Maximum Finite-time Lyapunov Exponents Research Articles

Sensitivity and robustness of Lagrangian coherent structures in coastal water systems

In coastal water systems, horizontal chaotic dispersion plays a significant role in the distribution and fate of pollutants. Lagrangian Coherent Structures (LCSs) provide useful tools to study the problem of the transport of pollutants and have only recently been applied to coastal waters. While the fundamentals of the LCS approach using idealised analytical flow fields are well established in the literature, there are limited studies on their practical implementations in coastal waters where effects of boundaries and bathymetry frequently become significant. Due to their complex bathymetry and boundaries, unstructured grid systems are commonly used in modelling of coastal waters. For convenient derivation of LCS diagnostics, structured grids are commonly used. Here we examine the effect of mesh resolution, interpolation schemes and additive random noise on the LCS diagnostics in relation to coastal waters. Two kinematic model flows, the double gyre and the meandering jet, as well as validated outputs of a hydrodynamic model of Moreton Bay, Australia, on unstructured grids are used. The results show that LCSs are quite robust to the errors from interpolation schemes used in the data conversion from unstructured to structured grid. Attributed to the divergence in the underlying flow field, the results show that random errors in the order of 1–10% cause a breakdown in the continuity of ridges of maximum finite-time Lyapunov exponents and closed orbit elliptic LCSs. The result has significant implications on the suitability of applying LCS formulations based on a deterministic flow field to diffusive coastal waters.

The validation of new phase-dependent gait stability measures: a modelling approach.

Identification of individuals at risk of falling is important when designing fall prevention methods. Current measures that estimate gait stability and robustness appear limited in predicting falls in older adults. Inspired by recent findings on changes in phase-dependent local stability within a gait cycle, we devised several phase-dependent stability measures and tested for their usefulness to predict gait robustness in compass walker models. These measures are closely related to the often-employed maximum finite-time Lyapunov exponent and maximum Floquet multiplier that both assess a system's response to infinitesimal perturbations. As such, they entail linearizing the system, but this is realized in a rotating hypersurface orthogonal to the period-one solution followed by estimating the trajectory-normal divergence rate of the swing phases and the foot strikes. We correlated the measures with gait robustness, i.e. the largest perturbation a walker can handle, in two compass walker models with either point or circular feet to estimate their prediction accuracy. To also test for the dependence of the measures under state space transform, we represented the point feet walker in both Euler–Lagrange and Hamiltonian canonical form. Our simulations revealed that for most of the measures their correlation with gait robustness differs between models and between different state space forms. In particular, the latter may jeopardize many stability measures' predictive capacity for gait robustness. The only exception that consistently displayed strong correlations is the divergence of foot strike. Our results admit challenges of using phase-dependent stability measures as objective means to estimate the risk of falling.

Trunk Dynamic Stability Assessment for Individuals With and Without Nonspecific Low Back Pain During Repetitive Movement.

This study aimed to employ nonlinear dynamic approaches to assess trunk dynamic stability with speed, symmetry, and load during repetitive flexion-extension (FE) movements for individuals with and without nonspecific low back pain (NSLBP). Repetitive trunk FE movement is a typical work-related LBP risk factor contingent on speed, symmetry, and load. Improper settings/adjustments of these control parameters could undermine the dynamic stability of the trunk, hence leading to low back injuries. The underlying stability mechanisms and associated control impairments during such dynamic movements remain elusive. Thirty-eight male volunteers (19 healthy, 19 NSLBP) enrolled in the current study. All participants performed repetitive trunk FE movements at high/low speeds, in symmetric/asymmetric directions, with/without a wearable loaded vest. Trunk instantaneous rotation angle was computed for each trial to be assessed in terms of local and orbital stability, using maximum finite-time Lyapunov exponents (LyEs) and Floquet multipliers (FMs), respectively. Both groups demonstrated equivalent competency in terms of trunk control and stability, suggesting functional adaptation strategies may be used by the NSLBP group. Wearing the loaded vest magnified the effects of trunk control impairment for the NSLBP group. The combined presence of high-speed and symmetrical FE movements was associated with least trunk local stability. Nonlinear dynamic techniques, particularly LyE, are potentially effective for assessing trunk dynamic stability dysfunction for individuals with NSLBP during various activities. This work can be applied toward the development of quantitative personalized spinal evaluation tools with a wide range of potential occupational and clinical applications.

