Achilles tendon (AT) injuries are common in runners. The AT withstands high magnitudes of stress during running which may contribute to injury. Our purpose was to examine the effects of foot strike pattern and step frequency on AT stress and strain during running utilizing muscle forces based on a musculoskeletal model and subject-specific ultrasound-derived AT cross-sectional area. Nineteen female runners performed running trials under 6 conditions, including rearfoot strike and forefoot strike patterns at their preferred cadence, +5%, and -5% preferred cadence. Rearfoot strike patterns had less peak AT stress (P < .001), strain (P < .001), and strain rate (P < .001) compared with the forefoot strike pattern. A reduction in peak AT stress and strain were exhibited with a +5% preferred step frequency relative to the preferred condition using a rearfoot (P < .001) and forefoot (P=.005) strike pattern. Strain rate was not different (P > .05) between step frequencies within each foot strike condition. Our results suggest that a rearfoot pattern may reduce AT stress, strain, and strain rate. Increases in step frequency of 5% above preferred frequency, regardless of foot strike pattern, may also lower peak AT stress and strain.
Tendon stress may be one of the important risk factors for running-related tendon injury. Several methods have been used to estimate Achilles tendon (AT) loading during a human performance such as inverse dynamics (ID) and inverse dynamics-based static optimisation (IDSO). Our purpose was to examine differences between ID and IDSO estimates of AT loading during running. Kinematic data were captured simultaneously with kinetic data. Imaging of the AT cross-sectional area was performed with ultrasound for 17 healthy runners (height: 170.2 ± 6.2 cm, mass: 63.9 ± 11.0 kg, age: 21.8 ± 1.4 years). AT stress, strain, and force were estimated from both ID and IDSO approaches. The two methods resulted in minimal differences (3.6-4.7%) in estimated peak AT stress, strain, and force (P = 0.051-0.054); however, IDSO estimates were greater (32.7-36.8%) during early-stance phase of running (P = 0.000-0.008). This difference in AT load during early-stance may be due to the inability of the ID to account muscle coactivation. The similarity between the peak AT loading for ID and IDSO methods revealed that the advantage of IDSO used to estimate muscle forces had little effect on the ankle plantar flexor peak forces during running. Therefore, the use of IDSO with a higher computational cost compared with ID may not be necessary for estimating AT stress during running.
Noncontact mechanisms, such as landing from a jump, account for over 70% of all anterior cruciate ligament injuries. Increased knee and hip flexion during landing has been suggested to decrease anterior cruciate ligament tension; however, current literature utilizing knee modeling approaches has not investigated this. Our purpose was to compare estimated anterior cruciate ligament tension in females between a typical and flexed knee and hip drop landing performance. A sagittal plane knee model based on kinematic, kinetic, electromyography, and cadaveric data was used to estimate forces on the anterior cruciate ligament during a typical and flexed drop landing for 23 females. Model estimated peak anterior cruciate ligament tension decreased by 10% during the flexed landing performance (p=0.008). This was accounted for by an increase in hamstring shear force by 6% of body weight and a reduction in patellar tendon shear force and femur-tibia shear force by 3% of body weight each. Results suggest that simple verbal cues for increased knee and hip flexion during landing may be effective in reducing anterior cruciate ligament tension and potential risk of injury during landing.
2D kinematics can predict 3D frontal-plane hip and knee position at IC during a single-leg landing but predict 3D frontal-plane knee excursion with far less accuracy.
The current paradigm for understanding galaxy formation in the universe depends on the existence of self-gravitating collisionless dark matter. Modeling such dark matter systems has been a major focus of astrophysicists, with much of that effort directed at computational techniques. Not surprisingly, a comprehensive understanding of the evolution of these self-gravitating systems still eludes us, since it involves the collective nonlinear dynamics of many-particle systems interacting via long-range forces described by the Vlasov equation. As a step towards developing a clearer picture of collisionless self-gravitating relaxation, we analyze the linearized dynamics of isolated one-dimensional systems near thermal equilibrium by expanding their phase space distribution functions f (x, v) in terms of Hermite functions in the velocity variable, and Legendre functions involving the position variable. This approach produces a picture of phase-space evolution in terms of expansion coefficients, rather than spatial and velocity variables. We obtain equations of motion for the expansion coefficients for both test-particle distributions and self-gravitating linear perturbations of thermal equilibrium. N -body simulations of perturbed equilibria are performed and found to be in excellent agreement with the expansion coefficient approach over a time duration that depends on the size of the expansion series used.
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