A robust method to estimate the largest Lyapunov exponent of noisy signals: A revision to the Rosenstein’s algorithm

This study proposed a revision to the Rosenstein’s method of numerical calculation of the largest Lyapunov exponent (LyE) to make it more robust to noise. To this aim, the effect of increasing number of initial neighboring points on the LyE value was investigated and compared to values obtained by filtering the time series. Both simulated (Lorenz and passive dynamic walker) and experimental (human walking) time series were used to calculate the LyE. The number of initial neighbors used to calculate LyE for all time series was 1 (the original Rosenstein’s method), 2, 3, 4, 5, 10, 15, 20, 25, and 30 data points. The results demonstrated that the LyE graph reached a plateau at the 15-point neighboring condition implying that the LyE values calculated using at least 15 neighboring points were consistent. The proposed method could be used to calculate more consistent LyE values in experimental time series acquired from biological systems where noise is omnipresent.     

A new parameter for quantifying the variability of surface electromyographic signals during gait: The occurrence frequency

Natural variability of myoelectric activity during walking was recently analyzed considering hundreds of strides. This allowed assessing a parameter seldom considered in classic surface EMG (sEMG) studies: the occurrence frequency, defined as the frequency each muscle activation occurs with, quantified by the number of strides when a muscle is recruited with that specific activation modality. Aim of present study was to propose the occurrence frequency as a new parameter for assessing sEMG-signal variability during walking. Aim was addressed by processing sEMG signals acquired from Gastrocnemius Lateralis, Tibialis Anterior, Rectus Femoris and Biceps femoris in 40 healthy subjects in order to: (1) show that occurrence frequency is not correlated with ON/OFF instants (R_mean = 0.11 ± 0.07; P > 0.05) and total time of activation (R_mean = 0.15 ± 0.08; P > 0.05); (2) confirm the above results by two handy examples of application (analysis of gender and age) which highlighted that significant (P < 0.05) gender-related and age-related differences within population were detected in occurrence frequency, but not in temporal sEMG parameters. In conclusion, present study demonstrated that occurrence frequency is able to provide further information, besides those supplied by classical temporal sEMG parameters and thus it is suitable to complement them in the evaluation of variability of myoelectric activity during walking.     

The 3D path of body centre of mass during adult human walking on force treadmill

Three-dimensional (3D) path of the body centre of mass (CM) over an entire stride was computed from ground reaction forces during walking at constant average speed on a treadmill mounted on 3D force sensors. Data were obtained from 18 healthy adults at speeds ranging from 0.30 to 1.40 m s^?1, in 0.1 m s^?1 increments. Six subsequent strides were analyzed for each subject and speed (total strides=1296). The test session lasted about 30 min (10 min for walking). The CM path had an upward concave figure-of-eight shape that was highly consistent within and across subjects. Vertical displacement of the CM increased monotonically as a function of walking speed. The forward and particularly lateral displacements of the CM showed a U-shaped relationship to speed. The same held for the total 3D displacement (25.6–16.0 cm, depending on the speed). The results provide normative benchmarks and suggest hypotheses for further physiologic and clinical research. The familiar inverted pendulum model might be expanded to gyroscopic, “spin-and-turn” models. Abnormalities of the 3D path might flag motor impairments and recovery.     

Interstitial fluid glucose time-lag correction for real-time continuous glucose monitoring

Time lag between subcutaneous interstitial fluid and plasma glucose decreases the accuracy of real-time continuous glucose monitors. However, inverse filters can be designed to correct time lag and attenuate noise enabling the blood–glucose profile to be reconstructed in real time from continuous measurements of the interstitial-fluid glucose. We designed and tested a Wiener filter using a set of 20 sensor-glucose tracings (～30 h each) with a 1-min sample interval. Delays of 10 ± 2 min (mean ± SD) were introduced into each signal with additive Gaussian white noise (SNR = 40 dB). Performance of the filter was compared to conventional causal and non-causal seventh-order finite-impulse response (FIR) filters. Time lags introduced an error of 5.3 ± 2.7%. The error increased in the presence of noise (to 5.7 ± 2.6%) and attempts to remove the noise with conventional low-pass filtering increased the error still further (to 7.0 ± 3.5%). In contrast, the Wiener filter decreased the error attributed to time delay by ～50% in the presence of noise (from 5.7% to 2.60 ± 1.26%) and by ～75% in the absence of noise (5.3% to 1.3 ± 1%). Introducing time-lag correction without increasing sensitivity to noise can increase CGM accuracy.     

