130 J. W. WOODBURY AND W. E. CRILL 



EXTRACELLULAR FLUID RESISTANCE 



At first thought (Crill and Woodbury, 1 960) it would appear that the narrow 

 spaces between cells would form a high resistance path for current flow and 

 thus might account for the short space constant. A calculation of the space 

 constant in which it was assumed that the cell was cylindrical with negligible 

 internal resistance and that there was a 200 A spacing between cells gave the 

 satisfactorily short value of about 60 /x. The matter need be pursued no far- 

 ther, for these measurements were made on surface fibers and the extra- 

 cellular resistance could not have been appreciable in comparison with intra- 

 cellular resistance. Further, the calculation cannot apply even to deep cells 

 since none of these is much more than a half a space constant from a large 

 extracellular space between trabecular bundles. There may be some limita- 

 tions in this regard during activity when all cells in a transverse plane through 

 a trabecula may be active. The space constant is much shorter and simultane- 

 ous activity may limit the current pathways available to internal cells. 



INTRACELLULAR AND INTERCELLULAR RESISTANCE 



The experimental evidence establishes the fact that a large part of an intra- 

 cellularly applied current passes through other cells before returning to the 

 indifferent electrode via the extracellular spaces and the bathing medium. The 

 anatomy of a cell suggests that current passes from cell to cell via the inter- 

 calated disk. The close spacing and highly folded membrane are both charac- 

 teristics one would expect to find as means of improving the current trans- 

 mission. The narrow gap would increase the resistance to current flow parallel 

 to the disk membrane and the increased membrane area would decrease the 

 resistance to current flow through the membrane. 



The resistivity of an excitable membrane is 10'' times that of Ringer's 

 solution, so it is not evident that effective intercellular conduction is assured 

 by the small gap if the disk membrane has the same resistivity as non-disk 

 membrane. The precise calculation of the distribution of current between the 

 extracellular gap and the adjoining disk membrane is a difficult boundary 

 value problem. A satisfactory answer to the question can be obtained, how- 

 ever, by assuming that the whole surface of a cell except the disk is com- 

 pletely depolarized at some instant and calculating the potential in the inter- 

 disk region as a function of radius (Fig. 3). The differential equation describing 

 this situation is — de/d/- = /(?« — 2e)/A'-. The solution for e = at /• = ro is 

 e = 8a{\ - exp - (ro/A)2 [1 - ir/ro)^}/2 where A = \/(2SRmd/pe) is the 

 space constant and Rmd is the specific resistance of disk membrane. The 

 important parameter is evidently (a'o/A)-. The appearance of the space constant 

 squared suggests an "area" constant. Plots of ^ against /• for different values 

 of (a'o/A) are shown in Fig. 3. The current density entering the upper cell 

 from the lower, active cell is proportional to e as shown on the left-hand 



