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

de Melo Quintela, Bárbara; Hervas-Raluy, Silvia; Garcia-Aznar, Jose Manuel; Walker, Dawn; Wertheim, Kenneth Y.; Viceconti, Marco


Bárbara de Melo Quintela

Silvia Hervas-Raluy

Jose Manuel Garcia-Aznar

Dawn Walker

Marco Viceconti


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.


de Melo Quintela, B., Hervas-Raluy, S., Garcia-Aznar, J. M., Walker, D., Wertheim, K. Y., & Viceconti, M. (2022). A theoretical analysis of the scale separation in a model to predict solid tumour growth. Journal of Theoretical Biology, 547, Article 111173.

Journal Article Type Article
Acceptance Date May 19, 2022
Online Publication Date May 27, 2022
Publication Date Aug 21, 2022
Deposit Date Jan 23, 2023
Journal Journal of Theoretical Biology
Print ISSN 0022-5193
Electronic ISSN 1095-8541
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 547
Article Number 111173
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