Endpoint error in smoothing and differentiating raw kinematic data: An evaluation of four popular methods

‘Endpoint error’ describes the erratic behavior at the beginning and end of the computed acceleration data which is commonly observed after smoothing and differentiating raw displacement data. To evaluate endpoint error produced by four popular smoothing and differentiating techniques, Lanshammar's (1982, J. Biomechanics 15, 99–105) modification of the Pezzack et al. (1977, J. Biomechanics, 10, 377–382) raw angular displacement data set was truncated at three different locations corresponding to the major peaks in the criterion acceleration curve. Also, for each data subset, three padding conditions were applied. Each data subset was smoothed and differentiated using the Butterworth digital filter, cubic spline, quintic spline, and Fourier series to obtain acceleration values. RMS residual errors were calculated between the computed and criterion accelerations in the endpoint regions. Although no method completely eliminated endpoint error, the results demonstrated clear superiority of the quintic spline over the other three methods in producing accurate acceleration values close to the endpoints of the modified Pezzack et al. (1977) data set. In fact, the quintic spline performed best with non-padded data (cumulative error=48.0 rad s⁻²). Conversely, when applied to non-padded data, the Butterworth digital filter produced wildly deviating values beginning more than the 10 points from the terminal data point (cumulative error=226.6 rad s⁻²). Each of the four methods performed better when applied to data subsets padded by linear extrapolation (average cumulative error=68.8 rad s⁻²) than when applied to analogous subsets padded by reflection (average cumulative error=86.1 rad s⁻²).     

Filtering of kinematic signals using the Hodrick-Prescott filter

The use of the Hodrick-Prescott (HP) filter is presented as an alternative to the traditional digital filtering and spline smoothing methods currently used in biomechanics. In econometrics, HP filtering is a standard tool used to decompose a macroeconomic time series into a nonstationary trend component and a stationary residual component. The use of the HP filter in the present work is based on reasonable assumptions about the jerk and noise components of the raw displacement signal. Its applicability was tested on 4 kinematic signals with different characteristics. Two are well known signals taken from the literature on biomechanical signal filtering, and the other two were acquired with our own motion capture system. The criterion for the selection of cutoff frequency was based on the power spectral density of the raw displacement signals. The results showed the technique to be well suited to filtering biomechanical displacement signals in order to obtain accurate higher derivatives in a simple and systematic way. Namely, the HP filter and the generalized cross-validated quintic spline (GCVSPL) produce similar RMS errors on the first (0.1063 vs. 0.1024 m/s2) and second (23.76 vs. 23.24 rad/s2) signals. The HP filter performs slightly better than GCVSPL on the third (0.209 vs. 0.236 m/s2) and fourth (1.596 vs. 2.315 m/s2) signals.     

Effects of the Racket Polar Moment of Inertia on Dominant Upper Limb Joint Moments during Tennis Serve

This study examined the effect of the polar moment of inertia of a tennis racket on upper limb loading in the serve. Eight amateur competition tennis players performed two sets of 10 serves using two rackets identical in mass, position of center of mass and moments of inertia other than the polar moment of inertia (0.00152 vs 0.00197 kg.m²). An eight-camera motion analysis system collected the 3D trajectories of 16 markers, located on the thorax, upper limbs and racket, from which shoulder, elbow and wrist net joint moments and powers were computed using inverse dynamics. During the cocking phase, increased racket polar moment of inertia was associated with significant increases in the peak shoulder extension and abduction moments, as well the peak elbow extension, valgus and supination moments. During the forward swing phase, peak wrist extension and radial deviation moments significantly increased with polar moment of inertia. During the follow-through phase, the peak shoulder adduction, elbow pronation and wrist external rotation moments displayed a significant inverse relationship with polar moment of inertia. During the forward swing, the magnitudes of negative joint power at the elbow and wrist were significantly larger when players served using the racket with a higher polar moment of inertia. Although a larger polar of inertia allows players to better tolerate off-center impacts, it also appears to place additional loads on the upper extremity when serving and may therefore increase injury risk in tennis players.     

