Radiotherapy Complete Mathematical Demonstration for Biological Tumor Control Cumulative Probability Integral Equation Model with Applications

descriptionPublicationkeyboard_double_arrow_right Article 12 Oct 2022Publisher:Everant JournalsJournal:International Journal of Mathematics And Computer Research, volume 10 (eissn: 2320-7167,

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Authors: Casesnoves, Francisco;

doi: 10.47191/ijmcr/v10i10.01 , 10.5281/zenodo.7157208 , 10.5281/zenodo.7157207

Radiotherapy Complete Mathematical Demonstration for Biological Tumor Control Cumulative Probability Integral Equation Model with Applications

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Abstract

The complete mathematical biological Integral Equation Model (IEM) for Tumor Control Cumulative Probability (TCCP) development and demonstration is explained. Results for algebraic variables change to obtain a suitable Tumor Control Probability (TCP) in convolution at IEM for getting an analytic solution is detailed step by step. Results comprise estimates with further explanations. Solutions for algebraic variable changes to make the Integral Operator analytically solved are demonstrated. Applications in Radiotherapy Treatment Planning Optimization (TPO) with biological Linear Quadratic Model based on 2D [ α and β biological modelling parameters ] are explained.

Keywords

Mathematical Methods (MM), Biological Models (BM), Clonogenes Population Survival Rate, (SR), Integral Equation (IE), Integral Equation Model (IEM), Linear Quadratic Model (LQM), Tumor Control Probability (TCP), Tumor Control Cumulative Probability (TCCP), Normal Tissue Complication Probability (NTCP), Radiation Photon-Dose (RD), Organ at Risk (OAR), Nonlinear Optimization, Integral Approximations, Anisotropic Analytic Model (AAA), Radiotherapy Treatment Planning Optimization (TPO).

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