Concurrent validity of a wearable IMU for objective assessments of functional movement quality and control of the lumbar spine

Inertial measurement units (IMUs) are being recognized in clinical and rehabilitation settings for their ability to assess movement-related disorders of the spine for better guidance of treatment-planning and tracking of recovery. This study evaluated the Mbientlab MetaMotionR IMUs, relative to Vicon motion capture equipment in measuring local dynamic stability of the spine (quantified using maximum finite-time Lyapunov exponent; λmax), lumbopelvic coordination (quantified using mean absolute relative phase; MARP), and intersegmental motor variability (quantified using deviation phase; DP) of lumbopelvic segments in 10 participants during 35 cycles of repetitive spine flexion–extension (FE). Intraclass correlations were strong between systems when using both the FE angle time-series and the sum of squares (SS) time-series to measure local dynamic stability (0.807 ≤ICC2,1λmax,FE ≤ 0.919; 0.738 ≤ ICC2,1λmax,SS ≤ 0.868), sagittal-plane lumbopelvic coordination (0.961 ≤ICC2,1MARP ≤ 0.963), and sagittal-plane lumbopelvic variability (0.961 ≤ICC2,1DP ≤ 0.963). It was concluded that the MetaMotionR IMUs can be reliably used for measuring features associated with spine movement quality and motor control during a repetitive FE task. Future work will assess the reliability of sensor placement, performance during multi-directional movements, and ability to discern clinical and healthy populations based on assessment of movement quality and control.

A comparison of methods to quantify control of the spine

Low back pain (LBP) affects many individuals worldwide. The established association between LBP and spine motor control has led to the development of many control assessment techniques. To understand spine control and LBP, it is essential to know the relationship between assessment techniques. Systems identification (SI) and local dynamic stability (LDS) are two methods of quantifying spine control. SI provides a detailed description of control but uses linearity assumptions, whereas LDS provides a “black box” non-linear assessment during dynamic movements. Therefore, the purpose of this project was to compare control outcomes of SI and LDS. 15 participants completed two tasks (SI and LDS) in a random order. For the SI task, participants were seated and ventrally perturbed at the 10th thoracic vertebrae. They were instructed to resist the perturbations (resist condition) or to relax the trunk (relax condition). Admittance was computed, and a neuromuscular control model quantified lumbar stiffness, damping and muscle spindle feedback gains. For the LDS task, participants completed three repetitive movement blocks consisting of flexion/extension, axial rotation, and complex movements. In each block, the maximum finite-time Lyapunov exponent (λmax) was estimated. A stepwise linear regression determined that λmax during the rotation task was best predicted by SI outcomes in the relax condition (adjusted R2 = 0.83). Many conditions demonstrated no relationship between λmax and SI outcomes. These findings outline the importance of a consistent framework for the assessment of spine control. This could clarify research comparisons and the understanding of the cause/effect role of LBP on spine control.

