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J Appl Physiol 97: 648-654, 2004. First published March 26, 2004; doi:10.1152/japplphysiol.01250.2003
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Finite element analysis of active Eustachian tube function

Samir N. Ghadiali,1,2,3 Julie Banks,3 and J. Douglas Swarts2,3

1Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem 18015; 2Department of Otolaryngology, University of Pittsburgh School of Medicine, and 3Department of Pediatric Otolaryngology, Children's Hospital of Pittsburgh, Pittsburgh, Pennsylvania 15213

Submitted 21 November 2003 ; accepted in final form 22 March 2004


   ABSTRACT
TOP
 ABSTRACT
METHODS AND MATERIALS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
The inability to open the collapsible Eustachian tube (ET) has been related to the development of chronic otitis media. Although ET dysfunction may be due to anatomic and/or mechanical abnormalities, the precise mechanisms by which these structural properties alter ET opening phenomena have not been investigated. Previous investigations could only speculate on how these structural properties influence the tissue deformation processes responsible for ET opening. We have, therefore, developed a computational technique that can quantify these structure-function relationships. Cross-sectional histological images were obtained from eight normal adult human subjects, who had no history of middle ear disease. A midcartilaginous image from each subject was used to create two-dimensional finite element models of the soft tissue structures of the ET. ET opening phenomena were simulated by applying muscle forces on soft tissue surfaces in the appropriate direction and were quantified by calculating the resistance to flow (Rv) in the opened lumen. A sensitivity analysis was conducted to determine the relative importance of muscle forces and soft-tissue elastic properties. Muscle contraction resulted in a medial-superior rotation of the medial lamina, stretching deformation in the Ostmann's fatty tissue, and lumen dilation. Variability in baseline Rv values correlated with tissue size, whereas the functional relationship between Rv and a given mechanical parameter was consistent in all subjects. ET opening was found to be highly sensitive to the applied muscle forces and relatively insensitive to cartilage elastic properties. These computational models have, therefore, identified how different tissue elements alter ET opening phenomena, which elements should be targeted for treatment, and the optimal mechanical properties of these tissue constructs.

Young's modulus; biomechanics; elasticity; respiratory airway; compliance; fluid-structure interactions; mathematical modeling

THE DEVELOPMENT OF PERSISTENT OTITIS MEDIA (OM) has long been associated with an inability to open the collapsible Eustachian tube (ET), i.e., ET dysfunction. The ET, which connects the nasopharynx (NP) with the middle ear (ME), has three physiological functions: 1) protection of the ME from opportunistic pathogens of the NP, 2) clearance of ME fluids, and 3) ventilation of the ME to ambient pressures (4). Although the ET normally exists in a "closed" configuration to protect the ME, the clearance and ventilation functions require periodic openings of the ET. In healthy individuals, these openings occur during swallowing, where muscle contraction deforms the surrounding soft tissue resulting in an increase in the cross-sectional lumen area and a reduction in the resistance to airflow (3). In the absence of these openings, the balance between gas adsorption by the ME mucosa and resupply via the ET is disrupted (10). The inability to ventilate the ME via the ET results in negative ME pressures (relative to atmospheric), fluid transudation into the ME, and infection/inflammation of the ME mucosa, i.e., OM. Although an inability to open the ET is the primary etiology of OM (4), standard treatment therapies (e.g., typmanostomy tubes and antibiotics) do not address the underlying mechanical and/or anatomic abnormalities responsible for ET dysfunction. The development of novel treatment therapies for persistent OM will therefore require an understanding of how these structural properties influence ET opening phenomena.

The anatomic structure of the ET is highly complex in that the lumen is surrounded by several muscular, cartilaginous, and fat tissue elements (see Fig. 1) and is bounded by fluid-coated mucosal tissue. Several investigators have demonstrated that paralysis of the tensor veli palatini muscle (TVPM), the primary muscle associated with ET function, results in negative ME pressures (7), fluid accumulation in the ME (1), and a significant decrease in the compliance or elastic properties of the ET (14). Although it is well established that contraction of the TVPM is required for normal ET function, several other mechanical properties may also play a role in opening the collapsed ET. For example, previous investigations (15, 29) have suggested that the elastic and viscoelastic properties of the cartilage and/or fat tissue may be important determinants of ET function. Specifically, hypercompliant tissue properties may impair the active opening of the ET by diminishing the forces transmitted to the lumen, whereas very large muscle forces may be required to open rigid or inelastic ETs. The opening of the ET may also depend on the surface tension, adhesive, and inflammatory properties of the ET mucosa (5, 11, 13). Although these tissue mechanical properties have been implicated in ET dysfunction, the relative importance of the various tissue elements as well as a quantitative understanding of how variations in mechanical properties affect opening phenomena have not been investigated.



