Reconstruction of Vocal Fold Medial Surface 3D Trajectories: Effects of Neuromuscular Stimulation and Airflow

Abstract

Introduction:

Analysis of medial surface dynamics of the vocal folds (VF) is critical to understanding voice production and treatment of voice disorders. We analyzed VF medial surface vibratory dynamics, evaluating the effects of airflow and nerve stimulation using 3D reconstruction and Empirical Eigenfunctions (EEF).

Study Design:

In vivo canine hemilarynx phonation.

Methods:

An in vivo canine hemilarynx was phonated while graded stimulation of the recurrent and superior laryngeal nerves (RLN and SLN) was performed. For each phonatory condition, vibratory cycles were 3D reconstructed from tattooed landmarks on the VF medial surface at low, medium, and high airflow. Parameters describing medial surface trajectory shape were calculated and underlying patterns were emphasized using EEFs. Fundamental frequency and smoothed cepstral peak prominence (CPPS) were calculated from acoustic data.

Results:

Convex hull area of landmark trajectories increased with increasing flow and decreasing nerve activation level. Trajectory shapes observed included circular, ellipsoid, bent, and figure-eight. They were more circular on the superior and anterior VF, and more elliptical and line-like on the inferior and posterior VF. The EEFs capturing synchronal opening and closing (EEF1) and alternating convergent/divergent (EEF2) glottis shapes were mostly unaffected by flow and nerve stimulation levels. CPPS increased with higher airflow except for low RLN activation and very dominant SLN stimulation.

Conclusion:

We analyzed VF vibration as a function of neuromuscular stimulation and airflow levels. Oscillation patterns such as figure-eight and bent trajectories were linked to high nerve activation and flow. Further studies investigating longer sections of 3D reconstructed oscillations are needed.

Lay Summary:

3D reconstruction of movement paths of landmarks tattooed on a vocal fold during vibration reveals specific patterns of oscillation dependent on laryngeal nerve stimulation and airflow.

INTRODUCTION

While the importance of three-dimensional assessment of vocal fold (VF) oscillations has been acknowledged^{1, 2, 3, 4}, the vertical component of VF vibration is still neglected in many studies^{5, 6, 7}. Using an in-vivo canine hemilarynx model, we can assess glottal 3D oscillation patterns. The larynx is innervated by two major laryngeal nerves on both sides, the superior laryngeal nerve (SLN) and the recurrent laryngeal nerve (RLN), that control the pre-phonatory posture. The SLN exclusively controls the cricothyroid muscle responsible for elongating the VF and thinning the vertical segment. Sub-branches of the RLN innervate the remaining laryngeal muscles regulating VF adduction (primarily interarytenoid and lateral cricoarytenoid muscles (LCA+IA)) and bulging (thyroarytenoid muscle (TA), thus increasing the vertical height)^{8, 9}.

In an early study, Berry et al. applied an ex-vivo canine hemilarynx model to track landmarks on the medial surface during phonation for 3D reconstruction¹⁰. Trajectories from nine VF fleshpoints of one vertical line of the medial surface were 3D-reconstructed, exploring basic mechanisms of self-sustained oscillation. This approach was expanded upon by Döllinger et al. tracking a grid of 30 micro sutures for different distinct phonatory conditions in an excised human larynx with sustained VF oscillation^{11, 12}. Using Empirical Eigenfunctions (EEFs) they investigated changes in oscillation patterns dependent on different variables such as flow, adduction, and VF pre-stress. Using an advanced version of the 3D reconstruction setup previously used by Döllinger et al¹³, in a canine in vivo model, Reddy et al. 3D-reconstructed a grid of 35 ink landmarks and interpolated the medial surface in-between¹⁴.

