Advertisement

Mathematical Modelling of Radiobiological Parameters

  • Piernicola Pedicini
  • Lidia StrigariEmail author
  • Luigi Spiazzi
  • Alba Fiorentino
  • Paolo Tini
  • Luigi Pirtoli
Chapter
  • 632 Downloads
Part of the Current Clinical Pathology book series (CCPATH)

Abstract

All treatment strategies are studied at the preclinical and clinical level, and the related endpoints are used to extract radiobiological parameters in mathematical models. This chapter aims to provide an overview of these approaches based on clinical and cellular data.

Keywords

Glioma Cell Radiation Response Biological Effective Dose Clonogenic Cell Tumour Control Probability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    AAPM TG 43. Quality assessment and improvement of dose response models: some effects of study weaknesses on study findings. “C’est Magnifique?” AAPM report 43, 1993Google Scholar
  2. 2.
    Joiner MC, Van der Kogel AJ, Steel GG. Introduction: the significance of radiobiology and radiotherapy for cancer treatment. In: Joiner MC, Van der Kogeleds A, editors. Basic clinical radiobiology. 4th ed. London: Hodder Arnold; 2009.Google Scholar
  3. 3.
    Los M, Rashedi I, Panigrahi S, Klonisch T, Schulze-Osthoff K. Tumor growth and cell proliferation. In: Molls M, Vaupel P, Nieder C, Anschereds MS, editors. The impact of tumor biology on cancer treatment and multidisciplinary strategies. Berlin: Springer; 2009.Google Scholar
  4. 4.
    Willers H, Beck-Bornholdt HP. Origins of radiotherapy and radiobiology: separation of the influence of dose per fraction and overall treatment time on normal tissue damage by Reisner and Miescher in the 1930s. Radiother Oncol. 1996;38:171–3.CrossRefPubMedGoogle Scholar
  5. 5.
    Bentzen SM. Quantitative clinical radiobiology. Acta Oncol. 1993;32(3):259–75.CrossRefPubMedGoogle Scholar
  6. 6.
    Strandquist M. A study of the cumulative effects of fractionated X-ray treatment based on the experience gained at radiumhemmet with the treatment of 280 cases of carcinoma of the skin and lip. Acta Radiol. 1944;55(Suppl):300–4.Google Scholar
  7. 7.
    Munro TR, Gilbert CW. The relation between tumour lethal doses and the radiosensitivity of tumour cells. Br J Radiol. 1961;34:246–51.CrossRefPubMedGoogle Scholar
  8. 8.
    Ellis F. Dose, time and fractionation a clinical hypothesis. Clin Radiol. 1969;20(1):1–7.CrossRefPubMedGoogle Scholar
  9. 9.
    Walker MD, Strikes TA, Sheline GE. An analysis of dose-effect relationship in the radiotherapy of malignant glioma. Int J Radiat Oncol Biol Phys. 1979;5:1725–31.CrossRefPubMedGoogle Scholar
  10. 10.
    Mikhael MA. Radiation necrosis of the brain: correlation between computed tomography, pathology, and dose distribution. J Comput Assist Tomogr. 1978;2(1): 71–80.CrossRefPubMedGoogle Scholar
  11. 11.
    Fowler JF. The linear quadratic formula and progress in fractionated radiotherapy. Br J Radiol. 1989;62:679–94.CrossRefPubMedGoogle Scholar
  12. 12.
    Fowler JF. Sensitivity analysis of parameters in linear-quadratic radiobiologic modeling. Int J Radiat Oncol Biol Phys. 2009;73(5):1532–7.CrossRefPubMedGoogle Scholar
  13. 13.
    Kellerer AM. Studies of the dose-effect relation. Experientia. 1989;45:13–21.CrossRefPubMedGoogle Scholar
  14. 14.
    Joiner MC, Bentzen SM. Fractionation: the linear quadratic approach. In: Joiner MC, Van der Kogeleds A, editors. Basic clinical radiobiology. 4th ed. London: Hodder Arnold; 2009.Google Scholar
  15. 15.
