Case in Points: Developing a Patient-specific Model of the Human Left Ventricle using the Material Point Method

Abstract

The heart is an extremely important organ in the human body and has been studied using numerical models for many years, typically using Finite Element Analysis to model the myocardium. However, heart simulations will normally require large deformation mechanics which means that a finite element mesh may encounter large mesh distortion and volumetric locking. An intensive pre-processing stage is also required, using various software to segment the medical imaging data and generate the mesh.

The Material Point Method (MPM) discretises a physical domain using material points which deform through an unchanging background finite element mesh. This work develops the ``tools'' used to produce a patient-specific model of the Left Ventricle (LV) and analyse stress in the myocardium without the need for user input after the segmentation stage. B-spline boundary representations of the endocardial and epicardial surfaces are created using the segmented MRI data of a patient. These surfaces have two uses, to aid in the generation of the material point domain and to apply non-conforming boundary conditions throughout the analysis. Myocardium is often modelled as a rubber-like material, therefore, isotropic and anisotropic hyperelastic models are implemented here. As large deformation, non-linear analyses often encounter highly non-linear responses, the arc-length method is adapted for the MPM to overcome this issue and aid in validation of the material models. A study is performed using this new framework to investigate the effects of patient geometry and material properties on the stress and displacement fields of the LV model. Through this study, it was found that the orientation of the muscle fibres has the most substantial effect on the results of the analysis.