An Integrated Experimental-Computational Study of Vocal Fold Vibration in Type I Thyroplasty

Abstract

Subject-specific computational modeling of vocal fold (VF) vibration was integrated with an ex vivo animal experiment of type 1 thyroplasty to study the effect of the implant on the vocal fold vibration. In the experiment, a rabbit larynx was used to simulate type 1 thyroplasty, where one side of the vocal fold was medialized with a trans-muscular suture while the other side was medialized with a silastic implant. Vocal fold vibration was then achieved by flowing air through the larynx and was filmed with a high-speed camera. The three-dimensional computational model was built upon the pre-operative scan of the laryngeal anatomy. This subject-specific model was used to simulate the vocal fold medialization and then the fluid-structure interaction (FSI) of the vocal fold. Model validation was done by comparing the vocal fold displacement with postoperative scan (for medialization), and by comparing the vibratory characteristics with the high-speed images (for vibration). These comparisons showed the computational model successfully captured the effect of the implant and thus has the potential for presurgical planning.

Abstract

1 Introduction

The phonation or voice production process is a result of VF vibrations that are induced by the airflow passing through the narrow glottis and in turn converting the airflow into a pulsatile jet. This FSI process causes acoustic waves in the air, which are subsequently modified in the oral, nasal, and pharyngeal cavity to produce harmonic waves. Healthy voice production is an important tool in human life, as we are heavily dependent on oral communication to participate in professional and social settings. Prior to vibration, the VF housed in the larynx, colloquially known as the voice box, must be medialized or adducted toward the midplane through neuromuscular activities to create a narrowed or completely closed glottis to facilitate the flow-induced vibration [1]. Any disruption of the neuromuscular system may result in adverse effects on VF medialization and thus voice disorders [2,3]. One such example is unilateral vocal fold paralysis (UVFP), which is caused by injury or damage to the vagus nerve or the recurrent laryngeal nerve [4–6], e.g., iatrogenic injury, laryngeal cancers, and neurogenic disorders [7,8]. In this condition, the affected VF side cannot be medialized voluntarily, and the patients commonly present with symptoms of impaired voice quality (dysphonia), impaired swallowing function (dysphagia), and aspiration [9].

One of the most popular methods for UVFP treatment is surgical medialization of the paralyzed VF, known as type 1 thyroplasty [6,10]. During this procedure, medialization is achieved by pushing the paralyzed side toward the midline with a silastic implant (or other biotolerable materials) through a window created in the thyroid cartilage [11,12]. One of the challenges for the silastic type 1 thyroplasty procedure is its subjective nature in determining the optimal design and placement of the implant for vocal fold medialization [13]. Specifically, the reliance on anatomical landmarks and experiential judgment during the procedure can lead to significant inconsistencies and variations in the implant location and design of shape and size [8,14]. In addition to variabilities of individual patients, a few factors may complicate the outcome of the procedure. For example, the assessment of peri-operative factors such as inflammation and edema can be difficult, potentially resulting in under-medialization or over-medialization once the inflammation resolves, and customizing implant shape through intraoperative carving may thus be suboptimal [15,16]. Between 4.5% and 16% of patients require revision surgery due to postsurgical complications such as extrusion, migration, and resizing [17–20]. To address these limitations, the development of a presurgical planning tool becomes important. By utilizing computational models and pre-intervention scans, a planning tool can potentially provide quantitative and objective information on optimal implant placement and design, and also enable surgeons to visualize and simulate the effects of the implant, thus improving surgical precision and patient outcomes.

In the past, computational modeling of phonation has largely contributed to the understanding of its physical process and providing insights into various aspects such as vibratory characteristics, geometric and material parameters, and acoustic output [21–26] that were not available from experiments [27]. Earlier computational FSI studies using much simplified or idealized structural models of the larynx were able to simulate generic vibratory characteristics of the VF [28–32]. Recently, several studies have started to employ more realistic laryngeal models that were based on magnetic resonance imaging (MRI) or computerized tomography (CT) scans of individual subjects [21,33]. With the subject-specific anatomical details incorporated, such computational models may potentially be used to evaluate the effect of the implant on vocal fold vibration prior to the operation, thus serving as a planning tool to improve the surgical outcome.

