A three filament mechanistic model of musculotendon force and impedance.

The force developed by actively lengthened muscle depends on different structures across different scales of lengthening. For small perturbations, the active response of muscle is well captured by a linear-time-invariant (LTI) system: a stiff spring in parallel with a light damper. The force response of muscle to longer stretches is better represented by a compliant spring that can fix its end when activated. Experimental work has shown that the stiffness and damping (impedance) of muscle in response to small perturbations is of fundamental importance to motor learning and mechanical stability, while the huge forces developed during long active stretches are critical for simulating and predicting injury. Outside of motor learning and injury, muscle is actively lengthened as a part of nearly all terrestrial locomotion. Despite the functional importance of impedance and active lengthening, no single muscle model has all these mechanical properties. In this work, we present the viscoelastic-crossbridge active-titin (VEXAT) model that can replicate the response of muscle to length changes great and small. To evaluate the VEXAT model, we compare its response to biological muscle by simulating experiments that measure the impedance of muscle, and the forces developed during long active stretches. In addition, we have also compared the responses of the VEXAT model to a popular Hill-type muscle model. The VEXAT model more accurately captures the impedance of biological muscle and its responses to long active stretches than a Hill-type model and can still reproduce the force-velocity and force-length relations of muscle. While the comparison between the VEXAT model and biological muscle is favorable, there are some phenomena that can be improved: the low frequency phase response of the model, and a mechanism to support passive force enhancement.

A benchmark of muscle models to length changes great and small.

Digital human body models are used to simulate injuries that occur as a result of vehicle collisions, vibration, sports, and falls. Given enough time the body's musculature can generate force, affect the body's movements, and change the risk of some injuries. The finite-element code LS-DYNA is often used to simulate the movements and injuries sustained by the digital human body models as a result of an accident. In this work, we evaluate the accuracy of the three muscle models in LS-DYNA (MAT_156, EHTM, and the VEXAT) when simulating a range of experiments performed on isolated muscle: force-length-velocity experiments on maximally and sub-maximally stimulated muscle, active-lengthening experiments, and vibration experiments. The force-length-velocity experiments are included because these conditions are typical of the muscle activity that precedes an accident, while the active-lengthening and vibration experiments mimic conditions that can cause injury. The three models perform similarly during the maximally and sub-maximally activated force-length-velocity experiments, but noticeably differ in response to the active-lengthening and vibration experiments. The VEXAT model is able to generate the enhanced forces of biological muscle during active lengthening, while both the MAT_156 and EHTM produce too little force. In response to vibration, the stiffness and damping of the VEXAT model closely follows the experimental data while the MAT_156 and EHTM models differ substantially. The accuracy of the VEXAT model comes from two additional mechanical structures that are missing in the MAT_156 and EHTM models: viscoelastic cross-bridges, and an active titin filament. To help others build on our work we have made our simulation code publicly available.

Behavioral Motor Performance.

The human sensorimotor control system has exceptional abilities to perform skillful actions. We easily switch between strenuous tasks that involve brute force, such as lifting a heavy sewing machine, and delicate movements such as threading a needle in the same machine. Using a structure with different control architectures, the motor system is capable of updating its ability to perform through our daily interaction with the fluctuating environment. However, there are issues that make this a difficult computational problem for the brain to solve. The brain needs to control a nonlinear, nonstationary neuromuscular system, with redundant and occasionally undesired degrees of freedom, in an uncertain environment using a body in which information transmission is subject to delays and noise. To gain insight into the mechanisms of motor control, here we survey movement laws and invariances that shape our everyday motion. We then examine the major solutions to each of these problems in the three parts of the sensorimotor control system, sensing, planning, and acting. We focus on how the sensory system, the control architectures, and the structure and operation of the muscles serve as complementary mechanisms to overcome deviations and disturbances to motor behavior and give rise to skillful motor performance. We conclude with possible future research directions based on suggested links between the operation of the sensorimotor system across the movement stages. © 2024 American Physiological Society. Compr Physiol 14:5179-5224, 2024.

