Importance of initial aortic properties on the evolving regional anisotropy, stiffness and wall thickness of human abdominal aortic aneurysms

Complementary advances in medical imaging, vascular biology and biomechanics promise to enable computational modelling of abdominal aortic aneurysms to play increasingly important roles in clinical decision processes. Using a finite-element-based growth and remodelling model of evolving aneurysm geometry and material properties, we show that regional variations in material anisotropy, stiffness and wall thickness should be expected to arise naturally and thus should be included in analyses of aneurysmal enlargement or wall stress. In addition, by initiating the model from best-fit material parameters estimated for non-aneurysmal aortas from different subjects, we show that the initial state of the aorta may influence strongly the subsequent rate of enlargement, wall thickness, mechanical behaviour and thus stress in the lesion. We submit, therefore, that clinically reliable modelling of the enlargement and overall rupture-potential of aneurysms may require both a better understanding of the mechanobiological processes that govern the evolution of these lesions and new methods of determining the patient-specific state of the pre-aneurysmal aorta (or correlation to currently unaffected portions thereof) through knowledge of demographics, comorbidities, lifestyle, genetics and future non-invasive or minimally invasive tests.

Mechanics, mechanobiology, and modeling of human abdominal aorta and aneurysms

Biomechanical factors play fundamental roles in the natural history of abdominal aortic aneurysms (AAAs) and their responses to treatment. Advances during the past two decades have increased our understanding of the mechanics and biology of the human abdominal aorta and AAAs, yet there remains a pressing need for considerable new data and resulting patient-specific computational models that can better describe the current status of a lesion and better predict the evolution of lesion geometry, composition, and material properties and thereby improve interventional planning. In this paper, we briefly review data on the structure and function of the human abdominal aorta and aneurysmal wall, past models of the mechanics, and recent growth and remodeling models. We conclude by identifying open problems that we hope will motivate studies to improve our computational modeling and thus general understanding of AAAs.

On a Class of Admissible Constitutive Behaviors in Free-Floating Engineered Tissues

A commonly used assay for studying cell - matrix interactions is the free-floating fibroblast populated collagen lattice, which was introduced in 1979. Briefly, fibroblasts are seeded within an initially thin, amorphous, untethered, circular gel consisting of reconstituted fibrillar collagen. Although the gel remains traction free and circular, the cells typically contract the gel to less than 50% of its original diameter within hours to days. Cellular mechanotransduction mechanisms are fundamental to this contraction, but there has not been a careful study of the associated mechanics. In this paper, we model the initial contraction of a circular gel by assuming a homogeneous, axisymmetric finite deformation while allowing possible radial variations in material properties, including material symmetry. We show that trivial solutions alone (i.e., no deformation, no contraction) are admitted by equilibrium and boundary conditions unless radial variations exist in the material behavior, including cell contraction. Although more complete data are needed to model better this initial-boundary value problem, the present results are consistent with both the salient features of the gel assay and recent observations reported in the literature that cells often introduce regional variations in tissue properties in vivo in an attempt to achieve, maintain, or restore mechanical homeostasis.

Acute mechanical effects of elastase on the infrarenal mouse aorta: implications for models of aneurysms

Intraluminal exposure of the infrarenal aorta to porcine pancreatic elastase represents one of the most commonly used experimental models of the development and progression of abdominal aortic aneurysms. Morphological and histological effects of elastase on the aortic wall have been well documented in multiple rodent models, but there has been little attention to the associated effects on mechanical properties. In this paper, we present the first biaxial mechanical data on, and associated nonlinear constitutive descriptors of, the effects of elastase on the infrarenal aorta in mice. Quantification of the dramatic, acute effects of elastase on wall behavior in vitro is an essential first step toward understanding the growth and remodeling of aneurysms in vivo, which depends on both the initial changes in the mechanics and the subsequent inflammation-mediated turnover of cells and extracellular matrix that contributes to the evolving mechanics.

