A Biomechanical Model of Sagittal Tongue Bending

[+] Author and Article Information
Vitaly J. Napadow

Department of Health Sciences and Technology, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139

Roger D. Kamm, Richard J. Gilbert

Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139

J Biomech Eng 124(5), 547-556 (Sep 30, 2002) (10 pages) doi:10.1115/1.1503794 History: Received March 01, 2001; Revised June 01, 2002; Online September 30, 2002
Copyright © 2002 by ASME
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Grahic Jump Location
The phenomenon of anticlastic curvature arises from Poisson effects. When a beam is bent, the concave edge is under longitudinal compression, while the convex edge is under longitudinal tension. Poisson’s effect dictates that the contracted edge must expand orthogonally, while the edge under tension must contract orthogonally. This requirement creates a curvature (the anticlastic curvature) which is itself in a plane orthogonal to the plane of primary bending.
Grahic Jump Location
The spatial parameters used in the model were derived from either MRI images of the tongue, or from the Visible Human: Male database. (A) Coronal view MRI image (with tag lines superimposed) of the tongue depicting the width, b, of the tissue in the mid-anterior position, 32.6 mm. (B) Sagittal view MRI image of the tongue depicting the functional length (along its curvature) of the anterior tongue, 36.4 mm, and the composite height, h, 7.8 mm. (C) Sagittal view, cross-section of the muscular structure of the anterior tongue, derived from the Visible Human database, showing the relative composition percentage of the longitudinalis (25.8%) and transversus (74.2%) muscle layers.
Grahic Jump Location
The initial (A) and final (B) tongue curvatures were measured by fitting a circle to a set of points digitized along the approximate contour of the longitudinalis/transversus interface. The best-fit circle was derived by minimizing the rms error while varying circle location and radius. MRI images used were from the same subject.
Grahic Jump Location
Shown are the graphic representations of the 3D model of the tongue in the (A) initial configuration, (B) final configuration for longitudinalis only contraction, and (C) final configuration for synergistic longitudinalis and transversus muscle contraction. The initially concave-down bent beam was effectively straightened by longitudinalis muscle contraction, and achieved maximal bending with synergistic longitudinalis/transverses muscle contraction.
Grahic Jump Location
Modeled strain data (longitudinal strain, Exx; and through-plane strain, Ezz) for both contraction scenarios were computed and graphed versus location along the tongue cross-section. Empirical data points were plotted as circles on the same graph. The synergistic contraction scenario corresponded better to the empirical (Tagging MRI derived) data than did contraction of the longitudinalis muscle alone.
Grahic Jump Location
Sensitivity analysis of the equations involved in the model was completed by finding the effect induced on the computed curvature by varying a given model parameter. Model parameters were varied by ±10% and percentage effect on curvature was computed throughout. This analysis showed that curvature was most sensitive to α1 (the thermal expansion coefficient of the beam containing the superior longitudinalis muscle), and h2 (the height of beam the beam containing the transversus muscle).
Grahic Jump Location
The intrinsic musculature of the human tongue, as depicted by histological axial cross-section. The medial and lateral locations are shown. The longitudinalis m. runs along the tongue’s long axis; while the transversus m. (extending medial-laterally) and verticalis m. (extending inferior-superiorly) are seen in-plane in this figure. Approximate location through anterior tongue is visualized in the inset MRI sagittal image (upper right). [Image adapted from Gray’s Anatomy by Henry Gray. Crown Publishers, Inc., 1976.]
Grahic Jump Location
Analog model defined by two materials bonded together at an interface. The bimetal strip is initially concave-downward; each material is constitutively defined by its material properties and spatial dimensions (see Table 1). Upon contraction of the top material, the “bimetal strip” is subjected to the forces and moments defined on the schematic.



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