A differentiable, periodic function for pulsatile cardiac output based on heart rate and stroke volume

Many mathematical models of human hemodynamics, particularly those which describe pressure and flow pulses throughout the circulatory system, require as specified input a modeling function which describes cardiac output in terms of volume per unit time. To be realistic, this cardiac output function should capture, to the greatest extent possible, all relevant features observed in measured physical data. For model analysis purposes, it is also highly desirable to have a model function that is continuous, differentiable, and periodic. This paper addresses both classes of needs by developing such a function. Physically, the present function provides an accurate model for flow into the ascending aorta. It is completely specified by a minimal number of standard input parameters associated with left ventricle dynamics, including heart rate, mean cardiac output, and an estimation of the peak-to-mean flow ratio. Analytically, it can be expressed as a product of two continuous, differentiable and periodic factors. Further, the Fourier expansion of this model function is shown to be a finite Fourier series, and explicit closed-form expressions are given for the non-zero coefficients in this series.