calculate.simple.TFs: Calculation of simple MU - electrode transfer functions...

In ime-luebeck/semgsim: Simulating surface electromyographic (sEMG) and force signals

Calculation of simple MU - electrode transfer functions (wrapper)

Description

Calculate transfer functions from each motor unit (MU) to each electrode in a simple, distance-based, normalized, instantaneous fashion.

Usage

calculate.simple.TFs(.muscles, .electrodes, .vol.conductor, .freqs)

Arguments

.muscles	A data.frame containing data on the muscle geometry, especially a column 'MU.obj' containing MU objects.
.electrodes	A data.frame containing columns 'electrode' with the electrode ID and 'electrode.obj' containing the actual object.
.freqs	A numerical vector containing the frequencies at which the transfer function is to be evaluated. Results will be returned in order.
.volume.conductor	A volume conductor object. In fact, this argument is not required for the simple TFs computed here, and is íncluded solely for the purpose of interface consistency.

Details

The 'transfer functions' from a single muscle fiber to an electrode are given by

tfMF, Electrode(kt) = (dist_min / dist(MF, Electrode))^2 * j * kt,

where dist_min is a normalization term which is defined as the minimum over all MUs of

dist_MU = sqrt(sum(dist(MF, Electrode)^-2)),

with the sum being taken over all muscle fibers in that MU. This formula results from assuming a point-source solution

phi(xe, ye, ze) = (dist_min / dist(MF, Electrode))^2

and actually considering point sources with time course

i(t) = d/dz psi(-vt).

Fourier transformation then yields the above transfer function. The TF of a MU now results from the summation of the TFs of all its muscle fibers, yielding

tfMU, Electrode(kt) = dist_min^2 * j * kt * sum(dist(MF, Electrode)^-2).

Note that this simple summation is only valid if we assume the same conduction velocity (cv) in all muscle fibers located in the same MU.

Value

A data.frame containing the sampled transfer functions in column 'TF', represented as vectors of complex values.

ime-luebeck/semgsim documentation built on April 14, 2022, 11:02 p.m.