Evolving biaxial mechanical properties of mouse carotid arteries in hypertension

Quantifying the time course of load-induced changes in arterial wall geometry, microstructure, and properties is fundamental to developing mathematical models of growth and remodeling. Arteries adapt to altered pressure and flow by modifying wall thickness, inner diameter, and axial length via marked cell and matrix turnover. To estimate particular biomaterial implications of such adaptations, we used a 4-fiber family constitutive relation to quantify passive biaxial mechanical behaviors of mouse carotid arteries 0 (control), 7-10, 10-14, or 35-56 days after an aortic arch banding surgery that increased pulse pressure and pulsatile flow in the right carotid artery. In vivo circumferential and axial stretches at mean arterial pressure were, for example, 11% and 26% lower, respectively, in hypertensive carotids 35-56 days after banding than in normotensive controls; this finding is consistent with observations that hypertension decreases distensibility. Interestingly, the strain energy W stored in the carotids at individual in vivo conditions was also less in hypertensive compared with normotensive carotids. For example, at 35-56 days after banding, W was 24%, 39%, and 47% of normal values at diastolic, mean, and systolic pressures, respectively. The energy stored during the cardiac cycle, W(sys)-W(dias), also tended to be less, but this reduction did not reach significance. When computed at normal in vivo values of biaxial stretch, however, W was well above normal for the hypertensive carotids. This net increase resulted from an overall increase in the collagen-related anisotropic contribution to W despite a decrease in the elastin-related isotropic contribution. The latter was consistent with observed decreases in the mass fraction of elastin.

Regional atherosclerotic plaque properties in ApoE-/- mice quantified by atomic force, immunofluorescence, and light microscopy

Elucidating regional material properties of arterial tissue is fundamental to predicting transmural stresses and understanding how tissue stiffness influences cellular responses and vice versa. Atomic force microscopy (AFM) was used to measure point-wise the axial compressive stiffness of healthy aortas and atherosclerotic plaques at micron level separation distances. Cross sections of plaques were obtained from a widely used animal model of atherosclerosis (ApoE-/- mice). Median point-wise values of material stiffness were 18.7 and 1.5 kPa for the unloaded healthy wall (n = 25 specimens) and plaque (n = 18), respectively. When the healthy wall was distended uniformly during AFM testing, two mechanically distinct populations emerged from comparisons of normal cumulative distributions, with median values of 9.8 and 76.7 kPa (n = 16). The higher values of stiffness may have been due to extended elastin, which was not present in the plaques. Rather, most plaques were identified via standard and immunofluorescent histology to be largely lipid laden, and they exhibited a nearly homogeneous linear elastic behavior over the small AFM indentations. Understanding the mechanics and mechanobiological factors involved in lesion development and remodeling could lead to better treatments for those lesions that are vulnerable to rupture.

Mechanical properties of suprarenal and infrarenal abdominal aorta: implications for mouse models of aneurysms

Multiple mouse models have been developed to increase our understanding of the natural history of abdominal aortic aneurysms. An advantage of such models is that one can quantify the time course of changes in geometry, histology, cell biology, and mechanics as a lesion develops. One of the most commonly used mouse models yields lesions in the suprarenal abdominal aorta whereas most other models target the infrarenal abdominal aorta, consistent with the clinical observation that nearly all abdominal aneurysms in humans occur in the infrarenal aorta. Understanding reasons for similarities and differences between diverse mouse models and human lesions may provide increased insight that would not be possible studying a single situation alone. Toward this end, however, we must first compare directly the native structure and properties of these two portions of the abdominal aorta in the mouse. In this paper, we present the first biaxial mechanical data and nonlinear constitutive descriptors for the suprarenal and infrarenal aorta in mice, which reveals only subtle mechanical differences despite marked morphological and histological differences. Such data promise to increase our ability to understand and model the natural history of these deadly lesions.

Novel optical system for in vitro quantification of full surface strain fields in small arteries: II. Correction for refraction and illustrative results

In a companion paper, we described a theoretical foundation for and initial experimental implementation of a novel stereo-digital image correlation (DIC) method for quantifying the size, shape and deformation of small cylindrical specimens along their full length and around their entire circumference. In this paper, we further show that this panoramic-DIC method can be used to study mouse carotid arteries without affecting their native mechanical properties and show the advantage of the approach in studying more complex mouse aorta. In particular, we first resolve the ubiquitous issue of refraction in non-contacting optical measurements of strain while tissues are immersed in physiologic saline and we show that surface preparation for DIC does not affect the inferred mechanical properties either qualitatively or quantitatively, the latter via the use of a four-fibre family hyperelastic constitutive relation and associated estimation of material parameters using nonlinear regression. We thus submit that panoramic-DIC-based strain measurement has significant potential to increase our understanding of arterial mechanics in genetic models of arterial health and disease by allowing investigators to exploit advances in transgenic mice.

