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ABSTRACT: Leonard, C and Challis, JH. The expression of the force-length properties of the gastrocnemius in ice hockey players. J Strength Cond Res 38(9): 1635-1639, 2024-Although the force-length properties of muscles have an approximately parabolic shape, in vivo not all the force-length curve is necessarily used, only a portion of the curve is expressed (i.e., ascending, plateau, or descending regions of the force-length curve). The number of sarcomeres in series in a muscle fiber affects the expressed section of the force-length curve; this number can be influenced by the nature of activity the muscle experiences. It was hypothesized that the reduced range of motion ice skaters experience, because of the constraints imposed by the ice skates, that the gastrocnemii of a group of ice skaters will adapt and will more frequently express in vivo the plateau of the force-length curve compared with a nonspecifically trained population. Twelve NCAA Division I female ice hockey players volunteered for the study. Their maximum isometric ankle plantarflexion moments were recorded for 6 ankle angles and 3 knee angles. Exploiting the biarticularity of the gastrocnemius, the expressed sections of the subject's force-length curves were determined. Six subjects operated over the ascending limb, 5 operated over the plateau region, and 1 over the descending limb. This frequency of distribution for ice hockey players was statistically different to the distribution measured for 28 nonspecifically trained subjects from a previous study ( p < 0.0001). These results likely reflect morphological differences between the 2 groups for their gastrocnemii, potentially arising from the limited range of gastrocnemius length feasible in ice-skates. These results have implications for the specificity of their off-ice training for ice hockey players.

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The human foot's arch is thought to be beneficial for efficient gait. This study addresses the extent to which arch stiffness changes alter the metabolic energy requirements of human gait. Computational musculoskeletal simulations of steady state walking using direct collocation were performed. Across a range of foot arch stiffnesses, the metabolic cost of transport decreased by less than 1% with increasing foot arch stiffness. Increasing arch stiffness increased the metabolic efficiency of the triceps surae during push-off, but these changes were almost entirely offset by other muscle groups consuming more energy with increasing foot arch stiffness.

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The primary purpose of this study was to compare the ankle joint mechanics, during the stance phase of running, computed with a multi-segment foot model (MULTI; three segments) with a traditional single segment foot model (SINGLE). Traditional ankle joint models define all bones between the ankle and metatarsophalangeal joints as a single rigid segment (SINGLE). However, this contrasts with the more complex structure and mobility of the human foot, recent studies of walking using more multiple-segment models of the human foot have highlighted the errors arising in ankle kinematics and kinetics by using an oversimplified model of the foot. This study sought to compare whether ankle joint kinematics and kinetics during running are similar when using a single segment foot model (SINGLE) and a multi-segment foot model (MULTI). Seven participants ran at 3.1 m/s while the positions of markers on the shank and foot were tracked and ground reaction forces were measured. Ankle joint kinematics, resultant joint moments, joint work, and instantaneous joint power were determined using both the SINGLE and MULTI models. Differences between the two models across the entire stance phase were tested using statistical parametric mapping. During the stance phase, MULTI produced ankle joint angles that were typically closer to neutral and angular velocities that were reduced compared with SINGLE. Instantaneous joint power (p<0.001) and joint work (p<0.001) during late stance were also reduced in MULTI compared with SINGLE demonstrating the importance of foot model topology in analyses of the ankle joint during running. This study has highlighted that considering the foot as a rigid segment from ankle to MTP joint produces poor estimates of the ankle joint kinematics and kinetics, which has important implications for understanding the role of the ankle joint in running.

