Structural Derivative Model for Tissue Radiation Response

By means of a recently-proposed metric or structural derivative, called scale − q−derivative approach, we formulate differential equation that models the cell death by a radiation exposure in tumor treatments. The considered independent variable here is the absorbed radiation dose D instead of usual time. The survival factor, FS, for radiation damaged cell obtained here is in agreement with the literature on the maximum entropy principle, as it was recently shown and also exhibits an excellent agreement with the experimental data. Moreover, the well-known linear and quadratic models are obtained. With this approach, we give a step forward and suggest other expressions for survival factors that are dependent on the complex tumor structure.