Tendon compliance and preload must be considered when determining the in vivo force-velocity relationship from the torque-angular velocity relation.

In vivo, the force-velocity relation (F-v-r) is typically derived from the torque-angular velocity relation (T-ω-r), which is subject to two factors that may influence resulting measurements: tendon compliance and preload prior to contraction. The in vivo plantar flexors' T-ω-r was determined during preloaded maximum voluntary shortening contractions at 0-200°/s. Additionally, we used a two factor block simulation study design to independently analyze the effects of preload and tendon compliance on the resulting T-ω-r. Therefore, we replicated the in vivo experiment using a Hill-type muscle model of the gastrocnemius medialis. The simulation results matched a key pattern observed in our recorded in vivo experimental data: during preloaded contractions, torque output of the muscle was increased when compared with non-preloaded contractions from literature. This effect increased with increasing contraction velocity and can be explained by a rapidly recoiling tendon, allowing the contractile element to contract more slowly, thus developing higher forces compared with non-preloaded contractions. Our simulation results also indicate that a more compliant tendon results in increased ankle joint torques. The simulation and the experimental data clearly show that the deduction of the in vivo F-v-r from the T-ω-r is compromised due to the two factors preloading and tendon compliance.

Comparing the risk of low-back injury using model-based optimization: Improved technique versus exoskeleton assistance.

Although wearable robotic systems are designed to reduce the risk of low-back injury, it is unclear how effective assistance is, compared to improvements in lifting technique. We use a two-factor block study design to simulate how effective exoskeleton assistance and technical improvements are at reducing the risk of low-back injury when compared to a typical adult lifting a box. The effects of assistance are examined by simulating two different models: a model of just the human participant, and a model of the human participant wearing the SPEXOR exoskeleton. The effects of lifting technique are investigated by formulating two different types of optimal control problems: a least-squares problem which tracks the human participant's lifting technique, and a minimization problem where the model is free to use a different movement. Different lifting techniques are considered using three different cost functions related to risk factors for low-back injury: cumulative low-back load (CLBL), peak low-back load (PLBL), and a combination of both CLBL and PLBL (HYB). The results of our simulations indicate that an exoskeleton alone can make modest reductions in both CLBL and PLBL. In contrast, technical improvements alone are effective at reducing CLBL, but not PLBL. The largest reductions in both CLBL and PLBL occur when both an exoskeleton and technical improvements are used. While all three of the lifting technique cost functions reduce both CLBL and PLBL, the HYB cost function offers the most balanced reduction in both CLBL and PLBL.

Slow but Steady: Similar Sit-to-Stand Balance at Seat-Off in Older vs. Younger Adults.

Many older adults suffer injuries due to falls as the ability to safely move between sitting and standing degrades. Unfortunately, while existing measures describe sit-to-stand (STS) performance, they do not directly measure the conditions for balance. To gain insight into the effect of age on STS balance, we analyzed how far 8 older and 10 young adults strayed from a state of static balance and how well each group maintained dynamic balance. Static balance was evaluated using the position of the center-of-mass (COM) and center-of-pressure (COP), relative to the functional base-of-support (BOS). As the name suggests, static balance applies when the linear and angular velocity of the body is small in magnitude, in the range of that observed during still standing. Dynamic balance control was evaluated using a model-based balance metric, the foot-placement-estimator (FPE), relative to the COP and BOS. We found that the older adults stay closer to being statically balanced than the younger participants. The dynamic balance metrics show that both groups keep the FPE safely within the BOS, though the older adults maintain a larger dynamic balance margin. Both groups exhibit similar levels of variability in these metrics. Thus, the conservative STS performance in older adults is likely to compensate for reduced physical ability or reduced confidence, as their dynamic balance control does not seem affected. The presented analysis of both static and dynamic balance allows us to distinguish between STS performance and balance, and as such can contribute to the identification of those older adults prone to falling, thus ultimately reducing the number of falls during STS transfers.

