An impedance model for blood flow in the human arterial system. Part I: Model development and MATLAB implementation

An impedance model capable of predicting the time-dependent blood pressure and flow profiles in all of the vessels in the human arterial network has been developed. The model is based on a Womersley-type one-dimensional in space approximation of the pulsatile flow of a viscous fluid within elastic vessels. Nominal values from the literature are used to provide the input aortic pressure wave, the geometric dimensions of large arteries, various blood properties, vessel elasticity, etc. The necessary information to characterize the smaller arteries, arterioles and capillaries is taken from a physical scaling model [West, G. (1999). The origin of scaling laws in biology. Physica Acta, 263, 104–113]. The parameters, input setup, and the subsequent solution to the model equations have been efficiently implemented within MATLAB, which also allows for a variety of output information displays. The MATLAB implementation also allows for a comprehensive sensitivity analysis of the results to various input parameter values to be effortlessly obtained.