Validation of a smart shoe for estimating foot progression angle during walking gait

The foot progression angle is an important measurement related to knee loading, pain, and function for individuals with knee osteoarthritis, however current measurement methods require camera-based motion capture or floor-embedded force plates confining foot progression angle assessment to facilities with specialized equipment. This paper presents the validation of a customized smart shoe for estimating foot progression angle during walking. The smart shoe is composed of an electronic module with inertial and magnetometer sensing inserted into the sole of a standard walking shoe. The smart shoe charges wirelessly, and up to 160 h of continuous data (sampled at 100 Hz) can be stored locally on the shoe. For validation testing, fourteen healthy subjects were recruited and performed treadmill walking trials with small, medium, and large toe-in (internal foot rotation), small, medium, and large toe-out (external foot rotation) and normal foot progression angle at self-selected walking speeds. Foot progression angle calculations from the smart shoe were compared with measurements from a standard motion capture system. In general, foot progression angle values from the smart shoe closely followed motion capture values for all walking conditions with an overall average error of 0.1 ± 1.9 deg and an overall average absolute error of 1.7 ± 1.0 deg. There were no significant differences in foot progression angle accuracy across the seven different walking gait patterns. The presented smart shoe could potentially be used for knee osteoarthritis or other clinical applications requiring foot progression angle assessment in community settings or in clinics without specialized motion capture equipment.     

Effects of general fatigue induced by incremental maximal exercise test on gait stability and variability of healthy young subjects

The purpose of this study was to determine whether general fatigue induced by incremental maximal exercise test (IMET) affects gait stability and variability in healthy subjects. Twenty-two young healthy male subjects walked in a treadmill at preferred walking speed for 4 min prior (PreT) the test, which was followed by three series of 4 min of walking with 4 min of rest among them. Gait variability was assessed using walk ratio (WR), calculated as step length normalized by step frequency, root mean square (RMS_ratio) of trunk acceleration, standard deviation of medial-lateral trunk acceleration between strides (VAR_ML), coefficient of variation of step frequency (SFCV), length (SLCV) and width (SWCV). Gait stability was assessed using margin of stability (MoS) and local dynamic stability (λ_s). VAR_ML, SFCV, SLCV and SWCV increased after the test indicating an increase in gait variability. MoS decreased and λ_s increased after the test, indicating a decrease in gait stability. All variables showed a trend to return to PreT values, but the 20-min post-test interval appears not to be enough for a complete recovery. The results showed that general fatigue induced by IMET alters negatively the gait, and an interval of at least 20 min should be considered for injury prevention in tasks with similar demands.     

Rectification of SEMG as a tool to demonstrate synchronous motor unit activity during vibration

The use of surface electromyography (SEMG) in vibration studies is problematic since motion artifacts occupy the same frequency band with the SEMG signal containing information on synchronous motor unit activity. We hypothesize that using a harsher, 80–500 Hz band-pass filter and using rectification can help eliminate motion artifacts and provide a way to observe synchronous motor unit activity that is phase locked to vibration using SEMG recordings only. Multi Motor Unit (MMU) action potentials using intramuscular electrodes along with SEMG were recorded from the gastrocnemius medialis (GM) of six healthy male volunteers. Data were collected during whole body vibration, using vibration frequencies of 30 Hz, 35 Hz, 40 Hz or 50 Hz. A computer simulation was used to investigate the efficacy of filtering under different scenarios: with or without artifacts and/or motor unit synchronization. Our findings indicate that motor unit synchronization took place during WBV as verified by MMU recordings. A harsh filtering regimen along with rectification proved successful in demonstrating motor unit synchronization in SEMG recordings. Our findings were further supported by the results from the computer simulation, which indicated that filtering and rectification was efficient in discriminating motion artifacts from motor unit synchronization. We suggest that the proposed signal processing technique may provide a new methodology to evaluate the effects of vibration treatments using only SEMG. This is a major advantage, as this non-intrusive method is able to overcome movement artifacts and also indicate the synchronization of underlying motor units.     

