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Geometry of the cross-section of a blood vessel in a the reference configuration and b the deformed configuration.
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A novel, goal function-based formulation for the growth dynamics of arteries is introduced and used for investigating the development of growth instability in blood vessels. Such instabilities would lead to abnormal growth of the vessel, reminiscent of an aneurysm. The blood vessel is modeled as a thin-walled cylindrical tube, and the constituents...
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Citations
... A number of genes encoding proteins involved in cell mechanostability, including adhesion molecules and TLN2, have been linked with the progression of atherosclerosis (70)(71)(72)(73). The reduction of TLN2 in endothelial cells may impair the intercellular gap junctions and allow macrophage accumulation and consequent arterial wall thickening and plaque formation (73)(74)(75), consistent with our observed negative association between cIMT and genetically determined expression of TLN2. We examined results across all assessed tissues for TLN2 and each of the other five replicating genes from the S-PrediXcan analysis (Supplementary Material, Fig. S5A-F). ...
Carotid intima media thickness (cIMT) is a biomarker of subclinical atherosclerosis and a predictor of future cardiovascular events. Identifying associations between gene expression levels and cIMT may provide insight to atherosclerosis etiology. Here, we use two approaches to identify associations between mRNA levels and cIMT: differential gene expression analysis in whole blood and S-PrediXcan. We used microarrays to measure genome-wide whole blood mRNA levels of 5647 European individuals from four studies. We examined the association of mRNA levels with cIMT adjusted for various potential confounders. Significant associations were tested for replication in three studies totaling 3943 participants. Next, we applied S-PrediXcan to summary statistics from a cIMT genome-wide association study of 71 128 individuals to estimate the association between genetically determined mRNA levels and cIMT and replicated these analyses using S-PrediXcan on an independent genome-wide association study on cIMT that included 22 179 individuals from the UK Biobank. mRNA levels of TNFAIP3, CEBPD, and METRNL were inversely associated with cIMT, but these associations were not significant in the replication analysis. S-PrediXcan identified associations between cIMT and genetically determined mRNA levels for 36 genes, of which six were significant in the replication analysis, including TLN2, which had not been previously reported for cIMT. There was weak correlation between our results using differential gene expression analysis and S-PrediXcan. Differential expression analysis and S-PrediXcan represent complementary approaches for the discovery of associations between phenotypes and gene expression. Using these approaches, we prioritize TNFAIP3, CEBPD, METRNL, and TLN2 as new candidate genes whose differential expression might modulate cIMT.
... Many different parameters affect the stability; these include the intrinsic material stiffness as well as magnitudes of the gain parameters that control ECM production and the rate parameters that control its degradation. Similar findings were reported for a stability analysis based on rate equations for total potential energy (145), which again suggested that increased rates of production, decreased rates of degradation, or increased material stiffness can stabilize responses. Similar mechanobiological stability analyses can also be examined using the theory of kinematic growth (146). ...
Cells of the vascular wall are exquisitely sensitive to changes in their mechanical environment. In healthy vessels, mechanical forces regulate signaling and gene expression to direct the remodeling needed for the vessel wall to maintain optimal function. Major diseases of arteries involve maladaptive remodeling with compromised or lost homeostatic mechanisms. Whereas homeostasis invokes negative feedback loops at multiple scales to mediate mechanobiological stability, disease progression often occurs via positive feedback that generates mechanobiological instabilities. In this review, we focus on the cell biology, wall mechanics, and regulatory pathways associated with arterial health and how changes in these processes lead to disease. We discuss how positive feedback loops arise via biomechanical and biochemical means. We conclude that inflammation plays a central role in overriding homeostatic pathways and suggest future directions for addressing therapeutic needs.
... Liu and Kassab 2007) incorporated the same idea into a coronary arterial tree (Zhou, Kassab, and Molloi 1999) and concluded that total metabolic consumption is proportional to the entire arterial tree volume. More recently, Lindström et al. (Lindström, Satha, and Klarbring 2015;Satha, Lindström, and Klarbring 2014) extended Murray's law by including nonlinear mechanics of composite artery walls and introducing a goal-functionbased G&R. ...
Coupling hemodynamics with vessel wall growth and remodeling (G&R) is crucial for understanding pathology at distal vasculature to study progression of incurable vascular diseases, such as pulmonary arterial hypertension. The present study is the first modeling attempt that focuses on defining homeostatic baseline values in distal pulmonary vascular bed via, a so-called, homeostatic optimization. To define the vascular homeostasis and total hemodynamics in the vascular tree, we consider two time-scales: a cardiac cycle and a longer period of vascular adaptations. An iterative homeostatic optimization is performed at the slow-time scale and incorporates: an extended Murray's law, wall metabolic cost function, stress equilibrium, and hemodynamics. The pulmonary arterial network of small vessels is represented by a fractal bifurcating tree. The pulsatile blood flow is described by a Womersley's deformable wall analytical solution. A vessel wall mechanical response is described by the constrained mixture theory for an orthotropic membrane and then linearized around mean pressure. Wall material parameters are characterized by using available porcine pulmonary artery experiments and human data from literature. Illustrative examples for symmetric and asymmetric fractal trees are presented to provide homeostatic values in normal subjects. We also outline the key ideas for the derivation of a temporal multiscale formalism to justify the proposed one-way coupled system of governing equations and identify the inherent assumptions. The developed framework demonstrates a potential for advanced parametric studies and future G&R and hemodynamics modeling in pulmonary arterial hypertension.