    Fowler JF. 21 years of biologically effective dose. Br J Radiol. 2010;83:554–68.CrossRefPubMedPubMedCentralGoogle Scholar
  16. 16.
    Debus J, Abdollahi A. For the next trick: new discoveries in radiobiology applied to glioblastoma. Current concepts and future perspective in radiotherapy of glioblastoma. ASCO education book; 2014. e95–9.Google Scholar
  17. 17.
    Shahine BH, Ng CE, Raaphorst GP. Modelling of continuous low dose rate and accelerated fractionated high dose rate irradiation treatments in a human glioma cell line. Int J Radiat Biol. 1996;70(5):555–61.CrossRefPubMedGoogle Scholar
  18. 18.
    Williams JA, Williams JR, Yuan X, Dillehay LE. Protracted exposure radiosensitization of experimental human malignant glioma. Radiat Oncol Investig. 1998;6(6):255–63.CrossRefPubMedGoogle Scholar
  19. 19.
    Cordes N, Plasswilm L, Sauer R. Interaction of paclitaxel (Taxol) and irradiation. In-vitro differences between tumor and fibroblastic cells. Strahlenther Onkol. 1999;175(4):175–81.CrossRefPubMedGoogle Scholar
  20. 20.
    Nusser NN, Bartkowiak D, Röttinger EM. The influence of bromodeoxyuridine on the induction and repair of DNA double-strand breaks in glioblastoma cells. Strahlenther Onkol. 2002;178(9):504–9.CrossRefPubMedGoogle Scholar
  21. 21.
    Garcia LM, Leblanc J, Wilkins D, Raaphorst GP. Fitting the linear-quadratic model to detailed data sets for different dose ranges. Phys Med Biol. 2006;51(11):2813–23.CrossRefPubMedGoogle Scholar
  22. 22.
    Withers HR, Thames Jr HD, Peters LJ. A new isoeffect curve for change in dose per fraction. Radiother Oncol. 1983;1:187–91.CrossRefPubMedGoogle Scholar
  23. 23.
    Thames HD, Bentzen SM, Turesson I, Overgaard M, van den Bogaert W. Time-dose factors in radiotherapy: a review of the human data. Radiother Oncol. 1990;19:219–35.CrossRefPubMedGoogle Scholar
  24. 24.
    Roberts SA, Hendry JH. A realistic closed-form radiobiological model of clinical tumor-control data incorporating intertumor heterogeneity. Int J Radiat Oncol Biol Phys. 1998;41(3):689–99.CrossRefPubMedGoogle Scholar
  25. 25.
    Joiner MC, Marples B, Lambin P, Short SC, Turesson I. Low-dose hypersensitivity: current status and possible mechanisms. Int J Radiat Oncol Biol Phys. 2001;49(2):379–89.CrossRefPubMedGoogle Scholar
  26. 26.
    Joiner MC. Quantifying cell killing and cell survival. In: Joiner MC, Van der Kogeleds A, editors. Basic clinical radiobiology. 4th ed. London: HodderArnold; 2009.Google Scholar
  27. 27.
    Haas-Kogan DA, Yount G, Haas M, Levi D, Kogan SS, Hu L, Vidair C, Deen DF, Dewey WC, Israel MA. p53-dependent G1 arrest and p53-independent apoptosis influence the radiobiologic response of glioblastoma. Int J Radiat Oncol Biol Phys. 1996;36(1): 95–103.CrossRefPubMedGoogle Scholar
  28. 28.
    Williams JR, Zhang Y, Russell J, Koch C, Little JB. Human tumor cells segregate into radiosensitivity groups that associate with ATM and TP53 status. Acta Oncol. 2007;46(5):628–38.CrossRefPubMedGoogle Scholar
  29. 29.
    Williams JR, Zhang Y, Zhou H, Gridley DS, Koch CJ, Russell J, Slater JS, Little JB. A quantitative overview of radiosensitivity of human tumor cells across histological type and TP53 status. Int J Radiat Biol. 2008;84(4):253–64.CrossRefPubMedGoogle Scholar
  30. 30.
