Forecasting the growth of multicell tumour spheroids: implications for thedynamic growth of solid tumours

The growth dynamics of multicell tumour spheroids (MTS) were analysed by me ans of mathematical techniques derived from signal processing theory. Volum e vs. time trajectories of individual spheroids were fitted with the Gomper tz growth equation and the residuals (i.e. experimental volume determinatio ns minus calculated values by fitting) were analysed by fast fourier transf orm and power spectrum. Residuals were not randomly distributed around calc ulated growth trajectories demonstrating that the Gompertz model partially approximates the growth kinetics of three-dimensional tumour cell aggregate s. Power spectra decreased with increasing frequency following a 1/f(delta) power-law. Our findings suggest the existence of a source of 'internal' va riability driving the time-evolution of MTS growth. Based on these observat ions, a new stochastic Gompertzian-like mathematical model was developed wh ich allowed us to forecast the growth of MTS. In this model, white noise is additively superimposed to the trend described by the Gompertz growth equa tion and integrated to mimic the observed intrinsic variability of MTS grow th. A correlation was found between the intensity of the added noise and th e particular upper limit of volume size reached by each spheroid within two MTS populations obtained with two different cell lines. The dynamic forces generating the growth variability of three-dimensional tumour cell aggrega tes also determine the fate of spheroid growth with a strong predictive sig nificance. These findings suggest a new approach to measure tumour growth p otential.