RADIOTHERAPY COMPLETE MATHEMATICAL DEMONSTRATION FOR BIOLOGICAL TUMOR CONTROL CUMULATIVE PROBABILITY INTEGRAL EQUATION MODEL WITH APPLICATIONS

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.