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  		Fig. 1. Schematic representation of the Eustachian tube's (ET) global structure and surrounding soft tissue elements. OFT, Ostmann's fat tissue; LVPM, levator veli palatini muscle; TVPM, tensor veli palatini muscle.

 
In addition to the mechanical environment, several investigators (20, 24, 30) have utilized histological imaging techniques to identify the morphometric relationships that may contribute to ET dysfunction. The volume of cartilage and/or muscle tissue, curvature orientation of the lumen, height-to-width ratio of the ET cartilage, and insertion angle of the TVPM have all been suggested to be important determinants of ET function. Several three-dimensional (3D) anatomic features, including variations in muscle insertion angles and cartilage size along the length of the ET, may also influence ET function (25, 27). Although these investigations have identified the anatomic properties that may contribute to ET dysfunction, a major limitation of these observational studies is that they can only speculate on how the measured morphometric relationships influence the tissue deformation processes responsible for active ET opening. As a result, these studies cannot be used to obtain a detailed understanding of ET opening phenomena or to quantify the relative importance of the various anatomic properties.

Although insufficient ET opening during swallowing may be due to both mechanical and/or anatomic abnormalities, previous investigations of ET function were performed independently in that the interaction between the ET's mechanical and anatomic environment was not considered. As a result, the precise mechanisms by which these structural properties alter the function of the ET have not been investigated. The goal of the present study was to develop a two-dimensional (2D) finite element mathematical model of active ET opening phenomena, which can be used to investigate these structure-function relationships. Although the 3D structure may influence ET function, this study focuses on developing 2D modeling techniques that capture essential anatomic and mechanical features in a single cross section. These initial models are based on the mechanical and anatomic properties measured in normal adult subjects. Tissue deformation and lumen opening during swallowing are simulated by applying muscle forces on the appropriate soft tissue elements, and a flow resistance parameter is calculated to quantify the degree of lumen opening. A parameter variation analysis is conducted to determine the relative importance of various tissue mechanical properties, including muscle force magnitude and soft-tissue elastic properties. As a result, these models elucidate how the mechanical properties influence ET opening phenomena and identify which tissue elements are the most important determinates of ET function. The development of these computational models also elucidates how modifications in the anatomic and mechanical structure of the ET influence its function and, therefore, may be useful in the development of novel structure-based treatment therapies for OM.


   METHODS AND MATERIALS
TOP
 ABSTRACT
 METHODS AND MATERIALS
RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Protocol.   Data were obtained from eight adult human temporal bones, which included the ET cartilage, TVPM, levator veli palatini muscle (LVPM), and Ostmann's fatty tissue (OFT). Subjects had no documented history of ME disease or ET dysfunction, an age range of 39 ± 23 yr with no individual <18 yr in age, and equal numbers of female and male subjects. All specimens were processed histologically according to the technique developed by Sando et al. (23). Briefly, each specimen was fixed in 10% formalin, decalcified in 5% trichloroacetic acid, dehydrated in graded concentrations of ethanol, and embedded in celloidin. Serial 30-µm histology sections were cut vertically in the plane perpendicular to the long axis of the ET. Every 20th section was stained with hematoxylin and eosin for light microscopy. One cross-sectional image was selected from each subject for image analysis and construction of the 2D finite element models. The selection of this cross-sectional image was based on morphological features of the TVPM. The TVPM is a flat, ribbon-like muscle that attaches to the cranial base and lateral portions of the cartilage and OFT, descends inferiorly, and ends in a tendon that winds around the pterygoid hamulus (16) (see Fig. 1). In the proximal region of the ET (i.e., near the NP), the TVPM is primarily attached to the cranial base (not shown in Fig. 1). In contrast, the TVPM is only attached to the cartilage and OFT in distal regions. For this study, the most distal cross section in which the TVPM is not attached to the cranial base and is attached to the cartilage and OFT was selected. The definition of this midcartilaginous section is consistent with the observations of Takahashi and colleagues (28) with respect to the location of ET dysfunction. This definition also ensures that the selected cross sections are comparable between all subjects. All histological specimens were generously provided by the Elizabeth McCullough Knowles Otopathology Laboratory at the University of Pittsburgh.

