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.     

Osmotic swelling and residual stress in cardiovascular tissues

Osmotic swelling (OS) and residual stress (RS) significantly affect the function of cardiovascular (CVS) tissues and organs. The physical mechanisms of OS and RS are reviewed and analyzed with focus on the theoretical background and related experimental evidence. It will be shown that swelling of CVS tissues stems from the presence of charged proteoglycan macro-molecules in these tissues, and that this swelling is a key determinant of RS. In view of OS and RS functional significance in mechanical function, modeling attempts which incorporate them in CVS stress analysis will be presented and discussed.     

Model films from native cellulose nanofibrils. Preparation, swelling, and surface interactions

Native cellulose model films containing both amorphous and crystalline cellulose I regions were prepared by spin-coating aqueous cellulose nanofibril dispersions onto silica substrates. Nanofibrils from wood pulp with low and high charge density were used to prepare the model films. Because the low charged nanofibrils did not fully cover the silica substrates, an anchoring substance was selected to improve the coverage. The model surfaces were characterized using atomic force microscopy (AFM) and X-ray photoelectron spectroscopy (XPS). The effect of nanofibril charge density, electrolyte concentration, and pH on swelling and surface interactions of the model film was studied by quartz crystal microbalance with dissipation (QCM-D) and AFM force measurements. The results showed that the best coverage for the low charged fibrils was achieved by using 3-aminopropyltrimethoxysilane (APTS) as an anchoring substance and hence it was chosen as the anchor. The AFM and XPS measurements showed that the fibrils are covering the substrates. Charge density of the fibrils affected the morphology of the model surfaces. The low charged fibrils formed a network structure while the highly charged fibrils formed denser film structure. The average thickness of the films corresponded to a monolayer of fibrils, and the average rms roughness of the films was 4 and 2 nm for the low and high charged nanofibril films, respectively. The model surfaces were stable in QCM-D swelling experiments, and the behavior of the nanofibril surfaces at different electrolyte concentrations and pHs correlated with other studies and the theories of Donnan. The AFM force measurements with the model surfaces showed well reproducible results, and the swelling results correlated with the swelling observed by QCM-D. Both steric and electrostatic forces were observed and the influence of steric forces increased as the films were swelling due to changes in pH and electrolyte concentration. These films differ from previous model cellulose films due to their chemical composition (crystalline cellulose I and amorphous regions) and fibrillar structure and hence serve as excellent models for the pulp fiber surface.     

Osmotic stress as a factor in the detrimental effect of glycerol on human platelets

The aim of this work was to determine the importance of osmotic stress as a damaging factor in the detrimental effect of glycerol on human platelets. The severity of osmotic stress was mitigated by reducing the rate of change of glycerol concentration in the suspending medium. The classical permeability equations were used to predict cell volume changes in response to step changes in extracellular glycerol concentration. Protocols were devised that limited cellular shrinkage during glycerol addition and cellular swelling during glycerol dilution. When glycerol was added and diluted rapidly, the recovery of the hypotonic stress response with respect to untreated controls was unaffected by 0.25 mol/liter glycerol, but was reduced to ca. 65% after exposure to 0.5 mol/liter glycerol and to ca. 25% after exposure to 1 mol/liter glycerol. When 1 mol/liter glycerol was added and removed slowly such that cell volume remained within the range of 60-130% of normal volume, recovery of the hypotonic stress response was improved to ca. 50%, and the aggregation response was undiminished. Osmotic stress was therefore at least partly responsible for the damage caused by glycerol. However, platelets were damaged more after slow dilution from 1 mol/liter glycerol, when cellular swelling was limited to 116% of normal volume, than after rapid dilution from 0.25 or 0.5 mol/liter glycerol, which resulted in cellular swelling to 123% and 146% of normal volume, respectively. Thus, a possible toxic effect of glycerol cannot as yet be discounted.     

