Can sacral marker approximate center of mass during gait and slip-fall recovery among community-dwelling older adults?

Falls are prevalent in older adults. Dynamic stability of body center of mass (COM) is critical for maintaining balance. A simple yet accurate tool to evaluate COM kinematics is essential to examine the COM stability. The purpose of this study was to determine the extent to which the COM position derived from body segmental analysis can be approximated by a single (sacral) marker during unperturbed (regular walking) and perturbed (gait-slip) gait. One hundred eighty seven older adults experienced an unexpected slip after approximately 10 regular walking trials. Two trials, the slip trial and the preceding regular walking trial, monitored with a motion capture system and force plates, were included in the present study. The COM positions were calculated by using the segmental analysis method wherein, the COM of all body segments was calculated to further estimate the body COM position. These body COM positions were then compared with those of the sacral marker placed at the second sacral vertebra for both trials. Results revealed that the COM positions were highly correlated with those of the sacrum׳s over the time intervals investigated for both walking (coefficient of correlation R>0.97) and slip (R>0.90) trials. There were detectable kinematic difference between the COM and the sacral for both trials. Our results indicated that the sacral marker can be used as a simple approximation of body COM for regular walking, and to somewhat a lesser extent, upon a slip. The benefits from the simplicity appear to overweigh the limitations in accuracy.     

Pelvic kinematic method for determining vertical jump height

Sacral marker and pelvis reconstruction methods have been proposed to approximate total body center of mass during relatively low intensity gait and hopping tasks, but not during a maximum effort vertical jumping task. In this study, center of mass displacement was calculated using the pelvic kinematic method and compared with center of mass displacement using the ground-reaction force-impulse method, in experienced athletes (n = 13) performing restricted countermovement vertical jumps. Maximal vertical jumps were performed in a biomechanics laboratory, with data collected using an 8-camera motion analysis system and two force platforms. The pelvis center of mass was reconstructed from retro-reflective markers placed on the pelvis. Jump height was determined from the peak height of the pelvis center of mass minus the standing height. Strong linear relationships were observed between the pelvic kinematic and impulse methods (R2 = .86; p < .01). The pelvic kinematic method underestimated jump height versus the impulse method, however, the difference was small (CV = 4.34%). This investigation demonstrates concurrent validity for the pelvic kinematic method to determine vertical jump height.     

Gender differences in active musculoskeletal stiffness. Part II. Quantification of leg stiffness during functional hopping tasks.

Leg stiffness was compared between age-matched males and females during hopping at preferred and controlled frequencies. Stiffness was defined as the linear regression slope between the vertical center of mass (COM) displacement and ground-reaction forces recorded from a force plate during the stance phase of the hopping task. Results demonstrate that subjects modulated the vertical displacement of the COM during ground contact in relation to the square of hopping frequency. This supports the accuracy of the spring-mass oscillator as a representative model of hopping. It also maintained peak vertical ground-reaction load at approximately three times body weight. Leg stiffness values in males (33.9+/-8.7 kN/m) were significantly (p<0.01) greater than in females (26.3+/-6.5 kN/m) at each of three hopping frequencies, 3.0, 2.5 Hz, and a preferred hopping rate. In the spring-mass oscillator model leg stiffness and body mass are related to the frequency of motion. Thus male subjects necessarily recruited greater leg stiffness to drive their heavier body mass at the same frequency as the lighter female subjects during the controlled frequency trials. However, in the preferred hopping condition the stiffness was not constrained by the task because frequency was self-selected. Nonetheless, both male and female subjects hopped at statistically similar preferred frequencies (2.34+/-0.22 Hz), therefore, the females continued to demonstrate less leg stiffness. Recognizing the active muscle stiffness contributes to biomechanical stability as well as leg stiffness, these results may provide insight into the gender bias in risk of musculoskeletal knee injury.     

