Neural network model for control of muscle force based on the sizeprinciple of motor unit

A neural-network model consisting of a single motor cortex output cell, α motoneurons, Renshaw cells, and muscle units is proposed. Linear relations between motor cortex output and force output that were observed in monkeys and firing rate versus force relations in human skeletal muscles are explained by computer simulations. It is suggested that Renshaw recurrent inhibition has the effect of linearizing the gain between motor cortex output and force output, and it is confirmed that the orderly recruitment of motor units is governed by unit size in accordance with a classical observation. The model appears to represent a fundamental neural mechanism of force control because both firing rates and forces calculated from the model agree with experimental data in humans and monkeys     

Analysis and simulation of changes in EMG amplitude during high-level fatiguing contractions

Changes in surface electromyographic (EMG) amplitude during sustained, fatiguing contractions are commonly attributed to variations in muscle fiber conduction velocity (MFCV), motor unit firing rates, transmembrane action potentials and the synchronization or recruitment of motor units. However, the relative contribution of each factor remains unclear. Analytical relationships relating changes in MFCV and mean motor unit firing rates to the root mean square (RMS) and average rectified (AR) value of the surface EMG signal are derived. The relationships are then confirmed using model simulation. The simulations and analysis illustrate the different behaviors of the surface EMG RMS and AR value with changing MFCV and firing rate, as the level of motor unit superposition varies. Levels of firing rate modulation and short-term synchronization that, combined with variations in MFCV, could cause changes in EMG amplitude similar to those observed during sustained isometric contraction of the brachioradialis at 80% of maximum voluntary contraction were estimated. While it is not possible to draw conclusions about changes in neural control without further information about the underlying motor unit activation patterns, the examples presented illustrate how a combined analytical and simulation approach may provide insight into the manner in which different factors affect EMG amplitude during sustained isometric contractions.     

Manipulation of Muscle Force with Various Firing Rate and Recruitment Control Strategies

A computer-controlled, dual-channel neuromuscular stimulation system capable of manipulating skeletal muscle force with a wide range of action potential firing rates and motor-unit recruitment control strategies was designed and evaluated on the m. gastrocnemius muscle of the cat. The muscle force could be controlled with control strategies in which motor unit recruitment accounted for from 50 percent and up to 100 percent of the initial muscle force while firing rate induced the remaining force segment. The force response to linearly increasing recruitment was linear, whereas a saturation nonlinearity was evident in response to the firing rate input. Initial and terminal nonlinear force segments during 100 percent recruitment range were shown to be due to the viscoelastic components of the muscle fibers and their tendons. Recruitment of the muscle's motor units at rates that generated from 36 percent/s and up to 360 percent/s of the maximal force range was shown to correlate linearly to the input stimulus (R 0.9889). Reduction of the maximal firing rate from 55 to 40 pps showed that although minimization of fatigue at a cost of 10 percent reduction in the maximal force is possible, the correlation of the force response to the input signal remains high (R 0.9929) and linear. Some preliminary conclusions about rehabilitative applications were drawn based on the data presented in conjunction with previous studies.     

Autoregressive Modeling of Surface EMG and Its Spectrum with Application to Fatigue

The following is an investigation of the ability of the autoregressive (AR) model to describe the spectrum of the processes underlying the recorded surface EMG. Surface EMG (SEMG) spectrum is influenced by two major factors; one attributed to the motor units (MU) firing rate and the second, the higher frequency one, to the morphology of the action potentials (AP) traveling along the muscle fiber. In the present paper, SEMG measurements were carried out on the biceps brachii muscle with fixed surface electrodes arrangement and isotonic conditions. Sufficient averaging of 0.5 s segments enabled the identification of the low-frequency peak related to the firing rates of the MU's.     

The Nature and Etiology of Normal and Alcohol Withdrawal Tremor

Alcohol withdrawal tremor is principally a postural-type tremor. That is, the tremor manifests itself most when the limbs are voluntarily maintained in a stationary position. The tremor of alcohol withdrawal is typically 5 to 20 times as large and approximately the same frequency as normal postural tremor. The fact that withdrawal tremor is uncorrelated in both outstretched hands argues against the involvement of a central pacemaker in the genesis of the tremor. Both withdrawal and normal physiologic type hand tremors are associated with synchronous firing of extensor motor units in phase with tremor velocity at the frequency of limb resonance. Both kinds of tremor are reduced by the p-adrenergic receptor blocking drug, propranolol. The reduction in tremor is caused by a decrease in the synchrony of motor units and not a decrease in the total number of units involved in maintaining limb posture. It is proposed that increased tremor during withdrawal is due to the entrainment by 1 A muscle spindle afferents of asynchronously firing motoneurons. Tremor is also increased by entrainment of motoneurons firing synchronously at 9 to 10 Hz due to an oscillation in the stretch reflex control system. Tremor reduction following propranolol is due to a decrease in entrainment because of decreased 1 A afferent inflow to the spinal cord or because of reduced sensitivity of alpha motoneurons to 1 A spindle afferent discharges.     

