Depth and strain rate-dependent mechanical response of chondrocytes in reserve zone cartilage subjected to compressive loading

Biomechanics and Modeling in Mechanobiology - The role of the growth plate reserve zone is not well understood. It has been proposed to serve as a source of stem cells and to produce morphogens...     

Nutrient utilization by bovine articular chondrocytes: a combined experimental and theoretical approach

A combined experimental-numerical approach was adopted to characterize glucose and oxygen uptake and lactate production by bovine articular chondrocytes in a model system. For a wide range of cell concentrations, cells in agarose were supplemented with either low or high glucose medium. During an initial culture phase of 48 h, oxygen was monitored noninvasively using a biosensor system. Glucose and lactate were determined by medium sampling. In order to quantify glucose and oxygen uptake, a finite element approach was adopted to describe diffusion and uptake in the experimental model. Numerical predictions of lactate, based on simple relations for cell metabolism, were found to agree well for low glucose, but not for high glucose medium. Oxygen did not play a role in either case. Given the close association between chondrocyte energy metabolism and matrix synthesis, a quantifiable prediction of utilization can present a valuable contribution in the optimization of tissue engineering conditions.     

The mechanical environment of chondrocytes in articular cartilage

There is a growing literature concerning chondrocyte responses to mechanical loading, but relatively little is known about the mechanical environment these cells experience in a living joint. Calculations indicate that high forces are applied to limb joints whenever the joints are flexed, because flexion can cause body weight to act on long lever arms compared to the joint centre, whereas the muscles which extend the joint act on much shorter lever arms. As a result, joint reaction forces (which compress the cartilage) can rise to 3-6 times body weight during activities such as stair climbing. Articular cartilage tends to spread this load evenly over the joint surface, but is too thin to do this well, and compressive stresses can rise to 10-20 MPa. Within cartilage, matrix stresses vary locally, possibly as a result of variation in composition or undulations in the subchondral bone, and further modifications of stress occur within each chondron. Articular cartilage is a fibrous solid and cells within it are deformed by mechanical loading rather than subjected to a hydrostatic pressure. The mechanical environment of chondrocytes can best be reproduced in vitro by direct compression of the articular surface of cartilage which is supported naturally by adjacent cartilage and subchondral bone.     

Mechanical behaviour of in-situ chondrocytes subjected to different loading rates: a finite element study

Experimental findings indicate that in-situ chondrocytes die readily following impact loading, but remain essentially unaffected at low (non-impact) strain rates. This study was aimed at identifying possible causes for cell death in impact loading by quantifying chondrocyte mechanics when cartilage was subjected to a 5% nominal tissue strain at different strain rates. Multi-scale modelling techniques were used to simulate cartilage tissue and the corresponding chondrocytes residing in the tissue. Chondrocytes were modelled by accounting for the cell membrane, pericellular matrix and pericellular capsule. The results suggest that cell deformations, cell fluid pressures and fluid flow velocity through cells are highest at the highest (impact) strain rate, but they do not reach damaging levels. Tangential strain rates of the cell membrane were highest at the highest strain rate and were observed primarily in superficial tissue cells. Since cell death following impact loading occurs primarily in superficial zone cells, we speculate that cell death in impact loading is caused by the high tangential strain rates in the membrane of superficial zone cells causing membrane rupture and loss of cell content and integrity.     

Nonlinear mechanical property of tracheal cartilage: a theoretical and experimental study

BACKGROUND: Despite being the stiffest airway of the bronchial tree, the trachea undergoes significant deformation due to intrathoracic pressure during breathing. The mechanical properties of the trachea affect the flow in the airway and may contribute to the biological function of the lung. METHOD: A Fung-type strain energy density function was used to investigate the nonlinear mechanical behavior of tracheal cartilage. A bending test on pig tracheal cartilage was performed and a mathematical model for analyzing the deformation of tracheal cartilage was developed. The constants included in the strain energy density function were determined by fitting the experimental data. RESULT: The experimental data show that tracheal cartilage is a nonlinear material displaying higher strength in compression than in tension. When the compression forces varied from -0.02 to -0.03N and from -0.03 to -0.04N, the deformation ratios were 11.03+/-2.18% and 7.27+/-1.59%, respectively. Both were much smaller than the deformation ratios (20.01+/-4.49%) under tension forces of 0.02 to 0.01N. The Fung-type strain energy density function can capture this nonlinear behavior very well, whilst the linear stress-strain relation cannot. It underestimates the stability of trachea by exaggerating the displacement in compression. This study may improve our understanding of the nonlinear behavior of tracheal cartilage and it may be useful for the future study on tracheal collapse behavior under physiological and pathological conditions.     

