Estimates of the Outcome of Radiotherapy. Accuracy Requirements

Abstract

1. Assuming a precise dose delivery and a biologically homogeneous tumour cell population, it is possible to express the tumour control probability (TCP) in terms of a random cell kill (Poisson statistics). After a standard 60 Gy course of multifraction irradiation with a fraction size of 2 Gy, the TCP depends on the initial number of tumour clonogens, the SF2 (surviving fraction after 2 Gy which is a measure of intrinsic radiosensitivity), the degree of proliferation during the interfraction intervals and the number of fractions (i.e. the total dose). 2. A typical dose-response curve for tumour control has a sigmold-shape with a threshold. The steepness of the curve can be described in terms of the normalized dose response gradient γ defined as the per cent increase in the TCP per 1% increase in dose. The TCP curve has a maximum steepness between TCP values of 20 and 70%. The idealized curve is much steeper than most clinically observed TCP curves which have a median γ -value of 3.0. The reduced steepness of the clinical curve is attributed to: (a) uncertainties in dose delivery, and (b) biological heterogeneities. 3. Dosimetric uncertainties can result from random and systematic errors. The combined effect results in a reduced TCP and flattening of the TCP curve to a degree that depends on the standard deviation of the mean dose within the treated volume. Narrow variations of the dose distribution do not reduce the TCP seriously if the mean dose is used for dose prescription. In the case of wide variations, the minimum dose should be chosen. The precision required for dose delivery depends on the response gradient. If γ ≤ 3, the standard deviation should not exceed 5% of the mean dose but this should be reduced to 3% if γ exceeds 3. 4. The reduced control probability associated with an increased tumour volume is attributed to (a) increased number of clonogens, (b) increased hypoxia, and (c) appearance of radioresistant cell variants. The latter two factors play an increasing role in the large volume range. 5. The complication-free tumour control probability can be defined in terms of a utility function represented by the product of the TCP and the probability of escaping serious complications. Both dosimetric errors and biological heterogeneity result in a reduced utility function. This emphasizes the importance of dosimetric precision. Predictive assays may identify the radioresistant subpopulation whose poor response may diminish the overall curability rate of a clinically defined group of tumours.