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

Cadence Paradox in Cycling-Part 2: Theory and Simulation of Maximal Lactate Steady State and Carbohydrate Utilization Dependent on Cycling Cadence

PURPOSE

To develop and evaluate a theory on the frequent observation that cyclists prefer cadences (RPMs) higher than those considered most economical at submaximal exercise intensities via modeling and simulation of its mathematical description.

METHODS

The theory combines the parabolic power-to-velocity (v) relationship, where v is defined by crank length, RPM-dependent ankle velocity, and gear ratio, RPM effects on the maximal lactate steady state (MLSS), and lactate-dependent carbohydrate oxidation (CHO). It was tested against recent experimental results of 12 healthy male recreational cyclists determining the v-dependent peak oxygen uptake (VO2PEAKv), MLSS (MLSSv), corresponding power output (PMLSSv), oxygen uptake at PMLSSv (VO2MLSSv), and CHOMLSSv-management at 100 versus 50 per minute, respectively. Maximum RPM (RPMMAX) attained at minimized pedal torque was measured. RPM-specific maximum sprint power output (PMAXv) was estimated at RPMs of 100 and 50, respectively.

RESULTS

Modeling identified that MLSSv and PMLSSv related to PMAXv (IPMLSSv) promote CHO and that VO2MLSSv related to VO2PEAKv inhibits CHO. It shows that cycling at higher RPM reduces IPMLSSv. It suggests that high cycling RPMs minimize differences in the reliance on CHO at MLSSv between athletes with high versus low RPMMAX.

CONCLUSIONS

The present theory-guided modeling approach is exclusively based on data routinely measured in high-performance testing. It implies a higher performance reserve above IPMLSSv at higher RPM. Cyclists may prefer high cycling RPMs because they appear to minimize differences in the reliance on CHO at MLSSv between athletes with high versus low RPMMAX.

Non-Linearity in Motor Unit Velocity Twitch Dynamics: Implications for Ultrafast Ultrasound Source Separation

Ultrasound (US) muscle image series can be used for peripheral human-machine interfacing based on global features, or even on the decomposition of US images into the contributions of individual motor units (MUs). With respect to state-of-the-art surface electromyography (sEMG), US provides higher spatial resolution and deeper penetration depth. However, the accuracy of current methods for direct US decomposition, even at low forces, is relatively poor. These methods are based on linear mathematical models of the contributions of MUs to US images. Here, we test the hypothesis of linearity by comparing the average velocity twitch profiles of MUs when varying the number of other concomitantly active units. We observe that the velocity twitch profile has a decreasing peak-to-peak amplitude when tracking the same target motor unit at progressively increasing contraction force levels, thus with an increasing number of concomitantly active units. This observation indicates non-linear factors in the generation model. Furthermore, we directly studied the impact of one MU on a neighboring MU, finding that the effect of one source on the other is not symmetrical and may be related to unit size. We conclude that a linear approximation is partly limiting the decomposition methods to decompose full velocity twitch trains from velocity images, highlighting the need for more advanced models and methods for US decomposition than those currently employed.

Skeletal muscle models composed of motor units: A review

The mathematical muscle models should include several aspects of muscle structure and physiology. First, muscle force is the sum of forces of multiple motor units (MUs), which have different contractile properties and play different roles in generating muscle force. Second, whole muscle activity is an effect of net excitatory inputs to a pool of motoneurons innervating the muscle, which have different excitability, influencing MU recruitment. In this review, we compare various methods for modeling MU twitch and tetanic forces and then discuss muscle models composed of different MU types and number. We first present four different analytical functions used for twitch modeling and show limitations related to the number of twitch describing parameters. We also show that a nonlinear summation of twitches should be considered in modeling tetanic contractions. We then compare different muscle models, most of which are variations of Fuglevand's model, adopting a common drive hypothesis and the size principle. We pay attention to integrating previously developed models into a consensus model based on physiological data from in vivo experiments on the rat medial gastrocnemius muscle and its respective motoneurons. Finally, we discuss the shortcomings of existing models and potential applications for studying MU synchronization, potentiation, and fatigue.

Morphometric properties and innervation of muscle compartments in rat medial gastrocnemius

The rat medial gastrocnemius (MG) muscle is composed of the proximal and distal compartments. In this study, morphometric properties of the compartments and their muscle fibres at five levels of the muscle length and the innervation pattern of these compartments from lumbar segments were investigated. The size and number of muscle fibres in the compartments were different. The proximal compartment at the largest cross section (25% of the muscle length) had 34% smaller cross-sectional area but contained a slightly higher number of muscle fibres (max. 5521 vs. 5360) in comparison to data for the distal compartment which had the largest cross-sectional area at 40% of the muscle length. The muscle fibre diameters revealed a clear tendency within both compartments to increase along the muscle (from the knee to the Achilles tendon) up to 46.9 μm in the proximal compartment and 58.4 μm in the distal one. The maximal tetanic and single twitch force evoked by stimulation of L4, L5, and L6 ventral roots in whole muscle and compartments were measured. The MG was innervated from L4 and L5, only L5, or L5 and L6 segments. The proximal compartment was innervated by axons from L5 or L5 and L4, and the distal one from L5, L5 and L6, or L5 and L4 segments. The forces produced by the compartments summed non-linearly. The tetanic forces of the proximal and distal compartments amounted to 2.24 and 4.86 N, respectively, and their algebraic sums were 11% higher than the whole muscle force (6.37 N).

