Adaptive smartphone-based sensor fusion for estimating competitive rowing kinematic metrics.

Competitive rowing highly values boat position and velocity data for real-time feedback during training, racing and post-training analysis. The ubiquity of smartphones with embedded position (GPS) and motion (accelerometer) sensors motivates their possible use in these tasks. In this paper, we investigate the use of two real-time digital filters to achieve highly accurate yet reasonably priced measurements of boat speed and distance traveled. Both filters combine acceleration and location data to estimate boat distance and speed; the first using a complementary frequency response-based filter technique, the second with a Kalman filter formalism that includes adaptive, real-time estimates of effective accelerometer bias. The estimates of distance and speed from both filters were validated and compared with accurate reference data from a differential GPS system with better than 1 cm precision and a 5 Hz update rate, in experiments using two subjects (an experienced club-level rower and an elite rower) in two different boats on a 300 m course. Compared with single channel (smartphone GPS only) measures of distance and speed, the complementary filter improved the accuracy and precision of boat speed, boat distance traveled, and distance per stroke by 44%, 42%, and 73%, respectively, while the Kalman filter improved the accuracy and precision of boat speed, boat distance traveled, and distance per stroke by 48%, 22%, and 82%, respectively. Both filters demonstrate promise as general purpose methods to substantially improve estimates of important rowing performance metrics.

Correction: Validation of a Laboratory Method for Evaluating Dynamic Properties of Reconstructed Equine Racetrack Surfaces.

[This corrects the article DOI: 10.1371/journal.pone.0050534.].

A bioenergetic model for simulating athletic performance of intermediate duration.

Simulating factors affecting human athletic performance, including fatigue, requires a dynamic model of the bioenergetic capabilities of the athlete. To address general cases, the model needs inputs, outputs, and states with a set of differential equations describing how the inputs affect the states and outputs as functions of time. We improve an existing phenomenological muscle model, removing unnecessarily fast dynamic behavior, adding force-velocity dependence, and generalizing it to task level activities. This makes it more suitable for simulating and calculating optimal strategies of athletic events of medium duration (longer than a sprint but shorter than a marathon). To examine the validity and limitations of the model, parameters have been identified from numerical fits to published experimental data.

An object oriented implementation of the Yeadon human inertia model.

We present an open source software implementation of a popular mathematical method developed by M.R. Yeadon for calculating the body and segment inertia parameters of a human body. The software is written in a high level open source language and provides three interfaces for manipulating the data and the model: a Python API, a command-line user interface, and a graphical user interface. Thus the software can fit into various data processing pipelines and requires only simple geometrical measures as input.

Validation of a laboratory method for evaluating dynamic properties of reconstructed equine racetrack surfaces.

BACKGROUND: Racetrack surface is a risk factor for racehorse injuries and fatalities. Current research indicates that race surface mechanical properties may be influenced by material composition, moisture content, temperature, and maintenance. Race surface mechanical testing in a controlled laboratory setting would allow for objective evaluation of dynamic properties of surface and factors that affect surface behavior. OBJECTIVE: To develop a method for reconstruction of race surfaces in the laboratory and validate the method by comparison with racetrack measurements of dynamic surface properties. METHODS: Track-testing device (TTD) impact tests were conducted to simulate equine hoof impact on dirt and synthetic race surfaces; tests were performed both in situ (racetrack) and using laboratory reconstructions of harvested surface materials. Clegg Hammer in situ measurements were used to guide surface reconstruction in the laboratory. Dynamic surface properties were compared between in situ and laboratory settings. Relationships between racetrack TTD and Clegg Hammer measurements were analyzed using stepwise multiple linear regression. RESULTS: Most dynamic surface property setting differences (racetrack-laboratory) were small relative to surface material type differences (dirt-synthetic). Clegg Hammer measurements were more strongly correlated with TTD measurements on the synthetic surface than the dirt surface. On the dirt surface, Clegg Hammer decelerations were negatively correlated with TTD forces. CONCLUSIONS: Laboratory reconstruction of racetrack surfaces guided by Clegg Hammer measurements yielded TTD impact measurements similar to in situ values. The negative correlation between TTD and Clegg Hammer measurements confirms the importance of instrument mass when drawing conclusions from testing results. Lighter impact devices may be less appropriate for assessing dynamic surface properties compared to testing equipment designed to simulate hoof impact (TTD). POTENTIAL RELEVANCE: Dynamic impact properties of race surfaces can be evaluated in a laboratory setting, allowing for further study of factors affecting surface behavior under controlled conditions.

