Changes in shear wave propagation within skeletal muscle during active and passive force generation

Muscle force can be generated actively through changes in neural excitation, and passively through externally imposed changes in muscle length. Disease and injury can disrupt force generation, but it can be challenging to separate passive from active contributions to these changes. Ultrasound elastography is a promising tool for characterizing the mechanical properties of muscles and the forces that they generate. Most prior work using ultrasound elastography in muscle has focused on the group velocity of shear waves, which increases with increasing muscle force. Few studies have quantified the phase velocity, which depends on the viscoelastic properties of muscle. Since passive and active forces within muscle involve different structures for force transmission, we hypothesized that measures of phase velocity could detect changes in shear wave propagation during active and passive conditions that cannot be detected when considering only group velocity. We measured phase and group velocity in the human biceps brachii during active and passive force generation and quantified the differences in estimates of shear elasticity obtained from each of these measurements. We found that measures of group velocity consistently overestimate the shear elasticity of muscle. We used a Voigt model to characterize the phase velocity and found that the estimated time constant for the Voigt model provided a way to distinguish between passive and active force generation. Our results demonstrate that shear wave elastography can be used to distinguish between passive and active force generation when it is used to characterize the phase velocity of shear waves propagating in muscle.     

Correlation between active and passive isometric force and intramuscular pressure in the isolated rabbit tibialis anterior muscle

The purpose of this study was to quantify the relationship between intramuscular pressure (IMP) and muscle force during isometric muscle contraction of the rabbit tibialis anterior (TA) absent the effect of either bone or fascia. To quantify this relationship, length-tension experiments were performed on the isolated TA of the New Zealand White rabbit (mass=2.5+/-0.5kg, n=12). The knee was fixed in a custom jig, the distal tendon of the TA was attached to a servomotor, and a 360 microm fiber optic pressure transducer was inserted into the TA. The peroneal nerve was stimulated to define optimal length (L(0)). The length-tension curve was created using 40Hz isometric contractions with 2-min rest intervals between each contraction. Measurements began at L(0)-50%L(f) and progressed to L(0)+50%L(f), changing the length-tension in 5% L(f) increments after each contraction. Qualitatively, the length-tension curve for isometric contractions was mimicked by the length-pressure curve for both active and passive conditions. Linear regression was performed individually for each animal for the ascending and descending limb of the length-tension curve and for active and passive conditions. Pressure-force coefficients of determination ranged from 0.138-0.963 for the active ascending limb and 0.343-0.947 for the active descending limb. Passive pressure coefficients of determination ranged from 0.045-0.842 for the ascending limb and 0.672-0.982 for the descending limb. These data indicate that IMP measurement provide a fairly accurate index of relative muscle force, especially at muscle lengths longer than optimal.     

The origin of passive force enhancement in skeletal muscle

The aim of the present study was to test whether titin is a calcium-dependent spring and whether it is the source of the passive force enhancement observed in muscle and single fiber preparations. We measured passive force enhancement in troponin C (TnC)-depleted myofibrils in which active force production was completely eliminated. The TnC-depleted construct allowed for the investigation of the effect of calcium concentration on passive force, without the confounding effects of actin-myosin cross-bridge formation and active force production. Passive forces in TnC-depleted myofibrils (n = 6) were 35.0 +/- 2.9 nN/ microm(2) when stretched to an average sarcomere length of 3.4 microm in a solution with low calcium concentration (pCa 8.0). Passive forces in the same myofibrils increased by 25% to 30% when stretches were performed in a solution with high calcium concentration (pCa 3.5). Since it is well accepted that titin is the primary source for passive force in rabbit psoas myofibrils and since the increase in passive force in TnC-depleted myofibrils was abolished after trypsin treatment, our results suggest that increasing calcium concentration is associated with increased titin stiffness. However, this calcium-induced titin stiffness accounted for only approximately 25% of the passive force enhancement observed in intact myofibrils. Therefore, approximately 75% of the normally occurring passive force enhancement remains unexplained. The findings of the present study suggest that passive force enhancement is partly caused by a calcium-induced increase in titin stiffness but also requires cross-bridge formation and/or active force production for full manifestation.     

