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.     

Intramuscular pressure, force and blood flow in rabbit tibialis anterior muscles during single and repetitive contractions

The elevated intramuscular pressure (IMP) associated with sustained muscle contraction can affect blood flow, and could influence the long-term viability of functional skeletal muscle grafts. We therefore examined the relationship between force, peak IMP and blood flow in the tibialis anterior muscle of the anaesthetized rabbit. During isometric contractions, IMP was related linearly to force, and only the slope of the relationship varied between animals. During isotonic contractions, however, the highest values of IMP were found at the lowest force levels, and IMP appeared to be related to the amount and speed of shortening. During repeated isometric contractions, the ratio of IMP to force varied with time, stimulation pattern and subject. Mean blood flow did not differ appreciably between␣repetitive isometric contractions at duty cycles of 10–40%, and was unrelated to integrated pressure, integrated force, or depth from the surface. We conclude: (1) that IMP is unlikely to affect mean blood flow during cyclic activity that has a duty cycle less than 40%; and (2) that the clinical use of IMP as a predictor of muscle force appears to be justified only for single isometric contractions, and needs to be interpreted cautiously when contractions involve shortening or fatigue. Accepted: 17 November 1997     

Intramuscular pressure of human tibialis anterior muscle detects age-related changes in muscle performance

Intramuscular pressure (IMP) reflects forces produced by a muscle. Age is one of the determinants of skeletal muscle performance. The present study aimed to test whether IMP mirrors known age-related muscular changes. We simultaneously measured the tibialis anterior (TA) IMP, compound muscle action potential (CMAP), and ankle torque in thirteen older adults (60–80 years old) in vivo by applying different stimulation intensities and frequencies. We found significant positive correlations between the stimulation intensity and IMP and CMAP. Increasing stimulation frequency caused ankle torque and IMP to increase. The electromechanical delay (EMD) (36 ms) was longer than the onset of IMP (IMPD) (29 ms). Compared to the previously published data collected from young adults (21–40 years old) in identical conditions, the TA CMAP and IMP of older adults at maximum intensity of stimulation were 23.8% and 39.6% lower, respectively. For different stimulation frequencies, CMAP, IMP, as well as ankle torque of older adults were 20.5%, 24.2%, and 13.2% lower, respectively. Surprisingly, the EMD did not exhibit any difference between young and older adults and the IMPD was consistent with the EMD. Data supporting the hypotheses suggest that IMP measurement is an indicator of muscle performance in older adults.     

Muscle fatigue-induced enhancement of corticomuscular coherence following sustained submaximal isometric contraction of the tibialis anterior muscle

Oscillatory activity of the sensorimotor cortex shows coherence with muscle activity within the 15- to 35-Hz frequency band (β-band) during weak to moderate sustained isometric contraction. We aimed to examine the acute changes in this corticomuscular coupling due to muscle fatigue and its effect on the steadiness of the exerted force. We quantified the coherence between the electroencephalogram (EEG) recorded over the sensorimotor cortex and the rectified surface electromyogram (EMG) of the tibialis anterior muscle as well as the coefficient of variance of the dorsiflexion force (Force(CV)) and sum of the auto-power spectral density function of the force within the β-band (Force(β-PSD)) during 30% of maximal voluntary contraction (MVC) for 60 s before (prefatiguing task) and after (postfatiguing task) muscle fatigue induced by sustained isometric contraction at 50% of MVC until exhaustion in seven healthy male subjects. The magnitude of the EEG-EMG coherence increased in the postfatiguing task in six of seven subjects. The maximal peak of EEG-EMG coherence stayed within the β-band in both pre- and postfatiguing tasks. Interestingly, two subjects, who had no significant EEG-EMG coherence in the prefatiguing task, showed significant coherence in the postfatiguing task. Additionally, Force(CV) and Force(β-PSD) significantly increased after muscle fatigue. These data suggest that when muscle fatigue develops, the central nervous system enhances oscillatory muscular activity in the β-band stronger coupled with the sensorimotor cortex activity accomplishing the sustained isometric contraction at lower performance levels.     

The histochemical demonstration of myoglobin and succinic dehydrogenase activity in the tibialis anterior muscle of the rabbit

Summary The staining reactions for myoglobin and succinic dehydrogenase activity in the tibialis anterior of the rabbit demonstrate four types of muscle fibre. These may be distinguished by their intensity of staining for myoglobin and the distribution of the mitochondria shown by the dehydrogenase reaction.The large fibres (70–80 m diameter) which contain many mitochondria evenly scattered throughout the fibre contain much myoglobin. Smaller fibres (45–60 m diameter) which show an identical staining reaction for the dehydrogenase reaction contain less myoglobin. This suggests that myoglobin may be present to aid the diffusion of oxygen into muscle fibres.     

