Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Summary

Vocal fold polyps can disrupt vocal fold dynamics and thus can have devastating consequences on a patient's ability to communicate. Three-dimensional flow separation induced by a wall-mounted model polyp and its impact on the wall pressure loading are examined using particle image velocimetry, skin friction line visualization, and wall pressure measurements.

Abstract

The fluid-structure energy exchange process for normal speech has been studied extensively, but it is not well understood for pathological conditions. Polyps and nodules, which are geometric abnormalities that form on the medial surface of the vocal folds, can disrupt vocal fold dynamics and thus can have devastating consequences on a patient's ability to communicate. Our laboratory has reported particle image velocimetry (PIV) measurements, within an investigation of a model polyp located on the medial surface of an in vitro driven vocal fold model, which show that such a geometric abnormality considerably disrupts the glottal jet behavior. This flow field adjustment is a likely reason for the severe degradation of the vocal quality in patients with polyps. A more complete understanding of the formation and propagation of vortical structures from a geometric protuberance, such as a vocal fold polyp, and the resulting influence on the aerodynamic loadings that drive the vocal fold dynamics, is necessary for advancing the treatment of this pathological condition. The present investigation concerns the three-dimensional flow separation induced by a wall-mounted prolate hemispheroid with a 2:1 aspect ratio in cross flow, i.e. a model vocal fold polyp, using an oil-film visualization technique. Unsteady, three-dimensional flow separation and its impact of the wall pressure loading are examined using skin friction line visualization and wall pressure measurements.

Introduction

The vocal folds are two bands of tissue that stretch across the vocal airway. Voiced speech is produced when a critical lung pressure is achieved, forcing air through adducted vocal folds. The vocal folds are composed of many layers of tissue and are often represented by a simplified two-layer body-cover system¹. The extracellular matrix, which makes up the majority of the cover layer, is composed of collagen and elastin fibers, providing nonlinear stress-strain characteristics, which are important to the proper motion of the vocal folds^1,2. Aerodynamic forces impart energy to the tissue of the vocal folds and excite self-sustained oscillations³. As the vocal folds oscillate, the opening between them, referred to as the glottis, forms a temporally-varying orifice that transitions from a convergent to a uniform and then to a divergent passage before closing and repeating the cycle^4,6. Frequencies of vibration for normal speech typically span 100-220 Hz in males and females respectively, creating a pulsatile flow field that passes through the glottis⁷. The fluid-structure energy exchange process for normal speech has been studied extensively^8-12; however, the disruption of this process for some pathologies is not well understood. Pathological conditions of the vocal folds can result in dramatic changes in their dynamics and affect the ability to generate voiced speech.

Polyps and nodules are geometric abnormalities that form on the medial surface of the vocal folds. These abnormalities can affect a patient's ability to communicate¹³. Nevertheless, only recently has the disruption of the flow field due to a geometric protuberance such as a polyp been considered¹⁴. That study showed that the "normal" fluid-structure energy-exchange process of speech was drastically altered, and that the modification of the flow field was the most likely reason for the severe degradation of vocal quality in patients with polyps and nodules. No comprehensive understanding of the flow structures produced by three-dimensional flow separation from a polyp in pulsatile flow has been established. The generation and propagation of vortical structures from a polyp, and their subsequent impact on the aerodynamic loadings that drive vocal fold dynamics is a necessary critical component to advance surgical remediation of polyps in patients.

While flow separation from a wall mounted hemispheroid in steady flow has been investigated^15-23, surprisingly, there is little information regarding unsteady three-dimensional flow separation from a hemispheroid on a wall subject to pulsatile or unsteady flow conditions as are found in speech. The seminal work of Acarlar and Smith¹⁵ provided an analysis of the three-dimensional coherent structures generated by steady flow over a wall mounted hemispheroid within a laminar boundary layer. Acarlar and Smith identified two types of vortical structures. A standing horseshoe vortex was formed upstream of the hemispheroid protuberance and extended downstream of the protuberance on either side. Additionally, hairpin vortices were shed periodically from the wall mounted hemispheroid into the wake. The complex motion and progression of the hairpin vortices was investigated and described in detail.

