Leslie Decker

Human movement variability, nonlinear dynamics, and pathology: Is there a connection?

Fields studying movement generation, including robotics, psychology, cognitive science, and neuroscience utilize concepts and tools related to the pervasiveness of variability in biological systems. The concept of variability and the measures for nonlinear dynamics used to evaluate this concept open new vistas for research in movement dysfunction of many types. This review describes innovations in the exploration of variability and their potential importance in understanding human movement. Far from being a source of error, evidence supports the presence of an optimal state of variability for healthy and functional movement. This variability has a particular organization and is characterized by a chaotic structure. Deviations from this state can lead to biological systems that are either overly rigid and robotic or noisy and unstable. Both situations result in systems that are less adaptable to perturbations, such as those associated with unhealthy pathological states or absence of skillfulness.

Sensitivity of the Wolf’s and Rosenstein’s Algorithms to Evaluate Local Dynamic Stability from Small Gait Data Sets

The Wolf’s (W-algorithm) and Rosenstein’s (R-algorithm) algorithms have been used to quantify local dynamic stability (largest Lyapunov exponent, λ1) in gait, with prevalence of the latter one that is considered more suitable for small data sets. However, such a claim has never been investigated. To address it, the λ1 of the Lorenz attractor was estimated using small data sets and varied delays and embedding dimensions. Overall, the λ1 estimates from the R-algorithm got closer to the theoretical exponent than those from the W-algorithm. The W-algorithm also overestimated λ1 while the R-algorithm underestimated it, overlooking the attractor convergences and divergences, respectively. Local dynamic stability was then examined from 1-, 2- and 3-min long gait time series of younger (YA) and older adults (OA). The OA were found more locally unstable than the YA regardless of time series length with the W-algorithm but only for the longest time series with the R-algorithm. The lack of sensitivity to capture age-related decline in local dynamic stability from shorter time series is proposed to result from a drawback of the R-algorithm that overlooks the expansion of the attractor trajectories. The W-algorithm is advocated for use when examining local dynamic stability with small gait data sets.

New insights into anterior cruciate ligament deficiency and reconstruction through the assessment of knee kinematic variability in terms of nonlinear dynamics

PurposeInjuries to the anterior cruciate ligament (ACL) occur frequently, particularly in young adult athletes, and represent the majority of the lesions of knee ligaments. Recent investigations suggest that the assessment of kinematic variability using measures of nonlinear dynamics can provide with important insights with respect to physiological and pathological states. The purpose of the present article was to critically review and synthesize the literature addressing ACL deficiency and reconstruction from a nonlinear dynamics standpoint.MethodsA literature search was carried out in the main medical databases for studies published between 1990 and 2010.ResultsSeven studies investigated knee kinematic variability in ACL patients. Results provided support for the theory of “optimal movement variability”. Practically, loss below optimal variability is associated with a more rigid and very repeatable movement pattern, as observed in the ACL-deficient knee. This is a state of low complexity and high predictability. On the other hand, increase beyond optimal variability is associated with a noisy and irregular movement pattern, as found in the ACL-reconstructed knee, regardless of which type of graft is used. This is a state of low complexity and low predictability. In both cases, the loss of optimal variability and the associated high complexity lead to an incapacity to respond appropriately to the environmental demands, thus providing an explanation for vulnerability to pathological changes following injury.ConclusionSubtle fluctuations that appear in knee kinematic patterns provide invaluable insight into the health of the neuromuscular function after ACL rupture and reconstruction. It is thus critical to explore them in longitudinal studies and utilize nonlinear measures as an important component of post-reconstruction medical assessment.Level of evidenceII.

Use of Motor Abundance in Young and Older Adults during Dual-Task Treadmill Walking.

Motor abundance allows individuals to perform any task reliably while being variable in movements particulars. The study investigated age-related differences in this feature when young adults (YA) and older adults (OA) performed challenging tasks, namely treadmill walking alone and while performing a cognitive task. A goal function for treadmill walking was first defined, i.e., maintain constant speed at each step, which led to a goal equivalent manifold (GEM) containing all combinations of step time and step length that equally satisfied the function. Given the GEM, amounts of goal-equivalent and non-goal-equivalent variability were afterwards determined and used to define an index providing information about the set of effective motor solutions relative to the GEM. The set was limited in OA compared to YA in treadmill walking alone, indicating that OA made less flexible use of motor abundance than YA. However, this differentiation between YA and OA disappeared when concurrently performing the cognitive task. It is proposed that OA might have benefited from cognitive compensation.

