C. De Lazzari

A modular numerical model of the cardiovascular system for studying and training in the field of cardiovascular physiopathology

A modular numerical model of the cardiovascular system has been developed to reproduce the most important circulatory phenomena in terms of pressure and volume relationships. It is an easy tool to use, designed to be used with a friendly approach on any IBM or compatible personal computer: it offers a wide selection of graphical and numerical outputs and can be rearranged easily for a particular experiment. A set of subroutines related to different circulatory phenomena has been developed; they can be assembled easily together and communicate with each other by two variables. A full description of the existing subroutines is presented in this paper with three different application examples resulting from the rearrangement of the existing software modules: the first concerns the behaviour of the natural ventricle model itself and can be regarded as a ventricle stand-alone characterization test in terms of preload and afterload sensitivities, the second is related to the use of a pneumatic ventricle instead of the model of the natural ventricle, and the third is a full model of the cardiocirculatory system.

Computer simulation of haemodynamic parameters changes with left ventricle assist device and mechanical ventilation.

Left Ventricular Assist Device is used for recovery in patients with heart failure and is supposed to increase total cardiac output, systemic arterial pressure and to decrease left atrial pressure. Aim of our computer simulation was to assess the influence of Left Ventricular Assist Device (LVAD) on chosen haemodynamic parameters in the presence of ventilatory support. The software package used for this simulation reproduces, in stationary conditions, the heart and the circulatory system in terms of pressure and volume relationships. Different circulatory sections (left and right heart, systemic and pulmonary arterial circulation, systemic and pulmonary venous circulation) are described by lumped parameter models. Mechanical properties of each section are modelled by RLC elements. The model chosen for the representation of the Starlings law of the heart for each ventricle is based on the variable elastance model. The LVAD model is inserted between the left atrium and the aorta. The contractility of the heart and systemic arterial resistance were adjusted to model pathological states. Our simulation showed that positive thoracic pressure generated by mechanical ventilation of the lungs dramatically changes left atrial and pulmonary arterial pressures and should be considered when assessing LVAD effectiveness. Pathological changes of systemic arterial resistance may have a considerable effect on these parameters, especially when LVAD is applied simultaneously with mechanical ventilation. Cardiac output, systemic arterial and right atrial pressures are less affected by changes of thoracic pressure in cases of heart pathology.

Development of a hybrid (numerical-hydraulic) circulatory model:Prototype testing and its response to IABP assistance

Merging numerical and physical models of the circulation makes it possible to develop a new class of circulatory models defined as hybrid. This solution reduces the costs, enhances the flexibility and opens the way to many applications ranging from research to education and heart assist devices testing. In the prototype described in this paper, a hydraulic model of systemic arterial tree is connected to a lumped parameters numerical model including pulmonary circulation and the remaining parts of systemic circulation. The hydraulic model consists of a characteristic resistance, of a silicon rubber tube to allow the insertion of an Intra-Aortic Balloon Pump (IABP) and of a lumped parameters compliance. Two electro-hydraulic interfaces, realized by means of gear pumps driven by DC motors, connect the numerical section with both terminals of the hydraulic section. The lumped parameters numerical model and the control system (including analog to digital and digital to analog converters) are developed in LabVIEW™ environment. The behavior of the model is analyzed by means of the ventricular pressure-volume loops and the time courses of arterial and ventricular pressures and flows in different circulatory conditions. A simulated pathological condition was set to test the IABP and verify the response of the system to this type of mechanical circulatory assistance. The results show that the model can represent hemodynamic relationships in different ventricular and circulatory conditions and is able to react to the IABP assistance.

Modelling of cardiovascular system: development of a hybrid (numerical-physical) model.

Physical models of the circulation are used for research, training and for testing of implantable active and passive circulatory prosthetic and assistance devices. However, in comparison with numerical models, they are rigid and expensive. To overcome these limitations, we have developed a model of the circulation based on the merging of a lumped parameter physical model into a numerical one (producing therefore a hybrid). The physical model is limited to the barest essentials and, in this application, developed to test the principle, it is a windkessel representing the systemic arterial tree. The lumped parameters numerical model was developed in LabVIEW™ environment and represents pulmonary and systemic circulation (except the systemic arterial tree). Based on the equivalence between hydraulic and electrical circuits, this prototype was developed connecting the numerical model to an electrical circuit - the physical model. This specific solution is valid mainly educationally but permits the development of software and the verification of preliminary results without using cumbersome hydraulic circuits. The interfaces between numerical and electrical circuits are set up by a voltage controlled current generator and a voltage controlled voltage generator. The behavior of the model is analyzed based on the ventricular pressure-volume loops and on the time course of arterial and ventricular pressures and flow in different circulatory conditions. The model can represent hemodynamic relationships in different ventricular and circulatory conditions.

Mock circulatory system for in vitro reproduction of the left ventricle, the arterial tree and their interaction with a left ventricular assist device

A modular physical circuit for testing monoventricular and biventricular heart assist devices (HAD) is under development. The modules now available are assembled in an open-loop circuit and reproduce the function of the left ventricle and the systemic arterial tree. The left ventricle model reproduces Starlings law of the heart and can be easily controlled to modify other parameters such as contractility and timing (i.e. heart rate and systole/diastole ratio). This circuit, in connection with a left ventricular assist device (LVAD), can be used to evaluate the LVAD performance, its effect on the circulatory system and as a training system. This paper is devoted to a description of the circuit and of its interaction with a LVAD, which is analysed after the simulation of a low contractility pathology of the ventricle. Results obtained in these experiments are reported.

