Optimal footfall patterns for cost minimization in running

Increasing midtarsal joint stiffness reduces triceps surae metabolic costs in walking simulations but has little effect on total stance limb metabolic cost

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.

Resource allocation in mammalian systems

Cells execute biological functions to support phenotypes such as growth, migration, and secretion. Complementarily, each function of a cell has resource costs that constrain phenotype. Resource allocation by a cell allows it to manage these costs and optimize their phenotypes. In fact, the management of resource constraints (e.g., nutrient availability, bioenergetic capacity, and macromolecular machinery production) shape activity and ultimately impact phenotype. In mammalian systems, quantification of resource allocation provides important insights into higher-order multicellular functions; it shapes intercellular interactions and relays environmental cues for tissues to coordinate individual cells to overcome resource constraints and achieve population-level behavior. Furthermore, these constraints, objectives, and phenotypes are context-dependent, with cells adapting their behavior according to their microenvironment, resulting in distinct steady-states. This review will highlight the biological insights gained from probing resource allocation in mammalian cells and tissues.

Patterns of asymmetry and energy cost generated from predictive simulations of hemiparetic gait

Hemiparesis, defined as unilateral muscle weakness, often occurs in people post-stroke or people with cerebral palsy, however it is difficult to understand how this hemiparesis affects movement patterns as it often presents alongside a variety of other neuromuscular impairments. Predictive musculoskeletal modeling presents an opportunity to investigate how impairments affect gait performance assuming a particular cost function. Here, we use predictive simulation to quantify the spatiotemporal asymmetries and changes to metabolic cost that emerge when muscle strength is unilaterally reduced and how reducing spatiotemporal symmetry affects metabolic cost. We modified a 2-D musculoskeletal model by uniformly reducing the peak isometric muscle force unilaterally. We then solved optimal control simulations of walking across a range of speeds by minimizing the sum of the cubed muscle excitations. Lastly, we ran additional optimizations to test if reducing spatiotemporal asymmetry would result in an increase in metabolic cost. Our results showed that the magnitude and direction of effort-optimal spatiotemporal asymmetries depends on both the gait speed and level of weakness. Also, the optimal speed was 1.25 m/s for the symmetrical and 20% weakness models but slower (1.00 m/s) for the 40% and 60% weakness models, suggesting that hemiparesis can account for a portion of the slower gait speed seen in people with hemiparesis. Modifying the cost function to minimize spatiotemporal asymmetry resulted in small increases (~4%) in metabolic cost. Overall, our results indicate that spatiotemporal asymmetry may be optimal for people with hemiparesis. Additionally, the effect of speed and the level of weakness on spatiotemporal asymmetry may help explain the well-known heterogenous distribution of spatiotemporal asymmetries observed in the clinic. Future work could extend our results by testing the effects of other neuromuscular impairments on optimal gait strategies, and therefore build a more comprehensive understanding of the gait patterns observed in clinical populations.

Three-dimensional data-tracking simulations of sprinting using a direct collocation optimal control approach

Biomechanical simulation and modelling approaches have the possibility to make a meaningful impact within applied sports settings, such as sprinting. However, for this to be realised, such approaches must first undergo a thorough quantitative evaluation against experimental data. We developed a musculoskeletal modelling and simulation framework for sprinting, with the objective to evaluate its ability to reproduce experimental kinematics and kinetics data for different sprinting phases. This was achieved by performing a series of data-tracking calibration (individual and simultaneous) and validation simulations, that also featured the generation of dynamically consistent simulated outputs and the determination of foot-ground contact model parameters. The simulated values from the calibration simulations were found to be in close agreement with the corresponding experimental data, particularly for the kinematics (average root mean squared differences (RMSDs) less than 1.0° and 0.2 cm for the rotational and translational kinematics, respectively) and ground reaction force (highest average percentage RMSD of 8.1%). Minimal differences in tracking performance were observed when concurrently determining the foot-ground contact model parameters from each of the individual or simultaneous calibration simulations. The validation simulation yielded results that were comparable (RMSDs less than 1.0° and 0.3 cm for the rotational and translational kinematics, respectively) to those obtained from the calibration simulations. This study demonstrated the suitability of the proposed framework for performing future predictive simulations of sprinting, and gives confidence in its use to assess the cause-effect relationships of technique modification in relation to performance. Furthermore, this is the first study to provide dynamically consistent three-dimensional muscle-driven simulations of sprinting across different phases.