Novel optical system for in vitro quantification of full surface strain fields in small arteries: I. Theory and design

Recent advances in vascular biology and pathophysiology have revealed the need to understand better the genetic basis of arterial stiffness, disease progression and responses to clinical intervention. Towards this end, in vitro experiments on arteries from genetically modified mice promise to provide significantly increased insight into both health and disease. The need to test small arteries, often of complex shape, necessitates new methods for experimental arterial mechanics, however, ones that can provide information on local changes in geometry and strain. In this paper, we present a theoretical framework for a new panoramic digital image correlation-based method sufficient to collect such information and we demonstrate the utility of this approach via validation studies on phantoms having dimensions on the order of 500-1000 μm, similar to those of large mouse arteries. In particular, we show that placing the specimen within a conical mirror and imaging the specimen via a gimbal-mounted mirror using a single camera yields stereo information sufficient to quantify the size, shape and deformation along the full length and around the entire circumference of small arteries. In a companion paper, we show further that this approach can be implemented effectively while testing arteries within a physiological solution that maintains native biomechanical properties.

Differential Passive and Active Biaxial Mechanical Behaviors of Muscular and Elastic Arteries: Basilar Versus Common Carotid

Cerebrovascular disease continues to be responsible for significant morbidity and mortality. There is, therefore, a pressing need to understand better the biomechanics of both intracranial arteries and the extracranial arteries that feed these vessels. We used a validated four-fiber family constitutive relation to model passive biaxial stress-stretch behaviors of basilar and common carotid arteries and we developed a new relation to model their active biaxial responses. These data and constitutive relations allow the first full comparison of circumferential and axial biomechanical behaviors between a muscular (basilar) and an elastic (carotid) artery from the same species. Our active model describes the responses by both types of vessels to four doses of the vasoconstrictor endothelin-1 (10−10M, 10−9M, 10−8M, and 10−7M) and predicts levels of smooth muscle cell activation associated with basal tone under specific in vitro testing conditions. These results advance our understanding of the biomechanics of intracranial and extracranial arteries, which is needed to understand better their differential responses to similar perturbations in hemodynamic loading.

Perspectives on biological growth and remodeling

The continuum mechanical treatment of biological growth and remodeling has attracted considerable attention over the past fifteen years. Many aspects of these problems are now well-understood, yet there remain areas in need of significant development from the standpoint of experiments, theory, and computation. In this perspective paper we review the state of the field and highlight open questions, challenges, and avenues for further development.

New interpretation of arterial stiffening due to cigarette smoking using a structurally motivated constitutive model

Cigarette smoking is the leading self-inflicted risk factor for cardiovascular diseases; it causes arterial stiffening with serious sequelea including atherosclerosis and abdominal aortic aneurysms. This work presents a new interpretation of arterial stiffening caused by smoking based on data published for rat pulmonary arteries. A structurally motivated "four fiber family" constitutive relation was used to fit the available biaxial data and associated best-fit values of material parameters were estimated using multivariate nonlinear regression. Results suggested that arterial stiffening caused by smoking was reflected by consistent increase in an elastin-associated parameter and moreover by marked increase in the collagen-associated parameters. That is, we suggest that arterial stiffening due to cigarette smoking appears to be isotropic, which may allow simpler phenomenological models to capture these effects using a single stiffening parameter similar to the approach in isotropic continuum damage mechanics. There is a pressing need, however, for more detailed histological information coupled with more complete biaxial mechanical data for a broader range of systemic arteries.

Modelling carotid artery adaptations to dynamic alterations in pressure and flow over the cardiac cycle

Motivated by recent clinical and laboratory findings of important effects of pulsatile pressure and flow on arterial adaptations, we employ and extend an established constrained mixture framework of growth (change in mass) and remodelling (change in structure) to include such dynamical effects. New descriptors of cell and tissue behavior (constitutive relations) are postulated and refined based on new experimental data from a transverse aortic arch banding model in the mouse that increases pulsatile pressure and flow in one carotid artery. In particular, it is shown that there was a need to refine constitutive relations for the active stress generated by smooth muscle, to include both stress- and stress rate-mediated control of the turnover of cells and matrix and to account for a cyclic stress-mediated loss of elastic fibre integrity and decrease in collagen stiffness in order to capture the reported evolution, over 8 weeks, of luminal radius, wall thickness, axial force and in vivo axial stretch of the hypertensive mouse carotid artery. We submit, therefore, that complex aspects of adaptation by elastic arteries can be predicted by constrained mixture models wherein individual constituents are produced or removed at individual rates and to individual extents depending on changes in both stress and stress rate from normal values.

