Models of recruitment and rate coding organization in motor-unit pools.

“The relative contributions of the declines in motor unit force and maximal discharge rate to whole-muscle force can be evaluated with a model that has been developed for hand muscles.(74) The model comprises 100 motor units with properties that are based on experimental measurements.”

“For the FDI, we use the gain function derived by Fuglevand et al. (1993): g i j ¼ 1–e À 2 Tri =IPIj ð Þ 3 h i Tr i =IPI j À Á when Tr i =IPI j 4 0:4 and g ij ¼ 1 when Tr i =IPI j r 0:4 ð10Þ where g ij is the gain assigned to the jth firing of motor unit i, Tr i is the rise time of motor unit i, and…”

“Although it is possible that the motor unit mechanisms underlying the force fluctuations may be less evident in a large muscle mass such as quadriceps femoris (11), there were significant methodological differences between the studies that have been performed on quadriceps femoris and those that have examined other mu…”

“Fuglevand et al. (1993) developed a model to incorporate these nonlinearities in force production, which was used here.”

“motor-unit territory sizes proportional to the number of fibers per motor unit (Fuglevand et al., 1993; Roy et al., 1995; Yao et al., 2000; Monti et al., 2001), 6.”

“MU recruitment and spike trains were generated by the model proposed in [7] with the parameters adapted for the biceps brachii muscle.”

“The fiber transmembrane potential was represented by a multipole consisting of 50-point current sources, described by an empirically derived algebraic expression [34], Table I, rather than the more commonly used dipole or tripole representations [36], [37], [41].”

“To accept a train of spikes, a minimum of five interspike intervals was required during a constant level of force and the mean interspike interval had to have a coefficient of variation 30% (15).”

“…muscle fibers, the synaptic drive received by the spinal motor neurons should increase, as reflected by the increase in the electromyogramme (EMG) activity of the active muscles (Fuglevand et al., 1993; Hunter et al., 2003; Søgaard et al., 2006; Klass et al., 2008; Le´ve´nez et al., 2008).”

“…pool (defined as the set of motoneurons innervating a single muscle), which were based on the properties of motoneurons in deeply anesthetized preparations without significant levels of neuromodulation, revealed an approximately sigmoidal form (Fuglevand et al. 1993; Heckman and Binder 1991b).”

“3) based on an earlier model of motor unit recruitment and rate coding (Fuglevand et al. 1993a).”

“2012), the relatively small amount of force contributed by a single motor unit to the cumulative sum of the motor output (Fuglevand et al. 1993), and the low-pass filtering effect of muscles (Partridge, 1965; Baldissera, 1998) and motor neurons themselves (Farina et al.”

“Motor-Unit Synchronization Alters Spike-Triggered Average Force in Simulated Contractions”

“The reduction in discharge rate likely includes an increased variability in discharge (12, 23, 29, 30), which can decrease twitch fusion and increase the fluctuations in the forces exerted by individual motor units (12, 14).”

“Increases in both rate and recruitment result from raised synaptic drive to motoneurons (Fuglevand et al., 1993).”

“Noise is introduced by adjusting the firing instance of each pulse in the train following the equation (Fuglevand et al. 1993): ti,j ti,j 1 Z , (12) where ti,j is the time of the jth firing instance of motor unit i, ti,j 1 is the time occurrence of the preceding firing, is the mean firing rate of…”

“Motor unit properties The size of the evoked muscle potential is often monitored as a test of the efficacy of a stimulus to activate the motor unit pool in healthy subjects (Bigland-Ritchie et al. 1982; Fuglevand et al. 1993b; Zehr 2002) and patients (Chisari et al. 2001).”

“The motoneuron parameters were the same as those used by Cisi and Kohn (2008; see their Table 2) and were selected according to an exponential distribution over the pool of motoneurons (Fuglevand et al. 1993; Powers and Binder 1985).”

“…models of the neuromuscular system that significantly contributed to the knowledge of neuromuscular physiology, for example, the works by Fuglevand, Winter, and Patla (1993) and Heckman and Binder (1991), detailed structural and biophysical models of skeletal muscle contraction and the…”

“However, modeling work [16] as well as experimental evidence from animal [28] and human studies [18,22] clarified some of the underlying rules.”

“The combination of the parameters used in the simulations was selected based on previous experimental results on the behaviour of motor units in healthy individuals (e.g. Fuglevand et al. 1993).”

“Furthermore, because the system is an assemblage of many motor units acting in parallel, the twitches induced by a single motor unit are relatively small compared with the muscle forces that occur during most movements (Heckman and Binder, 1991; Fuglevand et al., 1993).”

“In those simulations, it was primarily due to the attainment of maximal force outputs of the muscle fibers, especially in high-threshold, high-force motor units (Fuglevand et al. 1993; Heckman and Binder 1991).”

“…properties of muscle fibres vary between fibre types (e.g. Burke et al. 1971; Bottinelli and Reggiani, 2000), so it is likely that the force developed by a whole muscle depends on the recruitment patterns and contractile properties of the different fibres within it (Fuglevand et al. 1993).”

“The number of fibers assigned to each motor unit was determined on the basis of the following experimental observations and assumptions (19).”

“Furthermore, the proportion of type II muscle fibers in the first dorsal 120 interosseous is approximately 50% (Fuglevand et al., 1993; Enoka and Fuglevand, 2001)while it is 30% in 121 the tibialis anterior (Henriksson-Larsén et al., 1983).”

