Development of a time-dependent numerical model for the assessment of non-stationary pharyngoesophageal tissue vibrations after total laryngectomy

Abstract

Laryngeal cancer due to, e.g., extensive smoking and/or alcohol consumption can necessitate the excision of the entire larynx. After such a total laryngectomy, the voice generating structures are lost and with that the quality of life of the concerning patients is drastically reduced. However, the vibrations of the remaining tissue in the so called pharyngoesophageal (PE) segment can be applied as alternative sound generator. Tissue, scar, and geometric aspects of the PE-segment determine the postoperative substitute voice characteristic, being highly important for the future live of the patient. So far, PE-dynamics are simulated by a biomechanical model which is restricted to stationary vibrations, i.e., variations in pitch and amplitude cannot be handled. In order to investigate the dynamical range of PE-vibrations, knowledge about the temporal processes during substitute voice production is of crucial interest. Thus, time-dependent model parameters are suggested in order to quantify non-stationary PE-vibrations and drawing conclusions on the temporal characteristics of tissue stiffness, oscillating mass, pressure, and geometric distributions within the PE-segment. To adapt the numerical model to the PE-vibrations, an automatic, block-based optimization procedure is applied, comprising a combined global and local optimization approach. The suggested optimization procedure is validated with 75 synthetic data sets, simulating non-stationary oscillations of differently shaped PE-segments. The application to four high-speed recordings is shown and discussed. The correlation between model and PE-dynamics is ≥ 97%.

Figures

Fig. 1

a After removing the larynx, the trachea is connected to the frontal neck (tracheostoma) to preserve breathing. The tissue in the changeover of esophagus and pharynx is called PE-segment. Closing the tracheostoma while exhaling forces the air to pass the voice prosthesis valve that connects trachea and esophagus. The mucosa tissue in the PE-segment is forced to oscillate what generates the acoustic signal for substitute voice. The dynamics of the PE-segment are registered by a high-speed camera. b Extracted frames of a HS recording of the PE-segment, representing one oscillation cycle. Visible is the pseudoglottis (dark area) and the surrounding mucosa tissue. For the analysis of the PE-dynamics, the PE-contour is segmented (white lines) and extracted in each frame

Fig. 2

The PEM(t) a consists of eight horizontally coupled two-mass oscillators (b). The pseudoglottis is represented by the minimum opening spanned by either the masses mi,s (i = 1, ..., 8) of the lower (s = 1) or upper (s = 2) plane. ki,sa,ki,sl, and kiv are the anchor, the longitudinal, and the vertical coupling spring, ai are the anchors corresponding to the masses mi,s⋅a¯i and ki,sa are imaginary anchors and corresponding anchor springs. For the purpose of clarity, dampers are not visualized. a PEM(t). b Two-mass oscillator-element. Left: Top view. Right: Front view

Fig. 3

Flow charts of adapting the dynamics of the PEM(t) to those of the PE-segment. The dynamics are separated into blocks with 4 oscillation cycles and 50 % overlap. a Each block is initialized with the optimized parameter set at half width of the previous block. The adaptation within a block is performed by loops of Simulated Annealing and Powell’s direction set method. The adaptation is completed after a predefined number of iterations or if the improvement between two consecutive iterations is smaller than a predefined threshold Γ. b For minimizing the objective function (SA and PDSM), the optimization parameters are linearly interpolated between the parameter sets of the first and last time step. The PEM(t) is scaled with the parameter sets, and the resulting dynamics are compared to those of the PE-segment. If the adaptation quality is not sufficient, the parameter set of the last time step is varied (a) Optimization procdure for block b (b) Minimization of objective function Γb

Fig. 4

Γ versus εrel for the optimizations of the 75 synthetic data sets with triangular (triangles), elliptic (squares), and circular (circles) model contours. The objective function was computed for the complete dynamics, i.e., after the optimization process. The relative error describes the mean over Q1[n], ..., Q8[n], QP[n]

Fig. 5

Adaptation results after fitting the PEM(t) to the dynamics of R1. a Area functions aPE[n] (solid line) and aPEM(t)[n] (dashed line) for a short sequence of non-stationary phonation. b Frequency over time for the PE-segment and the PEM(t) for the complete phonation process. c Extracted PE contour (black solid line), pseudoglottis (red area), and state of the PEM(t) (black dashed line). The squares indicate thepositions of the mass-elements m1 to m8. Mass m1 is color coded in gray, the remaining masses are arranged in clockwise order. Demonstrated is one oscillation cycle at the time steps marked with circles in subfigure (a). d Time development of the parameter set P[n], containing the nine optimization parameters of the PEM(t), over the complete phonation process. The symbols guide the eye and do not mark specific time steps

Fig. 6

Adaptation results after fitting the PEM(t) to the dynamics of R2. a Area functions aPE[n] (solid line) and aPEM(t) [n] (dashed line) for a short sequence of non-stationary phonation. b Frequency over time for the PE-segment and the PEM(t) for the complete phonation process. c Extracted PE contour (black solid line), pseudoglottis (red area), and state of the PEM(t) (black dashed line). The squares indicate thepositions of the mass-elements m1 to m8. Mass m1 is color coded in gray, the remaining masses are arranged in clockwise order. Demonstrated is one oscillation cycle at the time steps marked with circles in subfigure (a). d Time development of the parameter set P[n], containing the nine optimization parameters of the PEM(t), over the complete phonation process. The symbols guide the eye and do not mark specific time steps

Fig. 7

Adaptation results after fitting the PEM(t) to the dynamics of R3. a Area functions aPE[n] (solid line) and aPEM(t)[n] (dashed line) for a short sequence of non-stationary phonation. b Frequency over time for the PE-segment and the PEM(t) for the complete phonation process. c Extracted PE contour (black solid line), pseudoglottis (red area), and state of the PEM(t) (black dashed line). The squares indicate thepositions of the mass-elements m1 to m8. Mass m1 is color coded in gray, the remaining masses are arranged in clockwise order. Demonstrated is one oscillation cycle at the time steps marked with circles in subfigure (a). d Time development of the parameter set P[n], containing the nine optimization parameters of the PEM(t), over the complete phonation process. The symbols guide the eye and do not mark specific time steps

Fig. 8

Adaptation results after fitting the PEM(t) to the dynamics of R4. a Area functions aPE[n] (solid line) and aPEM(t)[n] (dashed line) for a short sequence of non-stationary phonation. b Frequency over time for the PE-segment and the PEM(t) for the complete phonation process. c Extracted PE contour (black solid line), pseudoglottis (red area), and state of the PEM(t) (black dashed line). The squares indicate thepositions of the mass-elements m1 to m8. Mass m1 is color coded in gray, the remaining masses are arranged in clockwise order. Demonstrated is one oscillation cycle at the time steps marked with circles in subfigure (a). d Time development of the parameter set P[n], containing the nine optimization parameters of the PEM(t), over the complete phonation process. The symbols guide the eye and do not mark specific time steps