In this study, we investigate VF oscillation patterns in a canine hemi-larynx model as a function of SLN and RLN nerve stimulation and airflow levels with synchronous recording of the acoustic signal. Previous studies relied on ex-vivo setups with no direct nerve stimulation^{11, 12}, stimulation of exclusively the RLN but not SLN^{13, 15} or did not investigate changing flow¹⁴. Hence, the questions we aim to answer are: (1) How do EEFs and trajectory shape change with different laryngeal nerve activation and pressures associated with flow? (2) Can we explain previously observed patterns of VF oscillations based on SLN and RLN activation states? (3) Are there previously overlooked relations between laryngeal nerve activation, flow, acoustics, and VF dynamics?

METHODS

In vivo canine hemilarynx phonation model

This work was undertaken in compliance with all policies regarding the use of laboratory animals and approved by the institutional animal research committee. The setup for canine hemilarynx experiments was described in detail in previous work ^{16, 17} and is therefore only briefly outlined here: a healthy male mongrel canine was anesthetized and placed in a supine position on an operating table. The larynx was exposed and a right hemilaryngectomy was performed. A grid of 30 India ink landmarks (7 columns, 3–5 rows per column, see Figure 1A) was tattooed on the medial surface of the remaining left VF. Exposed RLN and SLN nerve branches were connected to cuff electrodes (Ardiem Medical, Indiana, PA) for stimulation. A transparent right-angle glass prism was placed at the glottal midline against the VF. The prism provides two perspectives of VF vibration that are recorded for subsequent 3D reconstruction. Humidified airflow was provided to the larynx via a subglottic tube ¹⁸, achieving phonation and oscillation of the VF against the glass prism. VF oscillations were recorded through the glass prism with a high-speed camera (Phantom v210, Vision Research Inc., Wayne, NJ) at 3000 fps and 512×512-pixel resolution. The acoustic signal was recorded using a microphone (Model 4128; Brüel & Kjær North America, Norcross, GA) mounted flush to the inner wall of the subglottic tube.

Figure 1.

Illustration of data extraction: A) Coronal and axial landmarks on the medial surface tracked and used for 3D trajectory reconstruction. B) Illustration of convex and concave convex-hull area, and maximum and orthogonal Feret’s diameters being calculated for each trajectory (landmark C4 in phonatory condition SLN10 RLN5 high flow). C) Illustration of emphasizing effects by EEFs (landmark C1 in phonatory condition SLN10 RLN10 high flow). D) Video sections and acoustic signal (F0 and CPPS computation) windows chosen for analysis vs. flow and time.

Investigated neuromuscular phonatory conditions

SLN and RLN nerves were stimulated at 10 levels each, from threshold (SLN1 / RLN1) to maximum muscle activation (SLN10 / RLN10). Including no stimulation (SLN0/RLN0) conditions, thus a total of 121 distinct neuromuscular SLN/RLN activation pairs were available for analysis. Stimulation duration was 1500 ms, during which the airflow was ramped linearly from 400 ml/s to 1600 ml/s. Due to limitations in our data processing (detailed in limitations) we investigated only seven distinct nerve activation combinations at three levels of airflow (low, medium, high), for a total of 21 distinct phonatory conditions. Interval flow and time ranges for these phonatory conditions are illustrated in Figure 1D and given in Table S1. Each interval was chosen to contain a representative segment of local phonation consisting of three cycles of oscillation for segments after onset.

Vocal fold 3D reconstruction

The VF 3D reconstruction process was previously described in Reddy et al. ¹⁴ and only a summary is given here: After calibration, the 30 VF surface landmarks were manually tracked using a custom software tool (GLabel, Friedrich Alexander University Erlangen-Nürnberg) by two experts (initial marking and control). If landmarks could not be tracked for up to three frames in one or both 2D views, they were linearly interpolated. The 3D positions of the landmarks (tattooed grid) were then reconstructed. A validation study was performed showing that the average error is expected to not exceed 0.12 mm¹⁹.