A little damping goes a long way: a simulation study of how damping influences task-level stability in running.

It is currently unclear if damping plays a functional role in legged locomotion, and simple models often do not include damping terms. We present a new model with a damping term that is isolated from other parameters: that is, the damping term can be adjusted without retuning other model parameters for nominal motion. We systematically compare how increased damping affects stability in the face of unexpected ground-height perturbations. Unlike most studies, we focus on task-level stability: instead of observing whether trajectories converge towards a nominal limit-cycle, we quantify the ability to avoid falls using a recently developed mathematical measure. This measure allows trajectories to be compared quantitatively instead of only being separated into a binary classification of 'stable' or 'unstable'. Our simulation study shows that increased damping contributes significantly to task-level stability; however, this benefit quickly plateaus after only a small amount of damping. These results suggest that the low intrinsic damping values observed experimentally may have stability benefits and are not simply minimized for energetic reasons. All Python code and data needed to generate our results are available open source.

Biomechanical Analysis of the Slow-Twitch (Red) Muscle Force Transmission Pathways in Tunas.

In tunas, the slow-twitch red muscle, which has an elevated temperature, powers thunniform locomotion, a stiff-bodied swimming style. The anatomical placement and operating temperatures of red muscle vary widely among teleosts: in tunas, the red muscle is located centrally in the body, adjacent to the spine, and maintains an elevated temperature. In the majority of ectothermic teleosts, red muscle is located laterally in the body, adjacent to the skin, and operates at ambient temperature. The specialized physiology and biomechanics of red muscle in tunas are often considered important adaptations to their high-performance pelagic lifestyle; however, the mechanics of how muscular work is transmitted to the tail remains largely unknown. The red muscle has a highly pennate architecture and is connected to the spine through a network of bones (epicentral bones) and long tendons (posterior oblique tendons). The network of long tendons has been hypothesized to enhance the power transmitted to the tail. Here, we investigate the morphology and biomechanics of the tuna's red muscle and tendons to determine whether elasticity is exploited to reduce the cost of transport, as is the case in many terrestrial vertebrates. To address this question, we evaluate two hypotheses: (1) tendons stretch during red-muscle-actuated swimming and (2) tendons comprise the primary load transmission pathway from the red muscle to the spine. To evaluate these hypotheses, we measured the mechanical properties of the posterior oblique tendons and performed novel dissections to estimate the peak force that the red muscle can generate. The force-generating capacity of the red muscle is calculated to be much greater than the load-bearing capacity of the posterior oblique tendons. Thus, the long tendons likely stretch under force from the red muscle, but they are not strong enough to be the primary force transmission pathway. These results suggest that other pathways, such as serial load transmission through the red muscle myomeres to the great lateral tendon and/or the anterior oblique tendons to the skin, transmit appreciable force to the tail.

A Quick Turn of Foot: Rigid Foot-Ground Contact Models for Human Motion Prediction.

Computer simulation can be used to predict human walking motions as a tool of basic science, device design, and for surgical planning. One the challenges of predicting human walking is accurately synthesizing both the movements and ground forces of the stance foot. Though the foot is commonly modeled as a viscoelastic element, rigid foot-ground contact models offer some advantages: fitting is reduced to a geometric problem, and the numerical stiffness of the equations of motion is similar in both swing and stance. In this work, we evaluate two rigid-foot ground contact models: the ellipse-foot (a single-segment foot), and the double-circle foot (a two-segment foot). To evaluate the foot models we use three different comparisons to experimental data: first we compare how accurately the kinematics of the ankle frame fit those of the model when it is forced to track the measured center-of-pressure (CoP) kinematics; second, we compare how each foot affects how accuracy of a sagittal plane gait model that tracks a subjects walking motion; and third, we assess how each model affects a walking motion prediction. For the prediction problem we consider a unique cost function that includes terms related to both muscular effort and foot-ground impacts. Although the ellipse-foot is superior to the double-circle foot in terms of fit and the accuracy of the tracking OCP solution, the predictive simulation reveals that the ellipse-foot is capable of producing large force transients due to its geometry: when the ankle quickly traverses its u-shaped trajectory, the body is accelerated the body upwards, and large ground forces result. In contrast, the two-segment double-circle foot produces ground forces that are of a similar magnitude to the experimental subject because the additional forefoot segment plastically contacts the ground, arresting its motion, similar to a human foot.