Analysis of the Movement Track of Top Spinning Ball and Biomechanics in the Process of Hitting Tennis Ball

The aim of this study is to analyze the movement track of top spinning tennis ball and the biomechanics characteristics of tennis players. This study took ten tennis players as an example. The hitting process of the top spinning ball was captured by two PULNIX high-speed cameras. The images were processed by APAS motion analysis system. The results showed that the top spinning ball moved forward while rotating in the hitting process and showed a large attack force after rebounding from the land. In biomechanics, A and B had larger angles of upper limb joints and larger joint speed. The center of gravity was on the right. The knee joint flexed, obtained the reactive force through pedaling and stretching, and transferred the power to the racket. At the moment of hitting, the racket head speed of A and B was the largest, 18.3 m/s and 18.5 m/s, respectively. At the end of the follow-through, the shoulder and elbow angle angles of A and B were small. Larger power was provided to the racket by the rapid internal rotation. The power of hitting the ball should be increased to improve the hitting effect and speed. Corresponding guidance can be provided to players to improve their technical level.     

Estimation of musculotendon kinematics in large musculoskeletal models using multidimensional B-splines

We present a robust and computationally inexpensive method to estimate the lengths and three-dimensional moment arms for a large number of musculotendon actuators of the human lower limb. Using a musculoskeletal model of the lower extremity, a set of values was established for the length of each musculotendon actuator for different lower limb generalized coordinates (joint angles). A multidimensional spline function was then used to fit these data. Muscle moment arms were obtained by differentiating the musculotendon length spline function with respect to the generalized coordinate of interest. This new method was then compared to a previously used polynomial regression method. Compared to the polynomial regression method, the multidimensional spline method produced lower errors for estimating musculotendon lengths and moment arms throughout the whole generalized coordinate workspace. The fitting accuracy was also less affected by the number of dependent degrees of freedom and by the amount of experimental data available. The spline method only required information on musculotendon lengths to estimate both musculotendon lengths and moment arms, thus relaxing data input requirements, whereas the polynomial regression requires different equations to be used for both musculotendon lengths and moment arms. Finally, we used the spline method in conjunction with an electromyography driven musculoskeletal model to estimate muscle forces under different contractile conditions, which showed that the method is suitable for the integration into large scale neuromusculoskeletal models.     

Evaluation of a subject-specific, torque-driven computer simulation model of one-handed tennis backhand groundstrokes

A torque-driven, subject-specific 3-D computer simulation model of the impact phase of one-handed tennis backhand strokes was evaluated by comparing performance and simulation results. Backhand strokes of an elite subject were recorded on an artificial tennis court. Over the 50-ms period after impact, good agreement was found with an overall RMS difference of 3.3° between matching simulation and performance in terms of joint and racket angles. Consistent with previous experimental research, the evaluation process showed that grip tightness and ball impact location are important factors that affect postimpact racket and arm kinematics. Associated with these factors, the model can be used for a better understanding of the eccentric contraction of the wrist extensors during one-handed backhand ground strokes, a hypothesized mechanism of tennis elbow.     

Relationship between muscle coordination and forehand drive velocity in tennis

This study aimed at investigating the relationship between trunk and upper limb muscle coordination and stroke velocity during tennis forehand drive. The electromyographic (EMG) activity of ten trunk and dominant upper limb muscles was recorded in 21 male tennis players while performing five series of ten crosscourt forehand drives. The forehand drive velocity ranged from 60% to 100% of individual maximal velocity. The onset, offset and activation level were calculated for each muscle and each player. The analysis of muscle activation order showed no modification in the recruitment pattern regardless of the velocity. However, the increased velocity resulted in earlier activation of the erector spinae, latissimus dorsi and triceps brachii muscles, as well as later deactivation of the erector spinae, biceps brachii and flexor carpi radialis muscles. Finally, a higher level of activation was observed with the velocity increase in the external oblique, latissimus dorsi, middle deltoid, biceps brachii and triceps brachii. These results might bring new knowledge for strength and tennis coaches to improve resistance training protocols in a performance and prophylactic perspective.     

