a negative feedback in PoCV. Thus, the respirator adapts own work to the RS properties during PoCV, which protects against too big values of both P and Q. The difference between power controlled ventilation (PoCV) and volume

(VCV) or pressure (PCV) controlled ventilation from the cybernetic point of view.

To avoid the above risks, Darowski [45] proposed a new method: power controlled ventilation

(PoCV). In PoCV, neither the pressure (as in PCV) nor VT (as in VCV) is the independent,

presettable variable. Instead of that, the instantaneous power, i.e. the multiplication of the

pressure and airflow rate, is the independent variable that is preset and maintained at the defined

level during inspiration. Such a connection between the pressure and airflow with their

multiplication makes that:

• on the one hand, neither the pressure (as in PCV) nor the airflow rate (as in VCV) is the

control variable, and thus both depend on the lungs state;

• on the other hand, both are under partial control because of controlled multiplication.

For example, if the current airflow value causes that the pressure starts to be too great (e.g.

because of small lungs compliance), the airflow is decreased to keep the multiplication at the

defined level. Thus, there is some kind of adaptation of the respirator work to the lungs behavior

realized by means of a negative feedback between the pressure and airflow values (Figure 3c).

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A virtual RS seems to be the best tool for initial, comparative analysis of VCV, PCV, and PoCV

because ethical limitations would make impossible to perform such tests on real patients as the

tests require the use of all the modes in the same patient and observation which of the modes may

cause the most significant lungs injury. An example of such a comparative analysis is presented

in the Chapter 5.5.

Whether PCV, VCV or PoCV is used, the non-physiological positive pressures appear in the

lungs and thorax during the artificial ventilation. They may unfavorably influence both the lungs

and hemodynamics. This problem should be considered every time when artificial ventilation

support is applied in patients with heart or lung disease. New methods of artificial ventilation are

supposed to reduce partially these effects, maintaining the effectiveness of the breathing support.

One of such methods is PAV [46]. PAV reinforces the instantaneous patient’s breathing effort

and leaves the patient to control over many aspects of breathing (as the frequency or volume of

the inspired air).

The main assumption of the PAV mode is to produce the pressure being proportional to the

airflow, to the volume of the already inspired air, or to both. The aim of PAV is to decrease the

work of the respiratory muscles to compensate:

� muscle fatigue,

� a fall of the respiratory system compliance (C), and

� a rise of Raw.

The factors mentioned above result from different lung pathologies and the presence of the

endotracheal tube. Advantages of the PAV include:

o preservation of the patient’s own respiratory control,

o greater comfort to the patient in comparison with conventional support methods,

o smaller sedation,

o a lower risk of the patient’s over-ventilation,

o non-invasive ventilation is possible (by a face or nasal mask),

Besides advantages, PAV may has such disadvantages as:

• unfavorable dependence on patient’s respiratory activity,

• a risk of instability when the settings are incorrect or the conditions of the support change.

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A model of RS, esp. a virtual RS, can be a good tool for analysis when potential disadvantages of

PAV might become actual. An example of such analysis as well as comparison between PAV and

PSV are presented in the Chapter 5.7.

CPAP is usually a useful method of spontaneous breathing support. If the obstruction concerns

the upper airway (e.g. as in the sleep apnea), CPAP keeps the upper airways open. Sullivan et al.

used CPAP in sleep apnea as the first [47] and nasal CPAP is a standard therapy for obstructive

sleep apnea syndrome, now. If the obstruction that concerns smallest bronchi is connected with

atelectasis, CPAP keeps bronchiole open and prevents alveoli from collapse.

Obstruction in bronchi of middle generation is of the greatest meaning from the clinical point of

view because chronic obstructive pulmonary disease and asthma are such a type of obstruction.

Despite that meaning, the cause of CPAP efficacy in such cases is not so obvious.

As CPAP means increased pressure inside bronchi, it makes those bronchi wider because of

increased transmural pressure. However, although easier inspiration through wider bronchi is

usually supposed to be the CPAP efficacy cause, the expiration period seems to be much more

critical in that case. It is because both the obstruction and a transmural pressure2 fall during

expiration decrease expiratory airflow through such bronchi3. Therefore, the smaller the

transmural pressure because of increased intrapleural pressure during the expiration, the greater

the summarized effect on the airflow. As CPAP increases the transmural pressure, it may prevent

such bronchi against collapse causing airflow limitation4, and thus it can compensate obstruction

influence on expiratory airflow. Hence, it appears that CPAP may make expiration easier.

2 When CPAP is used, the transmural pressure is equal to the CPAP value less the intrapleural pressure. 3 See the Formula (10) in the Chapter 3.2, for example. 4 See also Chapters 5.4 and 5.8 where flow limitation during forced spirometry is deliberated.

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On the other hand, however, CPAP may make breathing harder because it shift the working point

of RS towards smaller lungs compliance (Figure 4). It can be proved that an intrathoracic

(intrapleural) pressure change (∆Pw) caused by a constant inspiratory muscles effort can be

determined with the following formula:

d

d d

Cw∆Pw=-Ps

Ca +Cw⋅ (1)

where:

Cwd, Cad – differential compliances of the chest wall and lungs, respectively;

Ps - the muscles effort expressed by the resultant pressure being an effect of that effort.

Figure 4 : Influence of the working point on the differential compliance of lungs. V – lungs volume, Pw –

the difference between the intrapleural and upper airways pressures being equal to the static

transpulmonary pressure when the air flow is equal to zero (thus, the broken line presents the lungs

compliance). The greater the lungs volume, the smaller the lungs volume increase (∆V) caused by a pressure increase (∆p), i.e. the greater the volume, the smaller the differential compliance Cad=∆V/∆p. Solid curves - the relationship between the volume and pressure for

breathing with the same frequency but different deepness of breaths.