Optimization of the visco-elastic parameters describing the heel-region of a prosthesis.

Although compliance (visco-elasticity) of a prosthesis has the potential to affect clinically relevant aspects of a lower extremity amputee's gait, it is currently unknown what the compliant parameter values should be. Here, a simple dynamical model is used to approximate walking with a compliant prosthesis. An exhaustive search is used to identify the optimal compliant element parameter set in terms of the model's stability as measured by the reciprocal of the gait sensitivity norm (rGSN). We identified a parameter set yielding a 17% larger rGSN than the best commercially available prosthesis; however, this is unlikely to be the global optimum for the physically realizable visco-elastic parameter space. Due to the nonlinear effects of the compliant elements, it is difficult to make generalizations about speed and step length, such difficulties are not present with simpler contact models. However, there is some evidence to support a possible trade-off between efficiency and stability.

Individualized optimal release angles in discus throwing.

The purpose of this study was to determine individualized optimal release angles for elite discus throwers. Three-dimensional coordinate data were obtained for at least 10 competitive trials for each subject. Regression relationships between release speed and release angle, and between aerodynamic distance and release angle were determined for each subject. These relationships were linear with subject-specific characteristics. The subject-specific relationships between release speed and release angle may be due to subjects' technical and physical characteristics. The subject-specific relationships between aerodynamic distance and release angle may be due to interactions between the release angle, the angle of attack, and the aerodynamic distance. Optimal release angles were estimated for each subject using the regression relationships and equations of projectile motion. The estimated optimal release angle was different for different subjects, and ranged from 35 degrees to 44 degrees . The results of this study demonstrate that the optimal release angle for discus throwing is thrower-specific. The release angles used by elite discus throwers in competition are not necessarily optimal for all discus throwers, or even themselves. The results of this study provide significant information for understanding the biomechanics of discus throwing techniques.

Hoof accelerations and ground reaction forces of Thoroughbred racehorses measured on dirt, synthetic, and turf track surfaces.

OBJECTIVE: To compare hoof acceleration and ground reaction force (GRF) data among dirt, synthetic, and turf surfaces in Thoroughbred racehorses. ANIMALS: 3 healthy Thoroughbred racehorses. PROCEDURES: Forelimb hoof accelerations and GRFs were measured with an accelerometer and a dynamometric horseshoe during trot and canter on dirt, synthetic, and turf track surfaces at a racecourse. Maxima, minima, temporal components, and a measure of vibration were extracted from the data. Acceleration and GRF variables were compared statistically among surfaces. RESULTS: The synthetic surface often had the lowest peak accelerations, mean vibration, and peak GRFs. Peak acceleration during hoof landing was significantly smaller for the synthetic surface (mean + or - SE, 28.5g + or - 2.9g) than for the turf surface (42.9g + or - 3.8g). Hoof vibrations during hoof landing for the synthetic surface were < 70% of those for the dirt and turf surfaces. Peak GRF for the synthetic surface (11.5 + or - 0.4 N/kg) was 83% and 71% of those for the dirt (13.8 + or - 0.3 N/kg) and turf surfaces (16.1 + or - 0.7 N/kg), respectively. CONCLUSIONS AND CLINICAL RELEVANCE: The relatively low hoof accelerations, vibrations, and peak GRFs associated with the synthetic surface evaluated in the present study indicated that synthetic surfaces have potential for injury reduction in Thoroughbred racehorses. However, because of the unique material properties and different nature of individual dirt, synthetic, and turf racetrack surfaces, extending the results of this study to encompass all track surfaces should be done with caution.

Influence of optimization constraints in uneven parallel bar dismount swing simulations.