    Mellor HR, Ferguson DJ, Callaghan R. A model of quiescent tumour microregions for evaluating multicellular resistance to chemotherapeutic drugs. Br J Cancer. 2005;93:302–9.CrossRefPubMedPubMedCentralGoogle Scholar
  31. 31.
    Scopelliti A, Cammareri P, Catalano V, Saladino V, Todaro M, Stassi G. Therapeutic implications of cancer initiating cells. Expert Opin Biol Ther. 2009;9:1005–16.CrossRefPubMedGoogle Scholar
  32. 32.
    Bao S, Wu Q, McLendon RE, Hao Y, Shi Q, Hjelmeland AB, Dewhirst MW, Bigner DD, Rich JN. Glioma stem cells promote radioresistance by preferential activation of the DNA damage response. Nature. 2006;444:756–60.CrossRefPubMedGoogle Scholar
  33. 33.
    Zhou W, Sun M, Li GH, Wu YZ, Wang Y, Jin F, Zhang YY, Yang L, Wang DL. Activation of the phosphorylation of ATM contributes to radioresistance of glioma stem cells. Oncol Rep. 2013;30(4):1793–801.PubMedGoogle Scholar
  34. 34.
    Gao X, McDonald JT, Hlatky L, Enderling H. Acute and fractionated irradiation differentially modulate glioma stem cell division kinetics. Cancer Res. 2013;73(5):1481–90.CrossRefPubMedGoogle Scholar
  35. 35.
    Yu V, Nguyen D, Kupelian P, Kaprealian T, Selch M, Low D, Pajonk F, Sheng K. SU-C-BRE-03: dual compartment mathematical modeling of glioblastoma multiforme (GBM). Med Phys. 2014;41:94.CrossRefGoogle Scholar
  36. 36.
    Palumbo S, Pirtoli L, Tini P, Cevenini G, Calderaro F, Toscano M, Miracco C, Comincini S. Different involvement of autophagy in human malignant glioma cell lines undergoing irradiation and temozolomide combined treatments. J Cell Biochem. 2012;113(7):2308–18.CrossRefPubMedGoogle Scholar
  37. 37.
    Tini P, Palumbo S, Cevenini G., Miracco C., Comincini S., Pirtoli L. Autophagy as potential therapeutical target in glioblastoma. Acts of XXII Italian Congress AIRO. Rome November 17–20th 2012.Google Scholar
  38. 38.
    Palumbo S, Comincini S. Autophagy and ionizing radiation in tumors: the “survive or not survive” dilemma. J Cell Physiol. 2013;228(1):1–8.CrossRefPubMedGoogle Scholar
  39. 39.
    Tucker SL, Thames HD, Taylor JMG. How well is the probability of tumor cure after fractionated irradiation described by Poisson statistics? Radiat Res. 1990; 124:273–82.CrossRefPubMedGoogle Scholar
  40. 40.
    Webb S, Nahum AE. A model for calculating tumour control probability in radiotherapy including the effects of inhomogeneous distribution of dose and clonogenic cell density. Phys Med Biol. 1993;38:653–66.CrossRefPubMedGoogle Scholar
  41. 41.
    Niemierko A, Goitein M. Implementation of a model for estimating tumour control probability for an inhomogeneously irradiated tumor. Radiother Oncol. 1993;29:140–7.CrossRefPubMedGoogle Scholar
  42. 42.
    Okunieff P, Morgan D, Niemierko A, et al. Radiation dose-response of human tumor. Int J Radiat Oncol Biol Phys. 1995;32:1227–37.CrossRefPubMedGoogle Scholar
  43. 43.