Along with this line of research, in recent years, we have performed a series of integrated study combining rabbit vocal fold experiments and computational models to explore the issues such as experiment protocol, model construction, computational efficiency and accuracy, model validation, and outcome assessment. For example, Chang et al. [33] modeled and validated the healthy phonation condition that was created in vivo in rabbits; Li et al. [34] developed a simplified one-dimensional pulsatile flow model that was enhanced by machine learning and also validated it against the same set of in vivo phonation data; Wilson et al. [3] created different vocal fold configurations in rabbits, including bilateral medialization, UVFP, and type 1 thyroplasty; and Li et al. [35] used a computational model to optimize the implant location for type 1 thyroplasty, and through a controlled experiment, they demonstrated the computational modeling and optimization led to improvement in implant medialization. In these studies, the use of rabbit models in investigating phonation and voice disorders is justified due to their similarities in anatomical, biological, and biomechanical vocal fold properties with those in the human larynx [36–39].

Despite the recent progress in the subject-specific modeling of vocal fold vibration and the efforts in the modeling of thyroplasty, there is still a lack of studies combining computational modeling with experimental outcomes to validate the model and to assess the model's performance in capturing the effect of the implant on the VF's vibratory characteristics. There have been a few recent works that used computational modeling to investigate implant medialization. For example, Smith et al. [40] studied the insertion depth of the implant on VF vibration and acoustic output using an idealized VF model, and their results agreed qualitatively with available experiment data. Wu and Zhang [25] studied the effect of implant stiffness on the VF vibratory characteristics using an MRI-based model, and their results also had qualitative agreement with the ex vivo experiment of human larynges by Cameron et al. [26]. A more recent work by Movahhedi et al. [23] studied the effect of the implant and performed virtual optimization by incorporating flow-structure-acoustics interaction and muscle activation of the VF, but there was no experiment validation in their study.

Following our previous works, in this study, we utilize an integrated approach to develop and validate the computation model based on rabbit phonation. However, different from previous works (e.g., Li et al. [35]), the current study is focused on modeling of implant medialization as well as subsequent VF vibration with the implant included, and we aim to capture the direct effect of the implant on VF vibration and to validate the results against the high-speed video (HSV) of the same VF sample. Next, we describe the experiments and computational modeling separately before presenting the results.

2 Method of Experiments

The animal procedures were approved by the University of Pittsburgh's Institutional Animal Care and Use Committee (#21220467) and were performed on a New Zealand white rabbit. The rabbit was sedated with an intramuscular injection of 17.5 mg/kg ketamine and 0.125 mg/kg dexmedesed, laid supine, shaved from sternal notch to submentum, with a single incision made down the midline of the neck. This was followed by dissection of the muscle and fascia to expose the larynx. The larynx was excised for ex vivo procedures following euthanization by intravenous overdose of Sodium Pentobarbital.

The excised larynx was placed in perfluorocarbon oil and scanned before the medialization procedure (i.e., pre-operative) using MRI with a Bruker® AV3HD 11.7 tesla/89 mm vertical-bore micro-imaging system. T-2 weighted images at an isotropic resolution of 60 μ were obtained using a fast spin-echo sequence. Additional details for the MRI scanning are described in our previous work [24]. The pre-operative scan was performed for the rest state with both VF sides abducted, i.e., rest configuration or configuration 0, and a postoperative scan was performed with the implant on one side and suture medialization on the other side (configuration 3, as described next). An intermediate configuration was also introduced with one side medialized using suture and the other side at the rest state. This configuration represented the phonation position at the UVFP configuration or configuration 2, where the paralyzed side (the rest side) could not medialize by itself. The healthy condition with both sides medialized naturally using laryngeal muscles, or configuration 1, did not need to be modeled in this study (a previous work of ours was concerned with this condition [22]). Figure 1(a) shows the MRI scan of the postoperative VF at configuration 3. The pre-operative scan of the rest configuration was used to build the finite-element method (FEM) model for the subsequent numerical analyses, while the postoperative scan was used to compare vocal fold displacement from actual medialization with the numerically simulated medialization. The overall experiment and computational procedures, including model validation, are shown in a flowchart (see Supplemental Materials on the ASME Digital Collection).