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Since Cad falls with lungs volume increase (Figure 4), the greater the volume, the greater the

∆Pw value caused by the same Ps (hence changes of the intrapleural pressure in Figure 5 are

bigger for the greater CPAP despite unchanged Ps). However, although ∆Pw rises with the lungs

volume, the volume increment (∆V) decreases because of the following dependence:

d

d d

CwV Ps

1 Cw / Ca∆ = ⋅

+ (2)

Hence it appears that CPAP may make breathing harder because the same respiratory muscle

effort causes less deep inspiration when CPAP is applied (Figure 5). Additionally, CPAP makes

the end-expiratory lungs volume greater, and thus a greater portion of used air is mixed with the

fresh air during inspiration, which causes that the alveolar partial pressure of O2 may be smaller.

Since, on the other hand, CPAP increasing the transmural pressure in bronchi of middle

generation should make breathing easier, it is necessary to analyze when CPAP should be applied

and when it is unprofitable (Figure 6). Thus again: investigations using a virtual RS may be

helpful. An example regarding the mechanical aspect is presented in the Chapter 5.6.

Figure 5 : Lung volume versus intrapleural pressure (from [48]) for normal airway resistance (Raw), four values of CPAP, and the breathing frequency equal to 15/min. Black points [Ppoint, Vpoint] determine the working points showed in Figure 4 (where Pw from that figure is equal to Ppoint-CPAP). Note that the greater the CPAP value, the more

horizontal the loop, i.e. the smaller the lungs volume increase.

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Figure 6 : Advantages (blue) and disadvantages (red) of the support with CPAP. It seems that only experiments, also those on a virtual respiratory system, can show whether

CPAP is profitable or not in an individual case.

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1.4. CIRCULATORY SYSTEM MODELING

Gianfranco Ferrari

The use of modeling to study, interpret and analyze circulatory phenomena is rather recent and

spread thanks to the parallel development of tools to solve and represent the equation systems at

the base of any model. The tools are of course one side of the medal, the other side is the

knowledge on cardiovascular patho-physiology that determines circulatory system modeling

evolution and complexity. From another point of view, the typically bi-directional relationship

between circulatory patho-physiology and modeling is the key point: in fact, if understanding the

circulatory phenomenon is the basis for constructing a model, the latter can suggest, reciprocally,

how to interpret or predict a circulatory phenomenon.

Another important remark is that each model is designed to represent a specific phenomenon and

that the model scope of application is consequently limited. Attention can be focused on different

aspects of circulation (fluidodynamics, blood volume distribution, interactions between different

systems as in the case of circulatory and respiratory systems) needing each of them a different

model. Finally, models can be developed to represent local or global circulatory phenomena

(taking into account the whole circulatory system). In the last case, the subject of this book,

models can be defined as comprehensive. A comprehensive model suffers from some limitations

due to the structure (mainly lumped parameters) and to the necessity to limit the model

complexity. Nevertheless, comprehensive models are valuable tools to study volume

displacements inside the circulatory network and the interaction between the heart, the arterial

system and mechanical circulatory assistance, if present.

The issue of artero-ventricular interaction deserves a brief history of its development and some

remarks. The study of the interaction between the heart and the vascular system has always been

the subject of considerable interest as it is strictly related to the most general issue of cardiac

output regulation. The possibilities offered by new analytic tools and new measurement

techniques permitted the passage from phenomenological observations to the quantitative

analysis of the heart/circulatory system interaction. These quantitative studies began in the fifties

[49],[50],[51],[52] of the last century and attained full maturity in the early seventies. It is

difficult to mention the most important studies in this field: contributions came from different

sources and, complementing each other, led to the creation of powerful instruments and

methodologies going deep into the mechanics of the heart and its interaction with the circulatory

16

system. Undoubtedly, the works of Guyton [53], Sagawa [54], Westerhof [55],[56],[57] and

Piene [58] are milestones in the study of artero-ventricular interaction.

An important achievement is the complementarity of different studies that permit, altogether, to

analyze different aspects of the same problem: the description of what happens in between the

ventricle and the circulatory system and, after all, what are the determinants of cardiac output

regulation. The first investigator to analyze the problem of cardiac output regulation and,

implicitly, of the mutual interaction between the heart and the circulatory system was Guyton

[53] who started these studies in the mid fifties of the last century: we are in debt to him of the

first analytical description of the complex interactions between different parts of the circulatory

system and, especially, of the concept of venous return and definition of the meaning and the role

of mean circulatory pressure. The studies of Sonnenblick [59], Suga [60] and Sagawa [54]

permitted to interpret ventricular mechanics and gave rise to the first models of ventricular

ejection that became more and more complete with contributions of investigators from all over

the world. In the seventies of the last century Westerhof focused his attention on arterial system

modeling, modifying the traditional windkessel [55] to fit the model to measured input

impedance of the arterial system. He was one of the first investigators to describe the heart as a

pump [56] and, on this basis, the interaction with the arterial system.

In conclusion, a set of useful tools is now available to model, analyze and interpret the behavior

of the ventricle and its interaction with the circulatory system in general and the arterial system in

particular. Ventricular modeling is well assessed and based on the variable elastance model that

from its basic definition [54] was progressively refined to include ventricular internal resistance

[61],[62] and active atria [63] . The introduction of the concepts of end-systolic ventricular

elastance and of effective arterial elastance [54] permitted to describe, on the pressure-volume

plane, the interaction between the ventricle and the arterial system by means of the working point

defined by the intersection of two lines. The approach shortly sketched here, besides being useful

in describing patho-physiological circulatory conditions, is an excellent starting point and a base

to develop methodologies facing the new challenges grown up with the quick development of

active or passive prosthetic devices developed to assist or replace the failing ventricular function

or parts of the circulatory system.

A-V interaction: graphical representation on the P-V plane

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The representation of artero-ventricular (A-V) interaction on the pressure-volume (P-V) plane

permits some interesting considerations. Figure 7 illustrates graphically A-V interaction on the P-

V plane: the working point PW is defined by the intersection between end-systolic pressure

volume relationship (ESPVR) line and effective arterial elastance (EAE) line. Any change in

ventricular or circulatory conditions is reflected by the displacements of the working point PW.

ESPVR line reflects the contractile state of the ventricle by its slope (Ees) and intercept (V0) on

the volume axis. EAE line slope (Ea) is arterial elastance. It is defined as the ratio of total

resistance (Rt) and cardiac cycle duration (Tc). Total resistance is defined as the ratio of

ventricular end-systolic pressure (Pes) and average ventricular flow (Q). For practical

applications, Pes can be replaced by average arterial pressure [54].