Pain catastrophizing moderates changes in spinal control in response to noxiously induced low back pain

It is generally accepted that spine control and stability are relevant for the prevention and rehabilitation of low back pain (LBP). However, there are conflicting results in the literature in regards to how these variables are modified in the presence of LBP. The aims of the present work were twofold: (1) to use noxious stimulation to induce LBP in healthy individuals to assess the direct effects of pain on control (quantified by the time-dependent behavior of kinematic variance), and (2) to assess whether the relationship between pain and control is moderated by psychological features (i.e. pain catastrophizing (PC) and kinesiophobia). Participants completed three conditions (baseline, pain, recovery) during a task involving completion of 35 cycles of a repetitive unloaded spine flexion/extension movement. The neuromuscular control of spine movements was assessed during each condition using maximum finite-time Lyapunov exponents (λmax). Nociceptive stimulus involved injection of hypertonic saline into the interspinous ligament, eliciting pain that was greater than baseline and recovery (p<0.001). Although there was no overall main effect of the nociceptive stimulation (i.e. pain) on λmax when the whole group was included in the statistical model (p=0.564), when data were considered separately for those with high and low PC, two distinct and well established responses to the pain were observed. Specifically, those with high PC tightened their control (i.e. stabilized), whereas those with low PC loosened their control (i.e. destabilized). This study provides evidence that individuals’ beliefs and attitudes towards pain are related to individual-specific motor behaviors, and suggests that future research studying spine control/stability and LBP should account for these variables.

On the use of a Euclidean norm function for the estimation of local dynamic stability from 3D kinematics using time-delayed Lyapunov analyses

Several different state-space reconstruction methods have been employed to assess the local dynamic stability (LDS) of a 3D kinematic system. One common method is to use a Euclidean norm (N) transformation of three orthogonal x, y, and z time-series’ followed by the calculation of the maximum finite-time Lyapunov exponent (λmax) from the resultant N waveform (using a time-delayed state space reconstruction technique). By essentially acting as a weighted average, N has been suggested to account for simultaneous expansion and contraction along separate degrees of freedom within a 3D system (e.g. the coupling of dynamic movements between orthogonal planes). However, when estimating LDS using N, non-linear transformations inherent within the calculation of N should be accounted for. Results demonstrate that the use of N on 3D time-series data with arbitrary magnitudes of relative bias and zero-crossings cause the introduction of error in estimates of λmax obtained through N. To develop a standard for the analysis of 3D dynamic kinematic waveforms, we suggest that all dimensions of a 3D signal be independently shifted to avoid the incidence of zero-crossings prior to the calculation of N and subsequent estimation of LDS through the use of λmax.

The acute effects of targeted abdominal muscle activation training on spine stability and neuromuscular control.

BackgroundTargeted activation of the transversus abdominis (TrA) muscle through the abdominal drawing-in maneuver (ADIM) is a frequently prescribed exercise for the prevention and rehabilitation of low back pain. However, there is still debate over the role the ADIM plays in maintaining a stable spine during movement. Thus, a single cohort pre/post-intervention protocol was used to examine whether 5 min of ADIM training prior to a dynamic movement task alters dynamic spine stability and control.MethodsThirteen healthy participants performed a repetitive spine flexion task twice, once before and once after they received biofeedback training on how to correctly perform the ADIM in standing. Abdominal and back muscle activation (indwelling and surface electromyography, EMG) and 3D kinematic data were recorded during all trials. EMG activation (percent maximum) and local dynamic stability of spine movement [maximum finite-time Lyapunov exponent (λmax)] were compared before and after the training using Friedman’s rank test and repeated-measures ANOVA, respectively. To assess the moderating effects of absolute changes in EMG (∆EMG) of each muscle after training on changes in stability, the ∆EMG (peak and mean) were added to the ANOVA as separate covariates (ANCOVA).ResultsFollowing ADIM training, there were greater peak and mean levels of activation in all tested abdominal muscles, including TrA, (p < 0.05), but not in the back muscles. The ANOVA showed no significant change in λmax following training (p = 0.633). However, after considering the moderating effects of the ∆EMG seen in each muscle with training, it was found that only changes in TrA EMG significantly influenced stability. The ANCOVA revealed a significant main effect of training on stability as well as a significant interaction effect between training and ∆EMG recorded from TrA (p < 0.05); those with larger increases in TrA activation demonstrated larger improvements in stability.ConclusionAs a group, 5 min of ADIM training did not change spine stability during dynamic movement. However, those who were most successful in improving TrA activation with a 5-min ADIM training session showed the greatest improvements in local dynamic spine stability after training. As such, dynamic spine stability in some individuals may benefit from ADIM training.Electronic supplementary materialThe online version of this article (doi:10.1186/s12984-016-0126-9) contains supplementary material, which is available to authorized users.

