Mathematical Modeling of Mitral Valve Dynamics: Nonlinear vs Linear Models

Abstract

A tractable mathematical model of the valve dynamics is developed for the real time computations and in silico planning of the biomechanically consistent surgery on the ruptured chordae of the mitral valve. The geometry and dynamics of the heart contraction and valve closure are restored by digitization of the 2d echocardiography data measured on a patient. The chordae are modeled as branched systems of viscoelastic strings with zero bending rigidity. Both linear and nonlinear rheology of the heart tissues are considered. The corresponding numerical procedure is worked out. The developed model can be used for comparative study of different existing strategy of surgical restoration for individual patients as well as for fast real time computations of optimal location of the neochordae directly during the surgery.