Theoretical and computational investigations of nonlinear wave propagations in arteries. (I)--A theoretical model of nonlinear pulse wave propagations.

In this paper, a new theoretical model of nonlinear wave propagations in arteries with surrounding tissues was put forward. The equations of motion for the blood vessels and their peripheral tissues as a system have been derived. These equations were expressed in terms of the stresses of the vessel wall and fluid, and the geometry of the blood vessel. They can be used to solve numerically the problems for the propagations of nonlinear pulse waves in arteries together with the momentum and continuity equations of incompressible-viscous flow, as well as the constitutive equations of fluid and vessel wall. The numerical solutions can involve pressure, velocities and flowrate of the blood flow, as well as displacements, velocities and stresses of the vessel wall. These physical variables of propagations of pulse waves in arteries are all of significance physiologically and clinically.