William Wan

Constitutive Modeling of Mouse Carotid Arteries Using Experimentally Measured Microstructural Parameters

Changes in the local mechanical environment and tissue mechanical properties affect the biological activity of cells and play a key role in a variety of diseases, such as cancer, arthritis, nephropathy, and cardiovascular disease. Constitutive relations have long been used to predict the local mechanical environment within biological tissues and to investigate the relationship between biological responses and mechanical stimuli. Recent constitutive relations for soft tissues consider both material and structural properties by incorporating parameters that describe microstructural organization, such as fiber distributions, fiber angles, fiber crimping, and constituent volume fractions. The recently developed technique of imaging the microstructure of a single artery as it undergoes multiple deformations provides quantitative structural data that can reduce the number of estimated parameters by using parameters that are truly experimentally intractable. Here, we employed nonlinear multiphoton microscopy to quantify collagen fiber organization in mouse carotid arteries and incorporated measured fiber distribution data into structurally motivated constitutive relations. Microscopy results demonstrate that collagen fibers deform in an affine manner over physiologically relevant deformations. The incorporation of measured fiber angle distributions into constitutive relations improves the models predictive accuracy and does not significantly reduce the goodness of fit. The use of measured structural parameters rather than estimated structural parameters promises to improve the predictive capabilities of the local mechanical environment, and to extend the utility of intravital imaging methods for estimating the mechanical behavior of tissues using in situ structural information.

Catalase overexpression in aortic smooth muscle prevents pathological mechanical changes underlying abdominal aortic aneurysm formation

The causality of the associations between cellular and mechanical mechanisms of abdominal aortic aneurysm (AAA) formation has not been completely defined. Because reactive oxygen species are established mediators of AAA growth and remodeling, our objective was to investigate oxidative stress-induced alterations in aortic biomechanics and microstructure during subclinical AAA development. We investigated the mechanisms of AAA in an angiotensin II (ANG II) infusion model of AAA in apolipoprotein E-deficient (apoE(-/-)) mice that overexpress catalase in vascular smooth muscle cells (apoE(-/-)xTg(SMC-Cat)). At baseline, aortas from apoE(-/-)xTg(SMC-Cat) exhibited increased stiffness and the microstructure was characterized by 50% more collagen content and less elastin fragmentation. ANG II treatment for 7 days in apoE(-/-) mice altered the transmural distribution of suprarenal aortic circumferential strain (quantified by opening angle, which increased from 130 ± 1° at baseline to 198 ± 8° after 7 days of ANG II treatment) without obvious changes in the aortic microstructure. No differences in aortic mechanical behavior or suprarenal opening angle were observed in apoE(-/-)xTg(SMC-Cat) after 7 days of ANG II treatment. These data suggest that at the earliest stages of AAA development H(2)O(2) is functionally important and is involved in the control of local variations in remodeling across the vessel wall. They further suggest that reduced elastin integrity at baseline may predispose the abdominal aorta to aneurysmal mechanical remodeling.

A 3-D constrained mixture model for mechanically mediated vascular growth and remodeling

In contrast to the widely applied approach to model soft tissue remodeling employing the concept of volumetric growth, microstructurally motivated models are capable of capturing many of the underlying mechanisms of growth and remodeling; i.e., the production, removal, and remodeling of individual constituents at different rates and to different extents. A 3-dimensional constrained mixture computational framework has been developed for vascular growth and remodeling, considering new, microstructurally motivated kinematics and constitutive equations and new stress and muscle activation mediated evolution equations. Our computational results for alterations in flow and pressure, using reasonable physiological values for rates of constituent growth and turnover, concur with findings in the literature. For example, for flow-induced remodeling, our simulations predict that, although the wall shear stress is restored completely, the circumferential stress is not restored employing realistic physiological rate parameters. Also, our simulations predict different levels of thickening on inner versus outer wall locations, as shown in numerous reports of pressure-induced remodeling. Whereas the simulations are meant to be illustrative, they serve to highlight the experimental data currently lacking to fully quantify mechanically mediated adaptations in the vasculature.

