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 descr ibed 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 s troboscopic set of tumor size measurements], by the initial or intrins ic 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 treatmen ts on this latter factor have not been adequately appreciated to date. In the present study a new method of comparison of growth processes i s introduced, which consists of two steps. (a) The corresponding growt h patterns are compared with each other on the basis of the Gompertzia n difference equation using an analysis of variance algorithm. The res ult indicates whether or not there is an alteration of the growth patt ern and, if there is one, whether it refers to alterations of the a an d/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 q uotient of the tumor sizes after and before perturbation to characteri ze 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 bi ological significance still to be evaluated. The application of this m ethod to the treatment with suramin of a human renal cell carcinoma xe nograft in nude mice reveals a complex alteration of its growth patter n. Suramin simultaneously inhibits both the initial or intrinsic growt h rate and the exponential rate of growth deceleration of this tumor. Consequently, this tumor starts with a lower growth rate in the presen ce of suramin; however, this rate also decelerates more slowly as a fu nction of tumor growth, so that treated tumors, although initially inh ibited, grow larger than controls.