Motor unit synchronization of the vasti muscles in closed and open chain tasks

Objectives: To investigate motor unit synchronization between medial and lateral vasti and whether such synchronization differs in closed and open chain tasks. Design: Electromyographic recordings of single motor unit action potentials were made from the vastus medialis obliquus (VMO) and multiunit recordings from vastus lateralis during isometric contractions at 30 degrees of knee flexion in closed and open chain conditions. Setting: Laboratory. Participants: Five volunteers with no history of knee pain (age, 30 +/- 3.32y). Interventions: Not applicable. Main Outcome Measure: The degree of synchronization between motor unit firing was evaluated by identifying peaks in the electromyographic averages of the vastus lateralis, triggered from motor unit action potentials in the VMO, and the proportion of power in the power spectral density of the triggered average at the firing frequency of the reference motor unit. The proportion of cases in which there was significant power and peaks in the triggered averages was calculated. Results: The proportion of trials with peaks in the triggered averages of the vastus lateralis electromyographic activity was greater than 61.5% in all tasks, and there was a significantly greater proportion of cases where power in the spectrum was greater than 7.5% (P = .01) for the closed chain condition. Conclusions: There was a high proportion of synchronized motor units between the 2 muscles during isometric contractions, with evidence for greater common drive between the VMO and vastus lateralis in closed chain tasks. This has implications for rehabilitation because it suggests that closed chain tasks may generate better coordination between the vasti muscles.

On the chaotic rotation of a liquid-filled gyrostat via the Melnikov-Holmes-Marsden integral

The non-linear motions of a gyrostat with an axisymmetrical, fluid-filled cavity are investigated. The cavity is considered to be completely filled with an ideal incompressible liquid performing uniform rotational motion. Helmholtz theorem, Euler's angular momentum theorem and Poisson equations are used to develop the disturbed Hamiltonian equations of the motions of the liquid-filled gyrostat subjected to small perturbing moments. The equations are established in terms of a set of canonical variables comprised of Euler angles and the conjugate angular momenta in order to facilitate the application of the Melnikov-Holmes-Marsden (MHM) method to investigate homoclinic/heteroclinic transversal intersections. In such a way, a criterion for the onset of chaotic oscillations is formulated for liquid-filled gyrostats with ellipsoidal and torus-shaped cavities and the results are confirmed via numerical simulations. (c) 2006 Elsevier Ltd. All rights reserved.

Analysis of chaotic instabilities in a rotating body with internal energy dissipation

Melnikov's method is used to analytically predict the onset of chaotic instability in a rotating body with internal energy dissipation. The model has been found to exhibit chaotic instability when a harmonic disturbance torque is applied to the system for a range of forcing amplitude and frequency. Such a model may be considered to be representative of the dynamical behavior of a number of physical systems such as a spinning spacecraft. In spacecraft, disturbance torques may arise under malfunction of the control system, from an unbalanced rotor, from vibrations in appendages or from orbital variations. Chaotic instabilities arising from such disturbances could introduce uncertainties and irregularities into the motion of the multibody system and consequently could have disastrous effects on its intended operation. A comprehensive stability analysis is performed and regions of nonlinear behavior are identified. Subsequently, the closed form analytical solution for the unperturbed system is obtained in order to identify homoclinic orbits. Melnikov's method is then applied on the system once transformed into Hamiltonian form. The resulting analytical criterion for the onset of chaotic instability is obtained in terms of critical system parameters. The sufficient criterion is shown to be a useful predictor of the phenomenon via comparisons with numerical results. Finally, for the purposes of providing a complete, self-contained investigation of this fundamental system, the control of chaotic instability is demonstated using Lyapunov's method.

Prediction of chaotic instabilities in a dragline bucket swing

The occurrence of chaotic instabilities is investigated in the swing motion of a dragline bucket during operation cycles. A dragline is a large, powerful, rotating multibody system utilised in the mining industry for removal of overburden. A simplified representative model of the dragline is developed in the form of a fundamental non-linear rotating multibody system with energy dissipation. An analytical predictive criterion for the onset of chaotic instability is then obtained in terms of critical system parameters using Melnikov's method. The model is shown to exhibit chaotic instability due to a harmonic slew torque for a range of amplitudes and frequencies. These chaotic instabilities could introduce irregularities into the motion of the dragline system, rendering the system difficult to control by the operator and/or would have undesirable effects on dragline productivity and fatigue lifetime. The sufficient analytical criterion for the onset of chaotic instability is shown to be a useful predictor of the phenomenon under steady and unsteady slewing conditions via comparisons with numerical results. (c) 2005 Elsevier Ltd. All rights reserved.

