Tammy L. Haut Donahue

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

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.

How the stiffness of meniscal attachments and meniscal material properties affect tibio-femoral contact pressure computed using a validated finite element model of the human knee joint

In an effort to prevent degeneration of articular cartilage associated with meniscectomies, both meniscal allografts and synthetic replacements are subjects of current interest and investigation. The objectives of the current study were to (1) determine whether a transversely isotropic, linearly elastic, homogeneous material model of the meniscal tissue is necessary to achieve a normal contact pressure distribution on the tibial plateau, (2) determine which material and boundary condition (attachments) parameters affect the contact pressure distribution most strongly, and (3) set tolerances on these parameters to restore the contact pressure distribution to within a specified error. To satisfy these objectives, a finite element model of the tibio-femoral joint of a human cadaveric knee (including both menisci) was used to study the contact pressure distribution on the tibial plateau. To validate the model, the contact pressure distribution on the tibial plateau was measured experimentally in the same knee used to create the model. Within physiologically reasonable bounds on five material parameters and four attachment parameters associated with a meniscal replacement, an optimization was performed under 1200 N of compressive load on the set of nine parameters to minimize the difference between the experimental and model results. The error between the experimental and model contact variables was minimized to 5.4%. The contact pressure distribution of the tibial plateau was sensitive to the circumferential modulus, axial/radial modulus, and horn stiffness, but relatively insensitive to the remaining six parameters. Consequently, both the circumferential and axial/radial moduli are important determinants of the contact pressure distribution, and hence should be matched in the design and/or selection of meniscal replacements. In addition, during surgical implantation of a meniscal replacement, the horns should be attached with high stiffness bone plugs, and the attachments of the transverse ligament and deep medial collateral ligament should be restored to minimize changes in the contact pressure distribution, and thereby possibly prevent the degradation of articular cartilage.

Comparison of viscoelastic, structural, and material properties of double-looped anterior cruciate ligament grafts made from bovine digital extensor and human hamstring tendons.

Due to ready availability, decreased cost, and freedom from transmissible diseases in humans such as hepatitis and AIDS, it would be advantageous to use tendon grafts from farm animals as a substitute for human tendon grafts in in vitro experiments aimed at improving the outcome of anterior cruciate ligament (ACL) reconstructive surgery. Thus the objective of this study was to determine whether an anterior cruciate ligament (ACL) graft composed of two loops of bovine common digital extensor tendon has the same viscoelastic, structural, and material properties as a graft composed of a double loop of semitendinosus and gracilis tendons from humans. To satisfy this objective, grafts were constructed from each tissue source. The cross-sectional area was measured using an area micrometer, and each graft was then pulled using a materials testing system while submerged in a saline bath. Using two groups of tendon grafts (n = 10), viscoelastic tests were conducted over a three-day period during which a constant displacement load relaxation test was followed by a constant amplitude, cyclic load creep test (first day), a constant load creep test (second day), and an incremental cyclic load creep test (third day). Load-to-failure tests were performed on two different groups of grafts (n = 8). When the viscoelastic behavior was compared, there were no significant differences in the rate of load decay or the final load (relaxation test) and rates of displacement increase or final displacements (creep tests) (p > 0.115). To compare both the structural and material properties in the toe region (i.e., < 250 N) of the load-elongation curve, the tangent stiffness and modulus functions were computed from parameters used in an exponential model fit to the load (stress)-elongation (strain) data. Although one of the two parameters in the functions was different statistically, this difference translated into a difference of only 0.03 mm in displacement at 250 N of load. In the linear region (i.e., 50-75 percent of ultimate load) of the load-elongation curve, the linear stiffness of the two graft types compared closely (444 N/mm for bovine and 418 N/mm for human) (p = 0.341). At failure, the ultimate loads (2901 N and 2914 N for bovine and human, respectively) and the ultimate stresses (71.8 MPa and 65.6 MPa for bovine and human, respectively) were not significantly different (p > 0.261). The theoretical effect of any differences in properties between these two grafts on the results of two types of in vitro experiments (i.e., effect of surgical variables on knee laxity and structural properties of fixation devices) are discussed. Despite some statistical differences in the properties evaluated, these differences do not translate into important effects on the dependent variables of interest in the experiments. Thus the bovine tendon graft can be substituted for the human tendon graft in both types of experiments.

3D Finite Element Model of Meniscectomy: Changes in Joint Contact Behavior

The goal of this study is to quantify changes in knee joint contact behavior following varying degrees of the medial partial meniscectomy. A previously validated 3D finite element model was used to simulate 11 different meniscectomies. The accompanying changes in the contact pressure on the superior surface of the menisci and tibial plateau were quantified as was the axial strain in the menisci and articular cartilage. The percentage of medial meniscus removed was linearly correlated with maximum contact pressure, mean contact pressure, and contact area. The lateral hemi-joint was minimally affected by the simulated medial meniscectomies. The location of maximum strain and location of maximum contact pressure did not change with varying degrees of partial medial meniscectomy. When 60% of the medial meniscus was removed, contact pressures increased 65% on the remaining medial meniscus and 55% on the medial tibial plateau. These data will be helpful for assessing potential complications with the surgical treatment of meniscal tears. Additionally, these data provide insight into the role of mechanical loading in the etiology of post-meniscectomy osteoarthritis.

