A Multiscale Mathematical Model of Tumour Invasive Growth

Abstract

Known as one of the hallmarks of cancer (Hanahan and Weinberg in Cell 100:57-70, 2000) cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease. This process explores and takes advantage of the reciprocal relation that solid tumours establish with the extracellular matrix (ECM) components and other multiple distinct cell types from the surrounding microenvironment. Through the secretion of various proteolytic enzymes such as matrix metalloproteinases or the urokinase plasminogen activator (uPA), the cancer cell population alters the configuration of the surrounding ECM composition and overcomes the physical barriers to ultimately achieve local cancer spread into the surrounding tissue. The active interplay between the tissue-scale tumour dynamics and the molecular mechanics of the involved proteolytic enzymes at the cell scale underlines the biologically multiscale character of invasion and raises the challenge of modelling this process with an appropriate multiscale approach. In this paper, we present a new two-scale moving boundary model of cancer invasion that explores the tissue-scale tumour dynamics in conjunction with the molecular dynamics of the urokinase plasminogen activation system. Building on the multiscale moving boundary method proposed in Trucu et al. (Multiscale Model Simul 11(1):309-335, 2013), the modelling that we propose here allows us to study the changes in tissue-scale tumour morphology caused by the cell-scale uPA microdynamics occurring along the invasive edge of the tumour. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as the tumour infiltrative growth patterns discussed in Ito et al. (J Gastroenterol 47:1279-1289, 2012).

Multiscale dynamics of a heterotypic cancer cell population within a fibrous extracellular matrix

“…On the other hand, recent works such as (Chauviere et al, 2007;Painter, 2008;Hillen et al, 2010;Schluter et al, 2012;Hillen et al, 2013;Engwer et al, 2015) have highlighted the vital importance that the composition of the ECM has on the overall invasion of cancer. Finally, the multi-scale nature of cancer invasion has received special attention over the past decade (Ramis-Conde et al, 2008b;Trucu et al, 2013;Peng et al, 2016;Shuttleworth and Trucu, 2018), with significant advancements towards two-scale approaches appropriately linking the spatio-temporal dynamics occurring at different scales being proposed in Trucu et al (2013); Shuttleworth and Trucu (2019).…”

Lattice and continuum modelling of a bioactive porous tissue scaffold

“…Comparisons between individual-based and continuum models of growing cell populations have suggested certain parameter regimes where the approaches agree and disagree, which has implications for applicability and computational tractability of each kind of model (Byrne and Drasdo, 2009;Osborne et al, 2017;Pillay et al, 2017). Hybdrid discrete and continuum models of vascular tumours have also been studied, where the vasculature itself has a discrete structure, but transport of nutrients, cell migration, and cell/ECM growth throughout the tumour is modelled as spatially continuous (Figueredo et al, 2013;Peng et al, 2017;Vilanova et al, 2017;Rieger, 2013, 2016;Wu et al, 2014). These hybdrid models offer the advantage of describing the discrete structure of the vasculature, but can be efficiently simulated computationally (de la Cruz et al, 2017).…”

Modeling the Human Bone–Tumor Niche: Reducing and Replacing the Need for Animal Data

“…Such a systems biology approach might be adopted in modeling the single tumor cell within a bone environment in a manner similar to that reported for the simulation of the complete Mycoplasma genitalium cell by Karr and colleagues, (41) where the effects of 525 genes were curated and grouped into functional modules. Previously, computational modeling has been applied to reveal mechanistic insight into cancer cell proliferation and invasion by modeling aspects such as cell division and death, hypoxia, adhesion of cancer cells to neighboring cells and the extracellular matrix, (42)(43)(44) angiogenesis, and interaction of cancer cells with immune cells and other cells of the microenvironment. Modeling the multiple steps involved in the metastatic spread of cancer cells from the primary site and including the dissolution of the basement membrane, intravasation, dissemination through the bloodstream or lymphatic supply, extravasation and seeding, dormancy and clonal expansion, is a challenging prospect.…”