The position and the slope of EAE line is modified by any change in ventricular end diastolic

volume (Ved) and in arterial circulatory parameters.

Pes

Ven

tric

ular

Pre

ssur

e

Ventricular Volume

V0 SV

PW

EAE ESPVR

P’W

SV’

EAE’

Ees

Ea E’a

VedVes

ESPVR’

Figure 7 : graphical description of artero-ventricular interaction

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The description of A-V interaction on the P-V plane is strictly related to ventricular energetics.

As it is shown in Figure 8, each of the elements graphically represented in Figure 7 contains

information directly or indirectly related to ventricular energetics. EW is ventricular external

work, PE - ventricular potential energy. Pressure-volume area (PVA) is related to ventricular

oxygen consumption VO2 [60]. Finally, CME is cardiac mechanical efficiency. So, while

describing artero-ventricular interaction, the pressure-volume plane representation gives valuable

information about the state of the ventricle (stroke volume, ventricular volumes), ventricular

energetics and, finally, the state of the arterial network. This background, as it will be shown in

the next chapters, can be usefully applied in the analysis of different patho-physiological

circulatory conditions including the effects of prosthetic devices or of mechanical heart assist

devices. In this regard, it is worthwhile to mention two important issues:

• the number of methods and devices supporting inefficient cardiovascular system

increased rapidly during the last few years.

• Clinical studies to assess advantages and limitations of circulatory support devices and to

optimise their use are long lasting and have obvious restrictions – the health risk and

ethical problems concerning investigations on patients and animals.

Mechanical heart assistance, A-V interaction and modeling

Pes

Ven

tric

ular

Pre

ssur

e

Ventricular Volume

V0 SV

PW

EAE ESPVR

Ees

Ea

VedVes

PE

EW

⋅2 1 2

2

PVA=PE+EW

VO =b PVA+b

EWCME=

VO

Figure 8 : the pressure-volume plane representation and ventricular energetics

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When mechanical heart assist devices exert their action, they affect directly or indirectly A-V

interaction: the development of circulatory models based on analytical tools able to represent A-

V interaction opens therefore interesting opportunities to assess and compare different

implantable devices, support devices, mechanical support methods and to improve circulatory

assistance.

Furthermore, by in vitro tests on simulators i.e. virtual patients, comprehensive models can help

to understand the complex heart/lung interaction especially during the frequent simultaneous

assistance of both respiratory and circulatory systems.

To complete this overview on circulatory assistance, it should be said that the fidelity

requirements for models or simulators are rapidly increasing both in the field of basic research

and in R&D investigations conducted mainly by Universities and Company laboratories. Finally,

another issue not yet mentioned is the increasing role of modeling and simulation in academic

education, both in technical and medical schools and in the training of medical staff to use the

new devices.

Coming back to the P-V plane representation, its potential importance lies in that the majority of

the existing active and passive prosthetic devices modify or affect ventricular volumes or

circulatory parameters or both of them. This implies a relevant direct or indirect effect on

ventricular energetics in the case of ventricular assistance or in the case of the functional

replacement of vessels sections and heart valves. Similar considerations are valid to describe the

effects of drugs or of any other therapy modifying ventricular or circulatory parameters. An

example can be paradigmatic: the IABP is an assist device that is often used to assist a failing left

ventricle. Without going into details now, its role is to unload the ventricle and improve coronary

perfusion by changing hemodynamic conditions during ventricular diastolic phase. This

mechanical action (caused by the inflation and deflation of the balloon), in spite of the limited

hemodynamic effects, changes in depth ventricular energetics. This can give rise to a virtuous

circle that improves ventricular elastance re-establishing the proper energetic relationships inside

the ventricle and permitting further recovery of the ventricle. One of the critical issues is

therefore the optimal use of the IABP to support the ventricular recovery. The analysis of the

pressure-volume loop during IABP assistance offers a powerful tool that permits to:

• merge information regarding ventricular volumes, hemodynamics and ventricular

energetics,

20

• identify criteria to optimize the control strategy of the balloon.

This framework identifies the problem of IABP assistance optimization, identifying at the same

time the requirements to develop a comprehensive circulatory model that should be aimed at

analyzing hemodynamic and energetics data predicting, to some extent, their trends during IABP

assistance.

Circulatory models, a brief history and their present

Coming back to modeling in strict sense, it should be said that the history of circulatory modeling

coincides widely with the history of bioengineering studies of the circulatory system. Circulatory

models were based from the beginning on different structures (usually numerical or physical)

reproducing the circulatory system at different levels of detail. From functional point of view,

they became progressively closer and closer to the theoretical background outlined above.

The first complex circulatory models were analogue [64] and their aim was to permit the study of

mechanical properties of the arterial beds. Only later, with the development of the first digital

computers, numerical circulatory models became fundamental and widespread [65],[66],[67].

The need for physical circulatory modeling arose and grew up with the development of the first

circulatory prosthetic devices and for research purposes [68],[69],[70],[71]. However, the growth

of circulatory modeling was to some extent independent of the methodologies developed to

analyze cardiovascular patho-physiology. Only later there was a convergence of tools (the

circulatory models) and methods (the pressure-volume plane approach to the study of artero-

ventricular interaction).

As it was said, cardiovascular research along with the development of cardiovascular

technologies stimulated the development of circulatory modeling. For example, the impulse to

the development of hydraulic modeling of the circulation came from the growth of total artificial

heart research. The development of such models is a good example of how physical models were

tailored to the specific applications. For total artificial heart in fact, the main problem was the

construction of a circuit able to simulate both systemic and pulmonary circulation, evidence the

unbalance between left and right ventricle and reproduce properly pressure-flow relationships at

the output of both ventricles. The necessary models were therefore rather simple and the many

prototypes essentially differed in the solutions chosen to realize and automate in some cases

hydraulic components [66],[68],[69],[70],[71].

