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

The ability to model biomechanical structures is becoming more important now that more
complex artificial organs are being designed and fitted into patients. Before being created ready for use, they
must 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 et
al. in 1994 . The MPM discretises a structure into particles which move through a background grid meaning
no element distortion takes place throughout the analysis. This means that the problem of large mesh distortion
is avoided allowing for problems to include large deformation mechanics, meaning more realistic simulations
can be run. As it is the particles that define the response of the structure, there is no need for remeshing
which 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 apply
boundary 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 vascularised
scaffold of microvascular fragments within a collagen gel, discretising it with a large amount of material points
and using the MPM to determine the stress response when uniaxial tension was applied. Lui et al. also used
the MPM to model a woodpeckers head as it pecks to determine the effect of the large forces present on the
birds brain. To the author's knowledge, these cases are the only studies into using the MPM to model
biomechanical 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 constantly
throughout our lives due to the large fluid pressures within each of its chambers. By modelling the heart walls
when they are subject to the various stresses that are imposed on them, we can gain a greater understanding
of how to more efficiently construct the artificial counterparts which are being used more frequently now. The
project will start with research into what techniques are currently being used for biomechanical modelling and
how the MPM can be used as an improvement on these techniques. A study into the benefits and challenges
of 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 scans
into numerical analysis as meshing is not required. Attempts to solve the issue of applying boundary conditions
within the MPM will be explored. An MPM code will be developed which will model the
response of the heart to an applied pressure and flow over the surface. Simulations will be run to determine to
effect of changing the heart's structural properties and varying the external conditions.