Osteochondral reconstruction of a non-weight-bearing joint using a high-density porous polyethylene implant

Currently, there is no reliable reconstructive modality allowing anatomic resurfacing of traumatic digital osteochondral articular defects. The purpose of the present study is to demonstrate the utility of Medpor, a high-density porous polyethylene (HDPP) scaffold biomaterial that can (1) be readily contoured to fit any joint defect, (2) permit stable internal fixation, and (3) permit osteocyte and chondrocyte ingrowth and subsequent articular cartilage resurfacing necessary to restore joint congruity. HDPP has gained wide acceptance for use in craniofacial and skeletal reconstruction and augmentation. An avian non-weight-bearing joint model was designed to study the role of the HDPP implant in small joint reconstruction. An osteochondral defect was created with a 5-mm circular punch in the humeral articular surface of both glenohumeral joints of 32 adult White Leghorn chickens. In each animal, one defect was press-fitted with a correspondingly sized HDPP implant (HDPP implant group); the contralateral defect was filled with the original osteochondral plug (isograft group) or left unrepaired (control group). At 2 weeks, and 1, 3, and 6 months,joints from each group were harvested and evaluated. Over the 6-month study period, joints in the control group demonstrated healing with dense collagenous scar tissue leaving residual defects at the articular surfaces and significant degenerative disease of the glenohumeral joints radiographically. Joints in the isograft group demonstrated near-complete resorption with some preservation of the cartilaginous cap but overall depression of the articular surface and significant degenerative joint disease. Joints in the HDPP implant group demonstrated stable fixation by highly mineralized bony trabecular ingrowth, preservation of the articular contour of the humeral head, and no evidence of significant degenerative joint disease. These findings indicate a potential role for this high-density porous polyethylene implant in the reconstruction of small joint articular and osseous defects.     

Assessment of the accuracy of a human arm model with seven degrees of freedom

We are proposing a human arm model that consists of three rigid segments with seven degrees of freedom. The shoulder joint was modeled as a ball-and-socket joint and the elbow and wrist joints were modelled as skew-oblique joints. Optimal parameters for this model were calculated on the base of in vivo recordings with a spatial tracking system. The criterion of optimality was defined as the minimum of the mean-square deviation between the experimentally obtained sensor positions and orientations and their positions and orientations calculated by solving the direct kinematics problem. The minimal value of the direct kinematics error was found to be 0.5-0.6cm for sensor positions and 5-7 degrees for sensor orientations. We are proposing that these values serve as the assessment for the accuracy of the arm model.     

Measurements of wrist and finger postures: a comparison of goniometric and motion capture techniques

A marker-based kinematic hand model to quantify finger postures was developed and compared to manual goniometric measurements. The model was implemented with data collected from static postures of five subjects. The metacarpal phalangeal (MCP) and proximal interphalangeal (PIP) joints were positioned in flexion of approximately 30, 60, and 90 degrees for 5 subjects. Wrist flexion/extension and ulnar/radial deviations were also examined. The model-based angles for the MCP and PIP joints were not statistically equivalent to the goniometric measurements, with differences of -1.8 degrees and +3.5 degrees, respectively. Differences between the two measurement methods for the MCP and PIP were found to be a function of the posture (i.e., 150, 120, or 90 degree blocks) used. Wrist measurements differed by -4.0 degrees for ulnar/radial deviation and +5.2 degrees for flexion/extension. Much of the difference between the model and goniometric measurements is believed due to inaccuracies in the goniometric measurements. The proposed model is useful for future investigations of finger-intensive activities by supplying accurate and unbiased measures of joint angles.     