Analysis of the tennis racket vibrations during forehand drives: Selection of the mother wavelet

The time–frequency analysis of the tennis racket and hand vibrations is of great interest for discomfort and pathology prevention. This study aimed to (i) to assess the stationarity of the vibratory signal of the racket and hand and (ii) to identify the best mother wavelet to perform future time–frequency analysis, (iii) to determine if the stroke spin, racket characteristics and impact zone can influence the selection of the best mother wavelet. A total of 2364 topspin and flat forehand drives were performed by fourteen male competitive tennis players with six different rackets. One tri-axial and one mono-axial accelerometer were taped on the racket throat and dominant hand respectively. The signal stationarity was tested through the wavelet spectrum test. Eighty-nine mother wavelet were tested to select the best mother wavelet based on continuous and discrete transforms. On average only 25 ± 17%, 2 ± 5%, 5 ± 7% and 27 ± 27% of the signal tested respected the hypothesis of stationarity for the three axes of the racket and the hand respectively. Regarding the two methods for the detection of the best mother wavelet, the Daubechy 45 wavelet presented the highest average ranking. No effect of the stroke spin, racket characteristics and impact zone was observed for the selection of the best mother wavelet. It was concluded that alternative approach to Fast Fourier Transform should be used to interpret tennis vibration signals. In the case where wavelet transform is chosen, the Daubechy 45 mother wavelet appeared to be the most suitable.     

不同球类运动对大学生上下肢骨密度及其方向性不对称的影响

为探究不同球类运动对上下肢骨密度及其方向性不对称的影响,特选取研究对象共210人,均分为7组,即篮球组、排球组、足球组、羽毛球组、乒乓球组、网球组和对照组,测量其上下肢的骨密度和方向性不对称性(DA)。结果显示,篮球组、排球组、羽毛球组、乒乓球组和网球组的上肢骨密度都是右侧明显高于左侧,下肢骨密度仅足球组表现为右侧高于左侧;不同组间的上下肢骨密度和DA具有统计学差异。结果还显示,左侧上肢骨密度的组间排序为排球组>足球组>第二亚组(乒乓球组、网球组和羽毛球组)>对照组,篮球组>乒乓球组、网球组和羽毛球组>对照组;右侧上肢骨密度的排序为网球组>乒乓球组、排球组和篮球组>足球组>对照组,乒乓球组>羽毛球组>足球组>对照组;左侧下肢骨密度的排序为足球组>篮球组、排球组、羽毛球组、乒乓球组和网球组>对照组;右侧下肢骨密度的排序为足球组>排球组、篮球组、网球组、羽毛球组和乒乓球组>对照组,排球组>羽毛球组和乒乓球组>对照组;DA的排序为网球组>乒乓球组、羽毛球组、篮球组和排球组,乒乓球组&g...     

Determining the optimal system-specific cut-off frequencies for filtering in-vitro upper extremity impact force and acceleration data by residual analysis

