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followed by an absolute value (absval) operation between the positive sensory stimulus and the RPFM SGL. Thus, a broad pulse input of pressure of height Po and of duration, 8, P(t) = Po [U(t) - U(t - 8)], will give rise to a generator potential, VG(t), of the form:

This VG(t) will give a burst of spikes when pressure is applied, and another when it is removed.

Other spiking receptors may adapt more slowly (e.g., the gravity receptors of Arenivaga, see Section 2.6). In this case, the absval operation is replaced with a half-wave rectifier.

4.3.4 Modeling Neural Fatigue

Many interneurons, driven by a single excitatory presynaptic neuron having a constant pulse frequency, will fire more slowly as time progresses. This gradual loss of response is called neural fatigue. Fatigue can be due to exhaustion of neurotransmitter, exhaustion of ATP reserves, failure of ion pumps in the membrane to keep up with Na+, K+, and Ca++ pumping, etc.

Functionally, fatigue can be modeled by passing the SGL output pulses through a low-pass filter having two or more real poles, and adding the LPF output to the firing threshold. This is illustrated below:

dv = -c*v + c*e - z " Analog LPF with inputs e and z. w = IF v > phi THEN 1 ELSE 0 s = DELAY (w, tau) x = w - s y = IF x > 0 THEN x ELSE 0 " y(t) is triangular: height = 1, base = 2tau.

z = y*phi/tau " The pulse z resets v to 0. u = y*Do/tau " RPFM SGL output pulses dp = -a*p + k*u " Feedback LPF dq = -b*q + p phi = phi0 + q " Phi is raised prop, to firing rate.

The time constants 1/a and 1/b should be long compared with the initial firing period of the SGL. The negative feedback from the LPF output raises phi, lowering the output frequency.

4.3.5 Discussion

It is clear from the discussion above that the RPFM SGL model is more realistic in applications such as the simulation of small assemblies of neurons. The input to an

RPFM SGL model is the spatiotemporal sum of epsps and ipsps arriving at synapses on dendrites or the cell body (soma). e is the depolarization (the positive voltage added to the negative resting potential, Vm0, that moves the net membrane potential, Vm, toward the firing threshold). Thus,

If the synaptic inputs to the neural model are purely inhibitory, e can go negative, forcing Vm < Vm0 (hyperpolarization of the GP). As has been seen, there is a practical, asymptotic negative value of e set by the Nernst potential for the gated ion participating in the ipsp generation. Thus, it adds a dimension of reality to the overall neural model to define a lower bound, or Nernst clamping level, for each ipsp.

Several examples in this text use the RPFM SGL model to simulate various hypothetical interactions between small assemblies of neurons.

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