Application of a user-friendly comprehensive circulatory model for estimation of hemodynamic and ventricular variables.

PURPOSE: Application of a comprehensive, user-friendly, digital computer circulatory model to estimate hemodynamic and ventricular variables. METHODS: The closed-loop lumped parameter circulatory model represents the circulation at the level of large vessels. A variable elastance model reproduces ventricular ejection. The circulatory model has been modified embedding an algorithm able to adjust the model parameters reproducing specific circulatory conditions. The algorithm reads input variables: heart rate, aortic pressure, cardiac output, and left atrial pressure. After a preliminary estimate of circulatory parameters and ventricular elastance, it adjusts the amount of circulating blood, the value of the systemic peripheral resistance, left ventricular elastance, and ventricular rest volume. Input variables and the corresponding calculated variables are recursively compared: the procedure is stopped if the difference between input and calculated variables is within the set tolerance. At the procedure end, the model produces an estimate of ventricular volumes and Emaxl along with systemic and pulmonary pressures (output variables). The procedure has been tested using 4 sets of experimental data including left ventricular assist device assistance. RESULTS: The algorithm allows the reproduction of the circulatory conditions defined by all input variable sets, giving as well an estimate of output variables. CONCLUSIONS: The algorithm permits application of the model in environments where the simplicity of use and velocity of execution are of primary importance. Due to its modular structure, the model can be modified adding new circulatory districts or changing the existing ones. The model could also be applied in educational applications.

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.

A hybrid mock circulatory system: development and testing of an electro-hydraulic impedance simulator.

Mock circulatory systems are used to test mechanical assist devices and for training and research purposes; when compared to numerical models, however, they are not flexible enough and rather expensive. The concept of merging numerical and physical models, resulting in a hybrid one, is applied here to represent the input impedance of the systemic arterial tree, by a conventional windkessel model built out of an electro-hydraulic (E-H) impedance simulator added to a hydraulic section. This model is inserted into an open loop circuit, completed by another hybrid model representing the ventricular function. The E-H impedance simulator is essentially an electrically controlled flow source (a gear pump). Referring to the windkessel model, it is used to simulate the peripheral resistance and the hydraulic compliance, creating the desired input impedance. The data reported describe the characterisation of the E-H impedance simulator and demonstrate its behaviour when it is connected to a hybrid ventricular model. Experiments were performed under different hemodynamic conditions, including the presence of a left ventricular assist device (LVAD).

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.

Mono and bi-ventricular assistance: their effect on ventricular energetics.

When mono- and bi-ventricular mechanical assistance is used for heart recovery, its control strategy and circulatory variables affect ventricular energetics (external work-EW, oxygen consumption-VO2, cardiac mechanical efficiency-CME). This study is based on the data obtained in vitro and presents an analysis of the effects of the mono- and bi-ventricular mechanical assistance on ventricular energetics. The assistance was conducted on the principle of counterpulsation with atrio-arterial connection. It includes the following stages: 1) the characterisation of the isolated ventricle model in terms of EW, VO2 and CME as a function of the filling pressure and peripheral resistance, 2) modelling of left ventricular and pulmonary dysfunction, followed by left ventricular and bi-ventricular assistance. Experimental data enable us to draw the following conclusions: * in general, the greatest hemodynamic improvement does not correspond to the highest energetic improvement, * LVAD assistance deteriorates left ventricular CME while its effect on right ventricular energetics depends on the value of right ventricular elastance (Emax). Right ventricular CME is deteriorated by BVAD assistance irrespective of right Emax, * the energetics optimisation in bi-ventricular assistance is closely related to the right Emax, which could probably be a deciding factor in the choice of the assistance mode.

IABP assistance: a test bench for the analysis of its effects on ventricular energetics and hemodynamics.

