Cumulative radiation effect. Part VI: simple nomographic and tabular methods for the solution of practical problems.

In five previous papers, the concept of the Cumulative Radiation Effect (CRE) has been presented as a scale of accumulative sub-tolerance radiation damage. The biological effect generated in normal connective tissue by fractionated or continuous radiation therapy given in any temporal arrangement is described by the CRE on a unified scale of assessment, so that a unique value of the CRE describes a specific level of radiation effect. The basic methods of evaluating CREs were shown in these papers to facilitate a full understanding of the fundamental aspects of the CRE-system, but these methods can be time-consuming and tediuous for complex situations. In this paper, simple nomographic and tabular methods for the solution of practical problems are presented. An essential feature of solving a CRE problem is firstly to present it in a concise and readily appreciated form, and, to do this, nomenclature is introduced to describe schedules and regimes as compactly as possible. Simple algebraic equations are derived to describe the CRE achieved by multi-schedule regimes. In these equations, the equivalence conditions existing at the junctions between schedules are not explicit and the equations are based on the CREs of the constituent schedules assessed individually without reference to their context in the regime as a whole. This independent evaluations of CREs for each schedule results in a considerable simplification in the calculation of complex problems. The calculations are further simplified by the use of suitable tables and nomograms, so that the mathematics involved is reduced to simple arithmetical operations which require at the most the use of a slide rule but can be done by hand. The order of procedure in the presentation and calculation of CRE problems can be summarised in an evaluation procedure sheet. The resulting simple methods for solving practical problems of any complexity on the CRE-system are demonstrated by a number of examples.