A reduced muscle model and planar musculoskeletal model fit for the simulation of whole-body movements.

Musculoskeletal models are made to reflect the capacities of the human body in general, and often a specific subject in particular. It remains challenging to both model the musculoskeletal system and then fit the modelled muscles to a specific human subject. We present a reduced muscle model, a planar musculoskeletal model, and a fitting method that can be used to find a feasible set of active and passive muscle parameters for a specific subject. At a minimum, the fitting method requires inverse dynamics data of the subject, a scalar estimate of the peak activation reached during the movement, and a plausible initial estimate for the strength and flexibility of that subject. While additional data can be used to result in a more accurate fit, this data is not required for the method solve for a feasible fit. The minimal input requirements of the proposed fitting method make it well suited for subjects who cannot undergo a maximum voluntary contraction trial, or for whom recording electromyographic data is not possible. To evaluate the model and fitting method we adjust the musculoskeletal model so that it can perform an experimentally recorded stoop-lift of a 15 kg box.

Predicting the influence of hip and lumbar flexibility on lifting motions using optimal control.

Computational models of the human body coupled with optimization can be used to predict the influence of variables that cannot be experimentally manipulated. Here, we present a study that predicts the motion of the human body while lifting a box, as a function of flexibility of the hip and lumbar joints in the sagittal plane. We modeled the human body in the sagittal plane with joints actuated by pairs of agonist-antagonist muscle torque generators, and a passive hamstring muscle. The characteristics of a stiff, average and flexible person were represented by co-varying the lumbar range-of-motion, lumbar passive extensor-torque and the hamstring passive muscle-force. We used optimal control to solve for motions that simulated lifting a 10 kg box from a 0.3 m height. The solution minimized the total sum of the normalized squared active and passive muscle torques and the normalized passive hamstring muscle forces, over the duration of the motion. The predicted motion of the average lifter agreed well with experimental data in the literature. The change in model flexibility affected the predicted joint angles, with the stiffer models flexing more at the hip and knee, and less at the lumbar joint, to complete the lift. Stiffer models produced similar passive lumbar torque and higher hamstring muscle force components than the more flexible models. The variation between the motion characteristics of the models suggest that flexibility may play an important role in determining lifting technique.

OpenSim: Simulating musculoskeletal dynamics and neuromuscular control to study human and animal movement.

Movement is fundamental to human and animal life, emerging through interaction of complex neural, muscular, and skeletal systems. Study of movement draws from and contributes to diverse fields, including biology, neuroscience, mechanics, and robotics. OpenSim unites methods from these fields to create fast and accurate simulations of movement, enabling two fundamental tasks. First, the software can calculate variables that are difficult to measure experimentally, such as the forces generated by muscles and the stretch and recoil of tendons during movement. Second, OpenSim can predict novel movements from models of motor control, such as kinematic adaptations of human gait during loaded or inclined walking. Changes in musculoskeletal dynamics following surgery or due to human-device interaction can also be simulated; these simulations have played a vital role in several applications, including the design of implantable mechanical devices to improve human grasping in individuals with paralysis. OpenSim is an extensible and user-friendly software package built on decades of knowledge about computational modeling and simulation of biomechanical systems. OpenSim's design enables computational scientists to create new state-of-the-art software tools and empowers others to use these tools in research and clinical applications. OpenSim supports a large and growing community of biomechanics and rehabilitation researchers, facilitating exchange of models and simulations for reproducing and extending discoveries. Examples, tutorials, documentation, and an active user forum support this community. The OpenSim software is covered by the Apache License 2.0, which permits its use for any purpose including both nonprofit and commercial applications. The source code is freely and anonymously accessible on GitHub, where the community is welcomed to make contributions. Platform-specific installers of OpenSim include a GUI and are available on simtk.org.

