Glycosaminoglycan network geometry may contribute to anisotropic hydraulic permeability in cartilage under compression.

Resistance to fluid flow within cartilage extracellular matrix is provided primarily by a dense network of rod-like glycosaminoglycans (GAGs). If the geometrical organization of this network is random, the hydraulic permeability tensor of cartilage is expected to be isotropic. However, experimental data have suggested that hydraulic permeability may become anisotropic when the matrix is mechanically compressed, contributing to cartilage biomechanical functions such as lubrication. We hypothesized that this may be due to preferred GAG rod orientations and directionally-dependent reduction of inter-GAG spacings which reflect molecular responses to tissue deformations. To examine this hypothesis, we developed a model for effects of compression which allows the GAG rod network to deform consistently with tissue-scale deformations but while still respecting limitations imposed by molecular structure. This network deformation model was combined with a perturbation analysis of a classical analytical model for hydraulic permeability based on molecular structure. Finite element analyses were undertaken to ensure that this approach exhibited results similar to those emerging from more exact calculations. Model predictions for effects of uniaxial confined compression on the hydraulic permeability tensor were consistent with previous experimental results. Permeability decreased more rapidly in the direction perpendicular to compression than in the parallel direction, for matrix solid volume fractions associated with fluid transport in articular cartilage. GAG network deformations may therefore introduce anisotropy to the permeability (and other GAG-associated matrix properties) as physiological compression is applied, and play an important role in cartilage lubrication and other biomechanical functions.     

Development and evaluation of a new methodology for the fast generation of patient-specific Finite Element models of the buttock for sitting-acquired deep tissue injury prevention

The occurrence and management of Pressure Ulcers remain a major issue for patients with reduced mobility and neurosensory loss despite significant improvement in the prevention methods. These injuries are caused by biological cascades leading from a given mechanical loading state in tissues to irreversible tissue damage. Estimating the internal mechanical conditions within loaded soft tissues has the potential of improving the management and prevention of PU. Several Finite Element models of the buttock have therefore been proposed based on either MRI or CT-Scan data. However, because of the limited availability of MRI or CT-Scan systems and of the long segmentation time, all studies in the literature include the data of only one individual. Yet the inter-individual variability can’t be overlooked when dealing with patient specific estimation of internal tissue loading. As an alternative, this contribution focuses on the combined use of low-dose biplanar X-ray images, B-mode ultrasound images and optical scanner acquisitions in a non-weight-bearing sitting posture for the fast generation of patient-specific FE models of the buttock. Model calibration was performed based on Ischial Tuberosity sagging. Model evaluation was performed by comparing the simulated contact pressure with experimental observations on a population of 6 healthy subjects. Analysis of the models confirmed the high inter-individual variability of soft tissue response (maximum Green Lagrange shear strains of 213 ± 101% in the muscle). This methodology opens the way for investigating inter-individual factors influencing the soft tissue response during sitting and for providing tools to assess PU risk.     

Anisotropic hydraulic permeability in compressed articular cartilage

The extent to which articular cartilage hydraulic permeability is anisotropic is largely unknown, despite its importance for understanding mechanisms of joint lubrication, load bearing, transport phenomena, and mechanotransduction. We developed and applied new techniques for the direct measurement of hydraulic permeability within statically compressed adult bovine cartilage explant disks, dissected such that disk axes were perpendicular to the articular surface. Applied pressure gradients were kept small to minimize flow-induced matrix compaction, and fluid outflows were measured by observation of a meniscus in a glass capillary under a microscope. Explant disk geometry under radially unconfined axial compression was measured by direct microscopic observation. Pressure, flow, and geometry data were input to a finite element model where hydraulic permeabilities in the disk axial and radial directions were determined. At less than 10% static compression, near free-swelling conditions, hydraulic permeability was nearly isotropic, with values corresponding to those of previous studies. With increasing static compression, hydraulic permeability decreased, but the radially directed permeability decreased more dramatically than the axially directed permeability such that strong anisotropy (a 10-fold difference between axial and radial directions) in the hydraulic permeability tensor was evident for static compression of 20-40%. Results correspond well with predictions of a previous microstructurally-based model for effects of tissue mechanical deformations on glycosaminoglycan architecture and cartilage hydraulic permeability. Findings inform understanding of structure-function relationships in cartilage matrix, and suggest several biomechanical roles for compression-induced anisotropic hydraulic permeability in articular cartilage.     

