A Hybrid Mock Circulatory System: Testing a Prototype Under Physiologic and Pathological Conditions GIANFRANCO FERRARI,* CLAUDIO DE LAZZARI,* MACIEJ KOZARSKI,† FABRIZIO CLEMENTE,* KRYSTYNA G´ ORCZY ´ NSKA,† RITA MIMMO,* ELIANA MONNANNI,* GIANCARLO TOSTI,* AND MARCO GUARAGNO* 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 accu- rate. 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 nu- merical model. Its interaction with the hydraulic sections is governed by measuring left atrial and systemic arterial pres- sures 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 he- modynamic variables. ASAIO Journal 2002; 48:487–494. H ydraulic models of circulation were developed in conjunc- tion with studies of the total artificial heart throughout the 1960s and 1970s. Their further development was limited by their cost and mechanical complexity in comparison with numerical models of the circulatory system that are also more flexible and accurate. 1,2 There are, however, specific applications where the use of physical models is necessary or suitable, such as mechanical assistance of circulation, when these models can be used for specific tests 3–8 or as training tools. 9 The structure and functions of hydraulic models of circula- tion are often a compromise between the reduction in me- chanical complexity of the model and the accuracy of the investigation, and they depend, of course, on the type of tests to be performed. Specifically, mechanical heart assist devices are usually tested to evaluate their behavior 6,7 in relation to given hemo- dynamic conditions. In this case, if fluid dynamic problems are disregarded, the simulation circuit can be a simple, lumped parameter model. If the investigation has to be extended to the mutual interaction between the device, the natural ventricle, and the circulatory network, the central problem is reproduc- tion of ventricular function and of the artero-ventricular inter- face. Coupling between ventricular and arterial functions is reliably described by the end systolic pressure-volume rela- tionship (ESPVR) and effective arterial elastance (EAE) lines, which are functionally connected to the reproduction of the most important of the self regulatory mechanisms of the ven- tricle: Starling’s law of the heart. To reproduce it, the variable elastance model 10 is usually adopted. The model, in its simpler form, can be described by the following equation: p v (t)=E(t)(v v (t)-V 0 ) (1) where p v (t) and v v (t) are intraventricular pressure and volume, respectively, and E(t) is the time varying elastance. Implemen- tation of equation 1 in a physical model implies a complex control system where pressure is the controlled variable. The approach proposed here to get around this problem is to merge the characteristics and the flexibility of numerical mod- els with the possibilities offered by physical models. The result is a hybrid model where numerical and physical sections are connected by an electrohydraulic interface. 11 The latter is, of course, the main problem, as the numerical model can easily be changed or modified if necessary, and the physical section has to be chosen relative to the tests to be performed. Specif- ically, in the closed loop model of circulation presented in this article, the hybrid model, consisting of the variable elastance model (numerical) and the electrohydraulic interface, repro- duces left ventricular function and interfaces with the model (physical) of circulation, which includes the pulmonary circulation. Materials and Methods Circulatory System Model and Basic Relationships Functional tests of circulatory mechanical assistance and prosthetic devices usually concern their fluid dynamic prop- erties or their influence on selected circulatory or ventricular variables. In the case of the latter, the analysis affects ventric- ular energetics and blood volume distribution inside the cir- culatory system. A lumped parameter model can be used to achieve this goal. In this study we used a model corresponding to the electric analog reproduced in Figure 1 (nomenclature in Table 1). This From the *Institute of Biomedical Technologies, CNR, Rome, Italy, and the †Institute of Biocybernetics and Biomedical Engineering, PAN, Warsaw, Poland. Submitted for consideration October 2001; accepted for publication in revised form April 2002. Correspondence: Dr. GianFranco Ferrari, Istituto di Tecnologie Bio- mediche CNR, Reparto di Ingegneria Cardiovascolare, Viale C. Marx 43, Rome, Italy 00137. DOI: 10.1097/01.MAT.0000026350.66193.B0 ASAIO Journal 2002 487