The paper considers active wave processes in changes in the lumina of vessels and cylindrical hollow organs. A mathematical model is proposed for autowave transport of theirs internal contents of based on mechanochemical interactions. The self-organization of changes in theirs shapes are discussed in application to lymphatic and blood vessels and other objects of living organisms. The presented nonlinear mathematical model is a sufficiently accurate approximation making it possible to describe the existence and propagation of mechanochemical kink contraction and extension waves. The given generalized universal model describes the complete contraction-restoration cycle of a vessel or organ. The proposed mechanism of the given active motion is capable of carrying out an important transport function of biological materials in cylindrical organs: pumping and pump peristaltic effects. Using the given model, it was possible to obtain clear visual solutions and analytic expressions for the autowave propagation velocity for the compression (recovery) of the lumen of an organ, the width of its front, and its shape. Their estimates obtained with the formulas are close to the experimental data and observations in animal lymphatic vessels. Note also that the described waves with close and comparable parameters were experimentally observed in other organs. From the viewpoint of biophysics, this is important for understanding specific physiological wave processes.
mathematical modeling, nonlinear waves, active transport in vessels and organs
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