Fig. 1.

(a) Postoperative MRI scan showing VF medialized by a unilateral suture (left side) and by silastic implant insertion (right side). The length between the anterior and posterior commissure is represented byL. (b) Image from the HSV showing an instantaneous moment of the VF vibration, where the straight line is where thekymograph was taken. (c) Kymograph showing VF vibration over time at the medialized state (configuration 3).

During thyroplasty surgery, an implant was inserted unilaterally via a window cut into the thyroid cartilage and secured below the VF muscle to medialize the VF. In the current study, a laser-cut silastic implant having a simple cuboidal implant shape of 1 mm  $\times$ 1 mm $\times 2$ mm was inserted. The opposing side was medialized using a transmucosal suture that entered the larynx via the thyrohyoid membrane and was secured by suturing through the thyroid cartilage and tied off with an overhand knot to maintain tension. This suture method was used to mimic medialization of the healthy side in the UVFP.

Following surgery and the postoperative MRI, the sample was removed from perfluorocarbon oil and rinsed with phospho-buffered saline, and ex vivo phonation was elicited at configuration 3. In this procedure, the larynx was mounted to pseudo-lung in an excised larynx cabinet and humidified air was supplied using a Neptune Conchatherm system (Medline, Northfield, IL) to elicit phonation, with subglottal pressure determined by an in-line digital pressure meter (Cole-Parmer, Vernon Hills, IL). Phonation was initially captured for configuration 3 at 8000 fps using a stabilized AX50 HSV camera (Photron, Tokyo, Japan). Following this, the implant was removed, and the phonation test was repeated at the intermediate or UVFP configuration. Finally, a control test was done for configuration 0 by removing the suture to recover the rest condition. Subglottal air condition was consistent for all configurations, with the air pressure maintained at the same level of 2 kPa as in configuration 3. Additional details of the experimental setup and methodologies can be found in Novaleski et al. [41] and Ge et al. [38]. The HSV was processed using a custom MATLAB code generously provided by Dr. Dimitar Deliyski from Michigan State University to Dr. Rousseau for digital kymograph analysis, as shown in Fig. 1(c). In the kymograph, the vocal fold waveform, with time represented on the x-axis, was extracted from the HSV.

3 Method of Computational Modeling

3.1 Model Construction.

The laryngeal geometry was reconstructed from the pre-operative MRI scan at the rest configuration, where both VF sides were abducted. Manual segmentation was used in this process [24], during which thyroid cartilage, arytenoid cartilage, cricoid cartilage, vocal fold body, and vocal fold cover were identified from the images and were separately segmented. Here, a two-layer structure, i.e., cover (epithelium and superficial lamina propria) and body (vocal fold ligament and muscles), was assumed for the vocal fold [21,33,42]. Another segmentation was done for the entire larynx, in which the lumen surface of the airway was excluded, and all the tissue components were combined as one body. The entire larynx and individual components were separately meshed in COMSOL Multiphysics (COMSOL Inc., Burlington, MA); then each individual component was registered on the unified mesh model of the entire larynx (Fig. 2) by comparing the unified mesh with the mesh of that component. Such an approach ensured that meshing of all the components was matched at the interface. Overall, the geometrical model contained a 10-node tetrahedral (TET10) mesh of 94,593 elements.

Fig. 2.

Reconstructed geometrical model showing the individual components from a supraglottal view (a)and from a posterior view (b). For clarity, the VF body and other connecting tissue are not shown here.

