The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity

Abstract

We present here a space- and phenotype-structured model of selection dynamics between cancer cells within a solid tumour. In the framework of this model, we combine formal analyses with numerical simulations to investigate in silico the role played by the spatial distribution of abiotic components of the tumour microenvironment in mediating phenotypic selection of cancer cells. Numerical simulations are performed both on the 3D geometry of an in silico multicellular tumour spheroid and on the 3D geometry of an in vivo human hepatic tumour, which was imaged using computerised tomography. The results obtained show that inhomogeneities in the spatial distribution of oxygen, currently observed in solid tumours, can promote the creation of distinct local niches and lead to the selection of different phenotypic variants within the same tumour. This process fosters the emergence of stable phenotypic heterogeneity and supports the presence of hypoxic cells resistant to cytotoxic therapy prior to treatment. Our theoretical results demonstrate the importance of integrating spatial data with ecological principles when evaluating the therapeutic response of solid tumours to cytotoxic therapy.

Evolutionary dynamics of competing phenotype-structured populations in periodically fluctuating environments

“…In particular, the plot of n L (x, t f ) is shown in row A, while the plots in rows B and C are, respectively, those of n L (x, t) and n H (x, t) at t = t 1 and t = t 2 , with t 1 and t 2 being highlighted in the corresponding plots in the left column. The dotted and dashed lines correspond to the exact phenotype distributions (13) with v i (t), µ i (t) and ρ i (t) given by the numerical solutions of the Cauchy problem (14) come T -periodic, with mean values given by (51) and (55), respectively. Moreover, the phenotype distribution of the surviving population remains Gaussian with variance given either by (60) or by (63).…”

“…An additional development of our study would be to incorporate into the model a spatial structure, as done for instance in [29,51,52,70,71,72], and let multiple nutrient sources with different inflows be distributed across the spatial domain. This would lead individuals to experience nutrient fluctuations of variable amplitudes and frequencies depending on their spatial position, thus leading to the emergence of multiple local niches whereby different phenotypic variants could be selected.…”

Discrete and continuum phenotype-structured models for the evolution of cancer cell populations under chemotherapy

“…Another track to follow might be to investigate the effect of stress-induced epimutations triggered by the selective pressure that chemotherapeutic agents exert on cancer cells [25]. An additional development of this study would be to include a spatial structure, for instance by embedding the cancer cells in the geometry of a solid tumour, and to take explicitly into account the effect of spatial interactions between cancer cells, therapeutic agents and other abiotic factors, such as oxygen and glucose [54,55]. In this case, the resulting individual-based model would be integrated with a system of PDEs modelling the dynamics of the abiotic factors, thus leading to a hybrid model [4,9,10,15,16,31,34,40,48,75,76].…”

Evolution of cancer cell populations under cytotoxic therapy and treatment optimisation: insight from a phenotype-structured model

“…The present study could also be extended by including a spatial structure. For instance, one could embed the cancer cells in the geometry of an avascular (or a vascular) tumour and introduce an equation for the evolution of the local concentration of the cytotoxic drug in the interior of the tumour [39,40]. As for the optimal control problem, in such a spatial setting one could select the total number of viable cells within the tumour as the state variable and the drug concentration at the boundary of the tumour (or in the blood vessels) as the control variable.…”

“…For this reason, increasing attention has been given to integrodifferential equations (IDEs) and nonlocal partial differential equations (PDEs) modelling adaptive dynamics in populations structured by physiological traits as possible tools to study in silico the dynamics of cancer cells and their response to cytotoxic drugs [11,52]. These models have been proven useful to test biological hypotheses and complement experimental research by enabling extrapolation beyond scenarios which can be investigated through in vitro and in vivo experiments [13,17,18,28,34,35,39,41]. Moreover, the results presented by Olivier & Pouchol [50] and Pouchol et al [56] have highlighted how optimal control of such IDE and PDE models can both inform the design of optimised anticancer treatments and raise new interesting mathematical questions.…”