Time-dependent circumferential deformation of cortical bone upon internal radial loading

Short and long duration tests were conducted on hollow femoral bone cylinders to study the circumferential (hoop) creep response of cortical bone subjected to an intramedullary radial load. It was hypothesized that there is a stress threshold above which nonlinear creep effects dominate the mechanical response and below which the response is primarily determined by linear viscoelastic material properties. The results indicate that a hoop stress threshold exists for cortical bone, where creep strain, creep strain rate and residual strain exhibited linear behavior at low hoop stress and nonlinear behavior above the hoop stress threshold. A power-law relationship was used to describe creep strain as a function of hoop stress and time and damage morphology was assessed.     

Mechanisms of mechanical strain memory in airway smooth muscle

We evaluated the hypothesis that mechanical deformation of airway smooth muscle induces structural remodeling of airway smooth muscle cells, thereby modulating mechanical performance in subsequent contractions. This hypothesis implied that past experience of mechanical deformation was retained (or "memorized") as structural changes in airway smooth muscle cells, which modulated the cell's subsequent contractile responses. We termed this phenomenon mechanical strain memory. Preshortening has been found to induce attenuation of both force and isotonic shortening velocity in cholinergic receptor-activated airway smooth muscle. Rapid stretching of cholinergic receptor-activated airway smooth muscle from an initial length to a final length resulted in post-stretch force and myosin light chain phosphorylation that correlated significantly with initial length. Thus post-stretch muscle strips appeared to retain memory of the initial length prior to rapid stretch (mechanical strain memory). Cytoskeletal recruitment of actin- and integrin-binding proteins and Erk 1/2 MAPK appeared to be important mechanisms of mechanical strain memory. Sinusoidal length oscillation led to force attenuation during oscillation and in subsequent contractions in intact airway smooth muscle, and p38 MAPK appeared to be an important mechanism. In contrast, application of local mechanical strain to cultured airway smooth muscle cells induced local actin polymerization and cytoskeletal stiffening. It is conceivable that deep inspiration-induced bronchoprotection may be a manifestation of mechanical strain memory such that mechanical deformation from past breathing cycles modulated the mechanical performance of airway smooth muscle in subsequent cycles in a continuous and dynamic manner.     

A novel formulation for blood trauma prediction by a modified power-law mathematical model

With the increasing use of artificial organs, blood damage has been raising ever more clinical concern. Blood trauma is in fact a major complication resulting from the implantation of medical devices and the use of life support apparatuses. Red blood cells damage predictive models furnish critical information on both the design and the evaluation of artificial organs, because their correct usage and implementation are thought to provide clear and rational guidance for the improvement of safety and efficacy. The currently adopted power-law shear-induced haemolysis prediction model lacks sensitivity with respect to the cumulative effect of previously applied stress magnitudes. An alternative model is proposed where a mechanical quantity was defined, able to describe the blood damage sustained by red cells under unsteady stress conditions, taking into account the load history. The proposed formulation predicted the same trend as the available experimental data. The obtained results have to be considered a preliminary validation of the basic hypothesis of this modified red blood cell damage prediction model. To date, the necessity to design further experiments to validate the proposed damage function clashes with the limitations inherent to current systems to get the time-varying shear stress completely under control.     

An Eulerian/XFEM formulation for the large deformation of cortical cell membrane

Most animal cells are surrounded by a thin layer of actin meshwork below their membrane, commonly known as the actin cortex (or cortical membrane). An increasing number of studies have highlighted the role of this structure in many cell functions including contraction and locomotion, but modelling has been limited by the fact that the membrane thickness (about 1?μm) is usually much smaller than the typical size of a cell (10-100?μm). To overcome theoretical and numerical issues resulting from this observation, we introduce in this paper a continuum formulation, based on surface elasticity, that views the cortex as an infinitely thin membrane that can resists tangential deformation. To accurately model the large deformations of cells, we introduced equilibrium equations and constitutive relations within the Eulerian viewpoint such that all quantities (stress, rate of deformation) lie in the current configuration. A solution procedure is then introduced based on a coupled extended finite element approach that enables a continuum solution to the boundary value problem in which discontinuities in both strain and displacement (due to cortical elasticity) are easily handled. We validate the approach by studying the effect of cortical elasticity on the deformation of a cell adhering on a stiff substrate and undergoing internal contraction. Results show very good prediction of the proposed method when compared with experimental observations and analytical solutions for simple cases. In particular, the model can be used to study how cell properties such as stiffness and contraction of both cytoskeleton and cortical membrane lead to variations in cell's surface curvature. These numerical results show that the proposed method can be used to gain critical insights into how the cortical membrane affects cell deformation and how it may be used as a means to determine a cell's mechanical properties by measuring curvatures of its membrane.     

