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The problem of quantifying muscular activity of the human body can be formulated as an optimal control problem. The current methods used with large-scale biomechanical systems are non-derivative techniques. These methods are costly, as they require numerous integrations of the equations of motion. Additionally, the convergence is slow, making them impractical for use with large systems. We apply an efficient numerical algorithm to the biomechanical optimal control problem. Using direct collocation with a trapezoidal discretization, the equations of motion are converted into a set of algebraic constraint equations. An augmented Lagrangian formulation is used for the optimization problem to handle both equality and inequality constraints. The resulting min-max problem is solved with a generalized Newton method. In contrast to the prevalent optimal control implementations, we calculate analytical first- and second-derivative information and obtain local quadratic convergence. To demonstrate the efficacy of the method, we solve a steady-state pedaling problem with 7 segments and 18 independent muscle groups. The computed muscle activations compare well with experimental EMG data. The computational effort is significantly reduced and solution times are a fraction of those of the non-derivative techniques.

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OBJECTIVE: The objective of this study is to analyze the biomechanics of the patellar component following total knee replacement. More specifically we investigated the effect of displacing the femoral component of an Insall-Burstein II total knee replacement on the patellar tracking and patello-femoral contact pressures. DESIGN: We used a validated computer simulation of the knee joint to virtually insert the femoral component with the following four types of placements: (1) no misplacement, (2) 5 degrees of internal rotation, (3) 5 degrees of external rotation and (4) 5 degrees of flexion rotation. The patellar 3D tracking and patello-femoral contact pressures were computed for each femoral component placement as a function of knee flexion angle. BACKGROUND: Complications at the patello-femoral joint are the among most frequent following total knee replacement. RESULTS: Femoral component placement unevenly affected the associated patellar tracking: a 5 degrees internal rotation tilted and rotated the patella laterally by about 5 degrees throughout knee flexion. A 5 degrees external rotation of the femoral component had less effect on patellar tracking. A rotation of 5 degrees in flexion primarily caused patellar rotation (5-10 degrees lateral rotation). Femoral component malalignment had only minor effects on the peak pressure distributions at the patello-femoral interface. CONCLUSION: These results suggest that femoral component positioning primarily affects patellar tracking, with a possible threat for patellar subluxation under external rotation of the femoral component. RELEVANCE: Precise alignment of the prosthetic components is difficult to control during total knee replacement due to the lack of precise anatomical landmarks in the human knee joint. Consequently, the position of each prosthetic component may differ from the ideal one suggested by the manufacturer. Improper alignment of the prosthetic components during total knee replacement may lead to premature implant failure.

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Significant ground reaction forces exceeding body weight occur during the heel-strike phase of gait. The standard methods of analytical dynamics used to solve the impact problem do not accommodate well the heel-strike collision due to the persistent contact at the front foot and presence of contact at the back foot. These methods can cause a non-physical energy gain on the order of the total kinetic energy of the system at impact. Additionally, these standard techniques do not quantify the contact force, but the impulse over the impact. We present an energy-conserving impact algorithm based on the penalty method to solve for the ground reaction forces during gait. The rigid body assumptions are relaxed and the bodies are allowed to penetrate one another to a small degree. Associated with the deformation is a potential, from which the contact forces are derived. The empirical coefficient-of-restitution used in the standard approaches is replaced by two parameters to characterize the stiffness and the damping of the materials. We solve two simple heel-strike models to illustrate the shortcomings of a standard approach and the suitability of the proposed method for use with gait.

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The development of normal joints depends on mechanical function in utero. Experimental studies have shown that the normal surface topography of diarthrodial joints fails to form in paralyzed embryos. We implemented a mathematical model for joint morphogenesis that explores the hypothesis that the stress distribution created in a functional joint may modulate the growth of the cartilage anlagen and lead to the development of congruent articular surfaces. We simulated the morphogenesis of a human finger joint (proximal interphalangeal joint) between days 55 and 70 of fetal life. A baseline biological growth rate was defined to account for the intrinsic biological influences on the growth of the articulating ends of the anlagen. We assumed this rate to be proportional to the chondrocyte density in the growing tissue. Cyclic hydrostatic stress caused by joint motion was assumed to modulate the baseline biological growth, with compression slowing it and tension accelerating it. Changes in the overall shape of the joint resulted from spatial differences in growth rates throughout the developing chondroepiphyses. When only baseline biological growth was included, the two epiphyses increased in size but retained convex incongruent joint surfaces. The inclusion of mechanobiological-based growth modulation in the chondroepiphyses led to one convex joint surface, which articulated with a locally concave surface. The articular surfaces became more congruent, and the anlagen exhibited an asymmetric sagittal profile similar to that observed in adult phalangeal bones. These results are consistent with the hypothesis that mechanobiological influences associated with normal function play an important role in the regulation of joint morphogenesis.

