Gianfranco Ferrari

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.

A hybrid mock circulatory system: Testing a prototype under physiologic and pathological conditions

Hydraulic models of circulation are used to test mechanical heart assist devices and for research and training purposes. However, when compared with numerical models, they are rather expensive and often not sufficiently flexible or accurate. Flexibility and accuracy can be improved by merging numerical models with physical models, thus obtaining a hybrid model where numerical and physical sections are connected by an electrohydraulic interface.This concept is applied here to represent left ventricular function. The resulting hybrid model is inserted into the existing closed loop model of circulation. The hybrid model reproduces ventricular function by a variable elastance numerical model. Its interaction with the hydraulic sections is governed by measuring left atrial and systemic arterial pressures and computing the left ventricular output flow by the resolution of the corresponding equations. This signal is used to control a flow generator reproduced by a gear pump driven by a DC motor.Results obtained under different circulatory conditions demonstrate the behavior of the ventricular model on the pressure-volume plane and report the trend of the main hemodynamic variables.

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.

A modular computational circulatory model applicable to VAD testing and training.

Aim of this work was to develop a modular computational model able to interact with ventricular assist devices (VAD) for research and educational applications. The lumped parameter model consists of five functional modules (left and right ventricles, systemic, pulmonary, and coronary circulation) that are easily replaceable if necessary. The possibility of interacting with VADs is achieved via interfaces acting as impedance transformers. This last feature was tested using an electrical VAD model. Tests were aimed at demonstrating the possibilities and verifying the behavior of interfaces when testing VADs connected in different ways to the circulatory system. For these reasons, experiments were performed in a purely numerical mode, simulating a caval occlusion, and with the model interfaced to an external left-VAD (LVAD) in two different ways: with atrioaortic and ventriculoaortic connection. The caval occlusion caused the leftward shift of the LV p–v loop, along with the drop in arterial and ventricular pressures. A narrower LV p–v loop and cardiac output and aortic pressure rise were the main effects of atrioaortic assistance. A wider LV p–v loop and a ventricular average volume drop were the main effects of ventricular-aortic assistance. Results coincided with clinical and experimental data attainable in the literature. The model will be a component of a hydronumerical model designed to be connected to different types of VADs. It will be completed with autonomic features, including the baroreflex and a more detailed coronary circulation model.

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.

Reproduction of Continuous Flow Left Ventricular Assist Device Experimental Data by Means of a Hybrid Cardiovascular Model With Baroreflex Control

Long-term mechanical circulatory assistance opened new problems in ventricular assist device-patient interaction, especially in relation to autonomic controls. Modeling studies, based on adequate models, could be a feasible approach of investigation. The aim of this work is the exploitation of a hybrid (hydronumerical) cardiovascular simulator to reproduce and analyze in vivo experimental data acquired during a continuous flow left ventricular assistance. The hybrid cardiovascular simulator embeds three submodels: a computational cardiovascular submodel, a computational baroreflex submodel, and a hydronumerical interface submodel. The last one comprises two impedance transformers playing the role of physical interfaces able to provide a hydraulic connection with specific cardiovascular sites (in this article, the left atrium and the ascending/descending aorta). The impedance transformers are used to connect a continuous flow pump for partial left ventricular support (Synergy Micropump, CircuLite, Inc., Saddlebrooke, NJ, USA) to the hybrid cardiovascular simulator. Data collected from five animals in physiological, pathological, and assisted conditions were reproduced using the hybrid cardiovascular simulator. All parameters useful to characterize and tune the hybrid cardiovascular simulator to a specific hemodynamic condition were extracted from experimental data. Results show that the simulator is able to reproduce animal-specific hemodynamic status both in physiological and pathological conditions, to reproduce cardiovascular left ventricular assist device (LVAD) interaction and the progressive unloading of the left ventricle for different pump speeds, and to investigate the effects of the LVAD on baroreflex activity. Results in chronic heart failure conditions show that an increment of LVAD speed from 20 000 to 22 000 rpm provokes a decrement of left ventricular flow of 35% (from 2 to 1.3 L/min). Thanks to its flexibility and modular structure, the simulator is a platform potentially useful to test different assist devices, thus providing clinicians additional information about LVAD therapy strategy.

A new hybrid electro-numerical model of the left ventricle

The paper presents a new project of a hybrid numerical-physical model of the left ventricle. A physical part of the model can be based on electrical or hydraulic structures. Four variants of the model with numerical and physical heart valves have been designed to investigate an effect of a heart assistance connected in series and in parallel to the natural heart. The LabVIEW real time environment has been used in the model to increase its accuracy and reliability. A prototype of the hybrid electro-numerical model of the left ventricle has been tested in an open loop and closed loop configuration.

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.

Simulation of apical and atrio-aortic VAD in patients with transposition or congenitally corrected transposition of the great arteries

Purpose VADs could be used for transportation of the great arteries (TGA) and for congenitally corrected transposition (ccTGA) treatment. A cardiovascular numerical model (NM) may offer a useful clinical support in these complex physiopathologies. This work aims at developing and preliminarily verifying a NM of ccTGA and TGA interacting with VADs. Methods Hemodynamic data were collected at the baseline (BL) and three months (FUP) after apical (atrio-aortic) VAD implantation in a TGA (ccTGA) patient and used in a lumped parameter NM to simulate the patients physiopathology. Measured (MS) and simulated (SIM) data were compared. Results MS and SIM data are in accordance at the BL and at FUP. Cardiac output (l/min): BL_m = 2.9 ± 0.4, BL_s = 3.0 ± 0.3; FUP_m = 4.2 ± 0.2, FUP_s = 4.1 ± 0.1. Right atrial pressure (mmHg): BL_m = 21.4 ± 4.1, BL_s = 18.5 ± 4.5; FUP_m = 13 ± 4, FUP_s = 14.8 ± 3.6. Pulmonary arterial pressure (mmHg): BL_m = 56 ± 6.3, BL_s = 57 ± 2, FUP_m = 37.5 ± 7.5, FUP_s = 35.5 ± 5.9. Systemic arterial pressure (mmHg): BL_m = 71 ± 2, BL_s = 74.6 ± 2.1; FUP_m = 84 ± 9, FUP_s = 81.9 ± 9.8. Conclusions NM can simulate the effect of a VAD in complex physiopathologies, with the inclusion of changes in circulatory parameters during the acute phase and at FUP. The simulation of differently assisted physiopathologies offers a useful support for clinicians.