Forward dynamics simulations of a dismount preparation swing on the uneven parallel bars were optimized to investigate the sensitivity of dismount revolution potential to the maximum bar force before slipping, and to low-bar avoidance. All optimization constraints were classified as 1-anatomical/physiological; limiting maximum hand force on the high bar before slipping, joint ranges of motion and maximum torques, muscle activation/deactivation timing and 2-geometric; avoiding low-bar contact, and requiring minimum landing distance. The gymnast model included torso/head, arm and two leg segments connected by a planar rotating, compliant shoulder and frictionless ball-and-socket hip joints. Maximum shoulder and hip torques were measured as functions of joint angle and angular velocity. Motions were driven by scaling maximum torques by a joint torque activation function of time which approximated the average activation of all muscles crossing the joint causing extension/flexion, or adduction/abduction. Ten joint torque activation values, and bar release times were optimized to maximize dismount revolutions using the downhill simplex method. Low-bar avoidance and maximum bar-force constraints are necessary because they reduce dismount revolution potential. Compared with the no low-bar performance, optimally avoiding the low bar by piking and straddling (abducting) the hips reduces dismount revolutions by 1.8%. Using previously reported experimentally measured peak uneven bar-force values of 3.6 and 4.0 body weight (BW) as optimization constraints, 1.40 and 1.55 revolutions with the body extended and arms overhead were possible, respectively. The bar-force constraint is not active if larger than 6.9 BW, and instead performances are limited only by maximum shoulder and hip torques. Bar forces accelerate the mass center (CM) when performing muscular work to flex/extend the joints, and increase gymnast mechanical energy. Therefore, the bar-force constraint inherently limits performance by limiting the ability to do work and reducing system energy at bar release.

Evaluation of a subject-specific female gymnast model and simulation of an uneven parallel bar swing.

A gymnast model and forward dynamics simulation of a dismount preparation swing on the uneven parallel bars were evaluated by comparing experimental and predicted joint positions throughout the maneuver. The bar model was a linearly elastic spring with a frictional bar/hand interface, and the gymnast model consisted of torso/head, arm and two leg segments. The hips were frictionless balls and sockets, and shoulder movement was planar with passive compliant structures approximated by a parallel spring and damper. Subject-specific body segment moments of inertia, and shoulder compliance were estimated. Muscles crossing the shoulder and hip were represented as torque generators, and experiments quantified maximum instantaneous torques as functions of joint angle and angular velocity. Maximum torques were scaled by joint torque activations as functions of time to produce realistic motions. The downhill simplex method optimized activations and simulation initial conditions to minimize the difference between experimental and predicted bar-center, shoulder, hip, and ankle positions. Comparing experimental and simulated performances allowed evaluation of bar, shoulder compliance, joint torque, and gymnast models. Errors in all except the gymnast model are random, zero mean, and uncorrelated, verifying that all essential system features are represented. Although the swing simulation using the gymnast model matched experimental joint positions with a 2.15cm root-mean-squared error, errors are correlated. Correlated errors indicate that the gymnast model is not complex enough to exactly reproduce the experimental motion. Possible model improvements including a nonlinear shoulder model with active translational control and a two-segment torso would not have been identified if the objective function did not evaluate the entire system configuration throughout the motion. The model and parameters presented in this study can be effectively used to understand and improve an uneven parallel bar swing, although in the future there may be circumstances where a more complex model is needed.

Role of arms in somersaulting from compliant surfaces: a simulation study of springboard standing dives.

The role of arms in compliant-surface jumping for maximizing backward somersault rotations is studied using multi-segment models and is applied to springboard diving. The surface (springboard) is modeled by a rigid bar with a rotational spring with a hinged end and point mass at the tip. Planar four- and five-segment human models are used (with the fifth segment representing the arms) and are driven by torque actuators at the ankle, knee, hip, and shoulder. Each joint torque is the product of maximum isometric torque and three variable functions depending on instantaneous joint angle, angular velocity, and activation level, respectively. Movement simulation starts from a balanced initial posture and ends at jump takeoff. The objective is to find joint torque activation patterns during board contact so that the number of backward rotations in flight is maximized. Kinematic differences in jumps with and without arms are mainly in smaller takeoff vertical velocity and more flexed knee and hip in the former. In both jumps, joint torque/activations are similar in their minor flexion-full extension patterns. Maximum hip torque is larger with arms but maximum knee torque is larger without arms. Except at the knee, more joint work can be done with arm swing. Total angular momentum is increased considerably by arm motion because of its remote contribution. Consequently segment remote contributions to total angular momentum are much larger in jumping with arms. Shoulder strength helps generate angular momentum only to a certain limit. If more work is used to generate horizontal velocity away from the board, the amount of total angular momentum is reduced.

Optimal discus trajectories.