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Image-based motion-analysis systems typically place markers on the bodies of interest. The error in determining segment attitude from these markers is a function the marker position errors, the number of markers, and the spatial distribution of the markers. The spatial distribution includes two factors: the mean square distance of these markers to their geometric center, and the degree of anisotropy in the marker distribution. The purposes of this study were to: (1) present a metric which quantifies the marker spatial distribution (anisotropic to isotropic) and (2) examine the influence of marker distribution on the accuracy of rigid body attitude determination. To test the influence of the marker distribution on body attitude determination 1000 criterion attitudes were determined. These attitudes then had to be estimated for two marker sets for which the marker distribution metric, noise levels, and root-mean-square distance of the markers were systematically varied. Anisotropic marker distributions were shown to negatively affect the accuracy of attitude determination. The influence of anisotropic marker distributions on attitude accuracy could be blunted by increasing the number of markers, increasing the root-mean-square distance of markers from their geometric center, and reducing noise levels. These results have implications for the measurement of the attitudes of body segments. For example, the ability to have a large spatial distribution of markers and a large number of markers to maximize the measurement accuracy of segment attitude is different for a small segment such as the fifth metacarpal compared with the thigh.

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The presence of successful female role models in biomechanics can encourage girls, women, and other underrepresented groups in STEM fields to pursue and remain within the discipline. It is, therefore, vital that women and their contributions to the field are publicly visible and recognized across all areas of professional biomechanical societies, such as the International Society of Biomechanics (ISB). Enhancing the visibility of female role models in biomechanics can act to mitigate current bias and stereotyping in the discipline by broadening what it looks like to be a biomechanist. Unfortunately, women are not publicly visible in many aspects of ISB activities, and finding details of women's contributions to ISB, particularly during ISB's formative years, is challenging. This review article aims to raise the visibility of female biomechanists, particularly women in ISB leadership positions who have helped shape the Society over the past 50 years. We summarize the unique backgrounds and contributions of some of these pioneering women who blazed pathways for other female biomechanists. We also recognize the women who were charter members of ISB, women who served on ISB Executive Councils and the portfolios they have held, women who have received the highest awards of the Society, and women awarded a Fellowship of ISB. Practical strategies to enhance women's participation in biomechanics also are presented so that women can thrive and progress in ISB leadership positions and awards and, in turn, serve as positive role models to encourage girls and women to pursue and remain within this unique discipline.

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The arch of the human foot has historically been likened to either a truss, a rigid lever, or a spring. Growing evidence indicates that energy is stored, generated, and dissipated actively by structures crossing the arch, suggesting that the arch can further function in a motor- or spring-like manner. In the present study, participants walked, ran with a rearfoot strike pattern, and ran with a non-rearfoot strike pattern overground while foot segment motions and ground reaction forces were recorded. To quantify the midtarsal joint's (i.e., arch's) mechanical behavior, a brake-spring-motor index was defined as the ratio between midtarsal joint net work and the total magnitude of joint work. This index was statistically significantly different between each gait condition. Index values decreased from walking to rearfoot strike running to non-rearfoot strike running, indicating that the midtarsal joint was most motor-like when walking and most spring-like in non-rearfoot running. The mean magnitude of elastic strain energy stored in the plantar aponeurosis mirrored the increase in spring-like arch function from walking to non-rearfoot strike running. However, the behavior of the plantar aponeurosis could not account for a more motor-like arch in walking and rearfoot strike running, given the lack of main effect of gait condition on the ratio between net work and total work performed by force in the plantar aponeurosis about the midtarsal joint. Instead, the muscles of the foot are likely altering the motor-like mechanical function of the foot's arch, the operation of these muscles between gait conditions warrants further investigation.

