ZMATH

Development and application of the numerical model for the simulation of human heart mitral valve (MV) transapical repair is presented. Transapical repair with neochordae implantation is a novel surgical technique allowing beating-heart correction of mitral regurgitation caused by chordae tendineae rupture through a minimally-invasive approach. In the present study, the structural finite element model of the MV decoupled from the blood flow is considered. It comprises two leaflets and chordae tendineae described by nonlinear material model. Geometry of the model and kinematic boundary conditions for fixed points of MV annulus, papillary muscles, and left ventricle apex are defined by patient-specific data. Decoupled behavior of blood is specified by the time-dependent physiologic transvalvular pressure. Personalized computational modelling strategy is applied to perform virtual transapical MV repair by positioning neochordae following the real-life surgery procedure executed by surgeons. A transient analysis in time frame between end-diastole and peak systole is conducted to evaluate post-repair MV function. Computational MV simulation and modelling results provide quantitative information about the neochordae contribution to the MV function improvement and present practical value for the surgical planning of transapical MV repair.

The modified nonlocal feedback controller is used to control the production of drugs in a simple bioreactor. This bioreactor is based on the enzymatic conversion of substrate into the required product. The dynamics of this device is described by a system of two nonstationary nonlinear diffusion–convection–reaction equations. The analysis of the influence of the convection transport is one the aims of this paper. The control loop is defined using the relation, which shows how the amount of the drug produced in the bioreactor and delivered into a human body depends on the substrate concentration specified on the external boundary of the bioreactor. The system of PDEs is solved by using the finite volume and finite difference methods, the control loop parameters are defined from the analysis of stationary linearized equations. The second aim of this paper is to solve the inverse problem and to determine optimal boundary conditions. These results enable us to estimate the potential accuracy of the proposed devices.