Histological image processing.   The selected cross-sectional image from each subject was visualized with a Diaphot inverted microscope (Nikon Instruments) with a charge-coupled device video camera attachment (Carl Ziess). Digital images were acquired at an average resolution of 0.039 ± 0.011 mm/pixel with the Metamorph image analysis package (Universal Imaging). High-quality contours of the cartilage and OFT as well as the medial lumen surface were obtained as shown in Fig. 2A. These contours were generated in a piecewise fashion such that important surface locations could be identified. Specifically, the medial-superior attachment of the cartilage to the cranial base (A in Fig. 2A), the attachment of the TVPM to the lateral portions of the cartilage and OFT (B and C in Fig. 2A), and the attachment of the LVPM to the inferior portions of the OFT and cartilage (D and E in Fig. 2A) were recorded. Finally, the insertion angle of the TVPM was measured at two locations, the superior OFT-cartilage junction ({theta}S) and the inferior insertion with the OFT ({theta}I).



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  		Fig. 2. A: histological midcartilaginous image used to determine cartilage and OFT contours, location of cranial base (A), location of load-bearing surfaces (B to E), and insertion angles of TVPM [superior ({theta}S) and inferior ({theta}I)]. B: finite element representation of cartilage and OFT soft-tissue elements, fixed boundary conditions, and location and directions of applied muscle loads. FLVPD and FLVPE, magnitudes of the forces applied by the LVPM in the y-z plane on sections D and E, respectively; FTVP, total force generated by the TVPM in the y-z plane.

 
Finite element modeling.   The geometric contour information from each subject was imported into the ADINA finite element program (Watertown, MA) for mesh generation and tissue deformation analysis. First, the cartilage and OFT regions in Fig. 2A were subdivided into small six-noded triangles or elements (see Fig. 2B) using free-form meshing techniques. The size and quality of these elements is directly related to the accuracy of the finite element technique. Note that the cartilage and OFT regions were meshed with two different element types to account for differences in mechanical properties (see below). These triangular elements were then used to solve the complex but well-established equations that govern tissue deformation and stress generation in 2D (2, 12). Specifically, standard 3D deformation equations were simplified with a 2D plain-strain analysis such that all deformations occur in the cross-sectional or y-z coordinate plane (Cartesian coordinates). Solution of these 2D plain-strain equations requires specification of several modeling parameters, including boundary conditions, applied loads, and tissue mechanical properties.

Fixed boundary conditions (i.e., no deformations) were specified on the medial-superior surface of the cartilage (section A in Fig. 2A) to approximate attachment to the nondeformable cranial base, whereas free boundary conditions (i.e., unrestrained deformations) were specified at all other non-load-bearing surfaces. Muscle contraction was simulated by applying forces on the load-bearing surfaces (sections B to E) in an anatomically consistent direction. First, although the LVPM does not directly insert into the cartilage or OFT, several investigations (19, 25) have indicated that LVPM contraction could effect tissue deformation and ET opening. Specifically, the course of the resting LVPM is primarily along the long axis (i.e., x-axis) of the ET as shown in Fig. 1, and therefore contraction of the LVPM, which is assumed to be incompressible, would result in expansion of muscle tissue in the cross-sectional y-z plane. This tissue expansion was simulated by applying normally directed distributed loads wD = FLVPD/LD to section D and wE = FLVPE/LE to section E (see Fig. 2B), where LD and LE are the length of the attached surfaces D and E and FLVPD and FLVPE are the magnitudes of the forces applied by the LVPM in the y-z plane on sections D and E, respectively. In contrast to the LVPM, the course of the TVPM near the NP is primarily in the y-z plane (see Fig. 1). Contraction of the TVPM, therefore, was simulated by applying a series of forces on the lateral surfaces of the cartilage and OFT (sections B and C). The direction of these forces was specified as a function of location to account for the variation in insertion angles observed by Takasaki et al. (30). Specifically, TVPM forces applied to section B were directed at an angle {theta}S, whereas the direction of the forces applied to section C varied linearly from {theta}S superiorly to {theta}I inferiorly. The magnitude of all TVPM force vectors were constant, Fv = FTVP/n, where Fv is the force vector, n is the total number of force vectors used to simulate muscle contraction, and FTVP is the total force generated by the TVPM in the y-z plane. Baseline force magnitudes used in this study, FLVPD = 5 N, FLVPE = 10 N, and FTVP = 50 N, were based on the muscle forces measured during human jaw movement (8, 18), where we have assumed that the medial expansion of the LVPM is greater than the superior expansion (i.e., FLVPD < FLVPE) and that FLVPE < FTVP to reflect contraction of the LVPM in the out-of-plane direction vs. the in-plane contraction of the TVPM.

