CELLULAR ELECTROPHYSIOLOGY OF THE HEART 



281 



100 200 



RADIAL DISTANCE (/i) 



300 



FIG. 30. Spatial decrement of electrotonic potential in a 

 rat atrial trabecula. Ordinate : change in membrane potential 

 per unit applied current [(£ — £r)/Is]- Abscissa: distance 

 from an intracellular current-applying electrode along radius 

 parallel to the trabecula edge. Dots are points from one experi- 

 ment; the solid line is the theoretical curve of voltage against 

 radial distance for a single planar cell. The space constant 

 (X) is indicated by the arrow at 1 70 ti. The theoretical curve, 

 a zero order Bessel function of the second kind with imaginary 

 argument was fitted to the experimental points by trial and 

 error. (Crill & Woodbury, unpublished data, i960.) 



visible intercalated discs. These discs frequently 

 cross a cell in a stepwise manner, the disc membrane 

 changing to a regular membrane when running 

 parallel to the fibrils between steps. This structure 

 has been formalized and schematized in figure 31 

 (93). Thus, difTerent cells oppose a particular cell 

 across the different steps. The tortuosity and close 

 spacing of the disc membranes strongly suggest that 

 the intercalated discs are the site at which intracellular 

 current is transferred from one cell to the next. The 

 increased surface area at the disc reduces transmem- 

 brane resistance and the narrow gap decreases the 

 leakage of intercellular current into larger interstitial 

 spaces. If the resistance of the discs is comparatively 

 low, the multiple connections to other cells through 

 them insure spread of the current in all directions 

 from any one cell, but preferentially in the fiber 

 direction (as shown by the current flow lines in fig. 

 31). Sjostrand et al. (108) suggest that the gap between 

 opposing disc rrembrancs is filled with lipids rather 

 than interstitial fluid. If true, this arrangement should 



aid transmission, since the poorly conducting lipids 

 would greatly reduce flow parallel to the disc mem- 

 brane but, being thin, would have a much lesser 

 effect perpendicular to it. However, theoretical 

 calculation (Woodbury and Crill in 41) shows that 

 transmission is efficient even if the gap is filled with 

 interstitial fluid. 



On a grosser scale, cardiac cells are not uniformly 

 closely packed. Bundles of closely packed cells are 

 separated from other bundles by larger interstitial 

 spaces containing capillaries. These bundles are no 

 more than about six cells in diameter, so that no cell 

 is more than three or four cell diameters from a large 

 extracellular fluid space. These bundles merge and 

 branch at short intervals, but tend to form even larger 

 bundles of the order of millimeters in diameter, called 

 "trabeculae," which in turn merge and branch in a 

 meshwork to form the myocardium. 



Analysis of Two-Dimensional Electrotonus in Atrium 



Theoretical analysis of the experimentally meas- 

 ured two-dimensional current spread in rat atrium 

 (Crill and Woodbury, unpublished results) gives 

 considerable insight into the detailed electrical prop- 

 erties of cardiac tissue in general and of the inter- 

 calated disc in particular. The results can be best 

 interpreted on the assumption that the intercalated 

 discs have low or negligible resistance to transverse 

 current flow so that the atrium is the two-dimensional 

 equivalent of a skeletal muscle fiber; i.e., this flat 

 tissue can \x represented electrically as one large 

 planar cell. Aside from the observed variation of cur- 

 rent spread with direction, this simple model served 

 to describe surprisingly well the steady-state distribu- 

 tion of potential as a function of radial distance (r). 

 Theoretically, this steady-state voltage as a function 

 of r is a Bessell function of zero order, of the second 

 kind and with imaginary argument. The solid curve 

 in figure 30 is such a function fitted to the variation 

 of potential with distance measured in the fiber 

 direction. The space constant is 160 /x. Measurements 

 made at right angles to the fiber direction are equally 

 well fitted by the Bessell function, but the space con- 

 stant is slightly more than half of that in the fiber 

 direction. The space constant and the area under 

 the 8,r curve can be used to calculate values of specific 

 membrane resistance and internal resistivity for this 

 tissue. These were about 40 fi-cm- and 1500 0-cm, 

 respectively (assuming that the equivalent planar cell 

 is 75 ij, thick). 



All of these values are markedly different from 

 corresponding values in other tissues. The space con- 



