Linear and nonlinear one-dimensional models of pulse wave transmission at high Womersley numbers

Abstract

The accuracy of nonlinear and linear one-dimensional models in describing pulse wave propagation in a uniform cylindrical viscoelastic tube, with Womersley's parameter α equal to 7.6 at 1 Hz, was evaluated. To this end calculations of wave propagation using these models were compared with the experimentally determined propagation of the pressure wave in the tube. The experimentally generated pressure pulse had an amplitude of 9.0 kPa and caused a relative radius change of about 17%. The static pressure vs cross-sectional area relation was found to be nonlinear for these pressure changes. Maximum fluid velocity was about 2.9 m s −1, while the phase velocity was about 5.4 m s −1. The radius change and the ratio of fluid and phase velocities violated the linear model assumptions. The nonlinear model with viscous fluid friction modelled on the basis of Poiseuille's law and treating the tube wall as purely elastic, underestimated the damping of the pulse wave and predicted the formation of shock waves, which were not found experimentally. In the linear models, the viscous friction of the blood was modelled according to either Poiseuille's law or Womersley's theory and the tube wall was treated as either linearly elastic or linearly viscoelastic. A description of the viscous friction of the blood based on Poiseuille's law underestimated damping. Disregarding the viscoelasticity of the tube wall resulted in an underestimation of both phase velocity and damping. In spite of the nonlinearity of the system, the linear viscoelastic Womersley model described the pulse wave propagation satisfactorily.