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The use of a mixed Poisson model for tumour control probability computation in non homogeneous irradiations

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Abstract

Tumour control probability (TCP) is the probability of destroying every clonogen in a tumour as a result of a Radiation Therapy treatment. Assuming absorbed dose homogeneity throughout the tumour volume, TCP can be easily derived from a cell survival model. If absorbed dose is non homogeneous, its distribution has to be taken into account, because survival fractions depend on dose. This work presents a method based on mixture probability distributions to introduce absorbed dose heterogeneity using dose volume histograms. Results are close to the ones provided by the standard voxel oriented method usually utilized, but the mixture method makes more robust assumptions about independence between voxels. Therefore, this method is more flexible, and could potentially deal with variations in survival fraction caused by other factors.

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References

  1. Källman P, Ågren A, Brahme A (1992) Tumour and normal tissue responses to fractionated non-uniform dose delivery. Int J Radiat Biol 62(2):249–262

    Article  PubMed  Google Scholar 

  2. Lyman JT (1985) Complication probabilities as assessed from dose-volume histograms. Radiat Res 104:S13–S19

    Article  Google Scholar 

  3. Kulik C, Mazurier J, Lartigau E (2002) Probabilités de contrôle tumoral et de complications (TCP/NTCP) après radiothérapie: aspects méthodologiques, physiques et biologiques. Cancer/Radiother 6(Suppl 1):155s–165s

    Article  Google Scholar 

  4. Webb S, Nahum AE (1993) A model for calculating tumour control probability in radiotherapy including the effects of inhomogeneous distributions of dose and clonogenic cell density. Phys Med Biol 38:653–666

    Article  PubMed  CAS  Google Scholar 

  5. Niemierko A, Goitein M (1990) Random sampling for evaluating treatment plans. Med Phys 17(5):753–762

    Article  PubMed  CAS  Google Scholar 

  6. Bulmer MG (1974) On fitting the Poisson lognormal distribution to species-abundance data. Biometrics 30:101–110

    Article  Google Scholar 

  7. Wise ME (1946) The use of the negative binomial distribution in an industrial sampling problem. Suppl J Roy Stat Soc 8(2):202–211

    Article  Google Scholar 

  8. Greenwood M, Yule U (1920) An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents. J Roy Stat Soc 83(2):255–279

    Article  Google Scholar 

  9. Deacon J, Peckman MJ, Steel GG (1984) The radioresponsiveness of human tumours and the initial slope of the cell survival curve. Radiother Oncol 2:317–323

    Article  PubMed  CAS  Google Scholar 

  10. Tucker Susan L, Thames Howard D, Taylor Jeremy MG (1990) How well is the probability of tumor cure after fractionated irradiation described by Poisson statistics? Radiat Res 124:273–282

    Article  Google Scholar 

  11. Willmott G (1987) Mixed compound Poisson models. ASTIN Bulletin 16:S59–S80

    Article  Google Scholar 

  12. Dimitris K, Evdotia X (2005) Mixed Poisson distributions. International Statistical Review 73(1):35–58

    Google Scholar 

Download references

Acknowledgments

We are very grateful to Kevin Miller and Mary Smith for their valuable comments and grammar revision.

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Correspondence to Francisco Cutanda Henríquez.

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Cutanda Henríquez, F., Vargas Castrillón, S. The use of a mixed Poisson model for tumour control probability computation in non homogeneous irradiations. Australas Phys Eng Sci Med 34, 267–272 (2011). https://doi.org/10.1007/s13246-011-0074-4

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  • DOI: https://doi.org/10.1007/s13246-011-0074-4

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