Cytoskeletal forces produced by extremely low‐frequency electric fields acting on extracellular glycoproteins

The physical mechanism by which cells transduce an applied electric field is not well understood. This article establishes for the first time a direct, quantitative model that links the field to cytoskeletal forces. In a previous article, applied electric fields of physiological strength were shown to produce significant mechanical torques at the cellular level. In this article, the corresponding forces exerted on the cytoskeleton are computed and found to be comparable in magnitude to mechanical forces known to produce physiological effects. In addition to the electrical force, the viscous drag force exerted by the surrounding medium and the restoring force exerted by the neighboring structures are considered in the analysis. For an applied electric field of 10 V/m, the force transmitted to the CD44 receptor of a hyaluronan chain in cartilage is about 1 pN at 10 Hz and 7 pN at 1 Hz. For an applied electric field of 100 V/m, the force transmitted to the cytoskeleton at one focus of the glycocalyx is about 0.5 pN at 10 Hz and 1.3 pN at 1 Hz. Mechanical forces of similar magnitude have been observed to produce physiological effects. Hence, this electromechanical transduction process is a plausible mechanism for the production of physiological effects by such electric fields. Bioelectromagnetics 31:77–84, 2010. © 2009 Wiley‐Liss, Inc.     

Integrins may serve as mechanical transducers for low-frequency electric fields

A hypothesis is presented that a transduction mechanism for low frequency electric fields of physiological strength ( approximately 1 V/cm) is the same as that for sinusoidal fluid shear stresses, the force exerted on an integrin. Simple calculations show that the forces exerted on a model integrin by transverse electric fields and fluid shears that produce cellular effects are comparable in magnitude, about 1 fN. The electric force is provided by the interaction of the surface charges on the integrin with the tangential component of the applied field. The mechanical shear force is the transverse fluid drag force exerted on the cylindrical surface of the integrin. Either force is coupled mechanically to the actin cortex within the cell. The mechanical network which exists within a cell and connects a cell to its surroundings would then be directly coupled to an applied electric field. The fundamental transduction mechanism for some electric field effects may then be ultimately mechanical in nature.     

Mechanically induced electrical potentials of articular cartilage

While there is increasing evidence that chondrocytes are affected by mechanically induced stimuli, endogenous force-related electrical potentials within articular cartilage have been so far observed only in-vitro. Using a porcine ex-vivo model (German Land Race), 8 knee joints were explanted and exposed to mechanical force (up to 800 N) using a special device. Electrodes were inserted into the cartilage matrix. With an amplifier and an A/D transducer the changes of electrical voltage between the electrodes as well as those of the force were recorded online and simultaneously on a computer. Additionally, we located one pair of electrodes on the surface of the cartilage tissue to detect electrical fields outside the cartilage tissue. In relation to the applied force we observed that electrical potentials derived from inside and outside the articular cartilage showed a correspondence. When an alternating force with an amplitude of 360 N and a frequency of about 0.2 Hz was periodically applied, we measured peak amplitudes ranging from 2.1 to 5.5 mV within the cartilage tissue with electrical negativity within the weight bearing area of the cartilage tissue. The measured voltages depended on the applied force, the location of the electrodes, and on anatomical variations. We found an almost linear relation between the magnitude of the applied force and the recorded voltage. With the help of the electrodes located outside and within the cartilage tissue, we were able to show that force dependent fields are generated inside the cartilage. There are several theories explaining the origin of these electrical phenomena, many of them focusing on the negative charges of the proteoglycans in relation to the flow of interstitial fluid and ions under compression. However, the consequences of these phenomena are yet not clear.     

A linearized formulation of triphasic mixture theory for articular cartilage,and its application to indentation analysis

The negative charges on proteoglycans significantly affect the mechanical behaviors of articular cartilage. Mixture theories, such as the triphasic theory, can describe quantitatively how this charged nature contributes to the mechano-electrochemical behaviors of such tissue. However, the mathematical complexity of the theory has hindered its application to complicated loading profiles, e.g., indentation or other multi-dimensional configurations. In this study, the governing equations of triphasic mixture theory for soft tissue were linearized and dramatically simplified by using a regular perturbation method and the use of two potential functions. We showed that this new formulation can be used for any axisymmetric problem, such as confined or unconfined compressions, hydraulic perfusion, and indentation. A finite difference numerical program was further developed to calculate the deformational, electrical, and flow behaviors inside the articular cartilage under indentation. The calculated tissue response was highly consistent with the data from indentation experiments (our own and those reported in the literature). It was found that the charged nature of proteoglycans can increase the apparent stiffness of the solid matrix and lessen the viscous effect introduced by fluid flow. The effects of geometric and physical properties of indenter tip, cartilage thickness, and that of the electro-chemical properties of cartilage on the resulting deformation and fluid pressure fields across the tissue were also investigated and presented. These results have implications for studying chondrocyte mechanotransduction in different cartilage zones and for tissue engineering designs or in vivo cartilage repair.     

