Thread 1. Computational Methods in Biomechanics and Mechanobiology T1.2 Computational Biomechanics of Arteries in Health and Disease $401

was selected to describe the nonlinear material properties where parameters were chosen from published data. Results show that (1) the study is able to predict stress distributions on each components of plaque; (2) high stress more likely occurs at the shoulder regions of plaque, especially where the fibrous caps are thin; and (3) for the entire plaque, larger differences of stress and displacement between the planar and non-planar models can be found on the plaque regions near carotid bulb where the out of plane bending started.

5769 Mo, 17:15-17:30 (P14) A h isto logical ly based anisot rop ic model of the abdominal aortic aneurysm T.C. Gasser 1 , M. Landuyt 1,2, G. Sommer 1 , M. Auer 3, P. Verdonck 2, J. Swedenborg 4, G.A. Holzapfel 1,3. 1Royal Institute of Technology (KTH), School of Engineering Sciences, Stockholm, Sweden, 2Gent University, Department of Civil Engineering, Gent, Belgium, 3 Graz University of Technology, Computational Biomechanics, Schiesstattgasse 14-B, A-8010 Graz, Austria, 4Karolinska University Hospital, Department of Vascular Surgery, N1:06, SE-17176 Stockholm, Sweden

Abdominal aortic aneurysms (AAAs) are frequently observed pathological enlargements of the infrarenal aorta. Untreated AAAs eventually enlarge until they rupture; an event with mostly mortal consequences. The pathogenesis of AAA seems to be linked to a failed arterial adaptation mechanism, where proteolytic degeneration of structural proteins collagen and elastin causes a continuous (instable) alteration of the arterial wall [1]. This study presents a novel histologically motivated finite element model of the AAA, which provides a powerful tool to probe mechanobiological aspects of these formations. The model's geometry is based on a 3D reconstruction of clinical imaging data and the constitutive description of the tissue accounts for the complex arrangement of collagen and elastin in the arterial wall. In particular, the histological distribution of the embedded collagen fibers is captured by the introduction of generalized structural tensors [2], and standard invariant theory is applied to formulate an anisotropic hyperelastic potential of the AAA wall. Hence, the constitutive model reflects the formation's histology, and captures its anisotropic mechanical property [3]. In that regard our finite element model states a further development of numerical AAA models currently available in the literature, where phenomenological and isotropic constitutive laws characterize the wall [4]. The work is a first step towards the implementation of a quanti- tative computer-based information framework to integrate mechanobiological theories for testing hypotheses of human AAA pathogenesis.

References [1] E. Choke et al. Eur. J. Vasc. Endovasc. Surg. 2005; 30: 227-244. [2] T.C. Gasser et al. J. R Soc. Interface 2006; 3. [3] J.P. Vande Geest et al. J. Biomech., in press. [4] D.A. Vorp, J.P. Vande Geest. Arterioscler. Thromb. Vasc. Biol. 2005; 25: 1558-

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4353 Tu, 08:15-08:30 (P17) Hybrid approach to the global circulation model ing A.S. Kholodov, S.S. Simakov. Department of Applied Mathematics, Moscow Institute of Physics and Technology, Moscow, Russia

It is hard to overestimate the role of the blood flow for every living organism. Particularly the global processes are of special interest for many applications in physiology and medicine. It is implied that such processes include feedbacks and interdependences among different regions of the organism. Some of the most characteristic examples are the loss of blood and matter transport within the whole organism. The models that allow to consider such global processes are rarely caught in modern literature. In this connection several approaches were proposed [1,2] dealing with blood flow in the heart, large vessels and capillary network. They based on the models of averaged by volume flow through the set of extensible spherical chambers, non-stationary flow of incompressible fluid through the network of elastic tubes and liquid filtration through the porous medium correspondingly. These models were combined into one closed model of the global circulation [3]. Since that time the model was improved by specifying more detailed structure of the vascular trees. Especially important are the specializations of such organs as stomach, liver, bowels, kidneys that were earlier considered as virtual vessels with averaged parameters. Vascular networks supplying muscular tissues were also improved. As a result several simulations were carried out that on the one hand validates proposed approach an on the other hand giving several interesting results attractive for some practical applications in oncology and ophthalmology.

