Resumen de Stochastic multi-scale modelling of tumour growth
Cancer is one of the principal causes of death in the world . Despite all the resources invested in research for the development of new targeted therapies, the most used treatments to fight cancer continue to be non-specific therapies, such as surgery, radiotherapy and chemotherapy, that affect both healthy and cancer cells. In contraposition to unspecific therapies, an alternative approach has been used in medicine that is commonly referred to as the magic bullet to guide the development of new targeted therapies. The concept consists of finding a drug with a specific target (gene, protein, etc.) implicated at a particular stage of development of the disease by killing just unhealthy cells whilst leaving normal cells unharmed. Although it is not a new approach, its impact on complex diseases has been discreet .
The lack of effectiveness of the magic bullet approach brings about two questions: Why does that approach fail in the case of cancer? and What do we do to improve its effectiveness? .
The behaviour and traits of biological systems are influenced by a complex network of interactions between genes and gene products which regulate gene expression. The non-linear, high-dimensional dynamical structures have undergone evolutionary changes by natural selection. As time progresses, the resilience of the phenotype against genetic alteration increases allowing canalisation (the ability to become more robust). Particularly, in malignancies these properties and structures are exploited by the tumour to increase its proliferative potential and resist therapies. The layers of complexities involved within the system, induce difficulties in predicting the effect of a perturbation applied in the system. In order to successfully address the issues, a huge amount of research has been undertaken involving analysis and development of multi-scale models. These models incorporate different sub-models corresponding to different biological levels such that the global tissue behaviour could be analysed as an emergent property of the coupled elements.
Multi-scale models are known to be affected by a number of issues. The principal aim of this thesis is the formulation and analysis of stochastic multi-scale model of the dynamics of cellular populations that shed light on:
• The effects of coupling between intrinsic fluctuations at the intracellular and population levels. We aim to establish how the different sources of noise affect global properties of growing tumours, such as the speed of invasion.
• Derive coarse-grained limits of these models so that the parameters of the multi- scale models can be lumped together into a smaller number of parameters. This will facilitate the task of parameter estimation.
• To formulate hybrid methods which allow us to simulate larger systems while losing none of the essential features of the multi-scale system.
To this end, we establish a systematic way to consider the noise in multi-scale models.
