Biomechanical differential equations of variables of the arterial pulse based on vessel wall and blood flow features.

A dynamic arterial vessel model with an associated flow resistance is deduced in Laplace-transformed form based on a linear dynamic muscle model and a laminar-instationary blood stream with accompanying parameters (such as elasticity, actin myosin overlap, movement resistances, blood stream resistance and blood mass). In addition, a flow resistance is connected at the outlet of the vessel. With the pulse pressure course as the given input, the Laplace-transformed definition enables, in a clearly arranged manner, the derivation of differential equations of several variables of the arterial pulse process--the changes of blood inflow, outflow, storage flow or volume, of the internal vessel pressure, of the output pressure, of the various pressure differences over the vessel, of the vessel wall tension, of the vessel radius and the vessel wall thickness. The derivations yield the order and the structures of these differential equations. The coefficients of these equations are complicated functions (sums and products) of the smooth-muscle, blood-flow and geometrical parameters. Only in special cases--with an open or the closed vessel at the outlet--are the coefficients simple functions of the vessels parameters.