Mathematical Modeling in Radiation Oncology

Rockne, Russell; Frankel, Paul

doi:10.1007/978-3-319-53235-6_12

Cited by 6 publications

(6 citation statements)

References 68 publications

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“…It has extensively been applied for corroborating hypotheses, generating testable predictions and suggesting unexplored research directions. A diverse set of mathematical models have been proposed to gain mechanistic insights into tumor growth and treatment responses (Enderling et al, 2006(Enderling et al, , 2010Powathil et al, 2007;Rockne et al, 2009;Rockne and Frankel, 2017). In addition, several models that describe tumor-immune system interactions have been also reported d'Onofrio, 2005;Eftimie et al, 2011;Matzavinos et al, 2004;Poleszczuk et al, 2016;Ramírez-Torres et al, 2015).…”

Section: Discussionmentioning

confidence: 99%

“…There are also several mathematical models of cancer treatment including RT, with the common overarching goals of expanding our knowledge on how tumor characteristics influence RT response and the development of novel optimized fractionation schedules (Alfonso et al, 2012;J. Alfonso et al, 2014; J. C. L. Alfonso et al, 2014;Enderling et al, 2006Enderling et al, , 2010Enderling et al, , 2019Ló pez-Alfonso et al, 2019;Powathil et al, 2007;Rockne et al, 2009;Rockne and Frankel, 2017;Serre et al, 2016). However, models of tumor-immune system interactions to explore the influence of functional degree of tumor-associated vascularity and immunostimulatory effects of RT on tumor control have not been reported so far.…”

Section: Introductionmentioning

confidence: 99%

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On the Immunological Consequences of Conventionally Fractionated Radiotherapy

et al. 2020

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Emerging evidence demonstrates that radiotherapy induces immunogenic death on tumor cells that emit immunostimulating signals resulting in tumor-specific immune responses. However, the impact of tumor features and microenvironmental factors on the efficacy of radiation-induced immunity remains to be elucidated. Herein, we use a calibrated model of tumor-effector cell interactions to investigate the potential benefits and immunological consequences of radiotherapy. Simulations analysis suggests that radiotherapy success depends on the functional tumor vascularity extent and reveals that the pre-treatment tumor size is not a consistent determinant of treatment outcomes. The onesize-fits-all approach of conventionally fractionated radiotherapy is predicted to result in some overtreated patients. In addition, model simulations also suggest that an arbitrary increase in treatment duration does not necessarily result in better tumor control. This study highlights the potential benefits of tumor-immune ecosystem profiling during treatment planning to better harness the immunogenic potential of radiotherapy.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Immunological Consequences of Conventionally Fractionated Radiotherapy

et al. 2020

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“…Clinical data are often insufficient to inform mathematical models (Chvetsov et al 2015). Both simple and more complex mathematical models are facing numerous hurdles in the attempt to integrate them into radiation oncology, and more work is needed to fully harness the potential of mathematical modelling for precision radiation oncology (Rockne and Frankel 2017).…”

Section: Periodic Surface In 'Treatment Space'mentioning

confidence: 99%

The Evolution of Tumour Composition During Fractionated Radiotherapy: Implications for Outcome

et al. 2018

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Current protocols for delivering radiotherapy are based primarily on tumour stage and nodal and metastases status, even though it is well known that tumours and their microenvironments are highly heterogeneous. It is well established that the local oxygen tension plays an important role in radiation-induced cell death, with hypoxic tumour regions responding poorly to irradiation. Therefore, to improve radiation response, it is important to understand more fully the spatiotemporal distribution of oxygen within a growing tumour before and during fractionated radiation. To this end, we have extended a spatially resolved mathematical model of tumour growth, first proposed by Greenspan (Stud Appl Math 51:317-340, 1972), to investigate the effects of oxygen heterogeneity on radiation-induced cell death. In more detail, cell death due to radiation at each location in the tumour, as determined by the well-known linear-quadratic model, is assumed also to depend on the local oxygen concentration. The oxygen concentration is governed by a reaction-diffusion equation that is coupled to an integro-differential equation that determines the size of the assumed spherically symmetric tumour. We combine numerical and analytical techniques to investigate radiation response of tumours with different intratumoral oxygen distribution profiles. Model simulations reveal a rapid transient increase in hypoxia upon regrowth of the tumour spheroid post-irradiation. We investigate the response to different radiation fractionation schedules and identify a tumour-specific relationship between inter-fraction time and dose per fraction to achieve cure. The rich dynamics exhibited by the model suggest that spatial heterogeneity may be important for predicting tumour response to radiotherapy for clinical applications.

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“…As a result of this limited data availability, mathematical models aimed towards clinical applications are often relatively simple; involving few model parameters that need to be estimated 12,13 . Consequently, such models may incorporate limited biological detail, often just considering the evolution of the GTV 4,12 .…”

Section: Introductionmentioning

confidence: 99%

Using mathematical modelling to identify data requirements for increased prediction accuracy in radiotherapy

Lewin¹,

Maini²,

Moros³

et al. 2022

Preprint

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Longitudinal gross tumour volume (GTV) clinical data from head and neck cancer patients show that tumours of a similar size and stage pre-treatment may respond very differently to the same radiotherapy fractionation protocol. Mathematical models of radiation response are often proposed as a means to predict treatment outcome and prescribe more personalised fractionation protocols. Predictive mathematical models aimed towards clinical applications should be sufficiently detailed to capture the range of dynamics observed in vivo while being sufficiently simple such that the model parameters are identifiable with respect to the data typically available for model calibration.In this paper we show that models describing the spatiotemporal heterogeneity of the intratumoural composition may better capture observed in vivo dynamics than those describing the evolution of the tumour volume alone. We compare the range of qualitative responses with respect to GTV data throughout radiotherapy treatment to those observed in a cohort of head and neck cancer patients. Synthetic data studies are used to address questions of identifiability and uncertainty quantification. Our results argue that, to develop accurate, predictive mathematical models, there is a simultaneous need for more detailed models (possibly incorporating some notion of tumour heterogeneity) along with more sophisticated data metrics with which to inform such models.

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Mathematical Modeling in Radiation Oncology

Cited by 6 publications

References 68 publications

On the Immunological Consequences of Conventionally Fractionated Radiotherapy

On the Immunological Consequences of Conventionally Fractionated Radiotherapy

The Evolution of Tumour Composition During Fractionated Radiotherapy: Implications for Outcome

Using mathematical modelling to identify data requirements for increased prediction accuracy in radiotherapy

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