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The aorta exhibits tremendous changes in geometry, composition, and mechanical properties during postnatal development. These changes are necessarily driven by transcriptional changes, both genetically programmed and mechano-responsive, but there has not been a careful comparison of time-course changes in the transcriptional profile and biomechanical phenotype. Here, we show that the greatest period of differential gene expression in the normal postnatal mouse aorta occurs prior to weaning at three weeks of age though with important evolution of many transcripts thereafter. We identify six general temporal patterns, including transcripts that monotonically decrease to lower or increase to higher steady state values as well as those that either peak or dip prior to or near weaning. We show that diverse transcripts within individual groupings correlate well over time, and that sub-sets of these groups correlate well with the developmental progression of different biomechanical metrics that are expected to be involved in mechano-sensing. In particular, expression of genes for elastin and elastin-associated glycoproteins tend to correlate well with the ratio of systolic-to-diastolic stress whereas genes for collagen fibers correlate well with the daily rate of change of systolic stress and genes for mechano-sensing proteins tend to correlate well with the systolic stress itself. We conclude that different groupings of genes having different temporal expression patterns correlate well with different measures of the wall mechanics, hence emphasizing a need for age-dependent, gene-specific computational modeling of postnatal development.

Vascular mechanics has been studied in depth since the early 1970s mainly following classical concepts from continuum mechanics. Yet, an important distinction of blood vessels, in contrast to typical engineering materials, is the continuous degradation and deposition of material in these living tissues. In this paper we examine mechanical consequences of such mass turnover. Motivated by Lyapunov’s stability theory, we introduce the new concepts of mechanobiological equilibrium and stability and demonstrate that blood vessels can maintain their structure and function under physiological conditions only if new material is deposited at a certain prestress and the vessels are both mechanically and mechanobiologically stable. Moreover, we introduce the concept of mechanobiological adaptivity as a third corner stone to understand vascular behavior on a continuum level. We demonstrate that adaptivity represents a key difference between the stability of mechanobiological and typical human-made systems. Based on these ideas, we suggest a change of paradigm that can be illustrated by considering a common arterial pathology. We suggest that aneurysms can be interpreted as mechanobiological instabilities and that predictions of their rupture risk should not only consider the maximal diameter or wall stress, but also the mechanobiological stability. A mathematical analysis of the impact of the different model parameters on the so-called mechanobiological stability margin, a single scalar used to characterize mechanobiological stability, reveals that this stability increases with the characteristic time constant of mass turnover, material stiffness, and capacity for stress-dependent changes in mass production. As each of these parameters may be modified by appropriate drugs, the theory developed in this paper may guide both prognosis and the development of new therapies for arterial pathologies such as aneurysms. [ABSTRACT FROM AUTHOR]

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.

A sustained change in blood flow results in an arterial adaptation that can be thought to consist of two general steps: an immediate vasoactive response that seeks to return the wall shear stress to its homeostatic value, and a long-term growth and remodeling process that seeks to restore the intramural stresses and, if needed, the wall shear stress toward their homeostatic values. Few papers present mathematical models of arterial growth and remodeling in general, and fewer yet address flow-induced changes. Of these, most prior models build upon the concept of “kinematic growth” proposed by Skalak in the early 1980s (Skalak R (1981) In: Proceedings of the IUTAM Symposium on finite elasticity. Martinus Nijhoff, The Hague, pp 347–355). Such approaches address important consequences of growth and remodeling, but not the fundamental means by which such changes occur. In this paper, therefore, we present a new approach for mathematically modeling arterial adaptations and, in particular, flow-induced alterations. The model is motivated by observations reported in the literature and is based on a locally homogenized, constrained mixture theory. Specifically, we develop a 3-D constitutive relation for stress in terms of the responses of the three primary load-bearing constituents and their time-varying mass fractions, with the latter accounting for the kinetics of the turnover of cells and extracellular matrix in changing, stressed configurations. Of particular importance is the concept that the natural configurations of the individual constituents can evolve separately and that this leads to changes in the overall material properties and empirically inferred residual stress field of the vessel. Potential applications are discussed, but there is a pressing need for new, theoretically motivated data to allow the prescription of specific functional forms of the requisite constitutive relations and the values of the associated material parameters.

Since its coming of age in the mid 1960s, continuum biomechanics has contributed much to our understanding of human health as well as to disease, injury, and their treatment. Nevertheless, biomechanics has yet to reach its full potential as a consistent contributor to the improvement of health–care delivery. Because of the inherent complexities of the microstructure and biomechanical behaviour of biological cells and tissues, there is a need for new theoretical frameworks to guide the design and interpretation of new classes of experiments. Because of continued advances in experimental technology, and the associated rapid increase in information on molecular and cellular contributions to behaviour at tissue and organ levels, there is a pressing need for mathematical models to synthesize and predict observations across multiple length– and time–scales. And because of the complex geometries and loading conditions, there is a need for new computational approaches to solve the boundaryand initial–value problems of clinical, industrial, and academic importance. Clearly, much remains to be done. The purpose of this paper is twofold: to review a few of the many achievements in the biomechanics of soft tissues and the tools that allowed them, but, more importantly, to identify some of the open problems that merit increased attention from those in applied mechanics, biomechanics, mathematics and mechanobiology.

