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Computer simulation of cardiac mechanics

Pacher Armando; Lombardo Roberto

Facultad de Ingeniería - Bioingeniería
Universidad Nacional de Entre Ríos
Paraná, Entre Ríos, Argentina

Abstract
Objectives
Material and Methods
Results
Discussion
Conclusions
Bibliography

Abstract
Objectives: To design and to develop a computer simulation of the cardiovascular system behavior in order to be applied in teaching cardiac mechanics.
Material and Methods: Automatism and conduction; cardiac chambers and valves; systemic arterial, capillary, and venous, coronary and pulmonary territories; and systemic arterial pressoreceptors were simulated using mathematical equations, and Visual Basic as programming language. All were simplified in order to allow they execution in real time.
Results: The program works in PCs. It operates in real time, and continually and simultaneously displays pressure, volume, volumetric flows, and derived curves; left ventricular stress, left and right ventricles pressure/volume loops; left ventricular stress/volume loop, arterial pressure/diameter loop, electrocardiogram, end of systole straight line, end of diastole and numerical values of significant variables function, and indexes of left ventricular diastolic and systolic function. It is possible to access simulations in basal conditions, and when there are acute or chronic modifications (changes either isolated or related in inotropism, relaxation, distensibility, action of pericardium, action of drugs and calcium, preload, peripheral resistance, elasticity of great vessels, mitral and aortic valve diseases, isovolumic cycles with fixed and variable volumes, acute coronary occlusion, step by step simultaneous generation of curves, loops and electrocardiogram). It was used as a pedagogical tool, which complemented teaching in pre and postgraduate courses on cardiac mechanics physiology and pathophysiology. Discussion: Computer simulation allows learning and practicing without emotional and time pressures, out of situations of crisis, with a minimum cost. This makes possible a wide use of it, being, as well, a complement to conventional methodology.
Conclusion: Programs showing their results in real time, and simultaneously by loops of pressure/volume, loops of stress/volume, and curves of pressure, fluxes, volumes, and instant stress, along the cardiac cycle, were not detected.

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Objectives:

To design and to develop a computer simulation of the cardiovascular system behavior to be applied in teaching cardiac mechanics, that simulates basal active and passive characteristics, shows in a continuos way curves in function of time, pressure/volume, stress/volume loops and quantitative values, simulates miocardiac, valvular, structural, acute and chronic alterations, reproduces experimental results, works in personal computers (PC) and used in the physiological and physiopatological teaching.

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Material and Methods:

For the simulation of the different characteristics of the cardiovascular system mathematical equations that were integrated in an algorithm, were used. MS visual Basic was used as a programming language. Simplifications to allow its execution in real time in computers of ample access, were made.

Automatism and conduction , cardiac valves (MV, AV, TV, PV), cardiac chambers (LA, LV, RA, RV) were simulated. The active characteristics (contractility, relaxation), the passive viscoelastics (distensibility) and its adjustment to the system were simulated in the chambers. Arterial territories, sistemic, venous, coronary, and pulmonar capillaries, and sistemic arterial presoreceptors were simulated. Instant value calculus((t) ) of automatism and conduction, stiffness, volumen, volumetric flow, pressure, stress LV, were programmed to be done every 5 miliseconds in each sector and calculate the indexes of LV systolic and diastolic function in each cycle.

Results:

The simplifications made in the design of this simulation allowed to obtain a programme which calculates and draws in real time in personal computers of ample access (PC-IBM Compatible from a minimun configuration of 386 with a RAM of 4 MB), and from 3 1/2" diskettes.

basic.gif (19361 bytes)
Fig 1: Inicial screen of curves and loops, with menu bars, right superior chart of numerical values, curves (from up to down)
LV volume, pressures of aortic root, left auricle and ventricle, ECG, LV P/V loop, end-systolic straight line and end-diastolic
function. Basal conditions.

 

They are drawn in simultaneous way in continuos curves (Fig. 1, Fig. 2 and Fig. 3) in function of the time of:

        Pressures (LA, LV, aortic root, nine systemic arterial segments, RA, RV, root of pulmonar artery)
        Volumes (LA, LV, RA, RV),
        LV instant stress,
        Volumetric flows (MV, AV, TV, PV, pulmonar venous, coronary [ LAD, RCA}),
        Derivatives (LV dP/dt, LV dS/dt ),
        Stiffness (LV, RV).

Loops of:

        Ventricular pressure/volumen (LV, RV),
        Arterial pressure/diameter,
        Left ventricular stress/volumen 

 Numerical values:

         LV: EDP, EDV, ESV, SV, EV, end-systolic P/V relation, P/V area, +dP/dtmax , +dP/dtmax /P, Stress (end-diastolic, start ejection, maximun,
        end ejection), +dP/dtmax , -dP/dtmax , +dP/dtmax/-dP/dtmax , +dP/dtmax /P, Tau, Time 1/2 of relaxation,
        twelve areas of volumenes,

P/V relationships:

        LV end-systolic,
        LV end-diastolic,

LVStress.gif (20704 bytes)

Fig. 2: Similar to Fig.1, adding LV instant stress curve and LV stress/volumen loop. The curve of aortic pressure
was suppressed in the 3rd and 4th cycle to facilitate the analysis of the instant stress curve. Basal conditions.