Parameters

Patterns of movement of the VF medial surface can be described using EEFs to extract the main components of the movement from tracked points on the VF surface¹². Spatial EEFs denote directions of movement patterns for each point and temporal EEFs denote the amplitude of a movement pattern over time¹¹. Together each pair of spatial and temporal EEFs is a one-dimensional movement in 3D space for each point. As each EEF pair contributes a distinct share of total movement variance, distinct trajectory movement patterns can be de-noised and emphasized by extracting EEFs and only summating the most dominant pairs of spatial and temporal EEFs until a certain share of variance (approx. 95%) is reached (Figure 1C)¹³. A more detailed explanation of EEFs is given in¹¹. For simplification, we will refer to the unity of the first and most dominant temporal and spatial EEF pair as EEF1, to the second and third pair as EEF2 and EEF3.

To capture the vertical and horizontal vibration patterns, one coronal and one axial section of the VF containing 5 landmarks each was selected. Both sections intersected at their third landmark as depicted in Figure 1A. As landmarks do not move significantly in the anterior or posterior direction, longitudinal displacements are neglected¹¹. For the movement trajectory of each landmark in each phonatory condition the following parameters were calculated: The 2D-area of the concave and convex hull resulting from lateral and vertical displacements, and Feret’s minimum and maximum diameter of the convex hull (as described in²⁰), see Figure 1B. Table S2 indicates which measures were calculated for the phonatory conditions.

Excluding low-flow conditions, spatial and temporal EEFs were calculated for each coronal and axial section as described in¹¹ for phonatory conditions given in Table S2. Trajectories were reconstructed using EEF1–3 as these covered at least 94% of the total variance in all cases. This process emphasizes the main underlying patterns of movement (see Figure 1 (C)).

Phonation onset was determined manually from acoustics and video data. Fundamental frequency (F0) and CPPS were calculated using Praat (version 6.1.38). F0 was calculated on the entire signal (detection range set to 50–600 Hz) and local averaged values were extracted every 0.05s (no overlap). CPPS was calculated in 0.3s windows with 0.05s steps (83.3% overlap). For the calculation of CPPS from each window the protocol given in ²¹ was used. Only windows with phonation were included as shown in Figure 1 (D).

RESULTS

3D movement trajectories were reconstructed for all coronal and axial landmarks. In some cases, when landmarks on these trajectories were obscured for more than three frames exceeding our stated criteria for interpolation, EEFs were not calculated as the missing data points would have impacted the extracted movement patterns. Similarly, if single landmark trajectories were partially obscured, areas and Feret’s diameters were only calculated for the remaining landmarks in the section.

Convex and concave hull areas

Convex and concave hulls of each trajectory represent the space occupied (convex-hull area) by the landmark during vibration (Figure 1B). In Figure 2, the convex area for all phonatory conditions is depicted. The first row in the figure shows plots for coronal sections for (A) low, (B) medium, and (C) high flow conditions. Analogously the second row shows plots for axial sections at (D) low, (E) medium, and (F) high flow. In each plot in the first row (A-C) parameter values are shown from the most superior (C1) to the most inferior (C5) trajectory. Respectively, in the second row (D-F) parameter values are plotted from posterior (A1) to anterior (A5).

Figure 2.

Convex convex-hull area for coronal sections for (A) low, (B) medium, and (C) high flow conditions for the 7 investigated nerve activation combinations. Parameter values are shown from the most superior (C1) to the most inferior (C5) trajectory. Analogously, convex convex-hull area for axial sections for (D) low, (E) medium, and (F) high flow conditions for all investigated nerve activation combinations. Areas are plotted from posterior (A1) to anterior (A5).

Overall convex area increased with increasing flow and decreasing nerve activation level. In the coronal section, the convex area increased mostly at the superior and less at the inferior landmarks. In axial direction, the second-most anterior trajectories showed the highest increase in convex area with rising flow while the convex area of the most posterior trajectories is almost unaffected by rising flow. In Figure 3, the ratio between convex and concave-hull areas (“area ratio) is illustrated. A value closer to one indicates a more circular or ellipsoid trajectory shape, while higher values indicate deviation from ellipsoid trajectory movement.

Figure 3.