A biphasic model for micro-indentation of a hydrogel-based contact lens

The stiffness and hydraulic permeability of soft contact lenses may influence its clinical performance, e.g., on-eye movement, fitting, and wettability, and may be related to the occurrence of complications; e.g., lesions. It is therefore important to determine these properties in the design of comfortable contact lenses. Micro-indentation provides a nondestructive means of measuring mechanical properties of soft, hydrated contact lenses. However, certain geometrical and material considerations must be taken into account when analyzing output force-displacement (F-D) data. Rather than solely having a solid response, mechanical behavior of hydrogel contact lenses can be described as the coupled interaction between fluid transport through pores and solid matrix deformation. In addition, indentation of thin membranes ( approximately 100 microm) requires special consideration of boundary conditions at lens surfaces and at the indenter contact region. In this study, a biphasic finite element model was developed to simulate the micro-indentation of a hydrogel contact lens. The model accounts for a curved, thin hydrogel membrane supported on an impermeable mold. A time-varying boundary condition was implemented to model the contact interface between the impermeable spherical indenter and the lens. Parametric studies varying the indentation velocities and hydraulic permeability show F-D curves have a sensitive region outside of which the force response reaches asymptotic limits governed by either the solid matrix (slow indentation velocity, large permeability) or the fluid transport (high indentation velocity, low permeability). Using these results, biphasic properties (Young's modulus and hydraulic permeability) were estimated by fitting model results to F-D curves obtained at multiple indentation velocities (1.2 and 20 microm/s). Fitting to micro-indentation tests of Etafilcon A resulted in an estimated permeability range of 1.0 x 10(-15) to 5.0 x 10(-15) m(4)N s and Young's modulus range of 130 to 170 kPa.     

A nonlinear anisotropic inverse method for computational dissection of inhomogeneous planar tissues

Quantification of the mechanical behavior of soft tissues is challenging due to their anisotropic, heterogeneous, and nonlinear nature. We present a method for the ‘computational dissection’ of a tissue, by which we mean the use of computational tools both to identify and to analyze regions within a tissue sample that have different mechanical properties. The approach employs an inverse technique applied to a series of planar biaxial experimental protocols. The aggregated data from multiple protocols provide the basis for (1) segmentation of the tissue into regions of similar properties, (2) linear analysis for the small-strain behavior, assuming uniform, linear, anisotropic behavior within each region, (3) subsequent nonlinear analysis following each individual experimental protocol path and using local linear properties, and (4) construction of a strain energy data set W(E) at every point in the material by integrating the differential stress–strain functions along each strain path. The approach has been applied to simulated data and captures not only the general nonlinear behavior but also the regional differences introduced into the simulated tissue sample.     

An integrated inverse model-experimental approach to determine soft tissue three-dimensional constitutive parameters: application to post-infarcted myocardium