Computational model of evolving lens capsule biomechanics following cataract-like surgery

Cataract surgery is an invasive procedure whereby lens fibers are removed through a permanent central hole, or capsulorhexis, in the surrounding lens capsule and replaced with an artificial intraocular lens (IOL). Remnant lens epithelial cells subsequently transdifferentiate to a more contractile and synthetic wound-healing phenotype, which causes significant structural and mechanical adaptations of the residual lens capsule. The goal of this study is to present a computational model capable of capturing salient features of the biomechanical evolution of the lens capsule following cataract-like surgery. The model is shown to predict marked long-term increases in thickness and stiffness of the lens capsule nearest the edge of the capsulorhexis comparable to reported measurements. Such models represent a first step toward understanding better the long-term interactions between the residual lens capsule and implanted IOL, thus initiating a new paradigm for the design of improved IOLs, including those having an accommodative feature.

On constitutive descriptors of the biaxial mechanical behaviour of human abdominal aorta and aneurysms

The abdominal aorta (AA) in older individuals can develop an aneurysm, which is of increasing concern in our ageing population. The structural integrity of the ageing aortic wall, and hence aneurysm, depends primarily on effective elastin and multiple families of oriented collagen fibres. In this paper, we show that a structurally motivated phenomenological 'four-fibre family' constitutive relation captures the biaxial mechanical behaviour of both the human AA, from ages less than 30 to over 60, and abdominal aortic aneurysms. Moreover, combining the statistical technique known as non-parametric bootstrap with a modal clustering method provides improved confidence intervals for estimated best-fit values of the eight associated constitutive parameters. It is suggested that this constitutive relation captures the well-known loss of structural integrity of elastic fibres owing to ageing and the development of abdominal aneurysms, and that it provides important insight needed to construct growth and remodelling models for aneurysms, which in turn promise to improve our ability to predict disease progression.

A mathematical model of evolving mechanical properties of intraluminal thrombus

Quantifying mechanical properties of blood clots is fundamental to understanding many aspects of cardiovascular disease and its treatment. Nevertheless, there has been little attention to quantifying the evolving composition, structure and properties when a clot transforms from an initial fibrin-based mesh to a predominantly collagenous mass. Although more data are needed to formulate a complete mathematical model of the evolution of clot properties, we propose a general constrained mixture model based on diverse data available from in vitro tests on fibrinogenesis, the stiffness of fibrin gels, and fibrinolysis as well as histological and mechanical data from clots retrieved from patients at surgery or autopsy. In particular, albeit resulting from complex kinetics involving many clotting factors, we show that the rapid (minutes) in vitro production of fibrin from fibrinogen can be modeled well by an Avrami-type relation and similarly that the fast (tens of minutes) in vitro degradation of fibrin in response to different concentrations of plasmin can be captured via a single "master function" parameterized by appropriate half-times that can be inferred from laboratory or clinical data. Accounting simultaneously for the production and removal of fibrin as well as chemo-mechano-stimulated production of fibrillar collagens yields predictions of changing mass fractions and bulk mechanical properties that correspond well to experimentally available data. Constrained mixture models thus hold considerable promise for modeling the biomechanics of clot evolution and can guide the design and interpretation of needed experiments and stress analyses.

