A mathematical study of the impact of cell plasticity on tumour control probability

Farinaz Forouzannia; Sivabal Sivaloganathan; Mohammad Kohandel; Farinaz Forouzannia; Sivabal Sivaloganathan; Mohammad Kohandel

doi:10.3934/mbe.2020284

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5250-5266. doi: 10.3934/mbe.2020284

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A mathematical study of the impact of cell plasticity on tumour control probability

Department of Applied Mathematics, University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, Canada

Received: 29 March 2020 Accepted: 29 July 2020 Published: 06 August 2020

The tumour control probability (TCP) is a treatment planning tool that evaluates the probability of tumour eradication and helps in the assessment of the relative efficacy of different radiotherapy regimens. The response of tumours to radiation differs greatly even between patients with same types of cancers. Tumour heterogeneity or cellular diversity among cancer cells has a pronounced impact on the success of administered radiotherapy protocols. Tumour heterogeneity can be explained using the cancer stem cells (CSCs) hypothesis, which posits that CSCs are responsible for tumour initiation and propagation as well as therapeutic resistance. Moreover, the existence of plasticity or bidirectional transition between CSCs and non-CSCs indicates that, sometimes, non-CSCs appear to mimic CSC phenotypes, resulting in an increase in resistance. Here, we have developed a stochastic model to investigate the impact of plasticity on the efficacy of radiotherapy. The effect of plasticity on TCP is explored by applying the model to standard and hyper-fractionated schedules for a three week period of treatment as well as standard, hyper-fractionated, and accelerated hyper-fractionated schedules with an equal total dose of 30 Gy. Our results confirm that tumour control becomes increasingly difficult in the presence of plasticity as well as for the most resistant tumours. For the case with equal total dose, it is observed that increasing fractionation, at first enhances the probability of CSCs and tumour removal, but ultimately results in lower TCP_S+P and TCP_S. In addition, the combination of radiotherapy and targeted therapy (with increasing CSC differentiation) improves both the probability of CSC and tumour removal, in the absence of plasticity. However, in the presence of plasticity, the impact of combination therapy is not significant.
- plasticity,
- tumor control probability,
- radiotherapy,
- stochastic model,
- cancer stem cell hypothesis
Citation: Farinaz Forouzannia, Sivabal Sivaloganathan, Mohammad Kohandel. A mathematical study of the impact of cell plasticity on tumour control probability[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5250-5266. doi: 10.3934/mbe.2020284

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Abstract

The tumour control probability (TCP) is a treatment planning tool that evaluates the probability of tumour eradication and helps in the assessment of the relative efficacy of different radiotherapy regimens. The response of tumours to radiation differs greatly even between patients with same types of cancers. Tumour heterogeneity or cellular diversity among cancer cells has a pronounced impact on the success of administered radiotherapy protocols. Tumour heterogeneity can be explained using the cancer stem cells (CSCs) hypothesis, which posits that CSCs are responsible for tumour initiation and propagation as well as therapeutic resistance. Moreover, the existence of plasticity or bidirectional transition between CSCs and non-CSCs indicates that, sometimes, non-CSCs appear to mimic CSC phenotypes, resulting in an increase in resistance. Here, we have developed a stochastic model to investigate the impact of plasticity on the efficacy of radiotherapy. The effect of plasticity on TCP is explored by applying the model to standard and hyper-fractionated schedules for a three week period of treatment as well as standard, hyper-fractionated, and accelerated hyper-fractionated schedules with an equal total dose of 30 Gy. Our results confirm that tumour control becomes increasingly difficult in the presence of plasticity as well as for the most resistant tumours. For the case with equal total dose, it is observed that increasing fractionation, at first enhances the probability of CSCs and tumour removal, but ultimately results in lower TCP_S+P and TCP_S. In addition, the combination of radiotherapy and targeted therapy (with increasing CSC differentiation) improves both the probability of CSC and tumour removal, in the absence of plasticity. However, in the presence of plasticity, the impact of combination therapy is not significant.

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