... Studies using the constrained mixture theory of §3 similarly use methods from dynamical systems, for example stability analyses, but in terms of different characteristic equations [96,[98][99][100]. In particular, consistent with equations (3.2)-(3.4), the focus turns towards rates of change in mass (equivalently, referential mass density r R ¼ (det F)r ¼ (det F) P r a ) and stress, with mechanobiological equilibrium requiring both mass densities and associated mechanically equilibrated stresses to remain unchanged during the period of interest [72,96]. ...
One of the most remarkable differences between classical engineering materials and living matter is the ability of the latter to grow and remodel in response to diverse stimuli. The mechanical behaviour of living matter is governed not only by an elastic or viscoelastic response to loading on short time scales up to several minutes, but also by often crucial growth and remodelling responses on time scales from hours to months. Phenomena of growth and remodelling play important roles, for example during morphogenesis in early life as well as in homeostasis and pathogenesis in adult tissues, which often adapt to changes in their chemo-mechanical environment as a result of ageing, diseases, injury or surgical intervention. Mechano-regulated growth and remodelling are observed in various soft tissues, ranging from tendons and arteries to the eye and brain, but also in bone, lower organisms and plants. Understanding and predicting growth and remodelling of living systems is one of the most important challenges in biomechanics and mechanobiology. This article reviews the current state of growth and remodelling as it applies primarily to soft tissues, and provides a perspective on critical challenges and future directions.
... The accuracy and precision of such measurements need to be high to identify true changes in the wall thickness and lumen diameter in patients over time, caused by either normal physiologic adaptation or by unfavorable pathophysiologic mechanisms that lead to vascular remodeling. Several theoretical models describing the adaptation of blood vessels have been proposed in recent years, [1][2][3][4] but without in vivo measurements of the evolution of the blood vessel geometry, there is little hope of properly validating the models or achieving the predictive capability needed to use them for planning treatments or surgical procedures, for example. ...
A method for computer-aided assessment of blood vessel geometries based on shape-fitting algorithms from metric vision was evaluated. Acoustic images of cross sections of the radial artery and cephalic vein were acquired, and medical practitioners used a computer application to measure the wall thickness and nominal diameter of these blood vessels with a caliper method and the shape-fitting method. The methods performed equally well for wall thickness measurements. The shape-fitting method was preferable for measuring the diameter, since it reduced systematic errors by up to 63% in the case of the cephalic vein because of its eccentricity.
... The constituents of the artery are deposited at a certain prestretch, which is also their homeostatic stretch. Consequently, each constituent carry a known circumferential stress in the homeostatic state (Satha et al., 2014). We assume that G&R is controlled locally. ...
... We start from a thick-walled tube geometry, and formulate a mechanical model using the finite elasticity constrained mixture theory (Humphrey and Rajagopal, 2002;Gleason and Humphrey, 2004;Valentín and Humphrey, 2009a;Valentín et al., 2009;Satha et al., 2014) including an active contribution to stress from the vascular smooth muscle. This together with mechanical equilibrium result in a governing equation (Sect. ...
... Constrained mixture theory (Humphrey and Rajagopal, 2002) has been successfully applied to growth of arteries in previous work (Gleason and Humphrey, 2004;Valentín and Humphrey, 2009b;Valentín et al., 2009;Satha et al., 2014;Lindström et al., 2015). In the following section we recapture and extend, by adding active smooth muscle behavior, the derivation of the basic thin-walled equilibrium Eq. (20). ...
The growth and remodeling of arteries, as controlled by the local stress state and the sensory input from the endothelial cells of the artery wall, is given a novel theoretical framework incorporating the active behavior of vascular smooth muscle. We show that local sensory input maps uniquely to the ratio between a target arterial wall cross-section area corresponding to homeostatic conditions and the current arterial wall area. A growth law is formulated by taking the production rates of individual constituents of the arterial wall to be functions of this target-to-current wall area ratio. We find that a minimum active stress response of vascular smooth muscle is necessary to achieve stable adaptation of the artery wall to dynamic flow conditions. With a sufficient active stress alteration in response to stretch, stable growth toward a homeostatic state can be observed for finite step changes or ramp changes in the transmural pressure or the flow rate.
... We will consider the case of remodeling-induced softening in future works; however, diseased, scarred, or injured tissues tend to undergo increased stiffening (Lu et al., 2011;Maurice, 1957;Stewart and Criner, 2013), as even seen in aortic aneurysms, which complicate obstruction (Raaz et al., 2015). Growth of aneurysms, on the contrary, is more likely to become unstable in elastin-deficient, softer vessels, whereas stiffened vessels have the tendency to stabilize the growth process (Satha et al., 2014;Zohdi et al., 2004). Here, we have initially limited the scope of our analysis to remodeling-induced stiffening. ...