Modeling tree water flow as an unsaturated flow through a porous medium

The electric circuit analogy has had a profound influence on how tree physiologists measure, model and think about tree water flow. For example, previous models that attempt to account for changes in saturation use the electric circuit analogy to define capacitance as the change in saturation per change in pressure. Given that capacitance is constant, this relationship implies that subjecting a block of wood to a pressure of -2.5 MPa for 2 min results in the same change in saturation as subjecting the same block to the same pressure for 2 days. Given the definition of capacitance, it is unclear how the electric circuit analogy could be used to predict changes in saturation separately from changes in pressure. The inadequacies in the electric circuit analogy discussed in this paper necessitate a new theory of tree water flow that recognizes the sapwood as being a porous medium and explicitly deals with the full implications of the unsaturated flow occurring in the sapwood. The theory proposed in this paper combines the Cohesion theory with a mathematical theory of multiphase flow through porous media. Based on this theory, both saturated and unsaturated tree water flow models are presented. Previous partial differential equation models of tree water flow based on the electric circuit analogy are shown to be mathematically equivalent to the model of saturated porous flow. The unsaturated model of tree water flow explicitly models the pressure profile and the rates of change in saturation and specific interfacial area (a measure of how the water in the unsaturated sapwood is partitioned between mobile and immobile components). The unsaturated model highlights the differences between saturated and unsaturated flow and the need to measure the variables governing tree water flow at higher spatial and temporal resolutions.     

Selective stimulation of in situ intermediary metabolism by free calcium in permeabilized rat adipocytes.

The hypothesis that ionized calcium [Ca2+]i may stimulate in situ rat adipocyte intermediary metabolism distal to glucose transport was tested. A metabolically active porous adipocyte model was employed in which pathway metabolism is exclusively pore-dependent using glucose 6-phosphate (G6P) as substrate. Cellular [Ca2+]i was, furthermore, directly adjusted to between 0-2.5 microM via the membrane pores. Three metabolic fluxes were examined, (1) glycolysis-Krebs ([6-14C]G6P oxidation), (2) glycolysis to lactate ([U-14C]G6P to [14C]lactate) and (3) pentose pathway ([1-14C]G6P oxidation). Glycolysis-Krebs oxidation was was found to be selectively (33% above basal P less than 0.001) stimulated by 0.625 microM free calcium. In contrast, there was no effect of [Ca2+]i on the other, exclusively cytoplasmic, pathways. The stimulation of glycolysis-Krebs by [Ca2+]i was inhibited by a mitochondrial calcium channel blocker (Ruthenium red) and persisted over a range of ATP/ADP ratios. Separate studies demonstrated that 2-[1-14C]ketoglutarate oxidation was also calcium-stimulated in the porous adipocytes (160% over baseline at 1 microM [Ca2+]i). These studies thus demonstrate that physiologically relevant increments in porous adipocyte [Ca2+]i enhance overall in situ glycolytic-Krebs pathway oxidation by a mechanism which entails mitochondrial calcium uptake. Methodologically, this metabolically active porous adipocyte model presents a novel experimental approach to investigations regarding the effects of ionized calcium on intermediary metabolism beyond glucose transport.     

Mathematical model for characterization of bacterial migration through sand cores

The migration of chemotactic bacteria in liquid media has previously been characterized in terms of two fundamental transport coefficients-the random motility coefficient and the chemotactic sensitivity coefficient. For modeling migration in porous media, we have shown that these coefficients which appear in macroscopic balance equations can be replaced by effective values that reflect the impact of the porous media on the swimming behavior of individual bacteria. Explicit relationships between values of the coefficients in porous and liquid media were derived. This type of quantitative analysis of bacterial migration is necessary for predicting bacterial population distributions in subsurface environments for applications such as in situ bioremediation in which bacteria respond chemotactically to the pollutants that they degrade.We analyzed bacterial penetration times through sand columns from two different experimental studies reported in the literature within the context of our mathematical model to evaluate the effective transport coefficients. Our results indicated that the presence of the porous medium reduced the random motility of the bacterial population by a factor comparable to the theoretical prediction. We were unable to determine the effect of the porous medium on the chemotactic sensitivity coefficient because no chemotactic response was observed in the experimental studies. However, the mathematical model was instrumental in developing a plausible explanation for why no chemotactic response was observed. The chemical gradients may have been too shallow over most of the sand core to elicit a measurable response. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 53: 487-496, 1997.     

A biomechanical model on muscle forces in the transfer of spinal load to the pelvis and legs.

