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.

The structural protein elastin endows large arteries with unique biological functionality and mechanical integrity, hence its disorganization, fragmentation, or degradation can have important consequences on the progression and treatment of vascular diseases. There is, therefore, a need in arterial mechanics to move from materially uniform, phenomenological, constitutive relations for the wall to those that account for separate contributions of the primary structural constituents: elastin, fibrillar collagens, smooth muscle, and amorphous matrix. In this paper, we employ a recently proposed constrained mixture model of the arterial wall and show that prestretched elastin contributes significantly to both the retraction of arteries that is observed upon transection and the opening angle that follows the introduction of a radial cut in an unloaded segment. We also show that the transmural distributions of elastin and collagen, compressive stiffness of collagen, and smooth muscle tone play complementary roles. Axial prestresses and residual stresses in arteries contribute to the homeostatic state of stress in vivo as well as adaptations to perturbed loads, disease, or injury. Understanding better the development of and changes in wall stress due to individual extracellular matrix constituents thus promises to provide considerable clinically important insight into arterial health and disease.

Cerebral vasospasm is a poorly understood clinical condition that appears to result from complex biochemical and biomechanical processes that manifest as yet another example of vascular growth and remodeling. We submit that mathematical modeling holds great promise to help synthesize diverse types of data and thereby to increase our understanding of vasospasm. Toward this ultimate goal, we present constitutive relations and parametric studies that illustrate the potential utility of a new theoretical framework that combines information on wall mechanics, hemodynamics, and chemical kinetics. In particular, we show that chemical and mechanical mediators of cellular and extracellular matrix turnover can differentially dominate the progression and resolution of vasospasm. Moreover, based on our simulations, endothelial damage can significantly alter the time-course and extent of vasospasm as can impairment of autoregulation. Although the present results are consistent with salient features of clinically reported vasospasm, and thus provide some new insight, we suggest that most importantly they reveal areas of pressing need with regard to the collection of additional experimental data. Without appropriate data, our understanding of cerebral vasospasm will remain incomplete.

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.

We implemented a constrained mixture model of arterial growth and remodeling (G&R) in a nonlinear finite element framework to facilitate numerical analyses of diverse cases of arterial adaptation and maladaptation, including disease progression, resulting in complex evolving geometries and compositions. This model enables hypothesis testing by predicting consequences of postulated characteristics of cell and matrix turnover, including evolving quantities and orientations of fibrillar constituents and non-homogenous degradation of elastin or loss of smooth muscle function. The non-linear finite element formulation is general within the context of arterial mechanics, but we restricted our present numerical verification to cylindrical geometries to allow comparisons to prior results for two special cases: uniform transmural changes in mass and differential G&R within a two-layered cylindrical model of the human aorta. The present finite element model recovers the results of these simplified semi-inverse analyses with good agreement.

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.

Many investigators have engineered diverse connective tissues having good mechanical properties, yet few tools enable a global understanding of the associated formation of collagen fibers, the primary determinant of connective tissue stiffness. Toward this end, we developed a biomechanical model for collagenous tissues grown on polymer scaffolds that accounts for the kinetics of polymer degradation as well as the synthesis and degradation of multiple families of collagen fibers in response to cyclic strains imparted in a bioreactor. The model predicted well both overall thickness and stress-stretch relationships for tubular engineered vessels cultured for 8 weeks, and suggested that a steady state had not yet been reached. To facilitate future refinements of the model, we also developed bioreactors that enable intravital nonlinear optical microscopic imaging. Using these tools, we found that collagen fiber alignment was driven strongly by nondegraded polymer fibers at early times during culture, with subsequent mechano-stimulated dispersal of fiber orientations as polymer fibers degraded. In summary, mathematical models of growth and remodeling of engineered tissues cultured on polymeric scaffolds can predict evolving tissue morphology and mechanics after long periods of culture, and related empirical observations promise to further our understanding of collagen matrix development in vitro.collagen | connective tissue | optical microscopy | tissue engineering

Arterial responses to diverse pathologies and insults likely occur via similar mechanisms. For example, many studies suggest that the natural process of aging and isolated systolic hypertension share many characteristics in arteries, including loss of functional elastin, decreased smooth muscle tone, and altered rates of deposition and/or cross-linking of fibrillar collagen. Our aim is to show computationally how these coupled effects can impact evolving aortic geometry and mechanical behavior. Employing a thick-walled, multi-layered constrained mixture model, we suggest that a coupled loss of elastin and vasoactive function are fundamental mechanisms by which aortic aging occurs. Moreover, it is suggested that collagenous stiffening, although itself generally an undesirable process, can play a key role in attenuating excessive dilatation, perhaps including the enlargement of abdominal aortic aneurysms.