Mathematical modelling of tumour response in primary breast cancer.

Although breast cancer is perceived to be relatively chemosensitive, cytotoxic drug therapy only leads to cure in the adjuvant setting. In advanced disease, primary resistance and inadequate cell kill may be important in determining the lack of a durable response to cytotoxics, but for an individual patient's tumour there is no consistent way of determining the importance of these two factors. An adaptation of Skipper's log cell kill model of tumour response to chemotherapy was applied to serial tumour measurements of 46 locally advanced primary breast carcinomas undergoing neoadjuvant chemotherapy. Assuming a log-normal distribution of errors in the clinically measured volumes, the model produced, for each tumour separately, in vivo estimates of proportional cell kill, initial resistance and tumour doubling times during therapy. After 4 weeks' treatment, these data could then be used to predict subsequent tumour volumes with good accuracy. In addition, for the 13 tumours that became operable after the neoadjuvant chemotherapy, there was a significant association between the final volume as predicted by the model and the final pathological volume (P < 0.05). This approach could be usefully employed to determine those tumours that are primarily resistant to the treatment regimen, permitting changes of therapy to more effective drugs at a time when the tumour is clinically responding but destined to progress.