Transversely isotropic tensile material properties of skeletal muscle tissue.

Of the plethora of work performed analyzing skeletal muscle tissue, relatively little has been done in the examination of its passive material properties. Previous studies of the passive properties of skeletal muscle have been primarily performed along the longitudinal material direction. In order to ensure the accuracy of the predictions of computational models of skeletal muscles, a better understanding of the tensile three-dimensional material properties of muscle tissue is necessary. To that end, the purpose of this study was to collect a comprehensive set of tensile stress-strain data from skeletal muscle tissue. Load-deformation data was collected from eighteen extensor digitorum longus muscles, dissected free of aponeuroses, from nine New Zealand White rabbits tested under longitudinal extension (LE), transverse extension (TE), or longitudinal shear (LS). The linear modulus, ultimate stress, and failure strain were calculated from stress-strain results. Results indicate that the linear modulus under LE is significantly higher than the modulus of either TE or LS. Additionally, the ultimate stress of muscle was seen to be significantly higher under LE than TE. Conversely, the failure strain was significantly higher under TE than under LE.

Geometry, time-dependent and failure properties of human meniscal attachments

Meniscectomies have been shown to lead to osteoarthritis and the success of meniscal replacements remains questionable. It has been suggested that the success of a meniscal replacement is dependent on several factors, one of which is the secure fixation and firm attachment of the replacement to the tibial plateau at the horn locations. To aid in the development of meniscal replacements, the objectives of the current study were to determine the time-dependent and failure properties of human meniscal attachments. In contrast to the time-dependent tests, during uniaxial failure testing a charge-coupled video camera was used to document the local strain and linear modulus distribution across the surface of the attachments. The lateral attachments were statistically smaller in cross-sectional area and longer than the medial attachments. The anterior attachments were statistically longer and had a smaller cross-sectional area than the posterior attachments. From the stress relaxation tests, the load and stress relaxation rates of the medial anterior attachment were statistically greater than the medial posterior attachment. There were no significant differences in the creep, structural properties or the ultimate stress between the different attachments. Ultimate strain varied between attachments, as well as along the length of the attachment. Ultimate strain in the meniscus region (10.4+/-6.9%) and mid-substance region (12.7+/-16.4%) was smaller than the bony insertion region (32.2+/-21.5%). The lateral and anterior attachments were also found to have statistically greater strain than the medial and posterior attachments, respectively. The linear modulus was statistically weaker in the bony insertion region (69.7+/-33.7MPa) compared to the meniscus region (153+/-123MPa) and mid-substance region (195+/-121MPa). Overall the anterior attachments (169+/-130MPa) were also found to be statistically stronger than the posterior attachments (90.8+/-64.9MPa). These results can be used to help design tissue-engineered replacement menisci and their insertions and show the differences in material properties between attachments, as well as within an attachment.

A Quantitative Study of the Microstructure and Biochemistry of the Medial Meniscal Horn Attachments

Little quantitative data is available on the structure of meniscal attachments. Therefore, as an aid to designing meniscal replacements as well as a possible explanation for mechanical behavior, this study was designed to further the knowledge of the microstructure and biochemistry of native meniscal attachments. Bovine medial meniscal attachments (the external ligamentous portion as well as the transition zones at the bony insertion) were removed and prepared for microstructural evaluation. After embedding in paraffin, the samples were sliced on a microtome and stained for quantitative analysis. The anterior and posterior insertion sites are known to contain three zones: subchondral bone, calcified fibrocartilage, and uncalcified fibrocartilage. Additionally, others have shown that the anterior insertion site contains a ligamentous zone. The insertion zones were further divided into proximal, middle, and distal zones. The posterior attachment’s insertion site had a significantly greater thickness of interdigitations, subchondral bone, uncalcified fibrocartilage, and calcified fibrocartilage zone thickness compared to the anterior attachment insertion. The anterior attachment’s insertion had the greatest GAG fraction in each zone when compared to the posterior attachment’s insertion. GAG fraction decreased from the meniscus to the subchondral bone. Both GAG fraction and normalized thickness varied within a given zone, decreasing from the distal to proximal regions in both the anterior and posterior attachments’ insertion zones. Crimp frequency of the collagen fibrils in the external ligamentous portion of the tissue was homogeneous along the length. The findings from this study agree with previously published material property data on the medial meniscal attachments, and could be used in the future to design methods of attachment for tissue engineered replacement menisci.

