Abstract
We present numerical solutions of the semi-phenomenological model of self-propagating fluid pulses (auto-pulses) in the channel branching into two thinner channels, which simulates branching of a hypothetical artificial artery. The model is based on the lubrication theory coupled with elasticity and has the form of a single nonlinear partial differential equation with respect to the displacement of the elastic wall as a function of the distance along the channel and time. The equation is solved numerically using the 1D integrated radial basis function network method. Using homogeneous boundary conditions on the edges of space domain and continuity condition at the branching point, we obtained and analyzed solutions in the form of auto-pulses penetrating through the branching point from the thick channel into the thin channels. We evaluated magnitudes of the phenomenological coefficients responsible for the active motion of the walls in the model.
Highlights
The arterial systems are characterised by branching with a network of larger arteries splitting into smaller arteries which continue to bifurcate into arterioles and into the capillaries
We applied the 1D-IRBF numerical method to solve the model of the flow between active walls adapted for a branching channel
We obtained and analyzed solutions in the form of auto-pulses penetrating through the branching point from the thick channel into the thin channel
Summary
The arterial systems are characterised by branching with a network of larger arteries splitting into smaller arteries which continue to bifurcate into arterioles and into the capillaries. In this paper we focus on simulation of pulses in branching channels. In our recent work [1] only non-branching (single) channels were considered; this is the major difference between the two studies. In the present paper we evaluate the empirical coefficients playing the key role in our model. We emphasize that the model simulates an artificial, not a real, artery. Note that the recent years saw a remarkable progress in design and fabrication of artificial muscles.
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