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.
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.
While much work has been completed analyzing the role of territory’s effect on conflict, less work has demonstrated how territory affects military budgets. I argue that a state’s defense spending is ...subsidized by clearly defined geographic focal points. Using geographic data, I show that states clearly defined by rivers and oceans spend less money on defense budgets as a proportion of GDP because the prospects of conflict are lower and internal social cohesion is higher, decreasing the need for large standing militaries for repression/expansion/defense. I contend that this effect is exogenous to threat. On the other hand, more mountainous states should spend more on defense due to increased costs of defense and decreased sense of identity among local populations. Situating this debate within the state development literature helps us answer important questions regarding state formation/consolidation and peaceful interactions with neighbors.
Abstract
We present far-infrared (FIR) spectroscopy of supernova remnants (SNRs) based on the archival data of the Infrared Space Observatory taken with the Long Wavelength Spectrometer (LWS). Our ...sample includes previously unpublished profiles of line and continuum spectra for 20 SNRs in the Galaxy and Magellanic Clouds. In several SNRs including G21.5–0.9, G29.7–0.3, the Crab Nebula, and G320.4–1.2, we find evidence for broad O
i
, O
iii
, N
ii
, and C
ii
lines with velocity dispersions up to a few 10
3
km s
−1
, indicating that they are associated with high-velocity SN ejecta. Our detection of Doppler-broadened atomic emission lines and a bright FIR continuum hints at the presence of newly formed dust in SN ejecta. For G320.4–1.2, we present the first estimate of an ejecta-dust mass of 0.1–0.2
M
⊙
, which spatially coincides with the broad-line emission, by applying a blackbody model fit with components of the SNR and background emission. Our sample includes raster maps of 63
μ
m, 145
μ
m O
i
, and 158
μ
m C
ii
lines toward SNRs Kes 79, CTB 109, and IC 443. Based on these line intensities, we suggest interacting shock types in these SNRs. Finally, we compare our LWS spectra of our sample SNRs with the spectra of several H
ii
regions, and discuss their FIR line intensity ratios and continuum properties. Follow-up observations with modern instruments (e.g., JWST and SOFIA) with higher spatial and spectral resolution are encouraged for an extensive study of the SN ejecta and the SN dust.
Abstract
We present our velocity measurements of 59 clumpy, metal-rich ejecta knots in the supernova remnant (SNR) of SN 1572 (Tycho). We use our 450 ks Chandra High Energy Transmission Grating ...Spectrometer observation to measure the Doppler shift of the He-like Si K
α
line-center wavelength emitted from these knots to find their line-of-sight (radial) velocities (
v
r
). We find
v
r
up to ∼5500 km s
−1
, with roughly consistent speeds between blueshifted and redshifted ejecta knots. We also measure the proper motions (PMs) for our sample based on archival Chandra Advanced CCD Imaging Spectrometer data taken from 2003, 2009, and 2015. We estimate PMs up to 0.″35 yr
−1
, which corresponds to a transverse velocity of about 5800 km s
−1
for the distance of 3.5 kpc to Tycho. Our
v
r
and transverse velocity measurements imply space velocities of ∼1900–6000 km s
−1
for the ejecta knots in Tycho. We estimate a new expansion center of R.A.(J2000) = 00
h
25
m
18
s
.725 ± 1
.ˢ
157 and decl.(J2000) = +64°08′02.″5 ± 11.″2 from our PM measurements, consistent to within ∼13″ of the geometric center. The distribution of space velocities throughout the remnant suggests that the southeast quadrant generally expands faster than the rest of the SNR. We find that blueshifted knots are projected more in the northern shell, while redshifted knots are more in the southern shell. The previously estimated reverse shock position is consistent with most of our estimated ejecta distribution; however, some ejecta show deviations from the 1D picture of the reverse shock.
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.
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.
We report our measurements of the bulk radial velocity from a sample of small, metal-rich ejecta knots in Kepler's supernova remnant (SNR). We measure the Doppler shift of the He-like Si K ...line-center energy in the spectra of these knots based on our Chandra High-Energy Transmission Grating Spectrometer observation to estimate their radial velocities. We estimate high radial velocities of up to ∼8000 km s−1 for some of these ejecta knots. We also measure proper motions for our sample based on the archival Chandra Advanced CCD Imaging Spectrometer data taken in 2000, 2006, and 2014. Our measured radial velocities and proper motions indicate that some of these ejecta knots are almost freely expanding after ∼400 yr since the explosion. The fastest moving knots show proper motions of up to ∼0 2 per year. Assuming that these high-velocity ejecta knots are traveling ahead of the forward shock of the SNR, we estimate the distance to Kepler's SNR d ∼ 4.4-7.5 kpc. We find that the ejecta knots in our sample have an average space velocity of vs ∼ 4600 km s−1 (at a distance of 6 kpc). We note that 8 of the 15 ejecta knots from our sample show a statistically significant (at the 90% confidence level) redshifted spectrum, compared to only two with a blueshifted spectrum. This may suggest an asymmetry in the ejecta distribution in Kepler's SNR along the line of sight; however, a larger sample size is required to confirm this result.
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 break with tradition: The cation, Ph3PNPPh3+ (PPN+), was found to provide a stabilizing η2‐arene interaction to the coordinatively unsaturated, tris‐isocyanide monoanion, ...Co(CNArMes2)3−(ArMes2=2,6‐(2,4,6‐Me3C6H2)C6H3); Co=purple, N=light purple, and P=orange). The resulting zwitterion is a source of Co(CNArMes2)3− anions, performing nucleophilic additions, carbon–element bond activations, and multistep decarbonylations.
PDF
