A bond graph model of the cardiovascular system

Abstract

The study of the autonomic nervous system (ANS) function has shown to provide useful indicators for risk stratification and early detection on a variety of cardiovascular pathologies. However, data gathered during different tests of the ANS are difficult to analyse, mainly due to the complex mechanisms involved in the autonomic regulation of the cardiovascular system (CVS). Although model-based analysis of ANS data has been already proposed as a way to cope with this complexity, only a few models coupling the main elements involved have been presented in the literature. In this paper, a new model of the CVS, representing the ventricles, the circulatory system and the regulation of the CVS activity by the ANS, is presented. The models of the vascular system and the ventricular activity have been developed using the Bond Graph formalism, as it proposes a unified representation for all energetic domains, facilitating the integration of mechanic and hydraulic phenomena. In order to take into account the electro-mechanical behaviour of both ventricles, an electrophysiologic model of the cardiac action potential, represented by a set of ordinary differential equations, has been integrated. The short-term ANS regulation of heart rate, cardiac contractility and peripheral vasoconstriction is represented by means of continuous transfer functions. These models, represented in different continuous formalisms, are coupled by using a multi-formalism simulation library. Results are presented for two different autonomic tests, namely the Tilt Test and the Valsalva Manoeuvre, by comparing real and simulated signals.

Figure 1

Example of a simple Bond Graph model of an RC circuit.

Figure 2

Schematic representation of the processes that lead to ventricular contraction and circulation of blood.

Figure 3

Bond Graph model of the ventricle and its coupling with the BR action potential model.

Figure 4

Bond Graph model of a vessel segment.

Figure 5

Bond Graph model of the circulation: a) a simple model distinguishing the pulmonary and systemic circulation b) a more detailed model differentiating the systemic circulation on the head, the abdomen and the legs.

Figure 6

Diagram showing the coupling between the model of the ANS and the models of the ventricles and the circulatory system.

Figure 7

a) components of the ANS model b) structure of each ANS regulation component.

Figure 8

Elements of the Bond Graph model that are under the influence of the ANS model on the simple circulatory model (a) and the more detailed model (b).

Figure 9

Systemic blood pressure dynamics during a typical Valsalva manoeuvre. The four phases of this autonomic test are presented.

Figure 10

Simulation of blood pressure a) and heart rate c), real data of blood pressure b) and heart rate d)

Figure 11

Blood pressure acquired at the level of the abdomen (a), the legs (b) and the upper body(c).

Figure 12

Comparison of simulated and observed data during a tilt test. Simulated blood pressure a) and heart rate c), real data of blood pressure b) and heart rate d).