A desk-top computer model of the circulatory system for heart assistance simulation: effect of an LVAD on energetic relationships inside the left ventricle

The study of the interaction between a pneumatic left ventricle assist device (LVAD), driven with different control strategies, and the cardiovascular system is the subject of this paper. It is performed by a modular numerical model of the cardiovascular system connected to a numerical model of the LVAD. The circulatory system is simulated by a lumped parameter numerical model. The ventricle is represented by a time-varying elastance model to reproduce the Starling law of the heart. The effect of the LVAD on the cardiovascular system is evaluated, on the left ventricle alone, by an open-loop circuit consisting of the models of the ventricle, the LVAD and the arterial tree. The analysis is performed in terms of energy variables (such as external work and oxygen consumption and cardiac mechanical efficiency versus control strategy. The LVAD is driven by different control strategies: a fixed heart rate (with different delays from the onset of the natural ventricle contraction) and a variable heart rate.

Computer simulation of coronary flow waveforms during caval occlusion.

OBJECTIVESnMathematical modeling of the cardiovascular system is a powerful tool to extract physiologically relevant information from multi-parametric experiments. The purpose of the present work was to reproduce by means of a computer simulator, systemic and coronary measurements obtained by in vivo experiments in the pig.nnnMETHODSnWe monitored in anesthetized open-chest pig the phasic blood flow of the left descending coronary artery, aortic pressure, left ventricular pressure and volume. Data were acquired before, during, and after caval occlusion. Inside the software simulator (CARDIOSIM) of the cardiovascular system, coronary circulation was modeled in three parallel branching sections. Both systemic and pulmonary circulations were simulated using a lumped parameter mathematical model. Variable elastance model reproduced Starlings law of the heart.nnnRESULTSnDifferent left ventricular pressure-volume loops during experimental caval occlusion and simulated cardiac loops are presented. The sequence of coronary flow-aortic pressure loops obtained in vivo during caval occlusion together with the simulated loops reproduced by the software simulator are reported. Finally experimental and simulated instantaneous coronary blood flow waveforms are shown.nnnCONCLUSIONSnThe lumped parameter model of the coronary circulation, together with the cardiovascular system model, is capable of reproducing the changes during caval occlusion, with the profound shape deformation of the flow signal observed during the in vivo experiment. In perspectives, the results of the present model could offer new tool for studying the role of the different determinants of myocardial perfusion, by using the coronary loop shape as a sensor of ventricular mechanics in various physiological and pathophysiological conditions.

The influence of left ventricle assist device and ventilatory support on energy-related cardiovascular variables

One of the main purposes in using Left Ventricle Assist Devices (LVAD) to assist recovery in patients with heart failure, is to reduce the external work (EW) of the left natural ventricle. The simultaneous presence of mechanical ventilatory support can affect the value of this variable. The aim of our computer simulation was to trace the influence of LVAD on EW, cardiac mechanical efficiency (CME) and pressure volume area (PVA) in the presence of ventilatory support. Pathological conditions of the heart were reproduced. Peripheral systemic arterial resistance (Ras) was also changed to model physiological and pathological states. The influence of mechanical ventilation was introduced by changing levels of mean thoracic pressure. In this way we were able to predict changes of EW, CME and PVA in both ventricles, during ventilatory (mechanical) and cardiovascular (LVAD) support. Our simulation showed that positive thoracic pressure seems to affect the energy-related cardiovascular variables and should be taken into account during the assessment of LVAD effectiveness. Pathological changes of systemic peripheral resistance have a considerable effect on EW, CME and PVA of left ventricle. On the other hand energy-related parameters of the right ventricle are not especially affected by changes in systemic peripheral resistance.

Study of systolic pressure variation (SPV) in presence of mechanical ventilation.

Systolic pressure variation (SPV) and its components (dUp and dDown) have been demonstrated to be of interest in assessing preload in mechanically ventilated patients. The aim of this paper is to analyse the sensitivity of these variables to preload and volemic changes during mechanical ventilation in different conditions of the cardiovascular system. Computer simulation experiments have been done using a modular lumped parameter model of the cardiovascular system. The effect of mechanical ventilation has been reproduced operating on intrathoracic pressure. Experiments have been performed varying preload through filling pressure. Sensitivity of SVP, dUp and dDown is described varying separately left ventricular elastance (Ev), systemic arterial resistance (Ras) and systemic arterial compliance (Cas). The sensitivity of SPV and dDown to preload and filling pressure is appreciable for high values of Ev and for a wide variation of Ras. Preliminary clinical data concerning the three parameters show good correlation with simulation results.

Ventricular energetics during mechanical ventilation and intraaortic balloon pumping?computer simulation

Computer simulation of a cardiovascular system enabled us to predict the effects of simultaneous application of mechanical ventilation (MV) and intraaortic ballon pumping (IABP) on ventricular energetics. External work (EW), pressure-volume area (PVA), potential energy (PE) and cardiac mechanical efficiency (CME) were calculated. Numerical simulation showed that changes of positive intrathoracic pressure have a considerable effect on left and right ventricular EW, PE, PVA and CME, whether IABP is used or not. The right ventricular energetics was much less influenced by systemic resistance (Ras) changes than the left ventricular one. Simultaneous application of IABP and MV showed a remarkable effect on left ventricular EW. The net result was reversed sensitivity to pulmonary resistance (Rap) and reduced sensitivity to Ras. PVA was generally reduced, while CME is increased by simultaneous presence of IABP and MV. The sensitivity of CME to Rap and Ras variation was diminished in this situation.