As a step towards developing a finite element model of the knee that can be used to study how the variables associated with a meniscal replacement affect tibio-femoral contact, the goals of this study were 1) to develop a geometrically accurate three-dimensional solid model of the knee joint with special attention given to the menisci and articular cartilage, 2) to determine to what extent bony deformations affect contact behavior, and 3) to determine whether constraining rotations other than flexion/extension affects the contact behavior of the joint during compressive loading. The model included both the cortical and trabecular bone of the femur and tibia, articular cartilage of the femoral condyles and tibial plateau, both the medial and lateral menisci with their horn attachments, the transverse ligament, the anterior cruciate ligament, and the medial collateral ligament. The solid models for the menisci and articular cartilage were created from surface scans provided by a noncontacting, laser-based, three-dimensional coordinate digitizing system with an root mean squared error (RMSE) of less than 8 microns. Solid models of both the tibia and femur were created from CT images, except for the most proximal surface of the tibia and most distal surface of the femur which were created with the three-dimensional coordinate digitizing system. The constitutive relation of the menisci treated the tissue as transversely isotropic and linearly elastic. Under the application of an 800 N compressive load at 0 degrees of flexion, six contact variables in each compartment (ie., medial and lateral) were computed including maximum pressure, mean pressure, contact area, total contact force, and coordinates of the center of pressure. Convergence of the finite element solution was studied using three mesh sizes ranging from an average element size of 5 mm by 5 mm to 1 mm by 1 mm. The solution was considered converged for an average element size of 2 mm by 2 mm. Using this mesh size, finite element solutions for rigid versus deformable bones indicated that none of the contact variables changed by more than 2% when the femur and tibia were treated as rigid. However, differences in contact variables as large as 19% occurred when rotations other than flexion/extension were constrained. The largest difference was in the maximum pressure. Among the principal conclusions of the study are that accurate finite element solutions of tibio-femoral contact behavior can be obtained by treating the bones as rigid. However, unrealistic constraints on rotations other than flexion/extension can result in relatively large errors in contact variables.

A Finite Element Model of the Human Knee Joint for the Study of Tibio-Femoral Contact

An asymptotic solution for the contact of two biphasic cartilage layers

Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict real area of contact and surface and subsurface stresses affecting friction and wear of an interface. When two macroscopically flat bodies with microroughness come in contact, the contact occurs at multiple asperities of arbitrary shapes, and varying sizes and heights. Deformation at the asperity contacts can be either elastic and/or elastic-plastic. If a thin liquid film is present at the interface, attractive meniscus forces may affect friction and wear. Historically, statistical models have been used to predict contact parameters, and these generally require many assumptions about asperity geometry and height distributions. With the advent of computer technology, numerical contact models of 3-D rough surfaces have been developed, particularly in the past decade, which can simulate digitized rough surfaces with no assumptions concerning the roughness distribution. In this article, a comprehensive review of modeling of multiple-asperity contacts in dry and wet conditions is presented. Contact models for homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented. The models reviewed in this paper fall into two groups: (a) analytical solutions for surfaces with well-defined height distributions and asperity geometry and (b) numerical solutions for real surfaces with asperities of arbitrary shape and varying size and height distributions. Implications of these models in friction and wear studies are discussed.

Contact mechanics of rough surfaces in tribology: multiple asperity contact

Deformational loading represents a primary component of the chondrocyte physical environment in vivo. This review summarizes our experience with physiologic deformational loading of chondrocyte-seeded agarose hydrogels to promote development of cartilage constructs having mechanical properties matching that of the parent calf tissue, which has a Young's modulus EY = 277 kPa and unconfined dynamic modulus at 1 Hz G*=7 MPa. Over an 8-week culture period, cartilage-like properties have been achieved for 60 × 106 cells/ml seeding density agarose constructs, with EY = 186 kPa, G*=1.64 MPa. For these constructs, the GAG content reached 1.74% ww and collagen content 2.64% ww compared to 2.4% ww and 21.5% ww for the parent tissue, respectively. Issues regarding the deformational loading protocol, cell-seeding density, nutrient supply, growth factor addition, and construct mechanical characterization are discussed. In anticipation of cartilage repair studies, we also describe early efforts to engineer cylindrical and anatomically shaped bilayered constructs of agarose hydrogel and bone (i.e., osteochondral constructs). The presence of a bony substrate may facilitate integration upon implantation. These efforts will provide an underlying framework from which a functional tissue-engineering approach, as described by Butler and coworkers (2000), may be applied to general cell-scaffold systems adopted for cartilage tissue engineering.

/pdf/a-paradigm-for-functional-tissue-engineering-of-articular-ma6qqd1lcj.pdf

A Paradigm for Functional Tissue Engineering of Articular Cartilage

Deformational loading represents a primary component of the chondrocyte physical environment in vivo. This review summarizes our experience with physiologic deformational loading of chondrocyte-seeded agarose hydrogels to promote development of cartilage constructs having mechanical properties matching that of the parent calf tissue, which has a Young's modulus E
Y = 277 kPa and unconfined dynamic modulus at 1 Hz G*=7 MPa. Over an 8-week culture period, cartilage-like properties have been achieved for 60 × 106 cells/ml seeding density agarose constructs, with E
Y = 186 kPa, G*=1.64 MPa. For these constructs, the GAG content reached 1.74% ww and collagen content 2.64% ww compared to 2.4% ww and 21.5% ww for the parent tissue, respectively. Issues regarding the deformational loading protocol, cell-seeding density, nutrient supply, growth factor addition, and construct mechanical characterization are discussed. In anticipation of cartilage repair studies, we also describe early efforts to engineer cylindrical and anatomically shaped bilayered constructs of agarose hydrogel and bone (i.e., osteochondral constructs). The presence of a bony substrate may facilitate integration upon implantation. These efforts will provide an underlying framework from which a functional tissue-engineering approach, as described by Butler and coworkers (2000), may be applied to general cell-scaffold systems adopted for cartilage tissue engineering.

/pdf/a-paradigm-for-functional-tissue-engineering-of-articular-4got1rc75j.pdf

A Paradigm for Functional Tissue Engineering of Articular Cartilage via Applied Physiologic Deformational Loading

The stress distribution in the region of contact between a layered elastic sphere and a layered elastic cavity is determined using an analytical model to stimulate contact of articulating joints. The purpose is to use the solution to analyze the effects of cartilage thickness and stiffness, bone stiffness and joint curvature on the resulting stress field, and investigate the possibility of cracking of the material due to tensile and shear stresses. Vertical cracking of cartilage as well as horizontal splitting at the cartilage-calcified cartilage interface has been observed in osteoarthritic joints. The current results indicate that for a given system (material properties mu and nu constant), the stress distribution is a function of the ratio of contact radius to layer thickness (a/h), and while tensile stresses are seen to occur only when a/h is small, tensile strain is observed for all a/h values. Significant shear stresses are observed at the cartilage-bone interface. Softening of cartilage results in an increase in a/h, and a decrease in maximum normal stress. Cartilage thinning increases a/h and the maximum contact stress, while thickening has the opposite effect. A reduction in the indenting radius reduces a/h and increases the maximum normal stress. Bone softening is seen to have negligible effect on the resulting contact parameters and stress distribution.

V. Vithoontien

Papers

An analytical model of joint contact.

The Interior Stress Field Caused by Tangential Loading of a Rectangular Patch on an Elastic Half Space

The interior stress field caused by tangential loading of a rectangular patch on an elastic half space.

Compliance of coated elastic bodies in contact