Modelling of laminated growing biological materials

Abstract

Wave propagation and reflection in the model of branching tree of viscoelastic cylindrical tubes filled with viscous fluid is considered when applied to pulse wave reflection in arterial networks. The dichotomous branching tree and the tree with two anastomoses between the second-order tubes are investigated. Influence of the geometrical and mechanical properties of the tree on the pulse wave propagation and spectral properties of the total admittance of the systems are investigated. It was found out that the admittance has a set of resonant harmonics. Any changes in parameters of microcirculatory bed and in blood rheology cause noticeable alterations of the amplitudes of resonant harmonics and negligible alterations of other harmonics. The set of resonant harmonics is independent of some variations in the tree geometry. The resonant properties of the models with and without anastomoses have some differences, that makes it possible to carry out the diagnosis of the state of inner organs with different types of vasculature. The results substantiate a possibility of the pulse diagnosis of inner organs’ states by observing the amplitudes of the resonant harmonics only, without preliminary knowledge of individual structure of the real vascular bed of an inner organ.