The effects of movement speed on kinematic variability and dynamic stability of the trunk in healthy individuals and low back pain patients

BackgroundComparison of the kinematic variability and dynamic stability of the trunk between healthy and low back pain patient groups can contribute to gaining valuable information about the movement patterns and neuromotor strategies involved in various movement tasks. MethodsFourteen chronic low back pain patients with mild symptoms and twelve healthy male volunteers performed repeated trunk flexion–extension movements in the sagittal plane at three different speeds: 20cycles/min, self-selected, and 40cycles/min. Mean standard deviations, coefficient of variation and variance ratio as variability measures; maximum finite-time Lyapunov exponents and maximum Floquet multipliers as stability measures were computed from trunk kinematics. FindingsHigher speed significantly reduced the kinematic variability, while it increased short-term Lyapunov exponents. Long-term Lyapunov exponents were higher at self-selected speed and lower in low back pain patients as compared to control volunteers. Floquet multipliers were larger at self-selected speed and during higher pace trunk movements. InterpretationOur findings suggest that slower pace flexion–extension trunk movements are associated with more motor variation as well as local and orbital stability, implying less potential risk of injury for the trunk. Individuals with and without low back pain consistently recruited a closed-loop control strategy towards achieving trunk stability. Chronic low back pain patients exhibited more stable trunk movements over long-term periods, indicating probable temporary pain relief functional adaption strategies. These results may be used towards the development of more effective personalized rehabilitation strategies and quantitative spinal analysis tools for low back pain detection, diagnosis and treatment, as well as improvement of workspace and occupational settings.

Sensor positioning and experimental constraints influence estimates of local dynamic stability during repetitive spine movements

Application of non-linear dynamics analyses to study human movement has increased recently, which necessitates an understanding of how dependent measures may be influenced by experimental design and setup. Quantifying local dynamic stability for a multi-articulated structure such as the spine presents the possibility for estimates to be influenced by positioning of kinematic sensors used to measure spine angular kinematics. Oftentimes researchers will also choose to constrain the spine׳s movement by physically restraining the pelvis and/or using targets to control movement endpoints. Ten healthy participants were recruited, and asked to perform separate trials of 35 consecutive cycles of spine flexion under both constrained and unconstrained conditions. Electromagnetic sensors that measure three-dimensional angular orientations were positioned over the pelvis and the spinous processes of L3, L1, and T11. Using the pelvic sensor as a reference, each sensor location on the spine was used to obtain a different representation of the three-dimensional spine angular kinematics. Local dynamic stability of each kinematic time-series was determined by calculating the maximum finite-time Lyapunov exponent (λmax). Estimates for λmax were significantly lower (i.e. dynamically more stable) for spine kinematic data obtained from the L3 sensor than those obtained from kinematic data using either the L1 or T11 sensors. Likewise, λmax was lower when the movement was constrained. These results emphasize the importance of proper placement of instrumentation for quantifying local dynamic stability of spine kinematics and are especially relevant for repeated measures designs where data are obtained from the same individual on multiple days.

A dynamical systems analysis of assisted and unassisted anterior and posterior hand-held load carriage

Load carriage is recognised as a primary occupational factor leading to slip and fall injuries, and therefore assessing balance maintenance during such tasks is critical in assessing injury risk. Ten males completed 55 strides under five carriage conditions: (1) unassisted anterior, (2) unassisted posterior, (3) assisted anterior, (4) assisted posterior and (5) unloaded gait (UG). Kinematic data were recorded from markers affixed to landmarks on the right side of each participant, in order to calculate segment angles for the foot, shank, thigh and pelvis. Continuous relative phase (CRP) variability was calculated for each segment pair and local dynamic stability was calculated for each segment in all three movement planes. In general, irrespective of the assistive device or movement plane, anterior load carriage was most stable (lower CRP variability and maximum finite-time Lyapunov exponents). Moreover, load carriage was less dynamically stable than UG, displaying the importance of objectively investigating safe load carriage practices.