The unified mesh model, with individual components identified on it, was then imported into COMSOL for medialization simulation and subsequent eigenmode analysis. The implant was modeled as a rectangular block of length 2 mm and a width and depth of 1 mm each (Fig. 3). The suture line was modeled as a flexible cylinder embedded in the tissue with a 0.3 mm diameter and 2 mm length. The specific locations of the implant and suture line are shown in Fig. 3(b). These precise locations were obtained from the postoperative scan of the larynx. A rectangular window on the thyroid cartilage was created to facilitate implant insertion in the numerical simulation. To mimic the tissue separation from the thyroid cartilage, a gap was created between the thyroid cartilage and the connective tissue adjacent to it. This gap spanned approximately 2 mm away from the implant edges in the longitudinal and anterior-posterior directions. A similar gap was created on the suture side. The region of tissue separation was approximated based on the observation in the postoperative MRI scan (Fig. 1; also highlighted later in Fig. 4).

Fig. 3.

The FEM model showing the implant (a), and a slice in the transverse plane showing the positions of implant and suture (b)

Fig. 4.

Comparison of VF displacement between the MRI images (a)–(c) and the numerical simulation (d)–(f). (a), (d) The initial rest configuration; (b), (e) medialized configuration in the axial view; (c), (f) medialized configuration in the coronal view. The dashed line in (b) and (c) indicates the tissues separation from the medialization.

For tissue mechanics, deformation of all the tissue components was assumed to be governed by the Saint-Venant Kirchhoff model [33,43], while Young's moduli of the VF cover and VF body were estimated based on the eigenmode analysis of the medialized state that is described next.

3.2 Simulation Setup.

The numerical simulation was divided into three steps [1]: a quasi-static simulation of medialization in which both the implant side and the suture side were adducted toward the midline [2]; an eigenmode analysis of the vocal fold to check if its natural frequency agreed with the vibration frequency obtained from HSV [3]; an FSI simulation in which the glottal airflow and VF vibration were simulated. Steps [1] and [2] were iterated a few times in which Young's moduli of the VF were adjusted accordingly and the eigenmodes were recalculated [33,44]. To repeat [1] and [2], the mesh model of the larynx on which individual components identified was imported into COMSOL to perform medialization simulation and determine the eigenfrequencies at the medialized configuration (i.e., the prestressed state). The first step of VF adduction simulation was attained by using a force ramp that gradually pushed both the implant and suture line toward the midline. The simulation was continued until the implant and suture line reached the equilibrium. In the FEM model, the outer surfaces of the thyroid and cricoid cartilages were fixed, and they had little deformation due to their high stiffness. The arytenoid cartilage and the inner lumen surfaces were free to move. Young's modulus for the cartilages and the suture line was assumed to be E = 2000 kPa, while the implant had a modulus of E = 20,000 kPa representing a stiffer material [23]. The densities for tissue and cartilage were 1040 kg/m³ and 1100 kg/m³, respectively [45]. For all the components, Poisson's ratio was set at ν = 0.3 [46].

Once Young's moduli of the VF body and VF cover were determined from steps 1 and 2, the FEM model was then imported to our in-house code for the three-dimensional (3D) FSI simulation of the vocal fold vibration. This was conducted on Stampede 2 of TACC (allocation provided through the NSF XSEDE program). The 3D FSI simulation was performed at configuration 3, where the two VF sides were respectively medialized by the implant and suture line. The initial flow domain was extracted from the lumen surface of the medialized laryngeal geometry as shown in Fig. 5, and the inlet and outlet were extended to accommodate the boundary conditions. At the inlet, the air pressure was set to be 2 kPa (gauge) to match the experiment, and at the outlet, the pressure was set to zero (gauge) [47]. The air density was 1.0 kg/m³. The mesh used in flow simulation was 156 in the axial direction, 108 in the lateral direction, and 108 in the anterior–posterior direction. This mesh resolution was verified in our previous studies of the healthy phonation [22,24]. The time-step for the FSI simulation was Δt = 10⁻⁴ centi-seconds (cs), which led to a Courant-Friedrichs-Lewy number around 0.8 to ensure numerical stability. Based on the half hydraulic diameter d = 2A/P = 0.66 mm for the current larynx sample (A is the glottal area and P is the perimeter of the cross section inside the glottis, both at the medialized state) and the air velocity at centerline V = 65 m/s, the jet Reynolds number was set to be 220. The overall time required for completing 2 centi-seconds, or around 15 vibration cycles, of 3D FSI simulations was 50 h when using 122 processor cores.