Modulation of passive force in single skeletal muscle fibres

In this study, we investigated the effects of activation and stretch on the passive force-sarcomere length relationship in skeletal muscle. Single fibres from the lumbrical muscle of frogs were placed at varying sarcomere lengths on the descending limb of the force-sarcomere length relationship, and tetanic contractions, active stretches and passive stretches (amplitudes of ca 10% of fibre length at a speed of 40% fibre length/s) were performed. The passive forces following stretch of an activated fibre were higher than the forces measured after isometric contractions or after stretches of a passive fibre at the corresponding sarcomere length. This effect was more pronounced at increased sarcomere lengths, and the passive force-sarcomere length relationship following active stretch was shifted upwards on the force axis compared with the corresponding relationship obtained following isometric contractions or passive stretches. These results provide strong evidence for an increase in passive force that is mediated by a length-dependent combination of stretch and activation, while activation or stretch alone does not produce this effect. Based on these results and recently published findings of the effects of Ca2+ on titin stiffness, we propose that the observed increase in passive force is caused by the molecular spring titin.     

Muscle material properties in passive and active stroke-impaired muscle

Stroke survivors routinely experience long-term motor and sensory impairments. In parallel with neurological changes, material properties of muscles in the impaired limbs, such as muscle stiffness, may also change progressively. However, these stiffness measures are routinely derived from individual joint stiffness, representing whole muscle groups. Here, we use shear wave (SW) ultrasound elastography to measure SW velocity, as a surrogate measure of stiffness, to quantify material properties in individual muscles. Accordingly, the purpose of this study was to compare muscle material properties of the bicep brachii in stroke survivors and in age-matched control subjects by measuring SW velocity at rest and different voluntary activation levels. Our main findings show that at rest, the SW velocity was on average 41% greater in the paretic muscle compared the contralateral non-paretic muscle. The mean passive SW velocity across all subjects were 2.34 ± 0.41 m/s for the non-paretic side, 3.30 ± 1.20 m/s for the paretic side, and 2.24 ± 0.18 for controls. SW velocity was significantly different in muscles of the paretic and non-paretic side (p < 0.001), but not between muscles of the non-paretic and controls (p = 0.47). As voluntary activation increased, SW velocity increased non-linearly, with an average power fit of r² = 0.83 ± 0.09 for the non-paretic side, r² = 0.61 ± 0.24 for the paretic side, and r² = 0.24 ± 0.15 for the healthy age-matched controls. In active muscle (10, 25, 50, 75, 100% maximum voluntary contraction), there was no significant difference in SW velocity between the non-paretic, paretic, and control muscles.These findings suggest that stroke-impaired muscles have potentially altered muscle material properties, specifically stiffness, and that passive and active stiffness may contribute differently to total muscle stiffness.     

Genetic Models in Applied Physiology. Merosin deficiency leads to alterations in passive and active skeletal muscle mechanics.

The role of extracellular elements on the mechanical properties of skeletal muscles is unknown. Merosin is an essential extracellular matrix protein that forms a mechanical junction between the sarcolemma and collagen. Therefore, it is possible that merosin plays a role in force transmission between muscle fibers and collagen. We hypothesized that deficiency in merosin may alter passive muscle stiffness, viscoelastic properties, and contractile muscle force in skeletal muscles. We used the dy/dy mouse, a merosin-deficient mouse model, to examine changes in passive and active muscle mechanics. After mice were anesthetized and the diaphragm or the biceps femoris hindlimb muscle was excised, passive length-tension relationships, stress-relaxation curves, or isometric contractile properties were determined with an in vitro biaxial mechanical testing apparatus. Compared with controls, extensibility was smaller in the muscle fiber direction and the transverse fiber direction of the mutant mice. The relaxed elastic modulus was smaller in merosin-deficient diaphragms compared with controls. Interestingly, maximal muscle tetanic stress was depressed in muscles from the mutant mice during uniaxial loading but not during biaxial loading. However, presence of transverse passive stretch increases maximal contractile stress in both the mutant and normal mice. Our data suggest that merosin contributes to muscle passive stiffness, viscoelasticity, and contractility and that the mechanism by which force is transmitted between adjacent myofibers via merosin possibly in shear.     

