where Sx is the deflection of the membrane in microns, and P is the sound pressure level at the membrane in dyn/cm2. Assume that the neurite is stretched by a sinusoidal Sx, and only the positive Sx leads to membrane depolarization. Thus, the generator potential can be expressed as a Simnon statement:
rVg = IF dx > 0 THEN Kc*dx ELSE 0 " dx is x, rVg is in mV.
The half-wave rectified rVg(t) is the input to the neuron RPFM SGL. As has been written before:
dv = -c*v + c*rVg - z z = y*phi/dT " z resets RPFM LPF.
x = w - s y = IF x > 0 THEN x ELSE 0 " Receptor output pulses.
a. Write a program to simulate the receptor's output pulses for various sound input frequencies. Let p(t) = Po sin(2nft), Po = 0.5 dyn/cm2. Let f range from 0.1 to 3 kHz. Let K = 1, Kc = 5, c = 0.2 r/ms, Q = 2.5, ron = 6.2832 r/ms, t in ms, dT = 0.001 ms (RPFM delay same as Euler integrator interval), phi = 1 mV. Plot p, rVg, v, and y. Make a plot of the average, steady-state firing frequency of the sensor model vs f.
b. Examine the system response to "chirps," i.e., bursts of sound of different lengths and frequencies.
4.7. A major problem in auditory neurophysiology is how animals locate sounds binaurally. The pressure waves from a point source of sound arrive at the two ears with different phases and amplitudes. Spikes on the two auditory nerves carry this amplitude and phase information to the brain where the cognitive function of source location takes place. As a first step in attempting to model this complex process, examine the properties of a simple model neural phase detector. The system architecture is shown in Figure P4.7. Two spike sources of the same frequency impinge on two RPFM SGLs, Nj and N2. N fires if fR > fL, and N2 fires when fL > fR.
K. Because the
The generator potential for Nj is Vgj = (epspR) - (ipspL)
average psps are proportional to the presynaptic frequencies, Vgj will be near zero for fR = fL, and will go positive toward the firing threshold of Nj when fR > fL. Simulate each synapse with so-called alpha function (two equal, real-pole) dynamics. For example, in Simnon notation,
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