Precision of estimates of local stability of repetitive trunk movements

Abstract

Purpose Local dynamic stability of trunk movements quantified by means of the maximum Lyapunov exponent (k max ) can provide information on trunk motor control and might offer a measure of trunk control in low-back pain patients. It is unknown how many repetitions are necessary to obtain sufficiently precise estimates of k max and whether fatigue effects on k max can be avoided while increasing the number of repetitions. Method Ten healthy subjects performed 100 repetitions of trunk movements in flexion, of trunk rotation and of a task combining these movement directions. k max was calculated from thorax, pelvis and trunk (thorax relative to pelvis) kinematics. Data series were analyzed using a bootstrap procedure; ICC and coefficient of variation were used to quantify precision as a function of the number of cycles analyzed. ANOVA was used to compare movement tasks and to test for effects of time.Results Trunk local stability reached acceptable precision level after 30 repetitions. k max was higher (indicating lower stability) in flexion, compared to rotation and combined tasks. There was no time effect (fatigue). k max of trunk movement was lower and less variable than that of thorax and pelvis movements. Conclusions The data provided allow for an informed choice of the number of repetitions in assessing local dynamic stability of trunk movements, weighting the gain in precision against the increase in measurement effort. Within the 100 repetitions tested, fatigue did not affect results. We suggest that increased stability during asymmetric movement may be explained by higher co-activation of trunk muscles.

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

“…Subjects were asked to reach targets synchronously with a metronome in order to establish the movement pace of 20 and 40 cycles/min similar to Granata et al experiment (Granata and England, 2006). The slow and fast paced trials lasted 90 and 45 s in duration, respectively, in order to obtain a continuous movement pattern having 30 cycles per trial, and to minimize the effects of fatigue (Dupeyron et al, 2013). For the self-selected paced trials, the subjects were asked to perform at least 30 continuous movement cycles at their own pace.…”

The effect of different ranges of motion on local dynamic stability of the elbow during unloaded repetitive flexion–extension movements

“…The measure of LDS has been validated in terms of statistical precision within a session (Dupeyron et al, 2013) and reproducibility between sessions (Graham, Sheppard, Almosnino, & Stevenson, 2012). LDS of the center of pressure during standing has been shown to be reduced in stroke patients, and improve with rehabilitation (Roerdink et al, 2006), and similarly LDS correlates with a risk of falling during gait (Su & Dingwell, 2007;Toebes, Hoozemans, Furrer, Dekker, & van Dieën, 2012;Bruijn, Meijer, Beek, & van Dieën, 2013;Reynard, Vuadens, Deriaz, & Terrier, 2014;) and improves with rehabilitation in multiple sclerosis patients who are at a higher risk of falling (Hilfiker et al, 2013).…”

“…This calculation gives an average maximal finite time Lyapunov (local divergence) exponent (k max ) which represents the logarithmic divergence of trajectories over time (Bruijn et al, 2009b;Dupeyron et al, 2013;Rosenstein et al, 1993;Strogatz, 2000). A negative exponent characterizes an average convergence of the system toward the intended trajectory (stable), while a positive exponent represents average divergence, and therefore instability (Bruijn et al, 2009b;Dupeyron et al, 2013;Granata & England, 2006;Rosenstein et al, 1993).…”

“…This variability about an intended trajectory can be measured within kinematic data using a Lyapunov analysis technique to give information on the local dynamic stability (LDS) of the system (Bruijn, van Dieën, Meijer, & Beek, 2009b;Dupeyron, Rispens, Demattei, & van Dieën, 2013;Granata & England, 2006;Rosenstein, Collins, & De Luca, 1993). This calculation gives an average maximal finite time Lyapunov (local divergence) exponent (k max ) which represents the logarithmic divergence of trajectories over time (Bruijn et al, 2009b;Dupeyron et al, 2013;Rosenstein et al, 1993;Strogatz, 2000). A negative exponent characterizes an average convergence of the system toward the intended trajectory (stable), while a positive exponent represents average divergence, and therefore instability (Bruijn et al, 2009b;Dupeyron et al, 2013;Granata & England, 2006;Rosenstein et al, 1993).…”

Quantifying Muscle Fatigue of the Low Back during Repetitive Load Lifting Using Lyapunov Analysis

“…These disorders have been hypothesized to occur when the equilibrium of the trunk forces is disturbed by internal (e.g., breathing) or external (e.g., being pushed) perturbations [7] as well as and more commonly by the transition from the neuromuscular non-fatigued to the fatigue stage leading to a change of the spine movement trajectories. Particularly, excessive small perturbations at the spine can lead to uncontrolled intervertebral movement with increased risk of injury [8]. Although a consensus of biomechanical and clinical definition of spinal stability is lacking in the literature, spinal stability is the basic requirement to protect the nervous system's structure and prevent the early mechanical deterioration of spinal components.…”