A phenomenological model and validation of shortening-induced force depression during muscle contractions

History-dependent effects on muscle force development following active changes in length have been measured in a number of experimental studies. However, few muscle models have included these properties or examined their impact on force and power output in dynamic cyclic movements. The goal of this study was to develop and validate a modified Hill-type muscle model that includes shortening-induced force depression and assess its influence on locomotor performance. The magnitude of force depression was defined by empirical relationships based on muscle mechanical work. To validate the model, simulations incorporating force depression were developed to emulate single muscle in situ and whole muscle group leg extension experiments. There was excellent agreement between simulation and experimental values, with in situ force patterns closely matching the experimental data (average RMS error <1.5 N) and force depression in the simulated leg extension exercise being similar in magnitude to experimental values (6.0% vs. 6.5%, respectively). To examine the influence of force depression on locomotor performance, simulations of maximum power pedaling with and without force depression were generated. Force depression decreased maximum crank power by 20–40%, depending on the relationship between force depression and muscle work used. These results indicate that force depression has the potential to substantially influence muscle power output in dynamic cyclic movements. However, to fully understand the impact of this phenomenon on human movement, more research is needed to characterize the relationship between force depression and mechanical work in large muscles with different morphologies.     

From single muscle fiber to whole muscle mechanics: a finite element model of a muscle bundle with fast and slow fibers

Muscles exhibit highly complex, multi-scale architecture with thousands of muscle fibers, each with different properties, interacting with each other and surrounding connective structures. Consequently, the results of single-fiber experiments are scarcely linked to the macroscopic or whole muscle behavior. This is especially true for human muscles where it would be important to understand of how skeletal muscles disorders affect patients’ life. In this work, we developed a mathematical model to study how fast and slow muscle fibers, well characterized in single-fiber experiments, work and generate together force and displacement in muscle bundles. We characterized the parameters of a Hill-type model, using experimental data on fast and slow single human muscle fibers, and comparing experimental data with numerical simulations obtained from finite element (FE) models of single fibers. Then, we developed a FE model of a bundle of 19 fibers, based on an immunohistochemically stained cross section of human diaphragm and including the corresponding properties of each slow or fast fiber. Simulations of isotonic contractions of the bundle model allowed the generation of its apparent force–velocity relationship. Although close to the average of the force–velocity curves of fast and slow fibers, the bundle curve deviates substantially toward the fast fibers at low loads. We believe that the present model and the characterization of the force–velocity curve of a fiber bundle represents the starting point to link the single-fiber properties to those of whole muscle with FE application in phenomenological models of human muscles.     

Differences between properties of male and female motor units in the rat medial gastrocnemius muscle.

Differences between motor units in hindlimb locomotor muscles of male and female Wistar rats were studied. The contractile and action potential properties of various types of motor units as well as proportions of these units in the medial gastrocnemius muscle were analyzed. Experiments were based on functional isolation and electrical stimulation of axons of single motor units. Composition of motor units was different for male and female subjects, with higher number of the fast fatigable and lower number of slow type units in male animals. The contraction and the half-relaxation times were significantly longer in male motor units, what might be due to differences in muscle size. Slower contraction of male motor units likely corresponds to lower firing rates of their motoneurons. On the other hand, no significant differences between sexes were observed with respect to force parameters of motor units (the twitch and the maximum tetanus forces), except the fast resistant units (higher force values in male muscles). The mass of the muscle was approximately 1.5 time bigger in male rats. However, the mean ratio of motor unit tetanus force to the muscle mass was almost twice smaller in this group, what indirectly suggests that muscles of male rats are composed of higher number of motor units. Finally, female muscles appeared to have higher fatigue resistance as the effect of higher proportion of resistant units (slow and fast resistant) and higher values of the fatigue index in respective motor unit types. The motor unit action potentials in female rats had slightly lower amplitudes and shorter time parameters although this difference was significant only for fast resistant units.     

