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Biologically guided intensity modulated radiation therapy planning optimization with fraction-size dose constraints

  • Special Issue Paper
  • Published:
Journal of the Operational Research Society

Abstract

Although intensity modulated radiation therapy plans are optimized as a single overall treatment plan, they are delivered over 30–50 treatment sessions (fractions) and both cumulative and per-fraction dose constraints apply. Recent advances in imaging technology provide more insight on tumour biology that has been traditionally disregarded in planning. The current practice of delivering physical dose distributions across the tumour may potentially be improved by dose distributions guided by the biological responses of the tumour points. The biological optimization models developed and tested in this paper generate treatment plans reacting to the tumour biology prior to the treatment as well as the changing tumour biology throughout the treatment while satisfying both cumulative and fraction-size dose limits. Complete computational testing of the proposed methods would require an array of clinical data sets with tumour biology information. Finding no open source ones in the literature, the authors sought proof of concept by testing on a simulated head-and-neck case adapted from a more standard one in the CERR library by blending it with available tumour biology data from a published study. The results show computed biologically optimized plans improve on tumour control obtained by traditional plans ignoring biology, and that such improvements persist under likely uncertainty in sensitivity values. Furthermore, adaptive plans using biological information improve on non-adaptive methods.

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Acknowledgements

This research is sponsored in part by NSF grant 0813896.

Author information

Authors and Affiliations

  1. Elekta Software, Treatment Planning Systems, Maryland Heights, MO, USA

    Behlul Saka

  2. University of Arkansas, Fayetteville, AR, USA

    Ronald L Rardin

  3. Indiana University, Indianapolis, IN, USA

    Mark P Langer

Authors
  1. Behlul Saka
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  2. Ronald L Rardin
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  3. Mark P Langer
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Corresponding author

Correspondence to Behlul Saka.

Appendices

Appendix A

A.1. Details of Tumour Control Probability (TCP) computation

Equation (17) computes TCP by multiplying TCP i across all tumour voxels. TCP i represents the probability that all the cells in voxel i are inactivated for ∀i∈T.

TCP i is a function of initial number of cells in each tumour voxel, denoted as n, and the surviving fraction of cells at voxel i (S N (d i )) after d i physical dose is delivered over N fractions. The effect of hypoxia is included in the surviving fraction formula in (19). Here, n is equal to tumour voxel size (mm3) times tumour cell density (cells/mm3). TCP i is computed in Equation (18) as follows:

The S N (d i ) at each tumour voxel i is computed by Equation (19) (Ruggieri et al, 2010). The first term of the exponential function is the cell killing effect over N fractions whereas the second term is the re-population effect (ie, tendency of tumour cells to regrow over the course of the treatment) over N fractions. Here, re-population parameters are denoted as following: Δt is the inter-fractional time interval, T eff is effective clonogenic doubling time, T d is delay time in clonogenic accelerated repopulation.

The tumour hypoxia at each voxel i is included in Equation (19) by the radiosensitivity parameters α i and β i . Here, α i =α o × λ i and β i =β o × (λ i )2 are used (Titz and Jeraj, 2008), where α o and β o are radiosensitivity parameters at well-oxygenated state.

The formula given in Equation (19) computes surviving fraction assuming same tumour point sensitivity over N uniform fractions. There is a need to use a slightly modified formula in the case of tumour point sensitivity change. Equation (20) computes the overall surviving fraction for tumour voxel i after d i 1 physical dose is delivered over N1 fractions in the first epoch taking into account initial hypoxia and d i 2 physical dose is delivered over N2 fractions in the second epoch taking into account updated hypoxia. Since the tumour point sensitivity (λ i ) changes between first and second epoch, radiosensitivity parameters (α i 1, β i 1) and (α i 2, β i 2) are defined for the first and second epoch, respectively. The first and second term of the exponential function in Equation (20) is the cell killing effects over the first and second epoch, respectively, whereas the last term incorporates the repopulation effect into the formula.

A.2. The parameter values used in TCP computation

For the TCP computation throughout the computational experiments, the following parameters are used based on a published paper (Ruggieri et al, 2010): Δt=1 day, T eff =3 days, T d =0 days, α o =0.35 Gy−1 and β o =0.035 Gy−2. The number of cells in each tumour voxel (n) is equal to 1 200 000 (voxel size (12 mm3) × cell density (105 cells/mm3)) where the used cell density of 105 cells/mm3 is an acceptable value between 104 cells/mm3 (Ruggieri et al, 2010) and 106 cells/mm3 (Titz and Jeraj, 2008). The TCP calculation for the plans presented in Section 4.1 uses the surviving fraction Equation (19) whereas the TCP calculation for the plans given in Section 4.2 uses the surviving fraction Equation (20).

Appendix B

Table B1 shows the input values (ie, SUV) for each tumour region sampled from their approximate range (approximated based on the colour code presented in Titz and Jeraj (2008)) and their corresponding pO2 and OMF values calculated based on the mathematical relationships given in Titz and Jeraj (2008).

Table b1 Detailed biological data information for the two base cases
Full size table

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Saka, B., Rardin, R. & Langer, M. Biologically guided intensity modulated radiation therapy planning optimization with fraction-size dose constraints. J Oper Res Soc 65, 557–571 (2014). https://doi.org/10.1057/jors.2013.144

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