Mechanical properties for both cartilage and OFT elements are specified based on a constitutive relationship, which describes the amount of tissue strain and/or deformation that would result from an applied load. Although the linear Hooke's law relationship, which quantifies tissue elastance or stiffness with the Young's modulus, is frequently utilized to describe simple materials, this relationship can only be used to describe biological tissue when the amount of strain or deformation is very small (i.e., <5%) (12). Because deformation of ET tissues during swallowing may be significantly larger than 5% (see Fig. 4), we utilized a neo-Hookean constitutive relationship, which can adequately describe large strains/deformations (2). This neo-Hookean relationship is defined by a shear modulus (G) and a bulk modulus ({kappa}), which depend on the Young's modulus (E).

(1)
where {nu} is a standard measure of tissue compressibility known as the Poisson's ratio. For the present study, both the cartilage and OFT are modeled as nearly incompressible, i.e., {nu}cart = {nu}OFT = 0.49. The baseline Young's modulus for the cartilage (3.4 MPa) is based on ex vivo measurements in conchal ear cartilage (31), whereas the baseline modulus for the OFT (0.5 MPa) is based on measurements in normal adult human subjects (see Human experiments for details).



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  		Fig. 4. Simulation of tissue deformation and ET opening during swallowing in subject e37 using a total applied TVPM force of 60 N (A), 120 N (B), and 180 N (C). Contour plots represent the effective strain or stretching within the soft-tissue elements, whereas the outlines represent the undeformed configuration.

 
Quantification of ET opening.   Application of the appropriate boundary conditions, muscle loads, and tissue mechanical properties results in tissue deformation and an opening of the ET lumen (see Fig. 4). This open lumen area was analyzed with a one-dimensional fluid-flow model, similar to the one utilized by Dai et al. (9), to calculate a viscous flow resistance parameter

(2)
where L is the assumed length of the ET (3 cm), µ is the viscosity of air, A is the cross-sectional area, {Delta}P is the change in pressure, is the volumetric flow rate, and {Gamma}s is a generalized hydraulic-geometric shape factor, which can be calculated from any arbitrary shape (see Ref. 15 for details). Rv, therefore, depends on both the cross-sectional area and the shape of the ET lumen and can be used to quantify the degree of opening, where a large Rv indicates minimal ET opening. Calculation of Rv via Eq. 2 requires a reasonably uniform cross-sectional lumen shape and area along the length of the ET. Previous histological measurements (25, 26) have demonstrated that axial variations in the lumen's cross-sectional shape and area, within the deformable cartilaginous region, are minimal, and therefore the use of Eq. 2 is justified. Note that Rv is consistent with the standard definition of resistance, i.e., the ratio of pressure to volumetric flow rate, and can therefore be compared with active flow resistance measurements obtained experimentally during the force-response test (3, 6).

