132 J. W. WOODBURY AND W. E. CRILL 



from ^-K diffusion studies in sheep myocardium tiiat Ruhi is of this same order 

 of magnitude. 



If it is assumed that the specific resistance of the disi<. membranes is of the 

 order of 1 Q. cm-, the contribution of the disk to intracellular resistance can 

 be calculated. For a cylindrical "cell" 16/^ in diameter the myoplasmic 

 resistance between disks separated by only 40 /x is 0-2 MQ, the resistance of 

 each disk is 0-5 MQ and the space constant is 300 ^. On the same basis, the 

 space constant for a two-dimensional model is 850 /x. In this case a space 

 constant of 130 /x requires that the disk resistance be forty times higher or 

 that the disks be forty times closer. Both possibihties seem unreasonable. 



MEMBRANE RESISTANCE 



A final possibiUty is that R„i is much lower than in other excitable tissues. 

 Rm would have to be about 25 O cm-, a value more characteristic of excited 

 than resting membrane. However, an alternative possibility is that the 

 effective area of the membrane is much greater than that used in computing 

 the expected space constant from the two-dimensional model. In the formula, 

 R,„ refers to the resistance of 1 cm- of surface. In a trabecular bundle com- 

 posed of closely packed cells, the area of excitable membrane in a square 

 centimeter of surface is much greater than 1 cm-, the exact area depending on 

 the diameter of the individual cells and the effective thickness of the bundle. 

 If the cells were square in cross-section, the actual area would be 4 cm- per 

 square centimetre surface and per cell layer. Since no cell is more than a 

 few cell layers from a large extracellular space, the thickness of the tissue in 

 ■'plane'" of the current applying electrode is probably no more than five 

 layers, quite possibly less. From a combination of these two factors, the area 

 of membrane per square centimeter of tissue surface may be as much as 20 

 cm2. The true membrane resistance could then be as large as 25 x 20 = 

 500 Q cm2, a reasonable value for R,n. 



These calculations are unlikely to be of more than order-of-magnitude 

 accuracy. Nevertheless, the agreement of the calculated value for /?,„,/ with 

 Weidmann's measurements and the reasonable value of R,n is rather astonish- 

 ing and constitutes a persuasive if not rigorous argument for the overall 

 validity of the two-dimensional model and the existence of a low disk- 

 membrane resistance. The conclusions drawn are: (i) transmission in cardiac 

 tissue is electrically mediated via low resistance intercalated disks; and 

 (ii) the apparently short space constant for two-dimensional spread is about 

 what would be expected from the cellular structure of cardiac muscle. It is 

 now clear what tissue properties are most important in determining the spread 

 of currents and further study of the temporal as well as the spatial aspects of 

 two-dimensional current spread may lead to a more quantitative analysis of 

 the passive electrical properties of cardiac muscle. 



