Comparative Gompertzian analysis of alterations of tumor growth patterns

We have shown previously that different patterns of growth (including classical Gompertzian, exponential, and hyperexponential) can be described based on the Gompertzian difference equation, In G(t+s) = a+b In G(t) [G(t), tumor size at time t; s, constant time interval of a stroboscopic set of tumor size measurements], by the initial or intrinsic growth rate, a, and the exponential rate of growth deceleration, b (I. D. Bassukas and B. Maurer-Schultze, Growth Dev. Aging, 52: 113-122, 1988). Particularly, the possible effects of antineoplastic treatments on this latter factor have not been adequately appreciated to date. In the present study a new method of comparison of growth process is introduced, which consists of two steps. (a) The corresponding growth patterns are compared with each other on the basis of the Gompertzian difference equation using an analysis of variance algorithm. The result indicates whether or not there is an alteration of the growth pattern and, if there is one, whether it refers to alterations of the a and/or b values for the growth patterns. (b) The ultimate effect of any perturbation is assessed by using the limit (for t-->infinity) of the quotient of the tumor sizes after and before perturbation to characterize it as stimulation or inhibition. The present approach introduces a new quality of tumor growth perturbations; tumor growth may be altered although being neither inhibited nor stimulated, a phenomenon with biological significance still to be evaluated. The application of this method to the treatment with suramin of a human renal cell carcinoma xenograft in nude mice reveals a complex alteration of its growth pattern. Suramin simultaneously inhibits both the initial or intrinsic growth rate and the exponential rate of growth deceleration of this tumor. Consequently, this tumor starts with a lower growth rate in the presence of suramin; however, this rate also decelerates more slowly as a function of tumor growth, so that treated tumors, although initially inhibited, grow larger than controls.