The fundamental nature of impact testing requires a cautious approach to signal processing, to minimize noise while preserving important signal information. However, few recommendations exist regarding the most suitable filter frequency cut-offs to achieve these goals. Therefore, the purpose of this investigation is twofold: to illustrate how residual analysis can be utilized to quantify optimal system-specific filter cut-off frequencies for force, moment, and acceleration data resulting from in-vitro upper extremity impacts, and to show how optimal cut-off frequencies can vary based on impact condition intensity. Eight human cadaver radii specimens were impacted with a pneumatic impact testing device at impact energies that increased from 20J, in 10J increments, until fracture occurred. The optimal filter cut-off frequency for pre-fracture and fracture trials was determined with a residual analysis performed on all force and acceleration waveforms. Force and acceleration data were filtered with a dual pass, 4th order Butterworth filter at each of 14 different cut-off values ranging from 60Hz to 1500Hz. Mean (SD) pre-fracture and fracture optimal cut-off frequencies for the force variables were 605.8 (82.7)Hz and 513.9 (79.5)Hz, respectively. Differences in the optimal cut-off frequency were also found between signals (e.g. Fx (medial-lateral), Fy (superior-inferior), Fz (anterior-posterior)) within the same test. These optimal cut-off frequencies do not universally agree with the recommendations of filtering all upper extremity impact data using a cut-off frequency of 600Hz. This highlights the importance of quantifying the filter frequency cut-offs specific to the instrumentation and experimental set-up. Improper digital filtering may lead to erroneous results and a lack of standardized approaches makes it difficult to compare findings of in-vitro dynamic testing between laboratories.     

Electromyographic patterns of individuals suffering from lateral tennis elbow.

This study investigated the applicability of using surface electromyography (EMG) as a tool for differentiating between persons suffering from lateral tennis elbow and the healthy age-matched adults. Temporal muscle activation patterns of the tennis elbow group were evaluated to determine if they varied between subject groups and if noted variations might be interpreted as arresting or exacerbating the injury. Sixteen subjects (Healthy Controls, n = 6; Tennis Elbow, n = 10) were tested under simulated tennis playing conditions. All subjects were males (Healthy group (CON) 38.8 +/- 13.1, Injured group (INJ) 40.8 +/- 10.8 yrs). EMG response data, temporal and spatial muscle activities, of the forearm extensors (Ext), the forearm flexors (Flex) and the triceps (Tri) were recorded for each subject during a single test session using all combinations of three different velocities on three different racket head impact locations. Data were collected at a frequency of 1000 Hz. Statistical analysis was performed using a 2 x 3 x 3 (Health status x Impact velocity x Impact location) ANOVA with repeated measures. Results indicated statistically significant differences (p < 0.05) between the CON and INJ subject groups for the response variables associated with forearm extensor muscle activation. During simulated play, the INJ group employed an earlier, longer, and greater activation of Ext than the CON group, such changes may be considered detrimental to the healing process. These results support the use of surface EMG to quantify differences in muscle activation strategies employed by individuals suffering from soft tissue muscle microtrauma injuries and healthy controls.     

Field hockey players have different values of ulnar and tibial motor nerve conduction velocity than soccer and tennis players

The aim of this study was to describe motor nerve conduction velocity in upper and lower extremities in sportsmen. Fifteen high-level field hockey players, seventeen soccer players and ten tennis players were recruited from the Polish National Field Hockey League, Polish Soccer League Clubs, and Polish Tennis Association clubs,respectively. The control group comprised of seventeen healthy, non-active young men. Nerve conduction velocities of ulnar and tibial nerve were assessed with NeuroScreen electromyograph (Toennies, Germany) equipped with standard techniques of supramaximal percutaneus stimulation with constant current and surface electrodes. No significant differences in motor nerve conduction velocities were found between dominant and non-dominant limbs in each studied group. Ulnar nerve conduction velocity measured from above elbow to below elbow was significantly lower only in the field hockey players' dominant limb. Tibial conduction velocity of the field hockey players' non-dominant lower limb was higher in comparison to the tennis players and the control group. There was no significant correlation between body mass and NCV as well as between height of subjects and NCV in both athletes or non-athletes. A slight trend towards a lower TCV values in athletes with longer duration of practicing sport was found. It was most pronounced in the non-dominant lower extremity of field hockey players.     

