Microenvironmental influence on microtumour infiltration patterns: 3D-mathematical modelling supported by in vitro studies

OpenEP: an open-source simulator for electroporation-based tumor treatments

Electroporation (EP), the increase of cell membrane permeability due to the application of electric pulses, is a universal phenomenon with a broad range of applications. In medicine, some of the foremost EP-based tumor treatments are electrochemotherapy (ECT), irreversible electroporation, and gene electrotransfer (GET). The electroporation phenomenon is explained as the formation of cell membrane pores when a transmembrane cell voltage reaches a threshold value. Predicting the outcome of an EP-based tumor treatment consists of finding the electric field distribution with an electric threshold value covering the tumor (electroporated tissue). Threshold and electroporated tissue are also a function of the number of pulses, constituting a complex phenomenon requiring mathematical modeling. We present OpenEP, an open-source specific purpose simulator for EP-based tumor treatments, modeling among other variables, threshold, and electroporated tissue variations in time. Distributed under a free/libre user license, OpenEP allows the customization of tissue type; electrode geometry and material; pulse type, intensity, length, and frequency. OpenEP facilitates the prediction of an optimal EP-based protocol, such as ECT or GET, defined as the critical pulse dosage yielding maximum electroporated tissue with minimal damage. OpenEP displays a highly efficient shared memory implementation by taking advantage of parallel resources; this permits a rapid prediction of optimal EP-based treatment efficiency by pulse number tuning.

An on-lattice agent-based Monte Carlo model simulating the growth kinetics of multicellular tumor spheroids

PURPOSE

To develop an on-lattice agent-based model describing the growth of multicellular tumor spheroids using simple Monte Carlo tools.

METHODS

Cells are situated on the vertices of a cubic grid. Different cell states (proliferative, hypoxic or dead) and cell evolution rules, driven by 10 parameters, and the effects of the culture medium are included. About twenty spheroids of MCF-7 human breast cancer were cultivated and the experimental data were used for tuning the model parameters.

RESULTS

Simulated spheroids showed adequate sizes of the necrotic nuclei and of the hypoxic and proliferative cell phases as a function of the growth time, mimicking the overall characteristics of the experimental spheroids. The relation between the radii of the necrotic nucleus and the whole spheroid obtained in the simulations was similar to the experimental one and the number of cells, as a function of the spheroid volume, was well reproduced. The statistical variability of the Monte Carlo model described the whole volume range observed for the experimental spheroids. Assuming that the model parameters vary within Gaussian distributions it was obtained a sample of spheroids that reproduced much better the experimental findings.

CONCLUSIONS

The model developed allows describing the growth of in vitro multicellular spheroids and the experimental variability can be well reproduced. Its flexibility permits to vary both the agents involved and the rules that govern the spheroid growth. More general situations, such as, e. g., tumor vascularization, radiotherapy effects on solid tumors, or the validity of the tumor growth mathematical models can be studied.