Functional tissue engineering of chondral and osteochondral constructs

Due to the prevalence of osteoarthritis (OA) and damage to articular cartilage, coupled with the poor intrinsic healing capacity of this avascular connective tissue, there is a great demand for an articular cartilage substitute. As the bearing material of diarthrodial joints, articular cartilage has remarkable functional properties that have been difficult to reproduce in tissue-engineered constructs. We have previously demonstrated that by using a functional tissue engineering approach that incorporates mechanical loading into the long-term culture environment, one can enhance the development of mechanical properties in chondrocyte-seeded agarose constructs. As these gel constructs begin to achieve material properties similar to that of the native tissue, however, new challenges arise, including integration of the construct with the underlying native bone. To address this issue, we have developed a technique for producing gel constructs integrated into an underlying bony substrate. These osteochondral constructs develop cartilage-like extracellular matrix and material properties over time in free swelling culture. In this study, as a preliminary to loading such osteochondral constructs, finite element modeling (FEM) was used to predict the spatial and temporal stress, strain, and fluid flow fields within constructs subjected to dynamic deformational loading. The results of these models suggest that while chondral ("gel alone") constructs see a largely homogenous field of mechanical signals, osteochondral ("gel bone") constructs see a largely inhomogeneous distribution of mechanical signals. Such inhomogeneity in the mechanical environment may aid in the development of inhomogeneity in the engineered osteochondral constructs. Together with experimental observations, we anticipate that such modeling efforts will provide direction for our efforts aimed at the optimization of applied physical forces for the functional tissue engineering of an osteochondral articular cartilage substitute.     

A hyperelastic biphasic fibre-reinforced model of articular cartilage considering distributed collagen fibre orientations: continuum basis,computational aspects and applications

Cartilage is a multi-phase material composed of fluid and electrolytes (68–85% by wet weight), proteoglycans (5–10% by wet weight), chondrocytes, collagen fibres and other glycoproteins. The solid phase constitutes an isotropic proteoglycan gel and a fibre network of predominantly type II collagen, which provides tensile strength and mechanical stiffness. The same two components control diffusion of the fluid phase, e.g. as visualised by diffusion tensor MRI: (i) the proteoglycan gel (giving a baseline isotropic diffusivity) and (ii) the highly anisotropic collagenous fibre network. We propose a new constitutive model and finite element implementation that focus on the essential load-bearing morphology: an incompressible, poroelastic solid matrix reinforced by an inhomogeneous, dispersed fibre fabric, which is saturated with an incompressible fluid residing in strain-dependent pores of the collagen–proteoglycan solid matrix. The inhomogeneous, dispersed fibre fabric of the solid further influences the fluid permeability, as well as an intrafibrillar portion that cannot be ‘squeezed out’ from the tissue. Using representative numerical examples on the mechanical response of cartilage, we reproduce several features that have been demonstrated experimentally in the cartilage mechanics literature.     

Purification, cloning, and functional expression of phenylalanine aminomutase: the first committed step in Taxol side-chain biosynthesis

The biomechanical functions of articular cartilage are governed largely by the composition and density of its specialized extracellular matrix. Relationships between matrix density and functional indices such as mechanical properties or interstitial solute diffusivities have been previously explored. However, direct correlations between mechanical properties and solute transport parameters have received less attention, despite potential application of this information for cartilage functional assessment both in vivo and in vitro. The objective of this study was therefore to examine relationships among solute diffusivities, mechanical properties, and matrix density of compressed articular cartilage. Matrix density varied due to natural variation among explants and due to applied static compression. Matrix density of statically compressed cartilage explants was characterized by glycoaminoglycan (GAG) weight fraction and fluid volume fraction, while diffusion coefficients of a wide range of solutes were measured to characterize the transport environment. Explant mechanical properties were characterized by a non-linear Young's modulus (axial stress-strain ratio) and a non-linear Poisson's ratio (radial-to-axial strain ratio). Solute diffusivities were consistently correlated with Young's modulus, as well as with explant GAG weight and fluid volume fractions. Therefore, in vitro mechanical tests may provide a means of assessing transport environments in cartilage-like materials, while in vivo measurements of solute transport (for example with magnetic resonance imaging) may be a useful complement in identifying localized differences in matrix density and mechanical properties.     

