Modeling investigation of learning a fast elbow flexion in the horizontal plane—prediction of muscle forces and motor units action

Experimental investigation of practicing a dynamic, goal-directed movement reveals significant changes in kinematics. Modeling can provide insight into the alterations in muscle activity, associated with the kinematic adaptations, and reveal the potential motor unit (MU) firing patterns that underlie those changes. In this paper, a previously developed muscle model and software (Raikova and Aladjov, Journal of Biomechanics, 35, 2002) have been used to investigate changes in MU control, while practicing fast elbow flexion to a target in the horizontal plane. The first trial (before practice) and the last trial (after extensive practice) of two subjects have been simulated. The inputs for the simulation were the calculated external moments at the elbow joint. The external moments were countered by the action of three flexor muscles and two extensor ones. The muscles have been modeled as a mixture of MUs of different types. The software has chosen the MU firing times necessary to accomplish the movement. The muscle forces and MUs firing statistics were then calculated. Three hypotheses were tested and confirmed: (1) peak muscle forces and antagonist co-contraction increase during training; (2) there is an increase in the firing frequency and the synchronization between MUs; and (3) the recruitment of fast-twitch MUs dominates the action.     

Experimental and modelling investigation of learning a fast elbow flexion in the horizontal plane

Changes in the kinematic and electromyographic characteristics that occur while learning to move as fast as possible have been studied experimentally. Experimental investigation of what happens to the individual motor units (MUs) is more difficult. Access to each MU is impossible, and the recruitment and force developing properties of all individual MUs cannot be known. Thus, what is currently known about MU firing is based on experiments that have recorded relatively few MUs compared to what exists in the entire muscle. A recently developed muscle model (Raikova and Aladjov, 2002, J. Biomechanics, 35, 1123-1135) composed of MUs with different properties can be used for such investigation. The process of learning fast elbow flexion in the horizontal plane was simulated and the results were compared with experimentally measured data. Comparing the simulation results of the very first trial of a particular subject with those of the last trail (at the end of the learning process), it can be concluded that the speed of limb motion and muscle forces increase initially as a result of the more synchronous MUs activation and the increase of firing rate of active MUs. Further improvement necessitated an appreciable reduction in the motor task requirements (i.e. less muscle force and less MUs' activity) set in the computational algorithm by optimization criteria. This forced the next process-inclusion of additional MUs.     

Simulation analysis of interference EMG during fatiguing voluntary contractions. Part II--changes in amplitude and spectral characteristics.

Capabilities of amplitude and spectral methods for information extraction from interference EMG signals were assessed through simulation and preliminary experiment. Muscle was composed of 4 types of motor units (MUs). Different hypotheses on changes in firing frequency of individual MUs, intracellular action potential (IAP) and muscle fibre propagation velocity (MFPV) during fatigue were analyzed. It was found that changes in amplitude characteristics of interference signals (root mean square, RMS, or integrated rectified value, IEMG) detected by intramuscular and surface electrodes differed. RMS and IEMG of surface detected interference signals could increase even under MU firing rate reduction and without MU synchronisation. IAP profile lengthening can affect amplitude characteristics more significantly than MU firing frequency. Thus, an increase of interference EMG amplitude is unreliable to reflect changes in the neural drive. The ratio between EMG amplitude and contraction response can hardly characterise the so-called 'neuromuscular efficiency'. The recently proposed spectral fatigue indices can be used for quantification of interference EMG signals. The indices are practically insensitive to MU firing frequency. IAP profile lengthening and decrease in MFPV enhanced the index value, while recruitment of fast fatigable MUs reduced it. Sensitivity of the indices was higher than that of indices traditionally used.     

