The effect of plate design, bridging span, and fracture healing on the performance of high tibial osteotomy plates: An experimental and finite element study.

OBJECTIVES: Opening wedge high tibial osteotomy (HTO) is an established surgical procedure for the treatment of early-stage knee arthritis. Other than infection, the majority of complications are related to mechanical factors - in particular, stimulation of healing at the osteotomy site. This study used finite element (FE) analysis to investigate the effect of plate design and bridging span on interfragmentary movement (IFM) and the influence of fracture healing on plate stress and potential failure. MATERIALS AND METHODS: A 10° opening wedge HTO was created in a composite tibia. Imaging and strain gauge data were used to create and validate FE models. Models of an intact tibia and a tibia implanted with a custom HTO plate using two different bridging spans were validated against experimental data. Physiological muscle forces and different stages of osteotomy gap healing simulating up to six weeks postoperatively were then incorporated. Predictions of plate stress and IFM for the custom plate were compared against predictions for an industry standard plate (TomoFix). RESULTS: For both plate types, long spans increased IFM but did not substantially alter peak plate stress. The custom plate increased axial and shear IFM values by up to 24% and 47%, respectively, compared with the TomoFix. In all cases, a callus stiffness of 528 MPa was required to reduce plate stress below the fatigue strength of titanium alloy. CONCLUSION: We demonstrate that larger bridging spans in opening wedge HTO increase IFM without substantially increasing plate stress. The results indicate, however, that callus healing is required to prevent fatigue failure.Cite this article: A. R. MacLeod, G. Serrancoli, B. J. Fregly, A. D. Toms, H. S. Gill. The effect of plate design, bridging span, and fracture healing on the performance of high tibial osteotomy plates: An experimental and finite element study. Bone Joint Res 2018;7:639-649. DOI: 10.1302/2046-3758.712.BJR-2018-0035.R1.

Parallel global optimization with the particle swarm algorithm.

Present day engineering optimization problems often impose large computational demands, resulting in long solution times even on a modern high-end processor. To obtain enhanced computational throughput and global search capability, we detail the coarse-grained parallelization of an increasingly popular global search method, the particle swarm optimization (PSO) algorithm. Parallel PSO performance was evaluated using two categories of optimization problems possessing multiple local minima-large-scale analytical test problems with computationally cheap function evaluations and medium-scale biomechanical system identification problems with computationally expensive function evaluations. For load-balanced analytical test problems formulated using 128 design variables, speedup was close to ideal and parallel efficiency above 95% for up to 32 nodes on a Beowulf cluster. In contrast, for load-imbalanced biomechanical system identification problems with 12 design variables, speedup plateaued and parallel efficiency decreased almost linearly with increasing number of nodes. The primary factor affecting parallel performance was the synchronization requirement of the parallel algorithm, which dictated that each iteration must wait for completion of the slowest fitness evaluation. When the analytical problems were solved using a fixed number of swarm iterations, a single population of 128 particles produced a better convergence rate than did multiple independent runs performed using sub-populations (8 runs with 16 particles, 4 runs with 32 particles, or 2 runs with 64 particles). These results suggest that (1) parallel PSO exhibits excellent parallel performance under load-balanced conditions, (2) an asynchronous implementation would be valuable for real-life problems subject to load imbalance, and (3) larger population sizes should be considered when multiple processors are available.

Bicycle drive system dynamics: theory and experimental validation.

Bicycle pedaling has been studied from both a motor control and an equipment setup and design perspective. In both cases, although the dynamics of the bicycle drive system may have an influence on the results, a thorough understanding of the dynamics has not been developed. This study pursued three objectives related to developing such an understanding. The first was to identify the limitations of the inertial/frictional drive system model commonly used in the literature. The second was to investigate the advantages of an inertial/frictional/compliant model. The final objective was to use these models to develop a methodology for configuring a laboratory ergometer to emulate the drive system dynamics of road riding. Experimental data collected from the resulting road-riding emulator and from a standard ergometer confirmed that the inertial/frictional model is adequate for most studies of road-riding mechanics or pedaling coordination. However, the compliant model was needed to reproduce the phase shift in crank angle variations observed experimentally when emulating the high inertia of road riding. This finding may be significant for equipment setup and design studies where crank kinematic variations are important or for motor control studies where fine control issues are of interest.

Crank inertial load has little effect on steady-state pedaling coordination.