Hyperelastic properties of human meniscal attachments

Meniscal attachments are ligamentous tissues anchoring the menisci to the underlying subchondral bone. Currently little is known about the behavior of meniscal attachments, with only a few studies quantitatively documenting their properties. The objective of this study was to quantify and compare the tensile mechanical properties of human meniscal attachments in the transverse direction, curve fit experimental Cauchy stress-stretch data to evaluate the hyperelastic behavior, and couple these results with previously obtained longitudinal data to generate a more complete constitutive model. Meniscal attachment specimens were tested using a uniaxial tension test with the collagen fibers oriented perpendicular to the loading axis. Tests were run until failure and load-optical displacement data was recorded for each test. The medial posterior attachment was shown to have a significantly greater elastic modulus (6.42±0.78 MPa) and ultimate stress (1.73±0.32 MPa) when compared to the other three attachments. The Mooney-Rivlin material model was selected as the best fit for the transverse data and used in conjunction with the longitudinal data. A novel computational approach to determining the transition point between the toe and linear regions is presented for the hyperelastic stress-stretch curves. Results from piece-wise non-linear longitudinal curve fitting correlate well with previous linear elastic and SEM findings. These data can be used to advance the design of meniscal replacements and improve knee joint finite element models.

Identification of Cross-Sectional Parameters of Lateral Meniscal Allografts That Predict Tibial Contact Pressure in Human Cadaveric Knees

To guide the development of improved procedures for selecting meniscal allografts, the objective of this study was to identify which cross-sectional parameters of a lateral meniscal allograft predict the contact pressure of the articular surface of the tibia. To meet the objective, the contact pressure of the articular surface of the tibia was measured with a lateral meniscal autograft and a lateral meniscal allograft using pressure sensitive film in 15 fresh-frozen human cadaveric knees. Allografts were matched only in transverse dimensions to the autograft but not in cross-sectional dimensions. Knees were loaded to 1200 N in compression at flexion angles of 0, 15, 30 and 45 degrees using a load application system that allowed unconstrained motion in the remaining degrees of freedom. Five cross-sectional parameters for both of the grafts in each of the anterior, middle, and posterior regions were derived from measurements obtained using a laser-based non-contacting three-dimensional coordinate digitizing system (3-DCDS) (Haut et al., J. Orthop Res, 2000). Five contact variables (i.e. the maximum pressure, mean pressure, contact area, and anterior-posterior and medial-lateral locations of the centroid of contact area) were determined from the pressure sensitive film. When each allograft was paired with the corresponding autograft, the root mean squared percent differences for the cross-sectional parameters ranged from a minimum of 28% for the width of the posterior region to 572% for the height of the posterior region. The root mean squared percent differences between the contact variables for paired grafts were 29% for the maximum pressure, 19% for the mean pressure, and 24% for the contact area. Differences in the cross-sectional parameters between the grafts were related to differences in the contact variables using regression analysis. Difference in the width was most often a predictor variable in the regression models with R2 values > or = 0.45. Differences in all of the four remaining cross-sectional parameters were also important predictor variables. Because failure to match cross-sectional parameters causes substantial difference in contact variables between an allograft and autograft and because cross-sectional parameters predict the contact pressure on the tibial plateau, protocols used to prospectively select allografts should concentrate on matching cross-sectional parameters and particularly the width to those of the original meniscus.

Traumatic Anterior Cruciate Ligament Tear and its Implications on Meniscal Degradation: A Preliminary Novel Lapine Osteoarthritis Model

BACKGROUND Injury patterns of the meniscus following impact trauma resulting in anterior cruciate ligament (ACL) rupture are not well understood. This study explored the spatial and temporal distribution of meniscal tears in a novel in vivo lapine model. METHODS Skeletally mature Flemish Giant rabbits were subjected to either tibiofemoral impaction resulting in ACL rupture or surgical ACL transection. Meniscal damage was assessed acutely and after 12 wk for traumatically torn, and after 12 wk in ACL transected animals. Morphological grading was assessed using previously established criteria, and descriptions of meniscal damage were diagnosed by a Board certified orthopedist. Histological assessment was also made on 12 wk traumatically torn and ACL transected animals using Fast-Green/Safranin-O staining. RESULTS Traumatic ACL rupture resulted in acute tears predominately in the lateral menisci. Animals subjected to both surgical transection and traumatic ACL rupture experienced degradation of the lateral and medial menisci 12 wk after injury. However, traumatic ACL rupture resulted in acute lateral damage and chronic degradation of the menisci, as well as more severe degradation of the menisci 12 wk after injury. CONCLUSIONS This study showed that unconstrained high-intensity impacts on the tibiofemoral joint lead to meniscal damage in conjunction with ACL ruptures. Both acute and chronic changes to the menisci following traumatic impaction were observed. This research has implications for the future use of lapine models for osteoarthritis, as it incorporates traumatic loading as a more realistic mode contributing to the progression of osteoarthritis (OA) compared to surgically transected models.