Fig. 5.

Boundary surface for the flow simulation shown as the triangular mesh, where the inlet and outlet were extended from the extracted lumen surface. The 3D laryngeal tissue model is shown here as a semitransparent structure surrounding the flow domain.

The airflow was assumed to be governed by the 3D viscous incompressible Navier–Stokes equation and was solved by using a Cartesian grid-based immersed-boundary method [21,27,48]. For the FSI simulation, the flow solver and the FEM solver were coupled using a partitioned method [49], in which the two solvers were modular and were iterated until convergence was reached at the end of each time-step. Readers can refer to our previous works [33,49] for detailed descriptions of the numerical method and extensive validation of the code.

4 Results and Discussions

4.1 Results of Vocal Fold Medialization.

The function of the medialization process is to reduce the glottal gap by positioning the two sides of the VF closer to the midline in order to promote and sustain flow-induced VF vibration for phonation. The postoperative scan showed that our experiment achieved type 1 thyroplasty medialization using the implant (Fig. 4(b)). As measured from the pre-operative scan in Fig. 4(a), the narrowest gap between the two sides at the rest configuration was 1.63 mm. After implant and suture medialization, this gap was reduced effectively by 1.33 mm, which could be measured from the postoperative scan.

The corresponding simulation result showed that such medialization was captured by the FEM model (Figs. 4(d)–4(f)). The initial glottis from the reconstructed larynx at the rest configuration (Fig. 4(d)), as well as the medialized glottis from the FEM simulation (Fig. 4(e)), closely resembled their respective shapes from the scan as seen from the axial view in Figs. 4(a) and 4(b). To achieve the medialization in the simulation, the total forces of 0.6 N and 0.85 N were used to displace the implant and the suture, respectively, by approximately 2 mm toward the midplane. The forces maintained the two sides at the equilibrium state, at which the medial surface (the outer surface of the VF cover) was displaced by 0.43 mm on the implant side and by 0.82 mm on the suture side. These results agreed with the measurements from the postoperative scan. The higher displacement on the suture side was attributed to localized tissue displacement surrounding the suture line. The asymmetric adduction of the two sides was expected since two different methods of medialization were employed in the current study.

The overall extent of medialization could be also measured by the amount of area reduction at the glottal section. From both the MRI scans and simulation results, the glottal areas were reduced from 11.6 mm² to 5.5 mm² and 6 mm², respectively, by the medialization. A unilateral medialization by suturing alone (i.e., the UVFP configuration without implant insertion) led to a greater glottal area of 8.4 mm². The degree of area reduction would have significant effects on the VF vibration as shown later.

Some differences between the experiment and simulation could be observed from the coronal view (Figs. 4(c) and 4(f)), especially for the suture side. Note that in Fig. 4(c), the tightened suture line created significant displacement of the false vocal fold that is above the true vocal fold, which led to narrowing of the supraglottal region. In the simulation, the suture line was not as soft as in the experiment and thus did not curve as much to cause deformation of the false vocal fold. Such differences were deemed acceptable since the medialization of the true vocal fold was reasonably captured by the simulation. In addition, the false vocal fold deformation of the suture side did not significantly affect the VF validation for the implant side.

One specific issue was caused by VF tissue separation from the thyroid cartilage when the VF was being pushed toward the midline. Such tissue separation was evident from the postoperative scan (Figs. 4(b) and 4(c)). To incorporate the presence of the separation, the gap between the thyroid cartilage and the VF body was created as described in Sec. 3.1. From the simulation results shown in Figs. 4(e) and 4(f), the enlargement of these gaps during medialization had significant effects on the VF displacement and thus was necessary to include in the modeling process.