Results from demineralized bone creep tests suggest that collagen is responsible for the creep behavior of bone

Cortical and trabecular bone have similar creep behaviors that have been described by power-law relationships, with increases in temperature resulting in faster creep damage accumulation according to the usual Arrhenius (damage rate approximately exp (-Temp.-1)) relationship. In an attempt to determine the phase (collagen or hydroxyapatite) responsible for these similar creep behaviors, we investigated the creep behavior of demineralized cortical bone, recognizing that the organic (i.e., demineralized) matrix of both cortical and trabecular bone is composed primarily of type I collagen. We prepared waisted specimens of bovine cortical bone and demineralized them according to an established protocol. Creep tests were conducted on 18 specimens at various normalized stresses sigma/E0 and temperatures using a noninvasive optical technique to measure strain. Denaturation tests were also conducted to investigate the effect of temperature on the structure of demineralized bone. The creep behavior was characterized by the three classical stages of decreasing, constant, and increasing creep rates at all applied normalized stresses and temperatures. Strong (r2 > 0.79) and significant (p < 0.01) power-law relationships were found between the damage accumulation parameters (steady-state creep rate d epsilon/dt and time-to-failure tf) and the applied normalized stress sigma/E0. The creep behavior was also a function of temperature, following an Arrhenius creep relationship with an activation energy Q = 113 kJ/mole, within the range of activation energies for cortical (44 kJ/mole) and trabecular (136 kJ/mole) bone. The denaturation behavior was characterized by axial shrinkage at temperatures greater than approximately 56 degrees C. Lastly an analysis of covariance (ANCOVA) of our demineralized cortical bone regressions with those found in the literature for cortical and trabecular bone indicates than all three tissues creep with the same power-law exponents. These similar creep activation energies and exponents suggest that collagen is the phase responsible for creep in bone.     

A finite element model predicts the mechanotransduction response of tendon cells to cyclic tensile loading

The importance of fluid-flow-induced shear stress and matrix-induced cell deformation in transmitting the global tendon load into a cellular mechanotransduction response is yet to be determined. A multiscale computational tendon model composed of both matrix and fluid phases was created to examine how global tendon loading may affect fluid-flow-induced shear stresses and membrane strains at the cellular level. The model was then used to develop a quantitative experiment to help understand the roles of membrane strains and fluid-induced shear stresses on the biological response of individual cells. The model was able to predict the global response of tendon to applied strain (stress, fluid exudation), as well as the associated cellular response of increased fluid-flow-induced shear stress with strain rate and matrix-induced cell deformation with strain amplitude. The model analysis, combined with the experimental results, demonstrated that both strain rate and strain amplitude are able to independently alter rat interstitial collagenase gene expression through increases in fluid-flow-induced shear stress and matrix-induced cell deformation, respectively.     

Duplication models for biological networks.

Are biological networks different from other large complex networks? Both large biological and nonbiological networks exhibit power-law graphs (number of nodes with degree k, N(k) approximately k(-beta)), yet the exponents, beta, fall into different ranges. This may be because duplication of the information in the genome is a dominant evolutionary force in shaping biological networks (like gene regulatory networks and protein-protein interaction networks) and is fundamentally different from the mechanisms thought to dominate the growth of most nonbiological networks (such as the Internet). The preferential choice models used for nonbiological networks like web graphs can only produce power-law graphs with exponents greater than 2. We use combinatorial probabilistic methods to examine the evolution of graphs by node duplication processes and derive exact analytical relationships between the exponent of the power law and the parameters of the model. Both full duplication of nodes (with all their connections) as well as partial duplication (with only some connections) are analyzed. We demonstrate that partial duplication can produce power-law graphs with exponents less than 2, consistent with current data on biological networks. The power-law exponent for large graphs depends only on the growth process, not on the starting graph.     