Based on musculoskeletal anatomy of the lower back, abdominal wall, pelvis and upper legs, a biomechanical model has been developed on forces in the load transfer through the pelvis. The aim of this model is to obtain a tool for analyzing the relations between forces in muscles, ligaments and joints in the transfer of gravitational and external load from the upper body via the sacroiliac joints to the legs in normal situations and pathology. The study of the relation between muscle coordination patterns and forces in pelvic structures, in particular the sacroiliac joints, is relevant for a better understanding of the aetiology of low back pain and pelvic pain. The model comprises 94 muscle parts, 6 ligaments and 6 joints. It enables the calculation of forces in pelvic structures in various postures. The calculations are based on a linear/non-linear optimization scheme. To gain a better understanding of the function of individual muscles and ligaments, deviant properties of these structures can be preset. The model is validated by comparing calculations with EMG data from the literature. For agonistic muscles, good agreement is found between model calculations and EMG data. Antagonistic muscle activity is underestimated by the model. Imposed activity of modelled antagonistic muscles has a minor effect on the mutual proportions of agonistic muscle activities. Simulation of asymmetric muscle weakness shows higher activity of especially abdominal muscles.     

Mass transport in a microchannel bioreactor with a porous wall

A two-dimensional flow model has been developed to simulate mass transport in a microchannel bioreactor with a porous wall. A two-domain approach, based on the finite volume method, was implemented. For the fluid part, the governing equation used was the Navier-Stokes equation; for the porous medium region, the generalized Darcy-Brinkman-Forchheimer extended model was used. For the porous-fluid interface, a stress jump condition was enforced with a continuity of normal stress, and the mass interfacial conditions were continuities of mass and mass flux. Two parameters were defined to characterize the mass transports in the fluid and porous regions. The porous Damkohler number is the ratio of consumption to diffusion of the substrates in the porous medium. The fluid Damkohler number is the ratio of the substrate consumption in the porous medium to the substrate convection in the fluid region. The concentration results were found to be well correlated by the use of a reaction-convection distance parameter, which incorporated the effects of axial distance, substrate consumption, and convection. The reactor efficiency reduced with reaction-convection distance parameter because of reduced reaction (or flux), and smaller local effectiveness factor due to the lower concentration in Michaelis-Menten type reactions. The reactor was more effective, and hence, more efficient with the smaller porous Damkohler number. The generalized results could find applications for the design of bioreactors with a porous wall.     

Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal,proteoglycan depleted and collagen degraded articular cartilage

Degradation of collagen network and proteoglycan (PG) macromolecules are signs of articular cartilage degeneration. These changes impair cartilage mechanical function. Effects of collagen degradation and PG depletion on the time-dependent mechanical behavior of cartilage are different. In this study, numerical analyses, which take the compression-tension nonlinearity of the tissue into account, were carried out using a fibril reinforced poroelastic finite element model. The study aimed at improving our understanding of the stress-relaxation behavior of normal and degenerated cartilage in unconfined compression. PG and collagen degradations were simulated by decreasing the Young's modulus of the drained porous (nonfibrillar) matrix and the fibril network, respectively. Numerical analyses were compared to results from experimental tests with chondroitinase ABC (PG depletion) or collagenase (collagen degradation) digested samples. Fibril reinforced poroelastic model predicted the experimental behavior of cartilage after chondroitinase ABC digestion by a major decrease of the drained porous matrix modulus (-64+/-28%) and a minor decrease of the fibril network modulus (-11+/-9%). After collagenase digestion, in contrast, the numerical analyses predicted the experimental behavior of cartilage by a major decrease of the fibril network modulus (-69+/-5%) and a decrease of the drained porous matrix modulus (-44+/-18%). The reduction of the drained porous matrix modulus after collagenase digestion was consistent with the microscopically observed secondary PG loss from the tissue. The present results indicate that the fibril reinforced poroelastic model is able to predict specifically characteristic alterations in the stress-relaxation behavior of cartilage after enzymatic modifications of the tissue. We conclude that the compression-tension nonlinearity of the tissue is needed to capture realistically the mechanical behavior of normal and degenerated articular cartilage.     

Macrokinetics of enzyme sorption on porous beads accompanied by complex formation with an immobilized ligand

A mathematical model has been proposed for enzyme sorption on porous beads accompanied by formation of a stable complex with an immobilized ligand. It has been experimentally verified by using the system trypsin (EC 3.2.21.4) - immobilized bovine basic polyvalent trypsin inhibitor on porous silica gel. The experimental results for kinetics of the non-specific/specific trypsin sorption on a carrier agree with the model. The value of the coefficient of trypsin diffusion in macroporous silica gel was calculated.     

A kinematic model of the human hand to evaluate its prehensile capabilities.

