Mathematical modelling of tumour growth in vitro
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Tutor / directorSáez Viñas, Pablo
Document typeMaster thesis
Rights accessRestricted access - author's decision
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It is now widely accepted that cells are mechanically integrated structures which dynamically respond to mechanical cues. Tumours are no exception to that rule but still little is known on how this mechano-transduction is carried out. With increasing evidence showing regulation of tumour proliferation by surrounding mechanical cues, understanding and predicting tumour response to environmental pressure can lead to new horizons in cancer treatment. In vivo, tumours interact with each other as well as with the extracellular matrix, and alter the mechanical properties of the matrix. It has been shown that such interaction leads to a virtuous circle for tumour proliferation. Therefore, understanding at microscopic level the dynamics of molecular interactions with the extracellular matrix can lead to understanding of how tumours effectively change the mechanical properties of the underlying stromal tissue. However, due to the difficulty to study tumours in vivo, multicellular spheroids are widely used as a 3-D in vitro avascular tumour growth models to study tumour evolution at macroscale. The size and mechanical properties of such spheroids can be adjustable and allows for the measurement of stress generated by growing tumours and studies have shown that in such context, tumour evolution is slowed down by the increasing stiffness of such environment. Consequently, several studies have been conducted to develop a mathematical model of tumour growth, from single-cell based model to continuum models such as diffusion-reaction equations or Euler-like equations. Until recently, the stress distribution inside a growing tumour has been difficult to measure experimentally due to the lack of appropriate tools for in vivo and in vitro studies. However, a new study has shown that the stress distribution of a growing tumour undergoes different levels of external pressure. In this work we intended to model such growth in a step-by-step manner, from a very simplified 1-D model to a more elaborate 3-D finite analysis model in which the growing tumour was undergoing non-linear deformation. We have shown that hyperelastic models are appropriate to describe the mechanical behaviour of tumours in such context and propose further line of work to bridge the gap between the microscopic and macroscopic scale.
DegreeMÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)