Dynamic shear behavior of mandibular condylar cartilage is dependent on testing direction

Little information is available on the direction-dependency of shear behavior in mandibular condylar cartilage. Therefore, we tested the hypothesis that such a dependency of the dynamic shear properties is present in mandibular condylar cartilage. From each of 17 condyles, two cartilage-bone plugs were dissected and tested in a simple shear sandwich configuration under a compressive strain of 10%. Sinusoidal shear strain (frequency range: 0.01-10 Hz) was applied in the medio-lateral or antero-posterior direction with an amplitude of 1.0%, 2.0%, and 3.0%. The magnitudes of the dynamic shear moduli, as calculated from the resulting shear stress, were found to increase with applied frequency and the shear strain amplitude. The values |G*|, G' and G' for a medio-laterally applied shear were about 20-33% of those in the antero-posterior shear, although the loss tangent (elasticity/viscosity ratio) was almost the same. In conclusion, the present results clearly show the direction-dependent characteristic of the mandibular condylar cartilage in dynamic shear.     

Visco- and poroelastic contributions of the zona pellucida to the mechanical response of oocytes

Probing mechanical properties of cells has been identified as a means to infer information on their current state, e.g. with respect to diseases or differentiation. Oocytes have gained particular interest, since mechanical parameters are considered potential indicators of the success of in vitro fertilisation procedures. Established tests provide the structural response of the oocyte resulting from the material properties of the cell’s components and their disposition. Based on dedicated experiments and numerical simulations, we here provide novel insights on the origin of this response. In particular, polarised light microscopy is used to characterise the anisotropy of the zona pellucida, the outermost layer of the oocyte composed of glycoproteins. This information is combined with data on volumetric changes and the force measured in relaxation/cyclic, compression/indentation experiments to calibrate a multi-phasic hyper-viscoelastic model through inverse finite element analysis. These simulations capture the oocyte’s overall force response, the distinct volume changes observed in the zona pellucida, and the structural alterations interpreted as a realignment of the glycoproteins with applied load. The analysis reveals the presence of two distinct timescales, roughly separated by three orders of magnitude, and associated with a rapid outflow of fluid across the external boundaries and a long-term, progressive relaxation of the glycoproteins, respectively. The new results allow breaking the overall response down into the contributions from fluid transport and the mechanical properties of the zona pellucida and ooplasm. In addition to the gain in fundamental knowledge, the outcome of this study may therefore serve an improved interpretation of the data obtained with current methods for mechanical oocyte characterisation.

     

Cartilage electromechanics--II. A continuum model of cartilage electrokinetics and correlation with experiments

We have formulated a continuum model for linear electrokinetic transduction in cartilage. Expressions are derived for the streaming potential and streaming current induced by oscillatory, uniaxial confined compression of the tissue, as well as the mechanical stress generated by a current density or potential difference applied to the tissue. The experimentally observed streaming potential and current-generated stress response, measured on the same specimens, are compared with the predictions of the theory over a wide frequency range. The theory compares well with the data for reasonable values of cartilage intrinsic mechanical parameters and electrokinetic coupling coefficients. Experiments also show a linear relationship between the stimulus amplitude and the transduction response amplitude, within the range of stimulus amplitudes of interest. This observation is shown to be consistent with the predictions of the linear theory.     

A Theoretical Analysis of Water Transport Through Chondrocytes

Because of the avascular nature of adult cartilage, nutrients and waste products are transported to and from the chondrocytes by diffusion and convection through the extracellular matrix. The convective interstitial fluid flow within and around chondrocytes is poorly understood. This theoretical study demonstrates that the incorporation of a semi-permeable membrane when modeling the chondrocyte leads to the following findings: under mechanical loading of an isolated chondrocyte the intracellular fluid pressure is on the order of tens of Pascals and the transmembrane fluid outflow, on the order of picometers per second, takes several days to subside; consequently, the chondrocyte behaves practically as an incompressible solid whenever the loading duration is on the order of minutes or hours. When embedded in its extracellular matrix (ECM), the chondrocyte response is substantially different. Mechanical loading of the tissue leads to a fluid pressure difference between intracellular and extracellular compartments on the order of tens of kilopascals and the transmembrane outflow, on the order of a nanometer per second, subsides in about 1 h. The volume of the chondrocyte decreases concomitantly with that of the ECM. The interstitial fluid flow in the extracellular matrix is directed around the cell, with peak values on the order of tens of nanometers per second. The viscous fluid shear stress acting on the cell surface is several orders of magnitude smaller than the solid matrix shear stresses resulting from the ECM deformation. These results provide new insight toward our understanding of water transport in chondrocytes.     