Anti-infective Acquisition Costs for a Stewardship Program: Getting to the Bottom Line.

BACKGROUND: Though antimicrobial stewardship programs (ASPs) are in place for patient safety, financial justification is often required. In 2016, the Infectious Diseases Society of America (IDSA) recommended that anti-infective costs be measured by patient-level administration data normalized for patient census. Few publications use this methodology. Here, we aim to compare 3 methods of drug cost analysis during 3 phases of an ASP as an example of this recommendation's implementation. METHODS: At a freestanding pediatric hospital, we retrospectively assessed anti-infective cost using pharmacy purchasing data, patient-level administration data from the electronic medical record (EMR), and patient-level administration data from the Pediatric Hospital Information Systems (PHIS) database, all normalized to patient census. Costs pre-ASP, while planning the ASP, and post-ASP were then compared for each method. RESULTS: Significant differences in costs between the methods were observed. Pharmacy purchasing endorsed minimal financial benefit (decrease planning to post-ASP of $590 dollars per 1000 patient-days), while the EMR and PHIS data endorsed a decrease of $12785 and $21380 per 1000 patient-days, respectively, for a total yearly cost savings of $54656 for pharmacy purchasing data, $1184336 for EMR data, and $2117522 for PHIS data. CONCLUSIONS: Pharmacy purchasing data underestimated cost savings compared with EMR and PHIS data, while EMR and PHIS data were comparable in magnitude of savings. At Children's Hospital Colorado, savings justified the full cost of the ASP. EMR patient-level administration data, normalized to patient census, offers a readily available and standardized measure of anti-infective costs over time.

Towards low back support with a passive biomimetic exo-spine.

Low-Back Pain (LBP) affects a large portion of the working population. Preventive exoskeletons have been proposed to reduce the moments on the lower back, specifically around the lumbosacral (L5/S1) joint. High correlation has been shown, between reducing the moments around the L5/S1 joint and intervertebral compression forces, which in turn have been identified as a risk factor for developing LBP. However, most passive back support exoskeletons use rigid plates or stiff beams to support the spine that limit the range of motion of the wearer. A large range of motion and versatility are especially desirable for industrial applications. To overcome these limitations, a passive biomimetic exo-spine has been designed, modelled and an initial prototype tested. Its potential to allow for a large range of motion, whilst at the same time limiting the most extreme and potentially harmful postures has been shown.

Optimal Control Based Stiffness Identification of an Ankle-Foot Orthosis Using a Predictive Walking Model.

Predicting the movements, ground reaction forces and neuromuscular activity during gait can be a valuable asset to the clinical rehabilitation community, both to understand pathology, as well as to plan effective intervention. In this work we use an optimal control method to generate predictive simulations of pathological gait in the sagittal plane. We construct a patient-specific model corresponding to a 7-year old child with gait abnormalities and identify the optimal spring characteristics of an ankle-foot orthosis that minimizes muscle effort. Our simulations include the computation of foot-ground reaction forces, as well as the neuromuscular dynamics using computationally efficient muscle torque generators and excitation-activation equations. The optimal control problem (OCP) is solved with a direct multiple shooting method. The solution of this problem is physically consistent synthetic neural excitation commands, muscle activations and whole body motion. Our simulations produced similar changes to the gait characteristics as those recorded on the patient. The orthosis-equipped model was able to walk faster with more extended knees. Notably, our approach can be easily tuned to simulate weakened muscles, produces physiologically realistic ground reaction forces and smooth muscle activations and torques, and can be implemented on a standard workstation to produce results within a few hours. These results are an important contribution toward bridging the gap between research methods in computational neuromechanics and day-to-day clinical rehabilitation.

Flexing computational muscle: modeling and simulation of musculotendon dynamics.