Predictability of in vivo changes in pennation angle of human tibialis anterior muscle from rest to maximum isometric dorsiflexion

The aim of this study was to assess the predictability of in vivo, ultrasound-based changes in human tibialis anterior (TA) pennation angle from rest to maximum isometric dorsiflexion (MVC) using a planimetric model assuming constant thickness between aponeuroses and straight muscle fibres. Sagittal sonographs of TA were taken in six males at ankle angles of -15 degrees (dorsiflexion direction), 0 degrees (neutral position), + 15 (plantarflexion direction) and + 30 degrees both at rest and during dorsiflexor MVC trials performed on an isokinetic dynamometer. At all four ankle angles scans were taken from the TA proximal, central and distal regions. TA architecture did not differ (P > 0.05) neither between its two unipennate parts nor along the scanned regions over its length at a given ankle angle and state of contraction. Comparing MVC with rest at any given ankle angle, pennation angle was larger (62-71%, P < 0.01), fibre length smaller (37-40%, P < 0.01) and muscle thickness unchanged (P > 0.05). The model used estimated accurately (P > 0.05) changes in TA pennation angle occurring in the transition from rest to MVC and therefore its use is encouraged for estimating the isometric TA ankle moment and force generating capacity using musculoskeletal modelling.     

Nonlinear summation of force in cat tibialis anterior: a muscle with intrafascicularly terminating fibers.

The complex connective tissue structure of muscle and tendon suggests that forces from two parts of a muscle may not summate linearly, particularly in muscles with intrafasciculary terminating fibers, such as cat tibialis anterior (TA). In four anesthetized cats, the TA was attached to a servomechanism to control muscle length and record force. The ventral roots were divided into two bundles, each innervating about half the TA, so the two parts could be stimulated alone or together. Nonlinear summation of force (F(nl)) was measured during isometric contractions. F(nl) was small and negative, indicating less than linear summation of the parts, which is consistent with the predicted F(nl) of muscle fibers connected in series. F(nl) was more significant when smaller parts of the muscle were tested (21.8 vs. 8% for whole muscle). These data were fit to a model where both parts of the muscle were assumed to stretch a common elasticity. Compensatory movements of the servomechanism showed the common elasticity is very stiff, and the model cannot account for F(nl) in cat TA.     

Capillary supply of the tibialis anterior muscle in young, healthy, and moderately active men and women.

Tibialis anterior muscle biopsies from moderately active men and women (21-30 yr; n = 30) were examined to determine potential gender differences in capillarization. The fiber type proportions [type I (T1) approximately 73%] were unaffected by gender. The men (M) had significantly (P < 0.001) larger fibers than the women (W), with a greater gender effect for type II (T2) fibers (P < 0.001). The M and W had similar capillary densities (CD approximately 390 capillaries/mm2), but the capillaries-to-fiber ratio (C/F) was higher in the M (M = 2.20 +/- 0.35, W = 1.66 +/- 0.32; P < 0.01). Capillary contacts (CC) were higher in T2 than T1 for the M (P < 0.01), but not W, and M had greater CC (P < 0.001). Both fiber area per capillary (FA/C) and fiber perimeter per capillary (FP/C) indicated that T1 fibers had greater capillarization than T2 fibers (P < 0.001). There were no gender differences in T1 FA/C and T2 FA/C or T1 FP/C, but a gender difference existed for T2 FP/C (M = 60.5 +/- 10.9, W = 70.6 +/- 13.4; P < 0.01). The gender difference for C/F could be explained by fiber size; however, the physiological implications of the difference in T2 FP/C remains to be determined. In conclusion, despite gender differences for fiber size, overall, capillarization was similar between the men and women.     

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.     

The relative changes in isometric force and work during fatigue and recovery in isolated toad sartorius muscle

Toad sartorius muscle was subjected to sinusoidal varying length changes at 2 Hz to measure work. Both isometric tetanic force and work per cycle were measured before, during, and after a 3-min fatigue. Both isometric tetanic force and positive work, the work done by the muscle during the shortening part of the cycle, rapidly decreased in parallel in the first 40 s of fatigue. Thereafter, force continued to decrease, but at a slower rate, to about 10% of prefatigue values, whereas positive work levelled off at about 30% of prefatigue values. Negative work, the work done on the muscle during the lengthening part of the cycle, increased during fatigue to the extent that net work became negative. This was due to a prolonged relaxation, which resulted in active force still being generated while the muscle was being stretched. Work and force recovered at about the same rate. Isometric force measurements alone do not give any clear indication that net work will be negative under a particular set of experimental conditions.     