The influence of posture variation on electromyographic signals in females obtained during maximum voluntary isometric contractions: A shoulder example

Surface electromyography (sEMG) is commonly used to estimate muscle demands in occupational tasks. To allow for comparisons, sEMG amplitude is normalized to muscle specific maximum voluntary contractions (MVCs) performed in a standardized set of postures. However, maximal sEMG amplitude in shoulder muscles is highly dependent on arm posture and therefore, normalizing task related muscular activity to standard MVCs may lead to misinterpretation of task specific muscular demands. Therefore, the purpose of this study was to investigate differences in commonly monitored shoulder muscles using normalized sEMG amplitude between maximal exertions at different hand locations and across force exertion directions relative to standard MVCs. sEMG was recorded from the middle deltoid, pectoralis major sternal head, infraspinatus, latissimus dorsi, and upper trapezius. Participants completed standardized muscle-specific MVCs and two maximal exertions in 5 hand locations (low left, low right, high left, high right, and central) in each of the four force directions (push, pull, up, and down). Peak sEMG was analyzed in the direction(s) that elicited the highest signal for each muscle. All muscles differed by location (p < 0.05). Latissimus dorsi had the greatest activation during pulls (32–135% MVC); upper trapezius and middle deltoid while exerting upwards (73–103% and 42–78% MVC, respectively); infraspinatus while pushing (38–79% MVC); and pectoralis major activation was the highest during downwards exertions (48–84% MVC). Normalization of location specific maximal exertions to standard muscle specific MVCs underestimated maximal activity across 90% of the tasks in all shoulder muscles tested, except for latissimus dorsi where amplitudes were overestimated in low right hand location. Normalization of location specific muscle activity to standard muscle specific MVCs often underestimates muscle activity in task performance and is cautioned against if the goal is to accurately estimate muscle demands.     

Reduction of neuromuscular redundancy for postural force generation using an intrinsic stability criterion

Postural control requires the coordination of multiple muscles to achieve both endpoint force production and postural stability. Multiple muscle activation patterns can produce the required force for standing, but the mechanical stability associated with any given pattern may vary, and has implications for the degree of delayed neural feedback necessary for postural stability. We hypothesized that muscular redundancy is reduced when muscle activation patterns are chosen with respect to intrinsic musculoskeletal stability as well as endpoint force production. We used a three-dimensional musculoskeletal model of the cat hindlimb with 31 muscles to determine the possible contributions of intrinsic muscle properties to limb stability during isometric force generation. Using dynamic stability analysis we demonstrate that within the large set of activation patterns that satisfy the force requirement for posture, only a reduced subset produce a mechanically stable limb configuration. Greater stability in the frontal-plane suggests that neural control mechanisms are more highly active for sagittal-plane and for ankle joint control. Even when the limb was unstable, the time-constants of instability were sufficiently great to allow long-latency neural feedback mechanisms to intervene, which may be preferential for movements requiring maneuverability versus stability. Local joint stiffness of muscles was determined by the stabilizing or destabilizing effects of moment-arm versus joint angle relationships. By preferentially activating muscles with high local stiffness, muscle activation patterns with feedforward stabilizing properties could be selected. Such a strategy may increase intrinsic postural stability without co-contraction, and may be useful criteria in the force-sharing problem.     

Interfiber tension transmission in series-fibered muscles of the cat hindlimb

Several muscles of the cat hindlimb, including biceps femoris and tenuissimus, are composed of short, in-series muscle fibers with tapered intrafascicular terminations. Tension generation and transmission within such muscles requires that active fibers should be mechanically coupled in series via myomyous junctions, specialized connective tissue attachments, or the endomysium. This report establishes that the tapered fibers of the cat biceps femoris and tenuissimus muscles have insignificant numbers of either myomyous or specialized connective tissue junctions. Tension appears to be transmitted in a distributed manner across the plasmalemma of the tapered (and probably the non-tapered) portions of the fibers to the connective tissue of the endomysium, which is therefore an essential series elastic element in these muscles. Subplasmalemmal dense plaques were identified and may play a role in transmembrane force transmission. In addition to the endomysium, passive muscle fibers may also serve to transmit tension between active fibers, and therefore should also be considered to be series elastic elements.     

