Abstract
In this research, a reduced order method (ROM) called the Proper Orthogonal Decomposition with Interpolation (PODI) is used to drastically reduce computation time of highly complex and nonlinear problems as encountered in simulating the heart. The idea behind the method is to first construct a database of pre-computed full-scale solutions using the Element Free Galerkin method (EFG) or the Finite Element Method (FEM), project the set of solutions to a low-dimensional space, use the Moving Least Square method to carry out the interpolation for the problem at hand and project it back to the original high-dimensional solution space.Calculations are carried out on a left and a bi-ventricle model taking into account the passive elastic and the active contraction behaviour of the heart. In order to address varying time increments of datasets used for interpolation, a time standardisation method is developed to facilitate full-cycle heart modelling. The performance and accuracy of the approach is investigated while considering variations of the hemodynamics in terms of pre- and afterload.
Published Version
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