Dynamical modeling of tissue electroporation.

In this paper, we propose a new dynamical model of tissue electroporation. The model is based on equivalent circuit approach at the tissue. Considering two current densities from cells and extracellular matrix, we identify the macroscopic homogenised contribution of the cell membranes. Our approach makes it possible to define a macroscopic homogenised electric field and a macroscopic homogenised transmembrane potential. This provides a direct link between the cell scale electroporation models and the tissue models. Finite element method adapted to the new non-linear model of tissue electroporation is used to compare experiments with simulations. Adapting the phenomenological electroporation model of Leguèbe et al. to the tissue scale, we calibrate the tissue model with experimental data. This makes two steps appear in the tissue electroporation process, as for cells. The new insight of the model lies in the well-established equivalent circuit approach to provide a homogenised version of cell scale models. Our approach is tightly linked to numerical homogenisation strategies adapted to bioelectrical tissue modeling.

[1]  K. Foster,et al.  Dielectric properties of mammalian tissues from 0.1 to 100 MHz: a summary of recent data. , 1982, Physics in medicine and biology.

[2]  Giuseppe Savaré,et al.  Degenerate Evolution Systems Modeling the Cardiac Electric Field at Micro- and Macroscopic Level , 2002 .

[3]  A. T. Esser,et al.  Microdosimetry for conventional and supra-electroporation in cells with organelles. , 2006, Biochemical and biophysical research communications.

[4]  Clair Poignard,et al.  “Classical” Electropermeabilization Modeling at the Cell Scale , 2014, Journal of mathematical biology.

[5]  B. Rubinsky,et al.  Synergistic Combination of Electrolysis and Electroporation for Tissue Ablation , 2016, PloS one.

[6]  J. Weaver,et al.  Theory of electroporation: A review , 1996 .

[7]  Tomaz Slivnik,et al.  Sequential finite element model of tissue electropermeabilization , 2005, IEEE Transactions on Biomedical Engineering.

[8]  C. Suárez,et al.  The Role of Ph Fronts in Tissue Electroporation Based Treatments , 2013, PloS one.

[9]  Damijan Miklavcic,et al.  Modeling of electric field distribution in tissues during electroporation , 2013, Biomedical engineering online.

[10]  Damijan Miklavčič,et al.  Effect of Blood Vessel Segmentation on the Outcome of Electroporation-Based Treatments of Liver Tumors , 2015, PloS one.

[11]  P. Bisegna,et al.  Evolution and memory effects in the homogenization limit for electrical conduction in biological tissues , 2004 .

[12]  James C Weaver,et al.  An approach to electrical modeling of single and multiple cells , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[13]  C. Kelley.  Iterative Methods for Linear and Nonlinear Equations , 1987 .

[14]  A. T. Esser,et al.  Towards Solid Tumor Treatment by Irreversible Electroporation: Intrinsic Redistribution of Fields and Currents in Tissue , 2007, Technology in cancer research & treatment.

[15]  L. Mir,et al.  Conducting and permeable states of cell membrane submitted to high voltage pulses: mathematical and numerical studies validated by the experiments. , 2014, Journal of theoretical biology.

[16]  Damijan Miklavcic,et al.  Real time electroporation control for accurate and safe in vivo non-viral gene therapy. , 2007, Bioelectrochemistry.

[17]  M. Rols,et al.  Mechanisms of cell membrane electropermeabilization: a minireview of our present (lack of ?) knowledge. , 2005, Biochimica et biophysica acta.

[18]  M. V. Levin.  The medical engineering industry in the third year of the tenth five-year period , 1978 .

[19]  Valerica Raicu,et al.  Dielectric properties of rat liver in vivo: analysis by modeling hepatocytes in the tissue architecture , 1998 .

[20]  W. Krassowska,et al.  Electroporation and Shock-Induced Transmembrane Potential in a Cardiac Fiber During Defibrillation Strength Shocks , 1998, Annals of Biomedical Engineering.

[21]  Assyr Abdulle,et al.  Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems , 2016 .

[22]  L. Dissado,et al.  A fractal interpretation of the dielectric response of animal tissues. , 1990, Physics in medicine and biology.

[23]  Lionel Cima,et al.  Macroscopic characterization of cell electroporation in biological tissue based on electrical measurements , 2004 .

[24]  Damijan Miklavčič,et al.  Advanced Electroporation Techniques in Biology and Medicine , 2010 .

[25]  Valerica Raicu,et al.  Dielectric properties of rat liver in vivo: a noninvasive approach using an open-ended coaxial probe at audio/radio frequencies , 1998 .

[26]  Damijan Miklavčič,et al.  Time course of transmembrane voltage induced by time-varying electric fields—a method for theoretical analysis and its application , 1998 .

[27]  Helen Kavnoudias,et al.  In vivo characterization and numerical simulation of prostate properties for non‐thermal irreversible electroporation ablation , 2014, The Prostate.

[28]  Charles Polk,et al.  CRC Handbook of Biological Effects of Electromagnetic Fields , 1986 .

[29]  Boris Rubinsky,et al.  In vivo electrical conductivity measurements during and after tumor electroporation: conductivity changes reflect the treatment outcome , 2009, Physics in medicine and biology.

[30]  Rafael V. Davalos,et al.  In Vivo Irreversible Electroporation Kidney Ablation: Experimentally Correlated Numerical Models , 2015, IEEE Transactions on Biomedical Engineering.

[31]  W. Krassowska,et al.  Modeling electroporation in a single cell. , 2007, Biophysical journal.

[32]  W. Krassowska,et al.  Modeling electroporation in a single cell. I. Effects Of field strength and rest potential. , 1999, Biophysical journal.

[33]  Hao Lin,et al.  Numerical simulation of molecular uptake via electroporation. , 2011, Bioelectrochemistry.

[34]  D. Miklavčič,et al.  ELECTRIC PROPERTIES OF TISSUES , 2006 .

[35]  C. Johnson,et al.  Phase-Shift Dynamics of Sea Urchin Overgrazing on Nutrified Reefs , 2016, PloS one.

[36]  M. Kranjc,et al.  Dynamic finite-element model for efficient modelling of electric currents in electroporated tissue , 2016, Scientific Reports.

[37]  Ponisseril Somasundaran,et al.  ENCYCLOPEDIA OF Surface and Colloid Science , 2006 .