Flow over a smoothly contoured axisymmetric hill has been previously studied in which both surface static pressure measurements and surface oil visualization were acquired on and downstream of the bump within a turbulent shear flow. Oil-film techniques enable the visualization of skin friction lines, high and low velocity regions, and separation and attachment points within a surface flow, and are useful to investigate the wake of a wall-mounted object. For this technique, the surface of interest is coated with a thin film of an oil-base and fine powder pigment (i.e. lampblack, graphite powder, or titanium dioxide) mixture. At the desired flow conditions, frictional forces cause the oil to move along the surface causing the pigment powder to be deposited in streaks. Critical or singularity points, locations where the shear stress is zero or two or more components of the mean velocity are zero, can be classified from the resulting skin friction line pattern as saddle points or nodal points^24-26.

For the hill geometry, no singularity caused by separation was found upstream; this was attributed to the smoothly ascending contour of the bump, which did not generate the adverse pressure gradient that occurs with a hemispheroid protuberance. Consequently, the flow was found to accelerate until the pinnacle of the bump after which, unsteady saddle-focus separation points developed shortly past the bump centerline, as would be expected from the formation of a hairpin vortex^27,28. In a study using similar experimental techniques with a different wall-mounted geometry, oil-film visualization around a surface-mounted cube in steady flow performed by Martinuzzi and Tropea²⁹ displayed two clear skin friction lines upstream of the object. The first skin friction line corresponded to the primary separation line caused by the adverse pressure gradient and the second skin friction line marked the time-averaged location of the horseshoe vortex. Surface pressure measurements performed upstream of the object showed a local minimum along the horseshoe vortex line and a local pressure maximum between the primary separation and horseshoe vortex lines. Similar upstream separation lines are formed with other surface-mounted geometries including a circular cylinder, pyramid, and cone^29-31. Surface visualization downstream of wall-mounted objects typically displays two foci caused by the recirculation region behind the object³⁰. Two vortices are generated at the foci positions and correspond to the "arch-type" or hairpin vortex seen in the wake of a wall-mounted hemispheroid³².

Particle image velocimetry (PIV) has been previously used to study the flow downstream of synthetic vocal fold models^33-35. PIV is a noninvasive visualization technique which images flow tracer particle movement within a plane at to capture spatio-temporal fluid dynamics^36. Three-dimensional coherent structures which form downstream of the oscillating vocal folds have been studied by Neubauer et al.³⁷; vortex generation and convection and jet flapping was observed. Recently, Krebs et al.³⁸ studied the three-dimensionality of the glottal jet using stereoscopic PIV and the results demonstrate glottal jet axis switching. Erath and Plesniak¹⁴ investigated the effect of a model vocal fold polyp on the medial surface of a 7.5 times scaled-up dynamically driven vocal fold model. A recirculation region was formed downstream of the polyp and the jet dynamics were affected throughout the phonatory cycle. The previous studies, barring the driven vocal fold polyp study by Erath and Plesniak¹⁴, have not explored the fluid dynamics induced by a medial vocal fold polyp or nodule.

It is important to understand the fluid dynamic effect of the model polyp within steady and pulsatile flow fields before including the additional complexity of the vocal fold moving walls, induced pressure gradients, confined geometric volume and other intricacies. The current work focuses on the signature of the flow structures on the downstream wall under both steady and unsteady flow conditions. The interactions between the vortical structures that are shed from a protrusion and the downstream wall is of great interest for the investigation of vocal fold polyps as well as other biological considerations, as these interactions elicit a biological response.

