Left-ventricular shape determines intramyocardial mechanical heterogeneity

Left-ventricular remodeling is considered to be an important mechanism of disease progression leading to mechanical dysfunction of the heart. However, the interaction between the physiological changes in the remodeling process and the associated mechanical dysfunction is still poorly understood. Clinically, it has been observed that the left ventricle often undergoes large shape changes, but the importance of left-ventricular shape as a contributing factor to alterations in mechanical function has not been clearly determined. Therefore, the interaction between left-ventricular shape and systolic mechanical function was examined in a computational finite-element study. Hereto, finite-element models were constructed with varying shapes, ranging from an elongated ellipsoid to a sphere. A realistic transmural gradient in fiber orientation was considered. The passive myocardium was described by an incompressible hyperelastic material law with transverse isotropic symmetry. Activation was governed by the eikonal-diffusion equation. Contraction was incorporated using a Hill model. For each shape, simulations were performed in which passive filling was followed by isovolumic contraction and ejection. It was found that the intramyocardial distributions of fiber stress, strain, and stroke work density were shape dependent. Ejection performance was reduced with increasing sphericity, which was regionally related to a reduction in the active fiber stress development, fiber shortening, and stroke work in the midwall and subepicardial region at the midheight level in the left-ventricular wall. Based on these results, we conclude that a significant interaction exists between left-ventricular shape and regional myofiber mechanics, but the importance for left-ventricular remodeling requires further investigation.     

Experimental and Computational Investigation of the Role of Stress Fiber Contractility in the Resistance of Osteoblasts to Compression

The mechanical behavior of the actin cytoskeleton has previously been investigated using both experimental and computational techniques. However, these investigations have not elucidated the role the cytoskeleton plays in the compression resistance of cells. The present study combines experimental compression techniques with active modeling of the cell’s actin cytoskeleton. A modified atomic force microscope is used to perform whole cell compression of osteoblasts. Compression tests are also performed on cells following the inhibition of the cell actin cytoskeleton using cytochalasin-D. An active bio-chemo-mechanical model is employed to predict the active remodeling of the actin cytoskeleton. The model incorporates the myosin driven contractility of stress fibers via a muscle-like constitutive law. The passive mechanical properties, in parallel with active stress fiber contractility parameters, are determined for osteoblasts. Simulations reveal that the computational framework is capable of predicting changes in cell morphology and increased resistance to cell compression due to the contractility of the actin cytoskeleton. It is demonstrated that osteoblasts are highly contractile and that significant changes to the cell and nucleus geometries occur when stress fiber contractility is removed.     

Stretch-induced actin remodeling requires targeting of zyxin to stress fibers and recruitment of actin regulators

Reinforcement of actin stress fibers in response to mechanical stimulation depends on a posttranslational mechanism that requires the LIM protein zyxin. The C-terminal LIM region of zyxin directs the force-sensitive accumulation of zyxin on actin stress fibers. The N-terminal region of zyxin promotes actin reinforcement even when Rho kinase is inhibited. The mechanosensitive integrin effector p130Cas binds zyxin but is not required for mitogen-activated protein kinase-dependent zyxin phosphorylation or stress fiber remodeling in cells exposed to uniaxial cyclic stretch. α-Actinin and Ena/VASP proteins bind to the stress fiber reinforcement domain of zyxin. Mutation of their docking sites reveals that zyxin is required for recruitment of both groups of proteins to regions of stress fiber remodeling. Zyxin-null cells reconstituted with zyxin variants that lack either α-actinin or Ena/VASP-binding capacity display compromised response to mechanical stimulation. Our findings define a bipartite mechanism for stretch-induced actin remodeling that involves mechanosensitive targeting of zyxin to actin stress fibers and localized recruitment of actin regulatory machinery.     

Tension is required but not sufficient for focal adhesion maturation without a stress fiber template

Focal adhesion composition and size are modulated in a myosin II-dependent maturation process that controls adhesion, migration, and matrix remodeling. As myosin II activity drives stress fiber assembly and enhanced tension at adhesions simultaneously, the extent to which adhesion maturation is driven by tension or altered actin architecture is unknown. We show that perturbations to formin and α-actinin 1 activity selectively inhibited stress fiber assembly at adhesions but retained a contractile lamella that generated large tension on adhesions. Despite relatively unperturbed adhesion dynamics and force transmission, impaired stress fiber assembly impeded focal adhesion compositional maturation and fibronectin remodeling. Finally, we show that compositional maturation of focal adhesions could occur even when myosin II-dependent cellular tension was reduced by 80%. We propose that stress fiber assembly at the adhesion site serves as a structural template that facilitates adhesion maturation over a wide range of tensions. This work identifies the essential role of lamellar actin architecture in adhesion maturation.     

