Tracheal procedural control samples (original magnification ×50 000) show immunogold labeling of microvilli (black arrow) and cilia (white arrow) for aquaporin 1 (A) and an absence of labeling in the plasma membrane of cilia and microvilli in negative controls (B).
Vocal fold epithelium samples under electron microscopy. Immunogold labeling of vocal fold epithelium shows immunogold particles in intimate association with the plasma membrane region and circular structures of luminal cells (region 1) exposed to aquaporin (AQP) 1 (A) (original magnification ×25 000) and AQP-2 (B) (original magnification ×80 000). C, Preexposure to antigen peptides decreased immunolabeling in tissue exposed to AQP-1 (original magnification ×80 000). D, Negative vocal fold procedural controls did not label (original magnification ×80 000).
Vocal fold epithelium samples under electron microscopy. Evident is immunogold labeling of the plasma membrane region and circular structures of cell region 2 exposed to aquaporin (AQP) 1 (A) (original magnification ×50 000) and AQP-2 (B) (original magnification ×50 000). The black arrows indicate labeling of the plasma membrane; white arrows, labeling of circular structures.
Vocal fold epithelium samples under electron microscopy. Decreased labeling was evident in the plasma membrane region and increased labeling of circular structures exposed to aquaporin (AQP) 1 (A) (original magnification ×25 000) and AQP-2 (B) (original magnification ×40 000). Black arrows indicate labeling of the plasma membrane; white arrows, labeling of circular structures.
Comparison of linear immunogold labeling densities of the plasma membrane across regions indicated a significant decrease in labeling between regions 1 and 3 for aquaporin (AQP) 1 (P = .02) and a significant decrease in labeling between regions 1 and 2 and region 3 for AQP-2 (P<.001). Error brackets indicate standard error. *Significant difference between groups for AQP-1. †Significant difference between groups for AQP-2.
Comparison of area immunogold labeling densities of the cytoplasm across regions indicated a significant increase in labeling between region 1 and regions 2 and 3 for aquaporin (AQP) 1 (P<.001) and a significant increase in labeling between regions 1 and 2 for AQP-2 (P = .02). Error brackets indicate standard error. *Significant difference between groups for AQP-1. †Significant difference between groups for AQP-2.
Lodewyck D, Menco B, Fisher K. Immunolocalization of Aquaporins in Vocal Fold Epithelia. Arch Otolaryngol Head Neck Surg. 2007;133(6):557-563. doi:10.1001/archotol.133.6.557
To investigate the presence of aquaporin (AQP) water channels 1, 2, and 3 in stratified squamous vocal fold epithelium.
Immunolocalization analysis of excised ovine vocal fold epithelia.
Ovine vocal fold epithelia were prepared for immunoelectron microscopy using primary antibodies directed against AQP-1, AQP-2, and AQP-3. Photographic profiles of epithelium exposed to each antibody were used to calculate the immunogold labeling density of the plasma membrane and cytoplasm.
Main Outcome Measures
Density of immunolabeling was compared across 3 regions that represent cell layers closest to the glottal lumen for the plasma membrane and cytoplasm, respectively.
Labeling densities of AQP-1 and AQP-2 were significantly greater for the plasma membrane region of the luminal cells than for deeper cell layers. Cytoplasmic labeling and labeling of circular structures was greatest for cell layers 2 through 5 beneath the vocal fold surface compared with the surface cell layer. Immunogold labeling of AQP-3, an aquaglyceroporin, in vocal fold epithelium was inconclusive.
Aquaporins 1 and 2, associated with the plasma membrane region of ovine vocal fold epithelial cells, demonstrate the presence of an intrinsic mechanism to permit transcellular water flux in response to osmotic gradients.
Vocal fold hydration is critical to maintain vocal fold oscillation in ex vivo canine models1 and to decrease the amount of subglottic pressure necessary to initiate and sustain human phonation.2,3 Therefore, the use of untested benign aerosols and other hydration remedies have long been components of vocal hygiene treatment. Fisher and colleagues4 have demonstrated bidirectional transepithelial water fluxes toward and away from the airway surface of native vocal folds. The pathways for the water flux are as yet unknown. Herein we report on the possible contribution of the transcellular pathway for these water fluxes. Explicit knowledge about water transport pathways of the vocal fold is critical to develop effective hydration therapeutics for treatment and prevention of voice disorders.