Knowledge of the complete three-dimensional (3D) mechanical behavior of soft tissues is essential in understanding their pathophysiology and in developing novel therapies. Despite significant progress made in experimentation and modeling, a complete approach for the full characterization of soft tissue 3D behavior remains elusive. A major challenge is the complex architecture of soft tissues, such as myocardium, which endows them with strongly anisotropic and heterogeneous mechanical properties. Available experimental approaches for quantifying the 3D mechanical behavior of myocardium are limited to preselected planar biaxial and 3D cuboidal shear tests. These approaches fall short in pursuing a model-driven approach that operates over the full kinematic space. To address these limitations, we took the following approach. First, based on a kinematical analysis and using a given strain energy density function (SEDF), we obtained an optimal set of displacement paths based on the full 3D deformation gradient tensor. We then applied this optimal set to obtain novel experimental data from a 1-cm cube of post-infarcted left ventricular myocardium. Next, we developed an inverse finite element (FE) simulation of the experimental configuration embedded in a parameter optimization scheme for estimation of the SEDF parameters. Notable features of this approach include: (i) enhanced determinability and predictive capability of the estimated parameters following an optimal design of experiments, (ii) accurate simulation of the experimental setup and transmural variation of local fiber directions in the FE environment, and (iii) application of all displacement paths to a single specimen to minimize testing time so that tissue viability could be maintained. Our results indicated that, in contrast to the common approach of conducting preselected tests and choosing an SEDF a posteriori, the optimal design of experiments, integrated with a chosen SEDF and full 3D kinematics, leads to a more robust characterization of the mechanical behavior of myocardium and higher predictive capabilities of the SEDF. The methodology proposed and demonstrated herein will ultimately provide a means to reliably predict tissue-level behaviors, thus facilitating organ-level simulations for efficient diagnosis and evaluation of potential treatments. While applied to myocardium, such developments are also applicable to characterization of other types of soft tissues.     

Mechanical characterization of anisotropic planar biological soft tissues using large indentation: a computational feasibility study

Traditionally, the complex mechanical behavior of planar soft biological tissues is characterized by (multi)axial tensile testing. While uniaxial tests do not provide sufficient information for a full characterization of the material anisotropy, biaxial tensile tests are difficult to perform and tethering effects limit the analyses to a small central portion of the test sample. In both cases, determination of local mechanical properties is not trivial. Local mechanical characterization may be performed by indentation testing. Conventional indentation tests, however, often assume linear elastic and isotropic material properties, and therefore these tests are of limited use in characterizing the nonlinear, anisotropic material behavior typical for planar soft biological tissues. In this study, a spherical indentation experiment assuming large deformations is proposed. A finite element model of the aortic valve leaflet demonstrates that combining force and deformation gradient data, one single indentation test provides sufficient information to characterize the local material behavior. Parameter estimation is used to fit the computational model to simulated experimental data. The aortic valve leaflet is chosen as a typical example. However, the proposed method is expected to apply for the mechanical characterization of planar soft biological materials in general.     

Validating a voxel-based finite element model of a human mandible using digital speckle pattern interferometry

Finite element analysis is a powerful tool for predicting the mechanical behaviour of complex biological structures like bones, but to be confident in the results of an analysis, the model should be validated against experimental data. In such validation experiments, the strains in the loaded bones are usually measured with strain gauges glued to the bone surface, but the use of strain gauges on bone can be difficult and provides only very limited data regarding surface strain distributions. This study applies the full-field strain measurement technique of digital speckle pattern interferometry to measure strains in a loaded human mandible and compares the results with the predictions of voxel-based finite element models of the same specimen. It is found that this novel strain measurement technique yields consistent, reliable measurements. Further, strains predicted by the finite element analysis correspond well with the experimental data. These results not only confirm the usefulness of this technique for future validation studies in the field of bone mechanics, but also show that the modelling approach used in this study is able to predict the experimental results very accurately.     

A model relating root permeability to flux and potentials: application to existing data from soybean and other plants

A model that relates hydraulic permeability to water flux and to gradients in pressure potential and solute potential was tested using soybean (Glycine max) plants. Water flux was varied by additions of polyethylene glycol 6,000 around one portion of a divided root system and by changing the light intensity and CO₂ concentration around the plants. The data are compatible with the model only if the hydraulic permeability varies with flux; however, the data were insufficient for rigorous testing. Three sets of published data fit the model only if hydraulic permeability varies. Evidence originally presented as involving constant hydraulic permeability is shown, rather, to require variable hydraulic permeability.     

