Fluctuations in Neural Thresholds 161 



given by its square root, leading to a variation of about 0.1 per cent. This 

 is several orders of magnitude below the range of threshold variation that he 

 observed. However, he points out that the number of ions actually effecting 

 excitation is probably considerably less than the value mentioned above and 

 the resultant variability correspondingly greater. Pecher also considers as 

 a possible source of threshold fluctuations local statistical variations of mem- 

 brane potential, of the sort discussed by Fatt and Katz. 



Hunt discusses two classes of possible sources of threshold fluctuation 

 for spinal motoneurons : (a) sources with a local origin such as we have mentioned 

 above, which give rise to an independent component of threshold variation 

 and (b) sources whose effect is felt by many fibers and which therefore produce 

 at least partially correlated variations in threshold. In the latter category 

 are included the effects of activity of spinal interneurons. By using a drug 

 (myanesin), in doses that block transmission through polysynaptic paths 

 without reducing monosynaptic reflex responses, a considerable reduction 

 in the range of variation of population response amplitudes was obtained. 

 On the basis of this result it appears likely that internuncial activity is important 

 in producing correlated threshold changes in spinal motoneurons. 



IV. A MATHEMATICAL MODEL 



Let us consider a mathematical model which is based on the concept of 

 fluctuating thresholds, and which attempts to derive the ensemble behavior 

 of large numbers of neural elements from assumed properties of neural units 

 in a specific area of the nervous system (9, 10, II). 



This model is based on data obtained from the peripheral auditory system 

 of the cat. When an electrode is placed near the round window of the cochlea, 

 responses to clicks can be detected; such responses contain a component that 

 represents the summated activity of peripheral auditory neurons. Fig. 9 shows 

 such population responses at a number of intensities. In Fig. 10 the average 

 peak-to-peak amplitude of such responses has been plotted as a function of 

 stimulus intensity. The resultant 'intensity function' relates the number of units 

 firing and the intensity of the stimulus. 



The present version of the model (11) postulates the existence of several 

 independent populations of neural units; within a population all units are 

 identical. The threshold of a unit is a fluctuating parameter which can be 

 described by a probability distribution; threshold variations in different units 

 occur independently. At a rate of stimulation slower than one per second the 

 'response no-response' sequence obtained from a single unit is assumed to 

 consist of a series of independent events. Thus we postulate units whose 

 statistical properties resemble those found by Pecher in the frog's sciatic nerve. 



The experiments used to test the model fall into three classes: two-click 

 experiments (9, 10), measurements of variability of response amplitude (II), 

 and studies of masking of click responses by noise. 



When two clicks are delivered at an interval of less than approximately 

 100 msec the population response to the second click is smaller than it would 

 be if the first click had not occurred. This effect is more pronounced the 

 stronger the first click and the smaller the interclick interval, as illustrated 