The effects of shoe traction and obstacle height on lower extremity coordination dynamics during walking

This study aims to investigate the effects of shoe traction and obstacle height on lower extremity relative phase dynamics (analysis of intralimb coordination) during walking to better understand the mechanisms employed to avoid slippage following obstacle clearance. Ten participants walked at a self-selected pace during eight conditions: four obstacle heights (0%, 10%, 20%, and 40% of limb length) while wearing two pairs of shoes (low and high traction). A coordination analysis was used and phasing relationships between lower extremity segments were examined. The results demonstrated that significant behavioral changes were elicited under varied obstacle heights and frictional conditions. Both decreasing shoe traction and increasing obstacle height resulted in a more in-phase relationship between the interacting lower limb segments. The higher the obstacle and the lower the shoe traction, the more unstable the system became. These changes in phasing relationship and variability are indicators of alterations in coordinative behavior, which if pushed further may have lead to falling.

Executive function orchestrates regulation of task-relevant gait fluctuations

Humans apply a minimum intervention principle to regulate treadmill walking, rapidly correcting fluctuations in the task-relevant variable (step speed: SS) while ignoring fluctuations in the task-irrelevant variables (step time: ST; step length: SL). We examined whether the regulation of fluctuations in SS and not in ST and SL depends on high-level, executive function, processes. Young adults walked on a treadmill without a cognitive requirement and while performing the cognitive task of dichotic listening. SS fluctuations became less anti-persistent when performing dichotic listening, meaning that taxing executive function impaired the ability to rapidly correct speed deviations on subsequent steps. Conversely, performing dichotic listening had no effect on SL and ST persistent fluctuations. Findings suggest that high-level brain processes are involved only in regulating gait task-relevant variables.

Sensitivity of the Wolf’s and Rosenstein’s Algorithms to Evaluate Local Dynamic Stability from Small Gait Data Sets: Response to Commentaries by Bruijn et al.

Assessing gait stability using the Largest Lyapunov Exponent (k1) has become popular, especially because it may be a key measure in evaluating gait abnormalities in patient populations. However, clinical settings usually involve having small gait data sets and accurate determination of k1 estimates from such sets is difficult. In an effort to address this issue, Cignetti et al. recently identified that k1 estimates using the algorithm of Wolf et al. (W-algorithm) were more sensitive than those using the algorithm of Rosenstein et al. (R-algorithm) in order to capture age-related decline in gait stability from small data sets. Thus, they advocated the use of the former algorithm. Some concerns about the study were expressed afterwards by Bruijn et al. and we welcome the opportunity to discuss them in the present letter. Bruijn et al. expressed four concerns about the validity of the methods used by Cignetti et al. that could have biased the results. First, they indicate that although speed difference between young adults (YA) and older adults (OA) was not significant, it does not exclude speed as a confounder of the aging effect on gait stability. Although we agree that a perfect matching of YA and OA with respect to speed would definitely avoid confounding, such matching is highly unlikely as YA walk usually faster than OA. Accordingly, matching statistically the two groups in terms of average speed appears to be the best compromise between ecological validity and methodological validity. However, a mean to further avoid the confounding of speed on k1 is to evaluate group difference by using analyses of covariance (ANCOVAs) instead of using analyses of variance (ANOVAs), thus controlling for speed effect. As reported in Table 1, results from ANCOVAs run on the data sets of Cignetti et al. confirmed previous results obtained using ANOVAs. In particular, with respect to the main effect of age, k1 remained significantly larger in OA as compared to YA regardless the size of the data set (i.e., 3600, 7200, and 10,800 data points) when using the W-algorithm. Such result was obtained only for the largest data set (i.e., 10,800 data points) when using the R-algorithm. Therefore, the difference in k1 between YA and OA reported by Cignetti et al. is not biased by the inter-group difference in walking speed. Second, Bruijn et al. argued that the time series of YA might have counted more strides than those of OA due to shorter stride time, increasing artificially k1. However, the stride time was the same in YA and OA with mean ± standard error values of 1.27 ± 0.03 and 1.26 ± 0.05 s, respectively (Table 2). These data are in agreement with previous studies that reported similar values of stride time in both YA and OA populations. Accordingly, k1 exponents were estimated in the study of Cignetti et al. from a similar number of strides for both groups. Specifically, the time series with 3600 data points contained 47 strides in both YA and OA, the time series with 7200 data points contained 94 strides in YA and 95 strides in OA, and the time series with 10,800 data points contained 141 strides in YA and 143 strides in OA (Table 2). Hence, Bruijn et al. were mistaken in assuming that an intergroup difference in stride time could have biased the difference in k1 between YA and OA in Cignetti et al.’s study. A third concern expressed by Bruijn et al., closely related to the previous one, relates with the fact that Cignetti et al. did not normalize time using average stride time when estimating k1 with the W-algorithm, Address correspondence to Fabien Cignetti, Nebraska Biomechanics Core Facility, University of Nebraska at Omaha, 6001 Dodge Street, Omaha, NE 68182-0216, USA. Electronic mail: fabien. cignetti@univ-amu.fr Annals of Biomedical Engineering, Vol. 40, No. 12, December 2012 ( 2012) pp. 2507–2509 DOI: 10.1007/s10439-012-0665-6

