For more than a century, a variety of ordinary differential equation growth models have been used to describe and predict the proliferation of human malignancies. Indeed, in the field of mathematical oncology, the growth of cell populations over time is typically represented by sigmoidal functions, such as logistic or Gompertz curves and their generalizations. These models are particularly focused on understanding and predicting the proliferation of cancer cells, including those from human glioblastomas, which can be very aggressive brain tumors with a survival rate of less than two years.

This research examines in vitro cell cultures of five lines of human glioblastoma using curve fitting and numerical parameter estimation of real datasets to separately describe the growth profile of all these cell populations lineages over time.

Cell culture experiments were performed in the Advanced Therapeutics Laboratory at FCF-UNICAMP. These included a well-established human glioblastoma cell line (NG97) and four other glioblastoma cell lines derived from clinical patients designated N07, C03, L09 and J01. Twelve repeated time series of experiments were collected for each cell line. Cell counting was performed daily on days 1 to 6. The drda R package was used for curve fitting of the measured data aiming to determine the intrinsic growth rate and other parameters for each of the five cell lines. The 5-parameter generalized logistic curve was used, and all the resulting models were analyzed under statistical criteria such as the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC).

Curve fitting analysis revealed significant diversity in the population growth of different cell lines. The drda R package proved to be highly effective in capturing these different behaviors and the unique sigmoidal shapes associated with them. Notably, the population growth of NG97 cells showed the least variability over time, with the narrowest confidence intervals for the fitted curves and their associated parameters. This consistency can be attributed to the fact that NG97 is a well-established cell lineage. In contrast, the new patient-derived cell lines showed a greater degree of uncertainty, particularly when their confidence intervals were extrapolated beyond the last day of measurement. This observation highlights the need for additional time points in in vitro experiments with newly derived human patient cells.

According to the numerical and graphical results, to AIC and BIC metrics, and also to the respective levels of provided uncertainty, the fitted models present a reasonable growth description of all the studied lineages of glioblastoma, regardless of cell line being well-established (NG97) or newly originated from human patients (N07, C03, L09, and J01). Further correlations between those results and prognostics and clinics may be of value for translational oncology.