Morphoelastic Modelling of Embryonic Growth

Title

Morphoelastic Modelling of Embryonic Growth

 Author

Wijntjes, Pascalle (TU Delft Electrical Engineering, Mathematics and Computer Science)

Contributor

Vermolen, Fred (mentor)
de Pont, Frank (graduation committee)

Degree granting institution

Delft University of Technology

 Programme

Applied Mathematics

 Date

2019-11-06

 Abstract

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.

 Subject

morphoelasticity
embryonic developments
FEM analysis
COMSOL Multiphysics

 To reference this document use:

http://resolver.tudelft.nl/uuid:5d5ca1d4-33f3-4b21-aaf0-127c2c1c0a62

 Embargo date

2019-11-06

 Part of collection

Student theses

 Document type

master thesis

 Rights

© 2019 Pascalle Wijntjes
Files
PDF Thesis_PascalleWijntjes.pdf 2.78 MB
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