28o 



HANDBOOK OF PHYSIOLOGY 



NEUROPHYSIOLOGY I 



neurophysiology, but, as is well known, these rhythmic 

 discharges are generally greatly affected by external 

 signals and need be considered as spontaneous only 

 in the sense that the energy required for their main- 

 tenance is freely available in the brain and that their 

 existence implies some sort of regenerative, retroactive 

 or feed-back loop. Even if, as several observers have 

 suggested (13, 21), the source of the rhythmicity may 

 be in the nerve cells themselves rather than in the 

 manner of their interconnection, there must still exist, 

 even within this intimate microcosm, a re-entrant 

 loop of energy transfer around which two sets of 

 variables can mutually control one another. The 

 physiological nature of the retroactive pathway is 

 hard to identify and around this point controversy 

 has raged for many years, involving many experiments 

 and strong feelings. Viewed without rancor, the 

 dispute seems academic; most of the claims and asser- 

 tions on both sides can be justified, few of the denials 

 can be confirmed. There seems little doubt that in 

 certain circumstances single nerve cells can discharge 

 spontaneously at a steady rate (3, 51). On the other 

 hand, large populations of healthy isolated brain 

 cells may remain quite inactive for long periods (17) 

 yet respond rhythmically when stimulated. 



Conditions Jor Oscillation 



SIMPLE H.\RMONic MOTION. It Can be shown that, when- 

 ever and wherever an oscillation appears, there must 

 be a retroactive mechanism of some kind. The most 

 familiar — though not perhaps most strictly relevant — 

 form of oscillation is the simple harmonic motion of a 

 pendulum. Even in the case of the simple pendulum, 

 sustained vibration depends on the regular transmu- 

 tations of position and velocity as shown in the basic 

 equations- 



dS 

 dt 



dV 



~dt 



= V, 



sin 5' 



where ^S' is angular position; I", velocity; g, constant of 

 gravitation; and L, length of pendulum 



From these it is seen that changes in 6' depend on 

 the value of V while changes in V depend on the value 

 of S. This is the basic condition for feedback, and 

 wherever two variables are thus interdependent 

 oscillatory behavior is likely to occur. From the 

 dynamic standpoint a swinging pendulum is not a 

 single object but a system of two variables. Whether 



the system will be ' spontaneously' active or stable is 

 another question and depends upon the sign of the 

 constants that determine the feed-back ratio. In the 

 case of the pendulum, the sign is negative, so the 

 system is stable near its resting state. An "ideal' 

 frictionless penduliun however would be unstable 

 because the random Brownian movement of its 

 molecules would inevitably set up an oscillation at its 

 natural frequency which, in the absence of damping, 

 would continue indefinitely. This effect can be ob- 

 served in the case of the very small light suspensions 

 of sensitive galvanometers. 



A large pendulum, however, is stable in the sense 

 that the frictional losses limit the extent and duration 

 of any o.scillation. In the 'ideal' case the feed-back 

 factor is unity; in any practical case it is less than 

 unity, so to sustain an oscillation energy must be 

 supplied from outside the system. Furthermore, the 

 more massive the system, the more precisely must the 

 energv be distributed in tiine so as to reinforce the 

 movement of the pendulum; it must be phase-locked 

 to the oscillatory element. 



This example of simple harmonic motion illustrates 

 two ways in which rhythmic activity may be gen- 

 erated: first by interaction between a 'noisy' or random 

 energy source and a small-scale or loss-free retroactive 

 system, second by interaction between a phase-con- 

 trolled energy source and a normally damped retro- 

 active system. Obviously intermediate conditions 

 between these extremes exist and many of them can 

 give the impression of ' spontaneity' because the 

 relation between the time-distribution of energy and 

 the degree of damping of the oscillatory system may 

 not be obvious without careful experiment. In such 

 a system, activity once initiated will tend to persist, 

 but the first cause may be obscure. 



RELAXATION osciLL.\TORS. Lcst it sliould be thought 

 that some sort of simple harmonic motion is the only 

 possible source of rhythmic activity, another mechani- 

 cal illustration should be considered. This is in the 

 class of 'relaxation oscillation"; a simple example is the 

 autosiphon in which one end of an inverted U tube is 

 connected to the outlet of a water tank with the top of 

 the n below the top of the tank and the open end of 

 the n near the bottom of the tank. If the tank be now 

 filled from a steady source, the level will rise in a 

 linear fashion until the water level reaches the top of 

 the n . At this point a siphon will be formed and the 

 water tank will empty through the siphon, if the rate of 

 flow through the fl is greater than that from the 

 source. When the water level falls below the open 



