Schematic representation of the 3DM for biomechanical modeling of human vocal fold dynamics. Every mass element is elastically connected to a rigid body with an anchor spring. Moreover, at each side every mass is connected to its adjacent masses with springs in vertical and longitudinal directions. The indices denote the different planes s and columns i for the mass elements.
Flow chart of the combined optimization algorithms. PSO, SA, and PDSM are applied to optimize the parameters Q to fit the model-generated dynamics to the vocal fold vibrations c i , s [n]. This is performed in each optimization phase, Fig. 3 .
General flow chart of the hybrid optimization procedure. represent the initial optimization parameters. represent the best optimization parameters. There are three coarse sub-procedures and a fine optimization process. Each coarse sub-procedure has three phases. In this flow chart, m, n, l temporarily denote the index of the coarse sub-procedure, the phase, and the loop, respectively.
Block charts for the three course optimization sub-procedures. Each sub-procedure is divided into three phases: Along each row, the intercommunities are vertical, lateral, and longitudinal, respectively.
Schematic representation of occurring glottal closure-types and corresponding modeling: (a) rectangle (RA), (b) hourglass (HG), (c) triangular-pointed dorsal (TPD), (d) triangular-pointed ventral (TPV), (e) convex (CV).
(Color online) Exemplary results of the 3D dynamics of the mass element m 4,4 are given. Synthetic trajectories (solid lines) and optimized trajectories (dotted lines) are presented for all three displacement directions. The corresponding accuracy values are: (Γ, κ, λ) = (0.05, 97%, 96%).
Comparison between the adapted optimization parameters and pre-defined values . The solid lines indicate the regression lines for the optimization parameters. The corresponding regression functions are shown including the 95% confidence interval. The distances between the regression lines and the confidence interval boundaries are indicated (Δ a , Δ b , Δ c exhibiting the reliability of the algorithm).
Boxplots of the accuracies λ i , s averaged over all 10 mass elements (i = 1,…, 10) at each plane (s = 1,…, 5) for the 50 synthetic data sets. The mean values are marked with *. Higher performances occur at the superior planes, while lower values occur at the inferior planes.
The rest positions of the 25 mass elements for one side are estimated in accordance to the mean values of the marker points placed on the hemilarynx. The marks × denote the rest position of the 25 mass elements.
(Color online) Results of the adapted 3DM (dotted lines) of the mass element m 3,3 located in the median cross section at the plane s = 3 on the right side of the model, compared to the hemilarynx trajectories (solid lines) at the corresponding suture-point. The fundamental frequency is 120 Hz.
Logarithmic charts for the optimized model parameters after application to a hemilarynx experimental data set. (a)–(d) describe the mass , anchor stiffness , longitudinal stiffness , and the vertical stiffness at/between different transverse planes s and coronal cross-sections i. occurs between the current plane and the next upper plane. occurs between the current cross section and the next one. The achieved subglottal pressure was equal to 19.0 cm H2O, and the estimated glottis length was 13.0 mm. i = 1,…, 5 denotes the coronal cross-sections from dorsal to ventral. s = 1,…, 5 denotes the transverse planes from inferior to superior. In general, the values of the model parameters at inferior plane (s = 1) are higher than those at superior plane (s = 5).
Fifty synthetic data sets with predefined parameters to be optimized. The data are separated by glottal closure types (Fig. 5 ) and gender.
Optimization results for the synthetic data: The global accuracy λ, correlation coefficient κ and objective function Γ exhibit sufficient good performance. Each glottal closure type covers 10 subjects (5 male, 5 female).
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