Hip chondrolabral mechanics during activities of daily living: Role of the labrum and interstitial fluid pressurization

Osteoarthritis of the hip can result from mechanical factors, which can be studied using finite element (FE) analysis. FE studies of the hip often assume there is no significant loss of fluid pressurization in the articular cartilage during simulated activities and approximate the material as incompressible and elastic. This study examined the conditions under which interstitial fluid load support remains sustained during physiological motions, as well as the role of the labrum in maintaining fluid load support and the effect of its presence on the solid phase of the surrounding cartilage. We found that dynamic motions of gait and squatting maintained consistent fluid load support between cycles, while static single-leg stance experienced slight fluid depressurization with significant reduction of solid phase stress and strain. Presence of the labrum did not significantly influence fluid load support within the articular cartilage, but prevented deformation at the cartilage edge, leading to lower stress and strain conditions in the cartilage. A morphologically accurate representation of collagen fibril orientation through the thickness of the articular cartilage was not necessary to predict fluid load support. However, comparison with simplified fibril reinforcement underscored the physiological importance. The results of this study demonstrate that an elastic incompressible material approximation is reasonable for modeling a limited number of cyclic motions of gait and squatting without significant loss of accuracy, but is not appropriate for static motions or numerous repeated motions. Additionally, effects seen from removal of the labrum motivate evaluation of labral reattachment strategies in the context of labral repair.     

Activation and Inactivation of Mechanosensitive Currents in the Chick Heart

The behavior of MS channels in embryonic chick ventricular myocytes activated by direct mechanical stimulation is strongly affected by inactivation. The amplitude of the current is dependent not only on the amplitude of the stimulus, but also the history of stimulation. The MS current inactivation appears to be composed of at least two contributions: (i) rearrangement of the cortical tension transducing elements and (ii) blocking action of an autocrine agent released from the cell. With discrete mechanical stimuli, the MS current amplitude in the second press of a double press protocol was always smaller than the amplitude of the first MS current. Occasionally, a large MS current occurred when the cell was first stimulated, but subsequently the cell became unresponsive. For a series of stimuli of varying amplitudes, the order in which they were applied to the cell affected the size of the observed MS current for a given stimulus magnitude. When continuous sinusoidal stimulation was applied to the cells, the MS current envelope either reached a steady state, or inactivated. With sinusoidal stimulation, the MS response could be enhanced or restored by simple perfusion of fluid across the cell. This suggests that mechanical stimulation of the cells produces an autocrine inhibitor of MS channels as well as resulting in cortical rearrangement. Received: 7 July 1999/Revised: 26 October 1999     

Load sharing between solid and fluid phases in articular cartilage: I--Experimental determination of in situ mechanical conditions in a porcine knee.

The in situ mechanical conditions of cartilage in the articulated knee were quantified during joint loading. Six porcine knees were subjected to a 445 N compressive load while cartilage deformations and contact pressures were measured. From roentgenograms, cartilage thickness before and during loading allowed the calculation of tissue deformation on the lateral femoral condyle at different times during the loading process. Contact pressures on the articular surface were measured with miniature fiber-optic pressure transducers. Results showed that the medial side of the lateral femoral condyle had higher contact pressures, as well as deformations. To begin to correlate the pressures and resulting deformations, the intrinsic material properties of the cartilage on the lateral condyle were obtained from indentation tests. Data from four normal control specimens indicated that the aggregate modulus of the medial side was significantly higher than in other areas of the condyle. These experimental measures of the in situ mechanical conditions of articular cartilage can be combined with theoretical modeling to obtain valuable information about the relative contributions of the solid and fluid phases to supporting the applied load on the cartilage surface (see Part II).     