21

A further stimulus came from the development of mechanical heart assistance and of several

prosthetic components that led to the construction of more sophisticated mock circulatory

systems (MCSs) tailored as well to the specific application [72],[73],[74],[75],[76]. Without

going into the details of heart assist device testing, it is interesting to point out here that, when

assistance is used for heart recovery, its role is to create the best conditions for this occurrence. In

this case, testing of the assist device should go beyond the simple evaluation of its performance

including the possibility to perform functional tests; that is to say the study of hemodynamics

conditions in relation to the control strategy of the device. More specifically, functional tests

involve the study of the mutual interaction among the heart, the circulatory network and the assist

device. That is to say, the study of A-V interaction in the presence of another pump that is the

assist device.

The situation sketched above implies the construction of circulatory models able to reproduce A-

V interactions and to react to the presence of a mechanical heart assist device.

These examples are not exhaustive as other stimuli come as well from education and from

clinical practice (surgical or intensive care procedures) where the request for hemodynamic data

analysis or trend prediction is strong and very specific. It is worthwhile to quote among the

possible applications of comprehensive circulatory modeling the study of specific environmental

conditions such as the effects of exercise, the absence or alteration of gravity, the effects of

diving.

Coming to the existing circulatory models, they are based essentially on two types of structures:

numerical and physical. The models are widely used to reproduce patho-physiological conditions

in research, education and in medical devices development and testing. Their role, beyond

education, is analyzing the experimental data and predicting the effect of care procedures

influencing, directly or indirectly, the circulatory system. Up to now, the models are computer

programs, if numerical, or specialized devices, modeling limited, strictly defined characteristics

of the circulatory system, if physical. Circulatory models may be therefore completely different

in the structure and complexity, privileging the reproduction of fluid-dynamics or volumetric

phenomena. This implies that results of simulations obtained by different investigators are often

incomparable, considerably diminishing the possible impact of the models on clinical practice.

Physical models of biological systems mechanics are generally made as physical analogues in the

form of parallel and in series connections of few fluidic lumped or distributed parameter resistors,

22

capacitances and tubes [73],[74],[75],[76]. They are of a rather simple structure and their

performance is strongly limited by the mechanical complexity, the difficult readjustment of

parameters, low long-term parameter stability and high costs. These features compromise the

evolution of models and their ability to support clinical application in a cost-effective manner.

The main limitation of a physical model is that it is always a mechanical realization of a

simplified mathematical model, while its main advantage is the possibility of its direct connection

to the devices to be tested and/or to measurement apparatus.

Numerical models, on the contrary, have a very flexible structure, with easily changeable

parameters and are much cheaper [77],[78],[79],[80]. They can have different structures (lumped

or distributed parameters, mono- and multi-dimensional) but can easily exchange data using, for

example, the multi-scale approach. However, numerical models cannot be directly connected to

devices (for assistance or measurement) working in a fluid environment. For example, a frequent

clinical interest concerns the optimization of working parameters of mechanical heart assistance

for various pathologies. The pathologies could be easily simulated in the numerical model of

cardiovascular or respiratory systems but the assist device cannot be connected to the numerical

model. A good example is again the IABP: the numerical solution of this problem implies the

necessity of using different mathematical models of the balloon in the aorta for each type and size

of the IABP. It would be difficult, if possible at all, to prove a required fidelity of these models

for different balloons and supporting devices.

Taking into account the present limitations of both physical and numerical models, a new type of

models, defined as hybrid (physical-numerical), is being developed [81],[82],[83]. Hybrid models

permit to merge numerical and physical models or devices optimizing their performance,

improving accuracy and reducing costs. In the hybrid simulators the advantages of numerical

models (flexibility, accuracy, low cost, stability) are connected with the main characteristic

feature of physical models, e.g. ability to interact directly with mechanical support devices or

measurement apparatus. It is to be remarked that hybrid models can make the model performance

independent of the structure opening the possibility to realize a modeling platform where the

structure (numerical, numerical-physical) can be easily changed without altering the model

performance and, what is more important, maintaining the possibility to compare the results in

any working condition.

23

1.5. RESPIRATORY SYSTEM MODELING

Marek Darowski, Tomasz Gólczewski

The human respiratory system like other physiological systems has a complex structure.

In order to acquaint with lungs physiology or pathology and with phenomena that takes place in

alveoli and airways we use specific tools. Measurements of flow and pressure inside the

respiratory system have a lot of limitations as they can not be invasive or because of ethical

issues. In fact, only upper airways flow and mouth pressure are usually available variables. Thus

models of the respiratory system are those specific tools that enable us to understand what is

going on inside the lungs, to help in diagnosis of lungs state or in assessment of the results of

treatment applied. There are two main research and clinical areas where models of the respiratory

system mechanics have been developed intensively during the last decades: spirometry and

mechanical ventilation of the lung. There are good reasons for this. The relatively common lung

pathology, Chronic Obstructive Pulmonary Disease (COPD) became one of the leading cause of

death recently. In order to better assess the lung patho-physiological state (COPD, asthma,

pulmonary fibrosis) a typical functional lung test, spirometry, should be supported by an

appropriate model of respiratory system mechanics.

The computer models used to simulate forced expiration during spirometry tests are morfometric,

complex models that take into account different mechanical properties of tracheal tree

generations (described by distributed or lumped parameters) and flow limitation

[84],[85],[86],[87],[88]. These models were developed assuming a symmetric [89] or an

asymmetric structure of the tracheal tree [90].

The respiratory system models used to simulate lungs mechanics during artificial ventilation were

usually based on much simpler, lumped parameter models proposed by Otis et al [91], Mead [92]

and Bates et al [93]. Otis took into account a parallel redistribution of gases in nonhomogenous

lungs, Mead included compliant airways into his model and Bates described a homogenous,

healthy lung with stress relaxation phenomenon in alveoli tissue.

The models proposed by Otis, Mead and Bates have now historical meaning. Recently,

researchers have concentrated their investigations on novel models of lung mechanics that would

better describe different patho-physiological state of lungs [88],[94],[95],[96].

In order to optimize ventilatory treatment of patients with lungs pathology new methods of

respiratory parameters estimation have been developed [97],[98],[99]. Patients with obstructive

24

airways are difficult for mechanical ventilation therapy. COPD is connected with expiratory flow

limitation, dynamic hyperinflation and rise in intrinsic end-expiratory pressure. Understanding

what are the basis of this pathology, its onset and development is of primary importance for

investigators nowadays.

