Nonsmooth analysis of the pulse pressured infusion fluid flow

Abstract

This work deals with forced oscillations of fluid flows generated by infusive pump connected to a human ventricular artery. Response curves are obtained and the nonlinearity is investigated for various geometrical conditions, excitation amplitudes, and periodic conditions. The nonlinearity related to the energy losses has been taken into considerations. An overall model for the study of an isothermal fluid flow across a highly incompressible medium is proposed. The main difficulty being that the infusion fluid flow results from a pressure prescribed over the venous artery involving impact boundary conditions. The proposed solution has been constructed by taking into account the interactions between all the solid and fluid components directly in mass balance and energy conservation equations. Applications of nonsmooth time transformations and introducing a unified physical basis for analyses of infusive fluid flow with essentially nonharmonic, and discontinuous time shapes revealed explicit links between impact dynamics and hyperbolic (complex) algebras analogously to the link between harmonic oscillations and conventional complex analyses. This study also deals with the coupling condition between the barrel fluid region and venous instantaneous states. This appears as prime importance for a global model of infusion processes.