Radiotherapy Biological Tumor Control Probability Integral Equation Improved Model with Analytic Determination

 Th e  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  t his Probability  Function alternative  based  on  a  Binomial  distribution  equation  approximation from literature.  Result, t hus,  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 th is P robability  F unction  into the  integral  model  to  sort longer/programming  numerical  methods and  determine an  analyt ical  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.