Comparison of whole-body vertical stiffness and leg stiffness during single-leg hopping in place in children and adults

In the hopping literature, whole-body vertical stiffness and leg stiffness are used interchangeably, due to most of the movement occurring in the vertical direction. However, there is some anterior/posterior movement of the center of mass and displacements of the foot during hopping in place in both children and adults. Further it is not understood if leg stiffness show a similar pattern as whole-body vertical stiffness when increasing hopping frequency. The purpose of this study was to test if whole-body vertical stiffness and leg stiffness are different during single-leg hopping in-place in children and adults, across a range of frequencies. Seventeen children aged 5–11 years and 16 young adults participated in this study. The subjects hopped at their preferred frequency as well as 20% below, 20% above and 40% above preferred frequency. Our results demonstrate that both whole-body vertical stiffness and leg stiffness increase when increasing hopping frequency for children and adults. However, whole-body vertical stiffness consistently overestimates leg stiffness due to a similar peak force but a greater leg length change compared to vertical COM displacement. This suggests a considerable horizontal COM movement from landing to mid-stance during hopping. Children aged 5–11 years old showed lower absolute values but higher normalized values of two stiffness measures than adults. This suggests somewhat adult-like stiffness control in children, but a reduced ability to manipulate the horizontal movement during single-leg hopping in place when compared to adults.     

Cross-correlations of center of mass and center of pressure displacements reveal multiple balance strategies in response to sinusoidal platform perturbations

Compared to static balance, dynamic balance requires a more complex strategy that goes beyond keeping the center of mass (COM) within the base of support, as established by the range of foot center of pressure (COP) displacement. Instead, neuromechanics must accommodate changing support conditions and inertial effects. Therefore, because they represent body's position and changes in applied moments, relative COM and COP displacements may also reveal dynamic postural strategies. To investigate this concept, kinetics and kinematics were recorded during three 12 cm, 1.25 Hz, sagittal perturbations. Forty-one individual trials were classified according to averaged cross-correlation lag between COM and COP displacement (lag(COM:COP)) and relative head-to-ankle displacement (Δ(head)/Δ(ankle)) using a k-means analysis. This process revealed two dominant patterns, one for which the lag(COM:COP) was positive (Group 1 (n=6)) and another for which it was negative (Group 2 (n=5)) . Group 1 (G1) absorbed power from the platform over most of the cycle, except during transitions in platform direction. Conversely, Group 2 (G2) participants applied power to the platform to maintain a larger margin between COM and COP position and also had larger knee flexion and ankle dorsiflexion, resulting in a lower stance. By the third repetition, the only kinematic differences were a slightly larger G2 linear knee displacement (p=0.008) and an antiphasic relationship of pelvis (linear) and trunk (angular) displacements. Therefore, it is likely that the strategy differences were detected by including COP in the initial screening method, because it reflects the pattern of force application that is not detectable by tracking body movements.     

Data Processing Techniques May Influence Numerical Results and Interpretation of Single Leg Stance Test

Purposeto evaluate how different data sampling and different analysis methods may effect numerical results and interpretation of single leg stance test using parameters derived from CoP trajectories.MethodsThirty healthy active subjects were recruited for this study on voluntary. Each participant was asked to stand as still as possible for 20 s on the dominant limb, with the supporting foot placed on the force platform. Balancing task in two conditions, with eyes open (EO) and closed (EC). Three trials were collected for each condition.Medial-lateral and anterior-posterior CoP force platform data were obtained and downsampling techniques was applied to get data at original (500 Hz), 100 Hz and 20 Hz of sampling frequencies.Time series data were then analysed to get CoP variables including medial-lateral total path, anterior-posterior total path, total path, maximal excursion for the ML plane and maximal excursion for the AP plane. Sway area was evaluated as 95% confidence ellipse area (CEA) and as 95% prediction ellipse area (PEA)Main findingsSignificant different results were obtained for the same variable evaluated at different sampling frequency. In addition, at all sampling frequencies variables were significantly different (p.<0.05) between EO and EC conditions. High correlation (>0.9) between the same CoP variable calculated at different sampling frequencies was found for all CoP variables. Regarding sway area calculation, both methods were able to distinguish between EO and EC conditions and high correlation was found between CEA and PEA methods.ConclusionOverall results of this study demonstrated the importance of reporting data processing techniques, which includes sampling frequency and variable calculation methods, as they shown to influence one leg stance CoP results, thus data analysed in different manner cannot be directly compared. However, for the variables included in the study, researchers can choose preferred data collection and data analysis methods as they all return same data analysis interpretation as long as they keep consistency in the method.     