Theory and Experiments for Mechanically-Induced Remodeling of Tissue Engineered Blood Vessels

There is a great unmet clinical need to develop small diameter tissue engineered blood vessels (TEBV) with low thrombogenicity and immune response and suitable mechanical properties. In this paper we describe experimental and computational frameworks to characterize the use of mechanical stimuli to improve the mechanical properties of TEBVs. We model the TEBV as a constrained mixture and track the production, degradation, mechanical state, and organization of each structural constituent. Specifically, we assume that individual load bearing constituents can co-exist within each neighborhood and, although they are constrained to deform together, each constituent within this neighborhood may have different natural (i.e., stress-free) configurations. Motivated by this theoretical framework, we have designed a bioreactor and biomechanical testing device for TEBVs. This device is designed to provide precise and independent control of mean and cyclic luminal flow rate, transmural pressure, and axial load over weeks and months in culture and perform intermittent biaxial biomechanical tests. This device also fits under a two-photon laser scanning microscope for 3-dimenstional imaging of the content and organization of cells and matrix constituents. These data directly support our theoretical model.

Collagen Fiber Angle Quantification of Carotid Arteries From Fibulin-5 Null Mice

Recent studies have revealed that carotid arteries from fibulin-5 (fbln5) null mice exhibit altered biomechanical and microstructural properties [1–2]. While the previous studies outline quantitative differences in mechanical properties of arteries from fbln5 null and wildtype mice, physical microstructural differences have yet to be quantified. Measurement of microstructural parameters will provide a crucial link between previously quantified mechanical properties and biological effects of knocking out the fbln5 gene. Characterizing microstructural properties will also provide experimental data to validate structurally-motivated constitutive relations and growth and remodeling models [3–4]. In this study, we quantified collagen fiber orientation in carotid arteries from fbln5 null and wildtype mice; collagen in mouse carotid arteries were imaged using multiphoton microscopy and analyzed using a fast Fourier transform algorithm.© 2011 ASME

Microstructurally Motivated Constitutive Models for Mouse Arteries

Vascular remodeling occurs as cells sense changes in their mechanical environment. Thus, quantifying the cells’ local environment in terms of stress and strain distributions is an important aspect in studies of vascular remodeling. Knowledge of the constitutive behavior of vessel will allow the local stresses and strains to be calculated given applied loads and geometry. The goal of this study is to determine material parameters for several constitutive models by fitting biaxial testing data from mouse carotid arteries cultured under different axial loading conditions [1].Copyright

A 3-D Constrained Mixture Model for Vascular Growth and Remodeling

It is known that arteries adapt and remodel to changes in their loading conditions. Evolution of mechanical properties of blood vessels is associated with numerous chronic and acute conditions such as hypertension and coronary thrombosis. In addition, treatments such as bypass surgery create loading conditions not seen in normal arteries. Blood vessels used in coronary bypass grafts experience abnormal loading conditions in both circumferential and axial directions. Blood vessels remodel by altering structural components to restore homeostatic values of stress. Such changes may include smooth muscle cell proliferation, migration and collagen synthesis, degradation, and remodeling. While biaxial mechanical tests and organ culture experiments provide values for global variables such as mean stresses and total thickness, mathematical models can help describe local mechanical properties at locations throughout the vessel wall. Experimental observations suggest that constituents of arteries turnover at different rates; thus, it is important that models are able to track individual constituents of the artery separately. Here, we present a 3D constrained mixture model for growth and remodeling of arteries exposed to large changes in flow, pressure, and axial stretch -induced.Copyright

Biomechanical and Microstructural Properties of Fibulin-5 Null Mice

Fibulin-5 is an extracellular matrix (ECM) protein that interacts with integrins and plays a critical role in organizing elastic fibers. Gross observation and histological examination reveal that carotid arteries from fibulin-5 knockout (fib5-/-) mice have disrupted elastic lamellae and are more tortuous [1]. The properties of fibulin-5 null mice provide a unique platform for developing constituent based models for vascular mechanics. While numerous models for blood vessels exist, there is a need to relate measurable microstructural metrics of structurally-based constitutive relations. We performed mechanical tests on carotid arteries from wildtype (WT) and fib5-/-mice and imaged live vessels under multiple loading scenarios to quantify microstructure during deformation. We also fit experimental results to a constitutive relation based on Holzapfel’s model [2]. These results provide a basis for further model development.Copyright