Wolff's law of trabecular architecture at remodeling equilibrium

An elastic constitutive relation for cancellous bone tissue is developed. This relationship involves the stress tensor T, the strain tensor E and the fabric tensor H for cancellous bone. The fabric tensor is a symmetric second rank tensor that is a quantitative stereological measure of the microstructural arrangement of trabeculae and pores in the cancellous bone tissue. The constitutive relation obtained is part of an algebraic formulation of Wolff's law of trabecular architecture in remodeling equilibrium. In particular, with the general constitutive relationship between T, H and E, the statement of Wolff's law at remodeling equilibrium is simply the requirement of the commutativity of the matrix multiplication of the stress tensor and the fabric tensor at remodeling equilibrium, T*H* = H*T*. The asterisk on the stress and fabric tensor indicates their values in remodeling equilibrium. It is shown that the constitutive relation also requires that E*H* = H*E*. Thus, the principal axes of the stress, strain and fabric tensors all coincide at remodeling equilibrium.     

A study of the viscoelastic effect in a bone remodeling model

The present paper addresses the following question can a simple regulatory bone remodeling model predict effects of viscosity on the trabecular morphology? For that, we propose an extension of a previous bone remodeling model by taking into account the viscosity properties of the tissue. Zener’s law is used to describe the mechanical behavior of the bone and a specific law of the apparent bone density rate is proposed. Based on stability analysis, numerical simulations are then performed to investigate the viscosity role on simulations of the bone remodeling process. We show that the viscous contribution affects the evolution of the apparent bone density, by slowing down the adaptation process, which seems to be confirmed by simulations with real data obtained from rat tibia.     

Genetic ablation of zyxin causes Mena/VASP mislocalization, increased motility, and deficits in actin remodeling

Focal adhesions are specialized regions of the cell surface where integrin receptors and associated proteins link the extracellular matrix to the actin cytoskeleton. To define the cellular role of the focal adhesion protein zyxin, we characterized the phenotype of fibroblasts in which the zyxin gene was deleted by homologous recombination. Zyxin-null fibroblasts display enhanced integrin-dependent adhesion and are more migratory than wild-type fibroblasts, displaying reduced dependence on extracellular matrix cues. We identified differences in the profiles of 75- and 80-kD tyrosine-phosphorylated proteins in the zyxin-null cells. Tandem array mass spectrometry identified both modified proteins as isoforms of the actomyosin regulator caldesmon, a protein known to influence contractility, stress fiber formation, and motility. Zyxin-null fibroblasts also show deficits in actin stress fiber remodeling and exhibit changes in the molecular composition of focal adhesions, most notably by severely reduced accumulation of Ena/VASP proteins. We postulate that zyxin cooperates with Ena/VASP proteins and caldesmon to influence integrin-dependent cell motility and actin stress fiber remodeling.     

A role for gelsolin in stress fiber-dependent cell contraction.

Gelsolin is an abundant actin binding protein that mediates the rapid remodeling of cortical actin filaments through severing, capping, and nucleating activities. Most of the attention on the intracellular function of gelsolin has focused on the remodeling of the cortical actin meshwork but the localization of gelsolin to other regions of the cell suggests that it may have other important functions elsewhere. In cultured fibroblasts, gelsolin is heavily enriched in stress fibers, where its function in these contractile organelles is unknown. To study gelsolin function during stress fiber formation and cell contraction, we first assessed gelsolin levels in stress fiber preparations from lysophosphatidic acid (LPA)-treated human fibroblasts. LPA induced a large, time-dependent, calcium-independent increase of actin, gelsolin, alpha-actinin, and tropomyosin in stress fiber preparations. A microinjected gelsolin antibody that inhibits severing by gelsolin reduced stress fibers. Anti-sense-transfected gelsolin-depleted 3T3 cell lines treated with LPA after serum starvation required approximately 6 h to form stress fibers and focal adhesions, in contrast to control lines transfected with vector only, which formed stress fibers 15 min after addition of LPA. In cells microinjected with the gelsolin antibody that inhibits severing, Mg-ATP-induced cell contraction was greatly reduced in approximately 90% of injected cells compared to cells injected with an irrelevant antibody. Gelsolin-depleted cells were incapable of collagen gel contraction and showed no apparent Mg-ATP-induced cell contraction compared to cell lines transfected with vector only. The involvement of gelsolin in cell contraction and remodeling of collagen gels suggests a novel role for gelsolin in stress fiber-dependent cell function.     