The effect of cyclical compressive loading on gene expression in articular cartilage

Osteoarthritis (OA) develops as a consequence of articular cartilage degeneration possibly initiated by excessive or abnormal loading of the joint, and potentially mediated through a proteinase/proteinase inhibitor imbalance. We have shown previously that physiological loads (0.5 MPa, 1 Hz, 3 hour) elicit increased expression and activation of the matrix metalloproteinases (MMPs) in articular cartilage explants in vitro. The objective of this study was to identify mechanically-regulated genes involved in the observed induction of MMP expression and enhanced activation. Differential RNA Display (DRD) was used to identify mechanically-regulated genes by comparing DRD products derived from loaded and unloaded cartilage. One gene up-regulated in cartilage after 10, 30 and 60 minute loading revealed 83% homology with Mus musculus thymosin beta_4 which is known to induce MMP gene expression. The identification of mechanically regulated genes will greatly enhance our understanding of matrix turnover providing an exciting future in elucidating the role of mechanically-regulated genes in the development of OA.     

Toward an MRI-based method to measure non-uniform cartilage deformation: an MRI-cyclic loading apparatus system and steady-state cyclic displacement of articular cartilage under compressive loading

Recent magnetic resonance imaging (MRI) techniques have shown potential for measuring non-uniform deformations throughout the volume (i.e. three-dimensional (3D) deformations) in small orthopedic tissues such as articular cartilage. However, to analyze cartilage deformation using MRI techniques, a system is required which can construct images from multiple acquisitions of MRI signals from the cartilage in both the underformed and deformed states. The objectives of the work reported in this article were to 1) design an apparatus that could apply highly repeatable cyclic compressive loads of 400 N and operate in the bore of an MRI scanner, 2) demonstrate that the apparatus and MRI scanner can be successfully integrated to observe 3D deformations in a phantom material, 3) use the apparatus to determine the load cycle necessary to achieve a steady-state deformation response in normal bovine articular cartilage samples using a flat-surfaced and nonporous indentor in unconfined compression. Composed of electronic and pneumatic components, the apparatus regulated pressure to a double-acting pneumatic cylinder so that (1) load-controlled compression cycles were applied to cartilage samples immersed in a saline bath, (2) loading and recovery periods within a cycle varied in time duration, and (3) load magnitude varied so that the stress applied to cartilage samples was within typical physiological ranges. In addition the apparatus allowed gating for MR image acquisition, and operation within the bore of an MRI scanner without creating image artifacts. The apparatus demonstrated high repeatability in load application with a standard deviation of 1.8% of the mean 400 N load applied. When the apparatus was integrated with an MRI scanner programmed with appropriate pulse sequences, images of a phantom material in both the underformed and deformed states were constructed by assembling data acquired through multiple signal acquisitions. Additionally, the number of cycles to reach a steady-state response in normal bovine articular cartilage was 49 for a total cycle duration of 5 seconds, but decreased to 33 and 27 for increasing total cycle durations of 10 and 15 seconds, respectively. Once the steady-state response was achieved, 95% of all displacements were within +/- 7.42 microns of the mean displacement, indicating that the displacement response to the cyclic loads was highly repeatable. With this performance, the MRI-loading apparatus system meets the requirements to create images of articular cartilage from which 3D deformation can be determined.     

Modelling of location- and time-dependent deformation of chondrocytes during cartilage loading.

Experimental evidence suggests that the biosynthetic activity of chondrocytes is regulated primarily by the mechanical environment. In order to study the mechanisms underlying remodeling, adaptation, and degeneration of articular cartilage in a joint subjected to changing loads, it is important to know the time-dependent fluid pressure and stress-strain state in chondrocytes. The purpose of the present study was to develop a theoretical model to simulate the mechanical behaviour of articular cartilage and to describe the time-dependent stress-strain state and fluid pressure distribution in chondrocytes during cartilage deformation. It was assumed that the volume occupied by the chondrocytes is small and that cartilage can be treated as a macroscopically homogenized material with effective material properties which depend on the material properties of the cells and matrix and the volumetric fraction of the cells. Model predictions on the time-dependent distribution of fluid pressure and stress and on the time-dependent cell deformation during confined and unconfined compression tests agree with previous theoretical predictions and experimental observations. The proposed model supplies the tools to study the mechanisms of degeneration, adaptation and remodelling of cartilage associated with cell loading and deformation.     