Effect of synchronization of firings of different motor unit types on the force variability in a model of the rat medial gastrocnemius muscle

The synchronized firings of active motor units (MUs) increase the oscillations of muscle force, observed as physiological tremor. This study aimed to investigate the effects of synchronizing the firings within three types of MUs (slow—S, fast resistant to fatigue–FR, and fast fatigable–FF) on the muscle force production using a mathematical model of the rat medial gastrocnemius muscle. The model was designed based on the actual proportion and physiological properties of MUs and motoneurons innervating the muscle. The isometric muscle and MU forces were simulated by a model predicting non-synchronized firing of a pool of 57 MUs (including 8 S, 23 FR, and 26 FF) to ascertain a maximum excitatory signal when all MUs were recruited into the contraction. The mean firing frequency of each MU depended upon the twitch contraction time, whereas the recruitment order was determined according to increasing forces (the size principle). The synchronization of firings of individual MUs was simulated using four different modes and inducing the synchronization of firings within three time windows (± 2, ± 4, and ± 6 ms) for four different combinations of MUs. The synchronization was estimated using two parameters, the correlation coefficient and the cross-interval synchronization index. The four scenarios of synchronization increased the values of the root-mean-square, range, and maximum force in correlation with the increase of the time window. Greater synchronization index values resulted in higher root-mean-square, range, and maximum of force outcomes for all MU types as well as for the whole muscle output; however, the mean spectral frequency of the forces decreased, whereas the mean force remained nearly unchanged. The range of variability and the root-mean-square of forces were higher for fast MUs than for slow MUs; meanwhile, the relative values of these parameters were highest for slow MUs, indicating their important contribution to muscle tremor, especially during weak contractions.     

The fatigability of two agonistic muscles in human isometric voluntary submaximal contraction: an EMG study. II. Motor unit firing rate and recruitment

The recruitment and firing rate of biceps brachii (BB) and brachioradialis (BR) motor units (MUs) were studied in the course of fatiguing isometric contractions at 20%-30% of maximal voluntary contraction (MVC). MU recruitment generally occurred throughout the maintained contraction and was similar for BB and BR muscles. Newly recruited MUs started to discharge in the form of bursts, the duration of which increased until a continuous rhythmical firing was achieved. Within each burst, the first interval between two consecutive discharges was usually the shortest. MU threshold was lowered just after the limit time of the maintained contraction. The MU's firing rate either increased or remained stable as a function of the elapsed time. It is concluded that (1) in fatiguing isometric contractions at 20%-30% MVC contractile failure is mainly compensated for by MU recruitment and a lowered MU threshold and (2) differences between in surface changes in the electromyogram of BB and BR muscles cannot easily be explained by related differences in MU firing rate and recruitment.     

Hierarchical genetic algorithm versus static optimization-investigation of elbow flexion and extension movements

The applicability of static optimization (and, respectively, frequently used objective functions) for prediction of individual muscle forces for dynamic conditions has often been discussed. Some of the problems are whether time-independent objective functions are suitable, and how to incorporate muscle physiology in models. The present paper deals with a twofold task: (1) implementation of hierarchical genetic algorithm (HGA) based on the properties of the motor units (MUs) twitches, and using multi-objective, time-dependent optimization functions; and (2) comparison of the results of the HGA application with those obtained through static optimization with a criterion "minimum of a weighted sum of the muscle forces raised to the power of n". HGA and its software implementation are presented. The moments of neural stimulation of all MUs are design variables coding the problem in the terms of HGA. The main idea is in using genetic operations to find these moments, so that the sum of MUs twitches satisfies the imposed goals (required joint moments, minimal sum of muscle forces, etc.). Elbow flexion and extension movements with different velocities are considered as proper illustration. It is supposed that they are performed by two extensor muscles and three flexor muscles. The results show that HGA is a suitable means for precise investigation of motor control. Many experimentally observed phenomena (such as antagonistic co-contraction, three-phasic behavior of the muscles during fast movements) can find their explanation by the properties of the MUs twitches. Static optimization is also able to predict three-phasic behavior and could be used as practicable and computationally inexpensive method for total estimation of the muscle forces.     

Simulation of the motor units control during a fast elbow flexion in the sagittal plane.

