Some comments on radiobiological models and the consistent Taylor series model.

• Alvarez, Gustavo Benitez ^[2] ; Lobão, Diomar Cesar ^[1]
  1. [1] Universidade Federal Fluminense

     Universidade Federal Fluminense

     Brasil

     
  2. [2] UFF/EEIMVR/VCE
• Localización: Pesquisa e Ensino em Ciências Exatas e da Natureza, ISSN-e 2526-8236, Vol. 7, Nº. 1, 2023 (Ejemplar dedicado a: Pesquisa e Ensino em Ciências Exatas e da Natureza), págs. 22-49
• Idioma: inglés
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• Resumen

  • Here it is mathematically shown that the Linear Quadratic model is insuffcient to adequately describe the survival curve of some cell lines, and that the β parameter of this model is dependent on the dose range used for curve fitting. Therefore, higher-order polynomials are needed to have a single formula that describes the survival of all cell lines at all dose ranges. Based on the Taylor series and two mathematical hypotheses, it is possible to show that the free parameters are dependent on each other. A new approach is proposed to eliminate this interdependence between the free parameters of the Taylor series expansion. The available experimental data on survival curves indicate that there are at least three different behaviors. The theoretical analysis is tested for these three different behaviors, including also five known models not based on Taylor series. Based on experimental cell survival data it is possible to generate charts on the isoeffective total dose in fractionation. A comparative study on the performance of each model in different fractionation schemes is carried out. Experimental data show that fractionation in the low and medium dose ranges can present a non-monotonic behavior, and that most models not based on the Taylor series are unable to reproduce this behavior. Furthermore, to reproduce this nonmonotonic behavior it is necessary to use polynomials of order greater than five. Finally, it is shown that for some cell lines, hyperfractionation presents a considerable therapeutic gain when compared to conventional fractionation, since there are cases in which the isoeffective total dose in hyperfractionation is much lower than the total dose in conventional fractionation.