$326 Journal o f Biomechanics 2006, Vol. 39 (Suppl 1)

5567 Mo, 17:00-17:15 (P13) The mechanics o f arter ies including smooth muscle contract ion

J. St~lhand 1 , A. Klarbring 1 , G.A. Holzapfel 2 . 1LinkSping University, LinkSping, Sweden, 2Royal Institute of Technology, Stockholm, Sweden

Active contraction of smooth muscles in soft biological tissues has a significant influence on the function and the mechanical properties, in particular for arteries. With a few exceptions, however, active contraction is rarely included in mechanical models, and studies are mainly restricted to passive character- istics. This study proposes an extended method that also accounts for active smooth muscle contraction in the arterial wall. The method includes a three- dimensional, continuum mechanical model of the smooth muscle contraction regulated by the intracellular Ca 2÷ concentration. Briefly, the model utilizes a multiplicative decomposition of the deformation gradient where one part is related to the residual stress and the other to the elastic deformation caused by the applied load. The passive stress in the non- contracting arterial constituents (collagen and elastin) is then computed using a strain-energy derivative, as is customary for nonlinear arterial models. The active contraction in the smooth muscles is modelled by two components: a biochemical model and a constitutive relation. The biochemical model relates the intracellular Ca2÷-concentratrion to the fraction of cycling and latch cross- bridges via a kinetic model for the interaction between actin (thin filament) and myosin (thick filament) proposed by Hai and Murphy (1988). The latch state represents a steady-state stress maintenance at low energy consumption found in smooth muscles and is thought to be related to a dephosphorylation of the myosin while the cross-bridges are still attached to actin. The constitutive relation accounts for the chemo-mechanical coupling by treating the filaments as rigid structures and postulating the active stress to be proportional to the sum of the phosphorylated and latch cross-bridges. It also reflects the stretch dependent variation in the active stress originating from filament overlap.

References Hai C.-M., Murphy R.A. (1988). Cross-bridge phosphorylation and regulation of

latch state in smooth muscle. Am. J. Physiol. 254: C99-C106.

6588 Mo, 17:15-17:30 (P13) A structural model for the arterial wall including sc leroprote in and vascular smooth mucle interact ion S. Roy, D. Miteva, G. Prod'horn, P. Silacci, N. Stergiopulos. Ecole Polytechnique F~d6rale de Lausanne, Hemodynamics and Cardiovascular Technology Laboratory, Lausanne, Switzerland

The three-dimensional biomechanical behavior of the vascular wall is best described by means of strain energy functions, which allow for the analysis of stresses over a wide range of deformations. We have earlier developed appropriate strain energy functions for the arterial wall [1]. The Zulliger et al. model uses a strain energy function, which accounts for the constituents and structural properties of the wall (i.e., collagen, elastin and vascular smooth muscle cell content as well as a statistical description for collagen engage- ment). The Zulliger et al. model was subsequently challenged by the work of Roy et al. [2], which showed that significant residual stresses are released when the arterial wall is decellularized, suggesting an in-series arrangement of the VSM with elastin. The in-series elastin would be in tension, whereas the in-parallel elastin would be in compression. Upon VSM disruption, the in- series elastin cannot bear tension anymore and thus the compressed elastin expands relieving the additional residual strains [2]. We have further studied the Roy et al. concept by examining the pressure- diameter curves obtained by destroying the VSM cytoskeleton by adding 10 -5 M Cytochalassin D (CCD). Six porcine carotids were treated with a strong dose of 10 -1 M sodium nitroprusside (SNP) to neutralize the vascular smooth muscle cells and Cytochalassin D and submitted to in vitro pressure-inflation testing. Results were compared to six arterial segments treated only with SNP and which were taken as controls (CTL). Compliance and incremental elastic modulus were derived. Results revealed no significant differences in pressure-diameter, compliance-pressure and elastic modulus-strain curves between the two groups. This suggests that, from a biomechanical standpoint, destruction of the cytoskeleton does not produce any further changes in the biomechanical properties of the arterial wall when the contractile machinery within the vascular smooth muscle cells is completely disengaged.

References [1] Zulliger MA, Fridez P, Hayashi K, Stergiopulos N. A strain energy function for

arteries accounting for wall composition and structure. J. Biomech. 2004; 37: 989-1000.