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A three-dimensional computer model is used, based on the finite element method, to investigate the effects of 1-, 1.5-, and 2-cm tibial tubercle elevations and of 0.5- and 1-cm medial displacements of the tuberosity, performed with different bone shingles. Patellar kinematics and patellofemoral interface peak pressure, between 45 degrees and 135 degrees of passive knee flexion, are compared for these different surgical parameters with those of a normal knee not surgically treated. The shingle lengths of 3, 5, 7, and 10 cm have little influence on the results. Augmenting tubercle medializations decrease the lateral peak pressure but result in an overpressure of the medial facet that is 154% of the normal peak value. With knee flexion between 45 degrees and 60 degrees, increasing tubercle elevations decreases later and medial peak pressures. With flexion of more than 60 degrees, increasing elevations decrease the lateral peak pressure, but they augment and even cause overpressure on the medial facet. An overpressure on the lateral facet also is seen in midrange knee flexion (75 degrees-90 degrees) for all tubercle elevation values. Increasing tubercle elevations and medializations appear to be the predominant parameters from a biomechanical point of view.

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In this paper, we look at the mechanobiological processes involved in mandibular distraction and, as a first approximation, propose an elastoplastic uniaxial model.

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The common approach to assess the stabilizing role of the ACL in the knee has been to measure the elongation of a few marked fibers in the ligament. A comparison of the relative elongation (RE) of these marked fibers between different specimens and studies is delicate due to the difficulty of marking the same fibers. More consistent comparisons would be achieved if the RE of the whole ligament surface was presented. Hence, we developed a mathematical method leading to a continuous description of the relative elongation of the ligament's surface based on experimental measurements of the RE of five fibers. The ligament fibers of two knee specimens were marked by radiopaque markers and a Roentgen Stereophotogrammetric Analysis system was used to reconstruct the three-dimensional positions of these artificial landmarks. The mathematical procedure used isoparametric cubic splines to interpolate the contours of the insertion sites. The results showed that the general pattern of the RE for both specimens was similar, characterized by an undulation near full flexion. In fact, close to full flexion all the RE of the fibers increased. Such a representation describes the changes in the RE for a given fiber during knee flexion and at the same time characterizes the RE distribution at a given flexion angle.

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A numerical model of a femoral total hip component based on the finite element method is developed to evaluate the relative micromotions at the bone-implant interface and the stress distribution in the femoral bone. The interface is modelled as unilateral contact involving Coulomb's dry friction between the bone and the implant. In addition, the model includes inhomogeneity, anisotropy as well as plasticity of both cortical and spongious bones. An automatic data processor coupled to a three-dimensional mesh generator is designed to extract cortical bone geometry and inhomogeneous distribution of trabecular bone density from data obtained with quantitative computed tomography (QCT). A preliminary application is conducted to evaluate the mechanical behaviour of an existing bone-prosthesis structure for two typical loadings: a load simulating the single leg stance and a load simulating the stair climbing stance. The obtained results are subdivided in two parts. Firstly, the characterization of stress transfer and micromotions at the bone-stem interface. The peak value of the shear micromotions reaches 600 microns in the proximal medial region with a friction coefficient equal to 0.6. An analysis of the influence of the friction coefficient reveals that the shear and distractive micromotions as well as the shear and normal stresses depend strongly on this coefficient. Secondly, the representation of stresses in the femoral bone. Determination of complementary invariants such as the hydrostatic pressure, the deviatoric stress and anisotropic stresses brings additional insights in the evaluation of the stress field in the femoral bone.

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A numerical model based on the finite element method was developed for the load transfer analysis at the tibial bone-implant interfaces in total knee replacement. A transverse isotropic material model, based on a quadratic elastic potential and on Hill's quadratic yield criterion, was next developed for bone constitutive laws. The bone-cement and bone-prosthesis interfaces were both assumed to be discontinuous. A dry friction model based on Coulomb's criterion was adopted for the interfaces friction. The model was shown to be able to give compressive and shear stresses distributions and distractive and relative shear micromotions at these interfaces. A preliminary application was conducted for cemented metal tray total condylar (MTTC) and for cemented and uncemented porous coated anatomic (PCA) tibial plateaus. The PCA plateaus were found to be more deformable and had greater global displacements than the MTTC one. Debonding of the bone-peg interface was observed for the uncemented PCA. Correspondingly, the stress peaks at the interface beneath the tray were lower for the uncemented PCA. Correspondingly, the stress peaks at the interface beneath the tray were lower for the PCA than for the MTTC. Shear micromotions appeared under the tray for both the two prostheses. We observed that bone anisotropy and interface discontinuity affected the results sensibly.

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Twelve anatomical values of the proximal femur and theirs variations in rotation (internal 12 degrees, neutral, external 12 degrees) have been measured radiologically by digitalization on a group of ten anatomical units. A computerized analysis has been performed considering the errors in the X-ray amplification and dispersion factors, as well as the methodological imprecisions. It came out that, except for the width of the medullary canal in AP view, all anatomical parameters were very sensitive to the different positions of the femur in rotation and were subject to significant variations. These fluctuations lead the authors to the following conclusion: during the pre-operating planning of cementless hip arthroplasties, the radiology still allows to choose the size of the femoral component so as to improve the fitting with the internal geometry of the femur. However, the radiology still remains insufficient as a basis to conceive and design a custom implant.

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