Partition and permeation of dextran in polyacrylamide gel.

Partition of sized FITC-dextrans in polyacrylamide gel showed a relationship between Kav and solute radius as predicted by the theory of Ogston, which is based solely on geometry of the spaces. Permeability data for the same dextrans were fit to several theories, including those based on geometry and those based on hydrodynamic interactions, and the gel structure predicted by the partition and permeability data were compared. The Brinkman effective-medium model (based on hydrodynamic interactions and requiring a measure of the hydraulic conductivity of the matrix) gave the best fit of permeability data with the values for fiber radius (rf) and void volume of the gel (epsilon) that were obtained from the partition data. The models based on geometry and the hydrodynamic screening model of Cukier, using the rf and epsilon from partition data, all predicted higher rates of permeation than observed experimentally, while the effective-medium model with added term for steric interaction predicted lower permeation than that observed. The size of cylindrical pores appropriate for the partition data predicted higher rates of permeation than observed. These relative results were unaffected by the method of estimating void volume of the gel. In sum, it appears that one can use data on partition of solute, combined with measurement of hydraulic conductivity, to predict solute permeation in polyacrylamide gel.     

Spreading dynamics of biomimetic actin cortices

Reconstituted systems mimicking cells are interesting tools for understanding the details of cell behavior. Here, we use an experimental system that mimics cellular actin cortices, namely liposomes developing an actin shell close to their inner membrane, and we study their dynamics of spreading. We show that depending on the morphology of the actin shell inside the liposome, spreading dynamics is either reminiscent of a bare liposome (in the case of a sparse actin shell) or of a cell (in the case of a continuous actin shell). We use a mechanical model that qualitatively accounts for the shape of the experimental curves. From the data on spreading dynamics, we extract characteristic times that are consistent with mechanical estimates. The mechanical characterization of such stripped-down experimental systems paves the way for a more complex design closer to a cell. We report here the first step in building an artificial cell and studying its mechanics.     

A theoretical analysis for determining the nonlinear hydraulic permeability of a soft tissue from a permeation experiment

The nonlinear nature of the hydraulic permeability, as well as the corresponding pressure and displacement fields, in a soft tissue are studied for steady-state permeation. From a two-phase continuum model analytical expressions are derived that can be used with the results from a permeation experiment to determine the dependence of the permeability on the strain. In the process it is found that, because of the compaction of the tissue arising from fluid flow, it is necessary to distinguish between the apparent and intrinsic permeability. The former, which is an averaged quantity, is the permeability usually obtained in permeation studies. However, as shown from the analysis, it can differ substantially from the latter, which is the local permeability in the tissue.     

Measuring principles of frictional coefficients in cartilaginous tissues and its substitutes

The frictional properties of cartilaginous tissues, such as the hydraulic permeability, the electro-osmotic permeability, the diffusion coefficients of various ions and solutes, and the electrical conductance, are vital data to characterise the extracellular environment in which chondrocytes reside. This paper analyses one-dimensional measurement principles of these coefficients. Particular attention is given to the deformation dependence of them and the highly deformable nature of the tissues. A suggested strategy is the combination of a diffusion experiment using radiotracer methods, an electro-osmotic flow experiment and an electro-osmotic pressure experiment at low electric current.     

