Real-time modelling of diastolic filling of the heart using the proper orthogonal decomposition with interpolation

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 non-linear problems as encountered in simulating the heart. The idea behind this method is to first construct a database of pre-computed full-scale solutions using the Element Free Galerkin method (EFG) and then project a selected subset of these solutions to a low dimensional space. Using the Moving Least Square method an interpolation is carried out for the problem at hand, before the resulting coefficients are projected back to the original high dimensional solution space. Computations are carried out on a bi-ventricle model to investigate the performance and accuracy varying the material parameters and to determine the sensitivity with respect to the parametric values. The PODI calculations are completed within 1.25 s on a normal desktop machine with the relative ℓ2 error norm not exceeding 2.5×10−3. Hence, it is demonstrated that real-time modelling of the heart can be successfully carried out at acceptable error levels.