Study of water transport in other epithelial tissues of the body has revealed channels called aquaporins (AQPs) that permit a rapid osmotic flow of water molecules via a transcellular path across the plasma membrane of cells.5,6 Since AQPs are the only channels that are predominantly selective to the osmotic flow of water, these channels may play an important role in the transport of water across vocal fold epithelium.
The superficial layer of the vocal folds includes stratified squamous epithelium, basal lamina, and the superficial layer of lamina propria. Wet, stratified squamous epithelia of the body (eg, those of vocal fold and buccal, esophageal, and vaginal mucosae) generate a potential difference and short-circuit current consistent with ion and water transport.7 In buccal and nasal mucosa, a water-specific pathway via AQP water channels has been identified.8 The vocal fold mucosa generates a transepithelial potential difference, short-circuit current, and bidirectional simultaneous transepithelial water fluxes.4 However, a pathway for the flux of water across the wet stratified squamous epithelium of the vocal fold has not been explicitly shown.
Aquaporin membrane proteins form water channels that provide a mechanism for water to transit the plasma membrane of epithelial cells. Epithelia in other systems of the body in which water flux is crucial to organ function (ie, kidney, eye, and lacrimal glands) contain AQP protein channels localized in the plasma membranes of their cells,5 which has been interpreted to indicate that a transcellular water pathway exists in these tissues.
Though 11 AQP water channel proteins have been identified to date in mammalian cells,6,9 3 are of particular relevance to the vocal fold: AQP-1 is a ubiquitous channel and most notably has been localized in another multilayer epithelium (lens10). Both AQP-1 and AQP-2 respond rapidly (within 1-40 minutes11) to osmotic gradient. Moreover, AQP-2 is found in tissues with large magnitudes of water flux and in a tissue composed of 2 simple epithelia arranged in series. Aquaporin 2 is known as the vasopressin-selective water channel and has been localized in the kidney,11 vas deferens,12 and inner ear.13 These tissues, like the vocal fold, rely on closely regulated water flux for optimal function. Aquaporin 3 is the only AQP yet localized in a wet stratified epithelium (eg, buccal) and is also present in airway epithelia of the trachea.
Given that vocal fold epithelial water fluxes regulate superficial vocal fold hydration,4 we posit that AQPs provide a cellular pathway for these fluxes. The present study used immunolocalization with transmission electron microscopy to examine whether AQP-1, AQP-2, and/or AQP-3 were present in the plasma membranes of stratified squamous epithelial tissue of the membranous vocal fold. As stratified epithelia have potential for specialized cell layers, and in the vocal fold osmotic stress is first seen by the luminal cells, of particular interest was the distribution of AQP water channels within the cell and across the stratified squamous vocal fold cell layers.
In accordance with approved protocols at Northwestern University, the larynges (n = 2) and tracheae (n = 2) from sheep purchased from the local abattoir were immediately immersed in 4°C Hanks balanced salt solution. Tissue preparation and immunocytochemical analysis followed validated procedures published elsewhere.14 The vocal fold and tracheal mucosae were dissected, transferred to 4% paraformaldehyde in 100mM Sorenson phosphate buffer supplemented with 0.15mM calcium chloride (pH 7.2). The specimens were fixed overnight at 4°C in the same fixative supplemented with 100mM bicarbonate (pH 9.4). Mucosae were removed from the fixative, rinsed at 4°C in Sorenson buffer, cryoprotected in sucrose/glycerol mixtures, and rapidly frozen in liquefied propane. The specimens were freeze substituted (Leica/Reichert CS Auto, Vienna, Austria) through methanol supplemented with 0.1% uranyl acetate at −80°C. Lowicryl K11M (Chemische Werke Lowi GmbH, Waldkraiburg, Germany) was used for infiltration (−80°C to −60°C) and embedding (−60°C to +25°C; all in the CS Auto device).
