Estimation of tumor cell kill from Gompertz growth curves.

The Gompertz function has been found to mathematically describe several types of biologic growth, including the growth of transplantable animal tumors. If it is assumed that treatment (chemotherapy, surgery, x-irradiation) of tumors causes cell death in a relatively short interval and that the surviving cells begin to repopulate immediately, producing tumor growth according to the Gompertz function before treatment, then the displacement in time between the two growth curves may be quantitatively related to tumor cell kill. This theory is developed and compared to bioassay values. It is also shown that tumor cell kill may be determined graphically without the necessity of computer-generated estimates of the Gompertz parameters.