A general 3-D dynamic model for men's and women's discus flight is presented including precession of spin angular momentum induced by aerodynamic pitching moment. Dependence of pitching moment coefficient on angle of attack alpha is estimated from experiment. Numerical integration of 11 equations of motion for nominal release speed v(0)=25 m/s and axial spin p(0)=42 rad/s also requires 3 other release conditions; initial discus flight path angle beta(0), pitch attitude theta(0), and roll angle phi(0). Optimal values for these release conditions are calculated iteratively to maximize range and are similar for both men and women. The optimal men's trajectory and range R=69.39 m is produced by the strategy beta(0)=38.4 degrees, theta(0)=30.7 degrees, and phi(0)=54.4 degrees. Initial angular velocities except spin are chosen to minimize wobble but an optimal initial spin rate p(0)=25.2 rad/s exists that also maximizes range. Optimal 3-D range exceeds that predicted by 2-D models because, although angle of attack and lift are negative initially, 3-D motion allows advantageous orientation of lift later in flight, with tilt of the axis of symmetry from vertical becoming much smaller at landing. Optimal strategies are discontinuous with wind speed, resulting in slicing and kiting strategies in large head and tail winds, respectively. Sensitivity of optimal range is largest to initial beta(0) and least to phi(0). Present calculations do not account for dependence of initial release angle or spin on release velocity or among other release conditions.

Optimal foot shape for a passive dynamic biped.

Passive walking dynamics describe the motion of a biped that is able to "walk" down a shallow slope without any actuation or control. Instead, the walker relies on gravitational and inertial effects to propel itself forward, exhibiting a gait quite similar to that of humans. These purely passive models depend on potential energy to overcome the energy lost when the foot impacts the ground. Previous research has demonstrated that energy loss at heel-strike can vary widely for a given speed, depending on the nature of the collision. The point of foot contact with the ground (relative to the hip) can have a significant effect: semi-circular (round) feet soften the impact, resulting in much smaller losses than point-foot walkers. Collisional losses are also lower if a single impulse is broken up into a series of smaller impulses that gradually redirect the velocity of the center of mass rather than a single abrupt impulse. Using this principle, a model was created where foot-strike occurs over two impulses, "heel-strike" and "toe-strike," representative of the initial impact of the heel and the following impact as the ball of the foot strikes the ground. Having two collisions with the flat-foot model did improve efficiency over the point-foot model. Representation of the flat-foot walker as a rimless wheel helped to explain the optimal flat-foot shape, driven by symmetry of the virtual spoke angles. The optimal long period foot shape of the simple passive walking model was not very representative of the human foot shape, although a reasonably anthropometric foot shape was predicted by the short period solution.

Optimal compliant-surface jumping: a multi-segment model of springboard standing jumps.

A multi-segment model is used to investigate optimal compliant-surface jumping strategies and is applied to springboard standing jumps. The human model has four segments representing the feet, shanks, thighs, and trunk-head-arms. A rigid bar with a rotational spring on one end and a point mass on the other end (the tip) models the springboard. Board tip mass, length, and stiffness are functions of the fulcrum setting. Body segments and board tip are connected by frictionless hinge joints and are driven by joint torque actuators at the ankle, knee, and hip. One constant (maximum isometric torque) and three variable functions (of instantaneous joint angle, angular velocity, and activation level) determine each joint torque. Movement from a nearly straight motionless initial posture to jump takeoff is simulated. The objective is to find joint torque activation patterns during board contact so that jump height can be maximized. Minimum and maximum joint angles, rates of change of normalized activation levels, and contact duration are constrained. Optimal springboard jumping simulations can reasonably predict jumper vertical velocity and jump height. Qualitatively similar joint torque activation patterns are found over different fulcrum settings. Different from rigid-surface jumping where maximal activation is maintained until takeoff, joint activation decreases near takeoff in compliant-surface jumping. The fulcrum-height relations in experimental data were predicted by the models. However, lack of practice at non-preferred fulcrum settings might have caused less jump height than the models' prediction. Larger fulcrum numbers are beneficial for taller/heavier jumpers because they need more time to extend joints.

Musculoskeletal modeling and dynamic simulation of the thoroughbred equine forelimb during stance phase of the gallop.

Because thoroughbred racehorses have a high incidence of forelimb musculoskeletal injuries, a model was desired to screen potential risk factors for injuries. This paper describes the development of a musculoskeletal model of the thoroughbred forelimb and a dynamic simulation of the motion of the distal segments during the stance phase of high-speed (18 m/s) gallop. The musculoskeletal model is comprised of segment, joint, muscle-tendon, and ligament information. The dynamic simulation incorporates a proximal forward-driving force, a distal ground reaction force model, muscle activations, and initial positions and velocities. A simulation of the gallop after transection of an accessory ligament demonstrated increased soft tissue strains in the remaining support structures of the distal forelimb. These data were consistent with those previously reported from in vitro experimental data and supported usefulness of the model for the study of distal forelimb soft tissue mechanics during the stance phase of the gallop.