Parameter sensitivity study of a constrained mixture model of arterial growth and remodeling

Computational models of arterial growth and remodeling promise to increase our understanding of basic biological processes, such as development, tissue maintenance, and aging, the biomechanics of functional adaptation, the progression and treatment of disease, responses to injuries, and even the design of improved replacement vessels and implanted medical devices. Ensuring reliability of and confidence in such models requires appropriate attention to verification and validation, including parameter sensitivity studies. In this paper, we classify different types of parameters within a constrained mixture model of arterial growth and remodeling; we then evaluate the sensitivity of model predictions to parameter values that are not known directly from experiments for cases of modest sustained alterations in blood flow and pressure as well as increased axial extension. Particular attention is directed toward complementary roles of smooth muscle vasoactivity and matrix turnover, with an emphasis on mechanosensitive changes in the rates of turnover of intramural fibrillar collagen and smooth muscle in maturity. It is shown that vasoactive changes influence the rapid change in caliber that is needed to maintain wall shear stress near its homeostatic level and the longer term changes in wall thickness that are needed to maintain circumferential wall stress near its homeostatic target. Moreover, it is shown that competing effects of intramural and wall shear stress-regulated rates of turnover can develop complex coupled responses. Finally, results demonstrate that the sensitivity to parameter values depends upon the type of perturbation from normalcy, with changes in axial stretch being most sensitive consistent with empirical reports.

Evaluation of fundamental hypotheses underlying constrained mixture models of arterial growth and remodelling

Evolving constituent composition and organization are important determinants of the biomechanical behaviour of soft tissues. In arteries, vascular smooth muscle cells and fibroblasts continually produce and degrade matrix constituents in preferred modes and at altered rates in response to changing mechanical stimuli. Smooth muscle cells similarly exhibit vasoactive changes that contribute to the control of overall structure, function and mechanical behaviour. Constrained mixture models provide a useful framework in which to quantify arterial growth and remodelling for they can account for cell-mediated changes in individual structurally significant constituents. Our simulations show that the combined effects of changing mass density turnover and vasoactivity, as well as the prestretch at which constituents are incorporated within extant matrix, are essential to capture salient features of bounded arterial growth and remodelling. These findings emphasize the importance of formulating biologically motivated constitutive relations in any theory of growth and remodelling and distinct advantages of the constrained mixture approach, in particular.

Coupling hemodynamics with vascular wall mechanics and mechanobiology to understand intracranial aneurysms

Arteries exhibit a remarkable ability to adapt in response to sustained alterations in hemodynamic loading, to heal in response to injuries, and to compensate in response to diverse disease conditions. Nevertheless, such compensatory adaptations are limited and many vascular disorders, if untreated, lead to significant morbidity or mortality. Parallel advances in vascular biology, medical imaging, biomechanics, and computational methods promise to provide increased insight into many arterial diseases, including intracranial aneurysms. In particular, although it may be possible to identify useful clinical correlations between either the blood flow patterns within or the shape of aneurysms and their rupture-potential, our ultimate goal should be to couple studies of hemodynamics with those of wall mechanics and the underlying mechanobiology so that we can understand better the mechanisms by which aneurysms arise, enlarge, and rupture and thereby identify better methods of treatment. This paper presents one such approach to fluid-solid-growth (FSG) modeling of intracranial aneurysms.

Ex vivo quantification of the time course of contractile loading of the porcine lens capsule after cataract-like surgery

Cataract surgery is an invasive procedure that replaces the quasi-spherical native lens fibers with a flat prosthetic device, which initially reduces mechanical stress within the remnant lens capsule and, ultimately, leads to contraction of the capsule about the implant. Although resultant changes in geometry have been quantified previously, little is known about the loads associated with this contraction. We present a novel experimental culture device to quantify ex vivo the time course of increases in tension within the contracting lens capsule after cataract-like surgery. Results demonstrate that contraction reaches steady state within approximately one month with a mean tension of 1.45 mN/mm and Cauchy (true) stress of 13.4 kPa. A significant increase in alpha-smooth muscle actin (alpha-SMA) was also found in post-cultured compared to fresh lens capsules, thus suggesting that transdifferentiated lens epithelial cells (LECs) modulated the contraction. Quantification of loads imparted by the contracting lens capsule is important for assessing implant/capsule interactions and implant stability in vivo. Because contraction of the capsule may be modulated in part by LECs attempting to restore their native mechanical environment, our results further suggest a possible mechanism for the long-term errant changes in capsular structure commonly observed after surgery.

