A theoretical analysis of the scale separation in a model to predict solid tumour growth.

Solid tumour growth depends on a host of factors which affect the cell life cycle and extracellular matrix vascularization that leads to a favourable environment. The whole solid tumour can either grow or wither in response to the action of the immune system and therapeutics. A personalised mathematical model of such behaviour must consider both the intra- and inter-cellular dynamics and the mechanics of the solid tumour and its microenvironment. However, such wide range of spatial and temporal scales can hardly be modelled in a single model, and require the so-called multiscale models, defined as orchestrations of single-scale component models, connected by relation models that transform the data for one scale to another. While multiscale models are becoming common, there is a well-established engineering approach to the definition of the scale separation, e.g., how the spatiotemporal continuum is split in the various component models. In most studies scale separation is defined as natural, linked to anatomical concepts such as organ, tissue, or cell; but these do not provide reliable definition of scales: for examples skeletal organs can be as large as 500 mm (femur), or as small as 3 mm (stapes). Here we apply a recently proposed scale-separation approach based on the actual experimental and computational limitations to a patient-specific model of the growth of neuroblastoma. The resulting multiscale model can be properly informed with the available experimental data and solved in a reasonable timeframe with the available computational resources.

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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.