On the Gompertzian growth in the fractal space-time.
An analytical approach to determination of time-dependent temporal fractal dimension b(t)(t) and scaling factor a(t)(t) for the Gompertzian growth in the fractal space-time is presented. The derived formulae take into account the proper boundary conditions and permit a calculation of the mean values b(t)(t) and a(t)(t) at any period of time. The formulae derived have been tested on experimental data obtained by Schrek for the Brown-Pearce rabbit's tumor growth. The results obtained confirm a possibility of successful mapping of the experimental Gompertz curve onto the fractal power-law scaling function y(t)=a(t)tb(t) and support a thesis that Gompertzian growth is a self-similar and allometric process of a holistic nature.
Molski
Marcin
M
Department of Theoretical Chemistry, Faculty of Chemistry, A. Mickiewicz University of Poznań, ul. Grunwaldzka 6, PL 60-780 Poznań, Poland. Marcin@rovib.amu.edu.pl
Konarski
Jerzy
J
D017709:Fractals; D008962:Models, Theoretical; D013997:Time Factors