Deformation-induced hydrolysis of a degradable polymeric cylindrical annulus

A thermodynamically consistent framework for describing the response of materials undergoing deformation-induced degradation is developed and applied to a particular biodegradable polymer system. In the current case, energy is dissipated through the mechanism of hydrolytic degradation and its effects are incorporated in the constitutive model by appropriately stipulating the forms for the rate of dissipation and for the degradation-dependent Helmholtz potential which changes with the extent of the degradation of the material. When degradation does not occur, the response of the material follows the response of a power-law generalized neo-Hookean material that fits the response of the non-degraded poly(l-lactic acid) under uniaxial extension. We study the inflation and extension of a degrading cylindrical annulus and the influence of the deformation on the mechanism of degradation and its consequent mechanical response. Depreciation of mechanical properties due to degradation confers time-dependent characteristics to the response of the biodegradable material: the material creeps when subjected to constant loads and stresses necessary to keep a fixed deformation relax.     

Mechanical behaviour of bio-inspired brittle-matrix nanocomposites under different strain rates using molecular dynamics

We study the generic mechanical behaviour of ceramic–ceramic nanocomposites inspired from biological materials. The nanocomposite models considered in our study are the regularly and stairwise staggered arrangements of stiff brittle platelets embedded in compliant brittle matrix. Molecular dynamics simulations are carried out to investigate the effect of strain rate on these nanocomposites. The variation in stress–strain behaviour and mechanical properties are analysed. The evolution of deformation processes is also investigated. Our results show the existence of different strain rate regimes separated by critical strain rate. Deformation mechanisms such as matrix cracking, crack bridging, interfacial debonding and hence platelet pullout are observed at lower strain rates. Amorphous deformation and direct debonding without matrix cracking are observed at higher strain rates.     

Axisymmetric optical-trap measurement of red blood cell membrane elasticity

The elastic properties of the cell membrane play a crucial role in determining the equilibrium shape of the cell, as well as its response to the external forces it experiences in its physiological environment. Red blood cells are a favored system for studying membrane properties because of their simple structure: a lipid bilayer coupled to a membrane cytoskeleton and no cytoplasmic cytoskeleton. An optical trap is used to stretch a red blood cell, fixed to a glass surface, along its symmetry axis by pulling on a micron-sized latex bead that is bound at the center of the exposed cell dimple. The system, at equilibrium, shows Hookean behavior with a spring constant of 1.5×10(-6)?N/m over a 1-2 μm range of extension. This choice of simple experimental geometry preserves the axial symmetry of the native cell throughout the stretch, probes membrane deformations in the small-extension regime, and facilitates theoretical analysis. The axisymmetry makes the experiment amenable to simulation using a simple model that makes no a priori assumption on the relative importance of shear and bending in membrane deformations. We use an iterative relaxation algorithm to solve for the geometrical configuration of the membrane at mechanical equilibrium for a range of applied forces. We obtain estimates for the out-of-plane membrane bending modulus B≈1×10(-19)?Nm and an upper limit to the in-plane shear modulus H<2×10(-6)?N/m. The partial agreement of these results with other published values may serve to highlight the dependence of the cell's resistance to deformation on the scale and geometry of the deformation.     

Modeling the Afferent Dynamics of the Baroreflex Control System

In this study we develop a modeling framework for predicting baroreceptor firing rate as a function of blood pressure. We test models within this framework both quantitatively and qualitatively using data from rats. The models describe three components: arterial wall deformation, stimulation of mechanoreceptors located in the BR nerve-endings, and modulation of the action potential frequency. The three sub-systems are modeled individually following well-established biological principles. The first submodel, predicting arterial wall deformation, uses blood pressure as an input and outputs circumferential strain. The mechanoreceptor stimulation model, uses circumferential strain as an input, predicting receptor deformation as an output. Finally, the neural model takes receptor deformation as an input predicting the BR firing rate as an output. Our results show that nonlinear dependence of firing rate on pressure can be accounted for by taking into account the nonlinear elastic properties of the artery wall. This was observed when testing the models using multiple experiments with a single set of parameters. We find that to model the response to a square pressure stimulus, giving rise to post-excitatory depression, it is necessary to include an integrate-and-fire model, which allows the firing rate to cease when the stimulus falls below a given threshold. We show that our modeling framework in combination with sensitivity analysis and parameter estimation can be used to test and compare models. Finally, we demonstrate that our preferred model can exhibit all known dynamics and that it is advantageous to combine qualitative and quantitative analysis methods.     