Evidence of residual force enhancement for multi-joint leg extension

Force enhancement is a well accepted property of skeletal muscle and has been observed at all structural levels ranging from single myofibrils to voluntarily activated m. quadriceps femoris in vivo. However, force enhancement has not been studied for multi-joint movements like human leg extension; therefore knowledge about its relevance in daily living remains limited. The purpose of this study was to determine whether there is force enhancement during maximal voluntary multi-joint leg extension. Human leg extension was studied (n=22) on a motor driven leg press dynamometer where external reaction forces under the feet as well as activity of 8 lower extremity muscles were measured. In addition, torque in the ankle and knee joints was calculated using inverse dynamics. The steady-state isometric force, joint torques, and muscle activation after active stretch (20° stretch amplitude at 60°/s) were compared with the corresponding values obtained during isometric reference contractions. There was consistent force enhancement during and following stretch for both forces and joint torques. Potentiation during stretch reached values between 26% and 30%, while a significant force enhancement of 10.5–12.3% and 4.3–7.4% remained 0.5–1 and 2.5–3 s after stretch, respectively. During stretch, EMG signals of m. gastrocnemius medialis and lateralis were significantly increased, while following stretch all analyzed muscles showed the same activity as during the reference contractions. We conclude from these results that force enhancement exists in everyday movements and should be accounted for when analyzing or modelling human movement.     

Functional and architectural complexity within and between muscles: regional variation and intermuscular force transmission

Over the past 30 years, studies of single muscles have revealed complex patterns of regional variation in muscle architecture, activation, strain and force. In addition, muscles are often functionally integrated with other muscles in parallel or in series. Understanding the extent of this complexity and the interactions between muscles will profoundly influence how we think of muscles in relation to organismal function, and will allow us to address questions regarding the functional benefits (or lack thereof) and dynamics of this complexity under in vivo conditions. This paper has two main objectives. First, we present a cohesive and integrative review of regional variation in function within muscles, and discuss the functional ramifications that can stem from this variation. This involves splitting regional variation into passive and active components. Second, we assess the functional integration of muscles between different limb segments by presenting new data involving in vivo measurements of activation and strain from the medial gastrocnemius, iliotibialis cranialis and iliotibialis lateralis pars preacetabularis of the helmeted guinea fowl (Numida meleagris) during level running on a motorized treadmill. Future research directions for both of these objectives are presented.     

Upper limb muscle volumes in adult subjects

Muscle force-generating properties are often derived from cadaveric studies of muscle architecture. While the relative sizes of muscles at a single upper limb joint have been established in cadaveric specimens, the relative sizes of muscles across upper limb joints in living subjects remain unclear. We used magnetic resonance imaging to measure the volumes of the 32 upper limb muscles crossing the glenohumeral joint, elbow, forearm, and wrist in 10 young, healthy subjects, ranging from a 20th percentile female to a 97th percentile male, based on height. We measured the volume and volume fraction of these muscles. Muscles crossing the shoulder, elbow, and wrist comprised 52.5, 31.4, and 16.0% of the total muscle volume, respectively. The deltoid had the largest volume fraction (15.2%+/-1%) and the extensor indicis propius had the smallest (0.2%+/-0.05%). We determined that the distribution of muscle volume in the upper limb is highly conserved across these subjects with a three-fold variation in total muscle volumes (1427-4426cm(3)). When we predicted the volume of an individual muscle from the mean volume fraction, on average 85% of the variation among subjects was accounted for (average p=0.0008). This study provides normative data that forms the basis for investigating muscle volumes in other populations, and for scaling computer models to more accurately represent the muscle volume of a specific individual.     

Muscle architecture and out‐force potential of the thoracic limb in the eastern mole (Scalopus aquaticus)

Moles have modified thoracic limbs with hypertrophied pectoral girdle muscles that allow them to apply remarkably high lateral out‐forces during the power stroke when burrowing. To further understand the high force capabilities of mole forelimbs, architectural properties of the thoracic limb muscles were quantified in the Eastern mole (Scalopus aquaticus). Architectural properties measured included muscle mass, moment arm, belly length, fascicle length, and pennation angle, and these were used to provide estimates of maximum isometric force, joint torque, and power. Measurements of muscle moment arms and limb lever lengths were additionally used to analyze the out‐force contributions of the major pectoral girdle muscles. Most muscles have relatively long fascicles and little‐to‐no pennation. The humeral abductor/rotators as a functional group are massive and are capable of relatively high force, power, and joint torque. Of this group, the bipennate m. teres major is the most massive and has the capacity to produce the highest force and joint torque to abduct and axially rotate the humerus. In general, the distal limb muscles are relatively small, but have the capacity for high force and mechanical work by fascicle shortening. The muscle architectural properties of the elbow extensors (e.g., m. triceps brachii) and carpal flexors (e.g., m. palmaris longus) are consistent with the function of these muscles to augment lateral out‐force application. The humeral abductor/rotators m. latissimus dorsi, m. teres major, m. pectoralis, and m. subscapularis are calculated to contribute 13.9 N to out‐force during the power stroke, and this force is applied in a ‘frontal’ plane causing abduction of the humerus about the sternoclavicular joint. Moles have several specializations of their digging apparatus that greatly enhance the application of out‐force, and these morphological features suggest convergence on limb form and burrowing function between New and Old World moles. J. Morphol. 274:1277–1287, 2013. © 2013 Wiley Periodicals, Inc.     