Effect of knee joint angle on motor unit synchronization

Activity of the vasti has been argued to vary through knee range of movement due to changes in passive support of the patellofemoral joint and the relative contribution of these muscles to knee extension. Efficient function of the knee is dependent on optimal control of the patellofemoral joint, largely through coordinated activity of the medial and lateral quadriceps. Motor unit synchronization may provide a mechanism to coordinate the activity of vastus medialis (VMO) and vastus lateralis (VL), and may be more critical in positions of reduced passive support for the patellofemoral joint (i.e., full extension). Therefore, the aim of this study was to determine whether the degree of motor unit synchronization between the vasti muscles is dependent on joint angle. Electromyographic (EMG) recordings of single motor unit action potentials (MUAPs) were made from VMO and multiunit recordings from VL during isometric contractions of the quadriceps at 0 degrees, 30 degrees, and 60 degrees of knee flexion. The degree of synchronization between motor unit firing was evaluated by identification of peaks in the rectified EMG averages of VL, triggered from MUA-Ps in VMO. The proportion of cases in which there was a significant peak in the triggered averages was calculated. There was no significant difference in the degree of synchronization between the vasti at different knee angles (p = 0.57). These data suggest that this basic coordinative mechanism between the vasti muscles is controlled consistently throughout knee range of motion, and is not augmented at specific angles where the requirement for dynamic control of stability is increased. (D 2006 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.

On the chaotic instability of a nonsliding liquid-filled top with a small spheroidal base via Melnikov-Holmes-Marsden integrals

Chaotic orientations of a top containing a fluid filled cavity are investigated analytically and numerically under small perturbations. The top spins and rolls in nonsliding contact with a rough horizontal plane and the fluid in the ellipsoidal shaped cavity is considered to be ideal and describable by finite degrees of freedom. A Hamiltonian structure is established to facilitate the application of Melnikov-Holmes-Marsden (MHM) integrals. In particular, chaotic motion of the liquid-filled top is identified to be arisen from the transversal intersections between the stable and unstable manifolds of an approximated, disturbed flow of the liquid-filled top via the MHM integrals. The developed analytical criteria are crosschecked with numerical simulations via the 4th Runge-Kutta algorithms with adaptive time steps.

Noninertial observers in special relativity and clock synchronization debates

Selleri's arguments that a consideration of noninertial reference frames in the framework of special relativity identify absolute simultaneity as being Nature's choice of synchronization are considered. In the case of rectilinearly accelerating rockets, it is argued by considering two rockets which maintain a fixed proper separation rather than a fixed separation relative to the inertial frame in which they start from rest, that what seems the most natural choice for a simultaneity convention is problem-dependent and that Einstein's definition is the most natural (though still conventional) choice in this case. In addition, the supposed problems special relativity has with treating a rotating disk, namely how a pulse of light traveling around the circumference of the disk can have a local speed of light equal to c everywhere but a global speed not equal to c, and how coordinate transformations to the disk can give the Lorentz transformations in the limit of large disk radius but small angular velocity, are addressed. It is shown that the theory of Fermi frames solves both of these problems. It is also argued that the question of defining simultaneity relative to a uniformly rotating disk does riot need to be resolved in order to resolve Ehrenfest's paradox.

Wave chaotic behaviour generated by linear systems

It is shown that regimes with dynamical chaos are inherent not only to nonlinear system but they can be generated by initially linear systems and the requirements for chaotic dynamics and characteristics need further elaboration. Three simplest physical models are considered as examples. In the first, dynamic chaos in the interaction of three linear oscillators is investigated. Analogous process is shown in the second model of electromagnetic wave scattering in a double periodical inhomogeneous medium occupying half-space. The third model is a linear parametric problem for the electromagnetic field in homogeneous dielectric medium which permittivity is modulated in time. © 2008 Springer Science+Business Media, LLC.

Nonlinear dynamics of a periodically driven Duffing resonator coupled to a Van der Pol oscillator

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1?:?1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequency-amplitude modulation. The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator. The stability of the dynamic motions is also analyzed. The coupled system shows a hysteretic response pattern and symmetry-breaking facets. Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.

Investigation of chaotic mixing in laminar fluid systems by the use of computational fluid dynamics

This work presents significant development into chaotic mixing induced through periodic boundaries and twisting flows. Three-dimensional closed and throughput domains are shown to exhibit chaotic motion under both time periodic and time independent boundary motions, A property is developed originating from a signature of chaos, sensitive dependence to initial conditions, which successfully quantifies the degree of disorder withjn the mixing systems presented and enables comparisons of the disorder throughout ranges of operating parameters, This work omits physical experimental results but presents significant computational investigation into chaotic systems using commercial computational fluid dynamics techniques. Physical experiments with chaotic mixing systems are, by their very nature, difficult to extract information beyond the recognition that disorder does, does not of partially occurs. The initial aim of this work is to observe whether it is possible to accurately simulate previously published physical experimental results through using commercial CFD techniques. This is shown to be possible for simple two-dimensional systems with time periodic wall movements. From this, and subsequent macro and microscopic observations of flow regimes, a simple explanation is developed for how boundary operating parameters affect the system disorder. Consider the classic two-dimensional rectangular cavity with time periodic velocity of the upper and lower walls, causing two opposing streamline motions. The degree of disorder within the system is related to the magnitude of displacement of individual particles within these opposing streamlines. The rationale is then employed in this work to develop and investigate more complex three-dimensional mixing systems that exhibit throughputs and time independence and are therefore more realistic and a significant advance towards designing chaotic mixers for process industries. Domains inducing chaotic motion through twisting flows are also briefly considered. This work concludes by offering possible advancements to the property developed to quantify disorder and suggestions of domains and associated boundary conditions that are expected to produce chaotic mixing.