Pulse wave reflection and resonant properties of arterial networks with anastomosis

The article is devoted to investigation of pressure waves propagation in the systems of elastic tubes filled with a fluid. The problem is connected with pulse wave propagation in the arterial beds and pulse diagnosis based on the investigation of the amplitude-frequency spectra of the pulse. The comparative analysis of the admittance of two networks is carried out. For the dichotomous branching beds the iterative procedure allows to calculate the admittance as a function of the parameters of the system. For the networks with anastomosis the problem is reduced to the decision of nonlinear algebraic system. The analytical solutions for the case of symmetric systems are investigated. It is shown that there is a set of resonant frequencies. The corresponding amplitudes significantly vary at the wave reflection conditions variation and their phases achieve the extremum. The parameters of resonant harmonics can be used in medical diagnostics. The set of harmonics is defined by the first order tube length and presence or absence of the anastomosis.