Modeling killing and repopulation kinetics of subclinical cancer: direct calculations from clinical data.

PURPOSE: Models for cell killing and repopulation can provide insight into the efficacy of therapies. Using clinical data on breast cancer recurrence after lumpectomy with or without radiotherapy (L+/-RT) and brain metastases after chemotherapy with or without prophylactic cranial irradiation (C+/-PCI) for small-cell lung cancer, estimates of cell killing and subclinical repopulation were tested against the results from simple radiobiologic models. METHODS AND MATERIALS: The rates of local breast cancer recurrence after L+/-RT and of brain metastases after C+/-PCI were extracted from published randomized trials. In Method 1, assuming simple exponential growth, the cell number distributions after L+/-RT and C+/-PCI were calculated from the clinical data, and the impact of RT on these distributions was determined. In Method 2, "classic" radiobiology dictates that a typical course of breast RT and PCI results in approximately =7 and approximately =4.5 log of cell kill, respectively. Using an assumption of uniform log-kill, the clinical doubling times (CDTs) can be calculated directly from the clinical data.
RESULTS: Using Method 1, for breast cancer and assuming a CDT of 110 days and a clinically detectable cell number of 10(9), the calculated cell number distribution would be approximately uniformly distributed from 1 to 10(8) cells, with RT reducing the frequency at all points by approximately =75%. From the brain metastasis data, assuming a CDT of 55 days, a cell number distribution of 10(3) to 10(8) cells would be calculated. PCI reduces the frequency of metastases by roughly 40%. For both the breast and the brain data, the effects of RT on the cell number distribution are not consistent with uniform radiosensitivity. Using Method 2, assuming a cell number of 10 after L+/-RT, the calculated CDTs range from 14 to 124 days. For the brain metastasis case, assuming a starting cell number of 3.16 x 10(3), the CDTs would primarily be in the 10-30-day range.
CONCLUSION: The distribution of clinical responses to adjuvant RT suggests a broad range of radiosensitivity, rather than uniform log cell kill. The subpopulation of tumors with minimal cell kill appears to be significant. This heterogeneity may be due to radioresistant subpopulations, failure to irradiate tumor cells, and/or new tumor formation. Similarly, the computed CDTs consistent with the clinical data are shorter than those reported in the literature. Simple radiobiologic models that fail to incorporate heterogeneity of radiosensitivity and/or tumor cell repopulation do not adequately describe clinical outcomes.