The fact that muscles are composed of different Motor Units (MUs) is often neglected when investigating motor control by macro models of human musculo-skeletal-joint systems. Each muscle is associated with one control signal. This simplification leads to difficulties when mechanical and electrical manifestations of the muscle activity are juxtaposed. That is why a new approach for muscle modelling was recently proposed (Journal of Biomechanics 2002;35:1123-1135). It is based on MUs twitches and a Hierarchical Genetic Algorithm (HGA) is implemented for choosing the moments of activation of the individual MUs, thus simulating the control of the nervous system. Its basic benefit is obtaining the complete information about the mechanical and activation behaviour of all MUs, respectively muscles, during the whole motion. Its possibilities are demonstrated when simulating fast elbow flexion. Three flexor and two extensor muscles, each consisting of approximately real number of different types of MUs, are modelled. The task is highly indeterminate and the optimization is performed according to a fitness function that is an assessed combination of criteria (minimal deviation from the given joint moment, minimal total muscle force and minimal MUs activation). The influence of the weight of the first criterion (the one that reflects the importance of the movement accuracy on the predicted results), is investigated. Two variants concerning the muscle MUs structure are also compared: each muscle is composed of four distinct types MUs and the MUs twitch parameters are uniformly distributed.     

Using two-dimensional spatial information in decomposition of surface EMG signals.

Recently, high-density surface EMG electrode grids and multi-channel amplifiers became available for non-invasive recording of human motor units (MUs). We present a way to decompose surface EMG signals into MU firing patterns, whereby we concentrate on the importance of two-dimensional spatial differences between the MU action potentials (MUAPs). Our method is exemplified with high-density EMG data from the vastus lateralis muscle of a single subject. Bipolar and Laplacian spatial filtering was applied to the monopolar raw signals. From the single recording in this subject six different simultaneously active MUs could be distinguished using the spatial differences between MUAPs in the direction perpendicular to the muscle fiber direction. After spike-triggered averaging, 125-channel two-dimensional MUAP templates were obtained. Template-matching allowed tracking of all MU firings. The impact of spatial information was measured by using subsets of the MUAP templates, either in parallel or perpendicular to the muscle fiber direction. The use of one-dimensional spatial information perpendicular to the muscle fiber direction was superior to the use of a linear array electrode in the longitudinal direction. However, to detect the firing events of the MUs with a high accuracy, as needed for instance for estimation of firing synchrony, two-dimensional information from the complete grid electrode appears essential.     

Differences between motor unit firing rate, twitch characteristics and fibre type composition in an agonistic muscle group in man

A comparison was carried out between the motor unit (MU) firing rate and the characteristics of the twitch and the fibre type composition of anconeus and triceps brachii. Fibre type composition (type I, type II) was determined in whole cross-sections of cadaver specimens. The proportion of type I fibre was 60%-67% in anconeus and 32-40% in the lateral head of triceps brachii. Reflecting these histochemical differences, the contraction time of anconeus and triceps was 92 +/- 9 ms and 68 +/- 9 ms respectively. It follows that anconeus can be classified as a slow muscle, as opposed to the lateral head of triceps. The relationship between MU firing rate and isometric force, tested at 90 degrees elbow flexion, differed between the two muscles for force values below 30% of maximal voluntary contraction. No significant increase in MU firing rate was found in anconeus at forces above 5% of maximal voluntary contraction. It is concluded that even within a single agonistic muscle group acting at a single joint there is an adaptation of MU firing rate to the contractile characteristics of each muscle.     

The influence of temperature on contractile properties of motor units in rat medial gastrocnemius

