Nicholas J. Altiero

Impact-Induced Fissuring of Articular Cartilage: An Investigation of Failure Criteria

Several candidate predictors for the occurrence of surface fissures in cartilage, including impact force, shear stress, and tensile strain have been previously proposed without an analytic basis. In this study a controlled impact experiment was performed where a dropped mass and three impact interfaces were used to identify loads associated with the initiation of fissuring. A Finite Element Model of each experiment was used to obtain stresses and strains associated with each impact event. The resulting experimental and analytical data were analyzed using logistic regression in order to determine the strongest predictor of a fissure, and thus to propose a failure criterion for articular cartilage during a blunt insult. The logistic regression indicated that shear stress, rather than impact force or drop height (an indicator of impact energy), was the strongest predictor for the occurrence of a fissure.

An approach for the stress analysis of transversely isotropic biphasic cartilage under impact load.

Stress analysis of contact models for isotropic articular cartilage under impacting loads shows high shear stresses at the interface with the subchondral bone and normal compressive stresses near the surface of the cartilage. These stress distributions are not consistent, with lesions observed on the cartilage surface of rabbit patellae from blunt impact, for example, to the patello-femoral joint. The purpose of the present study was to analyze, using the elastic capabilities of a finite element code, the stress distribution in more morphologically realistic transversely isotropic biphasic contact models of cartilage. The elastic properties of an incompressible material, equivalent to those of the transversely isotropic biphasic material at time zero, were derived algebraically using stress-strain relations. Results of the stress analysis showed the highest shear stresses on the surface of the solid skeleton of the cartilage and tensile stresses in the zone of contact. These results can help explain the mechanisms responsible for surface injuries observed during blunt insult experiments.

A boundary integral method applied to plates of arbitrary plan form

Abstract An integral equation method for the solution of thin elastic plates of arbitrary plan form has been presented. The method involves embedding the real plate in a fictitious plate for which the Greens function is known. An unknown load vector is then introduced on the boundary of the real plate (line load and line normal moment). The deflection field due to both known transverse and unknown boundary loads can then be found everywhere by superposition. Satisfaction of the boundary conditions on the real plate results in a vector integral equation in the unknown boundary vector. In concept, any consistent set of boundary conditions will yield a solution. Practically, boundary conditions requiring higher derivatives of the deflection are both very cumbersome and yield singularities in the integral equations which cause numerical difficulties. For these reasons only clamped boundary conditions are treated numerically in the present paper. For interior bending moments and deflections (greater than distances of the order of one boundary subdivision from the boundary) the method is both highly accurate and inexpensive. Errors right on the boundary, e.g. the clamping moment in the clamped boundary condition case, can be appreciable, however. While this can be improved by a more sophisticated treatment of the unknown boundary vector in the numerical solution (increased expense) it is shown in the paper that a simple boundary extrapolation procedure gives excellent accuracy there.

A poroelastic model that predicts some phenomenological responses of ligaments and tendons

Experimental evidence suggests that the tensile behavior of tendons and ligaments is in part a function of tissue hydration. The models currently available do not offer a means by which the hydration effects might be explicitly explored. To study these effects, a finite element model of a collagen sub-fascicle, a substructure of tendon and ligament, was formulated. The model was microstructurally based, and simulated oriented collagen fibrils with elastic-orthotropic continuum elements. Poroelastic elements were used to model the interfibrillar matrix. The collagen fiber morphology reflected in the model interacted with the interfibrillar matrix to produce behaviors similar to those seen in tendon and ligament during tensile, cyclic, and relaxation experiments conducted by others. Various states of hydration and permeability were parametrically investigated, demonstrating their influence on the tensile response of the model.

Estimation of in Situ Elastic Properties of Biphasic Cartilage Based on a Transversely Isotropic Hypo-Elastic Model

Articular cartilage is known to behave nonlinearly for large deformations. Mechanical properties derived from small strain experiments yield excessively large deformations in finite element models used in the study of severe blunt impact to joints. In this manuscript, a method is presented to determine the nonlinear elastic properties of biphasic cartilage based on a transversely isotropic hypo-elastic model. The elastic properties were estimated by fitting two force-displacement curves (in rapid loading and at equilibrium) obtained from large deformation indentation relaxation tests on cartilage using a nonporous spherical indentor. The solid skeleton of the cartilage was modeled as a transversely isotropic hypo-elastic material and a commercial finite element program was employed to solve the problem of a layer indented by a rigid sphere. Components of the hypo-elasticity tensor were made dependent on deformation according to the variations defined by a transversely isotropic hyperelastic formulation given earlier by others. Material incompressibility was assumed during the initial stage of rapid loading. The analysis was utilized for the determination of in situ properties of rabbit retropatellar cartilage at large deformations. The model was able to fit the material response to rapid loading and equilibrium indentation test data to approximately 50 percent strain. This material model suggested even higher percentage of stress supported by the fluid phase of cartilage than given earlier by small deformation theories of biphasic cartilage.