Hydration of pectic polysaccharides

The hydration and swelling of pectic polysaccharides was examined at different pHs and ionic strengths as a function of osmotic stress. For weakly charged pectic polysaccharides at low concentrations of a monovalent salt (20 mM), the main driving force for swelling originates from a polyelectrolyte effect due to the translational entropy of ions within the film. Swelling is reduced at higher salt concentrations and lower pHs. Polyelectrolyte collapse and minimal swelling is observed for more highly charged pectic polysaccharides. Replacement of the Na(+) counterion with Ca(2+) results in minimal swelling and the formation of network structures even for the weakly charged pectic polysaccharides.     

Updated Lagrangian finite element formulations of various biological soft tissue non-linear material models: a comprehensive procedure and review

Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.     

Analysis of the permeation of cryoprotectants in cartilage

Some tissues, such as cartilage and cornea, carry an internal fixed negative charge, leading to a swelling pressure that is balanced by tensile stress in the tissue matrix. During the addition and removal of cryoprotectants the changes in osmotic pressure will cause the tissue to deform. Because of the fixed charge and osmotic deformation, the permeation process in such tissues differs from ordinary diffusion processes. In this paper a biomechanical multi-solute theory is introduced to describe this process in cartilage tissue. Typical values for the physiological and biomechanical properties are used in the simulation. Several parameters - the aggregate modulus, the fixed charge density and the frictional parameter - are analyzed to show their impact on the process. It is shown that friction between water and cryoprotectant has the greatest influence but the fixed charge density is also important. The aggregate modulus and the frictional parameter between the cryoprotectant and the solid matrix have the least influence. Both the new biomechanical model and the conventional diffusion model were fitted to published experimental data concerning the time course of mean tissue cryoprotectant concentration when cartilage is immersed in solutions of dimethyl sulphoxide or propylene glycol: in all cases and with both models a good fit was obtained only when a substantial amount of non-solvent water was assumed.     

Finite element study of a tissue-engineered cartilage transplant in human tibiofemoral joint

Most tissue-engineered cartilage constructs are more compliant than native articular cartilage (AC) and are poorly integrated to the surrounding tissue. To investigate the effect of an implanted tissue-engineered construct (TEC) with these inferior properties on the mechanical environment of both the engineered and adjacent native tissues, a finite element study was conducted. Biphasic swelling was used to model tibial cartilage and an implanted TEC with the material properties of either native tissue or a decreased elastic modulus and fixed charged density. Creep loading was applied with a rigid impermeable indenter that represented the femur. In comparison with an intact joint, compressive strains in the transplant, surface contact stress in the adjacent native AC and load partitioning between different phases of cartilage were affected by inferior properties of TEC. Results of this study may lead to a better understanding of the complex mechanical environment of an implanted TEC.     

Finite element study of a tissue-engineered cartilage transplant in human tibiofemoral joint

Most tissue-engineered cartilage constructs are more compliant than native articular cartilage (AC) and are poorly integrated to the surrounding tissue. To investigate the effect of an implanted tissue-engineered construct (TEC) with these inferior properties on the mechanical environment of both the engineered and adjacent native tissues, a finite element study was conducted. Biphasic swelling was used to model tibial cartilage and an implanted TEC with the material properties of either native tissue or a decreased elastic modulus and fixed charged density. Creep loading was applied with a rigid impermeable indenter that represented the femur. In comparison with an intact joint, compressive strains in the transplant, surface contact stress in the adjacent native AC and load partitioning between different phases of cartilage were affected by inferior properties of TEC. Results of this study may lead to a better understanding of the complex mechanical environment of an implanted TEC.     