Injuries in racket sports among Slovenian players

On the sample of 83 top Slovenian athletes we have studied the frequency of injuries among table tennis, tennis and badminton players, types of injuries and severity of injuries--the latter based on data of players absences from training and/or competition processes. The most liable parts to injuries are shoulder girdle (17.27%), spine (16.55%) and ankle (15.83%), while foot (10.07%) and wrist (12.23%) are slightly less liable to injuries. The most frequent injuries in racket sports pertain to muscle tissues. According to this data, the majority of injuries occur halfway through a training session or a competition event, mostly during a competition season. The injuries primarily pertain to muscle tissues; these are followed by joint and tendon injuries. There are no differences between male and female players. Compared to other racket sports players, table tennis players suffer from fewer injuries.     

Trunk and upper limb muscle activation during flat and topspin forehand drives in young tennis players

This study compared EMG activity of young tennis players' muscles during forehand drives in two groups, GD-those able to raise by more than 150% the vertical velocity of racket-face at impact from flat to topspin forehand drives, and GND, those not able to increase their vertical velocity to the same extent. Upper limb joint angles, racket-face velocities, and average EMGrms values, were studied. At similar joint angles, a fall in horizontal velocity and a rise in racket-face vertical velocity from flat to topspin forehand drives were observed. Shoulder muscle activity rose from flat to topspin forehand drives in GND, but not for drives in GD. Forearm muscle activity reduced from flat to topspin forehand drives in GD, but muscle activation was similar in GND. The results show that radial deviation increased racket-face vertical velocity more at impact from the flat to topspin forehand drives than shoulder abduction.     

Influence of fatigue on upper limb muscle activity and performance in tennis

The study examined the fatigue effect on tennis performance and upper limb muscle activity. Ten players were tested before and after a strenuous tennis exercise. Velocity and accuracy of serve and forehand drives, as well as corresponding surface electromyographic (EMG) activity of eight upper limb muscles were measured. EMG and force were also evaluated during isometric maximal voluntary contractions (IMVC). Significant decreases were observed after exercise in serve accuracy (−11.7%) and velocity (−4.5%), forehand accuracy (−25.6%) and consistency (−15.6%), as well as pectoralis major (PM) and flexor carpi radialis (FCR) IMVC strength (−13.0% and −8.2%, respectively). EMG amplitude decreased for PM and FCR in serve, forehand and IMVC, and for extensor carpi radialis in forehand. No modification was observed in EMG activation timing during strokes or in EMG frequency content during IMVC. Several hypotheses can be put forward to explain these results. First, muscle fatigue may induce a reduction in activation level of PM and forearm muscles, which could decrease performance. Second, conscious or subconscious strategies could lead to a redistribution of muscle activity to non-fatigued muscles in order to protect the organism and/or limit performance losses. Otherwise, the modifications of EMG activity could also illustrate the strategies adopted to manage the speed-accuracy trade-off in such a complex task.     

Size and blood flow of central and peripheral arteries in highly trained able-bodied and disabled athletes.

In a cross-sectional study, central and peripheral arteries were investigated noninvasively in high-performance athletes and in untrained subjects. The diastolic inner vessel diameter (D) of the thoracic and abdominal aorta, the subclavian artery (Sub), and common femoral artery (Fem) were determined by duplex sonography in 18 able-bodied professional tennis players, 34 able-bodied elite road cyclist athletes, 26 athletes with paraplegia, 17 below-knee amputated athletes, and 30 able-bodied, untrained subjects. The vessel cross-sectional areas (CSA) were set in relation to body surface area (BSA), and the cross-section index (CS-index = CSA/BSA) was calculated. Volumetric blood flow was determined in Sub and Fem via a pulsed-wave Doppler system and was set in relation to heart rate to calculate the stroke flow. A significantly increased D of Sub was found in the racket arm of able-bodied tennis players compared with the opposite arm (19%). Fem of able-bodied road cyclist athletes and of the intact limb in below-knee amputated athletes showed similar increases. D of Fem was lower in athletes with paraplegia (37%) and in below-knee amputated athletes proximal to the lesion (21%) compared with able-bodied, untrained subjects; CS-indexes were reduced 57 and 31%, respectively. Athletes with paraplegia demonstrated a larger D (19%) and a larger CS-index in Sub (54%) than able-bodied, untrained subjects. No significant differences in D and CS-indexes of the thoracic and abdominal aorta were found between any of the groups. The changes measured in Sub and Fem were associated with corresponding alterations in blood flow and stroke flow in all groups. The study suggests that the size and blood flow volume of the proximal limb arteries are adjusted to the metabolic needs of the corresponding extremity musculature and underscore the impact of exercise training or disuse on the structure and the function of the arterial system.     

