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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.

Emaxis an important parameter to evaluate the state of the heart and of its contractile capability. Its determination is not easy and rather inaccurate: However, it can be clinically relevant during mechanical and/or pharmacological heart assistance as it can suggest how to modify pharmacological therapy or the control strategy of the device.Aim of this study is to develop a method based on ventricular energetics to evaluate Emax. If arterial elastance line slope is modified, for example by a slight peripheral resistance increase, Emax(assuming that it is constant) can be evaluated computing the energy transferred to the arterial elastance before and after the change. The corresponding equation contains known or easily computable variables and the difference ? between end diastolic volume and ventricular rest volume. If the ratio of s before and after the disturbance is near to 1, the equation returns a fair estimation of Emax. The method was tested in vitro, in different circulatory conditions, using an open loop numerical model of the circulation built out of a variable elastance model of the ventricle connected to a modified windkessel representing the systemic arterial tree.The results obtained in in vitro experiments suggest clinically testing this method.

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 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).

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.

Hydraulic models of the circulation are used to test mechanical devices and for training and research purposes; when compared to numerical models, however, they are not flexible enough and rather expensive. The solution proposed here is to merge the characteristics and the flexibility of numerical models with the functions of physical models. The result is a hybrid model with numerical and physical sections connected by an electro-hydraulic interface - which is to some extent the main problem since the numerical model can be easily changed or modified.The concept of hybrid model is applied to the representation of ventricular function by a variable elastance numerical model. This prototype is an open loop circuit and the physical section is built out of a reservoir (atrium) and a modified windkessel (arterial tree). The corresponding equations are solved numerically using the variables (atrial and arterial pressures) coming from the physical circuit. Ventricular output flow is the computed variable and is sent to a servo amplifier connected to a DC motor-gear pump system. The gear pump, behaving roughly as a flow source, is the interface to the physical circuit. Results obtained under different hemodynamic conditions demonstrate the behaviour of the ventricular model on the pressure-volume plane and the time course of output flow and arterial pressure.

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, VO2and 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 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 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·mm–2) with different loads and in comparison with data from the literature (Ey≈ 20.4 gf·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 1.125·10–3g–1cm4·sec2(1.5 cm3·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.

The aim of this study is the evaluation of end systolic ventricular elastance trend (as a measure of heart contractility) by hemodynamic variables available in intensive care units or during heart surgery: heart rate, cardiac output, left atrial, mean and diastolic arterial pressure. Its basic assumption is the description of ejection as the interaction between variable left ventricular and arterial compliances (reciprocal of the corresponding elastances) connected in parallel. As pressure is the same in each compliance at systole beginning and ending, ventricular elastance can be estimated by assuming that energy variation is the same on both compliances. The algorithm has been tested on a numerical simulator of the circulatory system and on six sheep at basal conditions and during drug infusion. Correlation function in numerical simulation, between true and computed ventricular elastance (range 0.45÷5 mm Hg-cm-3), yields 0.985. In vivo comparison between computed ventricular elastance trend and ventricular dp/dt trend yields a correlation function ranging between 0.87 and 0.99.The result of the algorithm cannot be assumed to be Emaxvalue. However, it can be considered a contractility index as it closely follows any change in dp/dt. It can be computed by simple calculations and needs no variables other than those usually measured in intensive care. It allows the extrapolation of useful information for evaluating the trend in heart contractility and for setting up a control strategy for mechanical or pharmacological assistance during heart recovery.

An electromagnetic actuator to substitute ventricular function presents some advantages compared with different energy converters. The drastic reduction of the moving parts leads to greater reliability and an accurate control system can be set up. Its major limitations concern weight, heat dissipation and, finally, the overall pump efficiency which is usually rather low. We investigated the possibility of using magnetic fluids in an electromagnetic actuator. Limitations intrinsic to the magnetic fluids prevent their being used as pumping elements but they can be useful to increase the pump efficiency by reducing losses in the magnetic circuit. A remarkable increase in pump efficiency was attained. It is necessary to point out that in designing the electromagnetic actuator the focus was on the pump efficiency with and without the magnetic fluids more than on its performance.