### Abstract

The purpose of this study was to determine the treatment protocol, in terms of dose fractions and interfraction intervals, which minimizes normal tissue complication probability in the spinal cord for a given total treatment dose and treatment time. We generalize the concept of incomplete repair in the linear-quadratic model, allowing for arbitrary dose fractions and interfraction intervals. This is incorporated into a previously presented model of normal tissue complication probability for the spinal cord. Equations are derived for both mono-exponential and bi-exponential repair schemes, regarding each dose fraction and interfraction interval as an independent parameter, subject to the constraints of fixed total treatment dose and treatment time. When the interfraction intervals are fixed and equal, an exact analytical solution is found. The general problem is nonlinear and is solved numerically using simulated annealing. For constant interfraction intervals and varying dose fractions, we find that optimal normal tissue complication probability is obtained by two large and equal doses at the start and conclusion of the treatment, with the rest of the doses equal to one another and smaller than the two dose spikes. A similar result is obtained for bi-exponential repair. For the general case where the interfraction intervals are discrete and also vary, the pattern of two large dose spikes is maintained, while the interfraction intervals oscillate between the smallest two values. As the minimum interfraction interval is reduced, the normal tissue complication probability decreases, indicating that the global minimum is achieved in the continuum limit, where the dose delivered by the "middle" fractions is given continuously at a low dose rate. Furthermore, for bi-exponential repair, it is seen that as the slow component of repair becomes increasingly dominant as the magnitude of the dose spikes decreases. Continuous low-dose-rate irradiation with dose spikes at the start and end of treatment yields the lowest normal tissue complication probability in the spinal cord, given a fixed total dose and total treatment time, for both mono-exponential and bi-exponential repair. The magnitudes of the dose spikes can be calculated analytically, and are in close agreement with the numerical results.

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

Pages (from-to) | 593-602 |

Number of pages | 10 |

Journal | Radiation Research |

Volume | 155 |

Issue number | 4 |

State | Published - 2001 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Agricultural and Biological Sciences (miscellaneous)
- Biophysics
- Radiology Nuclear Medicine and imaging
- Radiation

### Cite this

*Radiation Research*,

*155*(4), 593-602.

**A model for optimizing normal tissue complication probability in the spinal cord using a generalized incomplete repair scheme.** / Levin-Plotnik, D.; Hamilton, Russell J; Niemierko, A.; Akselrod, S.

Research output: Contribution to journal › Article

*Radiation Research*, vol. 155, no. 4, pp. 593-602.

}

TY - JOUR

T1 - A model for optimizing normal tissue complication probability in the spinal cord using a generalized incomplete repair scheme

AU - Levin-Plotnik, D.

AU - Hamilton, Russell J

AU - Niemierko, A.

AU - Akselrod, S.

PY - 2001

Y1 - 2001

N2 - The purpose of this study was to determine the treatment protocol, in terms of dose fractions and interfraction intervals, which minimizes normal tissue complication probability in the spinal cord for a given total treatment dose and treatment time. We generalize the concept of incomplete repair in the linear-quadratic model, allowing for arbitrary dose fractions and interfraction intervals. This is incorporated into a previously presented model of normal tissue complication probability for the spinal cord. Equations are derived for both mono-exponential and bi-exponential repair schemes, regarding each dose fraction and interfraction interval as an independent parameter, subject to the constraints of fixed total treatment dose and treatment time. When the interfraction intervals are fixed and equal, an exact analytical solution is found. The general problem is nonlinear and is solved numerically using simulated annealing. For constant interfraction intervals and varying dose fractions, we find that optimal normal tissue complication probability is obtained by two large and equal doses at the start and conclusion of the treatment, with the rest of the doses equal to one another and smaller than the two dose spikes. A similar result is obtained for bi-exponential repair. For the general case where the interfraction intervals are discrete and also vary, the pattern of two large dose spikes is maintained, while the interfraction intervals oscillate between the smallest two values. As the minimum interfraction interval is reduced, the normal tissue complication probability decreases, indicating that the global minimum is achieved in the continuum limit, where the dose delivered by the "middle" fractions is given continuously at a low dose rate. Furthermore, for bi-exponential repair, it is seen that as the slow component of repair becomes increasingly dominant as the magnitude of the dose spikes decreases. Continuous low-dose-rate irradiation with dose spikes at the start and end of treatment yields the lowest normal tissue complication probability in the spinal cord, given a fixed total dose and total treatment time, for both mono-exponential and bi-exponential repair. The magnitudes of the dose spikes can be calculated analytically, and are in close agreement with the numerical results.

AB - The purpose of this study was to determine the treatment protocol, in terms of dose fractions and interfraction intervals, which minimizes normal tissue complication probability in the spinal cord for a given total treatment dose and treatment time. We generalize the concept of incomplete repair in the linear-quadratic model, allowing for arbitrary dose fractions and interfraction intervals. This is incorporated into a previously presented model of normal tissue complication probability for the spinal cord. Equations are derived for both mono-exponential and bi-exponential repair schemes, regarding each dose fraction and interfraction interval as an independent parameter, subject to the constraints of fixed total treatment dose and treatment time. When the interfraction intervals are fixed and equal, an exact analytical solution is found. The general problem is nonlinear and is solved numerically using simulated annealing. For constant interfraction intervals and varying dose fractions, we find that optimal normal tissue complication probability is obtained by two large and equal doses at the start and conclusion of the treatment, with the rest of the doses equal to one another and smaller than the two dose spikes. A similar result is obtained for bi-exponential repair. For the general case where the interfraction intervals are discrete and also vary, the pattern of two large dose spikes is maintained, while the interfraction intervals oscillate between the smallest two values. As the minimum interfraction interval is reduced, the normal tissue complication probability decreases, indicating that the global minimum is achieved in the continuum limit, where the dose delivered by the "middle" fractions is given continuously at a low dose rate. Furthermore, for bi-exponential repair, it is seen that as the slow component of repair becomes increasingly dominant as the magnitude of the dose spikes decreases. Continuous low-dose-rate irradiation with dose spikes at the start and end of treatment yields the lowest normal tissue complication probability in the spinal cord, given a fixed total dose and total treatment time, for both mono-exponential and bi-exponential repair. The magnitudes of the dose spikes can be calculated analytically, and are in close agreement with the numerical results.

UR - http://www.scopus.com/inward/record.url?scp=0035088801&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035088801&partnerID=8YFLogxK

M3 - Article

C2 - 11260661

AN - SCOPUS:0035088801

VL - 155

SP - 593

EP - 602

JO - Radiation Research

JF - Radiation Research

SN - 0033-7587

IS - 4

ER -