Immunochemical analysis was performed using commercially available antibodies anti–AQP-1, anti–AQP-2, and anti–AQP-3 (Alomone Laboratories, Jerusalem, Israel). Anti−AQP-1 is a polyclonal antibody raised in rabbit against the highly purified peptide KVWTSGQVEEYDLDADDIN (AQP1243-261), corresponding to residues 243 through 261 of human AQP-1.15 Aquaporin 1 is recognized by anti–AQP-1.16 The anti–AQP-1 epitope is unique for AQP-1 and is not present in other known related proteins. It is identical in numerous mammalian species, including human, rodent, cattle, and most notably, sheep protein. Anti–AQP-2 is also a polyclonal antibody raised in rabbit, against the highly purified peptide (KY)RQSVELHSPQSLPRGSKA (AQP2254-271), corresponding to residues 254 through 271 of rat or mouse AQP-2,6 with additional N-terminal lysine and tyrosine. The peptide was conjugated to keyhole limpet hemocyanin with glutaraldehyde.17 Aquaporin 2 is recognized by anti–AQP-2.16 The anti–AQP-2 epitope is unique for AQP-2 and is not present in other known proteins. It is identical in rat and mouse protein and only slightly different in human and sheep (17 of 18 residues identical).
Ten sections of experimental tissue were exposed to each of AQP-1, AQP-2, or AQP-3 (30 total sections) to ensure multiple opportunities for visualization of immunolocalization. Negative controls were 3 vocal fold and 3 tracheal tissues prepared alongside the experimental sections and not exposed to the AQP-1, AQP-2, or AQP-3 antibodies. Positive tissue controls were tracheal and vomeronasal epithelia exposed to AQP-1 antibody. Presence and patterns of AQP-1 localization in these tissues have been demonstrated (kidney,17 trachea,18 and vomeronasal [unpublished data, B.M., 2003]). Additionally, a control antigen peptide was used against residues 243 through 261 of AQP-1 and residues 254 through 271 of AQP-2.
Sections were cut (AQP-1, n = 9; AQP-2, n = 9; and AQP-3, n = 4) at 150- to 200-nm thickness (LEO-Reichert Ultramicrotome S, Vienna, Austria). Each section was placed on a 300-mesh, hexagonal nickel grid. For the blocking procedure, the grids were immersed and gently shaken for 4 hours at room temperature in 0.01M Tris-buffered saline (TBS) (pH 8.0) supplemented with 0.5M sodium chloride and 0.1% acetylated bovine serum albumin (Ac-BSA) (Aurion; Electron Microscopy Sciences, Fort Washington, Pa). Each grid was blotted and transferred to a Robinson tube that contained primary antibody diluted (1:25) in the same Ac-BSA/TBS solution. Sections were incubated with primary antibodies at 4°C with gentle agitation.
Grids were removed from the primary antibody and jet-washed for 2 minutes by pipetting Ac-BSA/TBS over the sample. Subsequently, the grids were incubated for 2 hours with gold-conjugated (15-nm diameter) secondary goat antirabbit IgG 10-nm gold (optical density520 = 0.1) as the secondary probe to which the sections were exposed for 4 hours at room temperature. Grids were jet-washed by pipetting buffer supplemented with 0.1% Tween 20 detergent for 1 minute, followed by jet-washing with distilled water for 1 minute. Grids were dried in an evacuated desiccator and then stained with 0.5% methanolic (1:1 methanol in distilled water) uranyl acetate for 20 minutes followed by a 2-minute wash with distilled water. Dry grids were subsequently coated with formvar and carbon. Grids were examined at 120 kV in the JEM-100-CX II Transmission Electron Microscope (JEOL Ltd, Tokyo, Japan) and photographed.
An initial survey of the labeling densities of a narrow column across the entire epithelial sheet indicated that the cells closest to the luminal surface labeled most densely. Therefore, 3 cell regions were identified for further examination of immunogold labeling density. Region 1 was identified as the cell layer at the luminal surface. Region 2 was identified as the cell layer immediately under region 1. Region 3 was identified as an area of 2 cell layers under region 2. Region 3 consisted of 2 cell layers because complex interdigitation of cells prevented distinct identification of the cell layer.
Although quantitative methods for identification of immunolocalized labeling are rare, and no immunogold labeling studies were available for vocal fold epithelia, we adopted a method used reliably in immunolocalization studies.19 Areas from each region of cells were selected from photographs. Immunogold particles were counted per unit area or per unit length.20 Regions of interest in the vocal fold cells were the plasma membrane and circular bodies within the intracellular cytoplasm. For the plasma membrane, the linear density of immunolabeling was estimated by dividing the number of specific gold particles localized within 2 mm of the plasma membrane by the length of the pictured membrane. The length of the plasma membrane was estimated using the point-hit intersection method. A transparent grid with horizontal and vertical lines was superimposed over the plasma membrane, and the number of times the plasma membrane intersected a line was counted. The surface area of the circular bodies was estimated by the following equation: Length = ([number of intersections with plasma membrane] × [1 × 10−4m])/magnification.