The effects of hypothermia and hyperthermia on mammalian skeletal muscle function have previously been reported. However, their effects on the contractile properties of different motor unit (MU) types were not described. This study aimed to explore the effect of temperature on contractile properties of MUs in rat medial gastrocnemius kept at 25 °C (hypothermia), 37 °C (normothermia), and 41 °C (hyperthermia). Hypothermia prolonged the twitch time parameters of all MU types, shifting the steep part of the force-frequency curve towards lower frequencies and increasing its steepness. In addition, it reduced the rate of force development but not the twitch and tetanus forces of slow-twitch (S) MUs. Moreover, it reduced the tetanic force of fast-twitch fatigable (FF) MUs and increased the twitch force of fast-twitch fatigue-resistant (FR) MUs. In contrast, hyperthermia had opposite effects on twitch time properties and the force-frequency relationship. The twitch-to-tetanus ratio decreased for FF and FR MUs, and the steep part of the force-frequency curve shifted towards higher frequencies and decreased in steepness. Our findings indicate that FF MUs are the most sensitive and S MUs are the least sensitive to temperature. Furthermore, force control processes involving changes in motoneuronal firing frequency were radically modified for fast MUs, especially FF MUs.     

Effect of aging on properties of motor unit action potentials in the rat medial gastrocnemius muscle

The purpose of this study was to investigate whether age-related changes in motor unit (MU) contractile properties are reflected in parameters of motor unit action potentials (MUAPs). MUs of the medial gastrocnemius muscle were functionally isolated in anaesthetized Wistar rats. A control group of young animals (5–10 mo) was compared to two groups of old rats (24–25 mo and 28–30 mo). The basic contractile properties of MUs as well as the amplitude, total duration, peak-to-peak time, and number of turns within MUAPs were measured. Effects of aging were mainly observed for fast fatigable MUs (a prolongation of MUAPs and increased number of turns). The MUAP amplitude did not change significantly with aging in either MU type, but it correlated to the twitch or tetanic forces, which tended to increase with age, especially for slow MUs. We concluded that the prolongation of MUAPs and the greater incidence of signal turns was probably a result of a decrease in muscle fiber conduction velocity and/or an increase in their dispersion, and enlargement of MU territories – presumably caused by axonal sprouting of surviving motoneurons. The latter might also be responsible for the observed age-related tendency for a increase in MUAP amplitudes in slow MUs.     

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.     

Human motoneuron firing behavior and single motor unit F-wave

In motor control studies, the F-wave (a recurrent discharge evoked by an axonal antidromic volley) widely used for obtaining information on motoneuron pool behavior. However, such F-wave using is a matter of discussion and still has been not validated experimentally. The aim of the present study was investigation of F-wave properties of single firing motor units (MUs) in healthy humans, the properties, which could give evidence for F-wave origin in motoneuron soma and, therefore, could be used for estimation of a relation between MU firing and motoneuron firing behavior. In total, 91 MUs in five muscles of six healthy subjects, during gentle voluntary contractions, were studied. Peri-stimulus time histograms of single MUs were plotted. None of them revealed statistically significant increasing in MU firing probability at the F-wave latency. Analysis of relationships between characteristics of motoneuron firing behavior (mean firing frequency and target interspike interval duration) and properties of F-waves showed their independence. At the same time, it was found that F-waves were recorded in MUs, whose axons possessed the marked supernormal period in excitability recovery cycle after a discharge. Thus, the present results are in contrast to that which should be expected if the F-wave originated in the motoneuronal soma and could provide evidence for motoneuron firing behavior.     

Elbow and wrist joint contact forces during occupational pick and place activities

A three-dimensional, mathematical model of the elbow and wrist joints, including 15 muscle units, 3 ligaments and 4 joint forces, has been developed. A new strain gauge transducer has been developed to measure functional grip forces. The device measures radial forces divided into six components and forces of up to 250N per segment can be measured with an accuracy of +/-1%. Ten normal volunteers were asked to complete four tasks representing occupational activities, during which time their grip force was monitored. Together with kinematic information from the six-camera Vicon data, the moment effect of these loads at the joints was calculated. These external moments are assumed to be balanced by the internal moments, generated by the muscles, passive soft tissue and bone contact. The effectiveness of the body's internal structures in generating joint moments was assessed by studying the geometry of a simplified model of the structures, where information about the lines of action and moment arms of muscles, tendons and ligaments is contained. The assumption of equilibrium between these external and internal joint moments allows formulation of a set of equations from which muscle and joint forces can be calculated. A two stage, linear optimisation routine minimising the overall muscle stress and the sum of the joint forces has been used to overcome the force-sharing problem. Humero-ulnar forces of up to 1600N, humero-radial forces of up to 800N and wrist joint forces of up to 2800N were found for moderate level activity. The model was validated by comparison with other studies.     