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Fig.3: Similar to Fig. 2, adding (from up to down): LV dP/dt, volumetric flow of left descendent anterior
coronary artery, MV volumetric flow, RVpressure, RV pressure. Basal conditions

It is possible to access simulations in basal conditions and in front of acute and chronic modifications (isolated or related changes in inotropism, relaxation, distensibility, action of pericardium, action of drugs and calcium, preload, periferal resistance, elasticity of great vessels, mitral and aortic valve diseases (acute and chronic), isovolumic cycles with fixed and variable volumes, acute coronary occlusion, step by step simultaneous generation of curves, loops and electrocardiogram). An option (Basal > keep the screen) allows to compare the consequences of the isolated and related changes with the basal conditions (Fig. 4 Fig. 5Fig. 6 and Fig. 7).

Pump Failure.gif (17158 bytes)
Fig 4: Screen of loops, with P/V of LV (black) and RV (red) simultaneous graphics of loops in three situations:
basal , moderate and severe diminishing of left ventricular contractility. The Basal > keep the screen option
was used for the comparison of the situations. Numerical values chart of basal situation.


MR.gif (19535 bytes)
Fig.5: Simulation of mitral acute and severe insufficiency. Numerical values chart of basal situation.

distens.gif (19836 bytes)
Fig.6: Isolated modification of the left ventricular distensibility. Numerical values chart of basal situation.

Several.gif (9829 bytes)
Fig.7: Different options examples: A. Enlargement of the pressures scale and
a higher velocity of sweeping to analyze LV and LA diastolic pressures; B.
Isovolumetric cycles generation, C. Chronic valvular aortic stenosis and basal
conditions; D. LV P/V loop changes during the balloon blowing up in the
coronary angioplasty; E. LV and RV P/V loops in basal conditions and in
isolated diminishing of left ventricular contractility; F. LV and RV P/V loops
in an ventricular septal defect without significant pulmonary hypertension.

It was used as a complementary pedagogical tool for teaching of physiological and pathophysiological in cardiac mechanics in pre and postgraduated courses.

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Discussion:

Computer simulations allow learning and practising without emotional and time pressures, out of situations of crisis, with a minimum cost. This makes possible a wide use of it, being, as well, a complement to conventional methodology. The available programs generally do not work in real time ( simultaneous graphic and calculation ), except when using a high complexity computer, do not show curves and loops simultaneously, neither instant stress nor stress/volume loops and simulations and changes options are limited.

This simulation is aimed to be used by teachers as pedagogical tool for the knowledge of the cardiovascular mechanic functioning in basal conditions and in front of pathological cases, putting into practice since the possibilities to generate step by step the different curves in function of time and loops of pressure/volume and loops of stress/volume, up to the simulation of chronic and acute pathologies. This program was used in theory as well as in theory-practical activities with Medicine (Physiology), Bioengineering (Physiology and Physiopathology ) students and with assistants to Cardiology Post-grade courses (Echocardiography).

In spite the validity of the model being part of the process of modelling, in the case of simulations using for teaching purposes the main target is not contrasting and it is believed that making simplifications to allow its wide utilization originates responses that diminishes its accuracy. It is considered that the differences between the obtained answers to this simulation and those of the known experimental results (end-systolic straight line in all the conditions of simulation, modification of the slope only and not of the ordinate at the beginning of the end-systolic straight line in front of contractile state changes; after-load changes that do no modify neither the slope nor the one ordinate at the beginning of the end -systolic straight line; secondary changes to ischemia that modify only the slope of the end-systolic straight line; simplification of the aortic ventricular coupling; velocity of relaxation non depending on the after-load, peripheral responses limited to changes in the arteriolar resistance; discreet and static changes of frequency) or the expected ones (right and left auricular and right ventricular variables of less complexity than the left ventriculars, drawings in continuous and non-discreet intervals) without affecting its utilization as a pedagogical tool. These known limitations are listed in a window of the programme to be also known and assumed by the instructor as well as his students. In the revision made on the literature programmes with these characteristics were not found.

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Conclusions:

Programmes showing their results in real time, and simultaneously by loops of pressure/volume, loops of stress/volume, and curves of pressure, fluxes, volumes, and instant stress, along the cardiac cycle, were not detected. Its value as a complementary pedagogical tool should be analyzed through a comparative protocol.

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Bibliography

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Questions, contributions and commentaries to the Authors: send an e-mail message (up to 15 lines, without attachments) to heartfail-pcvc@pcvc.sminter.com.ar , written either in English, Spanish, or Portuguese.

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Update
Dic/23/1999