Finite element implementation of a generalized Fung-elastic constitutive model for planar soft tissues

Numerical simulations of the anisotropic mechanical properties of soft tissues and tissue-derived biomaterials using accurate constitutive models remain an important and challenging research area in biomechanics. While most constitutive modeling efforts have focused on the characterization of experimental data, only limited studies are available on the feasibility of utilizing those models in complex computational applications. An example is the widely utilized exponential constitutive model proposed by Fung. Although present in the biomechanics literature for several decades, implementation of this model into finite element (FE) simulations has been limited. A major reason for limited numerical implementations are problems associated with inherent numerical instability and convergence. To address this issue, we developed and applied two restrictions for a generalized Fung-elastic constitutive model necessary to achieve numerical stability. These are (1) convexity of the strain energy function, and (2) the condition number of material stiffness matrix set lower than a prescribed value. These constraints were implemented in the nonlinear regression used for constitutive model parameter estimation to the experimental biaxial mechanical data. We then implemented the generalized Fung-elastic model into a commercial FE code (ABAQUS, Pawtucket, RI, USA). Single element and multi-element planar biaxial test simulations were conducted to verify the accuracy and robustness of the implementation. Results indicated that numerical convergence and accurate FE implementation were consistently obtained. The present study thus presents an integrated framework for accurate and robust implementation of pseudo-elastic constitutive models for planar soft tissues. Moreover, since our approach is formulated within a general FE code, it can be straightforwardly adopted across multiple software platforms.     

Mechanical characterization of anisotropic planar biological soft tissues using finite indentation: experimental feasibility

Heart valve tissue engineering offers a promising alternative for current treatment and replacement strategies, e.g., synthetic or bioprosthetic heart valves. In vitro mechanical conditioning is an important tool for engineering strong, implantable heart valves. Detailed knowledge of the mechanical properties of the native tissue as well as the developing tissue construct is vital for a better understanding and control of the remodeling processes induced by mechanical conditioning. The nonlinear, anisotropic and inhomogeneous mechanical behavior of heart valve tissue necessitates a mechanical characterization method that is capable of dealing with these complexities. In a recent computational study we showed that one single indentation test, combining force and deformation gradient data, provides sufficient information for local characterization of nonlinear soft anisotropic tissue properties. In the current study this approach is validated in two steps. First, indentation tests with varying indenter sizes are performed on linear elastic PDMS rubbers and compared to tensile tests on the same specimen. For the second step, tissue constructs are engineered using uniaxial or equibiaxial static constrained culture conditions. Digital image correlation (DIC) is used to quantify the anisotropy in the tissue constructs. For both validation steps, material parameters are estimated by inverse fitting of a computational model to the experimental results.     

Compressive properties of mouse articular cartilage determined in a novel micro-indentation test method and biphasic finite element model

The mechanical properties of articular cartilage serve as important measures of tissue function or degeneration, and are known to change significantly with osteoarthritis. Interest in small animal and mouse models of osteoarthritis has increased as studies reveal the importance of genetic background in determining predisposition to osteoarthritis. While indentation testing provides a method of determining cartilage mechanical properties in situ, it has been of limited value in studying mouse joints due to the relatively small size of the joint and thickness of the cartilage layer. In this study, we developed a micro-indentation testing system to determine the compressive and biphasic mechanical properties of cartilage in the small joints of the mouse. A nonlinear optimization program employing a genetic algorithm for parameter estimation, combined with a biphasic finite element model of the micro-indentation test, was developed to obtain the biphasic, compressive material properties of articular cartilage. The creep response and material properties of lateral tibial plateau cartilage were obtained for wild-type mouse knee joints, by the micro-indentation testing and optimization algorithm. The newly developed genetic algorithm was found to be efficient and accurate when used with the finite element simulations for nonlinear optimization to the experimental creep data. The biphasic mechanical properties of mouse cartilage in compression (average values: Young's modulus, 2.0 MPa; Poisson's ratio, 0.20; and hydraulic permeability, 1.1 x 10(-16) m4/N-s) were found to be of similar orders of magnitude as previous findings for other animal cartilages, including human, bovine, rat, and rabbit and demonstrate the utility of the new test methods. This study provides the first available data for biphasic compressive properties in mouse cartilage and suggests a promising method for detecting altered cartilage mechanics in small animal models of osteoarthritis.     

