Physical properties of resistance vessel wall in peripheral blood flow regulation--I. Mathematical model

A mathematical model is introduced to investigate the influence of the physical properties of the resistance vessel wall on the metabolic and myogenic mechanisms. The resistance vessel wall is assumed to have an elastic property and the elastic modulus to be a function of pressure (myogenic) and flow (metabolic). Blood is Poiseuille's flow. The resulting mathematical equations for pressure-flow, pressure-diameter, pressure-wall tension and pressure-wall elastic modulus relationships introduced obey Laplace's law. Poiseuille's law and Hooke's law. In comparison with the experimental data (pressure diameter), the mathematical model is confirmed to explain well the dynamic behavior of the resistance vessel wall in vivo.