Thread 1. Computational Methods in Biomechanics and Mechanobiology T1.16 Computational Methods for Modeling of Hearing $433

and basilar arteries. Approximately, 50% of the population have incomplete COW. If there is shortage in blood supply due to certain pathological conditions such as occlusion or stenosis in one or more supplying arteries, stroke-like symptoms can result in an individual with incomplete COW. A 1-D mathematical model of the COW has been created and is being developed into a clinical tool to recognize stroke causes and at-risk patients and to gain more insight on how the brain regulates its own blood supply [1]. This model captures autoregulation mechanism using a dynamic controller. Autoregulation is a process maintaining constant supply of oxygenated blood irrespective of pressure variations via vasoconstriction and vasodilation of smooth muscle cells surrounding arterioles downstream of COW. As oxygen concentration plays an important role in determining how much blood is delivered to the brain, oxygen extraction algorithm is implemented in the model. Under normal conditions, oxygen extraction from blood is low as the amount of oxygen exceeds the demand required by cerebral mass. However, when the arterial pressure drops below the lower limit of autoregulation, oxygen extraction increases [2]. The flowrate through the COW encounters energy losses due the existence of several areas of bifurcations. These losses are implemented as they have great affects on the delivery of blood to the brain.

References [1] S.M. Moore, K.T. Moorhead, J.G. Chase, T. David, J. Fink. One-dimensional and

three-dimensional models of cerebrovascular flow. Journal of Biomechanical Engineering 2005; 127: 440-449.

[2] W.J. Thoman, J. Aa, S. Lampotang. Autoregulation in a simulator-based eu- cational model of intracranial physiology. Journal of Clinical Monitoring and Computing 1991; 15: 481-491.

5917 Mo, 15:15-15:30 ( P l l ) Stenting for the treatment of cerebral aneurysm

H. Meng 1,2,3, M. Kim 1,2, Y. Hoi 1,2, D. Taulbee 2, S. Woodward 1,2, L. Nelson Hopkins 1,3. 1 Toshiba Stroke Research Center, 2Department of Mechanical

3 and Aerospace Engineering Department of Neurosurgery, State University of New York at Buffalo, Buffalo, USA

The introduction of vascular stents to treating cerebral aneurysms has opened the possibility to thrombotic occlusion of aneurysms through stent placement alone. Few studies have explored the fact that stenting in realistic cerebral aneurysms depends on both the stent design and the aneurysm anatomy [1,2]. To this end, we investigate the effects of stent design on hemodynamics of aneurysms located on various curved vessels as well as patient-specific aneurysms through Computational Fluid Dynamics (CFD). First, we show with both experiments and CFD that stenting effect is sig- nificantly influenced by the local parent vessel geometry. With increasing vessel curvature, the stent effectiveness in creating a thrombogenic disturbed flow drastically decreases. Next, we compare different commercial stents of complex strut pattern designs in varying vessel geometries. The computational models fully resolve the three-dimensional stent patterns and provide detailed flow modification by specific stent designs. For low-porosity patches used in our asymmetric stents, we model the mesh by specifying a resistance layer across the aneurysm neck. This modeling technique allows us to incorporate simple computational meshes, which sig- nificantly reduces the computational costs, and allows us to explore multiple types of stents. We have further developed patient-specific asymmetric stents that aim at pro- tecting the aneurysm from impinging flow while maintaining the parent artery and perforators patent. Simulation results are compared with angiography. We suggest that each type of stent should be carefully evaluated in various types of aneurysm geometry in order to achieve desirable outcome. For biological response, we consider not only the stents' role in causing thrombosis in the aneurysm sac, but also in the reduction in hemodynamic stresses, and thus possibly the prevention of further growth, re-growth and rupture of aneurysms.

References [1] Cebral J.R., Rainald L. IEEE Trans. Med. Imaging 2004; 24(4): 468-476. [2] Imbesi S.G., Kerber C.W. AJNR Am. J. Neuroradiol. 2001; 22: 721-724.

