Morphoelastic Modelling of Embryonic Growth
Pascalle Wijntjes

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 Masters Thesis and a final presentation has been given.

For working address etc. we refer to our alumnipage.

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.

## Contact information: Kees Vuik

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