Complementary vasoactivity and matrix remodelling in arterial adaptations to altered flow and pressure

Arteries exhibit a remarkable ability to adapt to sustained alterations in biomechanical loading, probably via mechanisms that are similarly involved in many arterial pathologies and responses to treatment. Of particular note, diverse data suggest that cell and matrix turnover within vasoaltered states enables arteries to adapt to sustained changes in blood flow and pressure. The goal herein is to show explicitly how altered smooth muscle contractility and matrix growth and remodelling work together to adapt the geometry, structure, stiffness and function of a representative basilar artery. Towards this end, we employ a continuum theory of constrained mixtures to model evolving changes in the wall, which depend on both wall shear stress-induced changes in vasoactive molecules (which alter smooth muscle proliferation and synthesis of matrix) and intramural stress-induced changes in growth factors (which alter cell and matrix turnover). Simulations show, for example, that such considerations help explain the different rates of experimentally observed adaptations to increased versus decreased flows as well as differences in rates of change in response to increased flows or pressures.

Fundamental role of axial stress in compensatory adaptations by arteries

Arteries exhibit a remarkable ability to adapt to diverse genetic defects and sustained alterations in mechanical loading. For example, changes in blood flow induced wall shear stress tend to control arterial caliber and changes in blood pressure induced circumferential wall stress tend to control wall thickness. We submit, however, that the axial component of wall stress plays a similarly fundamental role in controlling arterial geometry, structure, and function, that is, compensatory adaptations. This observation comes from a review of findings reported in the literature and a comparison of four recent studies from our laboratory that quantified changes in the biaxial mechanical properties of mouse carotid arteries in cases of altered cell-matrix interactions, extracellular matrix composition, blood pressure, or axial extension. There is, therefore, a pressing need to include the fundamental role of axial wall stress in conceptual and theoretical models of arterial growth and remodeling and, consequently, there is a need for increased attention to evolving biaxial mechanical properties in cases of altered genetics and mechanical stimuli.

Vascular adaptation and mechanical homeostasis at tissue, cellular, and sub-cellular levels

Blood vessels exhibit a remarkable ability to adapt throughout life that depends upon genetic programming and well-orchestrated biochemical processes. Findings over the past four decades demonstrate, however, that the mechanical environment experienced by these vessels similarly plays a critical role in governing their adaptive responses. This article briefly reviews, as illustrative examples, six cases of tissue level growth and remodeling, and then reviews general observations at cell-matrix, cellular, and sub-cellular levels, which collectively point to the existence of a "mechanical homeostasis" across multiple length and time scales that is mediated primarily by endothelial cells, vascular smooth muscle cells, and fibroblasts. In particular, responses to altered blood flow, blood pressure, and axial extension, disease processes such as cerebral aneurysms and vasospasm, and diverse experimental manipulations and clinical treatments suggest that arteries seek to maintain constant a preferred (homeostatic) mechanical state. Experiments on isolated microvessels, cell-seeded collagen gels, and adherent cells isolated in culture suggest that vascular cells and sub-cellular structures such as stress fibers and focal adhesions likewise seek to maintain constant a preferred mechanical state. Although much is known about mechanical homeostasis in the vasculature, there remains a pressing need for more quantitative data that will enable the formulation of an integrative mathematical theory that describes and eventually predicts vascular adaptations in response to diverse stimuli. Such a theory promises to deepen our understanding of vascular biology as well as to enable the design of improved clinical interventions and implantable medical devices.

A theoretically-motivated biaxial tissue culture system with intravital microscopy

Many cell types produce, remodel, and degrade extracellular matrix in response to diverse stimuli, including mechanical loads. Much is known about the molecular biology and biochemistry of the deposition and degradation of collagen, the primary structural constituent of the extracellular matrix in many tissues, yet there has been little modeling of the associated mechanobiology. For example, we do not have quantitative descriptions, or rules, for the kinetics of collagen turnover as a function of altered mechanical loading and we do not know what governs the orientation and pre-stretch at which new fibers are incorporated within extant tissue. In this paper, we use a constrained mixture theory for growth and remodeling of planar soft tissues to motivate a new experimental approach for investigating competing hypotheses on, for example, how new collagen is aligned by synthetic cells. In particular, because stress and strain fields can be homogeneous in a central region of a biaxially tested tissue, and because biaxial testing admits diverse protocols wherein equal stresses can be imposed in the presence of unequal strains or stresses can be maintained in the absence of strain, we report simulations that illustrate the potential utility of biaxial culture studies. Finally, we describe the associated design of a computer-controlled system that allows intravital microscopic quantification of collagen density, orientation, and cross-linking at various stages during the adaptation of a native tissue or the development of a tissue engineered equivalent, each subjected to well controlled biaxial loads.