Protocol

In this work, a wall-mounted prolate hemispheroid, i.e. a model vocal fold polyp, is positioned on the test section floor of a suction type wind tunnel with a 5:1 contraction ratio. Unsteady, three-dimensional flow separation and its effect on the wall pressure loading are investigated using oil-flow visualization, wall pressure measurements, and particle image velocimetry. The unsteady pressure measurements are acquired using a sixteen channel scanning pressure transducer with piezoresistive pressure sensors. The pressure sensors have a frequency response of 670 Hz. Static pressure taps formed from stainless steel tubulations are flush-mounted upstream and downstream of the model vocal fold polyp to facilitate the surface pressure measurements and short-plumbed to the scanning pressure device. Oil-flow visualization and surface pressure measurements cannot be acquired simultaneously because oil would flow into the pressure taps causing fouling.

The following section provides the protocol for setting up and acquiring oil-film visualization and surface pressure measurements around a wall mounted prolate hemispheroid. Although phase-averaged and time resolved particle image velocimetry measurements are being acquired, the PIV acquisition is not included in this protocol. The authors suggest the references by Raffel et al.³⁶ and Adrian and Westerweel³⁹ for an in depth understanding of PIV experimental setup, data acquisition, and data processing.

1. Generate Protuberance (i.e. Model Polyp)

1. Build a three-dimensional computer-aided design (CAD) model with the desired geometry. Generate the model vocal fold polyp as a prolate hemispheroid measuring 5.08 cm long, 2.54 cm wide, and 1.27 cm tall. Mount a 2.54 cm square base that is 0.64 cm thick to the bottom of the model vocal fold polyp. This base will be used to anchor the model to the test section floor.
2. Export the 3D CAD model as a stereolithography (STL) file. The STL file format generates the model surface as a series of triangles. Choose an adequate resolution to ensure a smooth surface on the model polyp. A resolution of at least 600 dots/in is recommended.
3. Upload the STL file into the appropriate software and print the STL file using a high resolution three-dimensional printer or rapid prototyper with a build layer resolution of at least 20 μm.
4. The wind tunnel test section is approximately 30.48 cm x 30.48 cm x 121.92 cm with a removable bottom plate as shown in Figure 1. Mill a 2.54 cm square hole approximately 0.85 cm deep into the wind tunnel test section floor removable plate to mount the model vocal fold polyp for testing. The hole should be located in the center of the test section width and be located at the desired downstream location for testing.

2. Oil-flow Visualization Preparation

1. In order to prepare the test section, cover the test section surface inside of the wind tunnel with white adhesive paper. Carefully place and smooth the adhesive paper to ensure that the test section floor has no bumps due to air bubbles or creases in the adhesive paper. Cut a hole in the adhesive paper above the square hole in the test section floor for the model polyp anchor to attach to the test section wall.
2. Insert the protuberance (model vocal fold polyp) into the anchor position to prepare for testing. See Figure 1.
3. Mount a high resolution camera above the wind tunnel test section. Focus the camera for the chosen field of view including the model polyp and surrounding test section area. Set the camera acquisition parameters for testing. A video setting should be used to capture the transient portion of the oil-flow visualization or if unsteady or pulsatile flows are of interest.
4. Prepare the flow-visualization oil mixture by combining baby oil, copy toner powder, and kerosene in a 7:1:2 ratio by volume. For example: combine 35 ml baby oil, 5 ml copy toner powder, and 10 ml kerosene. Mix the baby oil and toner powder together in a container and stir until the toner is completely dissolved. Then add the kerosene and mix well.
5. Transfer the mixture to a spray bottle for easy application to the test section surface.

3. Oil-flow Visualization Measurements

1. Clean and dry the test section surface before each application of the oil mixture.
2. Use the spray bottle filled with the oil mixture to spray a thin, even layer of fluid over the section of interest. A thin, even oil mixture layer is important for producing proper oil-film visualization images.
3. Initiate the image or video acquisition on the camera. Begin the camera acquisition before the wind tunnel is powered on in order to capture the initial transient oil mixture motion.
4. Set the suction wind tunnel to the desired velocity. The oil mixture will begin to flow along the test section surface.
5. Once the oil mixture stops flowing and has reached a steady state (i.e. the patterns are stationary), or when the desired time has elapsed, stop the camera recording and power down the wind tunnel.
   Note: Video 1 displays the oil-mixture flowing until a steady state is reached and the skin friction pattern becomes stationary. In the video the flow is moving from left to right.

