THE PROBLEM OF IMPULSE CONDUCTION IN THE ATRIUM 129 



re = and /•/ = pJ8. This value can be reduced by 30",, if R,„ ^ 500 LI cm^, 

 a value obtained from the time constant of about 5 msec and an assumed 

 membrane capacity of 10 /nF/cm'-. On the other hand, S could be only 0-34 fx 

 if high internal resistance were the reason for the short space constant. This 

 discrepancy (150-fold in dimensions) is so large that the error most probably 

 lies in wrong assumptions on the values of the parameters rather than in 

 the model. There are three terms in the expression for the space constant — the 

 membrane and the internal longitudinal and external longitudinal resistances 

 — for which incorrect values may have been assumed. The short space 

 constant must be the result of a low Rm, of a high /•,■ or /> or of a combination 

 of low Rin and high (n -^ re). There are at least three possibilities: (i) The 

 spacing between the cells in a trabecula is small, about 200 A, suggesting 

 that re may be sufficiently high, (ii) The internal resistance may be much 

 higher than calculated from a resistivity of 100 12 cm owing to the presence 

 of intercalated disks in the intracellular current pathways. Since the disks 

 are membrane-like structures, they would be expected to have a rather high 

 resistance, (iii) Rm may be effectively much lower than in other tissues. Before 

 considering these possibilities the structure of trabeculae will be reviewed. 

 It should be added that the present data are sufficient to approximate both 

 Rm and (/v + rt) directly but the calculation, which is facilitated by an 

 accurate model, has not yet been made. 



Cardiac cells are shaped and stacked somewhat like bricks. A trabecula is 

 roughly a cylinder about 0-5 mm in diameter and several millimeters long. 

 Within the individual trabeculae there are cylindrical bundles about 50 ^ in 

 diameter, separated by comparatively large extracellular spaces containing 

 capillaries. The cells within a bundle are closely packed, the space between 

 cell membranes being from 200 to 300 A. Myofibrils are attached to thickened 

 regions of membrane, the intercalated disks, and appear at regions where 

 Z-bands would be expected (Muir, 1957; Sjostrand and Andersson-Ceder- 

 gren, 1960). The membrane is greatly folded in the disk area, the surface area 

 being about ten times greater than that calculated from disk diameter. In 

 contrast to non-disk membrane, the spacing between the opposing faces of 

 the disk is only about 80-100 A. The cell boundaries in cardiac muscle can 

 be distinguished with certainty only with the electron microscope. This is 

 particularly true of non-disk regions, where the membrane is relatively flat 

 and unthickened. The long dimension of a cell is out of the field in an electron 

 micrograph, so the length cannot be stated with any certainty. It appears to 

 be about 100 /x using a light microscope. If cardiac cells are regarded as 

 circular in cross-section, then a typical diameter would be about 15 fj.. The 

 intercalated disks occur in steps, the membrane running parallel to the myo- 

 fibrils between the steps (Muir, 1957). Eventually, of course, the disk must 

 cross the cell transversely, so the effective diameter of the disk is also 15 /a, 

 if no allowance is made for the folding of the membrane. 



10 