Biodiversity and multifunctionality in a microbial community: a novel theoretical approach to quantify functional redundancy

Ecosystems have a limited buffering capacity of multiple ecosystem functions against biodiversity loss (i.e. low multifunctional redundancy). We developed a novel theoretical approach to evaluate multifunctional redundancy in a microbial community using the microbial genome database (MBGD) for comparative analysis. In order to fully implement functional information, we defined orthologue richness in a community, each of which is a functionally conservative evolutionary unit in genomes, as an index of community multifunctionality (MF). We constructed a graph of expected orthologue richness in a community (MF) as a function of species richness (SR), fit the power function to SR (i.e. MF = cSR^a), and interpreted the higher exponent a as the lower multifunctional redundancy. Through a microcosm experiment, we confirmed that MF defined by orthologue richness could predict the actual multiple functions. We simulated random and non-random community assemblages using full genomic data of 478 prokaryotic species in the MBGD, and determined that the exponent in microbial communities ranged from 0.55 to 0.75. This exponent range provided a quantitative estimate that a 6.6–8.9% loss limit in SR occurred in a microbial community for an MF reduction no greater than 5%, suggesting a non-negligible initial loss effect of microbial diversity on MF.     

Histochemical evidence of a functional heterogeneity of the chondrocytes of adult canine articular cartilage

Synopsis Twenty humeral heads were collected from 10 adult English Pointer dogs, fixed in 15% formalin containing cetylpyridinium chloride, decalcified, processed for paraffin sections, and cut serially. The articular cartilage was studied by staining principally with Alcian Blue in the presence of 0.4 or 0.9m MgCl₂ with and without a van Gieson counterstain. The results of the differential staining procedures demonstrated the existence of two groups of chondrocytes with distinctly different staining affinities. One group reacted intensely for the presence of protein-polysaccharides within its cytoplasm while the other group completely lacked this property. An approximate proportionality of 31 of the protein polysaccharide-positive and-negative chondrocytes was observed in the tangential layer and upper intermediate zone. In the lower intermediate zone, radiate zone, and zone of calcified cartilage, the chondrocyte types were present in equal proportions. Staining with Alcian Blue in the presence of 0.9m MgCl₂ with and without a van Gieson counterstain indicated a further subdivision of the protein-polysaccharide positive group of chondrocytes. This blocking technique has been reported to distinguish between chondroitin sulphate and high mol. wt. keratosulphate. Thus, based upon a greatly decreased number of the blue-stained chondrocytes after staining with Alcian Blue in the presence of 0.9m MgCl₂ the hypothesis is put forward that some chondrocytes produce primarily chondroitin suphate and others produce both chondroitin sulphate and keratosulphate.     

26 Inversion approach to the origin of life: theoretical notions and experimental data

The essence of the inversion concept of the origin of life can be narrowed down to the following theses: (1) thermodynamic inversion is the key transformation of prebiotic microsystems leading to their transition into primary forms of life; (2) this transformation might occur only in the microsystems oscillating around the bifurcation point under far-from-equilibrium conditions. The transformation consists in the inversion of the balance “free energy contribution entropy contribution” (as well as “information contribution informational entropy contribution”), from negative to positive values. At the inversion moment, the microsystem radically reorganizes in accordance with the new negentropy (i.e. biological) way of organization. According to this concept, the origin-of-life process on the early Earth took place in oscillating hydrothermal medium. The process was taking two successive stages: (1) spontaneous self-assembly of initial three-dimensional prebiotic microsystems composed mainly of hydrocarbons, lipids, and simple amino acids, or their precursors, within the temperature interval of 100–300?°C (prebiotic stage); (2) nonspontaneous synthesis of sugars, ATP, and nucleic acids started at the inversion moment under the temperature 70–100?°C (biotic stage). Macro and microfluctuations of thermodynamic and physicochemical parameters able to sustain this way of chemical conversion have been detected in several contemporary hydrothermal systems (Kompanichenko, 2012). Conditions in potential hydrothermal medium for the origin of life were explored on the examples of several hydrothermal systems in Kamchatka peninsula. Temperature of water in hot springs ranges from?<?60 to 98?°C, in the bore holes water-steam temperature varies from?<?100 to 239?°C, and pressure from?<?1 to 35 bars at the wellheads; pH is within the interval 2.5–9.0. Pressure monitoring at the depth 950?meters in the borehole No. 30 (Mutnovsky field) has revealed high-amplitude (up to 1–2 bars) irregular macrofluctuations and low-amplitude quite regular microoscillations of pressure (amplitudes 0.1–0.3 bars). Hydrocarbons, lipid precursors, and simple amino acids are available in the fluid. The lifeless condensate of water-steam mixture (temperature 108–175?°C) contains aromatic hydrocarbons, n-alkanes, ketons, alcohols, and aldehydes. In addition to those, cycloalkanes, alkenes, dietoxyalkanes, naphtenes, fatty acids, ethyl ethers of fatty acids, and monoglycerides have been detected in hot solutions inhabited by thermophiles and hyperthermophiles (temperature 70–98?°C). According to Mukhin et al. (1979), glycine of probably abiotic origination was detected in lifeless condensate.     