Soft-cuticle biomechanics: A constitutive model of anisotropy for caterpillar integument

The mechanical properties of soft tissues are important for the control of motion in many invertebrates. Pressurized cylindrical animals such as worms have circumferential reinforcement of the body wall; however, no experimental characterization of comparable anisotropy has been reported for climbing larvae such as caterpillars. Using uniaxial, real-time fluorescence extensometry on millimeter scale cuticle specimens we have quantified differences in the mechanical properties of cuticle to circumferentially and longitudinally applied forces. Based on these results and the composite matrix-fiber structure of cuticle, a pseudo-elastic transversely isotropic constitutive material model was constructed with circumferential reinforcement realized as a Horgan-Saccomandi strain energy function. This model was then used numerically to describe the anisotropic material properties of Manduca cuticle. The constitutive material model will be used in a detailed finite-element analysis to improve our understanding of the mechanics of caterpillar crawling.     

Resistance to Water Diffusion in the Stratum Corneum Is Depth-Dependent

The stratum corneum (SC) provides a permeability barrier that limits the inflow and outflow of water. The permeability barrier is continuously and dynamically formed, maintained, and degraded along the depth, from the bottom to the top, of the SC. Naturally, its functioning and structure also change dynamically in a depth-dependent manner. While transepidermal water loss is typically used to assess the function of the SC barrier, it fails to provide any information about the dynamic mechanisms that are responsible for the depth-dependent characteristics of the permeability barrier. This paper aims to quantitatively characterize the depth-dependency of the permeability barrier using in vivo non-invasive measurement data for understanding the underlying mechanisms for barrier formation, maintenance, and degradation. As a framework to combine existing experimental data, we propose a mathematical model of the SC, consisting of multiple compartments, to explicitly address and investigate the depth-dependency of the SC permeability barrier. Using this mathematical model, we derive a measure of the water permeability barrier, i.e. resistance to water diffusion in the SC, from the measurement data on transepidermal water loss and water concentration profiles measured non-invasively by Raman spectroscopy. The derived resistance profiles effectively characterize the depth-dependency of the permeability barrier, with three distinct regions corresponding to formation, maintenance, and degradation of the barrier. Quantitative characterization of the obtained resistance profiles allows us to compare and evaluate the permeability barrier of skin with different morphology and physiology (infants vs adults, different skin sites, before and after application of oils) and elucidates differences in underlying mechanisms of processing barriers. The resistance profiles were further used to predict the spatial-temporal effects of skin treatments by in silico experiments, in terms of spatial-temporal dynamics of percutaneous water penetration.     

Optimization and scale up of industrial fermentation processes

To increase product yields and to ensure consistent product quality, key issues of industrial fermentations, process optimization and scale up are aimed at maintaining optimum and homogenous reaction conditions minimizing microbial stress exposure and enhancing metabolic accuracy. For each individual product, process and facility, suitable strategies have to be elaborated by a comprehensive and detailed process characterization, identification of the most relevant process parameters influencing product yield and quality and their establishment as scale-up parameters to be kept constant as far as possible. Physical variables, which can only be restrictedly kept constant as single parameters, may be combined with other pertinent parameters to appropriate mathematical groups or dimensionless terms. Process characterization is preferably based on real-time or near real-time data collected by in situ and on-line measurements and may be facilitated by supportive approaches and tools like neural network based chemometric data analysis and modelling, clarification of the mixing and stream conditions through computational fluid dynamics and scale-down simulations. However, as fermentation facilities usually are not strictly designed according to scale-up criteria and the process conditions in the culture vessels thus may differ significantly and since any strategy and model can only insufficiently consider and reflect the highly complex interdependence and mutual interaction of fermentation parameters, successful scale up in most cases is not the result of a conclusive and straight-lined experimental strategy, but rather will be the outcome of a separate process development and optimization on each scale. This article gives an overview on the problems typically coming along with fermentation process optimization and scale up, and presents currently applied scale-up strategies while considering future technologies, with emphasis on Escherichia coli as one of the most commonly fermented organisms.