Power line interference rejection from surface electromyography signal using an adaptive algorithm

This work focuses on the power line interference (PLI) rejection from surface EMG signal. It contains three parts: the algorithm, the experimental setting and the results. This study begins with describing the new technique, which consists in filtering respiratory surface electromyogram signals (EMG + PLI), then, becoming familiar with it. The proposed algorithm requires only one channel to both estimating the adaptive filter input reference noise and the EMG signal. The algorithm of PLI rejection has been organized into two steps. The first step insists to apply adaptive filter, especially the LMS one, in which the reference input is mathematically constructed using two different cosine functions; 50 Hz (the fundamental) function and 150 Hz (the first harmonic) function. Whereas, the second step applies the matching pursuit algorithm that uses the cosine packet dictionary to improve the result of PLI obtained at the first step. After trying statistical, as well as mathematical analysis, the complete investigation ensures that all details and steps make proof that our rigorous method is appropriate, we have also compared our method with the previous known techniques.     

The acute effects of local muscle vibration frequency on peak torque,rate of torque development,and EMG activity

PurposeVibratory stimuli enhance muscle activity and may be used for rehabilitation and performance enhancement. Efficacy of vibration varies with the frequency of stimulation, but the optimal frequency is unclear. The purpose of this study was to examine the effects of 30 Hz and 60 Hz local muscle vibration (LMV) on quadriceps function.MethodsTwenty healthy volunteers (age = 20.4 ± 1.4 years, mass = 68.1 ± 11.0 kg, height = 170.1 ± 8.8 cm, males = 9) participated. Isometric knee extensor peak torque (PT), rate of torque development (RTD), and electromyography (EMG) of the quadriceps were assessed followed by one of the three LMV treatments (30 Hz, 60 Hz, control) applied under voluntary contraction, and again immediately, 5, 15, and 30 min post-treatment in three counterbalanced sessions. Dependent variables were analyzed using condition by time repeated-measures ANOVA.ResultsThe condition × time interaction was significant for EMG amplitude (p = 0.001), but not for PT (p = 0.324) or RTD (p = 0.425). The increase in EMG amplitude following 30 Hz LMV was significantly greater than 60 Hz LMV and control.ConclusionsThese findings suggest that 30 Hz LMV may elicit an improvement in quadriceps activation and could be used to treat quadriceps dysfunction resulting from knee pathologies.     

An effective balancing response to lateral perturbations at pelvis level during slow walking requires control in all three planes of motion

In this study we investigated balancing responses to lateral perturbations during slow walking (0.85 m/s). A group of seven healthy individuals walked on an instrumented treadmill while being perturbed at the level of waist at left heel strike in outward and inward lateral directions. Centre of mass (COM) and centre of pressure (COP), rotation of pelvis around vertical axis, step lengths, step widths and step times were assessed. The results have shown that beside control of COP in lateral direction, facilitated by adequate step widths, control of COP in sagittal direction, slowing down movement of COM was present after commencement of lateral perturbations. Sagittal component of COM was significantly retarded as compared to unperturbed walking for both inward (4.32 ± 1.29 cm) and outward (9.75 ± 2.17 cm) perturbations. This was necessary since after an inward perturbation first step length (0.29 ± 0.04 m compared to 0.52 ± 0.02 m in unperturbed walking) and step time (0.45 ± 0.05 s compared to 0.61 ± 0.04 s in unperturbed walking) were shortened while after an outward perturbation first two step lengths (0.36 ± 0.05 m and 0.32 ± 0.11 m compared to 0.52 ± 0.03 m in unperturbed walking) were shortened that needed to be accommodated by the described modulation of COP in sagittal plane. In addition pronounced pelvis rotation assisted in bringing swing leg to new location. The results of this study show that counteracting lateral perturbations at slow walking requires adequate response in all three planes of motion.     

