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Original article
peer-reviewed

On the Inclusion of Short-distance Bystander Effects into a Logistic Tumor Control Probability Model



Abstract

Currently, interactions between voxels are neglected in the tumor control probability (TCP) models used in biologically-driven intensity-modulated radiotherapy treatment planning. However, experimental data suggests that this may not always be justified when bystander effects are important. We propose a model inspired by the Ising model, a short-range interaction model, to investigate if and when it is important to include voxel to voxel interactions in biologically-driven treatment planning. This Ising-like model for TCP is derived by first showing that the logistic model of tumor control is mathematically equivalent to a non-interacting Ising model. Using this correspondence, the parameters of the logistic model are mapped to the parameters of an Ising-like model and bystander interactions are introduced as a short-range interaction as is the case for the Ising model. As an example, we apply the model to study the effect of bystander interactions in the case of radiation therapy for prostate cancer. The model shows that it is adequate to neglect bystander interactions for dose distributions that completely cover the treatment target and yield TCP estimates that lie in the shoulder of the dose response curve. However, for dose distributions that yield TCP estimates that lie on the steep part of the dose response curve or for inhomogeneous dose distributions having significant hot and/or cold regions, bystander effects may be important. Furthermore, the proposed model highlights a previously unexplored and potentially fruitful connection between the fields of statistical mechanics and tumor control probability/normal tissue complication probability modeling.



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Original article
peer-reviewed

On the Inclusion of Short-distance Bystander Effects into a Logistic Tumor Control Probability Model


Author Information

David G. Tempel

Department of Radiation Oncology, Montefiore Medical Center/Albert Einstein College of Medicine

N. Patrik Brodin

Department of Radiation Oncology, Montefiore Medical Center/Albert Einstein College of Medicine

Wolfgang A. Tomé Corresponding Author

Department of Radiation Oncology, Montefiore Medical Center/Albert Einstein College of Medicine

Department of Neurology, Montefiore Medical Center/Albert Einstein College of Medicine


Ethics Statement and Conflict of Interest Disclosures

Human subjects: All authors have confirmed that this study did not involve human participants or tissue. Animal subjects: All authors have confirmed that this study did not involve animal subjects or tissue. Conflicts of interest: In compliance with the ICMJE uniform disclosure form, all authors declare the following: Payment/services info: DGT acknowledges the Einstein Research Fellowship for financial support. PB acknowledges support from the NIH/National Center for Advancing Translational Science (NCATS) Einstein-Montefiore CTSA Grant Number KL2TR001071 and UL1TR001073. Financial relationships: All authors have declared that they have no financial relationships at present or within the previous three years with any organizations that might have an interest in the submitted work. Other relationships: All authors have declared that there are no other relationships or activities that could appear to have influenced the submitted work.


Original article
peer-reviewed

On the Inclusion of Short-distance Bystander Effects into a Logistic Tumor Control Probability Model


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Original article
peer-reviewed

On the Inclusion of Short-distance Bystander Effects into a Logistic Tumor Control Probability Model

  • Author Information
    David G. Tempel

    Department of Radiation Oncology, Montefiore Medical Center/Albert Einstein College of Medicine

    N. Patrik Brodin

    Department of Radiation Oncology, Montefiore Medical Center/Albert Einstein College of Medicine

    Wolfgang A. Tomé Corresponding Author

    Department of Radiation Oncology, Montefiore Medical Center/Albert Einstein College of Medicine

    Department of Neurology, Montefiore Medical Center/Albert Einstein College of Medicine


    Ethics Statement and Conflict of Interest Disclosures

    Human subjects: All authors have confirmed that this study did not involve human participants or tissue. Animal subjects: All authors have confirmed that this study did not involve animal subjects or tissue. Conflicts of interest: In compliance with the ICMJE uniform disclosure form, all authors declare the following: Payment/services info: DGT acknowledges the Einstein Research Fellowship for financial support. PB acknowledges support from the NIH/National Center for Advancing Translational Science (NCATS) Einstein-Montefiore CTSA Grant Number KL2TR001071 and UL1TR001073. Financial relationships: All authors have declared that they have no financial relationships at present or within the previous three years with any organizations that might have an interest in the submitted work. Other relationships: All authors have declared that there are no other relationships or activities that could appear to have influenced the submitted work.

    Acknowledgements


    Article Information

    Published: January 01, 2018

    DOI

    10.7759/cureus.2012

    Cite this article as:

    Tempel D G, Brodin N, Tomé W A (January 01, 2018) On the Inclusion of Short-distance Bystander Effects into a Logistic Tumor Control Probability Model. Cureus 10(1): e2012. doi:10.7759/cureus.2012

    Publication history

    Received by Cureus: November 05, 2017
    Peer review began: November 08, 2017
    Peer review concluded: December 13, 2017
    Published: January 01, 2018

    Copyright

    © Copyright 2018
    Tempel et al. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 3.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

    License

    This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Abstract

Currently, interactions between voxels are neglected in the tumor control probability (TCP) models used in biologically-driven intensity-modulated radiotherapy treatment planning. However, experimental data suggests that this may not always be justified when bystander effects are important. We propose a model inspired by the Ising model, a short-range interaction model, to investigate if and when it is important to include voxel to voxel interactions in biologically-driven treatment planning. This Ising-like model for TCP is derived by first showing that the logistic model of tumor control is mathematically equivalent to a non-interacting Ising model. Using this correspondence, the parameters of the logistic model are mapped to the parameters of an Ising-like model and bystander interactions are introduced as a short-range interaction as is the case for the Ising model. As an example, we apply the model to study the effect of bystander interactions in the case of radiation therapy for prostate cancer. The model shows that it is adequate to neglect bystander interactions for dose distributions that completely cover the treatment target and yield TCP estimates that lie in the shoulder of the dose response curve. However, for dose distributions that yield TCP estimates that lie on the steep part of the dose response curve or for inhomogeneous dose distributions having significant hot and/or cold regions, bystander effects may be important. Furthermore, the proposed model highlights a previously unexplored and potentially fruitful connection between the fields of statistical mechanics and tumor control probability/normal tissue complication probability modeling.



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Create a free account to continue reading this article.

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David G. Tempel

Department of Radiation Oncology, Montefiore Medical Center/Albert Einstein College of Medicine

N. Patrik Brodin, Ph.D.

Department of Radiation Oncology, Montefiore Medical Center/Albert Einstein College of Medicine

Wolfgang A. Tomé, Ph.D., Professor

Department of Radiation Oncology, Montefiore Medical Center/Albert Einstein College of Medicine

For correspondence:
wolfgang.tome@einstein.yu.edu

David G. Tempel

Department of Radiation Oncology, Montefiore Medical Center/Albert Einstein College of Medicine

N. Patrik Brodin, Ph.D.

Department of Radiation Oncology, Montefiore Medical Center/Albert Einstein College of Medicine

Wolfgang A. Tomé, Ph.D., Professor

Department of Radiation Oncology, Montefiore Medical Center/Albert Einstein College of Medicine

For correspondence:
wolfgang.tome@einstein.yu.edu