Movement Stability Analysis of Surface Electromyography-Based Elbow Power Assistance

The use of power assistive devices that use surface electromyography (SEMG) signals may be limited by the noisy nature of SEMG signals. The aim of this study was to investigate the variation in human movement stability while the amount of SEMG-based assistive power was changed. A robotic device provided a torque that was proportional to the torque estimated by SEMG for assisting human movements, and 12 volunteers participated in the elbow flexion experiments. The maximum finite-time Lyapunov exponent (MFTLE), the average logarithmic rate of the divergence of neighboring trajectories, and the variability of the kinematic data were used to quantify the stability of the assisted elbow movements. The stability provided by the MFTLE decreased as the amount of assistive torque increased with respect to the amount of human torque. The kinematic variability increased with the increase in assistive torque. Therefore, by ensuring that the amount of SEMG-based assistive torque is less than the amount of human torque, the assistance may provide relatively natural movements. This study is the first to quantify movement stability as SEMG-based assistive power is applied. This study can provide a foundation for determining the appropriate amount of SEMG-based assistive power.

Walking at the preferred stride frequency maximizes local dynamic stability of knee motion

Healthy humans display a preference for walking at a stride frequency dependent on the inertial properties of their legs. Walking at preferred stride frequency (PSF) is predicted to maximize local dynamic stability, whereby sensitivity to intrinsic perturbations arising from natural variability inherent in biological motion is minimized. Previous studies testing this prediction have employed different variability measures, but none have directly quantified local dynamic stability by computing maximum finite-time Lyapunov exponent (λMax), which quantifies the rate of divergence of nearby trajectories in state space. Here, ten healthy adults walked 45m overground while sagittal motion of both knees was recorded via electrogoniometers. An auditory metronome prescribed 7 different frequencies relative to each individual's PSF (PSF; ±5, ±10, ±15strides/min). Stride frequencies were performed under both freely adopted speed (FS) and controlled speed (CS: set at the speed of PSF trials) conditions. Local dynamic stability was maximal (λMax was minimal) at the PSF, becoming less stable for higher and lower stride frequencies. This occurred under both FS and CS conditions, although controlling speed further reduced local dynamic stability at non-preferred stride frequencies. In contrast, measures of variability revealed effects of stride frequency and speed conditions that were distinct from λMax. In particular, movement regularity computed by approximate entropy (ApEn) increased for slower walking speeds, appearing to depend on speed rather than stride frequency. The cadence freely adopted by humans has the benefit of maximizing local dynamic stability, which can be interpreted as humans tuning to their resonant frequency of walking.

Viscoelastic creep induced by repetitive spine flexion and its relationship to dynamic spine stability

Repetitive trunk flexion elicits passive tissue creep, which has been hypothesized to compromise spine stability. The current investigation determined if increased spine flexion angle at the onset of flexion relaxation (FR) in the lumbar extensor musculature was associated with altered dynamic stability of spine kinematics. Twelve male participants performed 125 consecutive cycles of full forward trunk flexion. Spine kinematics and lumbar erector spinae (LES) electromyographic (EMG) activity were obtained throughout the repetitive trunk flexion trial. Dynamic stability was evaluated with maximum finite-time Lyapunov exponents over five sequential blocks of 25cycles. Spine flexion angle at FR onset, and peak LES EMG activity were determined at baseline and every 25th cycle. Spine flexion angle at FR increased on average by 1.7° after baseline with significant increases of 1.7° and 2.4° at the 50th and 100th cycles. Maximum finite-time Lyapunov exponents demonstrated a transient, non-statistically significant, increase between cycles 26 and 50 followed by a recovery to baseline over the remainder of the repetitive trunk flexion cycles. Recovery of dynamic stability may be the consequence of increased active spine stiffness demonstrated by the non-significant increase in peak LES EMG that occurred as the repetitive trunk flexion progressed.

