Abstract
In cancer, treatment failure and disease recurrence have been associated with small subpopulations of cancer cells with a stem-like phenotype. In this paper, we develop and investigate a phenotype-structured model of solid tumour growth in which cells are structured by a stemness level, which varies continuously between stem-like and terminally differentiated behaviours. Cell evolution is driven by proliferation and death, as well as advection and diffusion with respect to the stemness structure variable. Here, the magnitude and sign of the advective flux are allowed to vary with the oxygen level. We use the model to investigate how the environment, in particular oxygen levels, affects the tumour’s population dynamics and composition, and its response to radiotherapy. We use a combination of numerical and analytical techniques to quantify how under physiological oxygen levels the cells evolve to a differentiated phenotype and under low oxygen level (i.e., hypoxia) they de-differentiate. Under normoxia, the proportion of cancer stem cells is typically negligible and the tumour may ultimately become extinct whereas under hypoxia cancer stem cells comprise a dominant proportion of the tumour volume, enhancing radio-resistance and favouring the tumour’s long-term survival. We then investigate how such phenotypic heterogeneity impacts the tumour’s response to treatment with radiotherapy under normoxia and hypoxia. Of particular interest is establishing how the presence of radio-resistant cancer stem cells can facilitate a tumour’s regrowth following radiotherapy. We also use the model to show how radiation-induced changes in tumour oxygen levels can give rise to complex re-growth dynamics. For example, transient periods of hypoxia induced by damage to tumour blood vessels may rescue the cancer cell population from extinction and drive secondary regrowth.
Highlights
Understanding of the mechanisms by which cancer is initiated and progresses continues to increase, and, yet, cancer remains one of the leading causes of premature mortality worldwide and a major barrier to increasing average life-expectancy
Over the past twenty years, there has been a major shift in our perception of solid tumours; they are regarded as heteroge
We extend the model to account for treatment via a phenotypically-modulated linear-quadratic model of radiotherapy which accounts for differential radio-sensitivity of Cancer stem cells (CSCs) (Snyder et al, 2018)
Summary
Understanding of the mechanisms by which cancer is initiated and progresses continues to increase, and, yet, cancer remains one of the leading causes of premature mortality worldwide and a major barrier to increasing average life-expectancy. Most compartmental models are based on the CSC hypothesis which assumes that it is possible to distinguish between cancer stem cells and the tumour bulk This paradigm has been challenged by recent experimental studies (Dirkse et al, 2019; Soleymani Abyaneh et al, 2018) that highlight the phenotypic heterogeneity and plasticity of cancer cells, whose clonogenic (or stemness) potential can be altered by the surrounding micro-environment (extrinsic forces). We postpone consideration of such spatial complexity to future work and focus, instead, on a well-mixed setting where oxygen levels are homogeneous and prescribed This idealised scenario allows us to investigate how cell properties, such as proliferation, apoptosis and adaptive response to environmental signals, contribute to the emergence of heterogeneous stemness levels in the population and the long term tumour composition.
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