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Human foot rigidity is thought to provide a more effective lever with which to push against the ground. Tension of the plantar aponeurosis (PA) with increased metatarsophalangeal (MTP) joint dorsiflexion (i.e., the windlass mechanism) has been credited with providing some of this rigidity. However, there is growing debate on whether MTP joint dorsiflexion indeed increases arch rigidity. Further, the arch can be made more rigid independent of additional MTP joint dorsiflexion (e.g., when walking with added mass). The purpose of the present study was therefore to compare the influence of increased MTP joint dorsiflexion with the influence of added mass on the quasi-stiffness of the midtarsal joint in walking. Participants walked with a rounded wedge under their toes to increase MTP joint dorsiflexion in the toe-wedge condition, and wore a weighted vest with 15% of their body mass in the added mass condition. Plantar aponeurosis behavior, foot joint energetics, and midtarsal joint quasi-stiffness were compared between conditions to analyze the mechanisms and effects of arch rigidity differences. Midtarsal joint quasi-stiffness was increased in the toe-wedge and added mass conditions compared with the control condition (both p < 0.001). In the toe-wedge condition, the time-series profiles of MTP joint dorsiflexion and PA strain and force were increased throughout mid-stance (p < 0.001). When walking with added mass, the time-series profile of force in the PA did not increase compared with the control condition although quasi-stiffness did, supporting previous evidence that the rigidity of the foot can be actively modulated. Finally, more mechanical power was absorbed (p = 0.006) and negative work was performed (p < 0.001) by structures distal to the rearfoot in the toe-wedge condition, a condition which displayed increased midtarsal joint quasi-stiffness. This indicates that a more rigid foot may not necessarily transfer power to the ground more efficiently.

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Soft tissue moves relative to the underlying bone during locomotion. Research has shown that soft tissue motion has an effect on aspects of the dynamics of running; however, little is known about the effects of soft tissue motion on the joint kinetics. In the present study, for a single subject, soft tissue motion was modeled using wobbling components in an inverse dynamics analysis to access the effects of the soft tissue on joint kinetics at the knee and hip. The added wobbling components had little effect on the knee joint kinetics, but large effects on the hip joint kinetics. In particular, the hip joint power and net negative and net positive mechanical work at the hip was greatly underestimated when calculated with the model without wobbling components compared with that of the model with wobbling components. For example, for low-frequency wobbling conditions, the magnitude of the peak hip joint moments were 50% greater when computed accounting the wobbling masses compared with a rigid body model, while for high-frequency wobbling conditions, the peaks were within 15%. The present study suggests that soft tissue motion should not be ignored during inverse dynamics analyses of running.

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In a state-space representation of the equations of motion for a system of rigid bodies one component of these equations is the so-called inertia matrix. This matrix can be used for inverse dynamics and its inversion is necessary to perform direct dynamics analyses, and to perform induced acceleration analyses. The contents of the inertia matrix are a function of the lengths of the segments, the locations of the centers of masses, segment masses, segment moments of inertia, and joint angles. It is demonstrated that the inertia matrix is an ill-conditioned matrix meaning that, for example, small errors in joint moments cause correspondingly larger errors in the joint accelerations computed using the matrix. The ill-condition of the matrix can be quantified by computing its condition number; the magnitude of the error is bounded by the condition number. It is demonstrated for a two-rigid body system representing the upper-limb that the configuration of the system influences the magnitude of the condition number, and that because the mass and moment of inertia of the distal segment is smaller than the proximal segment a relatively low condition number is produced. For a three-segment system representing the shanks, thighs, and HAT (head, arms, and trunk) the closer each segment rotated towards the adjacent segment the lower the condition number. The magnification of errors due to the inertia matrix arise from the inertial properties of the human body segments and their configuration, not from errors per se in the components of that matrix.

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Human running can be simulated using a simple model called the spring-loaded inverted pendulum (SLIP). The SLIP model predicts some aspects of running including the self-stabilizing properties of running. In human locomotion energy is dissipated due to the passive motion of the soft tissue. However, little is known about the effects of this energy dissipation on the dynamics of running. This study utilizes a SLIP model with an additional spring-mass-damper system to study the effects of energy dissipation due to an additional wobbling mass on the self-stabilizing properties of human running. It was found that the additional spring-mass-damper system increased the self-stabilizing properties of the SLIP model and increased its robustness to perturbations. This suggests that increasing stability is one of the effects of energy dissipation due to the passive motion of a wobbling mass during human running.

