THE PROBLEM OF IMPULSE CONDUCTION IN THE ATRIUM 131 



0.0 



Fig. 3. (Above) — Highly simplified schematic diagram of two cells and the 

 intervening gap in the intercalated disk region. The right half defines the various 

 quantities used in calculating the potential profile in the gap and the membrane 

 charge distribution. The left half indicates approximately the current density 

 through the upper membrane due to the current flow between excited and 

 unexcited regions in the lower cell. The current density is simply e/Ro,,,^, where 

 R(y„,j is the specific resistance of the disk membrane (11 cm-). (Below) — Plot oft 

 vs. r for the indicated values of the parameter /o/A, where /.- = 2R„,^8lpi and pi 

 is the specific resistivity of myoplasm. It can be seen that most of the current flow 

 from the disk membrane of the lower cell passes through the upper cell if rj/'. is 

 3 or more, whereas practically none of it does \( rj?. is less than 1. 



side of Fig. 3. It can be seen that efficient transinission requires that /"o/A 

 be greater than about 3, whereas there is practically no transmission if the 

 space constant is greater than the cell radius. 



The equation for the space constant can be solved for disk resistance, 

 R^a = P6A2/2S. If A = ro/4 = 2 x IQ-^ cm, S = 80 ; lO'S cm and pe = 50 

 Q. cm, then R,nd = \-2 Q. cm'-. This is a maximum value for Rmd, just suffi- 

 cient for efficient transmission. Tissue values might well be 0-1 of this. On 

 the other hand, the surface area of the disk is about ten times the cross- 

 sectional area, so the actual Rmd might be as large as 12 Q cm^. Even 12 Q. crn'^ 

 is a low value, being of the order of the membrane resistance of a squid giant 

 axon at the peak of activity. The resistance of erythrocyte membrane is of 

 the order of 1 Q. cm- because it is highly permeable to CI'. Thus the require- 

 ments for effective intercellular transmission are stringent but not impossible. 

 Weidmann (personal communication, 1960) has recently obtained evidence 