Computer models concerning gas transport and exchange of gases have to take into account

different phenomena characteristic for both – respiratory and cardiovascular system. They may

help to investigate changes of gases concentrations in blood connected with some therapies [100]

or respiratory system control mechanisms [101].

Progress in both medicine and physiology requires experiments to test new methods of treatment

and support, to investigate scientific problems, verify new hypotheses, educate new staff

generation, etc. Although the final test, investigation or verification needs experiments on

animals or human beings (healthy volunteers or patients), an initial tests or verifications may be

performed with models: physical or computer (mathematical) ones. Such models might be

especially valuable in education.

The importance of the use of models increased recently because testing on patients is associated

with ethical problems.

Both mathematical (computer) and physical (e.g. mechanical) models have been developed

recently. Physical models are expensive (if they are not very simple) and difficult to adjust with

high fidelity.

Non-linear properties of the lungs are rather more difficult to be modeled by mechanical elements

than by a computer program. Moreover, the main advantage of computer models is the low cost

and easy adjustment of respiratory parameters. Indeed:

� computer models need not laboratories;

� there are no ethical problems with the use of them;

Because of the above reasons, to avoid high costs as well as ethical and economic problems

connected with experiments and investigations on animals or human beings (patients), different

computer models of RS have been developed.

Non–homogeneous mechanical properties of patient lungs are characteristic for respiratory

system pathology and create serious problems in their therapy by mechanical ventilation.

Distribution of ventilation and pressure in such complex structure is difficult to assess, also

because of difficulties with measurements. Modeling of lungs mechanics and simulation of

25

spontaneous breathing and ventilatory support may give some information and help to predict

these parameters changes according to applied ventilatory therapy. In this way, optimal

ventilatory strategy may be chosen among variety of ventilatory modes. This is only one of

potential applications of RS modeling. Medical personnel training and testing of new respirators

or new modes of ventilatory support are the next examples.

Constantly improving technology has created new types of simulators: virtual organs connected

to physical devices by means of virtual-to-real and real-to-virtual transducers. Such connection

enables researchers to utilize advantages of both computer and physical models. The above

forced us to consider a different approach that is testing physical respirators with the use of a

virtual RS. However, we have to be aware that not all models of RS can be treated as virtual RS.

26

1.6. REPRESENTATION OF CIRCULATORY-RESPIRATORY SYSTEM

INTERACTIONS

Tomasz Gólczewski, Marek Darowski

The chest contains both the respiratory system (RS) and a significant part of the cardiovascular

system (CS), i.e. the whole pulmonary circulation, left and right atriums and ventricles, great

vessels, and a part of the aorta. Therefore, cardiovascular system work is influenced by cyclic

thoracic pressure variations caused by the RS work. In particular, modeling of cardio-pulmonary

interaction has special meaning because non-physiological positive pressure, which appears in

the lungs during the artificial ventilation or ventilatory support, influences the hemodynamics

unfavorably [102],[103]. Respirators have been used for support of breathing for about 70 years.

Although many different modes of the support were tested during that time, some effects of the

positive thoracic pressure and airway pressure, being dangerous to the patient, could not be

completely eliminated. In particular, that fact concerns the adverse effect on the circulatory

system, which is manifested by a decrease of the venous return and pulmonary blood flow as well

as disturbance of filling of the heart ventricles. Thus, the existence of this mechanical interaction

suggests that modeling of CS cannot be really accurate without RS modeling unless a specific

problem is analyzed and the influence of RS may be neglected. For example, the interaction

between the respirator, RS, and CS should be considered each time when artificial ventilation or

support is applied in patients with heart disease.

On the other hand, both RS and CS realize the common task, i.e. they have to cooperate to

provide oxygen delivery to tissues and carbon dioxide removal. As the delivery and removal are

the main purpose of RS, the ventilation means both mechanical phenomena and airway gas

transfer as well as gas exchange causing blood oxygenation and decarbonation. Since the blood

oxygenation and decarbonation depend also on the pulmonary blood flow, they depend on the CS

mechanics. Certainly, oxygen and carbon dioxide transport to/from tissue with blood also depend

on the CS mechanics. For the above reasons, a comprehensive analysis of ventilation requires

models of RS and CS mechanics, airway gas transfer, gas exchange, and gas transport with blood.

Despite such meaning of the interactions between the RS and CS mechanics as well as gas

transfer and exchange, the number of models taking into account those interactions is relatively

small in comparison with the number of models simulating separately either RS or CS. Moreover,

27

usually at least one kind of the interactions is neglected in published papers: either mechanics of

one system or gas transfer and exchange is not taken into account. For example, the mechanical

interaction between both systems during breath-hold diving was simulated in detail by Fitz-

Clarke in his interesting paper [104], but neither gas transport nor exchange was analyzed. On the

other hand, both respiratory system mechanics and airway gas transfer as well as gas exchange

were taken into account in [105], however the mechanical interaction between the systems was

neglected. Moreover, in that model, gas is transported by a liquid, whereas the gas transports

‘itself’ during normal ventilation. In some other models (e.g. [106],[107],[108]), the

cardiovascular system mechanics is either simplified or neglected at all. In particular, cyclic

blood flow is replaced with the mean, constant flow equal to the cardiac output. For that reason,

for example, the models presented in [107],[108] ignore effects of superposition of periodic heart

work and cyclic changes of the thoracic pressure caused by ventilation. If, however, the thoracic

pressure is constant, as in a problem analyzed in [106], the blood flow may be also treated as

constant. Additionally, the gas transfer is not simulated in [107],[108], which causes that the dead

space ventilation could not be simulated, and in consequence the alveolar ventilation is the same

as the minute ventilation. Therefore, simulations of influence of the tidal volume or inspiratory

pattern on blood oxygenation may give incorrect results.

It seems that the cardio-pulmonary interactions were simulated most comprehensively in [109],

because the ensemble of models consists of both CS and RS mechanics models as well as a

model of gas exchange and transfer5.

