Tumor growth in the space-time with temporal fractal dimension

An improvement of the Waliszewski and Konarski approach [Waliszewski P, Konarski J. The Gompertzian curve reveals fractal properties of tumor growth. Chaos, Solitons & Fractals 2003;16:665-74] to determination of the time-dependent temporal fractal dimension b(t)(t) and the scaling factor a(t)(t) for the tumor formation in the fractal space-time is presented. The analytical formulae describing the time-dependence of b(t)(t) and a(t)(t), which take into account appropriate boundary conditions for t -> 0 and t -> infinity, are derived. Their validity is tested on the experimental growth curve obtained by Laird for the Flexner-Jobling rat's tumor. A hypothesis is formulated that tumorigenesis has a lot in common with the neuronal differentiation and synapse formation. These processes are qualitatively described by the same Gompertz function of growth and take place in the fractal space-time whose mean temporal fractal dimension is lost during progression. (c) 2006 Elsevier Ltd. All rights reserved.