Phase-dependent changes in local dynamic stability of human gait

Several methods derived from nonlinear time series analysis have been suggested to quantify stability in human gait kinematics. One of these methods is the definition of the maximum finite time Lyapunov exponent (λ) that quantifies how the system responds to infinitesimal perturbations. However, there are fundamental limitations to the conventional definition of λ for gait kinematics. First, exponential increase in initial perturbations cannot be assumed since real-life perturbations of gait kinematics are finite sized. Second, the transitions between single and double support phase within each stride cycle define two distinct dynamical regimes that may not be captured by a single λ. The present article presents a new method to quantify intra-stride changes λ(t) in local dynamical stability and employs the method to 3D lower extremity gait kinematics in 10 healthy adults walking on a treadmill at 3 different speeds. All participants showed an intra-stride change in λ(t) in the transition between single and double support phase. The intra-stride change reflected an both a increase and decrease in λ(t) at heel strike and toe off, respectively, with increased gait speed. Furthermore, a close relationship was found between the intra-stride change in standard deviation of foot velocity in the anterior–posterior direction and the intra-stride change of the initial perturbations. The present results indicate that local dynamical stability has gait phase-dependent changes that are not identified by conventional computation of a single λ.

IDENTIFYING NONSTATIONARY JAMMING SIGNAL VIA LAGRANGIAN COHERENT STRUCTURES

The anti-jamming scheme is an important issue in the modern communication system, where the spread-spectrum signals are usually adopted. In a complex electromagnetic environment where the jamming sources may be close to the communication devices, a large jamming-to-signal ratio is possible. How to achieve the desired accuracy for the communication system in the presence of strong jamming is a crucial and outstanding problem. To solve this problem, we propose a method to identify the desired signal and the nonstationary jamming signal via Lagrangian Coherent Structures (LCS), and a new algorithm for calculating the maximum Finite-Time Lyapunov Exponent (FTLE) is presented. As opposed to the current approach which requires a vector field in the state space at each instant time, the proposed algorithm is performed on the vector fields which are respectively built on the desired signal and the nonstationary jamming signal via Hilbert Transform. A simulation test is conducted on a binary offset carrier (BOC) modulated signal and a chirp signal. The results indicate that the proposed method can provide new features to efficiently identify the nonstationary jamming signal.

Maximum Lyapunov exponents as predictors of global gait stability: A modelling approach

To examine the stability of human walking, methods such as local dynamic stability have been adopted from dynamical systems theory. Local dynamic stability is calculated by estimating maximal finite time Lyapunov exponents (λS and λL), which quantify how a system responds continuously to very small (i.e. “local”) perturbations. However, it is unknown if, and to what extent, these measures are correlated to global stability, defined operationally as the probability of falling.We studied whether changes in probability of falling of a simple model of human walking (a so-called dynamic walker) could be predicted from maximum finite time Lyapunov exponents. We used an extended version of the simplest walking model with arced feet and a hip spring. This allowed us to change the probability of falling of the model by changing either the foot radius, the slope at which the model walks, the stiffness of the hip spring, or a combination of these factors.Results showed that λS correlated fairly well with global stability, although this relationship was dependent upon differences in the distance between initial nearest neighbours on the divergence curve. A measure independent of such changes (the log(distance between initially nearest neighbours after 50 samples)) correlated better with global stability, and, more importantly, showed a more consistent relationship across conditions. In contrast, λL showed either weak correlations, or correlations opposite to expected, thus casting doubt on the use of this measure as a predictor of global gait stability.Our findings support the use of λS, but not of λL, as measure of human gait stability.

