Many component model and its parameters to fractionated irradiation

In this study, a many component model has been formulated to address the contribution of various bio-molecules in radiation induced biological damage and this model is fitted to radiation isoeffect data to evaluate the parameter alpha/beta.

Every living cell contains a number of organic and inorganic molecules which may act as targets to lead radiation induced damage. During irradiation, many kinds of physical, chemical and biological products are produced which are due to active participation of aforesaid molecules. The many component model, hereinafter called linear-quadratic-cubic (LQC) model, is an attempt to provide a better mathematical formulation which could demonstrate the contribution of various kinds of biomolecules in biological effect of radiation. This model has only one independent parameter alpha/beta and a number of dependent parameters which are the derivatives of alpha/beta.

Three methods, for testing the fit of the proposed model and deriving the values of alpha/beta, are employed using multifractionation isoeffect data. These methods, i.e. (logDm-logDn) versus (dn-dm) plot, SFe-plot and logD versus d plot, provide their respective values of alpha/beta as 12.50 Gy, 12.51 Gy and 12.54 Gy for spleen. 7.41 Gy, 7.79 Gy and 7.42 Gy for kidney, 15.87 Gy, 15.09 Gy and 14.69 Gy for colon with 3 h interval, 12.50 Gy, 12.84 Gy and 12.45 Gy for colon with 12 h interval and 8.47 Gy, 8.84 Gy and 8.51 Gy for colon with 24 h interval. Since other parameters of the model are the derivatives of alpha/beta therefore can be derived using the values of alpha/beta.

Graphical representation of afore said sets of data show that the plotted points have a certain amount of scattering which is not at the wider scale and can be well or less well described by a straight line.

This model eliminates the shortcomings of LQ model and provides a satisfactory explanation of various radiobiological processes occurring during and after irradiation.