Coupled mathematical modeling of cisplatin electroporation.

The use of electrochemotherapy (ECT) is a well-established technique to increase the cellular uptake of cytotoxic agents within certain cancer treatment strategies. The study of the mechanisms that take part in this complex process is of high interest to gain a deeper knowledge of it, enabling the improvement of these strategies. In this work, we present a coupled multi-physics electroporation model based on a related previous one, to describe the effect of a set of electric pulses on cisplatin transport across the plasma membrane. The model applies a system of partial differential equations that includes Poisson's equation for the electric field, Nernst-Planck's equation for species transport, Maxwell's tensor and mechanical equilibrium equation for membrane deformation and Smoluchowski's equation for pore creation dynamics. Our numerical results were compared with previous numerical and experimental published data with good qualitative and quantitative agreement. These results indicate that pore aperture is favored at the cell poles by the electric field and mechanical stress forces, giving support to the dominant hypothesis of hydrophilic pore creation as the main mechanism of drug entry during an ECT treatment.

Cell membrane electroporation modeling: A multiphysics approach.

Electroporation-based techniques, i.e. techniques based on the perturbation of the cell membrane through the application of electric pulses, are widely used at present in medicine and biotechnology. However, the electric pulse - cell membrane interaction is not yet completely understood neither explicitly formalized. Here we introduce a Multiphysics (MP) model describing electric pulse - cell membrane interaction consisting on the Poisson equation for the electric field, the Nernst-Planck equations for ion transport (protons, hydroxides, sodium or calcium, and chloride), the Maxwell tensor and mechanical equilibrium equation for membrane deformations (with an explicit discretization of the cell membrane), and the Smoluchowski equation for membrane permeabilization. The MP model predicts that during the application of an electric pulse to a spherical cell an elastic deformation of its membrane takes place affecting the induced transmembrane potential, the pore creation dynamics and the ionic transport. Moreover, the coincidence among maximum membrane deformation, maximum pore aperture, and maximum ion uptake is predicted. Such behavior has been corroborated experimentally by previously published results in red blood and CHO cells as well as in supramolecular lipid vesicles.