4.2 Eigenmode Analysis and Vocal Fold Stiffness.

Eigenfrequencies from the eigenmode analysis were used to adjust the tissue stiffness properties, or Young's moduli of the vocal fold, of the sample, and also to study asymmetries in the vibration mode between the two sides of VF. The vibration frequency of the current sample at the medialized configuration was approximately 820 Hz according to the high-speed video. This frequency is consistent with the phonation frequency obtained in a previous experiment also using the rabbit larynx [39]. Although the eigenfrequency of the rest state is related to Young's modulus by f₀ ∝ (1/ $l^2$)[ $\sqrt{E/\rho }$], where l is the VF length, E is the material stiffness, and $\rho$ is the density [50,51], the presence of the internal stresses due to medialization may change the relationship by stiffening the tissue effectively [52,53]. After a few iterations of medialization simulation and eigenmode analysis, Young's moduli of the VF cover and VF body were adjusted so that eigenmode analysis of the medialized configuration produced frequencies of both sides that were close to the experimentally observed frequency. The final results are listed in Table S1 available in the Supplemental Materials on the ASME Digital Collection for clarity. The corresponding eigenmodes of the two sides are shown in Fig. S2 available in the Supplemental Materials. Although there were multiple modes from the eigenmode computation, only the mode that corresponded to the opening and closing of the glottis was chosen to guide the analysis.

This study resulted in Young's modulus for the VF cover E_c = 60 kPa and for the VF body E_b = 150 kPa, which led to an eigenfrequency of 768 Hz on the implanted side and 770 Hz on the suture side. Previously, experiments with the rabbit VF by Latifi et al. [44] showed that Young's modulus could be as high as 174 kPa for the VF cover. Oren et al. [54] explained tissue stiffness value as a function of strain and several other studies have reported higher E [55–59] when tested for high strain values. In comparison, Young's moduli adopted in the current work were in the ballpark of available data.

As a reference, eigenfrequencies of the rest configuration were also computed and listed in Table S1 available in the Supplemental Materials. The two sides corresponding to the implant side and suture side had an eigenfrequency of 600 Hz and 575 Hz, respectively, which were much lower compared to the frequencies at the medialized state. This result shows that medialization caused significant internal stresses, leading to tissue stiffening and increase of the vibratory frequency. After medialization, the Von-Mises stress was approximately 21 kPa on the implant side and 30 kPa on the suture side (measured at the midpoint of the VF length), indicating magnitude of stresses in the tissue due to medialization. At the medialized state, the eigenfrequencies of the two sides became much closer to each other. This frequency symmetry would be beneficial in general for restoration of VF vibration from the UVFP condition and thus could be a factor for consideration in addition to the extent of glottal area reduction.

4.3 Results From the Three Dimensional Fluid-Structure Interaction Simulation.

Two cases were considered for 3D FSI simulation: (1) the medialized condition (configuration 3), where both the implant and suture medializations were present; and, (2) the UVFP condition (configuration 2) with only the suture medialization present, which served as a reference case for comparison. In both cases, an inlet gauge pressure of 2 kPa was used to initiate flow-induced vibration.

4.3.1 The Unilateral Vocal Fold Paralysis Configuration.

In this disordered condition, the onset of phonation becomes difficult even though the healthy side can be medialized. This is because the glottal gap is wide, and the subglottal pressure may be insufficient to induce VF vibration. This situation was reflected from the phonation experiment as well as the FSI simulation of this configuration. As shown in Fig. 6(a), the simulated vibration amplitude of both rest side and suture side was small and less than 0.5 mm. An FFT analysis showed that the vibration frequency was 733 Hz for the suture side and 595 Hz for the rest side, which generally matched the respective eigenfrequencies of that side.

Fig. 6.

FSI simulation results for the UVFP configuration. (a) Displacement of the two VF sides measured around midpoint of the glottis. (b) The flow domain showing the coronal plane (horizontal slice in the figure) and the midsagittal plane (vertical slice) for visualization; also included is the orientation of the glottis. (c), (d) Velocity magnitude at the closing phase (c) and opening phase (d) in the coronal plane. (e), (f) Velocity magnitude at the closing phase (e) and opening phase (f) in the midsagittal plane. (g), (h) Pressure distribution in the coronal plane for the closing (g) and opening (h) phases.