Human experiments and model validation.   Although a majority of the mechanical parameters utilized in the finite element models are based on accepted literature values, the baseline magnitude of OFT tissue elastic modulus (EOFT) requires validation. This validation was accomplished by simulating the dynamics of a recently developed oscillatory force-response test (15). In this test, the ET is passively opened via inflation of the ME. Once opened, an oscillatory airflow rate is imposed, and the resulting oscillations in pressure are recorded. These pressure-flow rate relationships can be analyzed with a mathematical model of flow in a collapsible tube to determine mechanical properties of the surrounding tissue (15) including the overall compliance defined as dA/dP, where A is the cross-sectional lumen area, P is the applied pressure, and dA/dP represents the average slope of the area-pressure curve. This oscillatory force-response protocol was conducted in a separate group of healthy adult volunteers with no history of ME disease (age range of 33 ± 13 yr with no individual <21 yr old; 3 women and 5 men). Note that all subjects were examined by a qualified physician to document normal ME status before undergoing the voluntary myringotomy required to perform the oscillatory force-response protocol. This myringotomy (<1 mm) was performed by a qualified surgeon, and all myringotomies healed within 1 wk with no complications. Approval for obtaining these measurements, including the voluntary myringotomy, was obtained from the Human Rights Committee and Institutional Review Board at Children's Hospital of Pittsburgh. Analysis of this data resulted in an average compliance of 7.02 ± 6.31 x 10–7 cm2/mmH2O.

An analogous compliance parameter was obtained by modifying each histological subject's finite element model to account for experimental conditions. Specifically, unrestrained deformation boundary conditions and zero muscle forces were specified on surfaces B to E to emulate passive conditions. Loading was accomplished by applying a range of normal pressures, corresponding to experimental values (200–400 mmH2O) (15), on internal lumen surfaces. This loading resulted in an opened lumen cross-sectional area, which was calculated as a function of the applied pressure. Note that the current finite element models do not account for time-dependent viscoelastic effects, and thus the area calculation is independent of the rate of pressure application. For baseline mechanical properties of cartilage elastic modulus (Ecart) = 3.4 MPa and EOFT = 0.5 MPa, analysis of all eight finite element models yielded an average area-pressure slope of dA/dP = 7.71 x 10–7 ± 6.53 x 10–7 cm2/mmH2O. This value is in excellent agreement with the experimental measurements and therefore validates the magnitude of EOFT under baseline conditions.


   RESULTS
TOP
 ABSTRACT
 METHODS AND MATERIALS
 RESULTS
DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
The finite element models generated from each histological subject are shown in Fig. 3. Free-form meshing of the cartilage region resulted in an average of 1,017 ± 220 triangular elements per model, whereas meshing of the OFT region resulted in an average of 515 ± 77 elements per model. The average number of nodes used to create each model was 4,752 ± 615. In addition to the morphometric variability demonstrated in Fig. 3, histological measurements of the TVPM insertion angles resulted in {theta}S = 55.7 ± 18.2° and {theta}I = 25.1 ± 15.0°. For all subjects, surfaces A to E could be accurately identified, and therefore all models presented in Fig. 3 were analyzed for tissue deformation and ET lumen opening.



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  		Fig. 3. Finite element models generated using midcartilaginous sections from 8 histological subjects. Free-form techniques were used to mesh the ET cartilage and OFT regions.

 
The tissue deformation and lumen opening that occurred in a representative subject (subject e37) is shown in Fig. 4. These results utilize baseline mechanical properties of Ecart = 3.4 MPa, EOFT = 0.5 MPa, FLVPD = 5 N, FLVPE = 10 N, and three specific FTVP loading conditions (60, 120, and 180 N), which correspond to the range of muscle forces measured during human jaw movement (8). The outlines in Fig. 4 represent the undeformed configuration, whereas the contour plots represent the degree of stretching within the soft tissue as measured by the effective strain (21)

(3)
{epsilon}eff accounts for relative elongation in the y and z directions ({epsilon}yy and {epsilon}zz) and in-plane shearing ({epsilon}yz) but does not account for rigid body rotations. Figure 4 demonstrates that, at nominal FTVP magnitudes, lumen opening is relatively small compared with the opening observed at higher FTVP values. Figure 4 also demonstrates that a majority of tissue stretching occurs along the lateral wall of the OFT and that the magnitude of this stretching increases with the applied force. Finally, minimal stretching or strains develop in the medial lamina of the cartilage, indicating that deformation in this tissue is primarily a rotation about the fixed cranial base.

The finite element models shown in Fig. 3 were used to investigate how specific tissue mechanical properties influence active ET opening phenomena. Specifically, several simulations were performed by either varying FTVP, EOFT, or Ecart independently from the baseline conditions of Ecart = 3.4 MPa, EOFT = 0.5 MPa, FLVPD = 5 N, FLVPE = 10 N, and FTVP = 50 N. Figure 5A demonstrates that increasing the magnitude of the TVPM forces results in a significant decrease in Rv due to a large opening in the cross-sectional lumen area (see Fig. 4). In contrast, Fig. 5, B and C, demonstrates that increasing the Young's modulus of the OFT and the cartilage results in a stiffer ET, which is more difficult to open, and thus an increase in Rv.



