A Nonlinear Incompressible Model of the Human Tongue
Dr. William Levine, Professor
Dr. William Levine
The human tongue is important to the production of intelligible speech, to maintaining an airway during breathing, to swallowing, and to the processing of food in the mouth. An understanding of the tongue’s dynamics and control would be very helpful to those who would like to understand speech production, those who surgically treat macroglossia, and in some approaches to treating sleep apnea. The biomechanics of the tongue is unusual. There is no rigid structure, such as bone, in the tongue. This makes it one of a small group of biomechanical systems—other examples are the squid’s tentacles and the elephant’s trunk—known as muscular hydrostats. The rich collection of movements of these systems results from the interaction of actively contracting muscles with the incompressibility of the overall structure. Note also that, in the case of speech, it is the shape of the tongue that is important.
There have been many efforts to develop a computer model of the tongue’s dynamics. They all begin approximating the tongue by a technique known as finite elements. This amounts to assuming the tongue is made up of tiny masses interconnected by springs. Mathematical questions have been largely ignored. One of the novel features of our work is the creation of a genuine mathematical model of the tongue. This enables us to at least ask whether the finite element approximation might converge in the limit as the elements are made smaller and smaller.
Our model takes the form of a partial differential equation. This equation incorporates the biomechanical features of the tongue, including the individual muscles with their elastic behavior. This system is controlled by adjusting a group of functions that describe how the brain influences the activation of individual muscles. One question that greatly interests us is how much control the brain has over muscle activation. To answer this we have been collecting data on the tongue shape as people speak and computing the activations needed to produce these shapes under different assumptions about the amount of control available.
Figure 1 (above, left): One frame from an untagged cine MRI sequence of images of the mid-sagittal plane of a human head during normal speech. The image is black where there is bone or air. The tongue is the large blob in the middle of the frame. The speaker is saying "aaaaoooo" and the image is from the first frame of the sequence.
One of our results is illustrated in Figure 2 (below). The finite elements of the original position of the tongue are shown with dots at the vertices. The corresponding elements after displacement as determined from an MRI image of a person speaking are shown with x’s at the corners. The elements that correspond to the best possible approximation to what actually happens when we can use only one control per muscle are shown as the “inverse solution.”
Investigators: William S. Levine, Caroline Essex-Torcaso, Maureen L. Stone*, Emi Z. Murano, Jerry L. Prince, Vijay Parthasarathy, and Wei Tian
Source of funding: The University of Maryland Dental School as a subcontract on an NIH grant to Maureen L. Stone
More information can be found at the web site: http://www.siam.org/pdf/news/914.pdf.
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