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 bt(t) and the scaling factor at(t) for the tumor formation in the fractal space–time is presented. The analytical formulae describing the time-dependence of bt(t) and at(t), which take into account appropriate boundary conditions for t → 0 and t → ∞, 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.