Abstract: Intracranial saccular aneurysms remain an enigma; it is not known why they form, why they enlarge, or why only some of them rupture. Nonetheless, there is general agreement that mechanics plays an essential role in each aspect of the natural history of these potentially deadly lesions. In this paper, we review recent findings that discount limit point instabilities under quasi-static increases in pressure and resonance under dynamic loading as possible mechanisms of enlargement of saccular aneurysms. Indeed, recent histopathological data suggest that aneurysms enlarge due to a stress-mediated process of growth and remodeling of collagen, the primary load-bearing constituent within the wall. We submit that advanced theoretical, experimental, and numerical studies of this process are essential to further progress in treating this class of pathologies. The purpose of this review is to provide background and direction that encourages elasticians to contribute to this important area of research.

AbstractThe response of an intracranial saccular aneurysm to applied loads, whether blood pressure or endovascular intervention, depends on both the geometry and material properties of the lesion. Yet, in the development of animal models of these lesions little attention has been given to the evaluation of their mechanical behavior. Our goal was to compare the multiaxial mechanical behavior of a canine vein pouch model to published data on veins and human aneurysms. Nine vein pouches were created surgically in six mongrel dogs by anastomosing a 2 cm segment of the external jugular vein to the common carotid artery in an end-to-side fashion. The lesions were harvested one week post-surgery and subjected to cyclic inflation tests using a custom system. Pressure-regional strain data revealed that vein pouch aneurysms are very extensible for pressures up to 30 mmHg, especially in the axial direction, but stiff thereafter. None of the lesions ruptured in vivo or during inflation tests. Based on these data, we conclude that the overall behavior of canine vein pouch lesions, at one week post-surgery, did not mimic well that of human aneurysms. Thus, there is a need to pursue modifications or other models for the purposes of clinically relevant studies of lesion growth, rupture, and treatment. [Neurol Res 1999; 21: 569–573]

We employ a structurally-motivated phenomenological formulation to identify biomechanical experiments which can be used to determine a vascular constitutive relation directly from data. Large deformations, nonlinear material behavior, load-dependent anisotropy, material heterogeneity and incompressibility are accounted for in the analysis. For purposes of illustration, we outline a procedure for studying elastic arteries wherein the behavior of the media and adventitia is considered separately. This general approach for identifying vascular constitutive relations can be applied to any vessel or airway, however, and should provide certain advantages over previous microstructural or purely phenomenological formulations.

Quantitative histological studies were performed on the testis and epididymis of 80 normal bulls from beef herds in tropical Australia. Four age groups, ranging from nine months to over 10 years were established. Volumetric proportions of parenchymal and collagenous tissues, and tubular or duct surface to tissue volume ratios were determined at the dorsal, middle and ventral testicular regions and at the head, body and tail of the epididymis for each age group. Detailed volumetric analyses of the relative volumes of particular parenchymal and stromal elements were made at the middle testicular region. Lymphoid and Plasma cell populations were compared in all regions, including the efferent ducts.

There is a need in biomechanics to identify classes of experiments that allow direct determination of constitutive relations while preserving the natural geometry of the tissue. In this paper, we show how specific forms of response functions can be identified for nonlinear hyperelastic membranes by measuring principal stretch ratios, principal curvatures and distending pressures during quasi-static axisymmetric inflation tests. For completeness, we also list all of the equations that are needed to experimentally implement this new constitutive approach.

Well accepted descriptors of the thermoelastic behavior of elastomers undergoing finite strain remain elusive largely due to the continuing lack of appropriate multiaxial data. In this paper we present a new theoretical framework for inferring thermoelastic constitutive relations directly from biaxial data. In particular, we consider an experimentally natural decomposition of the motion into two parts – one due to traction-free uniform heating and one due to isothermal mechanical loading – and impose a mechanical incompressibility constraint on each motion. It is shown that, regardless of the order of the motions, one obtains a thermoelastic generalization of the classical result of Rivlin and Saunders for identifying response functions from (isothermal) biaxial data.

Abstract: We present a three-dimensional mathematical framework for modeling the evolving geometry, structure, and mechanical properties of a representative straight cylindrical artery subjected to changes in mean blood pressure and flow. We show that numerical predictions recover prior findings from a validated two-dimensional framework, but extend those findings by allowing effects of transmural gradients in wall constituents and vasoactive molecules to be simulated directly. Of particular note, we show that the predicted evolution of the residual stress related opening angle in response to an abrupt, sustained increase in blood pressure is qualitatively similar to measured changes when one accounts for a nonlinear transmural distribution of pre-stretched elastin. We submit that continuum-based constrained mixture models of arterial adaptation hold significant promise for deepening our basic understanding of arterial mechanobiology and thus for designing improved clinical interventions to treat many different types of arterial disease and injury. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]