Large deformation modelling of the human heart via the Material Point Method

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The ability to model biomechanical structures is becoming more important now that morecomplex artificial organs are being designed and fitted into patients. Before being created ready for use, theymust be designed and tested. This is where computational modelling is needed. The standard modelling techniques discretise the structure into very small elements which are distorted in response to external forces.The Material Point Method (MPM) is a particle method for history-dependent materials developed by Sulsky etal. in 1994 . The MPM discretises a structure into particles which move through a background grid meaningno element distortion takes place throughout the analysis. This means that the problem of large mesh distortionis avoided allowing for problems to include large deformation mechanics, meaning more realistic simulationscan be run. As it is the particles that define the response of the structure, there is no need for remeshingwhich can improve computational time. The MPM does however have some drawbacks for certain applications.For example, due to the non-matching nature of the physical boundaries and the mesh, it is difficult to applyboundary conditions as no edges are defined when analysed body/structure is represented by particles.Surprisingly, there has been very little research into using the MPM to model biological materials. In 2015,Guilkey et al. used the MPM to model multicellular constructs. This involved scanning a vascularisedscaffold of microvascular fragments within a collagen gel, discretising it with a large amount of material pointsand using the MPM to determine the stress response when uniaxial tension was applied. Lui et al. also usedthe MPM to model a woodpeckers head as it pecks to determine the effect of the large forces present on thebirds brain. To the author's knowledge, these cases are the only studies into using the MPM to modelbiomechanical problems.The aim of this research is to develop a method of using the MPM to model biomechanical structures with spe-cific focus on the heart. The heart is a very important organ which is under a great amount of stress constantlythroughout our lives due to the large fluid pressures within each of its chambers. By modelling the heart wallswhen they are subject to the various stresses that are imposed on them, we can gain a greater understandingof how to more efficiently construct the artificial counterparts which are being used more frequently now. Theproject will start with research into what techniques are currently being used for biomechanical modelling andhow the MPM can be used as an improvement on these techniques. A study into the benefits and challengesof using a meshless method such as the MPM will be undertaken.One potential benfit of the MPM in analysing the heart is simplifying the transition from voxelised heart scansinto numerical analysis as meshing is not required. Attempts to solve the issue of applying boundary conditionswithin the MPM will be explored. An MPM code will be developed which will model theresponse of the heart to an applied pressure and flow over the surface. Simulations will be run to determine toeffect of changing the heart's structural properties and varying the external conditions.