Mechanical Stimulation of Chondrocyte-agarose Hydrogels

Articular cartilage suffers from a limited repair capacity when damaged by mechanical insult or degraded by disease, such as osteoarthritis. To remedy this deficiency, several medical interventions have been developed. One such method is to resurface the damaged area with tissue-engineered cartilage; however, the engineered tissue typically lacks the biochemical properties and durability of native cartilage, questioning its long-term survivability. This limits the application of cartilage tissue engineering to the repair of small focal defects, relying on the surrounding tissue to protect the implanted material. To improve the properties of the developed tissue, mechanical stimulation is a popular method utilized to enhance the synthesis of cartilaginous extracellular matrix as well as the resultant mechanical properties of the engineered tissue. Mechanical stimulation applies forces to the tissue constructs analogous to those experienced in vivo. This is based on the premise that the mechanical environment, in part, regulates the development and maintenance of native tissue^1,2. The most commonly applied form of mechanical stimulation in cartilage tissue engineering is dynamic compression at physiologic strains of approximately 5-20% at a frequency of 1 Hz^1,3. Several studies have investigated the effects of dynamic compression and have shown it to have a positive effect on chondrocyte metabolism and biosynthesis, ultimately affecting the functional properties of the developed tissue^4-8. In this paper, we illustrate the method to mechanically stimulate chondrocyte-agarose hydrogel constructs under dynamic compression and analyze changes in biosynthesis through biochemical and radioisotope assays. This method can also be readily modified to assess any potentially induced changes in cellular response as a result of mechanical stimuli.     

Time-dependent behavior of cartilage surrounding a metal implant for full-thickness cartilage defects of various sizes: a finite element study

Recently, physiological and biomechanical studies on animal models with metal implants filling full-thickness cartilage defects have resulted in good clinical outcomes. The knowledge of the time-dependent macroscopic behavior of cartilage surrounding the metal implant is essential for understanding the joint function after treating such defects. We developed a model to investigate the in vivo time-dependent behavior of the tibiofemoral cartilages surrounding the metal implant, when the joint is subjected to an axial load for various defect sizes. Results show that time-dependent effects on cartilage behavior are significant, and can be simulated. These effects should be considered when evaluating the results from an implant. In particular, the depth into the cartilage where an implant is positioned and the mechanical sealing due to solidification of the poroelastic material need a time aspect. We found the maximal deformations, contact pressures and contact forces in the joint with time for the implant positioned in flush and sunk 0.3 mm into the cartilage. The latter position gives the better joint performance. The results after 60 s may be treated as the primary results, reflecting the effect of accumulation in the joint due to repeated short-time loadings. The wedge-shaped implant showed beneficial in providing mechanical sealing of cartilages surrounding the implant with time.     

Dynamics of a tightly coupled mechanism for flagellar rotation. Bacterial motility, chemiosmotic coupling, protonmotive force.

The bacterial flagellar motor is a molecular engine that couples the flow of protons across the cytoplasmic membrane to rotation of the flagellar filament. We analyze the steady-state behavior of an explicit mechanical model in which a fixed number of protons carries the filament through one revolution. Predictions of this model are compared with experimentally determined relationships between protonmotive force, proton flux, torque, and speed. All such tightly coupled mechanisms produce the same torque when the motor is stalled but vary greatly in their behavior at high speed. The speed at zero load predicted by our model is limited by the rates of association and dissociation of protons at binding sites on the rotor and by the mobility of force generators containing transmembrane channels that interact with these sites. Our analysis suggests that more could be learned about the motor if it were driven by an externally applied torque backwards (at negative speed) or forwards at speeds greater than the zero-load speed.     

A comparison between mechano-electrochemical and biphasic swelling theories for soft hydrated tissues

Biological tissues like intervertebral discs and articular cartilage primarily consist of interstitial fluid, collagen fibrils and negatively charged proteoglycans. Due to the fixed charges of the proteoglycans, the total ion concentration inside the tissue is higher than in the surrounding synovial fluid (cation concentration is higher and the anion concentration is lower). This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. In the last decade several mechano-electrochemical models, which include this mechanism, have been developed. As these models are complex and computationally expensive, it is only possible to analyze geometrically relatively small problems. Furthermore, there is still no commercial finite element tool that includes such a mechano-electrochemical theory. Lanir (Biorheology, 24, pp. 173-187, 1987) hypothesized that electrolyte flux in articular cartilage can be neglected in mechanical studies. Lanir's hypothesis implies that the swelling behavior of cartilage is only determined by deformation of the solid and by fluid flow. Hence, the response could be described by adding a deformation-dependent pressure term to the standard biphasic equations. Based on this theory we developed a biphasic swelling model. The goal of the study was to test Lanir's hypothesis for a range of material properties. We compared the deformation behavior predicted by the biphasic swelling model and a full mechano-electrochemical model for confined compression and 1D swelling. It was shown that, depending on the material properties, the biphasic swelling model behaves largely the same as the mechano-electrochemical model, with regard to stresses and strains in the tissue following either mechanical or chemical perturbations. Hence, the biphasic swelling model could be an alternative for the more complex mechano-electrochemical model, in those cases where the ion flux itself is not the subject of the study. We propose thumbrules to estimate the correlation between the two models for specific problems.