5 Some results obtained with this ensemble are presented in the Chapter 6.5

28

1.7. A NEW APPROACH TO MODELING – HYBRID MODELS

Gianfranco Ferrari, Marek Darowski, Maciej Kozarski

Hybrid models are a particular class of circulatory and respiratory models, based on numerical

and physical models merging, aimed at reducing the costs, improving accuracy and offering the

possibility to cut animal experiments. A numerical model, circulatory or respiratory, determining

the performance and possibilities of the whole model, is in general the basis of any hybrid model

as it is shown in the example of Figure 9. There two interfaces permit the merging of a numerical

circulatory model with a mechanical heart assist device. The main goal of hybrid modeling is to

test the interaction of mechanical assist devices (VADs, prosthetic devices, respirators) with the

circulatory and respiratory systems. Training of medical professionals and education are among

the possible and important applications of hybrid modeling.

The problem of circulatory and respiratory modeling

Circulatory and respiratory models are or can be applied in research, education and prosthetic

devices/components testing and development. The structure and performance of any circulatory

or respiratory model is determined by the aim it is built for. The use of such models as tools, for

example to support clinical decision, implies their exploitation in environments where velocity of

Right HeartPulmonaryCirculation

CoronaryCirculation

LVADPhysicaldevice

Hybrid model

Interface Interface

Left HeartSystemic

Circulation

Numerical model

Figure 9 : block diagram depicting a possible application of hybrid modeling

29

execution and simplicity of use are the main requirements. On the other hand, the models used as

instruments of analysis have accuracy as their main feature and imply often to measure variables

hardly available, for example, in surgical and Intensive Care Unit (ICU) environments. So, an

important issue is that the model structure is able to face the challenge of quickness of response

and simplicity to use together with the possibility to adapt easily the model to the performance

requested by specific applications. Evidently, not all types of models can meet such requirements.

A possible approach to this problem may consist in developing basic comprehensive models

characterized by a high degree of flexibility. The efforts should be therefore focused on models

simulating the whole systems considering that an appropriate design and organization of the

model could permit, together with the possibilities offered by hybrid modeling, to respond

adequately to different needs.

Hybrid models: general considerations

In the case of circulatory system, the genesis of physical models was already discussed as a

response to the development of total artificial heart and, later, of mechanical heart assist devices.

Similar considerations are valid for the respiratory system.

It has been pointed out as well that, in spite of the existence of powerful and flexible numerical

simulation tools [65],[66],[85],[110] physical models are still relevant as training tools [72], or

for specific tests [72],[73],[74],[75],[76],[85] including mechanical assist devices. However, the

structure and functions of the physical models are strictly related or even tailored to the type of

tests to be performed. Moreover, physical models represent often a compromise between the

reduction of the mechanical complexity of the model and the accuracy of the investigation.

Finally, it is often hard or even impossible to use a physical model to answer some of the

questions arising from research as in the case of mechanical circulatory assistance when it is used

for heart recovery. For example, mechanical heart assist devices can be tested in relation to their

ability to reproduce given hemodynamic conditions: in this case, the simulation circuit could be

limited to a simple lumped parameter model. If on the contrary, the investigation has to be

extended to the mutual interaction among the device, the natural ventricle and the circulatory

network, the reproduction of the ventricular function and of the artero-ventricular interaction

become fundamental. It is not trivial to point out that this is the test condition to be fulfilled

especially when mechanical heart assistance is used for heart recovery. Accurate descriptions

exist for both the reproduction of the ventricular function and of the artero-ventricular interaction

30

[54]: they are the bases of several numerical models that, however, cannot be used when it is

necessary to test a physical device. A physical device testing implies in most cases the

development of physical models that are strictly application dependent and to some extent,

tailored to the application for which they have been developed.

Limiting the attention to comprehensive lumped parameter models that have a wide field of

applications in heart assist device (HAD) and lung support testing, research and training, physical

models can hardly overcome the problems of their cost and poor flexibility together with their

limited performances. It is however important to point out that in a physical model designed for

example to test a HAD, the section of the model to be represented physically is limited to the

areas of insertion of the device (or the prosthetic device if this is the case).

With this remark in mind, the proposed solution is to merge the characteristics and the flexibility

of numerical models with the possibilities offered by physical models as it is schematized in

Figure 10 where are evidenced the possible applications of the original systems along with the

possible applications of the resulting merged “hybrid” system. The concept of “hybrid”

circulatory and respiratory modeling was developed in the last years [81],[83],[111] to overcome

Applications: Device testingTraining and

EducationResearch

Support to clinical decision

Physical models(hydraulic,electrical,

pneumatic…)

Numerical models

Hybrid model

Applications: Device testingTraining and

EducationResearch

Applications: EducationResearch

Support to clinicaldecision

Figure 10 : possible applications of a hybrid system in comparison with the possible applications of the original numerical and physical

systems

31

the traditional dichotomy between numerical and physical circulatory models preserving at the

same time the best features of both of them.

Basically, it consists in merging numerical and physical models (they can be, for example,

electrical, hydraulic or pneumatic). In this way characteristics and flexibility of numerical models

are preserved along with the possibilities offered by physical models. Their interfacing is of

course the main problem as the numerical model can be easily changed or modified if necessary

and the physical section has to be chosen in relation to the tests to be performed.

Approaches to hybrid modeling

The general concept of hybrid modeling is based on the merging of physical and numerical

models but it can be applied in different ways (Figure 11). One possibility is to start from a

physical model (hydraulic, pneumatic) and transform it into a hybrid replacing some of its parts

with a numerical model. The second possibility is to start from a basic numerical model and

modify it replacing, when and where necessary, some of its parts with a physical (hydraulic,

electrical, pneumatic) model. The third possibility is to interface a whole numerical model to a

physical device. In fact, the first application of the concept of hybrid modeling consisted in the

insertion of a numerical model into the existing physical model [81]. This solution is valid to

improve the performance of a physical model but it is not the best from the point of view of

flexibility. On the contrary, merging a physical model into the existing numerical model [82],[83]

Physical model (hydraulic,electrical,

pneumatic…)

Numerical model

Numerical model

Hybridmodel

Physical model: hydraulic, electrical,

pneumatic,…

Figure 11 : approaches to hybrid modeling

32

offers the maximal flexibility along with the possibility to minimize the physical model reduced

in this way to the barest essential.

