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.

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.

Modelling and simulation may become clinically applicable tools for detailed evaluation of the cardiovascular system and clinical decision-making to guide therapeutic intervention. Models based on pressure–volume relationship and zero-dimensional representation of the cardiovascular system may be a suitable choice given their simplicity and versatility. This approach has great potential for application in heart failure where the impact of left ventricular assist devices has played a significant role as a bridge to transplant and more recently as a long-term solution for non eligible candidates. We sought to investigate the value of simulation in the context of three heart failure patients with a view to predict or guide further management. CARDIOSIM© was the software used for this purpose. The study was based on retrospective analysis of haemodynamic data previously discussed at a multidisciplinary meeting. The outcome of the simulations addressed the value of a more quantitative approach in the clinical decision process. Although previous experience, co-morbidities and the risk of potentially fatal complications play a role in clinical decision-making, patient-specific modelling may become a daily approach for selection and optimisation of device-based treatment for heart failure patients. Willingness to adopt this integrated approach may be the key to further progress.

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.

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).

Mathematical modelling of the cardiovascular system (CVS) can help in understanding the complex interactions between both the ventricles and the septum. By describing the behaviour of the left (right) ventricular free wall, atria and septum using the variable elastance models, it is possible to reproduce their interactions. By relating the mechanical properties of both atria and both ventricles to the electrocardiogram (ECG) signal, it is possible to analyse the effects produced by different ECG delay on haemodynamic parameters. In the cardiovascular field, the incorrect interactions between septum and both ventricular free walls are based on many pathological conditions, i.e. symptomatic heart failure resulting from systolic dysfunction, ischemic dilated cardiomyopathy, and so on. The possible corrections that can be induced on the QRS complex duration in the ECG signal (i.e. cardiac resynchronisation therapy, CRT) can produce benefits improving the clinical status of the patient. The aim of this work was to evaluate, using our numerical simulator of the CVS, the effects induced on coronary blood flow (CBF) and aortic pressure using different ECG times, intra-ventricular and inter-ventricular delays. The results were obtained by reproducing the circulatory baseline and CRT conditions of seven patients described in literature. Haemodynamic simulated results are in accordance with literature data. Also the controversial results on CBF, in presence of CRT, are consistent with those described in the literature.