A theoretical consideration of biological effect of fractionated irradiation

Time dose fractionation schemes in radiotherapy of malignant disease are now widely used everywhere. Ellis proposed the NSD (Nominal Standard Dose) concept and Kirk described CRE (Cumulative Radiation Effect), which was generalized as a form of NSD for the assessment of damage at the level of tolerance. Now, we propose BCD (Biological Cumulative Dose) and CF (Cumulative Factor: 'r', 0<r<1), which represents the decreasing rate of dose per fraction (d) per day. BCD approaches full tolerance dose and is considered as SED (Single Equivalent Dose) or SECE (Single Equivalent Cumulative Effect), because single irradiation and fractionated irradiation are represented by the same formula. Formulas of different fractionated treatment regimes can be expressed by 'd' and 'r'. CF (r) can be fixed by experimental data which were acquired on mice and pigs. The fact that 'r' is smaller when 'd' is smaller implies a lesser cumulative effect. The number of fractions (n) can be determined when cumulative dose approaches 90 % of full tolerance dose. The BCD is calculated by 'n' and 'BCD/d' and can be expressed as follows: BCD = 1800 (rad). Close agreement between this value and NSD is obtained. In recordings on log-log graph paper with 'BCD/d' on the vertical axis and 'n' on the horizontal, the number of fractions that gives a dose equivalent to that of BCD can be indicated graphically on different fractionated treatment regimes. (author)