### Abstract

Recent technological advances allow precise radiation delivery to tumor targets. As opposed to more conventional radiotherapy-where multiple small fractions are given-in some cases, the preferred course of treatment may involve only a few (or even one) large dose(s) per fraction. Under these conditions, the choice of appropriate radiobiological model complicates the tasks of predicting radiotherapy outcomes and designing new treatment regimens. The most commonly used model for this purpose is the venerable linear-quadratic (LQ) formalism as it applies to cell survival. However, predictions based on the LQ model are frequently at odds with data following very high acute doses. In particular, although the LQ predicts a continuously bending dose-response relationship for the logarithm of cell survival, empirical evidence over the high-dose region suggests that the survival response is instead log-linear with dose. Here, we show that the distribution of lethal chromosomal lesions among individual human cells (lymphocytes and fibroblasts) exposed to gamma rays and X rays is somewhat overdispersed, compared with the Poisson distribution. Further, we show that such overdispersion affects the predicted dose response for cell survival (the fraction of cells with zero lethal lesions). This causes the dose response to approximate log-linear behavior at high doses, even when the mean number of lethal lesions per cell is well fitted by the continuously curving LQ model. Accounting for overdispersion of lethal lesions provides a novel, mechanistically based explanation for the observed shapes of cell survival dose responses that, in principle, may offer a tractable and clinically useful approach for modeling the effects of high doses per fraction.

Original language | English (US) |
---|---|

Article number | 318 |

Journal | Frontiers in Oncology |

Volume | 7 |

Issue number | DEC |

DOIs | |

State | Published - Dec 21 2017 |

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### Keywords

- Chromosomal aberrations
- Lethal lesions
- Linear-quadratic model
- Overdispersion
- Radiation
- Stereotactic radiotherapy
- Survival curve

### ASJC Scopus subject areas

- Oncology
- Cancer Research

### Cite this

**Straightening beta : Overdispersion of lethal chromosome aberrations following radiotherapeutic doses leads to terminal linearity in the alpha-beta model.** / Shuryak, Igor; Loucas, Bradford; Cornforth, Michael.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Straightening beta

T2 - Overdispersion of lethal chromosome aberrations following radiotherapeutic doses leads to terminal linearity in the alpha-beta model

AU - Shuryak, Igor

AU - Loucas, Bradford

AU - Cornforth, Michael

PY - 2017/12/21

Y1 - 2017/12/21

N2 - Recent technological advances allow precise radiation delivery to tumor targets. As opposed to more conventional radiotherapy-where multiple small fractions are given-in some cases, the preferred course of treatment may involve only a few (or even one) large dose(s) per fraction. Under these conditions, the choice of appropriate radiobiological model complicates the tasks of predicting radiotherapy outcomes and designing new treatment regimens. The most commonly used model for this purpose is the venerable linear-quadratic (LQ) formalism as it applies to cell survival. However, predictions based on the LQ model are frequently at odds with data following very high acute doses. In particular, although the LQ predicts a continuously bending dose-response relationship for the logarithm of cell survival, empirical evidence over the high-dose region suggests that the survival response is instead log-linear with dose. Here, we show that the distribution of lethal chromosomal lesions among individual human cells (lymphocytes and fibroblasts) exposed to gamma rays and X rays is somewhat overdispersed, compared with the Poisson distribution. Further, we show that such overdispersion affects the predicted dose response for cell survival (the fraction of cells with zero lethal lesions). This causes the dose response to approximate log-linear behavior at high doses, even when the mean number of lethal lesions per cell is well fitted by the continuously curving LQ model. Accounting for overdispersion of lethal lesions provides a novel, mechanistically based explanation for the observed shapes of cell survival dose responses that, in principle, may offer a tractable and clinically useful approach for modeling the effects of high doses per fraction.

AB - Recent technological advances allow precise radiation delivery to tumor targets. As opposed to more conventional radiotherapy-where multiple small fractions are given-in some cases, the preferred course of treatment may involve only a few (or even one) large dose(s) per fraction. Under these conditions, the choice of appropriate radiobiological model complicates the tasks of predicting radiotherapy outcomes and designing new treatment regimens. The most commonly used model for this purpose is the venerable linear-quadratic (LQ) formalism as it applies to cell survival. However, predictions based on the LQ model are frequently at odds with data following very high acute doses. In particular, although the LQ predicts a continuously bending dose-response relationship for the logarithm of cell survival, empirical evidence over the high-dose region suggests that the survival response is instead log-linear with dose. Here, we show that the distribution of lethal chromosomal lesions among individual human cells (lymphocytes and fibroblasts) exposed to gamma rays and X rays is somewhat overdispersed, compared with the Poisson distribution. Further, we show that such overdispersion affects the predicted dose response for cell survival (the fraction of cells with zero lethal lesions). This causes the dose response to approximate log-linear behavior at high doses, even when the mean number of lethal lesions per cell is well fitted by the continuously curving LQ model. Accounting for overdispersion of lethal lesions provides a novel, mechanistically based explanation for the observed shapes of cell survival dose responses that, in principle, may offer a tractable and clinically useful approach for modeling the effects of high doses per fraction.

KW - Chromosomal aberrations

KW - Lethal lesions

KW - Linear-quadratic model

KW - Overdispersion

KW - Radiation

KW - Stereotactic radiotherapy

KW - Survival curve

UR - http://www.scopus.com/inward/record.url?scp=85039957144&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85039957144&partnerID=8YFLogxK

U2 - 10.3389/fonc.2017.00318

DO - 10.3389/fonc.2017.00318

M3 - Article

AN - SCOPUS:85039957144

VL - 7

JO - Frontiers in Oncology

JF - Frontiers in Oncology

SN - 2234-943X

IS - DEC

M1 - 318

ER -