Since the amplitude of vibration was small and the glottal gap was relatively constant, a consistent jet of airflow was created from the glottis. At the narrowest cross section in the glottis, the flow velocity was about 57 m/s (Figs. 6(c) and 6(d)). This jet became asymmetric in the coronal plane and skewed toward the suture side (Figs. 6(c) and 6(d)). Since the VF was inclined at an angle of 23 degrees from the axial direction (Fig. 6(b)), the jet was guided toward the anterior side of the vocal fold and impinged on the supraglottal region's anterior end (Figs. 6(e) and 6(f)). Like the flow velocity, the pressure distribution along the axial direction also remained largely steady and did not change much between opening and closing phases (Figs. 6(g) and 6(h)).

4.3.2 Results From the Medialized Configuration.

In the UVFP configuration and the rest configuration, no clear VF vibration was observed in the experiment. With the suture and implant medialization, significant vibration was observed from the HSV, although the vibration was dominated by the implant side and the suture side had little vibration as seen from the kymograph in Fig. 1(c).

The corresponding FSI simulation achieved similar vibratory characteristics. From Fig. 7(a), the implant side had an amplitude about twice as high as the amplitude of the suture side. The vibration frequency in the simulation was 733 Hz and close to the frequency of 820 Hz that was measured from the HSV. Furthermore, the amplitude of the implant side was 0.16 mm, or 2.1% of the length of the glottis L (note that the HSV did not have a length scale; thus, a relative measurement was used here). In the HSV, the amplitude of the implant side was 2.6% of L. One difference between the simulation and experimental results was that the suture side in the experiment had less vibration than in the simulation. This was likely because in the experiment, the suture line created a significant tissue tear around the line (Figs. 4(b) and 4(c)). This torn region was not incorporated in the model but may have limited the amplitude of that side since there was less tissue mass involved in the vibration.

Fig. 7.

FSI simulation results for the medialized configuration. (a) Displacement of the two VF sides measured around midpoint of the glottis. (b) The flow domain showing the coronal plane (horizontal slice in the figure) and the midsagittal plane (vertical slice) for visualization; also included is the orientation of the glottis. (c), (d) Velocity magnitude at the closing phase (c) and opening phase (d) in the coronal plane. (e), (f) Velocity magnitude at the closing phase (e) and opening phase (f) in the midsagittal plane. (g), (h) Pressure distribution in the coronal plane for the closing (g) and opening (h) phases.

Overall, the amplitude, frequency, and left-right asymmetry of the simulated vibratory characteristic agreed with those from the phonation experiment. Therefore, the current computational model of type 1 thyroplasty was validated by the experiment in our study. Note that this is only limited validation using these said criteria. More extensive validation using additional criteria (e.g., flow characteristics) will be pursued in the future through coordinated experimental and computational studies.

We point out in human patients that the healthy side of the VF normally has a greater vibration amplitude than the implant side [60,61], which is opposite to the current rabbit study. We attribute this difference to the way that the “healthy side” was mimicked in the current study. Since a suture line was used to pull the VF toward the midline, the thin line had caused large displacements around the line and thus localized glottal narrowing (see Fig. 4(b)) as opposed to overall narrowing of the glottis. Furthermore, the localized displacements may have created significantly uneven tension in the tissue that did not necessarily promote the vibration. As a result, the suture side had a much lower amplitude as compared to the implant side in our study. The implication of this issue will be discussed further in Sec. 5.

Flow visualization of the medialized configuration using the simulation data showed certain characteristics as observed in healthy phonation that was studied previously in rabbits [22]. As seen in Fig. 8(a), the flowrate was pulsatile and overall periodic, although it did not reduce to zero at the closing phase due to incomplete closure of the VF. In the current configuration, the mean airflow rate was 235 cm³/s, while for the UVFP condition, it was 330 cm³/s. The lack of significant vibration amplitude in the UVFP configuration contributed to less variations in the flowrate between phonatory cycles as compared to the medialized configuration. From Figs. 7(c) and 7(d), the jet was mostly symmetric as viewed in the coronal plane despite the fact that the VF vibration was asymmetric. This improvement from the UVFP configuration was a result of medialization on both sides of the VF (so that the overall geometry was more symmetric in the medialized state). The presence of the false vocal fold in the supraglottal region also helped maintain the symmetry of the jet, which was beneficial for phonation [27,62].