Changes in force and tendinous tissue elongation during the early phase of tetanic summation in in vivo human tibialis anterior muscle

The purpose of this study was to determine the changes that occur in tendinous tissue properties during the early phase of tetanic summation in the in vivo human tibialis anterior muscle (TA). The torque response and tendinous tissue elongation following single stimuli, two-pulse trains, and three-pulse trains were recorded in the TA during isometric contractions. The elongation, compliance, and lengthening velocity of tendinous tissue were determined by real-time ultrasonography. The contribution of the response to the second stimulation (C2) was obtained by subtracting the response to the single stimulation (C1) from the response of doublet. The third contribution (C3) was obtained by subtracting the response to the doublet from that of the triplet. C2 (7.8±0.5 Nm) and C3 (7.3±0.6 Nm) had torque responses significantly higher than C1 (3.6±0.7 Nm). In contrast, the elongations of tendinous tissue for C2 (2.8±0.4 mm) and C3 (1.7±0.2 mm) were significantly lower than for C1 (4.9±0.3 mm), indicating that the summation pattern of tendinous tissue elongation is different from the summation pattern of torque response. In addition, this showed considerable difference both between C1 (0.12±0.01 mm/N; 83±4.6 mm/s) and C2 (0.03±0.005 mm/N; 50±6.3 mm/s) and between C1 and C3 (0.02±0.002 mm/N; 39±6.4 mm/s) in the compliance and lengthening velocity of tendinous tissue. These results suggest that changes in tendinous tissue properties between first and second contraction are related to different summation patterns of force and tendinous tissue elongation during early phase of tetanic summation.     

Effect of an ADP analog on isometric force and ATPase activity of active muscle fibers

The role played by ADP in modulatingcross-bridge function has been difficult to study, because it is hardto buffer ADP concentration in skinned muscle preparations. To solvethis, we used an analog of ADP, spin-labeled ADP (SL-ADP). SL-ADP bindstightly to myosin but is a very poor substrate for creatine kinase orpyruvate kinase. Thus ATP can be regenerated, allowing well-definedconcentrations of both ATP and SL-ADP. We measured isometric ATPaserate and isometric tension as a function of both [SL-ADP], 0.1-2mM, and [ATP], 0.05-0.5 mM, in skinned rabbit psoas muscle,simulating fresh or fatigued states. Saturating levels of SL-ADPincreased isometric tension (by P'), the absolute value of P' beingnearly constant, ~0.04 N/mm², in variable ATP levels, pH7. Tension decreased (50-60%) at pH 6, but upon addition ofSL-ADP, P' was still ~0.04 N/mm². The ATPase wasinhibited competitively by SL-ADP with an inhibition constant,K_i, of ~240 and 280 µM at pH 7 and 6, respectively. Isometric force and ATPase activity could both be fit bya simple model of cross-bridge kinetics.

     

Models of passive and active dendrite motoneuron pools and their differences in muscle force control

Motoneuron (MN) dendrites may be changed from a passive to an active state by increasing the levels of spinal cord neuromodulators, which activate persistent inward currents (PICs). These exert a powerful influence on MN behavior and modify the motor control both in normal and pathological conditions. Motoneuronal PICs are believed to induce nonlinear phenomena such as the genesis of extra torque and torque hysteresis in response to percutaneous electrical stimulation or tendon vibration in humans. An existing large-scale neuromuscular simulator was expanded to include MN models that have a capability to change their dynamic behaviors depending on the neuromodulation level. The simulation results indicated that the variability (standard deviation) of a maintained force depended on the level of neuromodulatory activity. A force with lower variability was obtained when the motoneuronal network was under a strong influence of PICs, suggesting a functional role in postural and precision tasks. In an additional set of simulations when PICs were active in the dendrites of the MN models, the results successfully reproduced experimental results reported from humans. Extra torque was evoked by the self-sustained discharge of spinal MNs, whereas differences in recruitment and de-recruitment levels of the MNs were the main reason behind torque and electromyogram (EMG) hysteresis. Finally, simulations were also used to study the influence of inhibitory inputs on a MN pool that was under the effect of PICs. The results showed that inhibition was of great importance in the production of a phasic force, requiring a reduced co-contraction of agonist and antagonist muscles. These results show the richness of functionally relevant behaviors that can arise from a MN pool under the action of PICs.     