Morphologic differences in skeletal muscle with age in normally active human males and their well-trained counterparts

In this study we elucidate the interaction of physical activity with aging as regards skeletal muscle fiber distribution and size. Thirty-three male athletes and 42 normally active counterparts served as subjects. They were assigned to younger (less than 25.5 years) and older (greater than 25.5 years) subgroups. Serial cross-sections from muscle biopsy samples (musculus vastus lateralis) were stained to distinguish fiber type: fast glycolytic (type IIb), fast oxidative-glycolytic (type IIa), or slow oxidative (type I). We also measured fiber diameters. A greater mean diameter of type I fibers was seen in older as opposed to younger athletes. Older controls had a smaller mean diameter of type IIb fibers than did younger controls. Athletes had a smaller mean percentage of type IIa fibers and a greater mean percentage of type I fibers than did controls. There was a greater mean percentage of type I fibers in older as opposed to younger controls, but this was not the case in athletes. Athletes may have larger fibers and a greater percentage of type I fibers at the expense of type IIa fibers. Atrophy of fibers with aging might be retarded by training, which might also reduce the age-associated rate of type IIb percentage loss and type I percentage gain.     

Velocity of ultrasound in active and passive cat medial gastrocnemius muscle.

The lengths and pinnation angles of muscle fibers in the medial gastrocnemius (MG) muscle have recently been measured in freely moving cats [Hoffer et al., Progr. Brain Res. 80, 75-85 (1989); Muscle Afferents and Spinal Control of Movement (1992)] using an ultrasound transit-time (USTT) technique. This method assumed that the velocity of ultrasound through intact muscles was constant, independent of fiber orientation, muscle activity, load, belly shape, or fiber movement. However, the velocity of ultrasound along and across the fibers has been reported to depend on the state of muscle activation in frog muscle experiments in vitro [Hatta et al., J. Physiol. 403, 193-209 (1988)]. In the present study, the assumption of constant velocity of ultrasound in the cat MG muscle was evaluated. In acute experiments, done in situ with intact blood supply, the USTT was measured along and across cat MG muscle fibers in the passive, reflexly activated and tetanically activated states, with and without changes in muscle fiber length, for situations that reproduced the length and force ranges normally used by cats during locomotion. The velocity of ultrasound was found to be independent of the state of activation or motion of the muscle, and independent of the direction of the measurement with respect to the fiber orientation, within a measurement uncertainty less than or equal to 0.2%. These results validate the use of the USTT technique for the measurement of intramuscular dimensions in freely moving animals.     

Models of skeletal muscle to explain the increase in passive stiffness in desmin knockout muscle

Absence of desmin in skeletal muscle was found to induce an increase in passive stiffness. The present study aimed at developing rheological models of passive muscle to explain this stiffening. Models were elaborated by using experimental data depicting muscle viscoelastic behaviour. The experimental protocol included stepwise extension tests applied on control and desmin knockout soleus muscles from mice. Linear and non-linear models were composed of elastic and viscous elements. They were constructed with the aim at taking the presence or absence of desmin into account by simulating desmin as an elastic element. Furthermore, associated adaptation of connective tissues in absence of desmin was modelled as an additional elastic element. Differences in passive behaviour induced by absence of desmin were predicted by using a linear model and a non-linear one. The non-linear model was selected because: (1) it is able to predict experimental viscoelastic kinetics accounting for the increase in passive stiffness in muscles lacking desmin, (2) its design is consistent with morphological data, and (3) stiffness characteristics of its elements are in accordance with the literature. Finally, this modelling approach demonstrates that both absence of desmin and adaptation of connective tissue are required to explain the increase in passive stiffness in desmin knockout muscles.     

Length dependence of active force production in skeletal muscle.

The sliding filament and cross-bridge theories of muscle contraction provide discrete predictions of the tetanic force-length relationship of skeletal muscle that have been tested experimentally. The active force generated by a maximally activated single fiber (with sarcomere length control) is maximal when the filament overlap is optimized and is proportionally decreased when overlap is diminished. The force-length relationship is a static property of skeletal muscle and, therefore, it does not predict the consequences of dynamic contractions. Changes in sarcomere length during muscle contraction result in modulation of the active force that is not necessarily predicted by the cross-bridge theory. The results of in vivo studies of the force-length relationship suggest that muscles that operate on the ascending limb of the force-length relationship typically function in stretch-shortening cycle contractions, and muscles that operate on the descending limb typically function in shorten-stretch cycle contractions. The joint moments produced by a muscle depend on the moment arm and the sarcomere length of the muscle. Moment arm magnitude also affects the excursion (length change) of a muscle for a given change in joint angle, and the number of sarcomeres arranged in series within a muscle fiber determines the sarcomere length change associated with a given excursion.     