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Time-differentiating kinematic signals from optical motion capture amplifies the inherent noise content of those signals. Commonly, biomechanists address this problem by applying a Butterworth filter with the same cutoff frequency to all noisy displacement signals prior to differentiation. Nonstationary signals, those with time-varying frequency content, are widespread in biomechanics (eg, those containing an impact) and may necessitate a different filtering approach. A recently introduced signal filtering approach wherein signals are divided into sections based on their energy content and then Butterworth filtered with section-specific cutoff frequencies improved second derivative estimates in a nonstationary kinematic signal. Utilizing this signal-section filtering approach for estimating running vertical ground reaction forces saw more of the signal's high-frequency content surrounding heel strike maintained without allowing inappropriate amounts of noise contamination in the remainder of the signal. Thus, this signal-section filtering approach resulted in superior estimates of vertical ground reaction forces compared with approaches that either used the same filter cutoff frequency across the entirety of each signal or across the entirety of all signals. Filtering kinematic signals using this signal-section filtering approach is useful in processing data from tasks containing an impact when accurate signal second derivative estimation is of interest.

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To examine segment and joint attitudes when using image-based motion capture, it is necessary to determine the rigid body transformation parameters from an inertial reference frame to a reference frame fixed in a body segment. Determine the rigid body transformation parameters must account for errors in the coordinates measured in both reference frames, a total least-squares problem. This study presents a new derivation that shows that a singular value decomposition-based method provides a total least-squares estimate of rigid body transformation parameters. The total least-squares method was compared with an algebraic method for determining rigid body attitude (TRIAD method). Two cases were examined: case 1 where the positions of a marker cluster contained noise after the transformation, and case 2 where the positions of a marker cluster contained noise both before and after the transformation. The white noise added to position data had a standard deviation from zero to 0.002 m, with 101 noise levels examined. For each noise level, 10 000 criterion attitude matrices were generated. Errors in estimating rigid body attitude were quantified by computing the angle, error angle, required to align the estimated rigid body attitude with the actual rigid body attitude. For both methods and cases, as the noise level increased the error angle increased, with errors larger for case 2 compared with case 1. The singular value decomposition (SVD)-based method was superior to the TRIAD algorithm for all noise levels and both cases, and provided a total least-squares estimate of body attitude.

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Humans are made up of mostly soft tissue that vibrates during locomotion. This vibration has been shown to store and dissipate energy during locomotion. However, the effects of soft tissue vibration (wobbling masses) on the dynamics of bipedal walking have not been assessed in terms of stability. Given that much of the human body is vibrating just following foot-ground contact, it may have dynamic implications on the stability of walking. A rigid bipedal walker and a bipedal walker with soft tissue were simulated to quantify the effects of soft tissue vibration on gait periodicity, orbital stability, global stability, and robustness to uneven terrain. It was found that moderate amounts of energy dissipation resulted in much more stable walking dynamics relative to that of a rigid bipedal walker.

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The three-dimensional description of rigid body kinematics is a key step in many studies in biomechanics. There are several options for describing rigid body orientation including Cardan angles, Euler angles, and quaternions; the utility of quaternions will be reviewed and elaborated. The orientation of a rigid body or a joint between rigid bodies can be described by a quaternion which consists of four variables compared with Cardan or Euler angles (which require three variables). A quaternion, q = (q 0, q 1, q 2, q 3), can be considered a rotation (Ω = 2 cos-1(q 0)), about an axis defined by a unit direction vector q 1 / sin Ω 2 q 2 / sin Ω 2 q 3 / sin Ω 2 . The quaternion, compared with Cardan and Euler angles, does not suffer from singularities or Codman's paradox. Three-dimensional angular kinematics are defined on the surface of a unit hypersphere which means numerical procedures for orientation averaging and interpolation must take account of the shape of this surface rather than assuming that Euclidean geometry based procedures are appropriate. Numerical simulations demonstrate the utility of quaternions for averaging three-dimensional orientations. In addition the use of quaternions for the interpolation of three-dimensional orientations, and for determining three-dimensional orientation derivatives is reviewed. The unambiguous nature of defining rigid body orientation in three-dimensions using a quaternion, and its simple averaging and interpolation gives it great utility for the kinematic analysis of human movement.