A Conceptual Blueprint for Making Neuromusculoskeletal Models Clinically Useful

The ultimate goal of most neuromusculoskeletal modeling research is to improve the treatment of movement impairments. However, even though neuromusculoskeletal models have become more realistic anatomically, physiologically, and neurologically over the past 25 years, they have yet to make a positive impact on the design of clinical treatments for movement impairments. Such impairments are caused by common conditions such as stroke, osteoarthritis, Parkinson’s disease, spinal cord injury, cerebral palsy, limb amputation, and even cancer. The lack of clinical impact is somewhat surprising given that comparable computational technology has transformed the design of airplanes, automobiles, and other commercial products over the same time period. This paper provides the author’s personal perspective for how neuromusculoskeletal models can become clinically useful. First, the paper motivates the potential value of neuromusculoskeletal models for clinical treatment design. Next, it highlights five challenges to achieving clinical utility and provides suggestions for how to overcome them. After that, it describes clinical, technical, collaboration, and practical needs that must be addressed for neuromusculoskeletal models to fulfill their clinical potential, along with recommendations for meeting them. Finally, it discusses how more complex modeling and experimental methods could enhance neuromusculoskeletal model fidelity, personalization, and utilization. The author hopes that these ideas will provide a conceptual blueprint that will help the neuromusculoskeletal modeling research community work toward clinical utility.

OpenSim Moco: Musculoskeletal optimal control

Musculoskeletal simulations are used in many different applications, ranging from the design of wearable robots that interact with humans to the analysis of patients with impaired movement. Here, we introduce OpenSim Moco, a software toolkit for optimizing the motion and control of musculoskeletal models built in the OpenSim modeling and simulation package. OpenSim Moco uses the direct collocation method, which is often faster and can handle more diverse problems than other methods for musculoskeletal simulation. Moco frees researchers from implementing direct collocation themselves-which typically requires extensive technical expertise-and allows them to focus on their scientific questions. The software can handle a wide range of problems that interest biomechanists, including motion tracking, motion prediction, parameter optimization, model fitting, electromyography-driven simulation, and device design. Moco is the first musculoskeletal direct collocation tool to handle kinematic constraints, which enable modeling of kinematic loops (e.g., cycling models) and complex anatomy (e.g., patellar motion). To show the abilities of Moco, we first solved for muscle activity that produced an observed walking motion while minimizing squared muscle excitations and knee joint loading. Next, we predicted how muscle weakness may cause deviations from a normal walking motion. Lastly, we predicted a squat-to-stand motion and optimized the stiffness of an assistive device placed at the knee. We designed Moco to be easy to use, customizable, and extensible, thereby accelerating the use of simulations to understand the movement of humans and other animals.

Efficient trajectory optimization for curved running using a 3D musculoskeletal model with implicit dynamics

Trajectory optimization with musculoskeletal models can be used to reconstruct measured movements and to predict changes in movements in response to environmental changes. It enables an exhaustive analysis of joint angles, joint moments, ground reaction forces, and muscle forces, among others. However, its application is still limited to simplified problems in two dimensional space or straight motions. The simulation of movements with directional changes, e.g. curved running, requires detailed three dimensional models which lead to a high-dimensional solution space. We extended a full-body three dimensional musculoskeletal model to be specialized for running with directional changes. Model dynamics were implemented implicitly and trajectory optimization problems were solved with direct collocation to enable efficient computation. Standing, straight running, and curved running were simulated starting from a random initial guess to confirm the capabilities of our model and approach: efficacy, tracking and predictive power. Altogether the simulations required 1 h 17 min and corresponded well to the reference data. The prediction of curved running using straight running as tracking data revealed the necessity of avoiding interpenetration of body segments. In summary, the proposed formulation is able to efficiently predict a new motion task while preserving dynamic consistency. Hence, labor-intensive and thus costly experimental studies could be replaced by simulations for movement analysis and virtual product design.

Drift-Free Foot Orientation Estimation in Running Using Wearable IMU

This study aimed to introduce and validate a new method to estimate and correct the orientation drift measured from foot-worn inertial sensors. A modified strap-down integration (MSDI) was proposed to decrease the orientation drift, which, in turn, was further compensated by estimation of the joint center acceleration (JCA) of a two-segment model of the foot. This method was designed to fit the different foot strike patterns observed in running and was validated against an optical motion-tracking system during level treadmill running at 8, 12, and 16 km/h. The sagittal and frontal plane angles obtained from the inertial sensors and the motion tracking system were compared at different moments of the ground contact phase. The results obtained from 26 runners showed that the foot orientation at mean stance was estimated with an accuracy (inter-trial median ± IQR) of 0.4 ± 3.8° and a precision (inter-trial precision median ± IQR) of 3.0 ± 1.8°. The orientation of the foot shortly before initial contact (IC) was estimated with an accuracy of 2.0 ± 5.9° and a precision of 1.6 ± 1.1°; which is more accurate than commonly used zero-velocity update methods derived from gait analysis and not explicitly designed for running. Finally, the study presented the effect initial and terminal contact (TC) detection errors have on the orientation parameters reported.