Control of muscle fibre and motoneuron diversification

Recent studies have elucidated both the mechanism of early formation of diverse muscle fibre types and the matching of diverse populations of motoneurons to their appropriate muscle targets. Highlights include the demonstration that distinct signals are necessary for the formation of several distinct myoblast populations in the vertebrate somite, the identification of motoneuron subtypes, studies of how motoneurons target appropriate muscles, and rapid progress on the Drosophila neuromuscular system. We propose a model in which four classes of decision control the patterning of both motoneurons and muscles.     

Variation in active and passive resource inputs to experimental pools: mechanisms and possible consequences for food webs

1. Cross‐ecosystem movements of resources, including detritus, nutrients and living prey, can strongly influence food web dynamics in recipient habitats. Variation in resource inputs is thought to be driven by factors external to the recipient habitat (e.g. donor habitat productivity and boundary conditions). However, inputs of or by ‘active’ living resources may be strongly influenced by recipient habitat quality when organisms exhibit behavioural habitat selection when crossing ecosystem boundaries. 2. To examine whether behavioural responses to recipient habitat quality alter the relative inputs of ‘active’ living and ‘passive’ detrital resources to recipient food webs, we manipulated the presence of caged predatory fish and measured biomass, energy and organic content of inputs to outdoor experimental pools of adult aquatic insects, frog eggs, terrestrial plant matter and terrestrial arthropods. 3. Caged fish reduced the biomass, energy and organic matter donated to pools by tree frog eggs by ～70%, but did not alter insect colonisation or passive allochthonous inputs of terrestrial arthropods and plant material. Terrestrial plant matter and adult aquatic insects provided the most energy and organic matter inputs to the pools (40–50%), while terrestrial arthropods provided the least (7%). Inputs of frog egg were relatively small but varied considerably among pools and over time (3%, range = 0–20%). Absolute and proportional amounts varied by input type. 4. Aquatic predators can strongly affect the magnitude of active, but not passive, inputs and that the effect of recipient habitat quality on active inputs is variable. Furthermore, some active inputs (i.e. aquatic insect colonists) can provide similar amounts of energy and organic matter as passive inputs of terrestrial plant matter, which are well known to be important. Because inputs differ in quality and the trophic level they subsidise, proportional changes in input type could have strong effects on recipient food webs. 5. Cross‐ecosystem resource inputs have previously been characterised as donor‐controlled. However, control by the recipient food web could lead to greater feedback between resource flow and consumer dynamics than has been appreciated so far.     

Models of contractile units and their assembly in smooth muscle

It is believed that the contractile filaments in smooth muscle are organized into arrays of contractile units (similar to the sarcomeric structure in striated muscle), and that such an organization is crucial for transforming the mechanical activities of actomyosin interaction into cell shortening and force generation. Details of the filament organization, however, are still poorly understood. Several models of contractile filament architecture are discussed here. To account for the linear relationship observed between the force generated by a smooth muscle and the muscle length at the plateau of an isotonic contraction, a model of contractile unit is proposed. The model consists of 2 dense bodies with actin (thin) filaments attached, and a myosin (thick) filament lying between the parallel thin filaments. In addition, the thick filament is assumed to span the whole contractile unit length, from dense body to dense body, so that when the contractile unit shortens, the amount of overlap between the thick and thin filaments (i.e., the distance between the dense bodies) decreases in exact proportion to the amount of shortening. Assembly of the contractile units into functional contractile apparatus is assumed to involve a group of cells that form a mechanical syncytium. The contractile apparatus is assumed malleable in that the number of contractile units in series and in parallel can be altered to accommodate strains on the muscle and to maintain the muscle's optimal mechanical function.     

A validated model of passive skeletal muscle to predict force and intramuscular pressure

The passive properties of skeletal muscle are often overlooked in muscle studies, yet they play a key role in tissue function in vivo. Studies analyzing and modeling muscle passive properties, while not uncommon, have never investigated the role of fluid content within the tissue. Additionally, intramuscular pressure (IMP) has been shown to correlate with muscle force in vivo and could be used to predict muscle force in the clinic. In this study, a novel model of skeletal muscle was developed and validated to predict both muscle stress and IMP under passive conditions for the New Zealand White Rabbit tibialis anterior. This model is the first to include fluid content within the tissue and uses whole muscle geometry. A nonlinear optimization scheme was highly effective at fitting model stress output to experimental stress data (normalized mean square error or NMSE fit value of 0.993) and validation showed very good agreement to experimental data (NMSE fit values of 0.955 and 0.860 for IMP and stress, respectively). While future work to include muscle activation would broaden the physiological application of this model, the passive implementation could be used to guide surgeries where passive muscle is stretched.     

