Differences in femoral morphology among the Orientals and Caucasians: a comparative study using plain radiographs.

The purpose of this study was to identify the differences in femoral dimensions among Caucasian and Oriental populations. A total of 268 femora were collected from China, Japan, Korea, Taiwan and the United States. Firstly, the dimensional parameters for measuring femur were identified. These were initially measured on bone specimens to determine the methodology, followed by measuring the same parameter on plane radiographs of the same bone specimen using a board, and digitized with the aim of verifying the repeatability and reliability of the data. Data were analyzed using ANOVA, paired students t test and Pearson's correlation analysis. The results revealed that Caucasian femora are significantly larger in maximum bone length (BL), head-neck length (HNL), lesser trochanter width and the total width of the distal epiphysis (Wdf). The Beijing femora were found to be the longest and the Japanese femora constituted the shortest bone lengths and smallest angle alpha among the Oriental populations. A strong correlation was observed between Wdf and HD, HNL, Wmc and Wlc in all the populations; however, correlation between Wdf and BL was mild. The angle alpha showed no correlation with BL. This study generated a large database of femoral geometry, which may help pharmaceutical companies to design orthopedic implants for Oriental populations.

Discrete element analysis in musculoskeletal biomechanics.

This paper is written to honor Professor Y. C. Fung, the applied mechanician who has made seminal contributions in biomechanics. His work has generated great spin-off utility in the field of musculoskeletal biomechanics. Following the concept of the Rigid Body-Spring Model theory by T. Kawai (1978) for non-linear analysis of beam, plate, and shell structures and the soil-gravel mixture foundation, we have derived a generalized Discrete Element Analysis (DEA) method to determine human articular joint contact pressure, constraining ligament tension and bone-implant interface stresses. The basic formulation of DEA to solve linear problems is reviewed. The derivation of non-linear springs for the cartilage in normal diarthrodial joint contact problem was briefly summarized. Numerical implementation of the DEA method for both linear and non-linear springs is presented. This method was able to generate comparable results to the classic contact stress problem (the Hertzian solution) and the use of Finite Element Modeling (FEM) technique on selected models. Selected applications in human knee and hip joints are demonstrated. In addition, the femoral joint prosthesis stem/bone interface stresses in a non-cemented fixation were analyzed using a 2D plane-strain approach. The DEA method has the advantages of ease in creating the model and reducing computational time for joints of irregular geometry. However, for the analysis of joint tissue stresses, the FEA technique remains the method of choice.

On foundations of discrete element analysis of contact in diarthrodial joints.

Information about the stress distribution on contact surfaces of adjacent bones is indispensable for analysis of arthritis, bone fracture and remodeling. Numerical solution of the contact problem based on the classical approaches of solid mechanics is sophisticated and time-consuming. However, the solution can be essentially simplified on the following physical grounds. The bone contact surfaces are covered with a layer of articular cartilage, which is a soft tissue as compared to the hard bone. The latter allows ignoring the bone compliance in analysis of the contact problem, i.e. rigid bones are considered to interact through a compliant cartilage. Moreover, cartilage shear stresses and strains can be ignored because of the negligible friction between contacting cartilage layers. Thus, the cartilage can be approximated by a set of unilateral compressive springs normal to the bone surface. The forces in the springs can be computed from the equilibrium equations iteratively accounting for the changing contact area. This is the essence of the discrete element analysis (DEA). Despite the success in applications of DEA to various bone contact problems, its classical formulation required experimental validation because the springs approximating the cartilage were assumed linear while the real articular cartilage exhibited non-linear mechanical response in reported tests. Recent experimental results of Ateshian and his co-workers allow for revisiting the classical DEA formulation and establishing the limits of its applicability. In the present work, it is shown that the linear spring model is remarkably valid within a wide range of large deformations of the cartilage. It is also shown how to extend the classical DEA to the case of strong nonlinearity if necessary.

Prediction of femoral head collapse in osteonecrosis.