Effect of Osmotic Stress on Ion Transport Processes and Phospholipid Composition of Wheat (Triticum aestivum L.) Mitochondria

The effect of osmotic stress on wheat (Triticum aestivum L.) mitochondrial activity and phospholipid composition was investigated. Preliminary growth measurements showed that osmotic stress (−0.25 or −0.5 megapascal external water potential) inhibited the rate of shoot dry matter accumulation while root dry matter accumulation was less sensitive. We have determined that differences in sensitivity to osmotic stress existed between tissues at the mitochondrial level. Mitochondria isolated from roots or shoots of stressed seedlings showed respiratory control and ADP/O ratios similar to control seedlings which indicates that stressed mitochondria were well coupled. However, under passive swelling conditions in a KCl reaction mixture, the rate and extent of valinomycin-induced swelling of shoot mitochondria were increased by osmotic stress while root mitochondria were largely unaffected. Active ion transport studies showed efflux transport by stressed-shoot mitochondria to be partially inhibited since mitochondrial contraction required the addition of N-ethylmaleimide or nigericin. Efflux ion transport by root mitochondria was not inhibited by osmotic stress which indicates that stress-induced changes in ion transport were largely limited to shoot mitochondria. Characterization of mitochondrial fatty acid and phospholipid composition showed an increase in the percentage of phosphatidylcholine in stressed shoot mitochondria compared to the control. Mitochondrial fatty acid composition was not markedly altered by stress. No significant changes in either the phospholipid or fatty acid composition of stressed root mitochondria were observed. Hence, these results suggest that a tissue-specific response to osmotic stress exists at the mitochondrial level.     

Swelling response of Golgi apparatus cisternae in cells treated with monensin is reduced by cell injury.

The effect of mechanical stress on Golgi apparatus was examined in thin slices of rat liver. The findings should be of relevance both to electron microscopists who routinely mince tissue, and to biochemists who homogenize tissues to isolate membranous components. The swelling response of Golgi apparatus to monensin was used as an assay because the swelling response is distinct and is thought to result from a well-characterized metabolic process, namely the acidification of vesicles. The results showed that the swelling response was compromised by monensin as far away as 6-7 cells from a cut surface even though other aspects of cell ultrastructure were not altered from normal. The monensin-induced swelling response was also evaluated in isolated Golgi apparatus and found to be similar to that with tissue. Thus, mechanical stress such as commonly used to mince tissue or isolate tissue components, appears to markedly alter Golgi apparatus function compared to the situation in vivo. In this example, the altered response of Golgi apparatus to monensin indicated that some aspects associated with the ATP-dependent proton-pumping machinery of the trans-most cisternae and trans Golgi network were compromised.     

Heterogeneous transmural proteoglycan distribution provides a mechanism for regulating residual stresses in the aorta

The arterial wall contains a significant amount of charged proteoglycans, which are inhomogeneously distributed, with the greatest concentrations in the intimal and medial layers. The hypothesis of this study is that the transmural distribution of proteoglycans plays a significant role in regulating residual stresses in the arterial wall. This hypothesis was first tested theoretically, using the framework of mixture theory for charged hydrated tissues, and then verified experimentally by measuring the opening angle of rat aorta in NaCl solutions of various ionic strengths. A three-dimensional finite element model of aortic ring, using realistic values of the solid matrix shear modulus and proteoglycan fixed-charge density, yielded opening angles and changes with osmolarity comparable to values reported in the literature. Experimentally, the mean opening angle in isotonic saline (300 mosM) was 15 +/- 17 degrees and changed to 4 +/- 19 degrees and 73 +/- 18 degrees under hypertonic (2,000 mosM) and hypotonic (0 mosM) conditions, respectively (n = 16). In addition, the opening angle in isotonic (300 mosM) sucrose, an uncharged molecule, was 60 +/- 16 degrees (n = 11), suggesting that the charge effect, not cellular swelling, was the major underlying mechanism for these observations. The extent of changes in opening angle under osmotic challenges suggests that transmural heterogeneity of fixed-charge density plays a crucial role in governing the zero-stress configuration of the aorta. A significant implication of this finding is that arterial wall remodeling in response to altered wall stresses may occur via altered deposition of proteoglycans across the wall thickness, providing a novel mechanism for regulating mechanical homeostasis in vascular tissue.     