Effects of medially posted insoles on foot and lower limb mechanics across walking and running in overpronating men

Anti-pronation orthoses, like medially posted insoles (MPI), have traditionally been used to treat various of lower limb problems. Yet, we know surprisingly little about their effects on overall foot motion and lower limb mechanics across walking and running, which represent highly different loading conditions. To address this issue, multi-segment foot and lower limb mechanics was examined among 11 overpronating men with normal (NORM) and MPI insoles during walking (self-selected speed 1.70 ± 0.19 m/s vs 1.72 ± 0.20 m/s, respectively) and running (4.04 ± 0.17 m/s vs 4.10 ± 0.13 m/s, respectively). The kinematic results showed that MPI reduced the peak forefoot eversion movement in respect to both hindfoot and tibia across walking and running when compared to NORM (p < 0.05–0.01). No differences were found in hindfoot eversion between conditions. The kinetic results showed no insole effects in walking, but during running MPI shifted center of pressure medially under the foot (p < 0.01) leading to an increase in frontal plane moments at the hip (p < 0.05) and knee (p < 0.05) joints and a reduction at the ankle joint (p < 0.05). These findings indicate that MPI primarily controlled the forefoot motion across walking and running. While kinetic response to MPI was more pronounced in running than walking, kinematic effects were essentially similar across both modes. This suggests that despite higher loads placed upon lower limb during running, there is no need to have a stiffer insoles to achieve similar reduction in the forefoot motion than in walking.     

Optimization of an ultra-fast silicon detector for proton and carbon beams using GEANT4 Monte Carlo toolkit

AimThe purpose of this study was to investigate the crosstalk effects between adjacent pixels in a thin silicon detector with 50 um thickness.BackgroundThere are some limitations in the applications of detectors in hadron therapy. So it is necessary to have a detector with concurrent excellent time and resolution. In this work, the GEANT4 toolkit was applied to estimate the best value for energy cutoff in the thin silicon detector in order to optimize the detector.Materials and MethodsGEANT4 toolkit was applied to simulate the transport and interactions of particles. Calculations were performed for a thin silicon detector (2 cm × 2 cm×0.005 cm) irradiated by proton and carbon ion beams. A two-dimensional array of silicon pixels in the x-y plane with 100 um × 100 um × 50 um dimensions build the whole detector. In the end, the ROOT package is used to interpret and analyze the resultsResultsIt is seen that by the presence of energy cutoff, pixels with small deposited energy are ignored. The best values for energy cutoff are 0.01 MeV and 0.7 MeV for proton and carbon ion beams, respectively. By applying these energy cutoff values, efficiency and purity values are maximized and also minimum output errors are achieved.ConclusionsThe results are reasonable, good and useful to optimize the geometry of future silicon detectors in order to be used as beam monitoring in hadron therapy applications.     

Ambulatory estimation of foot placement during walking using inertial sensors

This study proposes a method to assess foot placement during walking using an ambulatory measurement system consisting of orthopaedic sandals equipped with force/moment sensors and inertial sensors (accelerometers and gyroscopes). Two parameters, lateral foot placement (LFP) and stride length (SL), were estimated for each foot separately during walking with eyes open (EO), and with eyes closed (EC) to analyze if the ambulatory system was able to discriminate between different walking conditions. For validation, the ambulatory measurement system was compared to a reference optical position measurement system (Optotrak). LFP and SL were obtained by integration of inertial sensor signals. To reduce the drift caused by integration, LFP and SL were defined with respect to an average walking path using a predefined number of strides. By varying this number of strides, it was shown that LFP and SL could be best estimated using three consecutive strides. LFP and SL estimated from the instrumented shoe signals and with the reference system showed good correspondence as indicated by the RMS difference between both measurement systems being 6.5±1.0 mm (mean ±standard deviation) for LFP, and 34.1±2.7 mm for SL. Additionally, a statistical analysis revealed that the ambulatory system was able to discriminate between the EO and EC condition, like the reference system. It is concluded that the ambulatory measurement system was able to reliably estimate foot placement during walking.     

Statistical analysis of surface electromyographic signal for the assessment of rectus femoris modalities of activation during gait

Aim of the present study was to identify the different modalities of activation of rectus femoris (RF) during gait at self-selected speed, by a statistical analysis of surface electromyographic signal from a large number (hundreds) of strides per subject. The analysis of ten healthy adults showed that RF is characterized by different activation modalities within different strides of the same walk. RF most recurrent modality (observed in 53 ± 6% of total strides) consists of three activations, at the beginning of gait cycle, around foot-off and in the terminal swing. Further two modalities of RF activation differ from the most recurrent one because of the lack of activity around foot-off (26 ± 6%) or the splitting into two (or three) small activations around stance-to-swing transition (17 ± 2%). Despite the large variability, our statistical analysis allowed to identify two patterns of activation that characterize completely the behavior of rectus femoris during gait. The first pattern, around stance-to-swing transition, can be monophasic, biphasic or triphasic and is necessary to control knee extension and hip flexion from pre-swing to initial swing. The second pattern, from terminal swing to following mid-stance, is likely due to the contribution of low-level RF activity and cross-talk from surrounding vastii.     

