The reactions of a tumor cell population and a normal tissue cell population to irradiation are described by cell population kinetic models which consider factors such as repair, reoxygenation, and repopulation. The optimal treatment schedule is a schedule of treatment doses and recovery times which eliminates the tumor and does the minimum damage to the normal tissue. The process of obtaining the optimal treatment schedule by dynamic programming is described. In the sample calculations, the surviving fraction of normal tissue cells using the optimal treatment schedule is greater by a factor of two than the largest surviving fraction of normal tissue cells using schedules with equal doses and equal recovery times.

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