Potential Induced by a Point Source of Current in the Interior of a Spherical Cell

The potential is calculated for all time, everywhere inside a spherical cell and in the external bathing medium for the case of a point source of current turned on abruptly at t=0. The problem is solved by exact methods and by singular perturbation theory. The model for the cell consists of a sphere...

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Bibliographic Details
Main Authors: Peskoff,Arthur, Eisenberg,Robert S, Cole,Julian D
Format: Report
Language:English
Subjects:
Anatomy and Physiology
ASYMPTOTIC SERIES
BOUNDARY VALUE PROBLEMS
EIGENVECTORS
ELECTRIC CURRENT
Electricity and Magnetism
HARMONIC FUNCTIONS
LAPLACE EQUATION
MATHEMATICAL MODELS
MEMBRANES(BIOLOGY)
MIXED BOUNDARY VALUE PROBLEMS
PERTURBATION THEORY
PHYSIOLOGY
POTENTIAL THEORY
SPHERES
Theoretical Mathematics
VOLTAGE
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Summary:The potential is calculated for all time, everywhere inside a spherical cell and in the external bathing medium for the case of a point source of current turned on abruptly at t=0. The problem is solved by exact methods and by singular perturbation theory. The model for the cell consists of a sphere of radius a with an internal medium of conductivity sigma sub i surrounded by a membrane of thickness delta, conductivity Sigma sub m and surface capacity (C sub m), bathed in an external medium of conductivity Sigma sub 0. The solution is discussed for the physiologically interesting case of epsilon=Sigma sub m a/Sigma sub i much less than 1, that is, when the effective internal resistance is small compared to the effective membrane resistance. The most important physiological results are when the rapid transient has died out, for times much greater than (C sub m)a/Sigma sub i. (Author)