INTRINSIC RHYTHMS OF THE BRAIN 



281 



end of the pipe, the siphon will be broken and the 

 whole process will be repeated. The rate of change of 

 water level with respect to time o\er the cycle will 

 approximate to two intersectine; straight lines, the 

 slope of which will depend upon the rate of filling and 

 the rate of emptying respectively. An interesting case 

 is when the rate at which the siphon empties is exactly 

 equal to the rate of filling; in these circumstances the 

 water level will rise linearly to a maximum and remain 

 there indefinitely. The system is stable, but the flow 

 of water is continuous. Obviously, in such conditions, 

 a slight change in flow rate at input or output will 

 engender relaxation oscillations of level. Instability 

 in this system will result from a rise or fall in input or 

 output, and only very careful examination of the 

 rate chart would disclose which, in any particular 

 occasion, was the most likely cause. 



Another interesting feature of this system is that a 

 transient change in, say, the rate of water input can 

 act as a " stimulus' to initiate a complete cycle of 

 operation provided the rate of change exceeds a 

 certain threshold. The value, form and scale of the 

 response to such a 'stimulus' will be independent of 

 the nature of the stimulus and will be all-or-none. It 

 will also have an absolute and a relative refractory 

 period. In fact, a system of this type is closely anal- 

 ogous to the schema generally proposed for nervous 

 action. The steady filling and emptying of the tank 

 corresponds with the metabolism of an excitable 

 structure, and the excitability-stability relation is 

 similarly dependent on the maintenance of a dynamic 

 equilibrium. Furthermore, there is illustrated a rela- 

 tion between excitability and homeostasis. If the 

 constancy of water level in the tank — or potential 

 diflference in a nerve cell — is regarded as an important 

 condition, then the system is evidently an admirable 

 device for autoregulation within certain limits of 

 external variation. The standard unit ' response' of 

 discharge — and replenishment — is a signal that the 

 limits of self control have been exceeded. Continued 

 rhythmic activity is a signal of sustained excess or 

 deficiency. 



DISTINCTION BErVVEEN SIMPLE H.^RMONIC .AND RELAXA- 

 TION OSCILLATORS. The behavior of this elementary 

 hydraulic model may be contrasted with the simple 

 harmonic motion of a pendulum; the waveform in the 

 first case is a series of asymmetric transients while in 

 the second it is of course strictly sinusoidal. The auto- 

 siphon shows no tendency to oscillate after a dis- 

 turbance is over whereas the pendulum exhibits a 

 damped train of vibrations. Similarly, the autosiphon. 



when stable, can be triggered to give a full cycle of 

 activity by a minimal but supraliminal stimulus, 

 whereas the pendulum requires either full scale tran- 

 sient deflection or repeated stimulation at its natural 

 frequency to evoke a maximal discharge. The res- 

 onance of the pendulum is typical of such systems; 

 the strict relation between sharpness of resonance and 

 length of build-up and die-away time is important. 

 The autosiphon exhibits no true resonance; its 

 response is all-or-none. However, it can display the 

 phenomenon of pararesonance; the maximum rate of 

 discharge is produced most economically when 

 stimuli are given at the same rate as the natural period 

 of the operation cycle. 



ELECTRIC EQUIVALENT OF HYDRAULIC MODEL. This 



detailed analogy is presented because appreciation of 

 the differences between the two main classes of 

 rhythmic activity is essential for understanding the 

 difliculties which still surround interpretation of the 

 rhythmic electrical phenomena in the nervous system. 



The character of the relaxation oscillator which is 

 most instructive physiologically is that it is a nonlinear 

 system; its operation depends upon the sharp thresh- 

 old which separates one regime from another. 



If the hydraulic model seems too trivial, the com- 

 ponents may be replaced with electrical ones, po- 

 tential difference for water-level, current for flow, 

 capacitors for the tank, resistors for the pipes, dis- 

 charge tubes with their nonlinear voltage-current 

 characteristics for the siphon. This produces a circuit 

 arrangement familiar to electronic designers as a time- 

 base or sawtooth oscillator. In fact, .such an electric 

 model has been built and is in regular use for teaching 

 and demonstration to illustrate the behavior of a 

 system containing several such circuits in a chain or 

 cascade C56). In this embodiment of the analogue, 

 a series of such systems, coupled together, can be seen 

 to provide for propagation, inhibition, unidirectional 

 synaptic transmission and other basic properties of 

 axonic and neuronic action. When more elaborate 

 forms of interconnection and switching are provided, 

 properties such as homeostasis and ultrastability 

 appear, as demonstrated by the machines constructed 

 by Ashby (4) and Uttley (52). 



The working hypothesis embodied in the simple 

 model of nervous action is that every element of a 

 nerve cell from soma to terminal dendrite is, in 

 effect, a miniature relaxation oscillator. Each element 

 thus considered is connected to tho.se on both sides of 

 it so as to facilitate by its own activity their tendency 

 to discharge. A crude hydraulic counterpart would 