Remodeling of conduit arteries in hypertension and flow-overload obeys a minimum energy principle

Arterial remodeling is an important process in physiology and pathophysiology. Based on an energy minimization method, Murray's law predicts the optimal inner radius. Application of Darcy's law in the wall results in an optimal outer radius. The average wall stress is computed by the Laplace's law. Using these formulas, a large porcine coronary artery in hypertension is studied. The results reveal how wall thickness and average circumferential stress change after increasing blood pressure and volume flow rate. The theoretical predictions are in good qualitative agreement with experimental observations. The advantage and limitation of the current approach are discussed.     

A time-dependent healing function for immediate loaded implants

Current interest in immediate dental implant loading has grown due to a number of clinical advantages this treatment modality offers. To obtain a deeper insight into the changing mechanical properties during the healing phase, results from removal torque tests are used in a biomechanical model. The ultimate removal torques, which depend on healing time, are described by a time-dependent healing function. The bone behavior is modeled using an elastic law with damage. The evolution of damage is represented with an incremental equation with an initial damage value and two material parameters. The nonlinear relationship between the torque and the angle of rotation up to the ultimate torque can be calculated. By changing the elastic parameter in the elastic damage law, the remodeling process can be characterized. In a further step, the elastic parameters and the limits for shear stress from the biomechanical model for the removal torque will be used in an FE analysis in order to obtain information on the axial loading limits of a dental implant at different healing times.     

Interaction of stress and growth in a fibrous tissue

The influence of stress on the growth and remodeling of a soft biological tissue is considered. For this purpose, the soft tissue is idealized as a fiber network. The stress-free lengths of the fibers composing the network are not fixed as in an inert elastic solid, but are assumed to evolve as a result of growth and stress adaptation. Similarly, the topology of the fiber network may also evolve under the application of stress. A set of constitutive equations are proposed which relate the tissue stress to the deformation of the tissue as well as to its growth and microstructure. It is shown that distinctly different growth patterns which may arise during initial growth or wound healing can be modeled by the proposed mathematical analysis.     

Flow-induced focal adhesion remodeling mediated by local cytoskeletal stresses and reorganization

Cells respond to fluid shear stress through dynamic processes involving changes in actomyosin and other cytoskeletal stresses, remodeling of cell adhesions, and cytoskeleton reorganization. In this study we simultaneously measured focal adhesion dynamics and cytoskeletal stress and reorganization in MDCK cells under fluid shear stress. The measurements used co-expression of fluorescently labeled paxillin and force sensitive FRET probes of α-actinin. A shear stress of 0.74 dyn/cm² for 3 hours caused redistribution of cytoskeletal tension and significant focal adhesion remodeling. The fate of focal adhesions is determined by the stress state and stability of the linked actin stress fibers. In the interior of the cell, the mature focal adhesions disassembled within 35-40 min under flow and stress fibers disintegrated. Near the cell periphery, the focal adhesions anchoring the stress fibers perpendicular to the cell periphery disassembled, while focal adhesions associated with peripheral fibers sustained. The diminishing focal adhesions are coupled with local cytoskeletal stress release and actin stress fiber disassembly whereas sustaining peripheral focal adhesions are coupled with an increase in stress and enhancement of actin bundles. The results show that flow induced formation of peripheral actin bundles provides a favorable environment for focal adhesion remodeling along the cell periphery. Under such condition, new FAs were observed along the cell edge under flow. Our results suggest that the remodeling of FAs in epithelial cells under flow is orchestrated by actin cytoskeletal stress redistribution and structural reorganization.     

Flow-induced focal adhesion remodeling mediated by local cytoskeletal stresses and reorganization

Cells respond to fluid shear stress through dynamic processes involving changes in actomyosin and other cytoskeletal stresses, remodeling of cell adhesions, and cytoskeleton reorganization. In this study we simultaneously measured focal adhesion dynamics and cytoskeletal stress and reorganization in MDCK cells under fluid shear stress. The measurements used co-expression of fluorescently labeled paxillin and force sensitive FRET probes of α-actinin. A shear stress of 0.74 dyn/cm² for 3 hours caused redistribution of cytoskeletal tension and significant focal adhesion remodeling. The fate of focal adhesions is determined by the stress state and stability of the linked actin stress fibers. In the interior of the cell, the mature focal adhesions disassembled within 35-40 min under flow and stress fibers disintegrated. Near the cell periphery, the focal adhesions anchoring the stress fibers perpendicular to the cell periphery disassembled, while focal adhesions associated with peripheral fibers sustained. The diminishing focal adhesions are coupled with local cytoskeletal stress release and actin stress fiber disassembly whereas sustaining peripheral focal adhesions are coupled with an increase in stress and enhancement of actin bundles. The results show that flow induced formation of peripheral actin bundles provides a favorable environment for focal adhesion remodeling along the cell periphery. Under such condition, new FAs were observed along the cell edge under flow. Our results suggest that the remodeling of FAs in epithelial cells under flow is orchestrated by actin cytoskeletal stress redistribution and structural reorganization.     