Ratio of active to passive muscle shortening in the canine diaphragm.

Active and passive shortening of muscle bundles in the canine diaphragm were measured with the objective of testing a consequence of the minimal-work hypothesis: namely, that the ratio of active to passive shortening is the same for all active muscles. Lengths of six muscle bundles in the costal diaphragm and two muscle bundles in the crural diaphragm of each of four bred-for-research beagle dogs were measured by the radiopaque marker technique during the following maneuvers: a passive deflation maneuver from total lung capacity to functional residual capacity, quiet breathing, and forceful inspiratory efforts against an occluded airway at different lung volumes. Shortening per liter increase in lung volume was, on average, 70% greater during quiet breathing than during passive inflation in the prone posture and 40% greater in the supine posture. For the prone posture, the ratio of active to passive shortening was larger in the ventral and midcostal diaphragm than at the dorsal end of the costal diaphragm. For both postures, active shortening during quiet breathing was poorly correlated with passive shortening. However, shortening during forceful inspiratory efforts was highly correlated with passive shortening. The average ratios of active to passive shortening were 1.23 +/- 0.02 and 1.32 +/- 0.03 for the prone and supine postures, respectively. These data, taken together with the data reported in the companion paper (T. A. Wilson, M. Angelillo, A. Legrand, and A. De Troyer, J. Appl. Physiol. 87: 554-560, 1999), support the hypothesis that, during forceful inspiratory efforts, the inspiratory muscles drive the chest wall along the minimal-work trajectory.     

The role of passive structures in force enhancement of skeletal muscles following active stretch

We recently found that force enhancement following active stretch in skeletal muscles is accompanied by an increase in passive force following deactivation (J. Exp. Biol. 205 (2002) 1275). However, it is not known if this increase in passive force contributes to the force enhancement observed in the active muscle, and if it is observed at all muscle lengths. The purposes of this study were to quantify the amount of passive force increase as a function of muscle lengths, and to determine if this passive force contributes to the force enhancement observed in the active muscle. Experiments were performed on cat soleus (n = 24) using techniques published previously (J. Biomech. 30(9) (1997) 865). Conceptually, tests involved comparisons of force enhancement and passive force increase for a variety of stretch tests in soleus. Furthermore, in one test, activation of the soleus was interrupted for 1s in the force-enhanced state, and soleus was then re-activated. We found that total force enhancement and passive force increase were positively correlated for all test conditions, that passive force increase following stretch of the active soleus only occurred at muscle lengths corresponding to the descending limb of the force-length relationship, that increases in passive force for a given stretch magnitude became greater at long muscle lengths, and that upon reactivation, there was a remnant passive force enhancement. We conclude from these results that the passive force enhancement following stretch of an active muscle contributes to the total force enhancement, that this passive contribution increases with increasing muscle length, and that there must be at least one other factor than passive force increase that contributes to the total force enhancement, as the passive force increase was always smaller than the total force enhancement. A by-product of this investigation was that we observed a shift in the passive force-length relationship that was dependent on muscle activation, stretch magnitude and muscle length. Therefore, the passive force-length relationship is not a constant property of skeletal muscle, but depends critically on the muscle's contractile history.     

Modeling of cardiac muscle thin films: pre-stretch, passive and active behavior

Recent progress in tissue engineering has made it possible to build contractile bio-hybrid materials that undergo conformational changes by growing a layer of cardiac muscle on elastic polymeric membranes. Further development of such muscular thin films for building actuators and powering devices requires exploring several design parameters, which include the alignment of the cardiac myocytes and the thickness/Young's modulus of elastomeric film. To more efficiently explore these design parameters, we propose a 3-D phenomenological constitutive model, which accounts for both the passive deformation including pre-stretch and the active behavior of the cardiomyocytes. The proposed 3-D constitutive model is implemented within a finite element framework, and can be used to improve the current design of bio-hybrid thin films and help developing bio-hybrid constructs capable of complex conformational changes.