The clinical significance of ratios of radiobiological parameters.

PURPOSE: Interindividual heterogeneity of the radiobiological characteristics of malignant and normal tissues hampers the derivation of radiobiological parameters from clinical data. Focusing on the ratio Dprolif, i.e., the dose to compensate 1 day of treatment interruption, this article investigates the hypothesis that ratios of parameters might be less sensitive to interpatient heterogeneity and may constitute a more reliable description of the radiobiological properties of tissues than the parameters themselves. METHODS AND MATERIALS: Analytic calculations were performed in an idealized example in which the only source of heterogeneity was the number of clonogenic cells. Computer simulations were used to assess the effects of heterogeneity in radiosensitivity and in proliferative capacity. Treatment outcome was simulated in pseudopatients with increasing dose-time correlation. RESULTS: Interindividual heterogeneity in clonogenic cell number, radiosensitivity, or proliferative ability results in a marked underestimation of the response parameters describing these processes. In contrast, the estimates of the ratio Dprolif were more stable. The coefficients of variation increased with increasing heterogeneity. However, this only became unacceptable when heterogeneity in radiosensitivity was marked, or when total dose and treatment time were closely correlated. CONCLUSION: Parameter ratios may provide more robust radiobiological information than single parameters estimated from clinical data except when interindividual heterogeneity is very large or when the treatment modalities are too highly correlated. As usual, caution is advised in the presence of patient selection, a correlation between treatment prescription and expected outcome, or limited ranges of dose-time treatment patterns.

Chronic radiation damage in the rat rectum: an analysis of the influences of fractionation, time and volume.

PURPOSE: Analysis of four different sets of experiments performed by the G.S.F. group in Munich investigating the late tolerance of the rat rectum to external or intracavitary irradiation. MATERIAL AND METHODS: The endpoint was late rectal stenosis in female Wistar rats. The raw data were fitted to the linear-quadratic model by means of a likelihood maximization method (Direct Analysis). The model was altered to allow for repopulation, incomplete repair, and varying irradiated lengths of the rectum. RESULTS: Fractionation sensitivity was high or intermediate (alpha/beta ratio values [95% confidence limits] ranging from 2.67 [0.86, 4.80] to 6.65 [2.21, 11.73] Gy). Significant repopulation occurred when treatments were longer than 5 days (Dprolif equal to 0.61 [0.20, 1.47] and 1.08 [0.58, 1.90] Gy/day, in fractions of 4 Gy). Another interpretation is that radiosensitivity changed during treatment. Repair half-time estimates ranged between 1.84 [1.52, 2.34] and 5.02 [2.83, 21.7] h. Finally, the present analysis indicated that the smallest surviving compartment capable of tissue rescue was about 1/50 to 1/100 of a 1 cm high cylinder of the rectum wall. CONCLUSIONS: The radiobiological features of late stenosis in the rats are consistent with combined injuries of early and late responding components of the rectal wall. This raises some concerns about the possible danger of hyperfractionated treatments, where the beneficial impact of fraction size reduction may be obviated for interfraction intervals that are too short. Also, accelerated irradiation may result in more late complications because of increased early reactions.

Is reseeding from the primary a plausible cause of node failure?

In a previous analysis of node failures in 1251 consecutive patients with node positive oropharyngeal and pharyngolaryngeal squamous cell carcinomas treated by external radiotherapy alone at the Institut Curie, the main reasons for patient exclusion were node recurrence associated with primary failure (N+T failures) and doses less than 55 Gy. These exclusions reduced the number of node failures from 399/1251 (32%) to 77/798 (10%). Multivariate analysis of node recurrence indicated that node size and fixity, treatment duration, and T stage of primary were significant (higher probability of isolated node failure for the T1-T2 primaries). In the present analysis, it is noted that 60% of the N+T failures were observed less than 1 month after the completion of the irradiation and, therefore, were not likely the result of reseeding from the primary tumor. When all 1251 patients were included in the analysis, the probability of nodal failure increased for larger nodes, T4 primaries, lower nodal doses, presence of contralateral node metastases, and nodal fixation to the surrounding structures. No influence of the primary site was found. Treatment duration was closely associated with total dose to the nodes. The best description of the data was obtained with a model including total dose and not treatment time. However, as in the previous analysis, the exclusion of low-dose (less than 55 Gy) treatments resulted in the loss of a significant dose-control relationship. We conclude that the majority of node failures is unlikely to result from reseeding from the primary tumor, and therefore should not be excluded from local-control analyses. From a more radiobiological point of view, the exclusion of palliative treatments is questionable when studying the effect of dose on local control.

Can modest escalations of dose be detected as increased tumor control?

Clinically defined groups of tumors are usually characterized by shallow dose-response curves, and this results from heterogeneity among individual dose-response curves, each of which is very likely quite steep. A review of published results for human tumors indicates that a 10% escalation of dose to tumors controlled at the 50% level, where changes in outcome are most likely to be detected, will be detectable in a population of unselected patients only in sizable clinical trials (130-300 patients per dose level). With a few exceptions, a dose escalation of 20% will be detectable in much smaller trials (50-130 patients per dose level). Therefore, clinical trials of improved treatment modalities will be confounded by patient heterogeneity, and modest improvements may go undetected in all but the largest trials. Mathematical modeling was used to study the effect on the steepness of the dose-response curve of selecting patients on the basis of the radiosensitivity measure SF2 (surviving fraction at 2 Gy). If SF2 is a faithful predictor of response in a group of tumors, then heterogeneity could be reduced by excluding the patients with the most sensitive (controlled with near certainty) and most resistant (recurring with near certainty) tumors. The resulting "stochastic fraction" (tumors for which treatment outcome is probabilistic) would be characterized by a steep dose response, and the number of patients required to demonstrate the effect of dose escalation would be substantially reduced (by about 50%).