    Verhaak RG, Hoadley KA, Purdom E, Wang V, Qi Y, Wilkerson MD, Miller CR, Ding L, Golub T, Mesirov JP, Alexe G, Lawrence M, O’Kelly M, Tamayo P, Weir BA, Gabriel S, Winckler W, Gupta S, Jakkula L, Feiler HS, Hodgson JG, James CD, Sarkaria JN, Brennan C, Kahn A, Spellman PT, Wilson RK, Speed TP, Gray JW, Meyerson M, Getz G, Perou CM, Hayes DN, Network CGAR. An integrated genomic analysis identifies clinically relevant subtypes of glioblastoma characterized by abnormalities in PDGFRA, IDH1, EGFR and NF1. Cancer Cell. 2010;17(1):98–110.CrossRefPubMedPubMedCentralGoogle Scholar
  44. 44.
    Vlashi E, McBride WH, Pajonk F. Radiation responses of cancer stem cells. J Cell Biochem. 2009;108(2): 339–42.CrossRefPubMedPubMedCentralGoogle Scholar
  45. 45.
    Manninoa M, Chalmers AJ. Radioresistance of glioma stem cells: intrinsic characteristic or property of the ‘microenvironment-stem cell unit’? Mol Oncol. 2011;5:374–86.CrossRefGoogle Scholar
  46. 46.
    Wein LM, Cohen JE, Wu JT. Dynamic optimization of a linear-quadratic model with incomplete repair and volume-dependent sensitivity and repopulation. Int J Radiat Oncol Biol Phys. 2000;47(4):1073–83.CrossRefPubMedGoogle Scholar
  47. 47.
    Thames Jr HD, Withers HR, Peters LJ, Fletcher GH. Changes in early and late radiation responses with altered dose fractionation: implications for dose-survival relationships. Int J Radiat Oncol Biol Phys. 1982;8(2):219–26.CrossRefPubMedGoogle Scholar
  48. 48.
    Pedicini P, Fiorentino A, Simeon V, Tini P, Chiumento C, Pirtoli L, Salvatore M, Storto G. Clinical radiobiology of glioblastoma multiforme: estimation of tumor control probability from various radiotherapy fractionation schemes. Strahlenther Onkol. 2014;190(10): 925–32. doi: 10.1007/s00066-014-0638-9. Epub 2014 Apr 4.CrossRefPubMedGoogle Scholar
  49. 49.
    Pedicini P. In regard to Pedicini et al. Int J Radiat Oncol Biol Phys. 2013;87(5):858.CrossRefPubMedGoogle Scholar
  50. 50.
    Bentzen SM. Dose-response relationship in radiotherapy. In: Steel GG, editor. Basic clinical radiobiology. 2nd ed. London: Arnold; 1997. p. 78–86.Google Scholar
  51. 51.
    Salazar OM, Rubin P, Feldstein ML, et al. High dose radiation therapy in the treatment of malignant gliomas: final report. Int J Radiat Oncol Biol Phys. 1979;5:1733–40.CrossRefPubMedGoogle Scholar
  52. 52.
    Salazar OM, Rubin P, McDonald JV, et al. High dose radiation therapy in the treatment of glioblastoma multiforme: a preliminary report. Int J Radiat Oncol Biol Phys. 1976;1:717–27.CrossRefPubMedGoogle Scholar
  53. 53.
    Qi XS, Schultz CJ, Li XA. An estimation of radiobiologic parameters from clinical outcomes for radiation treatment planning of brain tumor. Int J Radiat Oncol Biol Phys. 2006;64(5):1570–80.CrossRefPubMedGoogle Scholar
  54. 54.
    Brenner DJ, Hall EJ. Conditions for the equivalence of continuous to pulsed low dose rate brachytherapy. Int J Radiat Oncol Biol Phys. 1991;20:181–90.CrossRefPubMedGoogle Scholar
  55. 55.
    Ciammella P, Galeandro M, D’Abbiero N, Podgornii A, Pisanello A, Botti A, Cagni E, Iori M, Iotti C. Hypo-fractionated IMRT for patients with newly diagnosed glioblastoma multiforme: a 6 year single institutional experience. Clin Neurol Neurosurg. 2013;115(9):1609–14.CrossRefPubMedGoogle Scholar
  56. 56.