T1.16 Computational Methods for Modeling of Hearing 7535 Mo, 11:00-11:30 (P9) Radial profile of the basilar membrane in a coiled cochlea: Results and biological implications

D. Manoussaki 1, E.K. Dimitriadis 2, R.S. Chadwick 3. 1Department ef Mathematics, Vanderbilt University, Nashville, TN, USA, 2Division of Bioengineering & Physical Science, ORS/OD, NIH, Bethesda, MD, USA, 3Section on Auditory Mechanics, NIDCD, NIH, Bethesda, MD, USA

While, for many years, it had been postulated that the cochlea was coiled in order to conserve space inside the skull, we propose that the spiral shape has functional significance: It redistributes wave energy propagation pathways, and,

by a mechanism similar to that of the "whispering gallery", it focuses energy density towards the outer wall of the cochlear spiral. Increased energy density results in increased basilar membrane movement near the outside wall of the cochlea. At the same time, we predict that the amplitude of basilar membrane movement decreases near the inside wall. We recently suggested [1] that this change in amplitude results in radial shearing modes that stimulate the neurosensory hair cells in the organ of Corti. The effect is greater, the smaller the radius of curvature is, towards the apical end of the spiral, where low frequency sounds are processed. Our result involved a number of simplifications, inherent in the impedance model. With our current work we discuss the effect of these simplifications on the mechanics of the cochlea and suggest model extensions. By combining analytical and computational methodologies, we calculate the radial profile of the basilar membrane, and we discuss the biological implications of our results.

References [1] D. Manoussaki, E.K. Dimitriadis, R.S. Chadwick. The cochlea's graded curvature

effect on low frequency waves. Physical Review Letters 2006; to appear.

5424 Mo, 11:30-11:45 (P9) Middle ear acoustico-mechanical interactions using a multifrequency finite element approach

J.P. Tuck-Lee 1 , P.M. Pinsky 1 , S. Puria 1,2. 1Department ef Mechanical Engineering, Stanford University, Stanford, CA, USA, 2Department of Otolaryngology-Head and Neck Surgery, Stanford University, Stanford, CA, USA

Coupled models of the eardrum and middle ear cavities may be used to study structure and functional relationships of the middle ear and are also useful for surgical planning. Physics-based models require accurate representation of anatomical features and must provide resolution of vibrational responses over the physiological frequency range. In this work we describe an approach to modeling the middle ear that addresses the need for accurate geometry through ~tCT imaging, a new constitutive model for the eardrum based on the collagen fiber microstructure, and a computationally efficient solution algorithm for the resulting coupled problem. A direct finite element solution of the coupled middle ear problem over the physiological frequency range is impractical because resolution requirements lead to very large systems which require solution over many frequencies. A reduced-order model is introduced based on a Pade approximation of the system matrix about a reference frequency using an unsymmetric block Lanczos algorithm. The resulting model provides highly efficient multifrequency solutions over a frequency window for a selected sample point. An error-based frequency windowing approach is used to cover the desired frequency range. The reduced-order finite element model of the eardrum and middle ear cavities of the domestic cat is evaluated over the 50 Hz to 50 kHz frequency range. 3D reconstruction from ~tCT imaging of the isolated middle ear anatomy from a dissected cadaver specimen provides the necessary anatomical resolution. The microstructure of the eardrum, composed of two prestressed layers of aligned collagen fibers, is incorporated into a nonlinear constitutive model. A rank update modification to the multifrequency algorithm allows for the treatment of complex frequency-dependent impedances which arise from modeling ossicular and cochlear loading at the umbo. The model is verified against experimental data, and used to simulate myringotomy procedures of the eardrum and explore the role of the septum that divides the cat middle ear cavity into two.

7010 Mo, 11:45-12:00 (P9) Modeling cochlea using mixed finite element formulations

X.S. Wang. Department of Mathematical Sciences, New Jersey Institute ef Technology, University Heights, Newark, N J, USA

In linear acoustoelastic analysis, it has been widely reported that the displacement-based fluid elements employed in frequency or dynamic anal- yses exhibit spurious non-zero frequency circulation modes. Various ap- proaches have been introduced to obtain improved formulations, including a 4-node element based on a reduced integration technique, the displacement potential and pressure formulation, and the velocity potential formulation. The mixed displacement/pressure finite element formulation originally proposed by Wang and Bathe in 1997 has been proven to be reliable and free of spurious nonzero frequencies. A recent mathematical study of this formulation was also published in Bao, Wang and Bathe, 2001. In this paper, mixed finite element formulations are extended to the study of cochlea, in particular, the resonant frequency of the enclosed cavity with different geometries. In essence, immersed flexible structures with and without opening are compared at different physical parameters such as variable thickness, fluid and solid densities.