Osteology and myology of the wing of the Emu (Dromaius novaehollandiae), and its bearing on the evolution of vestigial structures

Emus have reduced their wing skeleton to only a single functional digit, but the myological changes associated with this reduction have never been properly described. Moreover, the intraspecific variability associated with these changes has not previously been examined, dissections having been restricted in the past to only one or two individuals. In this paper, the myology and osteology of the Emu wing is described for a sample of five female birds. The Emu showed a marked reduction in the number of muscles in the wing, even compared with other ratites. Many wing muscles showed diversity in structure, origin and insertion sites, number of heads, as well as presence-absence variation. This variability dramatically exceeds that found in flying birds. Evolutionary theory predicts that relaxed selection on vestigial organs should allow more variation to persist in the population, and corresponds to what is observed here. A large amount of fluctuating asymmetry was also detected, indicating reduced canalization of the wing during development.     

Development of myoglobin concentration and acid buffering capacity in harp (<Emphasis Type="Italic">Pagophilus groenlandicus</Emphasis>) and hooded (<Emphasis Type="Italic">Cystophora cristata</Emphasis>) seals from birth to maturity

Pinnipeds rely on muscle oxygen stores to help support aerobic diving, therefore muscle maturation may influence the behavioral ecology of young pinnipeds. To investigate the pattern of muscle development, myoglobin concentration ([Mb]) and acid buffering ability (β) was measured in ten muscles from 23 harp and 40 hooded seals of various ages. Adult [Mb] ranged from 28–97 to 35–104 mg g tissue⁻¹ in harp and hooded seals, respectively, with values increasing from the cervical, non-swimming muscles to the main swimming muscles of the lumbar region. Neonatal and weaned pup muscles exhibited lower (~30% adult values) and less variable [Mb] across the body than adults. In contrast, adult β showed little regional variation (60–90 slykes), while high pup values (~75% adult values) indicate significant in utero development. These findings suggest that intra-uterine conditions are sufficiently hypoxic to stimulate prenatal β development, but that [Mb] development requires additional postnatal signal such as exercise, and/or growth factors. However, because of limited development in both β and [Mb] during the nursing period, pups are weaned with muscles with lower aerobic and anaerobic capacities than those of adults.     

Measuring succession: methods for establishing long-term vegetation monitoring sites

Successional stages are often characterized by dominant plant species (species with the highest cover) and their effect on the structure and function of an area through time. However, the plant species determining the ecosystem properties and plant community dynamics may not be the dominant, especially when it is exotic. Understanding plant community dynamics in ecosystems that are uncharacterized and/or affected by invasive plant species requires a data-driven approach and proper placement of monitoring plots. To generate robust datasets on vegetation change through time, monitoring plot placement must consider the scale of ecological variation for both vegetation and soils and plots would ideally be replicated within similar ecological site types to quantify the consistency of successional transitions. We characterized soil and vegetation across and within seven floodplains affected by Russian olive (Elaeagnus angustifolia L.) along the Yellowstone River in southeastern Montana, USA. Using modern Classification and Regression Trees (CART) and multivariate net differentiation, we identified five distinct plant community types, or classes, characterized by their tertiary woody plant cover, not the primary species, Russian olive. Our findings indicate that Russian olive communities differ across space, and these riparian areas can be classified into distinct plant community types. Characterizing plant community types via this analytical approach should allow practitioners to modify management decisions and forecast succession within relevant plant communities.     