    Pedicini P, Nappi A, Strigari L, Jereczek-Fossa BA, Alterio D, Cremonesi M, Botta F, Vischioni B, Caivano R, Fiorentino A, Improta G, Storto G, Benassi M, Orecchia R, Salvatore M. Correlation between EGFR expression and accelerated proliferation during radiotherapy of head and neck squamous cell carcinoma. Radiat Oncol. 2012;7:143.CrossRefPubMedPubMedCentralGoogle Scholar
  57. 57.
    Pedicini P, Caivano R, Strigari L, Benassi M, Fiorentino A, Fusco V. In regard to Miralbell et al. Re: dose-fractionation sensitivity of prostate cancer deduced from radiotherapy outcomes of 5969 patients in seven international institutional datasets: alpha/beta = 1.4 (0.9–2.2) Gy. Int J Radiat Oncol Biol Phys. 2013;85(1):10–1.CrossRefPubMedGoogle Scholar
  58. 58.
    Pedicini P, Fiorentino A, Improta G, Nappi A, Salvatore M, Storto G. Estimate of the accelerated proliferation by protein tyrosine phosphatase (PTEN) over expression in postoperative radiotherapy of head and neck squamous cell carcinoma. Clin Transl Oncol. 2013;15(11):919–24.CrossRefPubMedGoogle Scholar
  59. 59.
    Pedicini P, Strigari L, Benassi M. Estimation of a self-consistent set of radiobiological parameters from hypofractionated versus standard radiation therapy of prostate cancer. Int J Radiat Oncol Biol Phys. 2013;85(5):e231–7.CrossRefPubMedGoogle Scholar
  60. 60.
    Daşu A, Toma-Daşu I, Fowler JF. Should single distributed parameters be used to explain the steepness of tumour control probability curves? Phys Med Biol. 2003;48:387–97.CrossRefPubMedGoogle Scholar
  61. 61.
    Swanson KR, Rostomily RC, Alvord EC. A mathematical modelling tool for predicting survival of individual patients following resection of glioblastoma: a proof of principle. Br J Cancer. 2008;98: 113–9.CrossRefPubMedGoogle Scholar
  62. 62.
    Rockne R, Alvord EC, Rockhill JK, Swanson KR. A mathematical model for brain tumor response to radiation therapy. J Math Biol. 2009;58:561–78.CrossRefPubMedGoogle Scholar
  63. 63.
    Wang CH, Rockhill JK, Mrugala M, Peacock DL, Lai A, Jusenius K, et al. Prognostic significance of growth kinetics in newly diagnosed glioblastomas revealed by combining serial imaging with a novel biomathematical model. Cancer Res. 2009;69:9133–40.CrossRefPubMedPubMedCentralGoogle Scholar
  64. 64.
    Rockne R, Rockhill JK, Mrugala M, Spence AM, Kalet I, Hendrickson K, Lai A, Cloughesy T, Alvord Jr EC, Swanson KR. Predicting the efficacy of radiotherapy in individual glioblastoma patients in vivo: a mathematical modeling approach. Phys Med Biol. 2010;55(12):3271–85.CrossRefPubMedPubMedCentralGoogle Scholar
  65. 65.
    Roniotis A, Marias K, Sakkalis V, Manikis GC, Zervakis M. Simulating radiotherapy effect in high-grade glioma by using diffusive modeling and brain atlases. J Biomed Biotechnol. 2012;2012:715812.CrossRefPubMedPubMedCentralGoogle Scholar
  66. 66.
    Tracqui P, Cruywagen GC, Woodward DE, Bartoo GT, Murray JD, Alvord Jr EC. A mathematical model of glioma growth: the effect of chemotherapy on spatio-temporal growth. Cell Prolif. 1995;28(1):17–31.CrossRefPubMedGoogle Scholar
  67. 67.
    Antipas VP, Stamatakos GS, Uzunoglu NK, Dionysiou DD, Dale RG. A spatio-temporal simulation model of the response of solid tumours to radiotherapy in vivo: parametric validation concerning oxygen enhancement ratio and cell cycle duration. Phys Med Biol. 2004;49(8):1485–504.CrossRefPubMedGoogle Scholar
  68. 68.