Passive and active mechanical properties of the superficial and deep digital flexor muscles in the forelimbs of anesthetized Thoroughbred horses.

The superficial (SDF) and deep digital flexor (DDF) muscles are critical for equine forelimb locomotion. Knowledge of their mechanical properties will enhance our understanding of limb biomechanics. Muscle contractile properties derived from architectural-based algorithms may overestimate real forces and underestimate shortening capacity because of simplistic assumptions regarding muscle architecture. Therefore, passive and active (=total - passive) force-length properties of the SDF and DDF muscles were measured directly in vivo. Muscles from the right forelimbs of four Thoroughbred horses were evaluated during general anesthesia. Limbs were fixed to an external frame with the muscle attached to a linear actuator and load cell. Each muscle was stretched from an unloaded state to a range of prefixed lengths, then stimulated while held at that length. The total force did not exceed 4000 N, the limit for the clamping device. The SDF and DDF muscles produced 716+/-192 and 1577+/-203 N maximum active isometric force (F(max)), had ascending force-length ranges (R(asc)) of 5.1+/-0.2 and 9.1+/-0.4 cm, and had passive stiffnesses of 1186+/-104 and 1132+/-51 N/cm, respectively. The values measured for F(max) were much smaller than predicted based on conservative estimates of muscle specific tension and muscle physiological cross-sectional area. R(asc) were much larger than predicted based on muscle fiber length estimates. These data suggest that accurate prediction of the active mechanical behavior of architecturally complex muscles such as the equine DDF and SDF requires more sophisticated algorithms.

Optimal jumping strategies from compliant surfaces: a simple model of springboard standing jumps.

A simple model of standing dives is used to investigate optimal jumping strategies from compliant surfaces and applied to springboard diving. The human model consists of a massless leg actuated by knee torque, and a lumped torso mass centered above the leg. The springboard is modeled as a mass-spring system. Maximum jump height for a male and a female is calculated by controlling knee-torque activation level as a function of time. The optimization includes constraints on minimum and maximum knee angle, rate of change of normalized activation level, and contact duration. Simulation results for maximal springboard depression and diver takeoff velocity agree reasonably with experimental data, even though larger board tip velocities are necessarily predicted earlier during the contact period. Qualitatively similar multiple pulse knee-torque activation patterns are found over various conditions and are different from those in rigid-surface jumping. The model is less able to predict accurately jump height at high fulcrum number since jumpers may have difficulty behaving optimally at non-preferred fulcrum settings. If strength is proportional to the product of mass and leg length, increasing leg length is more effective in increasing jump height than is increasing mass.

Determination of passive mechanical properties of the superficial and deep digital flexor muscle-ligament-tendon complexes in the forelimbs of horses.

OBJECTIVE: To determine the relative contributions of the muscles, tendons, and accessory ligaments to the passive force-length properties of the superficial (SDF) and deep digital flexor (DDF) myotendinous complexes. SAMPLE POPULATION: 8 cadaveric forelimbs from 6 adult Thoroughbreds. PROCEDURE: In vitro, limb configurations during slack position and myotendinous lengths during subsequent axial loading of forelimbs were recorded before and after transection of accessory ligaments. Expressions were derived to describe the force-length behavior of each muscle, tendon, and accessory ligament-tendon unit; linear stiffness was computed for these components. The elastic modulus was established for the SDF and DDF tendons. RESULTS; Linear stiffness was 2.80 +/- 0.38 kN/cm for the SDF muscle, 3.47 +/- 0.66 kN/cm for the DDF muscle, 2.73 +/- 0.18 kN/cm for the SDF tendon, 3.22 +/- 0.20 kN/cm for the DDF tendon, 6.46 +/- 0.85 kN/cm for the SDF accessory ligament, 1.93 +/- 0.11 kN/cm for the SDF accessory ligament-tendon unit, and 2.47 +/- 0.11 kN/cm for the DDF accessory ligament-tendon unit. The elastic modulus for the SDF and DDF tendons was 920 +/- 77 and 843 +/- 56 MPa, respectively. CONCLUSIONS AND CLINICAL RELEVANCE: Both the muscle-tendon and ligament-tendon portions of SDF and DDF myotendinous complexes had important roles in supporting the forelimb of horses. Although muscle tension can be enhanced by elbow joint flexion and active contraction, the accessory ligaments transmitted more force to the distal tendons than did the muscles under the conditions tested.