Arterial pulse propagation

Although our knowledge of pulse propagation in the arterial system is extensive, it has been useful to approximate the relationship between pressure and flow in a single artery or vascular bed. Such approximations have been referred to as reduced arterial system models of which the three element Windkessel is the most widely employed [Westerhof et al., 1971 Noordergraaf, 1978]. This Windkessel model is modified here to study the effects of peripheral resistance. 

The three element Windkessel model approximates the pulse propagation quality of the arterial system as a combination of an infinitely long tube, which is represented by its characteristic impedance, Zo,... 

The three-element Windkessel model approximates the pulse propagation quahty of the arterial system as a combination of an infinitely long tube, which is represented by its characteristic impedance, Z , in series with a parallel arrangement of a peripheral flow resistance, R, and a total arterial compliance, C,. Within a single cardiac cycle, these three parameters are generally assumed to be constants (Toorop et al, 1987). Recent studies have scrutinized this assumption. For example, compliance has been shown to depend on the level of arterial pressure (Bergel, 1961). Other studies have called into question the accuracy of the various methods employed to experimentally determine their values (Stergiopulos et al.. 

O.G. Martinsen and S. Grimnes, Bioimpedance and Bioelectricity Basics. Academic Press, 2011. K.S. Matthys, J. Alastruey, J. Peiro, et al, Pulse wave propagation in a model human arterial network Assessment of 1-D numerical simulations against in vitro measurements, Journal of biomechanics, vol. 40, no. 15, pp. 3476-3486, 2007. 

After the generation of static arterial tree model dynamics was introduced to the network that mimics pulse wave propagation in the tissue with each heart-beat. Then impedance electrodes were applied to both sides of the model and Finite Difference Method simulation of impedance was made for each time-slice of the dynamic model (total 60 time-slices for 1 second). 

K. Wang, Analysis of transverse wave as a propagation mode for the pressure pulse in large arteries, J. Appl. Phys. 102 064702, 2007. 

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