Keywords:-

Keywords: Mathematical Methods (MM), Biological Models (BM), Clonogenes Population Survival Rate, (SR), Integral Equation (IE), Tumor Control Probability (TCP), Radiation Photon-Dose (RD), Nonlinear Optimization, Integral Approximations, Anisotropic Analytic Model (AAA), Radiotherapy Treatment Planning Optimization (TPO).

Article Content:-

Abstract

The research objective was to obtain a fast/simple analytic solution for previously published Radiotherapy Tumor Control Probability (TCP) Integral Model by other authors. Finding, firstly, is a new/simpler Probability Function than Poisson distribution of survival clonogens which is developed from classical biological model algebraic/numerically modified equation. Solution obtained is this Probability Function alternative based on a Binomial distribution equation approximation from literature. Result, thus, is its use of for developing a fast/analytic solution of the 2D [ α and β biological modelling parameters ] Integral Model Cumulative TCP. The Gaussian Normal distribution convolution is implemented with this Probability Function into the integral model to sort longer/programming numerical methods and determine an analytical solution expression. As a complete result, a formulation for TCP based on Erf functions is obtained. Applications for radiotherapy treatment planning optimization improvements with biological models are explained.

References:-

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Casesnoves, F. (2022). Radiotherapy Biological Tumor Control Probability Integral Equation Model with Analytic Determination. International Journal Of Mathematics And Computer Research, 10(8), 2840-2846. https://doi.org/10.47191/ijmcr/v10i8.03