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Additive Damage Models for Cellular Pharmacodynamics of Radiation–Chemotherapy Combinations

  • Special Issue : Mathematical Oncology
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Abstract

Many cancer patients receive combination treatments with radiation and chemotherapy. Available mathematical models for cellular pharmacodynamics have limited ability to represent observed in vitro responses to radiochemotherapy. Here, a family of additive damage models is proposed to describe cell kill resulting from radiochemotherapy with fixed schedule and variable doses. The pathways by which the agents produce cellular damage are assumed to converge in a single cell death process, so that survival depends on total damage, which can be represented as a sum of contributions from the various damage pathways. Heterogeneity in response across the cell population is ascribed to variations in the damage threshold for cell kill. The family of proposed models includes effects of one or two pathways of damage for each agent, saturation in drug responses, and cooperative or antagonistic interactions between agents. Models from this family with 4–7 unknown parameters are tested for their ability to fit 218 in vitro literature data sets for a range of drugs and cell lines. Overall, the additive damage models are found to outperform models based on the existing concept of independent cell kill, according to the corrected Akaike Information Criterion. The results are used to assess the importance of the various effects included in the models. These additive damage models have potential applications to the optimization of treatment and to the analysis and interpretation of in vitro screening data for new drug–radiation combinations.

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Acknowledgements

This work was supported by NIH Grant T32 GM084905.

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Authors and Affiliations

  1. Program in Applied Mathematics, University of Arizona, Tucson, AZ, USA

    Katherine S. Williams, Timothy W. Secomb & Ardith W. El-Kareh

  2. Microcirculation Division, University of Arizona, Tucson, AZ, USA

    Timothy W. Secomb & Ardith W. El-Kareh

  3. Department of Physiology, University of Arizona, Tucson, AZ, USA

    Timothy W. Secomb

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  1. Katherine S. Williams
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Correspondence to Ardith W. El-Kareh.

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Williams, K.S., Secomb, T.W. & El-Kareh, A.W. Additive Damage Models for Cellular Pharmacodynamics of Radiation–Chemotherapy Combinations. Bull Math Biol 80, 1236–1258 (2018). https://doi.org/10.1007/s11538-017-0316-z

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