Multiscale Modelling of Vascular Tumour Growth in 3D: The Roles of Domain Size and Boundary Conditions

Abstract

We investigate a three-dimensional multiscale model of vascular tumour growth, which couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport, movement of, and interactions between, normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. In particular, we determine how the domain size, aspect ratio and initial vascular network influence the tumour's growth dynamics and its long-time composition. We establish whether it is possible to extrapolate simulation results obtained for small domains to larger ones, by constructing a large simulation domain from a number of identical subdomains, each subsystem initially comprising two parallel parent vessels, with associated cells and diffusible substances. We find that the subsystem is not representative of the full domain and conclude that, for this initial vessel geometry, interactions between adjacent subsystems contribute to the overall growth dynamics. We then show that extrapolation of results from a small subdomain to a larger domain can only be made if the subdomain is sufficiently large and is initialised with a sufficiently complex vascular network. Motivated by these results, we perform simulations to investigate the tumour's response to therapy and show that the probability of tumour elimination in a larger domain can be extrapolated from simulation results on a smaller domain. Finally, we demonstrate how our model may be combined with experimental data, to predict the spatio-temporal evolution of a vascular tumour.

A multi-scale analysis of drug transport and response for a multi-phase tumour model

“…The dynamics and effects of this proliferation are dependent on highly complex physical and biological phenomena across a range of spatial and temporal scales (see, e.g., Alarcón et al (2005) for a detailed discussion) such as genotypic and phenotypic heterogeneity (Gallaher and Anderson (2013)), the tumour micro-environment (Casciari et al (1992)), the structure of the surrounding tissue (Rejniak et al (2013)), etc. As a result, among the myriad technical challenges in mathematical and computational modelling of solid tumour growth, the question of how mechanisms occurring on multiple scales may be coupled in a meaningful and efficient manner has garnered much recent interest, see Alarcón et al (2003Alarcón et al ( , 2004Alarcón et al ( , 2005Alarcón et al ( , 2006, Frieboes et al (2007), Macklin et al (2009), Owen et al (2009, Perfahl et al (2011), Powathil et al (2015), and references therein. In particular, understanding this multiscale dependence is crucial in predicting the effect of a chemotherapeutic agent on a given tumour.…”

“…This transport is most appropriately modelled on the length scale associated with the full extent of the tumour tissue; however, the transport properties of the drug and growth dynamics of the tumour are highly dependent on the evolving microstructural properties of the tumour and its micro-vasculature , Perfahl et al (2011)). In this work we extend the multiscale analyses of O'Dea et al (2014), , and by employing a multiphase model of tumour growth, of the type developed in Breward et al (2002) and , and exploited in the context of vascular tumour growth in Breward et al (2004) and Hubbard and Byrne (2013), in which we explicitly incorporate microscale dynamics into a system of homogenized partial differential equations (PDEs) for tumour growth, response, and transport.…”

“…There is a growing literature associated with hybrid models of tumour growth, in which discrete populations of cells are simulated with continuous fields of nutrient, and possibly drug and angiogenic growth factor, see Alarcón et al (2003Alarcón et al ( , 2004Alarcón et al ( , 2005Alarcón et al ( , 2006, Chaplain et al (2006), Frieboes et al (2007), Macklin et al (2009), Owen et al (2009), Perfahl et al (2011), and Powathil et al (2015. The hybrid nature of these models allows the incorporation of effects that occur on multiple spatial and temporal scales.…”

A multiscale road map of cancer spheroids – incorporating experimental and mathematical modelling to understand cancer progression

“…Hybrid models have been used to investigate not only tumour growth (Drasdo and Hohme, 2005;Jiang et al, 2005;Macklin et al, 2010;Mansury et al, 2006;Stott et al, 1999), but also tumour-induced angiogenesis (Anderson and Chaplain, 1998;Macklin et al, 2009;Perfahl et al, 2011;Shirinifard et al, 2009) and tumour morphology Anderson et al, 2006). By their nature, these models incorporate spatial variables that are associated with the tumour architecture.…”

“…Recently, advanced experimental techniques that are capable of providing sufficient detail to allow a patient-specific calibration of model parameters have become available. Both discrete and continuum approaches have been used to incorporate patientderived parameters and resulted in predictive potential of patientspecific tumour growth (Dionysiou et al, 2006;Macklin et al, 2012;Perfahl et al, 2011) and response to radiotherapy (Neal et al, 2013;Rockne et al, 2010;Stamatakos et al, 2010). Patient-derived details that are used to individualise these models include 3D imaging of the tumour morphology, its histopathology and its genetic characteristics (Dionysiou et al, 2006;Neal et al, 2013;Rockne et al, 2010).…”