Increased musculoskeletal stiffness during load carriage at increasing walking speeds maintains constant vertical excursion of the body center of mass

The primary objective of this research was to determine changes in body and joint stiffness parameters and kinematics of the knee and body center of mass (COM), that result from wearing a backpack (BP) with a 40% body weight load at increasing speeds of walking. It was hypothesized that there would be speed and load-related increases in stiffness that would prevent significant deviations in the COM trajectory and in lower-extremity joint angles. Three independent biomechanical models employing kinematic data were used to estimate global lower-extremity stiffness, vertical stiffness and knee joint rotational stiffness in the sagittal plane during walking on a treadmill at speeds of 0.6-1.6 ms(-1) in 0.2 ms(-1) increments in BP and no backpack conditions. Kinematic data were collected using an Optotrak, three-dimensional motion analysis system. Knee angles and vertical excursion of the COM during the compression (loading phase) increased as a function of speed but not load. All three estimates of stiffness showed significant increases as a function of both speed and load. Significant interaction effects indicated a convergence of load-related stiffness values at lower speeds. Results suggested that increases in muscle-mediated stiffness are used to maintain a constant vertical excursion of the COM under load across the speeds tested, and thereby limit increases in metabolic cost that would occur if the COM would travel through greater vertical range of motion.     

A motion analysis marker-based method of determining centre of pressure during two-legged hopping

The fixed position of force plates has led researchers to pursue alternative methods of determining centre of pressure (CoP) location. To date, errors reported using alternative methods to the force plate during dynamic tasks have been high. The aim of this study was to investigate the accuracy of a motion analysis marker-based system to determine CoP during a two-legged hopping task. Five markers were attached to the left and right feet of eight healthy adults (5 females, 3 males, age: 25.0±2.8 years, height: 1.75±0.07 m, mass: 71.3±11.3 kg). Multivariate forward stepwise and forced entry linear regression was used with data from five participants to determine CoP position during quiet standing and hopping at various frequencies. Maximum standard error of the estimate of CoP position was 12 mm in the anteroposterior direction and 8 mm in the mediolateral. Cross-validation was performed using the remaining 3 participants. Maximum root mean square difference between the force plate and marker method was 14 mm for mediolateral CoP and 20 mm for anteroposterior CoP during 1.5 Hz hopping. Differences reduced to a maximum of 7 mm (mediolateral) and 14 mm (anteroposterior) for the other frequencies. The smallest difference in calculated sagittal plane ankle moment and timing of maximum moment was during 3.0 Hz hopping, and largest at 1.5 Hz. Results indicate the marker-based method of determining CoP may be a suitable alternative to a force plate to determine CoP position during a two-legged hopping task at frequencies greater than 1.5 Hz.     

Linear center-of-mass dynamics emerge from non-linear leg-spring properties in human hopping

Given the almost linear relationship between ground-reaction force and leg length, bouncy gaits are commonly described using spring–mass models with constant leg-spring parameters. In biological systems, however, spring-like properties of limbs may change over time. Therefore, it was investigated how much variation of leg-spring parameters is present during vertical human hopping. In order to do so, rest-length and stiffness profiles were estimated from ground-reaction forces and center-of-mass dynamics measured in human hopping. Trials included five hopping frequencies ranging from 1.2 to 3.6 Hz. Results show that, even though stiffness and rest length vary during stance, for most frequencies the center-of-mass dynamics still resemble those of a linear spring–mass hopper. Rest-length and stiffness profiles differ for slow and fast hopping. Furthermore, at 1.2 Hz two distinct control schemes were observed.     