Fig. 8.

Comparison between UVFP and medialized configurations for the flowrate (a),pressure (b), and flow velocity (c). The pressure and flow velocity were taken around midpoint in the glottis shown in (d).

Comparing temporal characteristics of the flow field with that of the UVFP, the jet velocity had more variations between the VF opening and closing phases for the medialized configuration (Figs. 7(c) and 7(d)). Like in UVFP, the jet in the medialized configuration was also directed toward the anterior side (Figs. 7(e) and 7(f)), a feature that was also observed in the healthy phonation of rabbits [22].

Because of a narrower glottal gap, the pressure in the glottis became negative and was significantly lower than that in the UVFP condition (Figs. 7(g) and 7(h)), especially when the VF was closing (Fig. 7(g)). This comparison could be further seen from the pressure oscillations in the glottis (Fig. 8(b)). Not only did the pressure oscillations show a greater magnitude in the medialized configuration, but also time average became negative. Such temporal characteristics were a direct result of VF vibration, which in turn helped to sustain flow-induced vibration. In Figs. 8(b) and 8(c), both the velocity and pressure displayed nearly periodical oscillations, corresponding to improved vibration of the VF in the UVFP condition.

5 Further Discussions

This study has a few important limitations. The experiment was carried out ex vivo because of difficulties associated with using the medialization approach described during in vivo surgery. Note that previously we had performed an in vivo study phonation and high-speed imaging using a rabbit model [22,33]. However, the current study involved different adduction methods for the two sides of the VF; the in vivo approach thus would be significantly more difficult to carry out. Thus, an ex vivo approach was adopted. Furthermore, the suture method was used here to mimic the VF adduction of the healthy side, which had created unnatural local stress and strain concentrations. As a result, that side vibrated at a lower amplitude to the implanted side, which differs from observations in human patients. Ideally, the healthy VF should be more uniformly adducted along the length, leading to a better glottal closure [63]. Lastly, we did not perform an optimization study to test the best insertion location or shape design parameters for the implant, as such a study would require repeated FSI simulations to assess the effect of the implant on the VF vibration (albeit an optimization study of the implant location on the extent of medialization was performed previously by our group [35]). Such optimization will be deferred to a future study.

Despite these limitations, the current study still represents an important step toward integrating animal experimentation with computer simulation to explore the development of a computational modeling based, individual-specific, surgical planning tool for type 1 thyroplasty. In this study, we have developed the key steps of the procedure that included pre-operative scan, construction of the computational model, estimate of the tissue stiffness properties, postoperative scan, phonation experiment, and validation of the computational model. Although the surgical adduction of the healthy VF side was not natural, the current study successfully demonstrated the capability of modeling the effect of the implant on the VF vibration. We anticipate that a similar procedure could be developed for a physical experiment that mimics the type 1 thyroplasty more closely. Furthermore, a follow-up optimization study would be straightforward to determine the best location and design of the implant, despite the high computational cost that could be involved.

6 Summary

An integrated experimental and computational study of type 1 thyroplasty was carried out using an ex vivo rabbit larynx. The experiments included various vocal fold configurations that were created surgically to mimic the unilateral vocal fold paralysis as well as the medialized configuration using a silastic implant. Additionally, both pre- and postoperative MRI scans of the larynx were performed, the flow was introduced to induce phonation, and high-speed imaging was conducted to film VF vibration. On the computational side, an FEM model was built based on the pre-operative scan, and medialization of both sides were simulated to achieve the adducted glottis. Young's moduli of the vocal fold were estimated by performing the eigenmode analysis and adjusting the eigenfrequencies. Finally, a 3D FSI simulation was performed to simulate the vibration, and the vibratory characteristics agreed with the phonation experiment, thus validating the computational model. Furthermore, the medialized vocal fold after thyroplasty showed favorable characteristics in vibration and flow field when compared to the UVFP condition. These results demonstrate the potential of using the current approach for surgical planning of implant design and placement in type 1 thyroplasty.

Data Availability Statement

The authors attest that all data for this study are included in the paper.

Supplementary Material

Supplementary Material

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