The Gompertzian curve reveals fractal properties of tumor growth

The normalized Gompertzian curve reflecting growth of experimental malignant tumors in time can be fitted by the power function y,(t) = at(b) with the coefficient of nonlinear regression r greater than or equal to 0.95, in which the exponent b is a temporal fractal dimension, (i.e., a real number), and time t is a scalar. This curve is a fractal, (i.e., fractal dimension b exists, it changes along the time scale, the Gompertzian function is a contractable mapping of the Banach space R of the real numbers, holds the Banach theorem about the fix point, and its derivative is less than or equal to 1). This denotes that not only space occupied by the interacting cancer cells, but also local, intrasysternic time, in which tumor growth occurs, possesses fractal structure. The value of the mean temporal fractal dimension decreases along the curve approaching eventually integer values; a fact consistent with our hypothesis that the fractal structure is lost during tumor progression. (C) 2002 Elsevier Science Ltd. All rights reserved.