Does the anthropometric model influence whole-body center of mass calculations in gait?

Examining whole-body center of mass (COM) motion is one of method being used to quantify dynamic balance and energy during gait. One common method for estimating the COM position is to apply an anthropometric model to a marker set and calculate the weighted sum from known segmental COM positions. Several anthropometric models are available to perform such a calculation. However, to date there has been no study of how the anthropometric model affects whole-body COM calculations during gait. This information is pertinent to researchers because the choice of anthropometric model may influence gait research findings and currently the trend is to consistently use a single model. In this study we analyzed a single stride of gait data from 103 young adult participants. We compared the whole-body COM motion calculated from 4 different anthropometric models (Plagenhoef et al., 1983; Winter, 1990; de Leva, 1996; Pavol et al., 2002). We found that anterior-posterior motion calculations are relatively unaffected by the anthropometric model. However, medial-lateral and vertical motions are significantly affected by the use of different anthropometric models. Our findings suggest that the researcher carefully choose an anthropometric model to fit their study populations when interested in medial-lateral or vertical motions of the COM. Our data can provide researchers a priori information on the model determination depending on the particular variable and how conservative they may want to be with COM comparisons between groups.     

Support force measures of midsized men in seated positions

Two areas not well researched in the field of seating mechanics are the distribution of normal and shear forces, and how those forces change with seat position. The availability of these data would be beneficial for the design and development of office, automotive and medical seats. To increase our knowledge in the area of seating mechanics, this study sought to measure the normal and shear loads applied to segmental supports in 12 seated positions, utilizing three inclination angles and four levels of seat back articulation that were associated with automotive driving positions. Force data from six regions, including the thorax, sacral region, buttocks, thighs, feet, and hand support were gathered using multi-axis load cells. The sample contained 23 midsized subjects with an average weight of 76.7 kg and a standard deviation of 4.2 kg, and an average height of 1745 mm with a standard deviation of 19 mm. Results were examined in terms of seat back inclination and in terms of torso articulation for relationships between seat positions and support forces. Using a repeated measures analysis, significant differences (p<0.05) were identified for normal forces relative to all inclination angles except for forces occurring at the hand support. Other significant differences were observed between normal forces behind the buttocks, pelvis, and feet for torso articulations. Significant differences in the shear forces occurred under the buttocks and posterior pelvis during changes in seat back inclination. Significant differences in shear forces were also identified for torso articulations. These data suggest that as seat back inclination or torso articulation change, significant shifts in force distribution occur.     

The spring-mass model for running and hopping

A simple spring-mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function of speed. The bouncing mechanism itself results in a confinement of the free parameter space where solutions can be found. In particular, bouncing frequency and vertical displacement are closely related. Only a few parameters, such as the vector of the specific landing velocity and the specific leg length, are sufficient to determine the point of operation of the system. There are more physiological constraints than independent parameters. As constraints limit the parameter space where hopping is possible, they must be tuned to each other in order to allow for hopping at all. Within the range of physiologically possible hopping frequencies, a human hopper selects a frequency where the largest amount of energy can be delivered and still be stored elastically. During running and hopping animals use flat angles of the landing velocity resulting in maximum contact length. In this situation ground reaction force is proportional to specific contact time and total displacement is proportional to the square of the step duration. Contact time and hopping frequency are not simply determined by the natural frequency of the spring-mass system, but are influenced largely by the vector of the landing velocity. Differences in the aerial phase or in the angle of the landing velocity result in the different kinematic and dynamic patterns observed during running and hopping. Despite these differences, the model predicts the mass specific energy fluctuations of the center of mass per distance to be similar for runners and hoppers and similar to empirical data obtained for animals of various size.     