Area ratio (Convex-hull area / Concave-hull area) for coronal section trajectories for (A) low, (B) medium, and (C) high flow conditions for the 7 investigated nerve activation combinations. Area ratios are shown from the most superior (C1) to the most inferior (C5) trajectory. Analogously Area ratio for axial section trajectories for (D) low, (E) medium, and (F) high flow conditions for all investigated nerve activation combinations. Area ratios are plotted from posterior (A1) to anterior (A5). A value closer to one indicates a more circular or ellipsoid trajectory shape, while higher values indicate deviation from ellipsoid trajectory movement.

No general trends were observable in low flow conditions (A and D) as during this airflow level the hemi-larynx was often at various stages of pre-onset or onset. Hence trajectories were very small and relative differences were not meaningful. Notable differences especially in medium and high flow inferior coronal sections (Figures 3B and 3C) are explainable by an arising slight bend in otherwise ellipsoid trajectory movement. Due to the smaller overall trajectory size this relative difference is larger in medium Flow conditions (Figures 3B and 3E). In Figure 4, different trajectory shapes with (A) circular, (B) ellipsoid and (C) bent are depicted for phonatory condition SLN 10 RLN 5 medium flow.

Figure 4.

Examples of different trajectory shapes from phonatory condition SLN 10 RLN 5 medium flow showing (A) circular (landmark C1), (B) ellipsoid (landmark CA) and (C) bent (landmark C4) with marked difference area in convex and concave hulls.

Maximum and orthogonal Feret’s diameters

Maximum and orthogonal Feret’s diameters function as measures for the length and width of trajectory hulls. Analogously to Figure 3, in Figure 5 the “Feret’s ratio” between measured Feret’s diameters (Orthogonal diameter / Maximum diameter) is given. A value closer to one indicates a more circular shape of the trajectory, while a value closer to zero indicates a more line-like shape. Analogously to the area ratio, no general trends were observable in low flow conditions (A and D) due to small trajectory sizes. For higher flow conditions a trend arose in coronal and axial sections, showing the trajectories to be more circular on the superior and anterior end for all conditions, and more line-like at the inferior and posterior ends.

Figure 5.

Feret’s ratio for coronal section landmarks for (A) low, (B) medium, and (C) high flow conditions for the 7 investigated nerve activation combinations. Feret’s ratios are shown from the most superior (C1) to the most inferior (C5) trajectory. Analogously, Feret’s ratios for axial section landmarks for (D) low, (E) medium, and (F) high flow conditions for all investigated nerve activation combinations. Feret’s ratios are plotted from posterior (A1) to anterior (A5). A value closer to one indicates a more circular shape of the trajectory, while a value closer to zero indicates a more line-like shape.

Oscillation patterns

The first three EEFs of coronal and axial sections covered 94–99% of the total variance. Figure 6 depicts the EEFs of one coronal (SLN10 RLN10 high flow) and one axial section (SLN5 RLN5 medium flow) landmarks. The first row of the figure shows (A) EEF1, (B) EEF2, and (C) EEF3 of the coronal section and the trajectories reconstructed from EEF1–3. Each arrow indicates the direction (spatial EEF) and amplitude (temporal EEF) of oscillatory movement of one landmark while the dotted and solid lines act as an indicator of EEF-induced surface shape at cycle extrema. Analogously Figures 6D–F show EEF1–3 for the axial section and the reconstructed trajectory of the axial section. Similar plots for all remaining phonation conditions are provided in Files S3 and S4.

Figure 6.

(A) EEF1, (B) EEF2 and (C) EEF3 of the coronal section and the corresponding trajectories for condition SLN10 RLN10 high flow. Analogously (D) EEF1, (E) EEF2 and (F) EEF3 of the axial section and corresponding trajectories for condition SLN5 RLN5 medium flow. Each arrow indicates the direction (spatial EEF) and amplitude (temporal EEF) of oscillatory movement of one landmark. The dotted and solid lines connecting arrow tips and bases act as an indicator of EEF-induced surface shape at cycle extrema.