IABP assistance is frequently used to support heart recovery, improving coronary circulation and re-establishing the balance between oxygen availability and consumption. Hemodynamic and energetic parameters (endocardial viability ratio, ventricular energetics) are used to evaluate its effectiveness which depends on internal (timing, balloon volume and position) and external factors (circulatory conditions). Considering short, medium and long-term effects of IABP, the first depends on its mechanical action, the latter on the changes induced in circulatory parameters. The analysis of the first is important because conditions for the onset of a virtuous cycle able to support ventricular recovery are created. Simulation systems could be helpful in this analysis for the implicit reliability and reproducibility of the experiments, provided that they are able to reproduce both hemodynamic phenomena and energetic relationships. The aim of this paper is to present a system originally developed to test mechanical heart assist devices and modified for IABP testing. Data reported here are obtained from in vitro experiments. A partial verification, obtained from the literature is presented.

A physical model of the human systemic arterial tree.

A physical model of the human arterial tree has been developed to be used in a computer controlled mock circulatory system (MCS). Its aim is to represent systemic arterial tree properties and extend the capacity of the MCS to intraortic balloon pump (IABP) testing. The main problem was to model the aorta simply and to accurately reproduce aortic impedance and related flow and pressure waveforms at different sections. The model is composed of eight segments; lumped parameter models are used for its peripheral loads. After the numerical simulation, the physical model was reproduced as a silicon rubber tapered tube. This rubber was chosen for its stability over time and the acceptable behaviour of its Young's modulus (Ey = 22.23 gf x mm(-2)) with different loads and in comparison with data from the literature (Ey approximately 20.4 gf x mm(-2)). The properties of each segment of the aorta were defined in terms of compliance, resistance and inertance as a function of length, radius and thickness. The variable thickness was obtained using positive and negative molds. Total static compliance of the aorta model is about 1.125 x 10(-3) g(-1) x cm4 x sec2 (1.5 cm3 x mmHg(-1)). Measurements were performed both on numerical and physical models (in open and closed loop configuration). Data reported show pressure and flow waveforms along with input impedance modulus and phase. The results are in good agreement with data from the literature.

A computer controlled mock circulatory system for mono- and biventricular assist device testing.

The clinical use of heart assist devices for heart recovery, implies the problem of their in vitro testing and training to use. In a mock circulatory system developed to this aim, the main problem is reproducing interaction among the device, the ventricle and the circulatory network. This can be analysed by the position, on the p-v plane, of the working point defined by the intersection between end systolic ventricular (ESPVR) and arterial elastance lines. The system developed on this basis, connectable to mono- and biventricular parallel assist devices, was a closed loop model including systemic and pulmonary circulation. The arterial trees were reproduced by two windkessels with adjustable peripheral resistance, and the Starling's law of the heart by a variable elastance model. The software controls and monitors circulatory parameters and variables. Results showed the behavior of the system with preload or afterload changes. Further, the reproduction of physiological, pathological (obtained by modifying slope and volume intercept of the ESPVR line) and LVAD assisted circulatory conditions was shown. The assistance effect was underlined by the changes in the ventricular work cycle and in hemodynamics variables. The evaluation of the effect of device control strategy on the ventricle and its energetics (on p-v plane) were among the main characteristics of this system, which ought to be further improved to test devices such as the IABP, which requires a different aortic model.

In vitro testing of a left ventricular assist device. Study of the effect of its control strategy on energetic relationships inside the left ventricle.

In this study an original left ventricular assist device is tested on an open loop modular physical circuit reproducing Starling's law of the heart to set an optimal control strategy for heart recovery. It is assumed that the goals of the assistance are reduction of oxygen consumption, external work and improvement of cardiac mechanical efficiency. The assistance is evaluated by the position of a working point on the characteristic surfaces of the ventricle defined by peripheral resistance, atrial pressure and selected variables pertaining to energy (pressure-volume area, external work and cardiac mechanical efficiency). In this frame an optimal assistance for heart recovery is a compromise among different requirements corresponding to a restricted set of control parameters values: driving pressure PZB = 35 kPa and timing values T1 and T2 (systole beginning and systole ending in relation to QRS complex and cardiac cycle duration T) T1 = 0.55.T and T2 = 0.73.T.