Evolution of bone inhomogeneity around a hole in an orthotropic plate of bone: theoretical predictions.

The problem of the evolution of bone inhomogeneity around a hole in a plate of bone with orthotropic symmetry is considered. The internal remodeling theory of Cowin and Hegedus is employed to show the existence of final inhomogeneity following stress concentration. The speed of remodeling around the hole and its variation with respect to distance is investigated. Results indicate that the effect of stress concentration around a hole is slightly less pronounced if bone is considered orthotropic rather than transversely isotropic. The speed of remodeling is found to be unaffected but the amplitude of inhomogeneity with respect to distance drops and disappears slightly faster if bone is considered orthotropic.     

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.     

Remodeling of the collagen fiber architecture due to compaction in small vessels under tissue engineered conditions

Mechanical loading protocols in tissue engineering (TE) aim to improve the deposition of a properly organized collagen fiber network. In addition to collagen remodeling, these conditioning protocols can result in tissue compaction. Tissue compaction is beneficial to tissue collagen alignment, yet it may lead to a loss of functionality of the TE construct due to changes in geometry after culture. Here, a mathematical model is presented to relate the changes in collagen architecture to the local compaction within a TE small blood vessel, assuming that under static conditions, compaction is the main factor responsible for collagen fiber organization. An existing structurally based model is extended to incorporate volumetric tissue compaction. Subsequently, the model is applied to describe the collagen architecture of TE constructs under either strain based or stress based stimulus functions. Our computations indicate that stress based simulations result in a helical collagen fiber distribution along the vessel wall. The helix pitch angle increases from a circumferential direction in the inner wall, over about 45 deg in the middle vessel layer, to a longitudinal direction in the outer wall. These results are consistent with experimental data from TE small diameter blood vessels. In addition, our results suggest a stress dependent remodeling of the collagen, suggesting that cell traction is responsible for collagen orientation. These findings may be of value to design improved mechanical conditioning protocols to optimize the collagen architecture in engineered tissues.     

An evolutionary Wolff's law for trabecular architecture.

A continuum model is proposed to describe the temporal evolution of both the density changes and the reorientation of the trabecular architecture given the applied stress state in the bone and certain material parameters of the bone. The data upon which the proposed model is to be based consist of experimentally determined remodeling rate coefficients and quantitative stereological and anisotropic elastic constant measurements of cancellous bone. The model shows that the system of differential equations governing the temporal changes in architecture is necessarily nonlinear. This nonlinearity is fundamental in that it stems from the fact that, during remodeling, the relationship between stress and strain is changing as the stress and strain variables themselves are changing. In order to preserve the remodeling property of the model, terms that are of the order strain times the changes in density and/or microstructural properties must be retained. If these terms were dropped, there would be no feedback mechanism for architectural adaptation and no adaptation of the trabecular architecture. There is, therefore, no linearized version of the model of the temporal evolution of trabecular architecture. An application of the model is illustrated by an example problem in which the temporal evolution of homogeneous trabecular architecture is predicted. A limitation of the proposed continuum model is the length scale below which it cannot be applied. The model cannot be applied in regions of cancellous bone where the trabecular bone architecture is relatively inhomogeneous or at a bone-implant interface.     

A closed-form structural model of planar fibrous tissue mechanics

Structural models of tissue mechanics, in which the tissue is represented as a sum or integral of fiber contributions for a distribution of fiber orientations, are a popular tool to represent the complex mechanical behavior of soft tissues. A significant practical challenge, however, is evaluation of the integral that defines the stress. Numerical integration is accurate but computationally demanding, posing an impediment to incorporation of structural models into large-scale finite-element simulations. In this paper, a closed-form analytic evaluation of the integral is derived for fibers distributed according to a von Mises distribution and an exponential fiber stress–strain law.     

Yield stress of pretreated corn stover suspensions using magnetic resonance imaging

Cellulose fibers in water form networks that give rise to an apparent yield stress, especially at high solids contents. Measuring the yield stress and correlating it with fiber concentration is important for the biomass and pulp industries. Understanding how the yield stress behaves at high solids concentrations is critical to optimize enzymatic hydrolysis of biomass in the production of biofuels. Rheological studies on pretreated corn stover and various pulp fibers have shown that yield stress values correlate with fiber mass concentration through a power‐law relationship. We use magnetic resonance imaging (MRI) as an in‐line rheometer to measure velocity profiles during pipe flow. If coupled with pressure drop measurements, these allow yield stress values to be determined. We compare our results with literature values and discuss the accuracy and precision of the rheo‐MRI measurement, along with the effects of fiber characteristics on the power‐law coefficients. Biotechnol. Bioeng. 2011;108: 2312–2319. © 2011 Wiley Periodicals, Inc.