Human motor unit recruitment and derecruitment during long lasting intermittent contractions.

Seven healthy subjects were investigated in cyclic ramp-and-hold long lasting isometric contractions. Wire branched electrodes were used for selective recording of single motor unit (MU) potentials from m. biceps brachii. MU behaviour was defined in terms of recruitment/derecruitment thresholds (RT and DT) and the duration of interspike intervals (ISI). A total of 63 MUs was investigated: 40 units were active from the beginning of the task performance and another 23 were recruited later. There were no changes in the recruitment pattern of MUs with fatigue development - a short first ISI followed by a very long second one and an almost constant firing rate after this transient phase. The tendency of RT to gradually decrease dominates the results. Thus, the required constant rate of force increase with fatigue development was maintained mostly by the mechanisms of space coding (i.e., decrease of RT and recruitment of additional MUs). Oppositely, the time behaviour of the DT changes was not uniform and rate coding was an essential mechanism in the adaptation of MU activity to muscle fatigue during relaxation phases. The recruitment pattern and fatigue related behaviour of the additionally recruited MUs were similar to those of MUs active from the first cycle of the motor task performance.     

Synchronization of human motor unit firing during voluntary contraction of muscle and the tonic vibration reflex

We constructed cross-correlograms (CCGs) of action potentials of pairs of motor units (MUs) of human soleus, triceps brachii, and the first and second dorsal interosseous muscles. During voluntary muscle contraction, a pronounced peak in the zero bin was found in 21 out of 126 pairs investigated with the aid of the CCG; this indicates that the number of coincidental firings exceeded chance. The width of the peak did not exceed 5 msec (synchronization for a brief interval, i.e., short-term synchronization). When motoneurons of the soleus muscle were activated by vibration, correlations were found in 12 out 89 pairs of MUs investigated. On the CCGs of action potentials of MU pairs in two muscles (the first and second dorsal interosseous muscles), such correlations were found in four out of 10 pairs investigated. In all of these cases, the ratio of above-change coincidences relative to the total number of MU discharges was small, from 3.0 to 6.1%. Synchronization within a brief time interval can be considered a result of simultaneous creation of EPSPs in motoneourons reached by endings of a single pre-motor nerve fiber. In some pairs of MUs, long term synchronization (clustering) occurred, ie., synchronization lasting several tens of milliseconds. The long-term synchronization can be considered a manifestation of fatigue accompanying tremor.Institute for Problems of Information Transmission, Russian Academy of Sciences, Moscow. Translated from Neirofiziologiya, Vol. 23, No. 6, pp. 691–698, November–December, 1991.     

Modelling motor units in 3D: influence on muscle contraction and joint force via a proof of concept simulation

Functional heterogeneity is a skeletal muscle’s ability to generate diverse force vectors through localised motor unit (MU) recruitment. Existing 3D macroscopic continuum-mechanical finite element (FE) muscle models neglect MU anatomy and recruit muscle volume simultaneously, making them unsuitable for studying functional heterogeneity. Here, we develop a method to incorporate MU anatomy and information in 3D models. Virtual fibres in the muscle are grouped into MUs via a novel “virtual innervation” technique, which can control the units’ size, shape, position, and overlap. The discrete MU anatomy is then mapped to the FE mesh via statistical averaging, resulting in a volumetric MU distribution. Mesh dependency is investigated using a 2D idealised model and revealed that the amount of MU overlap is inversely proportional to mesh dependency. Simultaneous recruitment of a MU’s volume implies that action potentials (AP) propagate instantaneously. A 3D idealised model is used to verify this assumption, revealing that neglecting AP propagation results in a slightly less-steady force, advanced in time by approximately 20 ms, at the tendons. Lastly, the method is applied to a 3D, anatomically realistic model of the masticatory system to demonstrate the functional heterogeneity of masseter muscles in producing bite force. We found that the MU anatomy significantly affected bite force direction compared to bite force magnitude. MU position was much more efficacious in bringing about bite force changes than MU overlap. These results highlight the relevance of MU anatomy to muscle function and joint force, particularly for muscles with complex neuromuscular architecture.

