This section examines several simple, theoretical neural models for conditioning and selecting "features" from a train of spikes from a receptor or interneuron. Such mechanisms may, in fact, exist in nature. Whether they can be identified in natural neurophysiological systems depends on future research in neural signal processing and neuroanatomy. They are considered biomedical engineers because they offer useful signal processing paradigms with simple structures. Their actual existence in nature would not be surprising.

In discussing the fine structure of a neural spike sequence, the sequence is treated as a point process characterized by unit impulses occurring at the times of the peaks of the nerve spikes. That is,

where {tk} are the times of spike occurrence. One important descriptor of PT(t) is the element of instantaneous frequency, {rk}, defined as the reciprocal of the time between two adjacent pulses:

Thus, every pulse train, PT(t), has a corresponding instantaneous frequency sequence:

Note that the index k starts at 2 because one needs two pulses to define an interpulse interval, hence instantaneous frequency element.

The original work on "resonant networks" was done by Reiss (1964). This section illustrates some of Reiss's models using the Simnon RPFM neuron model developed above. Reiss described a 1:1 neuron model, a T-neuron, and several types of frequency-selective neural models called band detectors. The 1:1 neuron fires a single output pulse every time it receives an (excitatory) input pulse. There is a synaptic plus axonal transport delay associated with the T-neuron. The other models are described below.

A T-neuron has two (or more) excitatory inputs, P and Q. If a second (Q) input pulse occurs more than T seconds after the first (P) pulse, the T-neuron will not fire. If the Q input pulse occurs less that T seconds following the P pulse, the T-neuron will produce a single output pulse at t = T. The T-neuron thus behaves like an AND gate with a memory, T. It does not matter which pulse is first; an output pulse will occur if P follows Q in less than T seconds, as well.

A Simnon model for a T-neuron is given below. The two input delta function "spikes" are conditioned by low-pass filters with two real poles, generating epsps. The epsps are summed and form the generator potential, Vex, for an RPFM model for the SGL.

continuous system TNeuron " 4/22/99 Use EULER integration with Dt .001.

STATE x1 x2 x3 x4 v DER dx1 dx2 dx3 dx4 dv TIME t " msec.

dx2 = -b*x2 + a*b*x1 " x2 is output epsp dx3 = -a*x3 + Vs2 " 2-pole, synaptic LPF

Vex = x2 + x4 " Two epsps summed to form generator potential.

" RPFM T-NEURON

dv = -c*v + c*Vex - z w = IF v > phir THEN 1 ELSE 0

" INPUT PULSES:

" PARAMETERS: tau:.001 dt:.001 Vso:1. phir:.2 a: 1 b:1 c: 1 t2:1

Units radians/ms.

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