A Hybrid (Numerical-physical) Model of the Left Ventricle

Abstract

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.

Circulatory Modelling as a Clinical Decision Support and an Educational Tool

“…Among others, the modules sketched in Fig.1 contain a complex of simpler models of systemic and pulmonary circulation, 7-8 models of congenital heart defects 9 and of surgical procedures, 10 interfaces to respiratory models, now under development, models of heart assist devices (LVAD, RVAD, BVAD, IABP, BIV pacing), [11][12][13] models of autonomic controls (in this moment baroreflex and metabolic controls, the second one under development), 8,14 and interfaces for educational use of the platform. 8 The polymorphism of the structure has been achieved through implementation of the concept of hybrid modelling, [15][16][17][18][19] in cooperation with the Nałecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Science. In short, hybrid models permit to merge computational and physical models when and if necessary.…”

“…It was adopted for its adaptability to real time equation solving, necessary for hybrid applications. 15 The solution of lumped parameters model equations is rather simple as it is based on the application of the basic circuital laws. The heart modules are composed of atrial and ventricular modules.…”

A new hybrid (hydro-numerical) model of the circulatory system

“…In this instance, the above mentioned numerical part was connected to the physical one, representing the assist device -an intra-aortic balloon pump (IABP) or a left ventricular assist device (LVAD). Impedance transformers (converters) [3,4] play the role of interfaces connecting these two different signal environments and transfer signals in both directions. Interfaces can be connected in any place of the circulatory model; their role is to open "gates" to enable flow in both directions: from the physical to numerical part and back, e.g.…”

“…An adequate tool was found in a gear pump driven by an electrical servomotor playing the role of a voltage-controlled flow source as well as a flowmeter [3]. In the period of 2001-2005 we were the first and only team applying such "research technology" [3][4][5][6][7][8][9].…”

A modular computational circulatory model applicable to VAD testing and training

“…Some of them developed the idea to merge computational and hydraulic models [3][4][5] to test mechanical heart assist devices in conditions as close as possible to the real ones. Many attempts performed so far focused on the realization of single components merging computational and hydraulic features [3,[6][7][8]. Another possible approach is to use a comprehensive computational circulatory model, ''interfaceable'' if necessary with different environments, to create the prerequisites to test mechanical heart assist devices [9].…”