A new numerical method for the analysis of anisotropic thin-plate bending problems

Abstract A new method is presented for the analysis of anisotropic thin-plate bending problems. This method appears to enjoy several advantages over other numerical methods for linear problems. In concept the present method is quite simple. Using the influence function for an infinite plate of the same material, the solution to the problem of interest is expressed as the superposition of the effect of the actual lateral load plus 2N unknown point loads located outside the region occupied by the plate. These 2N loads are then determined through imposition of the boundary conditions at N selected locations. An interesting numerical question arises regarding the selection of the 2N external points. It is shown that proper distribution of these points leads to excellent results with minimal computer effort. Several example problems are presented, demonstrating the ability of the method to deal with difficult geometries and boundary conditions and with material anisotropy.

An Analytical Model to Study Blunt Impact Response of the Rabbit P-F Joint

While mechanisms of post-traumatic osteoarthrosis are largely unknown, excessive stresses and strains generated in articular cartilage and the underlying bone may play a role. In this manuscript a technique is described for studying the impact response of a diarthrodial joint. A mathematical model of the rabbit PF joint indicated that contact pressures predicted by a quasi-static plane strain linear elastic model compared well with experimental data when Poissons ratio and Youngs modulus of the cartilage were 0.49 and 2 MPa, respectively. This value for the elastic modulus compared well with that obtained from elastic analysis of short-time indentation experiments on cartilage from a previous study. The model analysis also suggested that surface fissuring of patellar cartilage occurs near areas where shear stresses and tensile strains are high. Impact location on the patella significantly influenced the distributions of shear stress along the bone-cartilage interface and tensile strains in the cartilage. These results may help explain some of the mechanisms of initial tissue damage reported elsewhere. Limited experimental data are presented here but the value of such mathematical models for estimation of material properties and for analysis of damage creation is clearly demonstrated.

A boundary integral method applied to plates of arbitrary plan form and arbitrary boundary conditions

Abstract An integral equation method which has been applied to thin elastic clamped plates of arbitrary plan form[1] has been extended to include arbitrary boundary conditions. Numerical difficulties which arise in the case of free boundaries have been avoided by defining an integration contour which differs from the actual plate boundary. Thus second order singularities which arise in the integrand of the equations are avoided. The method is applied to two rectangular plates with mixed boundary conditions (i.e. clamped, simply-supported and free edges). Average errors are 1.5% for displacements and 3% for bending moments.

An Investigation of Biphasic Failure Criteria for Impact-Induced Fissuring of Articular Cartilage

Articular cartilage consists of both solid and fluid phases with fissures observed on the surface occurring in the solid portion. In order to determine which of the solid phase stresses provides the best predictor for the initiation of a fissure, elastic stresses from a series of in vitro impact experiments were used to derive stresses in the solid phase of the cartilage. This stress information was then analyzed using a logistic regression to identify the best predictor of fissuring. The mechanical analysis indicated that low-magnitude tensile solid hoop stress develops in the solid phase within the contact zone in impacts involving the two smaller radius interfaces. The logistic regression, however, indicated that maximum shear stress in the solid (which is equal to the shear stress from the elastic analysis) was the best predictor of the occurrence of a fissure. This study helps support the suggestion that in stress fields dominated by compression, the maximum shear stress from an elastic analysis may be used to predict fissure initiation in cartilage.

THE INFLUENCE OF IMPACT INTERFACE ON HUMAN KNEE INJURY: IMPLICATIONS FOR INSTRUMENT PANEL DESIGN AND THE LOWER EXTREMITY INJURY CRITERION

A single impact at 27 J of energy with a rigid interface was delivered to one knee of isolated joint preparations of six cadavers resulting in an average peak load of 5 kN. Contralateral knee were impacted with a padded interface at an additional level of energy at approximately the same load. Math modeling of the patellae showed reduced tensile and shear stresses in the bone with padding. Increasing contact area over the knee reduces stresses in the bone and prevents both gross bone fracture and bone and cartilage microdamage. Language: en