33

1.8. A NEW APPROACH TO MODELING – VIRTUAL ORGANS AND E-

LEARNING

Tomasz Gólczewski, Marek Darowski

Virtual organs and models

Depending on model application, two kinds of models might be distinguished. Models utilized in

medical practice are of the first kind. They are used to estimate – in the case of an individual, real

patient - the values of some parameters basing on measurement data. Since precise measurement

of many factors would be impossible in everyday practice and fitting a complex model to these

measurements would be a sophisticated mathematical problem, if possible at all, models of the

first kind have to be very simple with a few parameters. Thus, simplicity of such models is an

advantage rather than an imperfection.

It has to be stressed, however, that usually parameters of such models do not correspond exactly

to their 'physical' name. For example, such a parameter as airways resistance (Raw) described

with one number (the model in Figure 12a), e.g. that is used in the Proportional Assist

Ventilation6, does not exist, in fact. In real RS, airways resistance is nonlinear and changeable: it

depends on the thoracic (intrapleural) pressure, lungs volume, alveolar pressure as well as the rate

and direction of airflow7.

Figure 12 : Fundamental models of the respiratory system. a) the simplest model characterizing the most fundamental properties of RS, i.e. the airway

resistance (R) and compliance of RS (C); Pr – respirator, Ps – spontaneous breathing) b) Otis's model, which takes into account non-homogeneity of RS (parts of different time

constant) causing gas redistribution in lungs; c) Mead's model taking into account the compliance of airways (Caw);

6 See the Chapters 1.3 and 5.7 7 See the Chapter 3.2

34

d) Mount's model (developed by Bates), which takes into account visco-elastic properties of tissues and surfactant (Rt, Ct) causing the relaxation phenomenon.

Models of the second kind simulate particular phenomena or are used in analysis of such

phenomena. Figure 12b-d present the most known simple models of RS. The simplest,

“classical” RC model (Figure 12a) is still utilized for many purposes. A bit more complicated

models take into account inertial phenomena. The most complicated of these models make

possible to reproduce lung visco-elastic properties. Now, these models have rather educational

meaning only. Present models consist of much greater number of elements; some of them may be

nonlinear, etc. Although they are much sophisticated, the general idea is usually the same: models

are used to examine or analyze a particular problem or phenomenon defined before creation of a

model.

Constantly increasing abilities of computers caused that a new, third kind of models has

appeared: virtual organs. Such artificial organs may replace animals or human patients in several

applications, such as medical education or initial scientific experiments, for example. The

difference between virtual organs and 'normal' models can be expressed with the following

statement:

A model follows a problem that is intended to be analyzed, while a virtual organ is created to

analyze a whole class of problems which are not known or clearly defined before virtual organ

creation.

To be a virtual organ, a computer model has to be sufficiently complex to be able to behave

accurately under conditions not pre-determined precisely before the model building. For example,

properties of a new respirator tested are not known before tests, and thus an observer who

manipulates this respirator should not be able to recognize whether the respirator ventilates real

lungs or virtual ones to draw accurate conclusions. The above is even more clear if a model is

intended to be used as a virtual organ in medical education. Indeed, nobody can know which

‘experiments’ a student is going to perform but results of each possible experiment should be

correct to avoid wrong education.

To simulate cases, which had been not known before the virtual organ creation, a model has to be

both complex and specific. 'Normal' models may describe mathematically different physiological

phenomena, while the virtual organ has to reflect physical and physiological properties that are

35

the cause of those phenomena. For example, both the model of RS that is presented by Schuessler

et al. [112] and the virtual RS elaborated by Golczewski and Darowski [85] simulate airflow

limitation during forced expiration. However, in Schuessler’s model, Raw and the flow limitation

are described with two different formulas, which is some kind of consistency lack. In the virtual

RS, Raw is described in such a way that Raw means ‘normal’ resistance during normal breathing

and reflects flow limitation during forced expiration. Moreover, the formula that describes the

flow limitation in [112] is not derived from physiological properties; it is an assumed formula

with such values of parameters which give agreement between the phenomenon and the formula

results. In the virtual RS, Raw is derived from a physiological property that is the commonly

known experimental dependence of Raw on the lungs volume8.

Fitting parameters of a simpler model to measurement data is usually a goal of its use. In

particular, such fitting is the task of models of the first kind. In the case of virtual organs, such

fitting parameters to measurement data seems to be rather impossible. Indeed, such fitting in a

case of real organs is called diagnosing and is one of the two most fundamental, sophisticated

problems of medicine (treatment is the second one). Since virtual organs should be enough

complex to imitate real organs, diagnosing rather than fitting could be regarded in the case of

such models. Therefore, any application assuming fitting parameters of a virtual organ to

measurement data is rather pointless; direct diagnosis of real patients would be more rationale.

The meaning of virtual organs increases in the modern science. For example, Virtual

Physiological Human is one of three long-term strategic priorities recommended to the attention

of the European Commission by European Alliance for Medical and Biological Engineering and

Science (EAMBES). In the connection with the 7th Framework Program of the European

Community for research, technological development and demonstration activities (2007 to 2013

yr), EAMBES proposed to create virtual organs, which will be connected in the one virtual

human in the future [113].

Anticipating such global tendency, the virtual RS mentioned above was developed as a kind of

artificial organ for respirators and support methods testing [114],[115],[116] as well as a medical

education tool [117]. However, a stand-alone virtual RS would be too simple tool to replace the

real RS in more advanced research or education. Indeed, oxygen delivery to tissues and carbon

8 The derivation is presented in the Chapter 3.2

36

dioxide removal are the final goal of RS. Both the delivery and removal depend on work of the

cardiovascular system. On the other hand, the work of the cardiovascular system depends on

activity of RS because of influence of the thoracic and alveolar pressures on the pulmonary

circulation, heart work, and venous return. Additionally, the work of both system depends on gas

tensions in blood. Hence it appears that more advanced studies have to regard mechanical activity

of both systems as well as gas transport and exchange. Figure 13 illustrates a framework of such

studies.