The area labeling density of the circular bodies was estimated by dividing the number of specific gold particles within the circular body by the surface area of the circular body. To estimate the surface area of the circular bodies, the point-hit intersection method was used. A transparent grid with horizontal and vertical lines was superimposed over the randomly selected circular bodies, and the number of intersecting points within the circular body was counted. The surface area of the circular bodies was estimated by the following equation: Surface area = ([number of intersecting points] × [1 × 10−4m])/magnification2. The labeling densities of the plasma membrane and cytoplasm were compared for the most luminal 3-cell regions by a factorial analysis of variance.
No evidence of immunogold labeling was observed in tracheal or vocal fold experimental samples exposed to the AQP-3 antibody (data not shown). Therefore, the results reported here will focus on immunogold labeling with AQP-1 and AQP-2.
Tracheal positive procedural controls using AQP-1 (Figure 1A) indicated the expected sparse labeling of the microvilli (black arrow) and cilia (white arrow) of the epithelial surface, consistent with the sparse antibody binding to tracheal epithelium found by Hasegawa and colleagues.18 Negative trachea procedural controls prepared alongside experimental samples but not exposed to primary antibody showed no evidence of immunogold labeling (Figure 1B). Vomeronasal specificity controls of AQP-1 indicated labeling of the stereocilia of nonsensory cells, and no labeling of stereocilia of sensory cells (data not shown), consistent with labeling of vomeronasal epithelium (unpublished data, B.M., 2003).
Immunogold labeling of vocal fold epithelium using the AQP-1 (Figure 2A) and AQP-2 (Figure 2B) antibodies was present in surface epithelial cells lining the glottal lumen (region 1). Substantial labeling was associated with the plasma membrane region and interior of microvilli that populate the surface of luminal cells (region 1), as shown for AQP-1 (Figure 2A) and AQP-2 (Figure 2B). Sparse cytoplasmic labeling for AQP-1 and AQP-2 within the cell cytoplasm was noted in some specimens (eg, Figure 2A). Preadsorption of vocal fold procedural controls with control antigen peptides against AQP-1 (Figure 2C) and AQP-2 before exposure to their respective antibodies resulted in decreased immunolabeling of the plasma membrane of luminal cells. Negative vocal fold procedural controls prepared alongside experimental samples but not exposed to primary antibody showed no evidence of immunogold labeling (Figure 2D). Results were qualitatively similar in the 2 animals.
Labeling of the vocal fold plasma membrane region was also present in region 2 (Figure 3). Owing to the tortuous interdigitation of cells, it was often unclear whether immunogold particles were associated with the plasma membrane of the basal surface of cells in region 1 or with the apical surface of the cell below (Figure 3A, black arrow). Labeling of the cytoplasm was evident in 43 (56%) of 76 profiles from region 2 for AQP-1 and 31 (49%) of 63 profiles from region 2 for AQP-2. Of these, immunogold particles were often associated with circular bodies adjacent to the plasma membrane (Figure 3A, white arrow). While circular bodies could be associated with the paracellular space surrounding microvilli in other planes of the tissue, labeling of vesicular structures is commonly observed.11,21
Labeling of the plasma membrane region was less evident in region 3 (Figure 4). As with region 2, it was difficult to distinguish whether immunogold particles were associated with the basal surface of the cell above or the apical surface of the cell below. In contrast, labeling of the cytoplasm, especially of circular bodies within the cytoplasm, was quite dense, as seen in both panels of Figure 4.
Labeling densities of plasma membrane (Figure 5) and cytoplasm (Figure 6) for AQP-1 and AQP-2 differed significantly by region. For the plasma membrane region, linear labeling density of AQP-1 was significantly greater for region 1 than for region 3 (P = .02) (Figure 5). For AQP-2, linear labeling density of the plasma membrane region was significantly greater in regions 1 and 2 than in region 3 (P<.001) (Figure 5). In contrast, for the cytoplasm, area labeling density was significantly greater in regions 2 and 3 than in region 1 for AQP-1 (P<.001) (Figure 6). Labeling of cytoplasmic AQP-2 was significantly more dense in region 2 than in region 1 (P = .02) (Figure 6). These results indicate greater presence of plasma membrane AQP-1 and AQP-2 in association with cells at or near the airway lumen but greater presence of cytoplasmic AQP-1 and AQP-2 in association with cells just beneath but not in contact with the luminal surface.
