Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth
Cruz Moreno, Roberto de la, (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Guerrero, Pilar (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Calvo, Juan (Universidad de Granada. Departamento de Matemática Aplicada)
Alarcón Cor, Tomás (Centre de Recerca Matemàtica)

Data:	2017
Resum:	The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i. e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i. e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.
Ajuts:	Ministerio de Economía y Competitividad MTM2015-71509-C2-1-R Ministerio de Economía y Competitividad MTM2014-53406-R Ministerio de Economía y Competitividad MDM-2014-0445 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-1307
Drets:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Multi-scale modelling ; Hybrid methods ; Age-structured model ; Reaction-diffusion systems ; Tumour growth
Publicat a:	Journal of computational physics, Vol. 350 (Dec. 2017) , p. 974-991, ISSN 0021-9991

DOI: 10.1016/j.jcp.2017.09.019
PMID: 29200499

18 p, 918.2 KB

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