References [1] Kholodov A.S. Some dynamical models of external breathing and blood circu-

lation regarding to their interaction and substances transfer. In: Computational Models and Medical Progress. 2001, Nauka, Moscow, pp. 127-163.

[2] Evdokimov A.V., Kholodov A.S. Pseudo-steady spatially distributed model of human circulation. In: Computational Models and Medical Progress. 2001, Nauka, Moscow, pp. 164-193.

[3] Simakov, S.S., Kholodov A.S., Evdokimov A.V., Kholodov Y.A.. Matter transport simulations using 2D model of peripheral circulation coupled with the model of large vessels. In: Proceedings of II International Conference on Computational Bioengineering, H. Rodrigues et al. (Eds.). 2005; IST Press, Vol. 1, pp. 479-490.

4876 Tu, 08:30-08:45 (P17) Multi-scale oxygen d i f fus ion and t ranspor t in the cerebral micro- vasculature C. Hadjistassou, K. Moyle, '~1 Ventikos. F/uidics and Biocomp/exity Group & Institute of Biomedical Engineering, Dept. of Engineering Science, University of Oxford, UK

Although fMRI is based on the Blood Oxygenation Level Dependent effect, the physiological mechanism giving rise to BOLD is currently incompletely understood. With the prospect of elucidating the BOLD effect, we consider the multi-scale efflux of oxygen from capillary erythrocytes into plasma and eventually into cerebral tissue. We address the multi-scalar nature of the problem (diffusion/dissociation scale - erythrocyte scale - capillary/system scale) by considering transport at the cell level and also at the capillary level. For the latter, we map oxygen transport through an idealised cerebral capillary, measuring 8~tm in diameter by 160~tm in length, surrounded by a coaxial tissue compartment 25 ~tm in thickness. At this scale, oxygen diffuses from the vessel, which is subdivided into a plasma stratum and an RBC zone, into the neuron region. Oxyhaemoglobin, deoxyhaemoglobin and oxygen are tracked along with flow for the determination of extraction rate variations under neuron inactivity-to-activity transitions. On the other hand, microscopic modelling deals with oxygen flux from a single (or up to three) erythrocyte into the plasma and subsequently the tissue. A single file of equidistantly arranged erythrocytes, which measure 7.2~tm by 3.25 ~tm and with a distinct and separate membrane layer 20 nm in thickness, is studied. We show that the cascade of oxygen from erythrocytes to neurons is respon- sive even to minute changes in oxygen tension in the tissue. Macroscopically, both the radial and axial oxygen transport rate and magnitude decrease in an exponential fashion as oxygen is advected downstream. Microscopically, we demonstrate coupling of erythrocyte shape deformation (estimated by solving the relevant fluid-structure interaction problem) with the oxygen diffusion process and the haemoglobin-oxygen dissociation process.

5328 Tu, 08:45-09:00 (P17) Effects of local geometry on the fluid dynamics of coronary artery segments with implanted stents S. Vigmostad 1 , A. Wahle 2, M.E. Olszewski 2, J.D. Rossen 3, M. Sonka 2, K.B. Chandran 1 . 1Department of Biomedical Engineering, 2Department of Electrical and Computer Engineering3 Department of Internal Medicine, The University of Iowa, USA

Coronary artery disease (CAD) is the leading cause of death in industrialized nations. Intervention for atherosclerotic plaques resulting from CAD typically consists of angioplasty followed by stent implantation. Approximately 20 to 30 percent of these patients suffer from restenosis. Low wall shear stresses and recirculation have been suggested as possible causes. A computational fluid dynamic (CFD) analysis was performed to assess the effects of stent placement on coronary geometry and hemodynamics. Fusion of intravascular ultrasound and angiographic images from 15 patients before and after stent placement yielded 3D reconstructions of coronary artery segments for the CFD analysis. Geometric and hemodynamic parameters, including curvature, torsion, wall shear stress, and local cross-sectional area, were examined before and after intervention. In several stented segments, low wall shear stress was present in the distal region of the stent, a common location of restenosis. Higher cross-sectional areas, possibly resulting from post-stenotic dilatation, were associated with the distal regions of these stents, indicating that restenosis risk may be readily identifiable after stent placement. Significant increases in curvature and torsion were also observed in all 15 patients after stent placement. The effects of stent placement on geometric parameters, such as curvature and torsion, are important because of their impact on hemodynamics and mass transport in the coronary arteries, and warrant further investigation.