Immobilization of the rabbit tibialis anterior muscle in a lengthened position causes addition of sarcomeres in series and extra-cellular matrix proliferation

Rabbits were immobilized for 3 weeks with the ankle in plantar flexion, midrange position or dorsal extension (n=15). The left leg was used as control. Sarcomere lengths were measured by laser diffraction in vivo in the tibialis anterior (TA) muscle. Legs immobilized in the midrange position showed coherent diffraction patterns through the range of motion, but in those immobilized with TA in the stretched position no diffraction patterns in vivo could be obtained. Morphological analyses revealed increased fibrosis and occurrence of whorled fibers in these muscles. On 15 more likewise immobilized rabbits, a technique of measuring sarcomere lengths in vitro by first digesting the collagen in nitric acid was developed. These in vitro measurements showed shorter sarcomeres in the muscles immobilized in a lengthened position compared to the control, indicating an addition of sarcomeres in series.     

Estimation of the interplay between groups of fast and slow muscle fibers of the tibialis anterior and gastrocnemius muscle while running.

Electromyograms recorded from the lower limbs of humans while running were submitted to a time/frequency analysis using wavelets. The results of the wavelet analysis yielded intensity spectra at every time point during the swing and the stance phase. It was previously shown that more or less high frequency components get activated during different periods of the movement. The purpose of this study was to test to what extent the spectra can be reconstructed by a linear superposition of two generating spectra that were associated to groups of fast and slow muscle fibers. The terms fast and slow do not only refer to the conduction velocity but also to the shape of the motor unit action potential and are used to characterize the groups in a broader sense. The principal component analysis of the spectra confirmed that a two dimensional spectral space was appropriate. A parametric spectral decomposition was used to extract the generating spectra within the two dimensional spectral space. The generating spectra were in turn used to compute the power with which the groups of muscle fibers contribute to the measured spectra and thus to the overall muscular activity. The power that was obtained for the different time points during the movement reflects the biomechanically important interplay between the groups of muscle fibers while running.     

Proteomic analysis of rat soleus and tibialis anterior muscle following immobilization

A proteomic analysis was performed comparing normal slow twitch type fiber rat soleus muscle and normal fast twitch type fiber tibialis anterior muscle to immobilized soleus and tibialis anterior muscles at 0.5, 1, 2, 4, 6, 8 and 10 days post immobilization. Muscle mass measurements demonstrate mass changes throughout the period of immobilization. Proteomic analysis of normal and atrophied soleus muscle demonstrated statistically significant changes in the relative levels of 17 proteins. Proteomic analysis of normal and atrophied tibialis anterior muscle demonstrated statistically significant changes in the relative levels of 45 proteins. Protein identification using mass spectrometry was attempted for all differentially regulated proteins from both soleus and tibialis anterior muscles. Four differentially regulated soleus proteins and six differentially regulated tibialis anterior proteins were identified. The identified proteins can be grouped according to function as metabolic proteins, chaperone proteins, and contractile apparatus proteins. Together these data demonstrate that coordinated temporally regulated changes in the proteome occur during immobilization-induced atrophy in both slow twitch and fast twitch fiber type skeletal muscle.     

Temporal relationships between isometric force, phosphorylase, and protein kinase activities in vascular smooth muscle

Vascular smooth muscle contractility is tightly coupled to ATP production by intermediary metabolism. To elucidate mechanisms underlying coordination of metabolism and contractility we studied the time course of isometric force, and the activation of phosphorylase and cAMP-dependent protein kinases during stimulation of bovine coronary arterial strips with KCl. Isometric force reached a maximum after 10 min of exposure to 30 mM KCl (ED90) and was sustained throughout the subsequent 20-min period of contraction. In contrast, activation of phosphorylase was biphasic: enzymic activity reached a maximum (176 +/- 10% of control) after 3 min of contraction and then, though remaining above control, activity declined to a lower level (135 +/- 7% of control). However, no change occurred in the activity ratios for cAMP-dependent protein kinase assessed in either the presence (type II isozyme) or absence (type I isozyme) of 0.5 M NaCl. These data suggest that the activation of phosphorylase during K+-induced contraction is independent of the cAMP system. The biphasic activation of phosphorylase may reflect transient changes in the intracellular concentration of Ca2+ or the activation of a phosphatase(s) during the response.