How to construct a 3D mathematical/computer model of the left ventricle

Background: How can mathematics help us to understand the mechanism of the cardiac motion? The best known approach is to take a mathematical model of the fibered structure and insert it into a more-or-less complex model of a cardiac architecture. Objectives: We provide a new mathematical tool by introducing the notions strains, which are two-by-two and three-by-three matrices. Materials and Methods: Using motion and deformation echocardiographic data, force vectors of myocardial samples were estimated by MATLAB software, interfaced in the echocardiograph system. Dynamic orientation contraction (through the cardiac cycle) of every individual myocardial fiber could be created by adding together the sequential steps of the multiple fragmented sectors of that fiber. Results: Myocardial fibers initiate from the posterior basal region of the heart, continue through the left ventricular free wall, reach the septum, loop around the apex, ascend, and end at the superior-anterior edge of the left ventricle. Conclusions: These studies will enable physicians to diagnose and follow up many cardiac diseases when this software is interfaced within echocardiographic machines.