Aging alters contractile properties and fiber morphology in pigeon skeletal muscle

In this study, we tested the hypothesis that skeletal muscle from pigeons would display age-related alterations in isometric force and contractile parameters as well as a shift of the single muscle fiber cross-sectional area (CSA) distribution toward smaller fiber sizes. Maximal force output, twitch contraction durations and the force–frequency relationship were determined in tensor propatagialis pars biceps muscle from young 3-year-old pigeons, middle-aged 18-year-old pigeons, and aged 30-year-old pigeons. The fiber CSA distribution was determined by planimetry from muscle sections stained with hematoxylin and eosin. Maximal force output of twitch and tetanic contractions was greatest in muscles from young pigeons, while the time to peak force of twitch contractions was longest in muscles from aged pigeons. There were no changes in the force–frequency relationship between the age groups. Interestingly, the fiber CSA distribution in aged muscles revealed a greater number of larger sized muscle fibers, which was verified visually in histological images. Middle-aged and aged muscles also displayed a greater amount of slow myosin containing muscle fibers. These data demonstrate that muscles from middle-aged and aged pigeons are susceptible to alterations in contractile properties that are consistent with aging, including lower force production and longer contraction durations. These functional changes were supported by the appearance of slow myosin containing muscle fibers in muscles from middle-aged and aged pigeons. Therefore, the pigeon may represent an appropriate animal model for the study of aging-related alterations in skeletal muscle function and structure.     

ISOFIT: a model-based method to measure muscle–tendon properties simultaneously

Summary Estimation of muscle parameters specifying force–length and force–velocity behavior requires in general a large number of sophisticated experiments often including a combination of isometric, isokinetic, isotonic, and quick-release experiments. This study validates a simpler method (ISOFIT) to determine muscle properties by fitting a Hill-type muscle model to a set of isovelocity data. Muscle properties resulting from the ISOFIT method agreed well with muscle properties determined separately in in vitro measurements using frog semitendinosus muscles. The force–length curve was described well by the results of the model. The force–velocity curve resulting from the model coincided with the experimentally determined curve above approximately 20% of maximum isometric force (correlation coefficient R>0.99). At lower forces and thus higher velocities the predicted curve underestimated velocity. The stiffness of the series elastic component determined with direct experiments was approximately 10% lower than that determined by the ISOFIT method. Use of the ISOFIT method can decrease experimental time up to 80% and reduce potential changes in muscle parameters due to fatigue.     

Coupled expression of troponin T and troponin I isoforms in single skeletal muscle fibers correlates with contractility

Striated muscle contraction is powered by actin-activated myosin ATPase. This process is regulated by Ca(2+) via the troponin complex. Slow- and fast-twitch fibers of vertebrate skeletal muscle express type I and type II myosin, respectively, and these myosin isoenzymes confer different ATPase activities, contractile velocities, and force. Skeletal muscle troponin has also diverged into fast and slow isoforms, but their functional significance is not fully understood. To investigate the expression of troponin isoforms in mammalian skeletal muscle and their functional relationship to that of the myosin isoforms, we concomitantly studied myosin, troponin T (TnT), and troponin I (TnI) isoform contents and isometric contractile properties in single fibers of rat skeletal muscle. We characterized a large number of Triton X-100-skinned single fibers from soleus, diaphragm, gastrocnemius, and extensor digitorum longus muscles and selected fibers with combinations of a single myosin isoform and a single class (slow or fast) of the TnT and TnI isoforms to investigate their role in determining contractility. Types IIa, IIx, and IIb myosin fibers produced higher isometric force than that of type I fibers. Despite the polyploidy of adult skeletal muscle fibers, the expression of fast or slow isoforms of TnT and TnI is tightly coupled. Fibers containing slow troponin had higher Ca(2+) sensitivity than that of the fast troponin fibers, whereas fibers containing fast troponin showed a higher cooperativity of Ca(2+) activation than that of the slow troponin fibers. These results demonstrate distinct but coordinated regulation of troponin and myosin isoform expression in skeletal muscle and their contribution to the contractile properties of muscle.     

Intrinsic properties of pharyngeal and diaphragmatic respiratory motoneurons and muscles.