A kinematic model has been developed for simulation and prediction of the prehensile capabilities of the human hand. The kinematic skeleton of the hand is characterized by ideal joints and simple segments. Finger-joint angulation is characterized by yaw (abduction-adduction), pitch (flexion-extension) and roll (axial rotation) angles. The model is based on an algorithm that determines contact between two ellipsoids, which are used to approximate the geometry of the cutaneous surface of the hand segments. The model predicts the hand posture (joint angles) for power grasp of ellipsoidal objects by 'wrapping' the fingers around the object. Algorithms for two grip types are included: (1) a transverse volar grasp, which has the thumb abducted for added power; and (2) a diagonal volar grasp, which has the thumb adducted for an element of precision. Coefficients for estimating anthropometric parameters from hand length and breadth are incorporated in the model. Graphics procedures are included for visual display of the model. In an effort to validate the predictive capabilities of the model, joint angles were measured on six subjects grasping circular cylinders of various diameters and these measured joint angles were compared with angles predicted by the model. Sensitivity of the model to the various input parameters was also determined. On an average, the model predicted joint flexion angles that were 5.3% or 2.8 degrees +/- 12.2 degrees larger than the measured angles. Good agreement was found for the MCP and PIP joints, but results for DIP were more variable because of its dependence on the predictions for the proximal joints.     

Reduction of porous media permeability from in situ Leuconostoc mesenteroides growth and dextran production

In situ growth of bacteria in a porous medium can alter the permeability of that media. This article reveals that the rate of permeability alteration can be controlled by the inoculation strategy, nutrient concentrations, and injection rates. Based on experimental observations a phenomenological model has been developed to describe the inoculation of the porous medium, the in situ growth of bacteria, and the permeability decline of the porous medium. This model consists of two phases that describe the bacteria in the porous medium: (1) the nongrowth phase in which cell transport and retention are occurring; and (2) the growth phase in which the retained cells grow and plug the porous media. Transition from the transport phase to the growth phase is governed by the growth lag time of the cells within the porous medium. The importance of the inoculum injection strategy and the nutrient injection strategy is illustrated by the model. (c) 1996 John Wiley & Sons, Inc.     

A mixed boundary representation to simulate the displacement of a biofluid by a biomaterial in porous media

Characterization of the biomaterial flow through porous bone is crucial for the success of the bone augmentation process in vertebroplasty. The biofluid, biomaterial, and local morphological bone characteristics determine the final shape of the filling, which is important both for the post-treatment mechanical loading and the risk of intraoperative extraosseous leakage. We have developed a computational model that describes the flow of biomaterials in porous bone structures by considering the material porosity, the region-dependent intrinsic permeability of the porous structure, the rheological properties of the biomaterial, and the boundary conditions of the filling process. To simulate the process of the substitution of a biofluid (bone marrow) by a biomaterial (bone cement), we developed a hybrid formulation to describe the evolution of the fluid boundary and properties and coupled it to a modified version of Darcy's law. The apparent rheological properties are derived from a fluid-fluid interface tracking algorithm and a mixed boundary representation. The region- specific intrinsic permeability of the bone is governed by an empirical relationship resulting from a fitting process of experimental data. In a first step, we verified the model by studying the displacement process in spherical domains, where the spreading pattern is known in advance. The mixed boundary model demonstrated, as expected, that the determinants of the spreading pattern are the local intrinsic permeability of the porous matrix and the ratio of the viscosity of the fluids that are contributing to the displacement process. The simulations also illustrate the sensitivity of the mixed boundary representation to anisotropic permeability, which is related to the directional dependent microstructural properties of the porous medium. Furthermore, we compared the nonlinear finite element model to different published experimental studies and found a moderate to good agreement (R(2)=0.9895 for a one-dimensional bone core infiltration test and a 10.94-16.92% relative error for a three-dimensional spreading pattern study, respectively) between computational and experimental results.     

Effects of inserting a pressensor film into articular joints on the actual contact mechanics.