Inertial load can affect the control of a dynamic system whenever parts of the system are accelerated or decelerated. During steady-state pedaling, because within-cycle variations in crank angular acceleration still exist, the amount of crank inertia present (which varies widely with road-riding gear ratio) may affect the within-cycle coordination of muscles. However, the effect of inertial load on steady-state pedaling coordination is almost always assumed to be negligible, since the net mechanical energy per cycle developed by muscles only depends on the constant cadence and workload. This study test the hypothesis that under steady-state conditions, the net joint torques produced by muscles at the hip, knee, and ankle are unaffected by crank inertial load. To perform the investigation, we constructed a pedaling apparatus which could emulate the low inertial load of a standard ergometer or the high inertial load of a road bicycle in high gear. Crank angle and bilateral pedal force and angle data were collected from ten subjects instructed to pedal steadily (i.e., constant speed across cycles) and smoothly (i.e., constant speed within a cycle) against both inertias at a constant workload. Virtually no statistically significant changes were found in the net hip and knee muscle joint torques calculated from an inverse dynamics analysis. Though the net ankle muscle joint torque, as well as the one- and two-legged crank torque, showed statistically significant increases at the higher inertia, the changes were small. In contrast, large statistically significant reductions were found in crank kinematic variability both within a cycle and between cycles (i.e., cadence), primarily because a larger inertial load means a slower crank dynamic response. Nonetheless, the reduction in cadence variability was somewhat attenuated by a large statistically significant increase in one-legged crank torque variability. We suggest, therefore, that muscle coordination during steady-state pedaling is largely unaffected, though less well regulated, when crank inertial load is increased.

A state-space analysis of mechanical energy generation, absorption, and transfer during pedaling.

Seated ergometer pedaling is a motor task ideal for studying basic mechanisms of human bipedal coordination because, in contrast to standing and walking, fewer degrees of freedom are being controlled and upright balance is not a factor. As a step toward understanding how individual muscles coordinate pedaling, we investigated how individual net muscle joint torques and non-muscular (e.g. centripetal, coriolis, and gravity) forces of the lower limbs generate, absorb, and transfer mechanical energy in order to propel the crank and recover the limb. This was accomplished using a mechanical power analysis derived entirely from the closed-form state-space dynamical equations of a two-legged pedaling model that accounted for both the limb segmental and crank load dynamics. Based on a pedaling simulation that reproduced experimental kinematic and kinetic trajectories, we found that the net ankle and hip extensor joint torques function 'synergistically' to deliver energy to the crank during the downstroke. The net hip extensor joint torque generates energy to the limb, while the net ankle extensor joint torque transfers this energy from the limb to the crank. In contrast, net knee extensor and flexor joint torques function 'independently' by generating energy to the crank through the top and bottom of the stroke, respectively. The net ankle joint torque transfers and the net knee joint torque generates energy to the crank by contributing to the driving component of the pedal reaction force. During the upstroke, net ankle extensor joint torque transfers energy from the crank to the limb to restore the potential energy of the limb. In both halves of the crank cycle, gravity forces augment the crank-limb energy transfer performed by the net ankle extensor joint torque.

A solidification procedure to facilitate kinematic analyses based on video system data.

When video-based motion analysis systems are used to measure segmental kinematics, the major source of error is the displacement of skin-fixed markers relative to the underlying skeletal structure. Such displacements cause the marker representation of the segment to deform, thereby decreasing the accuracy of subsequent three-dimensional kinematic calculations. We have developed a two-step solidification procedure to address this problem. First, the mean rigid shape is computed which best represents the time-varying marker configuration of each segment. Second, a least-squares minimization is used to replace the measured marker coordinates with those corresponding to the best-fit mean rigid shape. Rigid body theory can then be applied unambiguously to perform kinematic analyses. To evaluate this approach, we defined an unperturbed three-dimensional reference movement using kinematic data from the swing phase of gait. After perturbing the marker coordinates with artificial noise, the rotation matrix and translation vector (absolute and relative movement) between each pair of successive images were computed using (1) reference frames fixed directly to the perturbed marker coordinates, (2) a least-squares minimization procedure found in the literature, and (3) the proposed solidification procedure. The least-squares and solidification procedures produced extremely similar results which, relative to the direct calculation, reduced kinematic errors on average by 20-25% when the maximum distance between markers was small (e.g. < 15 cm). The solidification methodology therefore combines the numerical benefits of the least-squares method with the conceptual benefits of a rigid body method.