Neurogenic adaptation contributes to the afferent response to mechanical stimulation

This study aimed to characterize the effect of mechanical stimuli on mesenteric afferent nerve signaling in the isolated rat jejunum in vitro. This was done to determine the effect of mechanical stresses and strains relative to nonmechanical parameters (neurogenic adaptation). Mechanical stimulations were applied to a segment of jejunum from 15 rats using ramp distension with water at three rates of distension, a relaxation test (volume maintained constant from initial pressure of 20 or 40 mmHg), and a creep test (pressure maintained constant). Circumferential stress and strain and the spike rate increase ratio were calculated for evaluation of afferent nerve activity during the mechanical stimulations. Ramp distension evoked two distinct phases of afferent nerve signaling as a function of circumferential stress or strain. Changing the volume distension rate did not change the stress-strain relationship, but faster distension rate increased the afferent firing rate (P < 0.05). In the stress relaxation test, the spike rate declined faster and to a greater extent than the stress. In the creep test, the spike rate declined, despite a small increase in the strain. Three classes of mechanosensitive single-afferent units (low, wide dynamic range, and high threshold units) showed different response profiles against stress and strain. Low-threshold units exhibited a near linear relationship against the strain (R(2) = 0.8095), whereas high-threshold units exhibited a linear profile against the stress (R(2) = 0.9642). The afferent response is sensitive to the distension speed and to the stress and strain level during distension. However, the afferent nerve response is not a simple function of either stress or strain. Nonmechanical time-dependent adaptive responses other than those related to viscoelasticity also play a role.     

Strain Energy Function of Red Blood Cell Membranes

The several widely different values of the elastic modulus of the human red blood cell membrane which have been reported in the literature are incorporated into a single strain energy function consisting of two terms. One term gives the small stresses and low elastic modulus which is observed when the red cell membrane is deformed at constant area. The second term contributes a large isotropic stress dependent on the change of area. The strain energy function is applied to the process of sphering of red blood cells in a hypotonic solution. It is shown that a nearly perfect sphere can result even though the red blood cell membrane is homogeneous in all areas of the cell. Results pertinent to sieving and micropipette experiments are also explored.     

Quantitative evaluation of threshold fiber strain that induces reorganization of cytoskeletal actin fiber structure in osteoblastic cells

The cytoskeletal stress fiber structure plays essential roles in various kinds of cellular functions such as shape maintenance, active motility and mechanosensing, and its structure is dynamically reorganized under each functional process. In known reorganization mechanisms of the stress fibers, a change in its mechanical condition has been suggested as one of the key mediators that affect the reorganization process. Some experimental studies have clarified that tension release in the stress fibers induces fiber depolymerization that is considered to be the initial phase of the reorganization process. However, quantitative mechanical values such as strain or stress that induce depolymerization have still not been evaluated. This study is aimed at the quantitative evaluation of the mechanical value that induces stress fiber depolymerization, to gain a basic understanding of the reorganization phenomenon from a mechanical viewpoint. Osteoblastic cells (MC3T3-E1) were cultured on prestretched silicone rubber substrate. Compressive deformation was applied to the cells by uniaxially releasing the prestretched substrate strain and change in the stress fiber structure was observed. The results indicated that the compressive strain magnitude, not in the whole cell body but in the stress fiber itself, is important to induce disassembly of the stress fiber structure. The existence of a threshold strain magnitude for initiating fiber disassembly was also suggested; the threshold strain magnitude was evaluated as approximately -0.20.     

Inertia effects on characterization of dynamic response of brain tissue

Modeling and simulation of traumatic brain injury (TBI) resulted from collision or blast loading requires characterization of mechanical response over a wide range of loading rates under valid testing conditions. In this study, mechanical response of fresh bovine brain tissue was studied using the two modified Kolsky bar techniques. Radial deformation behavior of annular specimens, which are typically used to characterize the dynamic uniaxial compressive response of biological tissues, was examined using a modified Kolsky bar and a high speed camera to collect images while the specimen deforms at an axial strain rate of 2000s(-1). The high-speed images revealed inhomogeneous specimen deformation possibly brought about by radial inertia and causing a multi-axial stress state. To acquire valid stress-strain results that can be used to produce constitutive behavior of the soft materials, a novel torsion technique was developed to obtain pure shear response at dynamic loading rates. Experimental results show clear differences in the material response using the two methods. These results indicate that the previously demonstrated annular specimen geometry aimed at reducing inertia induced stress components for high rate soft materials uniaxial-compressive testing may still possess a significant component of radial inertia induced radial stress which consequently caused the observed inhomogeneous deformation in brain tissue test samples.     

A new method for measuring the yield stress in thin layers of sedimenting blood.

