Numerical simulation of dynamic processes in the problem of pressure transfer from an artery to an occlusal cuff

Background. To date, the process of pressure transfer from the artery to the hydro-cuff has not been studied. Therefore, obtaining theoretical knowledge about the physical processes underlying the formation of oscillations in it, with radial limitations of mechanical vibrations, is an urgent task in solving the problem of improving the accuracy of estimating hemodynamic parameters. Materials and methods. To simulate the stress-strain state of the cuff-tissue-artery system, the Boltzmann-Volterra integral model is used, reflecting the hysteresis of mass movements and changes in their elastic deformation over time during compression and decompression. Results and conclusions. An effective iterative numerical method for solving the nonlinear weakly singular Volterra integral equation underlying the model is proposed. Two numerical approaches are proposed for the numerical solution of linear integral equations arising in the iterative process, one of which uses asymptotic information about the behavior of the exact solution. Numerical results of solving a number of model problems are presented, confirming the effectiveness of the proposed approach.