Computational and experimental investigation of local stress fiber orientation in uniaxially and biaxially constrained microtissues

The orientation of cells and associated F-actin stress fibers is essential for proper tissue functioning. We have previously developed a computational model that qualitatively describes stress fiber orientation in response to a range of mechanical stimuli. In this paper, the aim is to quantitatively validate the model in a static, heterogeneous environment. The stress fiber orientation in uniaxially and biaxially constrained microscale tissues was investigated using a recently developed experimental system. Computed and experimental stress fiber orientations were compared, while accounting for changes in orientation with location in the tissue. This allowed for validation of the model, and additionally, it showed how sensitive the stress fiber orientation in the experimental system is to the location where it is measured, i.e., the heterogeneity of the stress fiber orientation. Computed and experimental stress fiber orientations showed good quantitative agreement in most regions. A strong local alignment near the locations where boundary conditions were enforced was observed for both uniaxially and biaxially constrained tissues. Excepting these regions, in biaxially constrained tissues, no preferred orientation was found and the distribution was independent of location. The stress fiber orientation in uniaxially constrained tissues was more heterogeneous, and stress fibers mainly oriented in the constrained direction or along the free edge. These results indicate that the stress fiber orientation in these constrained microtissues is mainly determined by the local mechanical environment, as hypothesized in our model, and also that the model is a valid tool to predict stress fiber orientation in heterogeneously loaded tissues.     

Biorheology and fluid flux in swelling tissues. I. Bicomponent theory for small deformations, including concentration effects

A theory for the rheological behavior and fluid flux in swelling tissues under small deformations is presented. Tissues are considered as bicomponent solid-fluid mixtures. Concentration effects are included. The driving forces (body, surface and interactive), are discussed and their constitutive relationships to the tissue's deformation are specified. Mass and momentum balance equations are developed for each component and for the tissue as a whole. The concept of swelling stress emerges from the theory as an anisotropic generalization of the commonly used swelling pressure. It is shown to be a measure of the total chemical potential combining both mechanical and concentration effects. The theory shows that concentration effects modify the tissue's bulk stiffness in a manner consistent with experimental observations.     

Apparatus for measuring the swelling dependent electrical conductivity of charged hydrated soft tissues

This paper describes a new apparatus and method for measuring swelling dependent electrical conductivity of charged hydrated soft tissues. The apparatus was calibrated using a conductivity standard. Swelling dependent specific conductivity of porcine annulus fibrosis (AF) samples was determined. The conductivity values for porcine AF were similar to those for human and bovine articular cartilage found in the literature. Results revealed a significant linear correlation between specific conductivity and water content for porcine AF tissues tested in phosphate buffered saline (PBS).     

Water Transfer and Cell Structure in Isolated Crayfish Muscle Fibers

Changes in volume of crayfish single muscle fibers in response to changes in ionic or electrical conditions have been studied in conjunction with electrophysiological measurements and electron microscopic examinations. The occurrence of at least three mechanisms of water movements is revealed, two being processes which are superimposed on the normal osmotic water movement that results from a change in the concentration of solute in the medium. Differences between the time courses of the changes in volume and potential on changing K_i/K_o indicate that water may be distributed unequally for a time within compartments of the fiber. Electron micrographs reveal a selective accumulation of water at the periphery of the fiber under certain conditions. A correlation of H₂O transfer with a change in membrane potential is apparent in crayfish muscle fibers and is probably due to electroosmotic effects. Electrokinetic water movements are produced whenever the membrane potential is changed to a considerable degree by changing the level of K and/or Cl in the medium, or by applying currents with an intracellular microelectrode. Depolarizations cause shrinkage. Hyperpolarizations or repolarizations cause swelling. The volume changes are independent of the occurrence or absence of swelling in the anion-permselective transverse tubular system. They indicate that the fiber membrane along the surface is heterogeneous, not only with respect to the signs of its fixed charge sites, but also with respect to the sizes and relative permselectivities of these charged channels.     

