Systemic arteries of cardiovascular system (assuming linearity and by neglecting systemic vein pressure) can be uniquely described by the input impedance (the ratio of arterial root pressure to aortic valve flow in the frequency domain). The value of the input impedance at the zero frequency corresponds to the total vascular resistance, and this parameter is one of the basic parameters in cardiovascular modelling. This parameter is the same, regardless of using Windkessel model, 1D or 3D models of cardiovascular system. This is because at zero frequency (steady flow) the compliance and inertance do not play a role.

For clinical practice it is convenient to consider the arterial system as a chamber, and to model it by the Windkessel model. The simplest one is the Frank’s two element model (2WK – capacitor in parallel to resistance), but it is known that 2WK cannot describe arterial input impedance properly (the input impedance at high frequencies tends to zero instead to the characteristic impedance). The total arterial compliance (defined as the ratio of system volume change and pressure change – let us call this as a static compliance definition since it is defined at steady conditions) is considered as the important clinical parameter, and many methods for estimating it are based on 2WK model. My questions for discussion are:

1) Can such defined total arterial compliance (TAC) serve as a useful the clinical parameter, since it is based on a model of the arterial system for which we know that is inappropriate? It is not related to the input impedance and cannot be measured directly (we cannot close all capillaries and measure the pressure change with volume change). The value of TAC obtained from 2WK model will give pure results when applied in Westerhof’s 3WK or 4WK models. Also 3WK model and inertial Windkessel model after Burratini (series of resistor and capacitor in parallel to resistor) results in the same input impedance with different values of compliance! Obviously, the TAC depends on the Windkessel model in which it would be applied, and we need a gold standard for Windkessel model which will serve as a basis for TAC definition. Also note that TAC is defined at zero frequency at which the compliance does not play a role.

2) The alternative definition of compliance (maybe more appropriate for a dynamics) could be: C=(dV/dt)/(dp/dt) – the volume rate of change over the pressure rate of change. In such a definition C will not a real number, it should be considered in the frequency domain and will be represented by a complex number at each frequency. At zero frequency C is undetermined (definition results in ratio 0/0) which can be easily explained by the fact that at zero frequency C does not play a role (same as the inertance). We can use the amplitude at the fundamental frequency as the characteristic one (as the clinical parameter for comparison different subjects). I would like to hear your opinion about this idea.