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HANDBOOK OF PHYSIOLOGY -^^ CIRCULATION I 



FIG. 31. Simplified and formalized diagram illustrating the electrical structure of a portion of a 

 rat atrial trabecula. Thin straight lines represent regular, excitable cell membranes having high 

 electrical resistance; thickened heavy lines represent intercalated disc membranes having low re- 

 sistance. Each cell is completely surrounded by membrane. Large dot in center indicates location of 

 an intracellular current electrode. Lines with arrowheads indicate the major pathways of current 

 flow from the electrode in the intracellular fluid. Current flow through regular membranes into the 

 extracellular fluid is small and is not shown; most of this current flows perpendicularly to the dia- 

 gram to enter large extratrabecular spaces. Intracellular current flow at right angles to the fiber 

 direction follows a zigzag path of least resistance largely through the intercalated discs. This struc- 

 ture accounts for the spatially nonuniform spread of current. Contractile material is not sliown for 

 simplicity. 



Slant is extremely short in comparison to space con- 

 stants of skeletal muscle, nerve fibers, and Purkinje 

 strands which are of the order of millimeters (66, 

 126). The space constant of the two-dimensional 

 model is given by (R„,6pi)"-, where R„, is specific 

 memijrane resistance (l]-cm-), 6 is the thickness of 

 the model cell (cm), and pi is the specific resistivity 

 of the cell fluid (Q-cm). In the model the external 

 resistance was assumed to be negligible. It might be 

 supposed that the close packing of the cells makes 

 extracellular resistance sufficiently high to invalidate 

 the equation and give rise to a short space constant; 

 however, no cell is more than two or three cell diame- 

 ters from a large extracellular space. Hence, such a 

 supposition is unlikeK- to be correct. Rather, the 

 reason for the short space constant is a low specific 

 membrane resistance, 40 S2-cm-. Corresponding values 

 in other tissues are 1000 to 5000 J2-cm-. It was at 

 first thought that this low value for heart invalidated 

 the model, but further analysis led to the following 

 interpretation. The theoretical model is based on the 

 assumption that the atrium behaves like a single 

 planar cell; but the actual tissue, though planar, has 

 a membrane area many times greater than the surface 

 area of the model cell. Thus the calculated specific 



membrane resistance is the resistance of all cell mem- 

 branes throughout the thickness of the tissue under r 

 cm- of surface area. This is true because an applied 

 current flows through all membranes as it spreads 

 away from the electrode (fig. 31). Consequenth', 

 the actual change in voltage produced by a current 

 at a given distance will become less as the actual 

 membrane area per unit surface area increases. If 

 atrial tissue is effectively only five cell diameters thick, 

 the actual membrane area is 20 times the surface 

 area of the tissue. Since the calculated membrane 

 resistance is about 40 fl-cm'-, the actual resistance \vill 

 be of the order of 20 X 40 Si-cm- = 800 S2-cm-, a 

 value near the usual range of values for specific 

 memi)rane resistance. This interpretation also ac- 

 counts reasonably for the low specific resistance of the 

 membrane and short space constant, and hence for 

 the low membrane resistance (280 fi-cm-) and high 

 capacity (30 /jF 'cm-") fotmd by Trautwein et al. (122) 

 in frog atrial strips. 



The measured \alue of p,, 1500 S2-cm, is 15 times 

 the value found by W'cidmann (126) in Purkinje 

 fibers. Pi's for other tissues (66) are about double 

 external resistivities (p,.). p,. for mammalian tissues is 

 about 60 i2-cin. Thus Weidmann's value of 100 