Muscle-driven simulations of human and animal motion are widely used to complement physical experiments for studying movement dynamics. Musculotendon models are an essential component of muscle-driven simulations, yet neither the computational speed nor the biological accuracy of the simulated forces has been adequately evaluated. Here we compare the speed and accuracy of three musculotendon models: two with an elastic tendon (an equilibrium model and a damped equilibrium model) and one with a rigid tendon. Our simulation benchmarks demonstrate that the equilibrium and damped equilibrium models produce similar force profiles but have different computational speeds. At low activation, the damped equilibrium model is 29 times faster than the equilibrium model when using an explicit integrator and 3 times faster when using an implicit integrator; at high activation, the two models have similar simulation speeds. In the special case of simulating a muscle with a short tendon, the rigid-tendon model produces forces that match those generated by the elastic-tendon models, but simulates 2-54 times faster when an explicit integrator is used and 6-31 times faster when an implicit integrator is used. The equilibrium, damped equilibrium, and rigid-tendon models reproduce forces generated by maximally-activated biological muscle with mean absolute errors less than 8.9%, 8.9%, and 20.9% of the maximum isometric muscle force, respectively. When compared to forces generated by submaximally-activated biological muscle, the forces produced by the equilibrium, damped equilibrium, and rigid-tendon models have mean absolute errors less than 16.2%, 16.4%, and 18.5%, respectively. To encourage further development of musculotendon models, we provide implementations of each of these models in OpenSim version 3.1 and benchmark data online, enabling others to reproduce our results and test their models of musculotendon dynamics.

How muscle fiber lengths and velocities affect muscle force generation as humans walk and run at different speeds.

The lengths and velocities of muscle fibers have a dramatic effect on muscle force generation. It is unknown, however, whether the lengths and velocities of lower limb muscle fibers substantially affect the ability of muscles to generate force during walking and running. We examined this issue by developing simulations of muscle-tendon dynamics to calculate the lengths and velocities of muscle fibers from electromyographic recordings of 11 lower limb muscles and kinematic measurements of the hip, knee and ankle made as five subjects walked at speeds of 1.0-1.75 m s(-1) and ran at speeds of 2.0-5.0 m s(-1). We analyzed the simulated fiber lengths, fiber velocities and forces to evaluate the influence of force-length and force-velocity properties on force generation at different walking and running speeds. The simulations revealed that force generation ability (i.e. the force generated per unit of activation) of eight of the 11 muscles was significantly affected by walking or running speed. Soleus force generation ability decreased with increasing walking speed, but the transition from walking to running increased the force generation ability by reducing fiber velocities. Our results demonstrate the influence of soleus muscle architecture on the walk-to-run transition and the effects of muscle-tendon compliance on the plantarflexors' ability to generate ankle moment and power. The study presents data that permit lower limb muscles to be studied in unprecedented detail by relating muscle fiber dynamics and force generation to the mechanical demands of walking and running.

Gait stability in children with Cerebral Palsy.

Children with unilateral Cerebral Palsy (CP) have several gait impairments, amongst which impaired gait stability may be one. We tested whether a newly developed stability measure (the foot placement estimator, FPE) which does not require long data series, can be used to asses gait stability in typically developing (TD) children as well as children with CP. In doing so, we tested the FPE's sensitivity to the assumptions needed to calculate this measure, as well as the ability of the FPE to detect differences in stability between children with CP and TD children, and differences in walking speed. Participants were asked to walk at two different speeds, while gait kinematics were recorded. From these data, the FPE, as well as the error that violations of assumptions of the FPE could have caused were calculated. The results showed that children with CP walked with marked instabilities in anterior-posterior and mediolateral directions. Furthermore, errors caused by violations of assumptions in calculation of FPE were only small (≈ 1.5 cm), while effects of walking speed (≈ 20 cm per m/s increase in walking speed) and group (≈ 5 cm) were much larger. These results suggest that the FPE may be used to quantify gait stability in TD children and children with CP.