Track 14. Cardiovascular Mechanics 14.13. Vascular Wall Mechanics -Ac t i ve Behavior of Arterial Walls $325

can estimate that the LL is valid for many biological vessels when TIR is less than -0.01. This criterion is rarely met. Furthermore to obtain true stiffness, only the part of the stress related to distension should be plotted against strain. Our aims were (1) to analyze the validity of the LL for application to biological vessels, and (2) to propose a replacement to the LL that is valid for plotting against strain to measure true stiffness. We solved exactly the model problem of an axisymmetric pressurized cylinder of arbitrary thickness, linearly elastic isotropic material without residual wall stress. Using geometry and parameters from physiological data for the GI tract and blood vessels, we analyzed the LL in detail. We developed a more accurate alternative and compared it to the LL. We find that the LL is not even approximately valid for GI applications, and many vascular applications, at all physical distensions. We also find that the way in which the LL is misused gives it qualitatively sensible behavior, but that, as used, can be in error by 40-80%. We derive a replacement to the LL that is almost as easy to apply as the LL itself and which corrects the 40-80% error when applied properly.

9998 Mo, 15:15-15:30 (P11) Biomechanics o f human carotid arteries: experimental testing and material model ing

G. Sommer 1 , P. Regitnig 2, G.A. Holzapfel 1,3. 1Royal Institute ef Technology (KTH), School of Engineering Sciences, Stockholm, Sweden, 2Medical University Graz, Institute of Pathology, Graz, Austria, 3 Graz University of Technology, Computational Biomechanics, Graz, Austria

The knowledge of blood vessel elasticity is of utmost importance in physiology and pathophysiology involving balloon angioplasty with or without stenting, surgery, tissue remodeling and tissue engineering. Arteries such as common carotid arteries (CCA) and internal carotid arteries (ICA) are of particular biomedical and clinical interest since they are prone to form atherosclerotic lesions which frequently undergo interventional treatments to prevent stroke. Since an artery is a heterogeneous structured composite consisting of three layers with different (visco)elastic properties, a thorough understanding of its mechanical behavior requires data on the mechanical response of each of the layers. In the present study we perform extension-inflation tests on tube specimens of intact human CCA and ICA, and, subsequently, on the corresponding adventitia and media-intima layers. In addition, we also perform uniaxial tension tests of strip specimens oriented in the circumferential and axial directions of the individual layers of the CCA and ICA; ultimate tensile stretches and stresses are also recorded. A comparative study of the individual tissue responses is presented and discussed. In order to describe the mechanical properties of the arterial wall and its individual layers, we used a recently proposed 3D hyperelastic constitutive model that is able to describe the typical nonlinear and anisotropic material response.

14.13.4. Active Behavior of Arterial Walls

4169 Mo, 16:00-16:30 (P13) Ventral-dorsal d i f ference in act ive contract i le response o f rabbit thoracic aortas: Correlat ion with local compl iance T. Matsumoto, T. Shirono, M. Ohoka, K. Nagayama. Biemech Lab, Dept Mech Engng, Nagoya Inst Tech, Nagoya, Japan

Difference in mechanical properties and smooth muscle (SM) contraction between ventral and dorsal sides was studied in rabbit thoracic aortas. Ventral- dorsal difference was observed by a longitudinal observation method (Sugita et al.: Trans JSME Ser A 69~77 , 43-48, 2003): Four small needles were stuck perpendicularly into the wall of excised aortic segment at equal intervals on a circumference. Displacement of the needles during pressurization and isobaric smooth muscle contraction at 80 mmHg induced with norepinephrine was observed in an aerated Krebs-Henseleit solution at 37°C in longitudinal direction with a CCD camera and laterally with two digital cameras placed in an opposite direction across the aorta. Images taken by the cameras were used to identify the point at penetration of each needle. Circumferential length between the penetration points was obtained assuming that the aortic segment had circular cross section. Circumferential stretch ratio at 120 mmHg in reference to dimensions at 40mmHg was significantly higher in ventral side (1.6±0.1, mean±SEM, n = 5)than in dorsal (1.3±0.1), indicating mechanical heterogene- ity in the circumferential direction. Norepinephrine-induced contraction was significantly higher in ventral side (25±4%) than in dorsal (17±3%). To study the difference in contractility at cellular level, SM cells were isolated from aortic tissue by enzymatic digestion. Norepinephrine-induced contraction was larger in the cells isolated from ventral tissue (46%) than from dorsal tissue (37%). Immunofluorescence analysis showed that the ventral cells were abundant in contractile proteins such as myosin heavy chain and actin filaments than the dorsal cells. Thoracic aortas are constrained with the vertebral column in dorsal side, while they are open to the thoracic cavity in ventral side. Such difference may cause ventral-dorsal difference in the mechanical properties.