... In addition, endothelium functions as a barrier for large molecules to enter the vessel wall and trigger pathological processes in the inner vessel layers [40,41]. In other words, the mechanostability of endothelial cells including the endothelial intercellular gap and tight junction maintenance is crucial for healthy vessel wall. ...
Background and aims:
Focal adhesions (FA) play an important role in the tissue remodeling and in the maintenance of tissue integrity and homeostasis. Talin and vinculin proteins are among the major constituents of FAs contributing to cellular well-being and intercellular communication.
Methods:
Microarray analysis (MA) and qRT-PCR low-density array were implemented to analyze talin-1, talin-2, meta-vinculin and vinculin gene expression in circulating blood and arterial plaque.
Results:
All analyzed genes were significantly and consistently downregulated in plaques (carotid, abdominal aortic and femoral regions) compared to left internal thoracic artery (LITA) control. The use of LITA samples as controls for arterial plaque samples was validated using immunohistochemistry by comparing LITA samples with healthy arterial samples from a cadaver. Even though the differences in expression levels between stable and unstable plaques were not statistically significant, we observed further negative tendency in the expression in unstable atherosclerotic plaques. The confocal tissue imaging revealed gradient of talin-1 expression in plaque with reduction close to the vessel lumen. Similar gradient was observed for talin-2 expression in LITA controls but was not detected in plaques. This suggests that impaired tissue mechanostability affects the tissue remodeling and healing capabilities leading to development of unstable plaques.
Conclusions:
The central role of talin and vinculin in cell adhesions suggests that the disintegration of the tissue in atherosclerosis could be partially driven by downregulation of these genes, leading to loosening of cell-ECM interactions and remodeling of the tissue.
... Note that the stabilizing effects of collagen production capacity, half-life and stiffness shown mathematically in [12], and related herein to computational as well as clinical and experimental findings, agree qualitatively with results reported in [39] for a simple scalar arterial model with a goal-function based G&R. However, the theory of mechanobiological stability pursued herein is applicable to arbitrary vascular geometries and material compositions and does not experience the probably unphysiological oscillatory G&R observed partially in [39]. ...
... Note that the stabilizing effects of collagen production capacity, half-life and stiffness shown mathematically in [12], and related herein to computational as well as clinical and experimental findings, agree qualitatively with results reported in [39] for a simple scalar arterial model with a goal-function based G&R. However, the theory of mechanobiological stability pursued herein is applicable to arbitrary vascular geometries and material compositions and does not experience the probably unphysiological oscillatory G&R observed partially in [39]. ...
Static and dynamic mechanical instabilities were previously suggested, and then rejected, as mediators of aneurysmal development, which leaves open the question of the underlying mechanism. In this paper, we suggest as a new paradigm the interpretation of aneurysms as mechanobiological instabilities. For illustrative purposes, we compare analytical calculations with computational simulations of the growth and remodelling of idealized fusiform abdominal aortic aneurysms and experimental and clinical findings. We show that the concept of mechanobiological stability is consistent with the impact of risk factors such as age, smoking or diabetes on the initiation and enlargement of these lesions as well as adaptive processes in the healthy abdominal aorta such as dilatation during ageing or in hypertension. In general, high stiffness, an increased capacity for stress-mediated matrix production, and slow matrix turnover all improve the mechanobiological stability of blood vessels. This theoretical understanding may help guide prognosis and the development of future therapies for aneurysms as it enables systematic ways to attenuate enlargement.
... Finally, simulations based on the data provided here can only account for a single point in time, no long-term behavior and biological response can be predicted with our fitted constitutive model. To simulate the time evolution of an aneurysm, growth models (see, e.g., Satha et al., 2014) or remodeling models for collagen networks (see, e.g., Hadi et al., 2012) must be implemented. Nevertheless, for predicting failure and quantifying damage immediately after supraphysiological loading, e.g., stent insertion, the model provided here suffices. ...
Development of aortic aneurysms includes significant morphological changes within the tissue: collagen content increases, elastin content reduces and smooth muscle cells degenerate. We seek to quantify the impact of these changes on the passive mechanical response of aneurysms in the supra-physiological loading range via mechanical testing and constitutive modeling. We perform uniaxial extension tests on circumferentially and axially oriented strips from five thoracic (65.6 years±13.4, mean±SD) and eight abdominal (63.9 years±11.4) aortic fusiform aneurysms to investigate both continuous and discontinuous softening during supra-physiological loading. We determine the significance of the differences between the fitted model parameters: diseased thoracic versus abdominal tissues, and healthy (Weisbecker et al., J. Mech. Behav. Biomed. Mater. 12, 93–106, 2012) versus diseased tissues. We also test correlations among these parameters and age, Body Mass Index (BMI) and preoperative aneurysm diameter, and investigate histological cuts. Tissue response is anisotropic for all tests and the anisotropic pseudo-elastic damage model fits the data well for both primary loading and discontinuous softening which we interpret as damage. We found statistically relevant differences between model parameters fitted to diseased thoracic versus abdominal tissues, as well as between those fitted to healthy versus diseased tissues. Only BMI correlated with fitted model parameters in abdominal aortic aneurysmal tissues.
