Modelling extracellular electrical stimulation: IV. Effect of the cellular composition of neural tissue on its spatio-temporal filtering properties

OBJECTIVE The objective of this paper is to present a concrete application of the cellular composite model for calculating the membrane potential, described in an accompanying paper. APPROACH A composite model that is used to determine the membrane potential for both longitudinal and transverse modes of stimulation is demonstrated. MAIN RESULTS Two extreme limits of the model, near-field and far-field for an electrode close to or distant from a neuron, respectively, are derived in this paper. Results for typical neural tissue are compared using the composite, near-field and far-field models as well as the standard isotropic volume conductor model. The self-consistency of the composite model, its spatial profile response and the extracellular potential time behaviour are presented. The magnitudes of the longitudinal and transverse components for different values of electrode-neurite separations are compared. SIGNIFICANCE The unique features of the composite model and its simplified versions can be used to accurately estimate the spatio-temporal response of neural tissue to extracellular electrical stimulation.

[1]  A. Tarakanova,et al.  Molecular modeling of protein materials: case study of elastin , 2013 .

[2]  D. Durand,et al.  Modeling the effects of electric fields on nerve fibers: Determination of excitation thresholds , 1992, IEEE Transactions on Biomedical Engineering.

[3]  R. Plonsey,et al.  Analysis of excitable cell activation: relative effects of external electrical stimuli , 1990, Medical and Biological Engineering and Computing.

[4]  Bahman Tahayori,et al.  Modeling extracellular electrical stimulation: I. Derivation and interpretation of neurite equations , 2012, Journal of neural engineering.

[5]  P. Sterling,et al.  How the Optic Nerve Allocates Space, Energy Capacity, and Information , 2009, The Journal of Neuroscience.

[6]  P. Basser,et al.  Axcaliber: A method for measuring axon diameter distribution from diffusion MRI , 2008, Magnetic resonance in medicine.

[7]  P. Basser,et al.  New currents in electrical stimulation of excitable tissues. , 2000, Annual review of biomedical engineering.

[8]  J. Latikka,et al.  Conductivity of living intracranial tissues. , 2001, Physics in medicine and biology.

[9]  G. Stuart,et al.  Direct measurement of specific membrane capacitance in neurons. , 2000, Biophysical journal.

[10]  N. Trayanova,et al.  Extracellular potentials and currents of a single active fiber in a restricted volume conductor , 2006, Annals of Biomedical Engineering.

[11]  F. Rattay,et al.  The basic mechanism for the electrical stimulation of the nervous system , 1999, Neuroscience.

[12]  B. Roth How the anisotropy of the intracellular and extracellular conductivities influences stimulation of cardiac muscle , 1992 .

[13]  Bahman Tahayori,et al.  Modelling extracellular electrical stimulation: III. Derivation and interpretation of neural tissue equations , 2014, Journal of neural engineering.

[14]  Frank Rattay,et al.  Electrical Nerve Stimulation , 1990 .

[15]  W. Crill,et al.  Specific membrane resistivity of dye-injected cat motoneurons. , 1971, Brain research.

[16]  D. Copenhagen,et al.  Passive electrical cable properties and synaptic excitation of tiger salamander retinal ganglion cells , 1996, Visual Neuroscience.

[17]  F. Rattay Analysis of Models for External Stimulation of Axons , 1986, IEEE Transactions on Biomedical Engineering.

[18]  J. B. Ranck,et al.  Specific impedance of rabbit cerebral cortex. , 1963, Experimental neurology.

[19]  Frank Rattay,et al.  Simulation of artificial neural reactions produced with electric fields , 1993, Simul. Pract. Theory.

[20]  R. Plonsey,et al.  Point source nerve bundle stimulation: effects of fiber diameter and depth on simulated excitation , 1990, IEEE Transactions on Biomedical Engineering.

[21]  Alain Glière,et al.  Current approaches to model extracellular electrical neural microstimulation , 2014, Front. Comput. Neurosci..

[22]  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.

[23]  Joseph F. Rizzo,et al.  Visual prosthesis and opthalmic devices : new hope in sight , 2007 .

[24]  J. Patrick Reilly,et al.  Electrostimulation : Theory, applications, and computational model , 2011 .