“Based on a modelling study of motor-unit pools, Fuglevand et al. (1993) indicate that the difference between muscles that exhibit the linear as opposed to the nonlinear form of the EMG–torque relationship may be related to differences in firing rate behaviour rather than due to differences in…”

“The fiber compartments in series-fibered muscle can either be separated by tendinous inscriptions, as, for example, in cat and human semitendinosus muscle, or the muscle fibers are arranged in short overlapping arrays (Loeb et al., 1987; Paul, 2001; Woodley and Mercer, 2005).”

“The developed torque for each motor unit was obtained by convolution of eqn (3) with the simulated discharge pattern of the unit (Fuglevand et al. 1993).”

“A modelling study has demonstrated that spontaneous regular bursting at high frequencies (approximately 40±50 Hz) occurs in the surface EMG signal, when many independent motor units began to discharge at about the same ®ring rate (Fuglevand et al. 1993a).”

“The experimentally-determined values for discharge variability, obtained across a range of activation levels, enhanced the ability of a mathematical model (Fuglevand et al. 1993) to reproduce the force variability (Moritz et al. 2005).”

“The recruitment thresholds of motor neurons were distributed in accordance with the principle proposed in [31].”

“…amplitude as an index of muscle activation, an increase during and immediately following sustained submaximal contractions is usually considered to indicate an enhancement of the central drive (Bigland-Ritchie et al. 1986b; Fuglevand et al. 1993a), although it can be influenced by surges in Na -”

“It is well established that the size of MEPs increases with voluntary EMG (Farina et al. 2004; Fuglevand et al. 1993; Rothwell et al. 1991).”

“Motor unit force was simulated based on the motoneuron discharge rate using a model of isometric force (Fuglevand et al., 1993), and scaled according to force–length and force– velocity relations (Zajac, 1989).”

“…and recording electrode, factors such as changes in muscle Wber conduction velocity, motor unit recruitment, and motor unit synchronization will alter the amplitude of the surface EMG, independent of Wring rate (Fuglevand et al. 1993; Person and Libkind 1970; Yao et al. 2000; Zhou and Rymer 2004).”

“The MU firing pattern was generated as per [18], with the parameters adapted to the BB muscle.”

“…corresponding to the largest MU, for which msRPTT LN 30/ ); 3) a non-linear (sigmoid) relation between force and stimulus rate as described in (Fuglevand et al 1993) was finally included in the model introducing a gain factor ng 10 depending on the n th MU considered and on the firing…”

“T U fiber density was 20 fibers/mm2 while the fiber densit n the muscle was 200 fibers/mm2 (Fuglevand et al., 1993). he EMG recording system was bipolar with 20 mm in lectrode distance.”

“Linear or non-linear rate coding models can be used 46 – 48 .”

“This saturation, well-documented experimentally (Powers & Binder, 2001) and included in many models of the motoneuron pool (Fuglevand et al., 1993; Zhou, Suresh, & Rymer, 2007), was a key factor that influenced the simulated recovery dynamics, as described below.”

“Fuglevand et al. (1993) developed a model to incorporate these nonlinearities in force production.”

“This effect of ageing is especially noticeable t low forces, where each motor unit has a large contribution to he net force (Fuglevand et al., 1993).”

“A simulation approach (Fuglevand et al., 1993) including different maximum but fixed firing rates and recruitment ranges of all respective MUs revealed contrasting results; only if MUs were recruited over a broad force range, could a linear SEMG amplitude–force relationship be seen.”

“This latter comparison is justifiable on the basis that slowly increasing muscle force may be related in a near-linear manner to a slowly increasing depolarizing pressure on the MNs whose axons supply the MUs generating the force.(9,41) This article also addresses some of the unresolved issues concerning the functiona…”

“(11) with randomly applied superimposed twitches gives the variations in ITT one would expect based on the findings in this study.”

“[23], as shown in Röhrle [16], or to a biophysical model like the one by Negro and Farina [24].”

“9 Some other muscle models have incorporated different fiber-type properties, but have also been 10 limited to simulations of isometric contractions (Bol et al., 2011; Fuglevand et al., 1993).”

“Furthermore, computer models have shown isometric muscle force to be a near-linear function of this distributed excitatory synaptic current over most of the force range (Heckman & Binder, 1991; Fuglevand et al. 1993).”

“The synthetic clean EMG signals were simulated using a motoneuron recruitment model [23] and a convolution”

“(30), the desired magnitude of the decline in discharge rate due to IAI described by Eq.”

“(11), it seems that the variations in the STF of a knee extensor muscle with 300 motor units (22) can be decreased to 1% of the mean STF.”

“This type of EMG-force relation has been observed previously in computer models of motor unit activation and has been attributed to a narrowing of the force range over which motor units are recruited (12).”

“This opposite non-linearity has been predicted theoretically using motor unit based models of EMG (Milner-Brown and Stein, 1975; Fuglevand et al., 1993).”

“In particular, the performance of CNS feedback control systems must be evaluated carefully given that transcortical round trip (long-loop) signal transmission delays to and from trunk and ankle are on the order of 60–80 ms, respectively, and additional phase lags occur due to neuromuscular excitation–activation coupli…”

“[7] suggested that a bi-polar electrode configuration, with similar specifications to those used in the present study, have a myoelectric detection field largely limited to the underlying muscle tissue.”

“The increase in force with MU recruitment is believed to be more than proportional due to the size principle phenomenon in which larger MUs are recruited at higher contraction levels (Fuglevand et al., 1993).”