Vertical stiffness during one-legged hopping with and without using a running-specific prosthesis

Although athletes with unilateral below-the-knee amputations (BKAs) generally use their affected leg, including their prosthesis, as their take-off leg for the long jump, little is known about the spring-like leg behavior and stiffness regulation of the affected leg. The purpose of this study was to investigate vertical stiffness during one-legged hopping in an elite-level long jump athlete with a unilateral BKA. We used the spring-mass model to calculate vertical stiffness, which equals the ratio of maximum vertical ground reaction force to maximum center of mass displacement, while the athlete with a BKA hopped on one leg at a range of frequencies. Then, we compared the vertical stiffness of this athlete to seven non-amputee elite-level long-jumpers. We found that from 1.8 to 3.4 Hz, the vertical stiffness of the unaffected leg for an athlete with a BKA increases with faster hopping frequencies, but the vertical stiffness of the affected leg remains nearly constant across frequencies. The athlete with a BKA attained the desired hopping frequencies at 2.2 and 2.6 Hz, but was unable to match the lowest (1.8 Hz) and two highest frequencies (3.0 and 3.4 Hz) using his affected leg. We also found that at 2.5 Hz, unaffected leg vertical stiffness was 15% greater than affected leg vertical stiffness, and the vertical stiffness of non-amputee long-jumpers was 32% greater than the affected leg vertical stiffness of an athlete with a BKA. The results of the present study suggest that the vertical stiffness regulation strategy of an athlete with a unilateral BKA is not the same in the unaffected versus affected legs, and compared to non-amputees.     

Center of pressure and center of mass behavior during gait initiation on inclined surfaces: A statistical parametric mapping analysis

This study analyzed gait initiation (GI) on inclined surfaces with 68 young adult subjects of both sexes. Ground reaction forces and moments were collected using two AMTI force platforms, of which one was in a horizontal position and the other was inclined by 8% in relation to the horizontal plane. Departing from a standing position, each participant executed three trials in the following conditions: horizontal position (HOR), inclined position at ankle dorsi-flexion (UP), and inclined position at ankle plantar-flexion (DOWN). Statistical parametric mapping analysis was performed over the entire center of pressure (COP) and center of mass (COM) time series. COP excursion did not show significant differences in the medial-lateral (ML) direction in both inclined conditions, but it was greater in the anterior-posterior (AP) direction for both inclined conditions. COP velocities are smaller in discrete portions of GI for the UP and DOWN conditions. COM displacement was greater in the ML direction during anticipatory postural adjustments (APA) in the UP condition, and COM moves faster in the ML direction during APA in the UP condition but slower at the end of GI for both the UP and the DOWN conditions. The COP-COM vector showed a greater angle in the DOWN condition. We observed changes for COP and COM in GI in both the UP and the DOWN conditions, with the latter showing changes for a great extent of the task. Both the UP and the DOWN conditions showed increased COM displacement and velocity. The predominant characteristic during GI on inclined surfaces, including APA, appears to be the displacement of the COM.     

Calculation of vertical ground reaction force estimates during running from positional data

The purpose of this study was to calculate, as a function of time, segmental contributions to the vertical ground reaction force F_z from positional data for the landing phase in running. In order to evaluate the accuracy of the method, time histories of the sum of the segmental contributions were compared to F_z(t) measured directly by a force plate.

The human body was modeled as a system of seven rigid segments. During running the positions of markers defining these segments were monitored using a video analysis system operating at 200 Hz. Special care was taken to minimize marker movement relative to the mass centers of segments, and low-pass cutoff frequencies of 50 Hz (markers defining leg segments) and 15–20 Hz (markers defining upper body) were used in filtering the position time histories so as to ensure that high signal frequencies were preserved. The magnitude of the high-frequency peak in F_z, also known as ‘impact force peak’, was estimated with errors <10%, while the time of occurrence of the peak was estimated with errors <5 ms. It would appear that the positional data were sufficiently accurate to be used for calculation of intersegmental forces and moments during the landing phase in running.

