Mathematical model > Some modelling aspects of total artificial heart (TAH)

On a basis of our mathematical model of blood circulation system we will define base approaches to an algorithmicbuilding of the TAH control. Its main purpose is a level control of a minute blood volume in enough wide band of functional loads. In the control system of the minute volume we can emphasize two contours:

•  Control contour of a cardiac (artificial) cycle duration, including phases of artificial ventricular reduction (systole) and artificial ventricular filling (diastole);


•  Control contour of artificial ventricular output. 

The main aim of the control in the contour of cycle duration is a calculation of neurohumoral factor γ according to (51), (52). To solve this problem it is necessary to calculate a total cardiac center activity nS according to (52). The problem can be successfully solved, if sensors are available (they help to calculate the following values in a real-time operation mode): P_AL - aortic pressure, P_VL - venous systemic pressure, AO₂ – VO₂ - arteriovenous oxygen difference. Let also we have a numerical estimation of an organism physical activity as RO₂ – consumption oxygen level. Then according to formulas of oxygen metabolism model (4), (5) and (6) values of oxygen delivery to tissues and oxygen debt DO₂ are calculated. So, we have all necessary data for the calculation of the cardiac (artificial) cycle duration according to (15).

The main aim of the control in the contour of artificial ventricular output is a calculation of ventricular pressures in the different phases of the cycle. Let we have pressure measurements in cavity inputs and outputs of artificial heart, namely: P_AL - aortic pressure, P_VL - venous systemic pressure, P_AR - arterial pulmonary pressure, P_VR - venous pulmonary pressure. The systolic ventricular pressure control is constructed by a principle of degenerative feedback from the difference between actual and nominal systolic duration according to a recursion scheme (19). The diastolic ventricular pressure control is constructed according to the expression (22).