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  		Fig. 5. Variation in resistance to airflow (Rv) in the actively opened ET lumen as a function of FTVP (A), OFT tissue elastic modulus (B), and cartilage elastic modulus (C).

 

   DISCUSSION
TOP
 ABSTRACT
 METHODS AND MATERIALS
 RESULTS
 DISCUSSION
GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
An impaired ability to open the ET and increase the cross-sectional lumen area during swallowing has been related to the development of OM. Although several anatomic and mechanical soft tissue properties may be responsible for this debility, previous investigations could only speculate on how these structural properties influence ET opening phenomena. The goal of this study was to overcome this limitation by developing finite element models of the tissue deformation processes responsible for ET opening. These models were constructed using histological data from eight normal adult subjects, and model parameters were validated by comparing theoretical and experimental cross-sectional area-pressure relationships. These 2D finite element models were then used to simulate active ET opening by applying muscle forces to the appropriate soft-tissue surfaces. Opening of the ET lumen was quantified with a flow resistance parameter, and a parameter variation study was conducted to determine the influence of various tissue mechanical properties on opening phenomena.

The models developed in this study (Fig. 3) demonstrate significant variability with respect to tissue size and minimal variability with respect to tissue morphology, except for a large OFT height-to-width ratio in subject e38. For equivalent mechanical properties, simulation of ET opening in these models resulted in significant variability in Rv (see Fig. 5A; Rv at FTVP = 60 N). This variability in Rv was correlated to the variability in tissue size by performing a least-squared regression between the closed lumen length in the cross-sectional y-z plane and the magnitude of Rv–1 calculated under baseline conditions. This analysis, which resulted in a statistically significant correlation (r2 = 0.63, P < 0.02), indicates that for constant tissue mechanical properties, ETs with long lumens are easier to open (smaller Rv) and that the magnitude of Rv is strongly influenced by tissue size. Although the magnitude of Rv varies significantly between subjects, Fig. 5 indicates that all models exhibit similar trends with respect to Rv as a function of FTVP, EOFT, and Ecart. These similarities may be due to the consistent tissue morphologies demonstrated in Fig. 3. However, future studies, which model tissue deformation in OM patients with varying morphologies, are required to ascertain the precise relationship between tissue morphology, tissue mechanics, and ET function. In particular, a detailed understanding of how tissue mechanical properties influence opening phenomena under different anatomic conditions may be useful in identifying which tissue-based treatments may be most effective in patient populations with different morphological properties (e.g., cleft palate, chromosomal aberrations, and chronic OM patients).

Unlike previous histological measurement techniques, the present mathematical models are able to simulate and quantify the tissue deformation processes responsible for ET opening as a function of the applied muscle load. For example, Fig. 4A indicates that inferior aspects of the cartilage's medial lamina undergo a medial-superior rotation during muscle contraction. This rigid body rotation, which is consistent with in vivo endoscopic observations (22), is not accompanied by significant tissue stretching or deformation, as indicated by the near-zero strains in the medial lamina. In contrast, Fig. 4, B and C, indicates that large tissue strains (~50–75%) develop in the OFT region at FTVP greater than ~120 N. Although these large FTVP values lead to a significant reduction in RV (see Fig. 5A), the large tissue strains could also result in tissue remodeling, which typically involves tissue fibrosis and hyperplasia (17), and an increase in EOFT, which would impair ET opening (see Fig. 5B). In addition, the eight healthy adult subjects described in Human experiments exhibited an average in vivo active resistance of 1.9 ± 0.64 mmH2O·ml–1·min [measured via a standard force response test (3)]. Therefore, a modest increase in FTVP to ~60 N (see Fig. 5A) may be sufficient to relieve ET dysfunction without creating excessive tissue strain.

