The oscillations, interactions and control mechanisms of the red blood cell and bone marrow stem cell system were studied. A mathematical formulation in the form of four difference‐differential simultaneous equations was established in the four variables of the system; (i) stem cell population, (ii) chalone mitotic inhibitor, (iii) red cell population, and (iv) erythropoietin; as postulated by Orr, Kirk, Gray and Anderson (1968). Numerical values of the constants in these equations were determined from a large range of data. Calculations on the behaviour of the formulation were carried out using an ICT 1902 digital computer. The predictions of the formulation were compared with three kinetic sets of experimental data, showing satisfactory agreement. Analysis of the system yields the value of the stem cell population. In conclusion, some properties of the oscillatory features of the system are discussed.

An optimization system using score functions to gauge the criteria used in treatment planning is described. A comparison is made between the results obtained by this system and the views of a group of radiotherapists. This comparison shows that the basic concept of calculated judgement by computer and t'he relatively simple and fast methods used are applicable to the majority of 4 Mev treatment planning situations. The role of this system in the development of radiotherapy is discussed.

1 . IXTRODUCTION IN treatment planning for supervoltage radiotherapy the selection of a satisfactory arrangement of fields has been simplified, in most cases, by the wide range of techniques developed over the years by radiotherapists and hospital physicists.

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A metabolic theory of cell survival after irradiation is presented and developed in the form of a mathematical model. The parameters which fit the model t o some published experimental data are given. The effects on survival of environmental changes are considered in terms of the model.