    Kim Y. Regulation of cell proliferation and migration in glioblastoma: new therapeutic approach. Front Oncol. 2013;3:53.PubMedPubMedCentralGoogle Scholar
  69. 69.
    Schuetz TA, Becker S, Mang A, Toma A, Buzug TM. A computational multiscale model of glioblastoma growth: regulation of cell migration and proliferation via microRNA-451, LKB1 and AMPK. Conf Proc IEEE Eng Med Biol Soc. 2012;2012:6620–3.PubMedGoogle Scholar
  70. 70.
    Swanson KR, Rockne RC, Claridge J, Chaplain MA, Alvord Jr EC, Anderson AR. Quantifying the role of angiogenesis in malignant progression of gliomas: in silico modeling integrates imaging and histology. Cancer Res. 2011;71(24):7366–75.CrossRefPubMedPubMedCentralGoogle Scholar
  71. 71.
    Holdsworth CH, Corwin D, Stewart RD, Rockne R, Trister AD, Swanson KR, Phillips M. Adaptive IMRT using a multiobjective evolutionary algorithm integrated with a diffusion-invasion model of glioblastoma. Phys Med Biol. 2012;57(24):8271–83. doi: 10.1088/0031-9155/57/24/8271. Epub 2012 Nov 29.CrossRefPubMedPubMedCentralGoogle Scholar
  72. 72.
    Leder K, Pitter K, Laplant Q, Hambardzumyan D, Ross BD, Chan TA, Holland EC, Michor F. Mathematical modeling of PDGF-driven glioblastoma reveals optimized radiation dosing schedules. Cell. 2014;156(3):603–16.CrossRefPubMedPubMedCentralGoogle Scholar
  73. 73.
    Jamali Nazari A, Sardari D, Vali AR, Maghooli K. Computer implementation of a new therapeutic model for GBM tumor. Comput Math Methods Med. 2014;2014:481935. Epub 2014 Aug 5.CrossRefPubMedPubMedCentralGoogle Scholar
  74. 74.
    Gorlia T, van den Bent MJ, Hegi ME, Mirimanoff RO, Weller M, Cairncross JG, Eisenhauer E, Belanger K, Brandes AA, Allgeier A, Lacombe D, Stupp R. Nomograms for predicting survival of patients with newly diagnosed glioblastoma: prognostic factor analysis of EORTC and NCIC trial 26981-22981/CE.3. Lancet Oncol. 2008;9(1):29–38. Epub 2007 Dec 21.CrossRefPubMedGoogle Scholar
  75. 75.
    Marko NF, Weil RJ, Schroeder JL, Lang FF, Suki D, Sawaya RE. Extent of resection of glioblastoma revisited: personalized survival modeling facilitates more accurate survival prediction and supports a maximum-safe-resection approach to surgery. J Clin Oncol. 2014;32(8):774–82. doi: 10.1200/JCO.2013.51.8886. Epub 2014 Feb 10.CrossRefPubMedPubMedCentralGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Piernicola Pedicini
    • 1
  • Lidia Strigari
    • 2
    Email author
  • Luigi Spiazzi
    • 3
  • Alba Fiorentino
    • 4
  • Paolo Tini
    • 5
    • 6
  • Luigi Pirtoli
    • 5
    • 7
  1. 1.I.R.C.C.S. Regional Cancer Hospital C.R.O.B.Rionero-in-VulturePZItaly
  2. 2.Laboratory of medical physics and expert systemsRegina Elena National Cancer InstituteRomeItaly
  3. 3.Physics DepartmentSpedali Civili HospitalBresciaItaly
  4. 4.Sacro Cuore Don Calabria HospitalNegrar-VeronaItaly
  5. 5.Tuscany Tumor InstituteFlorenceItaly
  6. 6.Unit of Radiation OncologyUniversity Hospital of Siena (Azienda Ospedaliera-Universitaria Senese)SienaItaly
  7. 7.Unit of Radiation Oncology, Department of Medicine, Surgery and NeurosciencesUniversity of SienaSienaItaly

Personalised recommendations