[25]  B. Roth,et al.  Electrical stimulation of cardiac tissue: a bidomain model with active membrane properties , 1994, IEEE Transactions on Biomedical Engineering.

[26]  Joseph F. Rizzo,et al.  Visual Prosthesis and Ophthalmic Devices , 2007 .

[27]  Masato Okada,et al.  Estimated distribution of specific membrane resistance in hippocampal CA1 pyramidal neuron , 2006, Brain Research.

[28]  Comments, with reply, on "Point source nerve bundle stimulation: effects of fiber diameter and depth on simulated excitation" by K.W. Altman and R. Plonsey , 1991 .

[29]  Socrates Dokos,et al.  Modeling extracellular electrical stimulation: II. Computational validation and numerical results , 2012, Journal of neural engineering.

[30]  Sébastien Joucla,et al.  Modeling extracellular electrical neural stimulation: From basic understanding to MEA-based applications , 2012, Journal of Physiology-Paris.

[31]  P. Fromherz,et al.  The extracellular electrical resistivity in cell adhesion. , 2006, Biophysical journal.

[32]  J T Rubinstein,et al.  Analytical theory for extracellular electrical stimulation of nerve with focal electrodes. II. Passive myelinated axon. , 1988, Biophysical journal.

[33]  Warren M. Grill,et al.  Prediction of myelinated nerve fiber stimulation thresholds: limitations of linear models , 2004, IEEE Transactions on Biomedical Engineering.

[34]  N. Cohen,et al.  Cochlear Implants , 2000 .

[35]  S. Laughlin,et al.  Ion-Channel Noise Places Limits on the Miniaturization of the Brain’s Wiring , 2005, Current Biology.

[36]  D. Mcneal Analysis of a Model for Excitation of Myelinated Nerve , 1976, IEEE Transactions on Biomedical Engineering.

[37]  David B. Grayden,et al.  Internal inconsistencies in models of electrical stimulation in neural tissue , 2013, 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

[38]  P. Sterling,et al.  Why Do Axons Differ in Caliber? , 2012, The Journal of Neuroscience.

[39]  C. Gabriel,et al.  Electrical conductivity of tissue at frequencies below 1 MHz , 2009, Physics in medicine and biology.

[40]  N. Spruston,et al.  Determinants of Voltage Attenuation in Neocortical Pyramidal Neuron Dendrites , 1998, The Journal of Neuroscience.

[41]  Hamish Meffin,et al.  The electrotonic length constant: A theoretical estimate for neuroprosthetic electrical stimulation , 2011, Biomed. Signal Process. Control..

[42]  A. Burkitt,et al.  Effect of soma polarization on electrical stimulation thresholds of retinal ganglion cells , 2013, 2013 6th International IEEE/EMBS Conference on Neural Engineering (NER).

[43]  Warren M Grill,et al.  Analysis of the quasi-static approximation for calculating potentials generated by neural stimulation , 2008, Journal of neural engineering.

[44]  R. Chitwood,et al.  Passive electrotonic properties of rat hippocampal CA3 interneurones , 1999, The Journal of physiology.

[45]  R. Plonsey,et al.  Development of a model for point source electrical fibre bundle stimulation , 1988, Medical and Biological Engineering and Computing.

[46]  J T Rubinstein,et al.  Analytical theory for extracellular electrical stimulation of nerve with focal electrodes. I. Passive unmyelinated axon. , 1988, Biophysical journal.

[47]  H. Lüscher,et al.  Passive electrical properties of ventral horn neurons in rat spinal cord slices. , 1998, Journal of neurophysiology.

[48]  Katsuhiko Ogata Designing Linear Control Systems with MATLAB , 1993 .

[49]  D. Shelton,et al.  Membrane resistivity estimated for the purkinje neuron by means of a passive computer model , 1985, Neuroscience.

[50]  Frank Rattay,et al.  Electrical Nerve Stimulation: "Theory, Experiments And Applications" , 2001 .

[51]  C. Nicholson,et al.  Diffusion in brain extracellular space. , 2008, Physiological reviews.

[52]  Johannes J. Struijk,et al.  Evaluation of the cable model for electrical stimulation of unmyelinated nerve fibers , 2001, IEEE Transactions on Biomedical Engineering.