felsheim2024
Adaptive leaky-integrate and firing probability (aLIFP) model of an electrically stimulated nerve fiber

Usage:

dists = felsheim2024(stim);
dists = felsheim2024(stim, fs);
dists = felsheim2024(stim, fs, varargin);

Input parameters:

`stim`	Time signal describing the pulsatile electric stimulation of a nerve fiber. The pulses must be biphasic. The two phases may have varying durations and and they may be separated by an interphase gap (IPG). The pulse may have varying amplitudes (in mA). In the current implementation only cathodic (negative) pulses are causing excitation in the model.
`fs`	Optional sampling frequency of the time signal (in Hz). Default: 1 MHz.
`vargin`	Optional parameters as key-value pairs, see below.

Output parameters:

dists

Structure array containing the spike distribution in response to each biphasic pulse in stim. Per negative phase in stim, spike_distributions containes a separate entry describing the probabilitiy following a Gaussian mixture distribution and containing the following fields:

total_probability: Total probability of spiking in response to the pulse.
mu: Mean values of the Gaussian mixture.
sigma: Standard deviations of the Gaussian mixture.
weights: Weights of each component of the Gaussian mixture.

Description:

felsheim2024(..) implements the adaptive leaky-integrate and fire (aLIFP) model, which simulates the electrical stimulation of a nerve fiber. Instead of predicting (stochastic) time points of spikes, the aLIFP model calculates the spike distribution in respone to each biphasic pulse in stim. The model incorporates latency and jitter of the nerve response and accounts for the facilitation, the refactory period and adaptation. The development of this model was inspired by the spiking model of Takanen and Seeber (2022).

The model parameters can be changed using the following key-value pairs:

`'leaky_integrator_tau',tau`
	Time constant (in s) of the leaky integrator. Default: 1.2 µs.
`'membrane_resistance',mr`
	Membrane resistance (in Ohm). Default: 28.986 Ohm.
`'threshold_mu',mu`	Mean threshold (in V) at the model start. Default: 10 mV.
`'threshold_sigma',sigma`
	Standard deviation threshold (in V) at the model start. Default: 431.9 µV.
`'varphi',phi`	Action potential initiation period (in s). It determines the duration during which a spike can be inhibited by further stimulation. Default: 20.5 µs.
`'jitter_coeffs',jitter`
	Vector of three parameters describing the dependency of the jitter on the membrane potential. Default: [5.449e-4, 3.159e-4, 1.30e-04].
`'latency_coeffs',latency`
	Vector of four parameters describing the dependency of the spike latency on the membrane potential. Default: [1.096e-4, 5.478e-04, 3.93e-04, 4.23e-04].
`'refractoriness_p',p`
	Parameter of the function describing the increase of the threshold due to the refractory period. Default: 0.377.
`'refractoriness_q',q`
	Parameter of the function describing the increase of the threshold due to the refractory period. Default: 0.102.
`'refractoriness_trrp',trrp`
	Time constant (in s) of the relative refractory period. Default: 2.56 ms.
`'refractoriness_tarp',tarp`
	Duration (in s) of the absolute refractory period. Default: 0.37 ms.
`'adaptation_tau',a_tau`
	Time constant (in s) of the adaptation function. Default: 0.27 s.
`'adaptation_c',c`	Multiplicative increase of the threshold due to adaptation after a spike. Default: 0.102.
`'max_adapt',max_adapt`
	Maximum overall adapation. Default: 1.7.
`'facilitation_coeffs',f_coeffs`
	Vector of five coefficients describing the facilitation curve. Default: [0.1e-3, -1.4e-3, 0.45 , 900, 0.5].
`'max_threshold_components',max_c`
	Maximum number of components in the Gaussian mixtures. Default: 20.
`'path_deletion_mean_eps',mean_eps`
	Factor applied to threshold_mu defining the numeric border for the test of equality of the threshold mean of two components. Default: 0.001.
`'path_deletion_std_eps',std_eps`
	Factor applied to threshold_sigma defining the numeric border for the test of equality of the threshold standard deviation of two components. Default: 0.001.
`'min_spike_probability',min_prob`
	Minimum spike probability required to add a new component in the threshold mixture. Default: 0.001.
`'lower_limit_std_b',std_limit`
	Limit of the standard deviation (relative to the threshold) required to avoid high spike probabilities without stimulation. Default: 1/3.

References:

R. C. Felsheim and M. Dietz. An adaptive leaky integrate and firing probability model of an electrically stimulated auditory nerve fiber. Trends in Heaaring, 2024. submitted.

M. Takanen and B. U. Seeber. A phenomenological model reproducing temporal response characteristics of an electrically stimulated auditory nerve fiber. Trends in Hearing, 26:23312165221117079, 2022. PMID: 36071660. [ DOI ]