4. Surface Pressure Measurement Preparation

1. Prepare the test section floor surface (removable plate) by drilling holes for mounting stainless steel tubulations (0.16 cm outer diameter and 2.54 cm long) into the test section floor to build static pressure taps. Starting at the midline of the anchor position of the prolate hemispheroid, drill the holes on a grid that spans 8.89 cm in the spanwise direction and 22.86 cm downstream with 1.27 cm spanwise grid spacing and 2.54 cm downstream grid spacing (see Figure 1). The stainless steel tubulations have a bulge on one end for attaching flexible tubing and are straight on the other end for mounting.
   Note: The static pressure taps can be positioned at closer intervals for a finer grid of pressure acquisition locations.
2. Mount the tubulations surrounding the anchor position of the wall mounted prolate hemispheroid (i.e. model vocal fold polyp) in the desired configuration on the test section floor to prepare for testing. The tubulations should be mounted flush with the test section floor.
3. Attach pieces of short flexible tubing (6.35 cm length, 0.159 cm inner diameter, 0.475 cm outer diameter clear polyvinyl chloride tubing) from the mounted stainless steel tubulations to the scanning pressure transducer measurement ports. The scanning pressure transducer has sixteen pressure ports.

5. Surface Pressure Measurement Acquisition

1. Connect the scanning pressure transducer to a computer and configure the acquisition parameters using the scanning pressure transducer software. Set the acquisition software to acquire data at 500 Hz for the desired duration of data acquisition.
   Note: Data was acquired at the maximum sampling rate of the scanning pressure transducer, 500 Hz, due to the small pressure variations at low oscillation frequencies.
2. Set the suction wind tunnel to the desired velocity.
3. Begin pressure measurement acquisition. The pressure measurements may be acquired simultaneously with any desired flow diagnostic technique (e.g. PIV, laser Doppler anemometry, hot wire anamometry, etc.)

Results

Previous work using a 7.5 times scaled-up dynamically driven vocal fold model has demonstrated that the presence of a geometric protuberance, model vocal fold polyp, disrupts the normal dynamics of the glottal jet throughout the phonatory cycle. Representative results from the previous driven vocal fold model study are displayed in Figure 2 and Video 2. The video demonstrates the motion of the driven vocal folds as they change from a convergent to a divergent geometry. The vocal fold mod...

Discussion

Understanding the formation and propagation of vortical structures from a geometric protuberance and their subsequent effect on the aerodynamic loadings that drive vocal fold dynamics, is necessary to provide insight and models in order to advance the treatment of vocal fold polyps and nodules. The variations in aerodynamic loadings caused by the model polyp in this experiment are expected to contribute to irregular vocal fold dynamics observed in patients with polyps^13,41. Future work includes investigat...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Rapid Prototyper	Objet	Objet24	Tray Size (X xY x Z): 240 x 200 x 150 mm Build layer thickness =  28 µm  Accuracy = 0.1 mm Build Resolution: X-axis: 600 dpi, Y-axis: 600 dpi, Z-axis: 900 dpi
Rapid Prototyper Model Material	Objet	VeroWhite Plus Fullcure 835
Rapid Prototyper Support Material	Objet	FullCure 705 Support
Copy Toner	Xerox
Kerosene	Sunnyside
Baby Oil	Johnson's
Adhesive Paper	Con-Tact Brand		White adhesive covering
Tygon Tubing	Tygon	PVC Tubing	1/16 in ID, 3/16 in OD
Pressure Scanner (16 channel)	Scanivalve	DSA3217	Used for gas pressure measurements Pressure range = ±5 in H2O Full scale accuracy = ±0.3% full scale accuracy.  Maximum scan rate = 500 Hz/channel
Stainless Steel Tubulations	Scanivalve	TUBN-063-1.0	0.063 in Diameter and 1 in Length