Mathematical modelling of tissue metabolism and growth

Catt, Christopher Joseph (2010) Mathematical modelling of tissue metabolism and growth. University of Southampton, School of Mathematics, Doctoral Thesis , 161pp.


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The work presented in this thesis is concerned with modelling the growth of tissue constructs,
with particular focus on the effects the local micro environment has on the cell cycle and
metabolism. We consider two cases; multicellular tumour spheroids and orthopaedic tissue
constructs. This thesis is divided into two parts. In the first part we will present a multispecies
model of an avascular tumour that studies how a cell’s metabolism affects the cell cycle,
spheroid growth and the mechanical forces that arise during growth. The second part consists
of a study of the growth of an engineered cartilaginous tissue layer. Experimental observations
will be compared to a model of the distribution of cells and extracellular matrix.

The efficiency of cancer treatments such as radiotherapy and chemotherapy are sensitive to the
local environment of a cell. Therefore an essential task in tumour biology is to understand the
microenvironment within a tumour. Many mathematical models study the effects of nutrients
and waste products, usually assuming growth is limited by the diffusion of a single nutrient.
We will look in detail at the metabolic pathways from which cells obtain energy (ATP). A
multispecies model is presented that considers the transition from aerobic to anaerobic respi-
ration and includes relevant chemical and ionic buffering reactions and transport mechanisms.
Results show that potential ATP production affects the cell cycle and consequently the rate
of growth. This model is simplified using mathematical analysis and is integrated with a
morphoelastic model to study the development of mechanical forces. The model shows that
mechanical effects are particularly important during necrosis, where large tensile forces are
shown to develop. A review of the equations governing nutrient conservation is given, by
developing alternative macroscopic equations based on the microscopic features of a tumour
using homogenization techniques.

The second part of this thesis studies the growth of cartilaginous tissue. Bio-materials are
being engineered in an attempt to replace dysfunctional tissue in the human body using cells
extracted from living organisms. We model the growth of a cartilaginous tissue construct that
has been grown from expanded chondrocytes seeded onto collagen coated filters. A model is
developed to explain the distribution of cells and the concentration and distribution of collagen
and GAGs. This is achieved by studying the local environment of the cells. Model predictions
are compared to a range of experimental data and show most of the growth takes place in the
upper region of the construct.

Item Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
Q Science > QH Natural history > QH301 Biology
Q Science > QP Physiology
Divisions: University Structure - Pre August 2011 > School of Mathematics
ePrint ID: 176447
Date Deposited: 24 May 2011 15:35
Last Modified: 27 Mar 2014 19:23

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