The theoretical and experimental study on dicalcium phosphate dehydrate loading with protocatechuic aldehyde

The aim of this study is to investigate the interaction between dicalcium phosphate dihydrate (CaHPO₄•2H₂O, DCPD) and Protocatechuic aldehyde (C₇H₆O₃, Pca), which is the water-soluble constituents of Chinese Medicine, Salvia Miltiorrhiza Bunge (SMB), by calculating the absorption energy through molecular dynamics simulation. Furthermore, the effects of functional groups of Pca and temperature on Pca adsorbed by DCPD are calculated respectively. DCPD/Pca and DCPD were analyzed by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR) and thermogravimetric analysis (TG). The simulation results showed that Pca mostly absorbed on the (0 2 0) surface of DCPD. The aldehyde group of Pca played a moren important role on the adsorption of Pca on DCPD than hydroxyl did, while temperature had no distinct effects on the adsorption. XRD results indicated that Pca induced the preferential growth of (0 2 0) crystal surface in DCPC/Pca whereas it had no influence on the crystal structure, the crystallinity and grain size of DCPD. FTIR and TG results showed that the characteristic peak of Pca was at 1295 cm^-1 and the content of Pca in DCPD was 16%, respectively. The present results show that molecular dynamics simulation is a very effective and complementary method to study the interaction between materials and medicine.     

Passive osmotic properties of in situ human articular chondrocytes within non-degenerate and degenerate cartilage

Osteoarthritis is characterized by many factors, including proteoglycan loss, decreased collagen stiffness, and increased cartilage hydration. Chondrocyte swelling also occurs, and correlates with the degree of osteoarthritis, however, the cause is unknown but might be related to alterations to their passive osmotic properties. We have used two-photon confocal laser scanning microscopy to measure the passive osmotic characteristics of in situ chondrocytes within relatively non-degenerate and degenerate human tibial plateau cartilage, and in chondrocytes isolated from relatively non-degenerate cartilage. Explants with bone attached were taken from a total of 42 patients undergoing arthroplasty and graded macroscopically and microscopically into two groups, grade 0 + 1 and grade 2 + 3. There was a significant increase in cartilage hydration between these two groups (P < 0.05), however, there was no change when medium osmolarity was varied over approximately 0-480 mOsm. The passive osmotic behavior of in situ chondrocytes (at 4 degrees C) was identical over a range of culture medium osmolarities ( approximately 0-515 mOsm), however, the maximum swelling of cells within degenerate cartilage and isolated chondrocytes was greater compared to those in non-degenerate cartilage. The swelling in the majority of in situ chondrocytes was accounted for by the reduced interstitial osmolarity occurring with cartilage degeneration. There was, however, a small population of in situ chondrocytes whose volume was in excess (>/=2,500 microm(3)) of that predicted from the decreased interstitial osmotic pressure. These results show that for the majority of cells studied, the differences in passive chondrocyte volume between relatively non-degenerate, degenerate, and isolated cells were entirely accounted for by changes to the extracellular osmolarity (180-515 mOsm).     

Disparate aggrecan gene expression in chondrocytes subjected to hypotonic and hypertonic loading in 2D and 3D culture

The effects of hypotonic (180 mOsm) and hypertonic (580 mOsm) medium loading on chondrocyte aggrecan gene expression in 2D monolayer and 3D hydrogel culture (agarose or alginate) were studied. Aggrecan promoter activity was monitored using a luciferase reporter gene assay and transient transfection. Osmotic loading was observed to differentially affect promoter activity, with hypotonic loading generally producing at least a 40% elevation in promoter activity, except for the case of alginate where a 50% suppression was observed. Hypertonic loading produced at least a 35% decrease in activity for all cultures. Similar osmolality-induced changes to aggrecan mRNA levels were observed in monolayer cells using qPCR. Deletion of exon 1 blocked the sensitivity of monolayer cells to hypertonic but not hypotonic medium changes. Confocal microscopy measurements suggested that the degree of hypotonic swelling in cells encapsulated in 3D matrix was restricted compared to monolayer cells whereas the degree of hypertonic shrinking was similar under both culture conditions.     

