232 THE BIOPHYSICAL PROBLEM OF NERVE CONDUCTION ■ 



tation. The minimum value of the potential V to accomplish this is 

 V Q . Therefore we may write 



kU = log 



V - B 



where B = kb/K. 



The validity of this relation may be tested by plotting experimental 

 values of log V /(Vo — B) as a function of t\. Blair used data obtained 

 by Lapicque from such diverse types of tissue as Spirogyra, the sciatic 

 gastrocnemius of the frog, and a nerve-muscle preparation of Helix; he 

 found that these results were in good agreement with this solution except 

 for occasional large values of time. 



Rashevsky [1936] showed that Blair's original differential equation can 

 express the velocity of propagation of the active current of the nerve. 

 This velocity is strictly constant if the time in which the potential has 

 risen to V is not taken into consideration. He deduced the natural 

 nerve-pulse velocity from electrochemical considerations to be equal to 



I Q - B k 



v = • — 



B a 



Rashevsky took into consideration the gradual increase of the current as 

 the depolarized section, associated with the pulse, advanced toward the 

 region under examination. In the above relation I is the maximum 

 value of this current. Thus, when 7 is less than B no propagation can 

 occur. When I > B then Iq — B is the excess of the action current 

 of the nerve over its minimal necessary value, and a 2 = 2(7 — l)p/y8p r. 

 Here 7 denotes the ratio of the resistance of unit length of the core 

 of the fiber to unit length of the outside medium while the nerve 

 fiber is immersed in a conducting electrolyte. The axis cylinder has 

 radius r and specific resistance p; its surrounding sheath of thickness 5 

 has specific resistance p . The value of a therefore depends on the 

 dimensions and property of the fiber, and it has the dimensions of the 

 reciprocal of length. 



The theoretical value of the velocity as calculated from this equation 

 can, of course, be only approximate since the values of the constants 

 involved in a are not well known. Rashevsky [1933], however, showed 

 that with reasonable assumptions for the less accurately known quanti- 

 ties the above relation leads to a value for the velocity of about 25 meters 

 per second, which is, as was experimentally established, of the right order 

 of magnitude. 



Blair [1934] has also shown this equation to be in fair agreement with 

 the data obtained by Blair and Erlanger [1933] for the velocity of propa- 

 gation of pulses in single fibers. 



