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A three-dimensional model of cellula...

Mori, Yoichiro.

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A three-dimensional model of cellular electrical activity.

Record Type:	Electronic resources : Monograph/item
Title/Author:	A three-dimensional model of cellular electrical activity./
Author:	Mori, Yoichiro.
Description:	276 p.
Notes:	Source: Dissertation Abstracts International, Volume: 67-09, Section: B, page: 5114.
Contained By:	Dissertation Abstracts International67-09B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3234163
ISBN:	9780542877834

A three-dimensional model of cellular electrical activity.
Mori, Yoichiro.

A three-dimensional model of cellular electrical activity. - 276 p.

Source: Dissertation Abstracts International, Volume: 67-09, Section: B, page: 5114.

Thesis (Ph.D.)--New York University, 2006.

This item must not be sold to any third party vendors.

We present a three-dimensional model of cellular electrical activity. This model takes into account the three dimensional geometry of biological tissue as well as ionic concentration dynamics, both of which are neglected in conventional models of electrophysiology. Biological tissue is viewed three dimensional space being partitioned into intracellular and extracellular spaces by the cell membrane. The concentration of each ionic species is governed by the drift-diffusion equation and the electrostatic potential is determined implicitly through the electroneutrality constraint. Capacitative and transmembrane currents are modeled as boundary conditions at the two faces of the cellular membrane. This results in a system of nonlinear partial differential equations satisfied in the intracellular and extracellular spaces coupled through evolutionary boundary conditions at the cell membrane.

ISBN: 9780542877834Subjects--Topical Terms:

515831
Mathematics.

A three-dimensional model of cellular electrical activity.
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020 $a 9780542877834
035 $a (MiAaPQ)AAI3234163
035 $a AAI3234163
040 $a MiAaPQ $c MiAaPQ
100 1 $a Mori, Yoichiro. $3 3170110
245 1 2 $a A three-dimensional model of cellular electrical activity.
300 $a 276 p.
500 $a Source: Dissertation Abstracts International, Volume: 67-09, Section: B, page: 5114.
500 $a Adviser: Charles S. Peskin.
502 $a Thesis (Ph.D.)--New York University, 2006.
506 $a This item must not be sold to any third party vendors.
506 $a This item must not be added to any third party search indexes.
520 $a We present a three-dimensional model of cellular electrical activity. This model takes into account the three dimensional geometry of biological tissue as well as ionic concentration dynamics, both of which are neglected in conventional models of electrophysiology. Biological tissue is viewed three dimensional space being partitioned into intracellular and extracellular spaces by the cell membrane. The concentration of each ionic species is governed by the drift-diffusion equation and the electrostatic potential is determined implicitly through the electroneutrality constraint. Capacitative and transmembrane currents are modeled as boundary conditions at the two faces of the cellular membrane. This results in a system of nonlinear partial differential equations satisfied in the intracellular and extracellular spaces coupled through evolutionary boundary conditions at the cell membrane.
520 $a We present a detailed asymptotic derivation of the model equations with the Poisson equation and the drift-diffusion equation as a starting point. This calculation reveals the presence of a hierarchy of mathematical models of cellular electrical activity, the proposed three-dimensional model being the most detailed, and traditional models being the simplest in the hierarchy. This analysis also shows that there are two disparate time scales, one associated with ionic diffusion, and the other with the electrotonic spread of membrane potential.
520 $a Under simplifying assumptions on the model equations, we obtain a global solvability result using convex analysis and weak compactness arguments. Our method of proof is constructive, allowing us to simultaneously prove convergence of a time-semidiscretized numerical scheme of the simplified system of equations.
520 $a A numerical method based on a cartesian grid finite volume method is developed. The presence of two disparate time scales necessitates an implicit time discretization, and the resulting nonlinear algebraic equations are solved using an iterative scheme. We perform a convergence study to check its order of accuracy. The numerical method allows us to check the validity of the foregoing asymptotic analysis by way of computational experiment.
520 $a The foregoing modeling methodology is applied to cardiac physiology. We show that simulations using this model can be used to explore the characteristics of a recently observed anomalous mode of cardiac action potential propagation: cardiac propagation without gap junctions.
590 $a School code: 0146.
650 4 $a Mathematics. $3 515831
650 4 $a Biophysics, General. $3 1019105
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690 $a 0786
710 2 $a New York University. $3 515735
773 0 $t Dissertation Abstracts International $g 67-09B.
790 $a 0146
791 $a Ph.D.
792 $a 2006
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3234163