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Impulse Response for all locations
Posted: Tue Apr 13, 2021 7:35 am
I have a NEURON ball and stick model (with Python) and I would like to compute the impulse response (Green's function) between each location and each other location (denoted as K_ij, by Zador 1995). For specific frequencies I know I can find the transfer impedance for a pure frequency using impedance.compute(freq), but I would like to find the transfer impedance for non-pure frequencies, which I believe requires knowledge of the impulse response.
Re: Impulse Response for all locations
Posted: Tue Apr 13, 2021 11:45 am
I know I can find the transfer impedance for a pure frequency
What constitutes an impure frequency?
What to do depends on whether you prefer to operate in the frequency domain or in the time domain. If you want to operate in the frequency domain, then for any pair of locations of interest you'll have to calculate the amplitude and phase of the transfer impedance between those two points over a wide range of frequencies sampled at appropriate intervals. The width of the frequency range, and the number and width of the frequency intervals, depend on on the power spectral density of the signals you're interested in and the temporal resolution you want if and when you return to the time domain.
If you want to operate in the time domain, then for any pair of locations of interest you can inject a brief current pulse at one location and observe the time course of membrane potential at the other location. It will be convenient if the current pulse duration is identical to the fixed time step used in the simulation. The current pulse amplitude should be large enough to elicit a voltage response large enough to "see" but not so large as to drive the cell out of the range of "apparent" linearity (you _have_ determined the cell's current-voltage relationship (peak amplitude of the voltage transient elicited by a brief current pulse vs. current pulse amplitude), and plotted it to verify linearity, right? and also generated an overlay of normalized voltage transients elicited by current pulses of various amplitudes to verify that the waveform does not change?). Divide the observed membrane potential transient (in mV) by the amplitude of the current pulse (in nA) and the result will be the impulse response in megohms; this can be convolved with an arbitrary input current waveform (in nA) to calculate the resulting voltage transient (as long as linearity is not violated).