Aquaporin 1 and AQP-2 water channels were associated with the plasma membrane of stratified squamous epithelial cells of the membranous vocal fold. Aquaporins in the plasma membrane of vocal fold epithelial cells indicate the presence of a transmembrane water pathway in this tissue. Immunolabeling of plasma membrane was significantly greater in regions at or near the lumen (regions 1 and 2), the area exposed to the challenging osmotic environment of the glottis. Labeling of the most superficial cell layers may suggest that these layers are specialized for response to changes in the osmotic environment of the glottis. As the wet, stratified epithelium of the vocal fold possesses AQP-1 and AQP-2 associated with the plasma membrane and multivesicular structures of the cell layers closest to the luminal surface, these AQPs may play a role in regulating superficial hydration in response to osmotic challenges in the airway. Furthermore, labeling of AQP-1 and AQP-2 was significantly greater in the cytoplasm and in association with circular bodies from the second and third layer of cells from the luminal surface. We propose that the second and third layer of cells in the vocal fold epithelium might contain an abundance of cytoplasmic AQPs that could be readily recruited to the plasma membrane surface, as would be consistent with the “shuttle hypothesis” describing rapid regulation of AQP in epithelia.22 The presence of these channels in vesicular bodies might also indicate a role in vesicular volume regulation in these cell layers.
To our knowledge, this is the first observation of AQP-1 in a wet, stratified squamous epithelium. Aquaporin 1, a ubiquitous protein, has been localized in both apical and basolateral plasma membrane of simple epithelia and endothelia (eg, renal proximal tubules and descending thin limbs,17 peribronchiolar endothelia,23 and tracheal endothelia24) and corneal and lens epithelia.24 These tissues, however, differ substantially in structure and function from that of the stratified squamous epithelium of the vocal fold. Transitional eye lens and ciliary epithelia possess multiple layers of cells with abundant AQP-1. Aquaporin 1 in the nonpigmented layer of the ciliary bilayer has been recently credited with optimizing the transport of fluid from the apical to the hyperosmotic basal side of the layer.10 Data to confirm the presence of AQP-1 in a dry, stratified epithelium or in any other wet stratified epithelium are presently unavailable.
The function of AQP-1 channels in other epithelia and endothelia in the body is widely believed to be the facilitation of transcellular water movement,25,26 possibly associated with environmental stress or wound healing. A recent study27 indicates that AQP-1 protein expression in culture is increased by hypertonic stress, which is a result of altered ubiquitination and stability of the protein. In the vocal folds, AQP-1 may play a role in transcellular water flux in response to osmotic challenges in the airway, as in the case of an ill-conditioned air supply.28 It has also been proposed that AQP-1 plays a role in recovery from tissue injury. Thiagarajah and Verkman25 found that the recovery of corneal transparency and thickness after hypotonic swelling by saline was remarkably delayed and reduced in AQP-1–null mice, suggesting involvement of AQP-1 in active extrusion of fluid from the cornea. They concluded that the up-regulation of AQP-1 expression in corneal endothelium may reduce corneal swelling following injury. Any role of AQP-1 in wound healing of the vocal fold remains a matter of speculation.
Aquaporin 2 is localized in the apical plasma membrane and in vesicular and multivesicular structures of epithelial cells that line the lumen of systems including the kidney collecting duct,11 vas deferens distal portion,12 and inner ear.13 The apical labeling reported previously is consistent with the labeling of AQP-2 in association with the apical plasma membrane of vocal fold epithelial cells. In the stratified squamous epithelium of the vocal fold, AQP-2 density was greatest in the apical plasma membrane of the luminal cell. In regions 2 and 3, labeling of the basally directed plasma membrane was also variably present, but some gold particles could not be readily assigned to basal or apical labeling owing to the intimate association of intracellular projections in this epithelium.