Figure 5 demonstrates that several tissue mechanical properties can alter ET opening behavior. For example, a reduction in Rv, which indicates greater ET opening, can be accomplished by either increasing the applied muscle forces (Fig. 5A) or decreasing the Young's modulus of the OFT and cartilage tissue (Fig. 5, B and C). However, equivalent changes in these mechanical properties do not produce equivalent changes in Rv. Therefore, the following sensitivity parameters were calculated to evaluate the relative importance of FTVP, EOFT, and Ecart


(4)

where {Delta}TVP, {Delta}OFT, and {Delta}cart were calculated from data in Figs. 5 and represent the amount of change in Rv for an order of magnitude change in the mechanical parameters. The results of this analysis ({Delta}TVP = 440x, {Delta}OFT = 48x, {Delta}cart = 9.4x) indicate that ET opening phenomena are highly sensitive to the applied muscle forces, whereas {Delta}OFT > {Delta}cart indicates that lumen opening is more sensitive to OFT properties than to cartilage properties. Although muscle forces appear to be the most important factor, it is important to recall that excessive FTVP could also result in large tissue strains as shown in Fig. 4.

In addition to analyzing data from OM-prone populations, future studies will include several model enhancements that could increase the utility of these computational models. First, although the 2D approximations made in the present models may be appropriate due to the relatively uniform lumen cross-sectional area reported in the literature (25, 26), these models cannot account for variations in cartilage or OFT morphology along the length of the ET and the complex 3D structure of the TVPM (see Fig. 1). Because these 3D morphological features could significantly influence the accuracy of our predictions, future studies should focus on developing and analyzing sophisticated 3D finite element models of the ET soft-tissue structure. It is important to note that, although 3D models may be more accurate, the present 2D models may be more clinically relevant since they would be easier to construct using nonhistological imaging data with lower resolution (i.e., MRI). The present modeling techniques also do not account for the adhesive and/or surface-tension forces within the ET mucosa. As a result, these models may only be appropriate when the adhesive properties are minimal. For example, during the force-response test of active ET function, muscle forces are applied to the soft tissues after the lumen has been partially opened via air inflation (6). In contrast, the lumen is completely collapsed before the application of muscle forces during normal swallowing events. Under these physiological conditions, the adhesive forces within the mucosa, which would be elevated during inflammation, serve to keep the ET closed until the stress at the lumen surface exceeds a yield value. As a result, any changes that diminish the stress transmitted to the lumen, such as a reduction in EOFT, could hinder ET opening. The incorporation of mucosal adhesion dynamics into the present tissue deformation models would therefore result in a more accurate description of ET opening phenomena under inflammatory conditions. Finally, the time-dependent or hysteretic pressure-flow behavior observed in experiments (15) can be accounted for by incorporating viscoelastic material properties, whereas the quantity of air/fluid transported during ET openings can be ascertained by incorporating fluid-structure modeling techniques.

In conclusion, we have developed 2D finite element models of the tissue deformation processes that govern ET opening. These modeling techniques were able to account for both anatomic variability in normal subjects and the interaction between the anatomic and mechanical environment. These models, which were validated by comparing theoretical and experimental data, were used to simulate the muscle-assisted opening of the ET during swallowing. Flow-resistance measurements were used to quantify this opening, and results indicate that ET opening is highly sensitive to the applied muscle forces and relatively insensitive to cartilage elastic properties. These models have therefore identified how different tissue elements alter ET opening phenomena, which elements should be targeted for treatment, and the optimal mechanical properties of these tissue constructs. Further development of these computational models will help elucidate how modifications in the anatomic and mechanical structure of the ET influence its function and, therefore, may be useful in the evaluation of novel structure-based treatment therapies for OM.


   GRANTS
TOP
 ABSTRACT
 METHODS AND MATERIALS
 RESULTS
 DISCUSSION
 GRANTS
ACKNOWLEDGMENTS
 REFERENCES
 
This research was supported by the National Institute for Deafness and Other Communication Disorders Grant R03 DC-005345.


   ACKNOWLEDGMENTS
TOP
 ABSTRACT
 METHODS AND MATERIALS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
REFERENCES
 
We thank Dr. Isamu Sando for providing the normal adult histological specimens used in this study and Dr. Charles Bluestone for performing myringotomies on normal adult subjects.


   FOOTNOTES
 

Address for reprint requests and other correspondence: S. N. Ghadiali, Dept. of Mechanical Engineering and Mechanics, Packard Laboratory, 19 Memorial Dr. West, Bethlehem, PA 18015 (E-mail: sag3{at}lehigh.edu).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 METHODS AND MATERIALS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 

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