Change in foot strike patterns and performance in recreational runners during a road race: A cross-sectional study

OBJECTIVES

To characterise foot strike and observe change in foot strike patterns with increasing distance during a 15km recreational running road race. To assess the impact of foot strike on running performance.

DESIGN

Observational cross-sectional study.

METHODS

Foot strike patterns were determined at the 3km and 13km checkpoints for 459 participants during the 2017 Melbourne City to Sea recreational running event. Foot strike patterns were categorised as either rearfoot strike (RFS) or non-rearfoot strike (NRFS) at both checkpoints and analyses were conducted on intra-individual change in foot strike as well as relationship to finishing time.

RESULTS

The most prevalent foot strike pattern at 3km and 13km was RFS with 76.9% (95% CI: 73.2%-80.5%) and 91.0% (95% CI: 88.7%-93.1%) using this pattern, respectively. Of the 105 participants who ran with a NRFS at 3km, 61% changed to RFS at 13km. Race completion time differed by foot strike pattern, where mean time for consistent NRFS (62.64±11.20min) was significantly faster than consistent RFS (72.58±10.84min; p<0.001) and those who changed from NRFS to RFS between checkpoints (67.93±10.60min; p=0.040).

CONCLUSIONS

While the majority of recreational distance runners RFS within race settings, the fastest runners were those who consistently ran with a NRFS. In runners that use a NRFS early, a large proportion change to RFS as distance increases. Further research is warranted to determine whether interventions aimed at reducing muscular fatigue can attenuate this change and enhance running performance.

Running economy - a comprehensive review for passive force generation

Running economy is considered a major determinant of distance running performance. Enhancing the body's ability for passive force generation could have a positive effect on running economy by minimizing the energy cost required for the propulsion of the body. Thus, the purpose of this comprehensive review was to provide a list of modifiable factors that promote this ability. The interest was focused on lower-limb stiffness, as it is a factor of great influence and at the same time can be modified with training and specific biomechanical adjustments. Although it appears that no clear instructions can be provided to athletes and coaches, it should be noted that careful consideration of the runners' anthropometric, physiological, and biomechanical characteristics are necessary for optimal performance results.

Optimal control simulation predicts effects of midsole materials on energy cost of running

Testing sports equipment with athletes is costly, time-consuming, hazardous and sometimes impracticable. We propose a method for virtual testing of running shoes and predict how midsoles made of BOOST^TM affect energy cost of running. We contribute a visco-elastic contact model and identified model parameters based on load-displacement measurements. We propose a virtual study using optimal control simulation of musculoskeletal models. The predicted reduction in energy cost of ∼1% for BOOST^TM in comparison to conventional materials is consistent with experimental studies. This indicates that the proposed method is capable of replacing experimental studies in the future.

Predictive Simulations of Neuromuscular Coordination and Joint-Contact Loading in Human Gait

We implemented direct collocation on a full-body neuromusculoskeletal model to calculate muscle forces, ground reaction forces and knee contact loading simultaneously for one cycle of human gait. A data-tracking collocation problem was solved for walking at the normal speed to establish the practicality of incorporating a 3D model of articular contact and a model of foot-ground interaction explicitly in a dynamic optimization simulation. The data-tracking solution then was used as an initial guess to solve predictive collocation problems, where novel patterns of movement were generated for walking at slow and fast speeds, independent of experimental data. The data-tracking solutions accurately reproduced joint motion, ground forces and knee contact loads measured for two total knee arthroplasty patients walking at their preferred speeds. RMS errors in joint kinematics were < 2.0° for rotations and < 0.3 cm for translations while errors in the model-computed ground-reaction and knee-contact forces were < 0.07 BW and < 0.4 BW, respectively. The predictive solutions were also consistent with joint kinematics, ground forces, knee contact loads and muscle activation patterns measured for slow and fast walking. The results demonstrate the feasibility of performing computationally-efficient, predictive, dynamic optimization simulations of movement using full-body, muscle-actuated models with realistic representations of joint function.

