Morphoelastic Modelling of Embryonic Growth
start of the project: February 2019
Site of the project: COMSOL Multiphysics
Supervisor TU Delft: Fred Vermolen
Supervisor Comsol: Frank de Pont
The Master project has been finished in November 2019
by the completion of the
and a final
has been given.
For working address etc. we refer to our
Summary of the master project:
In mathematical biology, a morphoelastic model, which combines elasticity and growth,
has been used for, e.g., wound healing and tumour growth modelling. Here, it is used
to model the growth of an embryo. In order to do so, a growth curve from literature
has been fitted to a morphoelastic model which has been extended with a PDE for the
normalised cell concentration. In the one dimensional situation, this fitting resulted
into a curve with a shape similar to the desired shape. Despite the similar shape, it
did not fulfil the total growth requirements; it fell short by a factor 100. Instead, a
Gaussian curve was used to represent the cell concentration. In one dimension this
gave a similar looking curve, with a relative error of 0.2316 for the first couple of weeks
of the gestational age of the embryo, where the length of an embryo is measured form
crown-to-rump. For the other weeks, when the length of the embryo is measured from
crown-to-heel, a relative error of 0.0507 was observed.
The one dimensional problem is solved using the finite element method with linear
basis functions and an Euler backwards time integration method. This is implemented
in matlab. The output is compared to results of a comsol multiphysics? file created
on this topic and verified to be similar.
In three dimensions, the model without the cell concentration contribution is verified.
For this, experiments have been done in which a force is applied in various
directions separately. All results were similar to the one dimensional model with a
pulling force. The model containing cell concentration is not verified in this thesis.
Further, the effects of the growth term and mesh choice have been investigated. These
calculations have all been done with COMSOL multiphysics.
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