Selective stimulation of human intrinsic laryngeal muscles: Analysis in a mathematical three‐dimensional space

Abstract

Objectives/Hypothesis Standard stimulating methods using square waves do not appropriately restore physiological control of individual intrinsic laryngeal muscles (ILMs). To further explore our earlier study of evoked orderly recruitment by quasitrapezoidal (QT) currents, we integrated the contribution of the cricothyroideus (CT) with attention to mutual activation in an additional patient, based on recent studies of appropriate responses via strict recurrent laryngeal nerve (RLN) stimulation. Study Design Basic science study. Methods The patient received functional electrical stimulation (FES) with QT pulses at 5 Hz, 60 to 2,000 μAmp, 100 to 500 μs pulse width, 0 to 500 μs decay. Ipsilateral electromyography (EMG) responses were calculated using the average maximum amplitude, area under the curve, and the root mean square of the rectified amplitude waveforms. The thyroarytenoideus (TA), posterior cricoarytenoideus (PCA), lateral cricothyroideus (LCA), and the CT were each interrogated via two monopolar electrodes, values were recorded in MATLAB, exported to Excel, and analyzed. Individual and mutual recruitment configurations and activation delays with stimulation were explored using multiple regression and exploration factor analyses. Results A total of 868 EMG data points based on 18 trials and up to 11 subtrials were captured from each of the four ILMs. Various combinations of pulse amplitude, pulse width, and exponential decay were found to produce significant (P ≤ .001) individual ILM responses. CT mirrored the LCA, whereas the TA and PCA exhibited separate interactions along shared trajectories in a three‐dimensional space. Conclusions FES calibrated to individual and coupled ILMs offers promise for restoring normal and pathological contraction patterns via strict RLN stimulation. Level of Evidence 5 Laryngoscope, 130:967–973, 2020

Some Theoretical Foundations of Bare-Simulation Optimization of Some Directed Distances between Fuzzy Sets Respectively Basic Belief Assignments

“…This definition (39) of the Belief-φ-divergence was first given in our paper [44]; later on, [49] used formally the same definition under the different (but deficient) assumptions that φ is only convex and satisfies φ(1) = 0, which leads to a violation of the basic divergence properties (take, e.g., φ(t) = 0 for all t, which implies D φ (P M 2 , P M 1 ) = 0 even if P M 2 ̸ = P M 1 ; such an effect is excluded in our setup due to our assumption (G4') being part of Υ(]a, b[)); as a technical remark let us mention that (as already indicated in Section 2) depending on φ, zero belief masses may have to be excluded for finiteness in (39). For instance, we can take in (39) the special case φ(t) := φ snKL,1 (t) (cf.…”

“…For divergence generators φ in Υ(]a, b[) with (say) 0 ≤ a < 1 < b and for two sets A, B ⊂ Y we can apply (1) to the corresponding membership functions and define the generalized φ-divergence D φ (B * , A * ) between the fuzzy sets B * and A * (on the same universe Y ) as (cf. [44])…”

“…Accordingly, we define the generalized φ-divergence D φ ( M2 , M1 ) between the rescaled BBAs M2 and M1 (in short, rescaled Belief-φ-divergence) as (cf. [44])…”

“…Analogously to (32) and (33), we can define the generalized φ-divergence D φ (B * * * , A * * * ) between the extended representation type ν-rung orthopair fuzzy sets B * * * and A * * * (on the same universe Y ) as (cf. [44])…”