Basic ingredients for mathematical modeling of tumor growth in vitro: cooperative effects and search for space

Simulation analysis for tumor radiotherapy based on three-component mathematical models

OBJECTIVE

To setup a three-component tumor growth mathematical model and discuss its basic application in tumor fractional radiotherapy with computer simulation.

METHOD

First, our three-component tumor growth model extended from the classical Gompertz tumor model was formulated and applied to a fractional radiotherapy with a series of proper parameters. With the computer simulation of our model, the impact of some parameters such as fractional dose, amount of quiescent tumor cells, and α/β value to the effect of radiotherapy was also analyzed, respectively.

RESULTS

With several optimal technologies, the model could run stably and output a series of convergent results. The simulation results showed that the fractional radiotherapy dose could impact the effect of radiotherapy significantly, while the amount of quiescent tumor cells and α/β value did that to a certain extent.

CONCLUSIONS

Supported with some proper parameters, our model can simulate and analyze the tumor radiotherapy program as well as give some theoretical instruction to radiotherapy personalized optimization.

The universal growth rate behavior and regime transition in adherent cell colonies

In this work, we used five cell lineages, cultivated in vitro, to show they follow a common functional form to the growth rate: a sigmoidal curve, suggesting that competition and cooperation (usual mechanisms for systems with this behavior) might be present. Both theoretical and experimental investigations, on the causes of this behavior, are challenging for the research field; since the sigmoidal form to the growth rate seems to absorb important properties of such systems, e.g., cell deformation and statistical interactions. We shed some light on this subject by showing how cell spreading affects the radius behavior of the growing colonies. Doing numerical time derivatives of the experimental data, we obtained the growth rates. Using reduced variables for the time and rates, we obtained the collapse of all colonies growth rates onto one curve with sigmoidal shape. This suggests a universal-type behavior, with regime transition related to a morphological transition of adherent cell colonies.