[2] Roy S, Silacci P, Stergiopulos N. Biomechanical properties of decellularized porcine common carotid arteries. Am. J. Physiol. Heart Circ. Physiol. 2005; 289: H1567-1576.

Oral Presentations

14.13.5. Mechanobiology of Aneurysms

4291 Tu, 14:00-14:30 (P22) Growth and stabi l i ty o f cerebral aneurysms J.D. Humphrey, S. Baek, K.R. Rajagopal. Biomedical and Mechanical Engineering, Texas A&M University, College Station, TX, USA

An intracranial aneurysm is a focal dilatation of the arterial wall that occurs in or near the circle of Willis, the primary network of arteries that supply the brain. The precise mechanisms by which these aneurysms develop, enlarge, and rupture remain unknown, but it is widely accepted that there is an early loss of intramural elastin, a concomitant loss of smooth muscle cells, and a dynamic remodeling of remnant collagen to reinforce the lesion as it thins and enlarges. We submit that the production, removal, and organization of aneurysmal collagen by (myo)fibroblasts is driven largely by dynamic changes in the biaxial intramural stress field and perhaps endothelial wall shear stress. Herein we develop a general theoretical framework that accounts for these correlates of growth and remodeling and that allows us to test consequences of competing hypotheses against available human data. One such hypothesis is that an initial insult (loss of elastin) perturbs the biaxial stresses in the wall from homeostatic values, and enlargement tends to restore these stresses toward homeostatic values. Whereas restoration of stresses to homeostatic values yields a stable lesion (note: most saccular aneurysms appear to be stable over long periods), deleterious effects of disturbed flows and low wall shear stress promote monocyte attachment and either increased protease activity or atherosclerosis, each of which can destabilize the lesion and thereby increase rupture potential. There is a pressing need to develop and explore such hypotheses, which can be done only by combining biofluid and biosolid mechanics with cell biology via models that include the kinetics of growth and remodeling. For illustrative purposes, we consider here an idealized (axisymmetric) fusiform aneurysm similar to those found on the basilar artery in patients and illustrate salient features of the wall biomechanics via finite element based simulations of stable and unstable enlargement.

6997 Tu, 14:30-14:45 (P22) A mult i -mechanism model for aneurysm wall en largement and remodel ing

R. Wulandana 1 , A.M. Robertson 2 . 1Department of Biomedical Engineering, Georgia Tech/Emory University, Atlanta, GA, USA, 2Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA, USA

Intracranial aneurysms (ICA) are saccular enlargements of cerebral arteries, most commonly found at apices of arterial bifurcations. ICA development is accompanied by morphological changes of vascular wall components. Elastin, which is normally present in the arterial walls, is fragmented and even missing in aneurysm walls. The collagen content of aneurysm walls shows changes in the distribution of collagen types and an increase in immature collagen. These changes are hypothesized to be due to elevated collagen degradation that is not properly balanced by regeneration and synthesis of new collagen. We previously presented a dual mechanism constitutive equation for early stage aneurysm development [1]. Arterial collagen and elastin were treated as two separate mechanisms, making it possible to model collagen recruitment and elastin failure. Using this constitutive equation we were able to predict thinning at the fundus, collagen recruitment and spatially inhomogeneous elastin fragmentation during aneurysm development [2]. To capture the growth and remodeling found in later stages of aneurysm development, we have extended the dual mechanism model to include a third mechanism representing aneurysmal collagen. The new collagen fibers are assumed to be laid down at varying configurations. In this work, we model further aneurysm development as inflation of a spherical membrane composed of a three mechanism model. Attention is given to the competition between arterial collagen degradation and synthesis of aneurysmal collagen in regulating growth and stabilizing the wall. Effects of low wall shear stress and risk factors such as smoking and alcohol intakes can be incorporated in the model through functional dependence of the collagen degradation rates on these factors.

References [1] Wulandana R, Robertson AM, A Multi-Mechanism Constitutive Model for the

Development of Cerebral Aneurysms. Biomech Modeling Mechanobiol. 2005; 4(4): pp. 235-248.

[2] Wulandana R, Robertson AM, A Model of Early Stage Aneurysm Development Based on an Inelastic Multi-Mechanism Constitutive Model. Proceedings of the ASME Summer Bioengineering Conference, Utah, 2001.