Synchronal opening and closing movements were captured by EEF1 along coronal and axial sections. EEF2 captured the alternating convergent/divergent surface shape (coronal sections) and the anterior/posterior mode (AP-mode) respectively (axial sections)²². EEF3 in coronal sections corresponded to a “figure-eight” shaped pattern in the superior section. This pattern was only distinct in high-flow and high-SLN+RLN conditions. EEF3 in axial sections was often insignificant (< 3% variance) and corresponded to opposing parts of surface movement.

Figure 7 shows the second-most inferior and superior coronal trajectories at (A) low, (B) medium, and (C) high flow as a function of the landmarks distance to the glass plate over time for nerve activation condition SLN0 RLN1. Analogously Figure 7 (D–F) shows the same (second-most anterior and posterior trajectories) for axial sections of SLN5 RLN5. The observed difference between opening and closing in Figure 7 was similar for all other phonatory conditions. There was a time delay between opening of the inferior and superior glottis in coronal sections, but no significant delay during closing. Similar plots for all remaining phonation conditions are provided in Files S5 and S6.

Figure 7.

Distance from glass plate over time for condition SLN0 RLN1 for (A) low, (B) medium and (C) high flow. Depicted are the second most superior (C2) and second most inferior (C4) landmark trajectories of the coronal section. Analogously distance from glass plate over time for condition SLN5 RLN5 for (D) low, (E) medium and (F) high flow. Depicted are the second most anterior (A4) and second most posterior (A2) landmark trajectories of the axial section.

Acoustic parameters

In Figure 8 (A, B) F0 and (C) CPPS are plotted as a function of flow and time for nerve activation conditions. Sudden F0 drops occurred in some low-mid SLN / mid-high RLN conditions after onset. Otherwise, F0 remained relatively stable only increasing between 4 and 12 Hz over time (Figure 8 (B)) with the higher increases being associated with lower SLN stimulation. In general, CPPS increased with flow in most conditions except SLN0 RLN1 and SLN4 RLN1. The only decreasing trend observable was in SLN0 RLN5 during the mode change. VF oscillation started with full-surface oscillations in conditions SLN10 RLN5 and SLN10 RLN10 which was also reflected by the initially higher CPPS.

Figure 8.

Computed acoustic parameters (A) F0, (B) F0 details and (C) CPPS vs. flow and time for all seven investigated phonatory conditions. For SLN5 RLN5, F0 could not be determined for some windows after onset.

DISCUSSION

Trajectory shape

The decrease of convex-hull area from superior to inferior was consistent with simulations by Palaparthi et al.²³ and findings by Döllinger et al.^{12, 24} Also, like in previous work, convex-hull area was higher towards the middle in anterior-posterior direction (Figure 2 E/F), and trajectories were observed to be more circular towards superior and more elongated towards inferior^{12, 24}. Bent trajectories¹² in coronal sections appeared to be more prominent at higher SLN stimulation and higher flow in our evaluation. A potential hypothesis to explain this could be an arising subtle gradient in tissue stiffness due to the superior part of the VF being elongated slightly more than the inferior part as the Thyroid cartilage folds forward during CT activation. Hence the inferior parts of the VF tissue get more restricted in their oscillation paths by the tenser, superior VF. However, for a meaningful comparison of oscillation patterns with model predictions²⁵, more data are necessary.

Oscillation patterns

The high fraction of total variance and the types of movement captured by the first two EEFs with negligible vibrations in anterior-posterior direction were in line with previous work^{11, 13, 24}. However, in this hemilarynx, the opening/closing pattern was more dominant than the convergent-divergent shape which was inverted in most^{11, 13, 12} but not all¹⁰ previous studies. This suggests that a higher share of energy put into the system via flow contributed to voice production which is likely due to the higher airflow used¹². The convergent/divergent shape only became more dominant in medium flow and high SLN conditions, indicating an induced delay in superior movement with SLN stimulation.

The superior “figure-eight” shaped pattern has also been observed before^{12, 24} and could be linked to high SLN and RLN stimulation at high flow. As the VF is tenser, its most superior part is not fully adducted during closing¹⁴ forcing superior landmarks in an upward trajectory. During opening the superior VF is pulled down and away from the glass as the inferior part opens, creating the “figure eight” pattern (See Figure 6A, Video S7).

