Cylindrical cell membranes in uniform applied electric fields: validation of a transport lattice method

The frequency and time domain transmembrane voltage responses of a cylindrical cell in an external electric field are calculated using a transport lattice, which allows solution of a variety of biologically relevant transport problems with complex cell geometry and field interactions. Here we demonstrate the method for a cylindrical membrane geometry and compare results with known analytical solutions. Results of transport lattice simulations on a Cartesian lattice are found to have discrepancies with the analytical solutions due to the limited volume of the system model and approximations for the local membrane model on the Cartesian lattice. Better agreement is attained when using a triangular mesh to represent the geometry rather than a Cartesian lattice. The transport lattice method can be readily extended to more sophisticated cell, organelle, and tissue configurations. Local membrane models within a system lattice can also include nonlinear responses such as electroporation and ion-channel gating.

[1]  Domenico Coppola,et al.  Effect of Electrochemotherapy on Muscle and Skin , 2002, Technology in cancer research & treatment.

[2]  Om Gandhi,et al.  An Impedance Method to Calculate Currents Induced in Biological Bodies Exposed to Quasi-Static Electromagnetic Fields , 1985, IEEE Transactions on Electromagnetic Compatibility.

[3]  Mojca Pavlin,et al.  Dependence of induced transmembrane potential on cell density, arrangement, and cell position inside a cell system , 2002, IEEE Transactions on Biomedical Engineering.

[4]  Tadej Kotnik,et al.  Sensitivity of transmembrane voltage induced by applied electric fields—A theoretical analysis , 1997 .

[5]  Damijan Miklavčič,et al.  Electric Field-Induced Transmembrane Potential Depends on Cell Density and Organizatio , 1998 .

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

[7]  H. Fricke,et al.  The Electric Permittivity of a Dilute Suspension of Membrane‐Covered Ellipsoids , 1953 .

[8]  Susan Rae Smith-Baish,et al.  The dielectric properties of tissues , 1991 .

[9]  Elise C. Fear,et al.  Modeling assemblies of biological cells exposed to electric fields , 1998 .

[10]  W. Pickard,et al.  A model for the acute electrosensitivity of cartilaginous fishes , 1988, IEEE Transactions on Biomedical Engineering.

[11]  ELECTRIC FIELD-INDUCED TRANSMEMBRANE POTENTIAL DEPENDS ON CELL DENSITY AND ORGANIZATION , 2004 .

[12]  Raphael C. Lee,et al.  Injury by electrical forces: pathophysiology, manifestations, and therapy. , 1997, Current problems in surgery.

[13]  J. Gimsa,et al.  Analytical description of the transmembrane voltage induced on arbitrarily oriented ellipsoidal and cylindrical cells. , 2001, Biophysical journal.

[14]  R. Lee,et al.  Biophysical injury mechanisms in electrical shock trauma. , 2000, Annual review of biomedical engineering.

[15]  Per-Olof Persson,et al.  A Simple Mesh Generator in MATLAB , 2004, SIAM Rev..

[16]  M A Stuchly,et al.  A novel equivalent circuit model for gap-connected cells. , 1998, Physics in medicine and biology.

[17]  J. Weaver,et al.  Transport lattice approach to describing cell electroporation: use of a local asymptotic model , 2004, IEEE Transactions on Plasma Science.

[18]  Gabriel Kron,et al.  Numerical Solution of Ordinary and Partial Differential Equations by Means of Equivalent Circuits , 1945 .

[19]  M.A. Stuchly,et al.  Modeling assemblies of biological cells exposed to electric fields , 1997, IEEE Transactions on Biomedical Engineering.

[20]  Airton Ramos,et al.  A new computational approach for electrical analysis of biological tissues. , 2003, Bioelectrochemistry.

[21]  Jannicke Hilland,et al.  Simple sensor system for measuring the dielectric properties of saline solutions , 1997 .

[22]  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.

[23]  R. Plonsey,et al.  The transient subthreshold response of spherical and cylindrical cell models to extracellular stimulation , 1992, IEEE Transactions on Biomedical Engineering.

[24]  I Segev,et al.  Untangling dendrites with quantitative models. , 2000, Science.

[25]  R. Astumian,et al.  Rectification and signal averaging of weak electric fields by biological cells. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[26]  L. Mir,et al.  Electrochemotherapy potentiation of antitumour effect of bleomycin by local electric pulses. , 1991, European journal of cancer.

[27]  James C. Weaver,et al.  Electroporation of biological membranes from multicellular to nano scales , 2003 .

[28]  M. Stuchly,et al.  Biological cells with gap junctions in low-frequency electric fields , 1998, IEEE Transactions on Biomedical Engineering.

[29]  S Muñoz San Martín,et al.  Modelling the internal field distribution in human erythrocytes exposed to MW radiation. , 2004, Bioelectrochemistry.

[30]  G. T. Martin,et al.  Transport lattice models of heat transport in skin with spatially heterogeneous, temperature-dependent perfusion , 2004, Biomedical engineering online.

[31]  James C. Weaver,et al.  Detection of weak electric fields by sharks, rays, and skates. , 1998, Chaos.

[32]  H. Pauly,et al.  Über die Impedanz einer Suspension von kugelförmigen Teilchen mit einer Schale , 1959 .

[33]  Joseph Mizrahi,et al.  Rigorous Green's function formulation for transmembrane potential induced along a 3-D infinite cylindrical cell , 2002, IEEE Transactions on Biomedical Engineering.