Aquaporin 2 was immunolocalized in vocal fold epithelium, yet it has not been localized in other airway epithelia. It is found in abundance in systems of the body in which the rapid movement and/or bulk flow of water is critical. Known as the “vasopressin-regulated water channel,” AQP-2 is rapidly targeted to plasma membrane and reinternalized, demonstrating regulation with a time constant ranging from 40 to 80 minutes.11 Aquaporin 2 present in luminal vocal fold epithelial cells may indicate that a mechanism for the hormonal regulation of protective water fluxes at the luminal surface.
No evidence of AQP-3 labeling was found in vocal fold epithelium in the present study. Although AQP-3 was not localized in the vocal folds, it is the only AQP that has been localized in any stratified squamous epithelium, ie, the wet, stratified squamous buccal epithelium and the dry, keratinized stratified squamous epithelium of the skin.8 Aquaporin 3 has also been localized in the transitional epithelia of the urinary tract, the stratified epithelia of the upper digestive tract, the simple and stratified epithelia of the lower digestive tract, and the pseudostratified ciliated epithelia of the respiratory tract.5 A common feature in all of these tissues is that AQP-3 is present at the basal aspects of the epithelia: in the basolateral membranes of simple epithelia and multilayered epithelia and in plasma membranes of basal to intermediate cells.8 While lack of labeling for AQP-3 might be owing to methods used in the present study, AQP-3 is notably found in a different phylogenetic cluster of AQPs than AQP-1 and AQP-2. Aquaporin 3 is considered to be an aquaglyceroporin because its structure permits glycerol and other small solutes to pass in addition to water molecules. The functional significance of any tissue or species difference in the expression of AQP-3 awaits further study.
Information regarding ion and water transport in the airway makes the ovine model useful for study of AQPs in vocal fold epithelia.4 We performed sequence similarity analysis between the ovine AQP-1 and AQP-2 genes with known AQP-1 and AQP-2 complementary DNA (cDNA) of other species. The nucleotide sequences were 98% identical to cow, 90% identical to human, and 89% identical to mouse and rat for AQP-1. Ovine cDNA was 97% identical to cow, 92% identical to human, and 88% identical to mouse and rat AQP-2 cDNA. A BLAST search (Basic Local Alignment Search Tool of the National Center for Biotechnology Information, Bethesda, Md) of nucleotide sequences producing similar alignments to the sequence recognized by the antibodies revealed a 100% alignment of identities in human, cow, rat, and mouse for AQP-1 and 100% alignment for cow, dog, rat, and mouse and 94% alignment for humans in AQP-2, indicating a high degree of preservation across species.
It will be important to determine any functional role for vocal fold AQP in the vocal fold. Aquaporin may provide a mechanism to maintain superficial hydration despite poor conditioning of inspired air. Osmotically driven water flux toward the surface may further aid clearance of inhaled particulates. If AQPs play a role in vocal fold epithelial cell volume, regulation of these water channels may permit manipulation of the contour of the vocal fold edge. As the contour of the vocal folds dictate such physiologic vocal measures as phonation threshold pressure, manipulation of this contour could lead to improvements in vocal fold oscillation.
Correspondence: Kimberly Fisher, PhD, Department of Communication Sciences and Disorders, Northwestern University, 2240 Campus Dr, Evanston, IL 60208 (firstname.lastname@example.org).
Submitted for Publication: August 16, 2005; final revision received June 3, 2006; accepted August 17, 2006.
Author Contributions: Drs Lodewycks and Fisher had full access to all the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis. Study concept and design: Lodewyck, Menco, and Fisher. Acquisition of data: Lodewyck and Menco. Analysis and interpretation of data: Lodewyck, Menco, and Fisher. Drafting of the manuscript: Lodewyck and Fisher. Critical revision of the manuscript for important intellectual content: Lodewyck, Menco, and Fisher. Statistical analysis: Lodewyck. Obtained funding: Fisher. Administrative, technical, and material support: Lodewyck and Fisher. Study supervision: Menco and Fisher.
Financial Disclosure: None reported.
Funding/Support: This work was supported by National Institute of Deafness and Other Communication Disorders Grant K230068 (Dr Fisher).
Previous Presentation: This study was presented at the third Biennial Conference on Vocal Fold Physiology and Biomechanics; September 13, 2002; Denver, Colo.
Acknowledgment: We thank Charles Larson, PhD, and Alvin Telser, PhD, for insightful discussions and Eugene Minner for able assistance.