Maintenance of muscle strength retains a normal metabolic cost in simulated walking after transtibial limb loss

Recent studies on relatively young and fit individuals with limb loss suggest that maintaining muscle strength after limb loss may mitigate the high metabolic cost of walking typically seen in the larger general limb loss population. However, these data are cross-sectional and the muscle strength prior to limb loss is unknown, and it is therefore difficult to draw causal inferences on changes in strength and gait energetics. Here we used musculoskeletal modeling and optimal control simulations to perform a longitudinal study (25 virtual “subjects”) of the metabolic cost of walking pre- and post-limb loss (unilateral transtibial). Simulations of walking were first performed pre-limb loss on a model with two intact biological legs, then post-limb loss on a model with a unilateral transtibial prosthesis, with a cost function that minimized the weighted sum of gait deviations plus metabolic cost. Metabolic costs were compared pre- vs. post-limb loss, with systematic modifications to the muscle strength and prosthesis type (passive, powered) in the post-limb loss model. The metabolic cost prior to limb loss was 3.44±0.13 J/m/kg. After limb loss, with a passive prosthesis the metabolic cost did not increase above the pre-limb loss cost if pre-limb loss muscle strength was maintained (mean -0.6%, p = 0.17, d = 0.17). With 10% strength loss the metabolic cost with the passive prosthesis increased (mean +5.9%, p < 0.001, d = 1.61). With a powered prosthesis, the metabolic cost was at or below the pre-limb loss cost for all subjects with strength losses of 10% and 20%, but increased for all subjects with strength loss of 30% (mean +5.9%, p < 0.001, d = 1.59). The results suggest that maintaining muscle strength may prevent an increase in the metabolic cost of walking following unilateral transtibial limb loss, and that a gait with minimal deviations can be achieved when muscle strength is sufficiently high, even when using a passive prosthesis.

Is changing footstrike pattern beneficial to runners?

Some researchers, running instructors, and coaches have suggested that the "optimal" footstrike pattern to improve performance and reduce running injuries is to land using a mid- or forefoot strike. Thus, it has been recommended that runners who use a rearfoot strike would benefit by changing their footstrike although there is little scientific evidence for suggesting such a change. The rearfoot strike is clearly more prevalent. The major reasons often given for changing to a mid- or forefoot strike are (1) it is more economical; (2) there is a reduction in the impact peak and loading rate of the vertical component of the ground reaction force; and (3) there is a reduction in the risk of a running-related injuries. In this paper, we critique these 3 suggestions and provide alternate explanations that may provide contradictory evidence for altering one's footstrike pattern. We have concluded, based on examining the research literature, that changing to a mid- or forefoot strike does not improve running economy, does not eliminate an impact at the foot-ground contact, and does not reduce the risk of running-related injuries.

Three-dimensional data-tracking dynamic optimization simulations of human locomotion generated by direct collocation

The aim of this study was to perform full-body three-dimensional (3D) dynamic optimization simulations of human locomotion by driving a neuromusculoskeletal model toward in vivo measurements of body-segmental kinematics and ground reaction forces. Gait data were recorded from 5 healthy participants who walked at their preferred speeds and ran at 2m/s. Participant-specific data-tracking dynamic optimization solutions were generated for one stride cycle using direct collocation in tandem with an OpenSim-MATLAB interface. The body was represented as a 12-segment, 21-degree-of-freedom skeleton actuated by 66 muscle-tendon units. Foot-ground interaction was simulated using six contact spheres under each foot. The dynamic optimization problem was to find the set of muscle excitations needed to reproduce 3D measurements of body-segmental motions and ground reaction forces while minimizing the time integral of muscle activations squared. Direct collocation took on average 2.7±1.0h and 2.2±1.6h of CPU time, respectively, to solve the optimization problems for walking and running. Model-computed kinematics and foot-ground forces were in good agreement with corresponding experimental data while the calculated muscle excitation patterns were consistent with measured EMG activity. The results demonstrate the feasibility of implementing direct collocation on a detailed neuromusculoskeletal model with foot-ground contact to accurately and efficiently generate 3D data-tracking dynamic optimization simulations of human locomotion. The proposed method offers a viable tool for creating feasible initial guesses needed to perform predictive simulations of movement using dynamic optimization theory. The source code for implementing the model and computational algorithm may be downloaded at http://simtk.org/home/datatracking.

Direct Methods for Predicting Movement Biomechanics Based Upon Optimal Control Theory with Implementation in OpenSim

The aim of this study was to compare the computational performances of two direct methods for solving large-scale, nonlinear, optimal control problems in human movement. Direct shooting and direct collocation were implemented on an 8-segment, 48-muscle model of the body (24 muscles on each side) to compute the optimal control solution for maximum-height jumping. Both algorithms were executed on a freely-available musculoskeletal modeling platform called OpenSim. Direct collocation converged to essentially the same optimal solution up to 249 times faster than direct shooting when the same initial guess was assumed (3.4 h of CPU time for direct collocation vs. 35.3 days for direct shooting). The model predictions were in good agreement with the time histories of joint angles, ground reaction forces and muscle activation patterns measured for subjects jumping to their maximum achievable heights. Both methods converged to essentially the same solution when started from the same initial guess, but computation time was sensitive to the initial guess assumed. Direct collocation demonstrates exceptional computational performance and is well suited to performing predictive simulations of movement using large-scale musculoskeletal models.