The role of tenascin-C in adaptation of tendons to compressive loading

Although most tendon regions are subjected primarily to high tensile loads, selected regions, primarily those that directly contact bones that change the direction of the tendon, must withstand high compressive loads as well. Compressed tendon regions differ from regions subjected to primarily tensile loads: they have a fibrocartilaginous structure with spherical cells surrounded by a matrix containing aggrecan and collagen types I and II, in contrast regions not exposed to compression have a fibrous structure with spindle shaped fibroblasts surrounded by a matrix of dense, longitudinally oriented type I collagen fibrils. The spherical shape of cells in fibrocartilagenous regions indicates these cells are more loosely attached to the matrix than their spindle-shaped counterparts in fibrous regions, a feature that may help to minimize cell deformation during tendon compression. We hypothesized that expression of tenascin-C, an anti-adhesive protein, is part of the adaptation of tendon cells to compression that helps establish and maintain fibrocartilaginous regions. To test this hypothesis we compared tenascin-C content and expression in compressed (distal) versus uncompressed (proximal) segments of bovine flexor tendons. Immunohistochemistry and immunoblot analyses showed that tenascin-C content was increased in the distal tendon where it co-distributed with type II collagen and aggrecan. Tendon cells from the distal segments expressed more tenascin-C than did cells from the proximal segments for up to four days in cell culture, indicating that increased tenascin-C expression is a relatively stable feature of the distal cells. These observations support the hypothesis that tenascin-C expression is a cellular adaptation to compression that helps establish and maintain fibrocartilagenous regions of tendons.     

A theoretical and experimental approach to the use of single wavelength calcium indicators

Fluorescent Ca(2+) indicators have been extremely valuable in understanding the role of intracellular Ca(2+). However, the presence of extracellular dye can confound interpretation of data due to indicator accumulation in the Ca(2+)-rich medium, which induces an increase in the fluorescence signal. By using a mathematical approach, we show that overlooking extracellular dye usually leads to overestimating cytosolic Ca(2+) ([Ca(2+)]) levels. We propose an experimental design and provide mathematical formulations to make the appropriate correction. We applied our model to determine [Ca(2+)] in Fluo-3-loaded bovine aortic endothelial cells (BAECs). Our results indicate that for basal level Ca(2+), the uncorrected value overestimates by a factor of 2.7 the result obtained when extracellular dye was accounted for. We also showed that both bradykinin (BK) and ATP significantly increase [Ca(2+)] in BAECs. For the uncorrected values, BK and ATP induced 2.3- and 3.3-fold apparent increases in [Ca(2+)], respectively. When applying the correction, there was a 4.5- and 5.4-fold induction of [Ca(2+)] for BK and ATP, respectively. Our theoretical and experimental models provide explanations and, at least in part, solutions to the dye leakage problem, and should thus be a valuable tool in clarifying the proper usage of fluorescent dyes for Ca(2+) measurements.     

Magnetic-field-induced vertigo: a theoretical and experimental investigation

Vertigo-like sensations or apparent perception of movement are reported by some subjects and operators in and around high field whole body magnetic resonance body scanners. Induced currents (which modulate the firing rate of the vestibular hair cell), magneto-hydrodynamics (MDH), and tissue magnetic susceptibility differences have all been proposed as possible mechanisms for this effect. In this article, we examine the theory underlying each of these mechanisms and explore resulting predictions. Experimental evidence is summarised in the following findings: 30% of subjects display a postural sway response at a field-gradient product of 1 T(2)m(-1); a determining factor for experience of vertigo is the total unipolar integrated field change over a period greater than 1 s; the perception of dizziness is not necessarily related to a high value of the rate of change of magnetic field; eight of ten subjects reported sensations ranging from mild to severe when exposed to a magnetic field change of the order of 4.7 T in 1.9 s; no subjects reported any response when exposed to 50 ms pulses of dB/dt of 2 Ts(-1) amplitude. The experimental evidence supports the hypothesis that magnetic-field related vertigo results from both magnetic susceptibility differences between vestibular organs and surrounding fluid, and induced currents acting on the vestibular hair cells. Both mechanisms are consistent with theoretical predictions.