The ventral cells may be exposed to higher cyclic strain during cardiac cycle than the dorsal cells due to higher compliance in ventral side. This may cause higher contractility of the ventral cells.

4388 Mo, 16:30-16:45 (P13) First approx imat ion o f the zero-stress state of arterial wall and contract ion o f SMC G.-Q. Wu 1 , L. Wang 2, J.-B. Xin 1 , W.-Z. Lin 1 . 1Department of Mechanics and Engineering Science, 2School of Life Science, Fudan University, Shanghai, China

Since residual strain and stress [1,2] were introduced into stress analysis of arterial wall, stress concentration effects have smoothened-out. However, it is still questionable if the open-up configuration represents the zero-stress state as evident by reports in [3-5], in which they showed that the layered opening angles are different with the larger angle in the inner layer. The discontinuity in circumferential stress, evaluated by the two-layered opening angles [4,6] has made the problem more complicated. Therefore, stress distributions on arterial wall remain a subject of further research. In this work, we found that the discontinuity of the circumferential stress resulted from existing residual stress in two angles even in open-up state. Thus, the initial arc lengths, which were stress-free, should be different from their apparent ones in the stress analysis. By modifying the stress-free condition through an iteration process, and matching both radial and circumferential strains at the interface of the two layers, we obtained a continuous and more uniform stress distribution. The result showed that the stress-free arc length of inner wall was longer, while that of outer wall was shorter than their apparent ones calculated from the opening angle. In this case, the opening angle of single layer can no longer be considered as the zero-stress state, but as a zeroth approximation, while the result of this work is named as the first approximation. To verify the difference between the real and apparent initial conditions, we digested smooth muscle cell (SMC) of bovine carotid artery selectively, layer-by-layer from the inner wall. It indicates that the contraction of SMC does influence the opening angle and the measurement of zero-stress state.

References [1] Vaishnav R.N., Vossoughi J., J. Biomech. 1987; 20: 235-239. [2] Chuong C.J., Fung Y.C., J. Biomech. Eng. 1986; 108: 189-192. [3] Vossoughi J., Hedjazi Z., and Borris FS., BioEngng. Conf. 1993; Breckenridge,

CO: ASME. [4] Stergiopulos N., Vulliemos S., Rachev A., et al. Vas. Res. 2001; 38: 237-246. [5] Matsumoto T., Sato M., JSME International Journal Series C 45 2002; (4): 906-

912. [6] Rachev, A, J. biomech. 1997; 30: 819427.

4803 Mo, 16:45-17:00 (P13) Tensegrity FE models of mechanical tests of individual cells J. Bursa, R. Lebis. Inst. of Solid Mechanics, Mechatronics and Biomechanics, Brae University of Technology, Brno, Czech Rep.

The paper deals with computational finite element modelling of various me- chanical tests carried out with individual cells. Our attention is focused on smooth muscle cells of the vascular wall. A changed loading of the vascular wall initiate a response of these cells in the form of tissue remodelation. The increased load is supposed to initiate exoskeleton stiffening with the aim to bring the cell load back to the physiological values. To understand these processes, it is necessary to know the mechanical properties of the cell and to model its mechanical behaviour. In our contribution FE models of an individual smooth muscle cell are presented, at various levels of the cell structure: a. Cell as a homogeneous isotropic hyperelastic continuum. b. Cell model consisting of nucleus, sarcoplasm, cortex (modelled by shell

elements on the cell surface) and endoskeleton (modelled as a simple tensegrity structure with 6 struts and 24 cables, all with linear elastic properties).

c. Cell model with a more complex tensegrity structure representing the endoskeleton. A model of endoskeleton containing 30 struts and 60 cables has been proposed and tested.

Simulation of tension tests and indentation tests (based on atomic force microscopy) using the above models will be presented in the paper. Attempts are made to identify the constitutive parameters of the models. In model a) an iterative identification of five parameters of the Mooney-Rivlin hyperelastic model was carried out. In models b) and c) the possibilities of identification of parameters are tested and the sensitivity of the results on the changes in elastic moduli of the individual components is investigated. Possibilities of creation of tensegrity models of the endoskeleton are also discussed.