Figure 13 : A framework of cardio-respiratory studies. As oxygen delivery and carbon dioxide removal are the fundamental goal of the cardio-

respiratory system, the model of gas transfer and exchange is the central point (it consists of modules of: AGT - airways gas transfer, GE - gas exchange, BGT - blood gas transport).

Respiratory system mechanics influences AGT, GE, and circulation. Cardiovascular system mechanics influences BGT and GE. A support of respiration and circulation can be both

simulated and realized with physical devices.

Virtual organs verification

A model can be treated as a virtual organ if it behaves as the real organ under different

conditions. In particular, all or almost all known fundamental physiological phenomena should be

observed. For that reason, accurate simulations of several such phenomena can be treated as

37

virtual organ verification. Such a kind of verification seems to be the most proper since if known

phenomena would be simulated inaccurately, a virtual organ could not be reliable when a new

unknown phenomenon is studied. Certainly, even the most accurate simulations of known

phenomena cannot be treated as a proof that results of unknown phenomenon study will be true

without any doubts. However, it is the property of all scientific theories: such a theory has to

describe the known knowledge correctly but its predictions should be always confirmed by means

of real, direct experiments. Considering the above, a virtual organ has to be verified like each

theory, i.e. it has to be checked

whether a theory called “the virtual organ” corresponds to all known facts or not.

The main feature of virtual reality is more or less impossibility of recognition of differences

between real and virtual objects. In the case of a virtual patient, the above means that it should be

difficult to recognize which results of a diagnostic examination concern real patients and which

have been obtained for a virtual patient. For example, as spirometry is the fundamental diagnostic

method in the case of RS, comparison between results of spirometry of the virtual RS and real

patients has been treated as a part of virtual RS verification9.

Virtual organs in e-learning

Virtual organs, as the other models, are useful in research, however, they may be of special

significance in medical education.

Education consists in learning facts, rules, and how to manipulate them. Learning may be

performed with Internet, which is the base of distal-learning being a kind of e-learning,

i.e. learning utilizing multimedial methods, especially those using computers. Recently,

the meaning of such methods increases very quickly. However, since medical education consists

also in practice with patients, it might seem that e-learning cannot be useful in medical education.

Nevertheless, since virtual patients can replace real patients partially, e-learning may be yet

possible in medical education, at least in an initial period.

9 Such virtual spirometry of the virtual RS is presented in the Chapter 5.4.

38

Application of virtual patients in education is of special significance because there are no ethical,

financial or legal problems when a student makes a mistake, even if he/she ‘kills’ such a patient.

Additionally:

• such a patient is easy to duplicate, and thus each student may have own patient,

• a student can choose a convenient place and time for learning,

• an instructor can simulate at each moment a disease that he want to discuss, while a real

patient suffering from a chosen disease may be not available in the lecture day.

In general, the virtual patient enables students either to ‘introduce’ a disease by themselves or to

manipulate the patient with a disease ‘introduced’ by an instructor. For example, a virtual organ

enables students to learn how a disease and its severity influence results of patient examination.

The Chapter 5.8 presents the Tgol.e-spirometry system [117] being such an application of

the virtual RS presented in [85]. That system is the virtual RS supplemented with a user interface

enabling medical students or instructors to ‘introduce’ obstructive and/or restrictive lungs disease

of various severity and observe results of the forced spirometry.

Figure 14 : An example of virtual patient use in medical education.

The following example of intensive care of a virtual patient may be another illustration of virtual

organs usefulness in professional advancement (Figure 14). In this example, a student should

manage long-term artificial volume controlled ventilation of an old patient who has to be turned

into the lateral position to avoid bed sore. The ventilation of such a patient may vary after his/her

position change, which leads to a fall of arterial blood oxygenation (Figure 15). A student should

find a method of profitable change of ventilation leading to blood oxygenation improvement.

39

Figure 15 : Arterial blood oxygenation falls after patient’s position change. The position of a virtual patient has been changed from the supine to the left lateral one. The

oxygenation is expressed with the percentage of oxygenated hemoglobin.

A student can observe at the computer screen that when position is changed, arterial blood

oxygenation falls significantly in two minutes. Student’s aim is to improve the oxygenation with:

• either an increase of the fraction of oxygen in the inspired air (FIO2)

• or an increase of the minute ventilation caused by an increase of the ventilation frequency or

tidal volume

• or change of ventilation method.

Probably, the student increases FIO2 as the first. In general, it would be justified since the minute

ventilation was correct before position change, and thus a problem with gas transfer or exchange

rather than with the volume controlled ventilation could be supposed. However, even significant

increase of FIO2 causes insufficient increase of the oxygenation (Figure 16). Further increasing

of toxic oxygen concentration seems to be not a good solution. Therefore, an increase of the

minute ventilation may be proposed by the student. However, if he/she tried to improve the

oxygenation with an increase of the ventilation frequency, it would not attain the goal. If he/she

tried to improve the oxygenation with an increase of the tidal volume, it would attain the goal not

before he/she increased the tidal volume two times (Figure 17).

40

Both too high FIO2 and too big VT are dangerous for lungs. Therefore, the student has to look for

better solution, and thus he/she should change the method of ventilation. If he/she chose the

independent ventilation, the oxygenation would be improved sufficiently with increase of neither

FIO2 nor VT.

The above exercise could be supplemented with some explanations or the student would have

possibility to perform some other simulations to find explanations by him/herself.

Figure 16 : Arterial blood oxygenation alteration after FiO2 increase.

Figure 17 : Arterial blood oxygenation alteration after tidal volume (VT) increase.

41

1.9. CONCLUSION

Circulatory and respiratory modeling have a long lasting history that was not always linear,

depending on the experimental and research demand. However the potential of modeling

approach to clinical and experimental needs has not been fully explored yet. The realization of

models that can be regarded as “virtual humans” is an ambitious scheme. However, having in

mind this goal, it is possible to pursue it in steps constructing models characterized by a high

degree of flexibility and modularity. The advantage lies in using the same models for different

applications raising the comparability and repeatability of results. The next chapters will address

this issue and will illustrate the model design and realization along with their possible

applications.

42

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