Summation of Motor Unit Force in Passive and Active Muscle

A model of the rat medial gastrocnemius muscle based on inputs to motoneurons and on an algorithm for prediction of the motor unit force

The muscle force is the sum of forces of multiple motor units (MUs), which have different contractile properties. During movements, MUs develop unfused tetani, which result from summation of twitch-shape responses to individual stimuli, which are variable in amplitude and duration. The aim of the study was to develop a realistic muscle model that would integrate previously developed models of MU contractions and an algorithm for the prediction of tetanic forces. The proposed model of rat medial gastrocnemius muscle is based on physiological data: excitability and firing frequencies of motoneurons, contractile properties, and the number and proportion of MUs in the muscle. The MU twitches were modeled by a six-parameter analytical function. The excitability of motoneurons was modeled according to a distribution of their rheobase currents measured experimentally. Processes of muscle force regulation were modeled according to a common drive hypothesis. The excitation signal to motoneurons was modeled by two form types: triangular and trapezoid. The discharge frequencies of MUs, calculated individually for each MU, corresponded to those recorded for rhythmic firing of motoneurons. The force of the muscle was calculated as the sum of all recruited MUs. Participation of the three types of MUs in the developed muscle force was presented at different levels of the excitation signal to motoneurons. The model appears highly realistic and open for input data from various skeletal muscles with different compositions of MU types. The results were compared with three other models with different distribution of the input parameters. NEW & NOTEWORTHY The proposed mathematical model of rat medial gastrocnemius muscle is highly realistic because it is based strictly on experimentally determined motor unit contractile parameters and motoneuron properties. It contains the actual number and proportion of motor units and takes into consideration their different contributions to the whole muscle force, depending on the level of the excitation signal. The model is open for input data from other muscles, and additional physiological parameters can also be included.

Three-dimensional ankle moments and nonlinear summation of rat triceps surae muscles

The Achilles tendon and epimuscular connective tissues mechanically link the triceps surae muscles. These pathways may cause joint moments exerted by each muscle individually not to sum linearly, both in magnitude and direction. The aims were (i) to assess effects of sagittal plane ankle angle (varied between 150° and 70°) on isometric ankle moments, in both magnitude and direction, exerted by active rat triceps surae muscles, (ii) to assess ankle moment summation between those muscles for a range of ankle angles and (iii) to assess effects of sagittal plane ankle angle and muscle activation on Achilles tendon length. At each ankle angle, soleus (SO) and gastrocnemius (GA) muscles were first excited separately to assess ankle-angle moment characteristics and subsequently both muscles were excited simultaneously to investigate moment summation. The magnitude of ankle moment exerted by SO and GA, the SO direction in the transverse and sagittal planes, and the GA direction in the transverse plane were significantly affected by ankle angle. SO moment direction in the frontal and sagittal planes were significantly different from that of GA. Nonlinear magnitude summation varied between 0.6±2.9% and −3.6±2.9%, while the nonlinear direction summation varied between 0.3±0.4° and −0.4±0.7° in the transverse plane, between 0.5±0.4° and 0.1±0.4° in the frontal plane, and between 3.0±7.9° and 0.3±2.3° in the sagittal plane. Changes in tendon length caused by SO contraction were significantly lower than those during contraction of GA and GA+SO simultaneously. Thus, moments exerted by GA and SO sum nonlinearly both in the magnitude and direction. The limited degree of nonlinear summation may be explained by different mechanisms acting in opposite directions.

Motor unit

Movement is accomplished by the controlled activation of motor unit populations. Our understanding of motor unit physiology has been derived from experimental work on the properties of single motor units and from computational studies that have integrated the experimental observations into the function of motor unit populations. The article provides brief descriptions of motor unit anatomy and muscle unit properties, with more substantial reviews of motoneuron properties, motor unit recruitment and rate modulation when humans perform voluntary contractions, and the function of an entire motor unit pool. The article emphasizes the advances in knowledge on the cellular and molecular mechanisms underlying the neuromodulation of motoneuron activity and attempts to explain the discharge characteristics of human motor units in terms of these principles. A major finding from this work has been the critical role of descending pathways from the brainstem in modulating the properties and activity of spinal motoneurons. Progress has been substantial, but significant gaps in knowledge remain.