The femoral head deteriorates in osteonecrosis. As a consequence of that, the cortical shell of the femoral head can buckle into the cancellous bone supporting it. In order to examine the buckling scenario we performed numerical analysis of a realistic femoral head model. The analysis included a solution of the hip contact problem, which provided the contact pressure distribution, and subsequent buckling simulation based on the given contact pressure. The contact problem was solved iteratively by approximating the cartilage by a discrete set of unilateral linear springs. The buckling calculations were based on a finite element mesh with brick elements for the cancellous bone and shell elements for the cortical shell. Results of 144 simulations for a variety of geometrical, material, and loading parameters strengthen the buckling scenario. They, particularly, show that the normal cancellous bone serves as a strong supporting foundation for the cortical shell and prevents it from buckling. However, under the development of osteonecrosis the deteriorating cancellous bone is unable to prevent the cortical shell from buckling and the critical pressure decreases with the decreasing Young modulus of the cancellous bone. The local buckling of the cortical shell seems to be the driving force of the progressive fracturing of the femoral head leading to its entire collapse. The buckling analysis provides an additional criterion of the femoral head collapse, the critical contact pressure. The buckling scenario also suggests a new argument in speculating on the femoral head reinforcement. If the entire collapse of the femoral head starts with the buckling of the cortical shell then it is reasonable to place the reinforcement as close to the cortical shell as possible.

Development and validation of a new approach for computer-aided long bone fracture reduction using unilateral external fixator.

An innovative computer-aided method to plan and execute long bone fracture reduction using Dynafix unilateral external fixator (EF) is presented and validated. A matrix equation, which represents a sequential transformation from proximal to distal ends, was derived and solved for the amount of rotation and translation required at each EF joint to correct for a displaced fracture using a non-linear least square optimization method. Six polyurethane-foam models of displaced fracture tibiae were used to validate the method. The reduction accuracy was quantified by calculating the residual translations (xr, yr, zr), the residual displacement (dr), and the residual angulations (alphar, betar, gammar) based on the X-Y-Z Euler angle convention. The experiment showed that the mean+/-S.D. of alphar, betar, gammar, xr, yr, zr and dr were 1.57+/-1.14 degrees, 1.33+/-0.90 degrees, 0.71+/-0.70 degrees, 0.98+/-1.85, 0.80+/-0.67, 0.30+/-0.27, and 0.50+/-0.77 mm, respectively, which demonstrated the accuracy and reliability of the method. Instead of adjusting the fixator joints in-situ, our method allows for off-site adjustment of the fixator joints and employs the adjusted EF as a template to guide the surgeons to manipulate the fracture fragments to complete the reduction process. Success of this method would allow surgeons to perform fracture reduction more objectively, efficiently and accurately yet reduce the radiation exposure to both the involved clinicians and patients and lessen the extent of periosteum and soft tissue disruption around the fracture site.

Fixation stiffness of Dynafix unilateral external fixator in neutral and non-neutral configurations.

A primary function of external fixator is to stabilize the fracture site after fracture reduction. Conventional fracture reduction method would result in fixator configurations deviated from its neutral configuration. How the non-neutral configurations would affect the biomechanical performance of unilateral external fixators is still not well-documented. We developed a finite element model to predict the fixation stiffness of the Dynafix unilateral external fixator at arbitrary configurations under compression, torsion, three-point, and four-point bending. Experimental testing was done to validate the model using six Dynafix unilateral external fixators in neutral and particular non-neutral configurations. Effects of loading directions on bending stiffness were also studied. It appeared that the model succeeded in revealing the relative stiffness of the neutral and non-neutral configuration in all the loading conditions. Our results also demonstrated that bending stiffness could vary substantially for different loading directions and the principle loading directions could be very different for different fixator configurations. Therefore, a more logical way to compare the bending stiffness is to identify the principle loading directions of each fixator configuration and used their maximum and minimum bending stiffness as comparison criteria. Given that fixator configurations could substantially change the stiffness properties of the bone-fixator system, computer simulation with finite element modeling of this kind will provide useful clinical information on the rigidity of certain configurations in stabilizing the fracture site for bone healing.

The effect of recombinant human osteogenic protein-1 on allograft incorporation.

We used a canine intercalary bone defect model to determine the effects of recombinant human osteogenic protein 1 (rhOP-1) on allograft incorporation. The allograft was treated with an implant made up of rhOP-1 and type I collagen or with type I collagen alone. Radiographic analysis showed an increased volume of periosteal callus in both test groups compared with the control group at weeks 4, 6, 8 and 10. Mechanical testing after 12 weeks revealed increased maximal torque and stiffness in the rhOP-1 treated groups compared with the control group. These results indicate a benefit from the use of an rhOP-1 implant in the healing of bone allografts. The effect was independent of the position of the implant. There may be a beneficial clinical application for this treatment.