Characterization of functionally distinct mitochondrial subpopulations

Mitochondrial stress results in changes in mitochondrial function, morphology and homeostasis (biogenesis, fission/fusion, mitophagy) and may lead to changes in mitochondrial subpopulations. While flow cytometric techniques have been developed to quantify features of individual mitochondria related to volume, Ca²⁺ concentration, mtDNA content, respiratory capacity and oxidative damage, less information is available concerning the identification and characterization of mitochondrial subpopulations, particularly in epithelial cells. Mitochondria from rabbit kidneys were stained with molecular probes for cardiolipin content (nonyl acridine orange, NAO) and membrane potential (tetramethylrhodamine, TMRM) and analyzed using flow cytometry. We validated that side scatter was a better indicator of volume and that as side scatter (SSC) decreased mitochondrial volume increased. Furthermore, those mitochondria with the highest NAO content had greater side scattering and were most highly charged. Mitochondria with average NAO content were of average side scattering and maintained an intermediate charge. Those mitochondria with low NAO content had minimal side scattering and exhibited minimal charge. Upon titration with the uncoupler carbonylcyanide-4-(trifluoromethoxy)-phenylhydrazone (FCCP), it was found that the high NAO content subpopulations were more resistant to uncoupling than lower NAO content populations. Ca²⁺-induced swelling of mitochondria was evaluated using probability binning (PB) analyses of SSC. Interestingly, only 30 % of the mitochondria showed changes in response to Ca²⁺, which was blocked by cyclosporine A. In addition, the small, high NAO content mitochondria swelled differentially in response to Ca²⁺ over time. Our results demonstrate that flow cytometry can be used to identify mitochondrial subpopulations based on high, mid and low NAO content and/or volume/complexity. These subpopulations showed differences in membrane potential, volume, and responses to uncoupling and Ca²⁺-induced swelling.     

Genetic and Environmental Effects on the Expression of Peptidases and Larval Viability in Drosophila Melanogaster

The peptidase system in Drosophila melanogaster, consisting of dipeptidase-A, dipeptidase-B, dipeptidase-C and the leucine aminopeptidases, was used as a model to study the adaptive significance of enzyme activity variation. The involvement of the peptidases in osmoregulation has been suggested from the ubiquitous distribution of peptidase activities in nearly all tissues and the high concentration of amino acids and oligopeptides in the hemolymph. Under this hypothesis, larvae counteract increases in environmental osmotic stress by hydrolyzing peptides into amino acids both intra- and extracellularly to increase physiological osmotic concentration. The expression of the peptidases was studied by assaying for peptidase activities in third instar larvae of isogenic lines, which were reared under increasing levels of environmental osmotic stress using either D-mannitol or NaCl. Second and third chromosome substitution isogenic lines were used to assess the relative contribution of regulatory and structural genes in enzyme activity variation. Results indicate that: (1) genetic variation exists for peptidase activities, (2) the effect of osmotic stress is highly variable among peptidases, (3) changes in peptidase activities in response to osmotic stress depend on both genetic background and osmotic effector and (4) peptidase activities are correlated with each other, but these phenotypic correlations depend on genetic background, osmotic effector, and level of osmotic stress. Osmotic concentration in the larval hemolymph is correlated with leucine aminopeptidase activity, but changes in hemolymph osmotic concentration in response to environmental osmotic stress depend on the osmotic effector in the environment. Although these findings suggest that genetic and environmental factors contribute significantly toward the expression of enzymes with similar functions, a relative larval viability study of genotypes that differed significantly in dipeptidase-B (DIP-B) activity revealed that low DIP-B activity did not confer any measurable reduction in larval viability under increasing levels of environmental osmotic stress. These negative results suggest that, either DIP-B does not play a major role in osmoregulation or differential osmoregulation is not related to egg to adult viability in these tests.