Estimation of musculoskeletal models from in situ measurements of muscle action in the rat hindlimb

Musculoskeletal models are often created by making detailed anatomical measurements of muscle properties. These measurements can then be used to determine the parameters of canonical models of muscle action. We describe here a complementary approach for developing and validating muscle models, using in situ measurements of muscle actions. We characterized the actions of two rat hindlimb muscles: the gracilis posticus (GRp) and the posterior head of biceps femoris (BFp; excluding the anterior head with vertebral origin). The GRp is a relatively simple muscle, with a circumscribed origin and insertion. The BFp is more complex, with an insertion distributed along the tibia. We measured the six-dimensional isometric forces and moments at the ankle evoked from stimulating each muscle at a range of limb configurations. The variation of forces and moments across the workspace provides a succinct characterization of muscle action. We then used this data to create a simple muscle model with a single point insertion and origin. The model parameters were optimized to best explain the observed force-moment data. This model explained the relatively simple muscle, GRp, very well (R(2)>0.85). Surprisingly, this simple model was also able to explain the action of the BFp, despite its greater complexity (R(2)>0.84). We then compared the actions observed here with those predicted using recently published anatomical measurements. Although the forces and moments predicted for the GRp were very similar to those observed here, the predictions for the BFp differed. These results show the potential utility of the approach described here for the development and refinement of musculoskeletal models based on in situ measurements of muscle actions.

Force-generating capacity of human myosin isoforms extracted from single muscle fibre segments

Muscle, motor unit and muscle fibre type-specific differences in force-generating capacity have been investigated for many years, but there is still no consensus regarding specific differences between slow- and fast-twitch muscles, motor units or muscle fibres. This is probably related to a number of different confounding factors disguising the function of the molecular motor protein myosin. We have therefore studied the force-generating capacity of specific myosin isoforms or combination of isoforms extracted from short single human muscle fibre segments in a modified single fibre myosin in vitro motility assay, in which an internal load (actin-binding protein) was added in different concentrations to evaluate the force-generating capacity. The force indices were the x-axis intercept and the slope of the relationship between the fraction of moving filaments and the α-actinin concentration. The force-generating capacity of the β/slow myosin isoform (type I) was weaker (P < 0.05) than the fast myosin isoform (type II), but the force-generating capacity of the different human fast myosin isoforms types IIa and IIx or a combination of both (IIax) were indistinguishable. A single fibre in vitro motility assay for both speed and force of specific myosin isoforms is described and used to measure the difference in force-generating capacity between fast and slow human myosin isoforms. The assay is proposed as a useful tool for clinical studies on the effects on muscle function of specific mutations or post-translational modifications of myosin.

The Influence of Modeling Separate Neuromuscular Compartments on the Force and Moment Generating Capacities of Muscles of the Feline Hindlimb

Functional electrical stimulation (FES) has the capacity to regenerate motion for individuals with spinal cord injuries. However, it is not straightforward to determine the stimulation parameters to generate a coordinated movement. Musculoskeletal models can provide a noninvasive simulation environment to estimate muscle force and activation timing sequences for a variety of tasks. Therefore, the purpose of this study was to develop a musculoskeletal model of the feline hindlimb for simulations to determine stimulation parameters for intrafascicular multielectrode stimulation (a method of FES). Additionally, we aimed to explore the differences in modeling neuromuscular compartments compared with representing these muscles as a single line of action. When comparing the modeled neuromuscular compartments of biceps femoris, sartorius, and semimembranosus to representations of these muscles as a single line of action, we observed that modeling the neuromuscular compartments of these three muscles generated different force and moment generating capacities when compared with single muscle representations. Differences as large as 4 N m (∼400% in biceps femoris) were computed between the summed moments of the neuromuscular compartments and the single muscle representations. Therefore, modeling neuromuscular compartments may be necessary to represent physiologically reasonable force and moment generating capacities of the feline hindlimb.

Endpoint force fluctuations reveal flexible rather than synergistic patterns of muscle cooperation

We developed a new approach to investigate how the nervous system activates multiple redundant muscles by studying the endpoint force fluctuations during isometric force generation at a multi-degree-of-freedom joint. We hypothesized that, due to signal-dependent muscle force noise, endpoint force fluctuations would depend on the target direction of index finger force and that this dependence could be used to distinguish flexible from synergistic activation of the musculature. We made high-gain measurements of isometric forces generated to different target magnitudes and directions, in the plane of index finger metacarpophalangeal joint abduction-adduction/flexion-extension. Force fluctuations from each target were used to calculate a covariance ellipse, the shape of which varied as a function of target direction. Directions with narrow ellipses were approximately aligned with the estimated mechanical actions of key muscles. For example, targets directed along the mechanical action of the first dorsal interosseous (FDI) yielded narrow ellipses, with 88% of the variance directed along those target directions. It follows the FDI is likely a prime mover in this target direction and that, at most, 12% of the force variance could be explained by synergistic coupling with other muscles. In contrast, other target directions exhibited broader covariance ellipses with as little as 30% of force variance directed along those target directions. This is the result of cooperation among multiple muscles, based on independent electromyographic recordings. However, the pattern of cooperation across target directions indicates that muscles are recruited flexibly in accordance with their mechanical action, rather than in fixed groupings.