Local dynamic stability of trunk movements during the repetitive lifting of loads

The local dynamic stability of trunk movements was assessed during repetitive lifting using nonlinear Lyapunov analyses. The goal was to assess how varying the load-in-hands affects the neuromuscular control of lumbar spinal stability. Thirty healthy participants (15M, 15F) performed repetitive lifting at 10 cycles per minute for three minutes under two load conditions: zero load and 10% of each participant’s maximum back strength. Short- and long-term maximum finite-time Lyapunov exponents (λmax−s and λmax−l), describing responses to infinitesimally small perturbations, were calculated from the measured trunk kinematics to estimate the local dynamic stability of the system. Kinematic variability was also assessed using mean standard deviations (MeanSD) across cycles. The results of a mixed-design repeated-measures ANOVA showed that increasing the load lifted significantly reduced λmax−s (μ0%−LOAD=0.379, μ10%−LOAD=0.335, p<.001), but not λmax−l (μ0%−LOAD=0.46E−03, μ10%−LOAD=2.41E−03, p=.055) or MeanSD (μ0%−LOAD=2.57, μ10%−LOAD=2.89, p=.164). There were no between–subject effects of sex, or significant interactions (α<.05). The present findings indicated improved dynamic spinal stability when lifting the heavier load; meaning that as muscular and moment demands increased, so too did participants’ abilities to respond to local perturbations. These results support the notion of greater spinal instability during movement with low loads due to decreased muscular demand and trunk stiffness, and should aid in understanding how lifting various loads contributes to occupational low back pain.

Local dynamic stability of the lifting kinematic chain

While a stable trunk and centre of mass (CoM) trajectory are required during lifting, it is unclear how stability is controlled. Thirty healthy participants (15M, 15F) performed repetitive, symmetric lifting at 10 cycles per minute for 3 min with a load-in-hands equivalent to 10% of their maximum back strength. Short- and long-term maximum finite-time Lyapunov exponents ( λ max-s and λ max-l), describing responses to small (local) perturbations, estimated the local dynamic stability of the foot, shank, thigh, pelvis, lower back, and upper back segments. Instability ( λ max-s) significantly increased when moving up the kinematic chain ( p < 0.001). Therefore, to maintain trunk equilibrium and accurately regulate CoM trajectory during lifting, stability of the distal (fixed) lower limb segments is prioritized. This is contrary to previous results observed during gait, indicating that trunk control via kinematic chain stability is accomplished differently for walking and lifting.

Does the personal lift-assist device affect the local dynamic stability of the spine during lifting?

The personal lift-assist device (PLAD) is an on-body ergonomic aid that reduces low back physical demands through the restorative moment of an external spring element, which possesses a mechanical advantage over the erector spinae. Although the PLAD has proven effective at reducing low back muscular demand, spinal moments, and localized muscular fatigue during laboratory and industrial tasks, the effects of the device on the neuromuscular control of spinal stability during lifting have yet to be assessed. Thirty healthy subjects (15M, 15F) performed repetitive lifting for three minutes, at a rate of 10 lifts per minute, with and without the PLAD. Maximum finite-time Lyapunov exponents, representing short-term ( λ max-s) and long-term ( λ max-l) divergence were calculated from the measured trunk kinematics to estimate the local dynamic stability of the lumbar spine. Using a mixed-design repeated-measures ANOVA, it was determined that wearing the PLAD did not significantly change λ max-s ( μ NP=0.335, μ P=0.321, p=0.225), but did significantly reduce λ max-l ( μ NP=0.0024, μ P=−0.0011, p=0.014, η 2=0.197). There were no between-subject effects of sex, or significant interactions ( p>0.720). The present results indicated that λ max-s was not statistically different between the device conditions, but that the PLAD significantly reduced λ max-l to a negative (stable) value. This shows that subjects’ neuromuscular systems were able to respond to local perturbations more effectively when wearing the device, reflecting a more stable control of spinal movements. These findings are important when recommending the PLAD for long-term industrial or clinical use.