Analysis of the segmental contributions to F_z(t) revealed that the first peak in F_z has its origin in the contribution of support leg segments, while its magnitude is determined primarily by the contribution of the rest of the body. These contributions could be varied independently by changing running style. It follows that if the possible relationship between ‘impact force peaks’ and injuries is to be investigated, or if the effects of running shoe and surface construction on these force peaks are to be evaluated, the calculation of segmental contributions to F_z(t) is a more suitable approach than measuring only F_z(t).     

Determining finger segmental centers of rotation in flexion-extension based on surface marker measurement

This paper describes the development of a novel algorithm for deriving finger segmental center of rotation (COR) locations during flexion-extension from measured surface marker motions in vivo. The algorithm employs an optimization routine minimizing the time-variance of the internal link lengths, and incorporates an empirically quantifiable relationship between the local movement of a surface marker around a joint (termed "surface marker excursion") and the joint flexion-extension. The latter relationship constrains and simplifies the optimization routine to make it computationally tractable. To empirically investigate this relationship and test the proposed algorithm, an experiment was conducted, in which hand cylinder-grasping movements were performed by 24 subjects (12 males and 12 females). Spherical retro-reflective markers were placed at various surface landmarks on the dorsal aspect of each subject's right (grasping) hand, and were measured during the movements by an opto-electronic system. Analysis of experimental data revealed a highly linear relationship between the "surface marker excursion" and the marker-defined flexion-extension angle: the average R(2) in linear regression ranged from 0.89 to 0.97. The algorithm successfully determined the CORs of the distal interphalangeal, proximal interphalangeal, and metacarpophalangeal joints of digits 2-5 during measured motions. The derived CORs appeared plausible as examined in terms of the physical locations relative to surface marker trajectories and the congruency across different joints and individuals.     

Wrist and digital joint motion produce unique flexor tendon force and excursion in the canine forelimb

The force and excursion within the canine digital flexor tendons were measured during passive joint manipulations that simulate those used during rehabilitation after flexor tendon repair and during active muscle contraction, simulating the active rehabilitation protocol. Tendon force was measured using a small buckle placed upon the tendon while excursion was measured using a suture marker and video analysis method. Passive finger motion imposed with the wrist flexed resulted in dramatically lower tendon force (approximately 5 N) compared to passive motion imposed with the wrist extended (approximately 17 N). Lower excursions were seen at the level of the proximal interphalangeal joint with the wrist flexed (approximately 1.5 mm) while high excursion was observed when the wrist was extended or when synergistic finger and wrist motion were imposed (approximately 3.5 mm). Bivariate discriminant analysis of both force and excursion data revealed a natural clustering of the data into three general mechanical paradigms. With the wrist extended and with either one finger or four fingers manipulated, tendons experienced high loads of approximately 1500 g and high excursions of approximately 3.5 mm. In contrast, the same manipulations performed with the wrist flexed resulted in low tendon forces (4-8 N) and low tendon excursions of approximately 1.5 mm. Synergistic wrist and finger manipulation provided the third paradigm where tendon force was relatively low (approximately 4 N) but excursion was as high as those seen in the groups which were manipulated with the wrist extended. Active muscle contraction produced a modest tendon excursion (approximately 1 mm) and high or low tendon force with the wrist extended or flexed, respectively. These data provide the basis for experimentally testable hypotheses with regard to the factors that most significantly affect functional recovery after digital flexor tendon injury and define the normal mechanical operating characteristics of these tendons.     

