A Perturbation Based Decomposition of Compound-Evoked Potentials for Characterization of Nerve Fiber Size Distributions

Abstract

The characterization of peripheral nerve fiber distributions, in terms of diameter or velocity, is of clinical significance because information associated with these distributions can be utilized in the differential diagnosis of peripheral neuropathies. Electro-diagnostic techniques can be applied to the investigation of peripheral neuropathies and can yield valuable diagnostic information while being minimally invasive. Nerve conduction velocity studies are single parameter tests that yield no detailed information regarding the characteristics of the population of nerve fibers that contribute to the compound-evoked potential. Decomposition of the compound-evoked potential, such that the velocity or diameter distribution of the contributing nerve fibers may be determined, is necessary if information regarding the population of contributing nerve fibers is to be ascertained from the electro-diagnostic study. In this work, a perturbation-based decomposition of compound-evoked potentials is proposed that facilitates determination of the fiber diameter distribution associated with the compound-evoked potential. The decomposition is based on representing the single fiber-evoked potential, associated with each diameter class, as being perturbed by contributions, of varying degree, from all the other diameter class single fiber-evoked potentials. The resultant estimator of the contributing nerve fiber diameter distribution is valid for relatively large separations in diameter classes. It is also useful in situations where the separation between diameter classes is small and the concomitant single fiber-evoked potentials are not orthogonal.

A Perturbative-Based Generalized Series Expansion in Terms of Non-Orthogonal Component Functions

“…It has been demonstrated, by way of the examples presented earlier, that, in the case of non-orthogonal component functions, the technique performs significantly better than the generalized Fourier series which can yield nonsensical results such as negative coefficient values. As may be seen from specific examples rela- ted to the inverse problem in electrophysiology presented in Szlavik [5], the accuracy of the estimated series coefficients degrades as the degree of temporal overlap, or non-orthogonality, of the component functions increases.…”

“…In the event that the fiber size classes are such that there is significant temporal overlap between their associated single fiber evoked potentials, the generalized Fourier series can yield nonsensical results. In such cases, the perturbative decomposition outlined in this paper may be used to obtain an estimate of the coefficients associated with the series expansion shown in Equation (1) as first demonstrated by Szlavik [5]. …”

Characterizing Neurotransmitter Receptor Activation with a Perturbation Based Decomposition Method

“…This research, along with Szlavik's work [28] forms the basis for a general mathematical method of biopotential signal analysis. Given a signal, such as a compound postsynaptic potential reading from a neuron, not much analysis can be done directly due to the complexity of the signal.…”

“…Szlavik [28] presented a novel technique for estimating the size distribution of nerve fibers contributing to a compound-evoked potential, Ψ(t). The technique uses functional representations for single fiber-evoked potentials from n different fiber diameter classes, Λ 1 (t), .…”

Perturbation Based Decomposition of sEMG Signals

“…The perturbative approximate series expansion, also termed perturbation based decomposition, was developed by Szlavik as a technique to estimate the distribution of nerve fiber diameter sizes contributing to a compound-evoked potential [23]. The technique has since been applied to the characterization of neurotransmitter receptor activation [24].…”