International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

Action potential propagation in cardiac tissue by using cable equations is studied. The work discusses a one-dimensional model of continuously coupled myocytes. Electrical behavior in cardiac tissue is averaged over many cells. Therefore, the transmembrane potential behavior for a single cell is studied. Using the monodomain model, in the absence of current at the beginning and end of the cable (cell), the initial-boundary problem is posed and solved analytically. The problem is solved by the method of separation of variables. Numerical modeling of transmembrane potential propagation is implemented. Transmembrane isopotential contours and graphs corresponding to the obtained numerical results are presented.

A spongy bone can be considered a multi-porous area with its fissures and pores as the most evident components of a double porous system. The work studies the stress-strain state of a spongy jawbone near the implant under occlusal loading. A mathematical model of the problem is the contact problem of the theory of elasticity between the implant and the jawbone. The problem is solved by using the boundary element methods, which are based on the solutions of Flamant’s (BEMF) and Boussinesq’s (BEMB) problems. The cases of various lengths of implant diameter are considered. Stressed contours (isolines) in the jawbone are drafted and the results obtained by BEMF and BEMB for the different diameter implants are compared.