Breathing is a complex act requiring the coordinated activity of multiple groups of muscles. Thoracic and abdominal respiratory muscles expand and contract the lungs, whereas pharyngeal and laryngeal respiratory muscles maintain upper airway patency and regulate upper airway resistance. An appreciation of the importance of the latter muscle group in maintaining ventilatory homeostasis and in the pathophysiology of sleep apnea has led to extensive studies examining the neural regulation of pharyngeal dilator muscles. The present review examines the role of heterogeneity in motoneuron and muscle properties in determining the diversity in the electrical and mechanical behaviors of thoracic compared with pharyngeal muscle groups. Specifically, phrenic and hypoglossal motoneuron electrophysiological properties influence whether and the extent to which these neurons will fire in response to a given synaptic input arising from chemo- and mechanoreceptors and from respiratory and nonrespiratory pattern generators. Furthermore, thoracic and pharyngeal muscle properties determine the mechanical response to motoneuronal activity, including the speed of contraction, relationships between motoneuron firing frequency and force production, and whether force is maintained during repetitive activation. Heterogeneity in the functional capabilities of these motoneurons and muscles is in turn determined by diversity of their structural and biochemical properties. Thus, intrinsic properties of respiratory motoneurons and muscles act in concert with neuronal drives in defining the complex electrical and mechanical behavior of pharyngeal and thoracic respiratory motor systems.     

Mechanical similarity across ontogeny of digging muscles in an Australian marsupial (Isoodon fusciventer)

Many mammals dig, either during foraging to access subsurface food resources, or in creating burrows for shelter. Digging requires large forces produced by muscles and transmitted to the soil via the skeletal system; thus fossorial mammals tend to have characteristic modifications of the musculoskeletal system that reflect their digging ability. Bandicoots (Marsupialia: Peramelidae) scratch-dig mainly to source food, searching for subterranean food items including invertebrates, seeds, and fungi. They have musculoskeletal features for digging, including shortened, robust forelimb bones, large muscles, and enlarged muscle attachment areas. Here, we compared changes in the ontogenetic development of muscles associated with digging in the Quenda (Isoodon fusciventer). We measured muscle mass (m _m), pennation angle, and fiber length (FL) to calculate physiological cross-sectional area (PCSA; a proxy of maximum isometric force) as well as estimate the maximum isometric force (Fmax) for 34 individuals ranging in body size from 124 to 2,390 g. Males grow larger than females in this bandicoot species, however, we found negligible sex differences in mass-specific m _m, PCSA or FL for our sample. Majority of the forelimb muscles PCSA showed a positive allometric relationship with total body mass, while m _m and FL in the majority of forelimb muscles showed isometry. Mechanical similarity was tested, and two thirds of forelimb muscles maximum isometric forces (Fmax) scaled with isometry; therefore the forelimb is primarily mechanical similar throughout ontogeny. PCSA showed a significant difference between scaling slopes between main movers in the power stroke, and main movers of the recovery stroke of scratch-digging. This suggests that some forelimb muscles grow with positive allometry, specially these associated with the power stroke of digging. Intraspecific variation in PCSA is rarely considered in the literature, and thus this is an important study quantifying changes in muscle architectural properties with growth in a mammalian model of scratch-digging.     

Using individual-muscle specific instead of across-muscle mean data halves muscle simulation error

Hill-type parameter values measured in experiments on single muscles show large across-muscle variation. Using individual-muscle specific values instead of the more standard approach of across-muscle means might therefore improve muscle model performance. We show here that using mean values increased simulation normalized RMS error in all tested motor nerve stimulation paradigms in both isotonic and isometric conditions, doubling mean simulation error from 9 to 18 (different at p?<?0.0001). These data suggest muscle-specific measurement of Hill-type model parameters is necessary in work requiring highly accurate muscle model construction. Maximum muscle force (F _max) showed large (fourfold) across-muscle variation. To test the role of F _max in model performance we compared the errors of models using mean F _max and muscle-specific values for the other model parameters, and models using muscle-specific F _max values and mean values for the other model parameters. Using muscle-specific F _max values did not improve model performance compared to using mean values for all parameters, but using muscle-specific values for all parameters but F _max did (to an error of 14, different from muscle-specific, mean all parameters, and mean only F _max errors at p?≤ 0.014). Significantly improving model performance thus required muscle-specific values for at least a subset of parameters other than F _max, and best performance required muscle-specific values for this subset and F _max. Detailed consideration of model performance suggested that remaining model error likely stemmed from activation of both fast and slow motor neurons in our experiments and inadequate specification of model activation dynamics.