Erratum to: Effects of aging on the relationship between cognitive demand and step variability during dual-task walking

In addition, Affiliations 1 and 2 were updated. The correct presentation is given in the following. 1. UMR-S 1075 INSERM and Université de Caen Normandie, Pôle des Formations et de Recherche en Santé, 2 Rue des Rochambelles, 14032 Caen Cedex 5, France 2. Center for Research in HumanMovement Variability, Department of Biomechanics, University of Nebraska at Omaha, 6160 University Drive South, Omaha, NE 68182-0860, USA 3. UMR 7291 CNRS and Aix-Marseille Université, 3 Place Victor-Hugo, 13331 Marseille Cedex 3, France GeroScience (2017) 39:357–358 DOI 10.1007/s11357-017-9974-x

Stepping over obstacles of different heights and varied shoe traction alter the kinetic strategies of the leading limb

This study aims to investigate the effects of shoe traction and obstacle height on friction during walking to better understand the mechanisms required to avoid slippage following obstacle clearance. Ten male subjects walked at a self-selected pace during eight different conditions: four obstacle heights (0%, 10%, 20% and 40% of limb length) while wearing two different pairs of shoes (low and high traction). Frictional forces were calculated from the ground reaction forces following obstacle clearance, which were sampled with a Kistler platform at 960 Hz. All frictional peaks increased with increases in obstacle height. Low traction shoes yielded smaller peaks than high traction shoes. The transition from braking to propulsion occurred sooner due to altered control strategies with increased obstacle height. Collectively, these results provided insights into kinetic strategies of leading limb when confronted with low traction and high obstacle environments. This study provides valuable information into the adaptations used to reduce the potential of slips/falls when confronted with environments characterised by low shoe–floor friction and obstacles. It also provides the necessary foundation to explore the combined effects of shoe traction and obstacle clearance in elderly people, more sensitive to slippage.

THE MINIMUM NUMBER OF DATA POINTS REQUIRED TO COMPUTE APPROXIMATE ENTROPY FOR GAIT DATA

Approximate Entropy (ApEn) is a widely used nonlinear tool to analyze biological data. ApEn quantifies the predictability or regularity of the fluctuations present in a time series, with smaller values indicating greater regularity, and larger values indicate more randomness or irregularity [Pincus, 1991; Pincus et al., 1991]. ApEn is robust with relatively short and noisy data unlike many other nonlinear tools, and the range of data point requirement is rather wide. It can be from 10 to 30, where parameter m is usually set to 2. In addition, since data length N is another parameter for ApEn, ApEn must be calculated for data sets with the same N to ensure appropriate comparisons.