Effect of prolonged walking with backpack loads on trunk muscle activity and fatigue in children

This study investigated the effect of prolonged walking with load carriage on muscle activity and fatigue in children. Fifteen Chinese male children (age = 6 years, height = 120.0 ± 5.4 cm, mass = 22.9 ± 2.6 kg) performed 20-min walking trials on treadmill (speed = 1.1 m s⁻¹) with different backpack loads (0%, 10%, 15% and 20% body weight). Electromyography (EMG) signals from upper trapezius (UT), lower trapezius (LT) and rectus abdominis (RA) were recorded at several time intervals (0, 5, 10, 15 and 20 min), and were normalized to the signals collected during maximum voluntary contraction. Integrated EMG signal (IEMG) was calculated to evaluate the muscle activity. Power spectral frequency analysis was applied to evaluate muscle fatigue by the shift of median power frequency (MPF). Results showed that a 15% body weight (BW) load significantly increased muscle activity at lower trapezius when the walking time reached 15 min. When a 20% BW load was being carried, increase in muscle activity was found from 5 min, and muscle fatigue was found from 15 min. In upper trapezius, increase of muscle activity was not found within the 20-min period, however, muscle fatigue was found from 10 min. No increased muscle activity or muscle fatigue was found in rectus abdominis. It is suggested that backpack loads for children should be restricted to no more than 15% body weight for walks of up to 20 min duration to avoid muscle fatigue.     

Automated detection and mapping of electrical activation when electrogram morphology is complex

BackgroundMapping of cardiac electrical activity can be difficult when electrogram morphology is complex. Complex morphology (multiple and changing deflections) causes activation maps to vary when constructed by different analysts, particularly at areas with spatially varying conduction pattern. An algorithm was developed to automatically detect electrogram activation time which is robust to complex morphology.MethodElectrograms, many of which were complex, were collected from 320 canine epicardial border zone sites in five experiments. A library of electrogram activation times were manually marked a priori by two expert analysts. Then an algorithm which combined correlation and error functions was used to compare each input electrogram to library electrogram patterns. The closest match of input to library electrogram was used to estimate activation time. Once activation times at 320 sites were determined, activation maps were automatically constructed on a computerized grid. The algorithm was validated by comparison with activation times determined by the analysts.ResultsThe mean difference between manual and automated marking of activation time in electrograms acquired during reentrant ventricular tachycardia was 2.1 ± 3.9 ms. The mean sensitivity and positive predictive value were 95.9% and 83.8% respectively. The computer-automated marking process was completed within a few seconds and was robust to fractionated electrograms. Measurement error was mostly attributable to 60 Hz noise, which can be rectified with filtering.ConclusionsThe automated algorithm is useful for rapid and accurate automatic marking of multichannel electrograms, some of which may be fractionated, as well as for real-time display of activation maps in clinical electrophysiology or research studies.     

Effect of mental fatigue on induced tremor in human knee extensors

In this study, the effects of mental fatigue on mechanically induced tremor at both a low (3–6 Hz) and high (8–12 Hz) frequency were investigated. The two distinct tremor frequencies were evoked using two springs of different stiffness, during 20 s sustained contractions of the knee extensor muscles at 30% maximum voluntary contraction (MVC) before and after 100 min of a mental fatigue task, in 12 healthy (29 ± 3.7 years) participants. Mental fatigue resulted in a 6.9% decrease in MVC and in a 9.4% decrease in the amplitude of the agonist muscle EMG during sustained 30% MVC contractions in the induced high frequency only. Following the mental fatigue task, the coefficient of variation and standard deviation of the force signal decreased at 8–12 Hz induced tremor by 31.7% and 35.2% respectively, but not at 3–6 Hz induced tremor. Similarly, the maximum value and area underneath the peak in the power spectrum of the force signal decreased by 55.5% and 53.1% respectively in the 8–12 Hz range only. In conclusion, mental fatigue decreased mechanically induced 8–12 Hz tremor and had no effect on induced 3–6 Hz tremor. We suggest that the reduction could be attributed to the decreased activation of the agonist muscles.     