Evaluation of the global optimisation method within the upper limb kinematics analysis

The aim of this study is to assess the performances of the global optimisation (GO) method (Bone position estimation from skin marker co-ordinates using GO with joint constraints. Journal of Biomechanics 32, 129-134) within the upper limb kinematics analysis. First the model of the upper limb is presented. Then we apply GO method in order to reduce skin movement artefacts that imply relative movement between markers and bones. The performances of the method are then evaluated with the help of simulated movements of the upper limb. Results show a significant reduction of the errors and of the variability due to skin movement.     

Kinematical models to reduce the effect of skin artifacts on marker-based human motion estimation

The estimation of the skeletal motion obtained from marker-based motion capture systems is known to be affected by significant bias caused by skin movement artifacts, which affects joint center and rotation axis estimation. Among different techniques proposed in the literature, that based on rigid body model, still the most used by commercial motion capture systems, can smooth only part of the above effects without eliminating their main components. In order to sensibly improve the accuracy of the motion estimation, a novel technique, named local motion estimation (LME), is proposed. This rests on a recently described approach that, using virtual humans and extended Kalman filters, estimates the kinematical variables directly from 2D measurements without requiring the 3D marker reconstruction. In this paper, we show how such method can be extended to include the computation of the local marker displacement due to skin artifacts. The 3D marker coordinates, expressed in the corresponding local reference coordinate frames, are inserted into the state vector of the filter and their dynamics is automatically estimated, with adequate accuracy, without assuming any particular deformation function. Simulated experiments of lower limb motion, involving systematic mislocations (5, 10, 20 mm) and random errors of the marker coordinates and joint center locations (+/-5, +/-10, +/-15 mm), have shown that artifact motion can be substantially decoupled from the global skeletal motion with an effective increase of the accuracy wrt standard techniques. In particular, the comparison between the nominal kinematical variables and the one recovered from markers attached to the skin surface proved LME to be sensibly superior (50% in the worse condition) to the methods imposing marker-bone rigidity. In conclusion, while requiring further validation on real movement data, we argue that the proposed method can constitute an appropriate approach toward the improvement of the human motion estimation.     

Side-to-side comparisons of bone mineral density in upper and lower limbs of collegiate athletes

This cross-sectional study investigated the effects of participation in various sports on side-to-side (contralateral) differences in bone mineral density (BMD) of the upper and lower limbs. The BMD of the arms and legs was measured using dual energy X-ray absorptiometry. The subjects were 184 collegiate athletes, both men and women, who participated in NCAA Division I-A baseball, basketball, football, golf, soccer, tennis, cross-country, indoor/outdoor track, and volleyball. Results revealed greater BMD of the right arms compared with the left arms for all teams, with the most pronounced differences observed in men's and women's tennis and men's baseball. Differences in the lower limbs were less common. No significant differences in lower limb BMD were found in the women. In men, differences in lower limb BMD were found in the football and tennis teams, with the nondominant leg having greater bone mass. Recognition of contralateral differences in bone density may be of particular interest to strength and conditioning professionals as they consider the need to include bilateral and unilateral training programs in an effort to maximize performance and minimize stress-related injuries.