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Rigid body attitude and single-joint kinematics are typically expressed using three Cardan angles which represent rotations in anatomical planes. It was recently shown in the Biomechanics literature that Cardan angles inaccurately estimate true mean attitude due to an important mathematical inadequacy: attitude under-representation; at least four quantities are needed to unambiguously specify attitude. Directional statistics, which is the multivariate generalization of (univariate) circular statistics, solves this problem using four-dimensional unit vectors and the mathematics of hyperspherical geometry. The purpose of this study was to compare the results of directional analysis to the results of uni- and multi-variate Cardan analysis for representative joint kinematic data during gait. We analyzed hip, knee and pelvis data from three open datasets and report exemplary results for knee kinematics in v-cut vs. side shuffle tasks. We also conducted Monte Carlo simulations, using synthetic data with precisely controlled true angular effects, to systematically compare directional and Cardan analyses. Results show that directional analysis yielded considerably smaller p values (p<0.03) than Cardan analysis (p>0.055) for the exemplary dataset. Simulation results confirmed that directional analysis is considerably more powerful (i.e., much more able to detect true angular effects) than both uni- and multi-variate Cardan analysis. These results suggest that directional statistics should be used to analyse attitude, including 3D joint kinematics, to avoid false negatives.

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Computing time derivatives is a frequent stage in the processing of biomechanical data. Unfortunately, differentiation amplifies the high frequency noise inherent within the signal hampering the accuracy of signal derivatives. A low-pass Butterworth filter is commonly used to reduce the sampled signal noise prior to differentiation. One hurdle lies in selecting an appropriate filter cut-off frequency which retains the signal of interest while reducing deleterious noise. Most biomechanics data processing approaches utilize the same cut-off frequency for the whole sampled signal, but the frequency components of a signal can vary with time. To accommodate such signals, the Automatic Segment Filtering Procedure (ASFP) is proposed which uses different automatically determined Butterworth filter cut-off frequencies for separate segments of a sampled signal. The Teager-Kaiser Energy Operator of the signal is computed and used to determine segments of the signal with different energy content. The Autocorrelation-Based Procedure (ABP) is used on each of these segments to determine filter cut-off frequencies. This new procedure was evaluated by estimating acceleration values from the test data set of Dowling (1985). The ASFP produced a root mean square error (RMSE) of 16.4 rad s-2 (26.6%) whereas a single ABP determined filter cut-off frequency applied to the whole Dowling (1985) signal, representing the common approach, produced a RMSE of 25.5 rad s-2 (41.4%). As a point of comparison, a Generalized Cross-Validated Quintic Spline, a common non-Butterworth filter, produced a RMSE of 23.6 rad s-2 (38.4%). This new automatic approach is advantageous in biomechanics for preserving high frequency content of non-stationary signals.

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Three-dimensional angular kinematics exist on the surface of a unit hypersphere, therefore the average attitude cannot always be accurately computed by averaging Cardan angles. This study derives and evaluates a method for determining average body attitude, by exploiting the singular value decomposition of the average of a set of attitude matrices. To test the method 1000 criterion attitudes were determined, and for each attitude 10 noisy attitude matrices generated. The new method and the averaging of Cardan angles extracted from the 10 noisy attitude matrices were evaluated for their ability to estimate the criterion attitude. At low attitude variance the two approaches provided equivalent results, but with increasing attitude variance levels the new procedure was superior. The method provides superior estimates of average attitude compared with averaging Cardan angles, by accounting for the geometric distribution of rigid body attitudes on the surface of a unit hypersphere.

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The study examined the sensitivity of two musculoskeletal models to the parameters describing each model. Two different models were examined: a phenomenological model of human jumping with parameters based on live subject data, and the second a model of the First Dorsal Interosseous with parameters based on cadaveric measurements. Both models were sensitive to the model parameters, with the use of mean group data not producing model outputs reflective of either the performance of any group member or the mean group performance. These results highlight the value of subject specific model parameters, and the problems associated with model validation.

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