Fuji film has been widely used in studies aimed at obtaining the contact mechanics of articular joints. Once sealed for practical use in biological joints, Fuji Pressensor film has a total effective thickness of 0.30 mm, which is comparable to the cartilage thickness in the joints of many small animals. The average effective elastic modulus of Fuji film is approximately 100 MPa in compression, which is larger by a factor of 100-300 compared to that of normal articular cartilage. Therefore, inserting a Pressensor film into an articular joint will change the contact mechanics of the joint. The measurement precision of the Pressensor film has been determined systematically; however, the changes in contact mechanics associated with inserting the film into joints have not been investigated. This study was aimed at quantifying the changes in the contact mechanics associated with inserting sealed Fuji Pressensor film into joints. Spherical and cylindrical articular joint contact mechanics with and without Pressensor film and for varying degrees of surface congruency were analyzed and compared by using finite element models. The Pressensor film was taken as linearly elastic and the cartilage was assumed to be biphasic, composed of a linear elastic solid phase and an inviscid fluid phase. The present analyses showed that measurements of the joint contact pressures with Fuji Pressensor film will change the maximum true contact pressures by 10-26 percent depending on the loading, geometry of the joints, and the mechanical properties of cartilage. Considering this effect plus the measurement precision of the film (approximately 10 percent), the measured joint contact pressures in a joint may contain errors as large as 14-28 percent.     

Staphylococcal arthritis in a white-tailed deer (Odocoileus virginianus)

A five and one-half year old deer (Odocoileus virginianus) developed an ankylosing periarticular hypertrophic arthritis due to a coagulase positive staphylococcus infection. Complete encasement of the tibio-tarsal (hock) joints with a hypertrophic, and porous osseous mass had occurred with complete loss of articular cartilage. The pathologic alterations of the tissues are compared to those occurring in swine due to Erysipelothrix insidiosa infection which produces a rheumatoid-like arthritis.     

A morphological model of vertebral trabecular bone

In their micro-structures, typical natural cellular materials such as vertebral trabecular bone have a network of doubly tapered struts, thickening near the strut joints. However, past analytical models for vertebral trabecular bone do not take account of the effect of strut taper on the mechanical properties.This paper presents an analytical cell model comprised of doubly tapered struts to predict the global mechanical properties of vertebral trabecular bone. The predicted results for male, female, and both sexes fit the experimental data well. By considering several strut taper geometries, it is shown that the horizontal Young's modulus and the horizontal uniaxial collapse stress are, in some cases, approximately 1.8- and 2.2-fold higher, respectively, than those of the uniform strut model. This finding illustrates the importance of increased trabecular thickening near the strut joints (i) for improving the accuracy of calculating the mechanical properties and (ii) for the effective treatment of aged bone using drug therapy. It also highlights the need to combine trabecular architecture measurements with information about the morphology near the strut joints.     

A porous elastic model for bacterial biofilms: application to the simulation of deformation of bacterial biofilms under microfluidic jet impingement

The presence of bacterial biofilms is detrimental in a wide range of healthcare situations especially wound healing. Physical debridement of biofilms is a method widely used to remove them. This study evaluates the use of microfluidic jet impingement to debride biofilms. In this case, a biofilm is treated as a saturated porous medium also having linear elastic properties. A numerical modeling approach is used to calculate the von Mises stress distribution within a porous medium under fluid-structure interaction (FSI) loading to determine the initial rupture of the biofilm structure. The segregated model first simulates the flow field to obtain the FSI interface loading along the fluid-solid interface and body force loading within the porous medium. A stress-strain model is consequently used to calculate the von Mises stress distribution to obtain the biofilm deformation. Under a vertical jet, 60% of the deformation of the porous medium can be accounted for by treating the medium as if it was an impermeable solid. However, the maximum deformation in the porous medium corresponds to the point of maximum shear stress which is a different position in the porous medium than that of the maximum normal stress in an impermeable solid. The study shows that a jet nozzle of 500 μm internal diameter (ID) with flow of Reynolds number (Re) of 200 can remove the majority of biofilm species.     

An analytical solution for the radial and tangential displacements on a thin hemispherical layer of articular cartilage

A simplified analytical solution has been obtained for the radial and tangential displacements on the surface of a thin, hemispherical layer of porous-elastic articular cartilage firmly bonded to a rigid foundation. A static pressure distributed according to a paraboloid of revolution is applied simulating cartilage compression by a porous indenter. The solution method is in the form of an asymptotic series and uses Laplace transforms. The analytical predictions are in qualitative agreement with the behaviour of biphasic articular cartilage reported in the literature. A direct comparison with numerical simulations using commercially available Finite Element Modelling (FEM) software was also carried out for conditions relevant to natural hip joints and the results show a good quantitative agreement overall.