Neural control of leg stiffness during hopping in boys and men

The purpose of the study was to investigate whether boys and men utilise different control strategies whilst hopping. Eleven boys (11–12 yr old) and ten men completed hopping at 1.5 Hz, 3.0 Hz and at their preferred frequency. A footswitch measured contact and flight times, from which leg stiffness was calculated. Simultaneously, surface electromyograms (EMGs) of selected lower limb muscles were recorded and quantified for each 30 ms period during the first 120 ms post-ground contact. At 1.5 Hz there were no differences between the groups in relative stiffness or muscle activity. At 3.0 Hz men had significantly shorter contact times (P = 0.013), longer flight times (P = 0.002), greater relative stiffness (P = 0.01) and significantly greater soleus (P = 0.012) and vastus lateralis (P < 0.001) activity during the initial 30 ms post-ground contact. At the preferred frequency men hopped significantly faster than the boys (P = 0.007), with greater leg stiffness (P < 0.01) and with more extensor activity in most time periods. Boys and men demonstrated similar control strategies when hopping at a slow frequency, but when hopping frequency increased men were able to better increase feedforward and reflex muscle activity to hop with greater relative stiffness.     

Lower limb joint stiffness and muscle co-contraction adaptations to instability footwear during locomotion

Unstable shoes (US) continually perturb gait which can train the lower limb musculature, but muscle co-contraction and potential joint stiffness strategies are not well understood. A shoe with a randomly perturbing midsole (IM) may enhance these adaptations. This study compares ankle and knee joint stiffness, and ankle muscle co-contraction during walking and running in US, IM and a control shoe in 18 healthy females. Ground reaction forces, three-dimensional kinematics and electromyography of the gastrocnemius medialis and tibialis anterior were recorded. Stiffness was calculated during loading and propulsion, derived from the sagittal joint angle-moment curves. Ankle co-contraction was analysed during pre-activation and stiffness phases. Ankle stiffness reduced and knee stiffness increased during loading in IM and US whilst walking (ankle, knee: p = 0.008, 0.005) and running (p < 0.001; p = 0.002). During propulsion, the opposite joint stiffness re-organisation was found in IM whilst walking (both joints p < 0.001). Ankle co-contraction increased in IM during pre-activation (walking: p = 0.001; running: p < 0.001), and loading whilst walking (p = 0.003), not relating to ankle stiffness. Results identified relative levels of joint stiffness change in unstable shoes, providing new evidence of how stability is maintained at the joint level.     

Pre-swing deficits in forward propulsion,swing initiation and power generation by individual muscles during hemiparetic walking

Clinical studies of hemiparetic walking have shown pre-swing abnormalities in the paretic leg suggesting that paretic muscle contributions to important biomechanical walking subtasks are different than those of non-disabled individuals. Three-dimensional forward dynamics simulations of two representative hemiparetic subjects with different levels of walking function classified by self-selected walking speed (i.e., limited community=0.4–0.8 m/s and community walkers=>0.8 m/s) and a speed-matched control were generated to quantify individual muscle contributions to forward propulsion, swing initiation and power generation during the pre-swing phase (i.e., double support phase proceeding toe-off). Simulation analyses identified decreased paretic soleus and gastrocnemius contributions to forward propulsion and power generation as the primary impairment in the limited community walker compared to the control subject. The non-paretic leg did not compensate for decreased forward propulsion by paretic muscles during pre-swing in the limited community walker. Paretic muscles had the net effect to absorb energy from the paretic leg during pre-swing in the community walker suggesting that deficits in swing initiation are a primary impairment. Specifically, the paretic gastrocnemius and hip flexors (i.e., iliacus, psoas and sartorius) contributed less to swing initiation and the paretic soleus and gluteus medius absorbed more power from the paretic leg in the community walker compared to the control subject. Rehabilitation strategies aimed at diminishing these deficits have much potential to improve walking function in these hemiparetic subjects and those with similar deficits.