Summation of slow motor unit forces at constant and variable interpulse intervals in rat soleus muscle

Effects of the summation of forces generated by functionally isolated slow-twitch motor units (MU) of the rat soleus muscle were examined in this study. Initially, the twitch, fused tetanic and unfused tetanic contractions evoked by trains of stimuli at variable interpulse intervals were recorded for each MU. Then, two, three or four MUs were co-activated, and the recorded forces were compared to the algebraic sum of the forces of individual MUs. The mean cumulative force of twitches and the mean cumulative force of fused tetani were not statistically different from the respective algebraic sums of forces, which revealed a high degree of linearity in the summation. However, relaxation of the recorded tetanic contractions (either fused or unfused) was faster than that predicted by the linear summation of individual contractions. Moreover, for twitch and tetanic contractions, a tendency to shorten relaxation with an increasing number of co-active MUs was noted. The results indicate that forces of rat soleus slow MUs sum up more linearly than in the respective cat muscle as well as more linearly than for fast MUs in the medial gastrocnemius muscle.

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.

Summation of motor unit forces in rat medial gastrocnemius muscle

The summation of contractile forces of motor units (MUs) was analyzed by comparing the recorded force during parallel stimulation of two and four individual MUs or four groups of MUs to the algebraic sum of their individual forces. Contractions of functionally-isolated single MUs of the medial gastrocnemius muscle were evoked by electrical stimulation of thin filaments of the split L5 or L4 ventral roots of spinal nerves. Additionally, contractions of large groups of MUs were evoked by stimuli delivered to four parts of the divided L5 ventral root. Single twitches, 40Hz unfused tetani, and 150Hz fused maximum tetani were recorded. In these experimental situations the summation was more effective for unfused tetani than for twitches or maximum tetani. The results obtained for pairs of MUs were highly variable (more- or less-than-linear summation), but coactivation of more units led to progressively weaker effects of summation, which were usually less-than-linear in comparison to the algebraic sums of the individual forces. The variability of the results highlights the importance of the structure of the muscle and the architecture of its MUs. Moreover, the simultaneous activity of fast and slow MUs was considerably more effective than that of two fast units.

Summation of Motor Unit Force in Passive and Active Muscle

Nonlinear summation of force has been observed between motor units. The complex structure of muscle suggests many reasons why this could happen. When large portions of the muscle are active, however, the nonlinearities are small, and generally explained by stretch of the common elasticity. This suggests that the type of nonlinearity observed between motor units may not be physiologically significant.

A 3D model of muscle reveals the causes of nonuniform strains in the biceps brachii

Biomechanical models generally assume that muscle fascicles shorten uniformly. However, dynamic magnetic resonance (MR) images of the biceps brachii have recently shown nonuniform shortening along some muscle fascicles during low-load elbow flexion (J. Appl. Physiol. 92 (2002) 2381). The purpose of this study was to uncover the features of the biceps brachii architecture and material properties that could lead to nonuniform shortening. We created a three-dimensional finite-element model of the biceps brachii and compared the tissue strains predicted by the model with experimentally measured tissue strains. The finite-element model predicted strains that were within one standard deviation of the experimentally measured strains. Analysis of the model revealed that the variation in fascicle lengths within the muscle and the curvature of the fascicles were the primary factors contributing to nonuniform strains. Continuum representations of muscle, combined with in vivo image data, are needed to deepen our understanding of how complex geometric arrangements of muscle fibers affect muscle contraction mechanics.

Properties of the two neuromuscular compartments in a split bipennate muscle

Bipennate muscles may be split along their distal aponeurosis, dividing each into two compartments. These sub-muscle units may be used in tendon transfers. This paper presents the contractile properties of the two sub-units of the flexor carpi ulnaris in a macaca fascicularis, after it was split by up to 80% of its length. The sub-muscle units were electrically stimulated and found to have independent isometric contraction, with minimal contraction recorded from the non-stimulated sub-unit. Also, the sum of the forces measured from each unit when stimulated individually, was found to be greater than the force of the whole muscle, given the same isometric conditions. The distal aponeurosis which is common allows force transmission between the compartments. Splitting the muscle along this distal aponeurosis alters this function and the force capacity of the muscle, providing a new potential for using the sub-units as grafts for tendon transfers.