90 



HANDBOOK OF PHYSIOLOGY 



NEUROPHYSIOLOGY I 



Wheatstone bridge. The ratio arms, ri and r-2 in the 

 figure, consist of ohmic resistors, r2-ri being io:i or 

 larger. The remaining arm consists of condensers 

 (C and C) and a resistor (/f). When a high fre- 

 quency alternating current is applied to the bridge, a 

 sinusoidal potential variation is produced across the 

 membrane. By proper adjustment of the variable 

 resistance and the capacity, however, it is po.ssible to 

 reduce the a.c. output of the bridge to zero. 



As has been mentioned above (p. 85) the axon 

 membrane can be represented by a condenser and 

 parallel resistance. The relationship between the po- 

 tential difference (F) across the membrane and the 

 current (/) through the membrane is expressed by 

 equation (4-1) which can be rewritten as 



Therefore, 



I = C \- GV, 



di 



(6-1) 



where G is the conductance of the membrane, i.e. the 

 reciprocal of resistance R in equation (4-1)- We are 

 now interested in the relation between a steady 

 sinu.soidal current and a sinusoidal voltage that satis- 

 fies equation (6-1). We denote the current by 



/ii sin ut 



and the voltage bv 



V = I'll sin (ail + 9), 



(6-2a) 



C6-2b) 



where /o and i'l, are the current amplitude and the 

 voltage amplitude, respectively, co is 27r times the 

 frequency and 9 the phase difference between the 

 current and the voltage. Introducing (6-2a and b) 

 into (6-1), we find that 



/o sin u>t = I'd o>C cos (u/ + d} + GVo sin (_uit + S) 

 = Vq (G cos 6 — o>C sin $') sin u/ 

 + Vo (C sin e + uC cos 9) cos oil 



The last equation is satisfied when (and only when) 

 the coefficient of cos a;/ is zero and simultaneously 

 when the coeflicients of sin oj/ on both sides of the 

 equation are equal. This leads to the relations 



(6-3a) 



and 



/u = Vd (C cos e — uC sin 9). 

 From equation (6-3a) it follows that 



— (jC G 



h = t'o y/o^C -f- G2 



Fo = /„ 



Vw^C' -I- (? ' 



(6-3b) 



y/ufC'^ -h G2 ' 



V"'C2 -I- G^ 



When the impedance bridge in the upper part of 

 figure 12 is roughly balanced for a given intensity of 

 the bridge a.c, the current / through the axon mem- 

 brane is determined by the variable condensers and 

 the variable resistance of the bridge, because r-i » 

 ri. Under these conditions, the amplitude \\ is pro- 

 portional to the impedance, i /-\/G- -|- co^C', of the 

 membrane. When G increases during activity, Fn de- 

 creases. In the method involving use of the impedance 

 bridge, small changes in the membrane impedance are 

 detected by balancing the bridge with the membrane 

 impedance at rest and recording small unbalances 

 after a high amplification. Under such circum- 

 stances, not only a change in the amplitude \'n but 

 also any change in the phase d brings about a bridge 

 unbalance. When the bridge is at balance, the voltage 

 between the two electrodes across the axon membrane 

 is completely cancelled by the voltage across ri. A 

 change in the phase 6 or in the amplitude Fo , makes 

 this cancellation imperfect. 



[In order to detect changes in the membrane im- 

 pedance during activity, it is necessary to make the 

 frequency of the bridge a.c. high enough so that in 

 the period to be examined there are a number of full 

 cycles of the a.c. The time resolution in the im- 

 pedance measurement is affected also by the char- 

 acteristic of the filter circuit in the recording system.] 



.After the Wheatstone bridge has been accurately 

 balanced for the membrane impedance at rest, a short 

 pulse of outward current is passed through the axon 

 membrane. If this pulse is well below the threshold, 

 the potential trace (the upper trace in the records of 

 fig. 12) shows an exponential decay of the membrane 

 potential after the end of the pulse; in this case there 

 is very little or no bridge unbalance detectable. When 

 the pulse intensity approaches the threshold, the fall 

 of the membrane potential after termination of the 

 pulse becomes slow and erratic (see p. 98); con- 

 comitantly there is a sign of a decrease in the mem- 

 brane impedance (record .-1) which can be recorded 

 distinctly by increasing the amplification of the a.c. 

 bridge output (record B). With supra threshold pulse 

 intensities, large unbalances of the bridge are ob- 

 served (record C), indicating that there is a marked 