The difference between the opening and closing phase delay in coronal sections may be explainable by an air-pressure effect. During opening, rising air from below pushes the VF laterally, which is a slower process than an arising elastic recoil and negative air pressure during closing, sucking the VF towards the glass.

Acoustics

CPPS increased with flow in most phonatory conditions. Conditions in which CPPS did not increase showed extremely low RLN activation with, in some cases, chaotic oscillation patterns (SLN4 RLN1). Changes in CPPS trends were linked to sudden F0 drops. These drops happened in three conditions (SLN0 RLN5, SLN0 RLN10, and SLN5 RLN5) briefly after onset. In these conditions, only a faster superior oscillation was induced before full VF oscillation ensued. This is surprising as previously SLN activation was thought to be required for these kinds of mode changes²⁶.

The observed mode changes briefly after onset in this work may be explainable due to a combination of multiple factors: the gradually increasing flow, lower SLN stimulation, and the VF resting against the glass surface. Additionally, subglottal resonances may have affected onset²⁷. Therefore, the force associated with flow was in these conditions initially only sufficient to set a part of the soft VF in motion.

Limitations

Only a single canine-hemilarynx was analyzed and only a single coronal and axial section was tracked. However, in previous work, it has been shown that different coronal and axial sections of the VF in regards to oscillation patterns are rather similar, so the loss of information should be minimal^{11, 12}. As the TA muscle was not stimulated separately and, according to Nasri et al., TA stimulation is a sigmoidal function of RLN stimulation, exact TA stimulation relative to LCA+IA stimulation remains unknown in this work²⁸. As discussed, the observed F0 drops after phonation onset may be in part an artifact of the hemilarynx-model and subglottal resonances. A similar effect could also explain the only minor increase of F0 of up to 12 Hz with increasing flow while an increase of over 15 Hz would have been expected for conditions without SLN stimulation^{12, 26}. This has to be investigated in further studies. As we work with a hemilarynx model laryngeal nerves are only stimulated one-sided and the distance between VF and the glass prism might have been slightly too high. This may have resulted in a smaller effect of SLN activation on F0 than expected. Lastly, subglottal pressure and subglottal resonances were not evaluated in this study.

CONCLUSION

In this paper we (1) showed how EEFs stayed relatively unaffected by nerve activation and pressures associated with flow except for a partial reversal of EEF1 on the superior end at high SLN conditions at medium flow and how trajectory shape became more circular towards superior and more elongated and “bent” towards inferior with rising SLN and RLN activation and higher airflow; (2) linked the previously observed “figure-8“ oscillation pattern to high SLN and RLN activation states and (3) showed synergy between increasing flow and nerve stimulation, leading to higher CPPS as a measure of voice quality. Nevertheless, we are limited to only qualitative observations by the current manual tracking approach. To 3D-reconstruct large sections of medial surface oscillations for quantitative investigations on more larynges, a fully automatized tracking algorithm will be required such as suggested for glottal area segmentation²⁹.

Supplementary Material

Video S7

Video S7. Illustration of trajectory movement and medial surface oscillation for condition SLN 10 RLN 10 high flow.

File S3

File S3. Coronal section trajectories with EEF overlay for all investigated phonatory conditions.

File S4

File S4. Axial section trajectories with EEF overlay for all investigated phonatory conditions.

File S5

File S5. Coronal section plots of landmarks distance to the glass plate over time for all investigated phonatory conditions.

File S6

File S6. Axial section plots of landmarks distance to the glass plate over time for all investigated phonatory conditions.

Table S1

Table S1. SLN and RLN stimulation levels (0 = No stimulation, 1 = threshold stimulation, 10 = maximum stimulation) and airflow ranges (in milliliters per second) for all investigated neuromuscular phonatory conditions.

Table S2

Table S2. Calculated measurements and performed evaluations for all phonatory conditions.