The growth dynamics of multicell tumour spheroids (MTS) were analysed by means of mathematical techniques derived from signal processing theory. Volume vs. time trajectories of individual spheroids were fitted with the Gompertz growth equation and the residuals (i.e. experimental volume determinations minus calculated values by fitting) were analysed by fast fourier transform and power spectrum. Residuals were not randomly distributed around calculated growth trajectories demonstrating that the Gompertz model partially approximates the growth kinetics of three‐dimensional tumour cell aggregates. Power spectra decreased with increasing frequency following a 1/f^δ power‐law. Our findings suggest the existence of a source of ‘internal’ variability driving the time‐evolution of MTS growth. Based on these observations, a new stochastic Gompertzian‐like mathematical model was developed which allowed us to forecast the growth of MTS. In this model, white noise is additively superimposed to the trend described by the Gompertz growth equation and integrated to mimic the observed intrinsic variability of MTS growth. A correlation was found between the intensity of the added noise and the 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 aggregates also determine the fate of spheroid growth with a strong predictive significance. These findings suggest a new approach to measure tumour growth potential.

Acidosis of the tumor microenvironment leads to cancer invasion, progression and resistance to therapies. We present a biophysical model that describes how tumor cells regulate intracellular and extracellular acidity while they grow in a microenvironment characterized by increasing acidity and hypoxia. The model takes into account the dynamic interplay between glucose and $$\hbox {O}_2$$O 2 consumption with lactate and $$\hbox {CO}_2$$CO 2 production and connects these processes to $$\hbox {H}^+$$H + and $$\hbox {HCO}_3^-$$HCO 3 - fluxes inside and outside cells. We have validated the model with independent experimental data and used it to investigate how and to which extent tumor cells can survive in adverse micro-environments characterized by acidity and hypoxia. The simulations show a dominance of the $$\hbox {H}^+$$H + exchanges in well-oxygenated regions, and of $$\hbox {HCO}_3^-$$HCO 3 - exchanges in the inner hypoxic regions where tumor cells are known to acquire malignant phenotypes. The model also includes the activity of the enzyme Carbonic Anhydrase 9 (CA9), a known marker of tumor aggressiveness, and the simulations demonstrate that CA9 acts as a nonlinear $$\hbox {pH}_i$$pH i equalizer at any $$\hbox {O}_2$$O 2 level in cells that grow in acidic extracellular environments.