Ability of the planar spring-mass model to predict mechanical parameters in running humans

The planar spring-mass model is a simple mathematical model of bouncing gaits, such as running, trotting and hopping. Although this model has been widely used in the study of locomotion, its accuracy in predicting locomotor mechanics has not been systematically quantified. We determined the percent error of the model in predicting 10 locomotor parameters in running humans by comparing the model predictions to experimental data from humans running in normal gravity and simulated reduced gravity. We tested the hypotheses that the model would overestimate horizontal impulse and the change in mechanical energy of the centre of mass (COM) during stance. The model provided good predictions of stance time, vertical impulse, contact length, duty factor, relative stride length and relative peak force. All predictions of these parameters were within 20% of measured values and at least 90% of predictions of each parameter were within 10% of measured values (median absolute errors: <7%). This suggests that the model incorporates all features of running humans that have a significant influence upon these six parameters. As simulated gravity level decreased, the magnitude of the errors in predicting each of these parameters either decreased or stayed constant, indicating that this is a good model of running in simulated reduced gravity. As hypothesised, horizontal impulse and change in mechanical energy of the COM during stance were overestimated (median absolute errors: 43.6% and 26.2%, respectively). Aerial time and peak vertical COM displacement during stance were also systematically overestimated (median absolute errors: 17.7% and 22.9%, respectively). Care should be taken to ensure that the model is used only to investigate parameters which it can predict accurately. It would be useful to extend this analysis to other species and gaits.     

Mechanical coupling between transverse plane pelvis and thorax rotations during gait is higher in people with low back pain

This study investigated whether people with low back pain (LBP) reduce variability of movement between the pelvis and thorax (trunk) in the transverse plane during gait at different speeds compared to healthy controls. Thirteen people with chronic LBP and twelve healthy controls walked on a treadmill at speeds from 0.5 to 1.72 m/s, with increments of 0.11 m/s. Step-to-step variability of the trunk, pelvis, and thorax rotations were calculated. Step-to-step deviations of pelvis and thorax rotations from the average pattern (residual rotations) were correlated to each other, and the linear regression coefficients between these deviations calculated. Spectral analysis was used to determine the frequencies of the residual rotations, to infer the relation of reduced trunk variability to trunk stiffness and/or damping. Variability of trunk motion (thorax relative to pelvis) was lower (P=0.02), covariance between the residual rotations of pelvis and thorax motions was higher (P=0.03), and the linear regression coefficients were closer to 1 (P=0.05) in the LBP group. Most power of segmental residual rotations was below stride frequency (~1 Hz). In this frequency range, trunk residual rotations had less power than pelvis or thorax residual rotations. These data show that people with LBP had lower variability of trunk rotations, as a result of the coupling of deviations of residual rotations in one segment to deviations of a similar shape (correlation) and amplitude (regression coefficient) in the other segment. These results support the argument that people with LBP adopt a protective movement strategy, possibly by increased trunk stiffness.     

Comparison of three methods to estimate the center of mass during balance assessment

Evaluation of postural control is generally based on the interpretation of the center of pressure (COP) and the center of mass (COM) time series. The purpose of this study is to compare three methods to estimate the COM which are based on different biomechanical considerations. These methods are: (1) the kinematic method; (2) the zero-point-to-zero-point double integration technique (GLP) and (3) the COP low-pass filter method (LPF). The COP and COM time series have been determined using an experimental setup with a force plate and a 3D kinematic system on six healthy young adult subjects during four different 30 s standing tasks: (a) quiet standing; (b) one leg standing; (c) voluntary oscillation about the ankles and (d) voluntary oscillation about the ankles and hips. To test the difference between the COM trajectories, the root mean square (RMS) differences between each method (three comparisons) were calculated. The RMS differences between kinematic-LPF and GLP-LPF are significantly larger than kinematic-GLP. Our results show that the GLP method is comparable to the kinematic method. Both agree with the unified theory of balance during upright stance. The GLP method is attractive in the clinical perspective because it requires only a force plate to determine the COP-COM variable, which has been demonstrated to have a high reliability.