Sympathetic-induced changes in discharge rate and spike-triggered average twitch torque of low-threshold motor units in humans

Animal and in vitro studies have shown that the sympathetic nervous system modulates the contractility of skeletal muscle fibres, which may require adjustments in the motor drive to the muscle in voluntary contractions. In this study, these mechanisms were investigated in the tibialis anterior muscle of humans during sympathetic activation induced by the cold pressor test (CPT; left hand immersed in water at 4 degrees C). In the first experiment, 11 healthy men performed 20 s isometric contractions at 10% of the maximal torque, before, during and after the CPT. In the second experiment, 12 healthy men activated a target motor unit at the minimum stable discharge rate for 5 min in the same conditions as in experiment 1. Intramuscular electromyographic (EMG) signals and torque were recorded and used to assess the motor unit discharge characteristics (experiment 1) and spike-triggered average twitch torque (experiment 2). CPT increased the diastolic blood pressure and heart rate by (mean +/- S.D.) 18 +/- 9 mmHg and 4.7 +/- 6.5 beats min(-1) (P < 0.01), respectively. In experiment 1, motor unit discharge rate increased from 10.4 +/- 1.0 pulses s(-1) before to 11.1 +/- 1.4 pulses s(-1) (P < 0.05) during the CPT. In experiment 2, the twitch half-relaxation time decreased by 15.8 +/- 9.3% (P < 0.05) during the CPT with respect to baseline. These results provide the first evidence of an adrenergic modulation of contractility of muscle fibres in individual motor units in humans, under physiological sympathetic activation.

In vivo behaviour of human muscle architecture and mechanomyographic response using the interpolated twitch technique

This study investigated the origin of curvilinear change in the superimposed mechanomyogram (MMG) amplitude of the human medial gastrocnemius muscle (MG) with increasing contraction intensity. The superimposed twitch amplitude, the superimposed MMG amplitude and the extent of fascicle shortening were measured using ultrasonic images of electrical stimulation during isometric plantar flexions at levels 20%, 40%, 60%, 80%, and 100% of the maximal voluntary contraction (MVC). The superimposed twitch amplitude, the superimposed MMG amplitude and the extent of fascicle shortening decreased with increasing contraction intensity. The superimposed MMG amplitude and the extent of fascicle shortening showed a curvilinear decrease, while the superimposed twitch amplitude showed a linear decrease at levels up to 80% of the MVC. There was a linear relationship between the superimposed MMG amplitude and the extent of fascicle shortening at different contraction intensities. These results indicate that the superimposed MMG amplitude reflects changes in the extent of fascicle shortening at different contraction intensities better than the superimposed twitch amplitude. Our study suggests that the origin of the curvilinear decrease of superimposed MMG amplitude is associated with a curvilinear decrease of the extent of fascicle shortening with increasing contraction intensity in the human MG.

Analysis of the effects of firing rate and synchronization on spike-triggered averaging of multidirectional motor unit torque

Spike-triggered averaging (STA) of muscle force transients has often been used to estimate motor unit contractile properties, using the discharge of a motor unit within the muscle as the triggering events. For motor units that exert torque about multiple degrees-of-freedom, STA has also been used to estimate motor unit pulling direction. It is well known that motor unit firing rate and weak synchronization of motor unit discharges with other motor units in the muscle can distort STA estimates of contractile properties, but the distortion of STA estimates of motor unit pulling direction has not been thoroughly evaluated. Here, we derive exact equations that predict that STA decouples firing rate and synchronization distortion when used to estimate motor unit pulling direction. We derive a framework for analyzing synchronization, consider whether the distortion due to synchronization can be removed from STA estimates of pulling direction, and show that there are distributions of motor unit pulling directions for which STA is insensitive to synchronization. We conclude that STA may give insight into how motoneuronal synchronization is organized with respect to motor unit pulling direction.