     

Intramuscular and surface electromyogram changes during muscle fatigue

Twelve male subjects were tested to determine the effects of motor unit (MU) recruitment and firing frequency on the surface electromyogram (EMG) frequency power spectra during sustained maximal voluntary contraction (MVC) and 50% MVC of the biceps brachii muscle. Both the intramuscular MU spikes and surface EMG were recorded simultaneously and analyzed by means of a computer-aided intramuscular spike amplitude-frequency histogram and frequency power spectral analysis, respectively. Results indicated that both mean power frequency (MPF) and amplitude (rmsEMG) of the surface EMG fell significantly (P less than 0.001) together with a progressive reduction in MU spike amplitude and firing frequency during sustained MVC. During 50% MVC there was a significant decline in MPF (P less than 0.001), but this decline was accompanied by a significant increase in rmsEMG (P less than 0.001) and a progressive MU recruitment as evidenced by an increased number of MUs with relatively large spike amplitude. Our data suggest that the surface EMG amplitude could better represent the underlying MU activity during muscle fatigue and the frequency powers spectral shift may or may not reflect changes in MU recruitment and rate-coding patterns.     

Motor unit synchronization in FDI and biceps brachii muscles of strength-trained males

Motor unit (MU) synchronization is the simultaneous or near-simultaneous firing of two MUs which occurs more often than would be expected by chance. The present study sought to investigate the effects of exercise training, muscle group, and force level, by comparing the magnitude of synchronization in the biceps brachii (BB) and first dorsal interosseous (FDI) muscles of untrained and strength-trained college-aged males at two force levels, 30% of maximal voluntary contraction (MVC) and 80% MVC. MU action potentials were recorded directly via an intramuscular needle electrode. The magnitude of synchronization was assessed using previously-reported synchronization indices: k′, E, and CIS. Synchronization was significantly higher in the FDI than in the BB. Greater synchronization was observed in the strength-trained group with CIS, but not with E or k′. Also, synchronization was significantly greater at 80% MVC than at 30% MVC with E, but only moderately greater with CIS and there was no force difference with k′. Synchronization prevalence was found to be greater in the BB (80.1%) than in the FDI (71.5%). Thus, although the evidence is a bit equivocal, it appears that MU synchronization is greater at higher forces, and greater in strength-trained individuals than in untrained subjects.     

Simulation analysis of interference EMG during fatiguing voluntary contractions. Part I: What do the intramuscular spike amplitude–frequency histograms reflect?

Decline in amplitude of EMG signals and in the rate of counts of intramuscularly recorded spikes during fatigue is often attributed to a progressive reduction of the neural drive only. As a rule, alterations in intracellular action potential (IAP) are not taken into account. To test correctness of the hypothesis, the effect of various discharge frequency patterns as well as changes in IAP shape and muscle fibre propagation velocity (MFPV) on the spike amplitude-frequency histogram of intramuscular interference EMG signals were simulated and analyzed. It was assumed that muscle was composed of four types of motor units (MUs): slow-twitch fatigue resistant, fast-twitch fatigue resistant, fast intermediate, and fast fatigable. MFPV and IAP duration at initial stage before fatigue as well as their changes differed for individual MU types. Fatigability of individual MU types in normal conditions as well as in the case of ischaemic or low oxygen conditions due to restricted blood flow was also taken into account. It was found that spike amplitude-frequency histogram is poorly sensitive to MU firing frequency, while it is highly sensitive to IAP profile lengthening. It is concluded that spike amplitude-frequency analysis can hardly provide a correct measure of MU rate-coding pattern during fatigue.