A new method is presented to describe the low shear rate behavior of blood. We observed the response of a thin layer of sedimenting blood to a graded shear stress in a wedge-shaped chamber. The method allows quantitation of the degree of phase separation between red cells and plasma, and extracts the yield stress of the cell phase as a function of hematocrit. Our studies showed that the behavior of normal human blood underwent a transition from a solid-like gel to a Casson fluid. This transition began at the Casson predicted yield stress. The viscoelastic properties of blood were examined at shear stresses below the yield stress. The measured Young's elastic moduli were in good agreement with published data. The yield stress of blood showed a linear dependence on hematocrit up to 60%, and increased more rapidly at higher hematocrit.     

Stability of adhesion clusters and cell reorientation under lateral cyclic tension

This work is motivated by experimental observations that cells on stretched substrate exhibit different responses to static and dynamic loads. A model of focal adhesion that can consider the mechanics of stress fiber, adhesion bonds, and substrate was developed at the molecular level by treating the focal adhesion as an adhesion cluster. The stability of the cluster under dynamic load was studied by applying cyclic external strain on the substrate. We show that a threshold value of external strain amplitude exists beyond which the adhesion cluster disrupts quickly. In addition, our results show that the adhesion cluster is prone to losing stability under high-frequency loading, because the receptors and ligands cannot get enough contact time to form bonds due to the high-speed deformation of the substrate. At the same time, the viscoelastic stress fiber becomes rigid at high frequency, which leads to significant deformation of the bonds. Furthermore, we find that the stiffness and relaxation time of stress fibers play important roles in the stability of the adhesion cluster. The essence of this work is to connect the dynamics of the adhesion bonds (molecular level) with the cell's behavior during reorientation (cell level) through the mechanics of stress fiber. The predictions of the cluster model are consistent with experimental observations.     

Potential fluid mechanic pathways of platelet activation

Platelet activation is a precursor for blood clotting, which plays leading roles in many vascular complications and causes of death. Platelets can be activated by chemical or mechanical stimuli. Mechanically, platelet activation has been shown to be a function of elevated shear stress and exposure time. These contributions can be combined by considering the cumulative stress or strain on a platelet as it is transported. Here, we develop a framework for computing a hemodynamic-based activation potential that is derived from a Lagrangian integral of strain rate magnitude. We demonstrate that such a measure is generally maximized along, and near to, distinguished material surfaces in the flow. The connections between activation potential and these structures are illustrated through stenotic flow computations. We uncover two distinct structures that may explain observed thrombus formation at the apex and downstream of stenoses. More broadly, these findings suggest fundamental relationships may exist between potential fluid mechanic pathways for mechanical platelet activation and the mechanisms governing their transport.     

Hierarchical Structure Controls Nanomechanical Properties of Vimentin Intermediate Filaments

Intermediate filaments (IFs), in addition to microtubules and microfilaments, are one of the three major components of the cytoskeleton in eukaryotic cells, playing a vital role in mechanotransduction and in providing mechanical stability to cells. Despite the importance of IF mechanics for cell biology and cell mechanics, the structural basis for their mechanical properties remains unknown. Specifically, our understanding of fundamental filament properties, such as the basis for their great extensibility, stiffening properties, and their exceptional mechanical resilience remains limited. This has prevented us from answering fundamental structure-function relationship questions related to the biomechanical role of intermediate filaments, which is crucial to link structure and function in the protein material''s biological context. Here we utilize an atomistic-level model of the human vimentin dimer and tetramer to study their response to mechanical tensile stress, and describe a detailed analysis of the mechanical properties and associated deformation mechanisms. We observe a transition from alpha-helices to beta-sheets with subsequent interdimer sliding under mechanical deformation, which has been inferred previously from experimental results. By upscaling our results we report, for the first time, a quantitative comparison to experimental results of IF nanomechanics, showing good agreement. Through the identification of links between structures and deformation mechanisms at distinct hierarchical levels, we show that the multi-scale structure of IFs is crucial for their characteristic mechanical properties, in particular their ability to undergo severe deformation of ≈300% strain without breaking, facilitated by a cascaded activation of a distinct deformation mechanisms operating at different levels. This process enables IFs to combine disparate properties such as mechanosensitivity, strength and deformability. Our results enable a new paradigm in studying biological and mechanical properties of IFs from an atomistic perspective, and lay the foundation to understanding how properties of individual protein molecules can have profound effects at larger length-scales.