FLUCTUATIONS IN NEURAL THRESHOLDS* 



Lawrence S. Frishkopf and Walter A. Rosenblithj 



Research Laboratory of Electronics, 

 Massachusetts Institute of Technology, Cambridge, Massachusetts 



Abstract — Over the past twenty-five years several independent investigations of the responsivity 

 of nerve tissue have led to the conclusion that the threshold of a resting neuron fluctuates 

 in time. The conclusion is based on the study of sensory and motor fibers, of monosynaptic 

 arcs and neuromuscular junctions. A number of these studies have been reviewed and com- 

 pared. The degree of threshold correlation among neurons of a given 'pool' or population 

 has been considered for several systems. A number of possible sources of threshold fluctuation, 

 giving rise to correlated and uncorrected threshold variations, have been distinguished. 



A mathematical model based on the concept of fluctuating thresholds has been described 

 and applied to the problem of ensemble response from the peripheral auditory nervous system. 

 The results of three experiments have been described and compared with the predictions of 

 the model. 



I. THE CONCEPT OF A FLUCTUATING THRESHOLD 



The threshold of a nerve fiber is defined as the minimum stimulus intensity 

 that will cause an action potential to propagate. If the threshold of a nerve 

 fiber were a fixed parameter — not changing in time — its value could be deter- 

 mined by presenting stimuli of increasing intensity. The fiber would fail to 

 respond to all stimuli less than some value Srp, and would respond to all stimuli 

 greater than Srp\ Sj, would then be the threshold of the fiber. However, 

 careful experiments on a number of specific neural systems — sensory and motor, 

 peripheral and central — have shown that such a unique value Sj, does not 

 exist; instead, there is a range of stimulus values, 5^ to ^'2, such that a stimulus 

 S lying within that range, when repeatedly presented at a rate well below that 

 which would involve the refractory period of the fiber, sometimes evokes and 

 sometimes fails to evoke a response. We find that the fiber responds in a fraction 

 p of all trials and that p{S) is a monotonic function that rises from zero to one 

 as the stimulus increases from S-^ to 5^2. Stimuli less than S^ never evoke a 

 response; stimuli greater than So always evoke a response. We conclude that 

 the threshold of a neuron which exhibits this behavior is a time-varying para- 

 meter. The value p approximates the fraction of the time that the threshold is 

 somewhere below the stimulus value S. An equivalent statement is that p 

 approximates (and for large sample size, approaches) the probability of finding 

 the threshold of a fiber below the value 5". 



* This work was supported in part by the U.S. Army (Signal Corps), the U.S. Air Force 

 (Ofiice of Scientific Research, Air Research and Development Command) and the U.S. Navy 

 (Office of Naval Research). 



t Also in the Department of Electrical Engineering, M.LT. 



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