A nonlinear model of the phasic dynamics of muscle activation

This paper presents a phasic excitation-activation (PEXA) model of the process of motoneuron excitation and the resultant activation and force development of a motor unit. The model input is an amount of depolarizing current (as when injected with an intracellular electrode) and the model output is muscle force. The model includes dynamics and nonlinearities similar to phenomena discovered experimentally by others: the firing rate response of motoneurons to steps of depolarizing current and the "catch-like enhancement" of force produced by overlapping motor neuron action potentials. The parameter values used in this model are derived from experimentally measured data and expressed in physical units, and model predictions extend to published data beyond those used in generating the model parameter values.     

Automatic decomposition of selective needle-detected myoelectricsignals

A procedure for the storage and documentation of myoelectric signals has been developed that consists of a selective needle signal detection protocol, a data collection-compression routine, an adaptive signal decomposition algorithm, and an error filter. The collection-compression routine stores only fixed-length signal epochs that contain motor unit action potentials (MUAPs) detected during individual motor unit firings. The decomposition algorithm assigns the collected MUAPs to candidate motor units, based on template matching using power-spectrum domain features and firing-time criteria calculated from the motor units' firing statistics. Power spectrum features allow the use of Nyquist sampling rates and remove the need for template alignment. The algorithm is adaptive and attempts to minimize dependent errors. The error filter, using firing statistics, accounts for unresolved superpositions and other decomposition errors. Using a standard TECA single-fiber needle electrode, signal recorded during isometric, constant, or slow force-varying contractions of up to 50% of the maximal voluntary contraction level, have been successfully analyzed     

Statistical encoding model for a primary motor cortical brain-machine interface

A number of studies of the motor system suggest that the majority of primary motor cortical neurons represent simple movement-related kinematic and dynamic quantities in their time-varying activity patterns. An example of such an encoding relationship is the cosine tuning of firing rate with respect to the direction of hand motion. We present a systematic development of statistical encoding models for movement-related motor neurons using multielectrode array recordings during a two-dimensional (2-D) continuous pursuit-tracking task. Our approach avoids massive averaging of responses by utilizing 2-D normalized occupancy plots, cascaded linear-nonlinear (LN) system models and a method for describing variability in discrete random systems. We found that the expected firing rate of most movement-related motor neurons is related to the kinematic values by a linear transformation, with a significant nonlinear distortion in about 1/3 of the neurons. The measured variability of the neural responses is markedly non-Poisson in many neurons and is well captured by a "normalized-Gaussian" statistical model that is defined and introduced here. The statistical model is seamlessly integrated into a nearly-optimal recursive method for decoding movement from neural responses based on a Sequential Monte Carlo filter.     

The contribution of motor unit pairs to the correlation functions computed from surface myoelectric signals

The contribution of motor unit action potential trains (MUAPT) of distinct motor units (MU) to the crosscorrelation function between myoelectric signals (MES) recorded at the skin surface is studied. In specific, the significance of the correlation between the firing activity of concurrently active MUs (which results in cross-terms in the overall correlation function) is compared to the representation obtained using the contributions of single MUs at each recording site (auto-terms). A model for the generation of surface MUAPs is combined with the generation of MU firing statistics in order to obtain surface MUAPTs. MU firing statistics are simulated to incorporate MU synchronization levels reported in the literature. Alternatively, experimental firing statistics are fed to the model generating the MUAPTs. The contribution of individual MU pairs to the global myoelectric signal correlation function is assessed. Results indicate that the cross-terms from different MUs decrease steadily contributing very little to the overall correlation for record lengths as short as 30 s. Thus, the error expected when computing the crosscorrelation function between two channels of MES as the superposition of the auto-terms contributed by single MUs (i.e., ignoring the cross-terms from different MUs) is shown to be very small.     

Modeling of muscle motor unit innervation process correlation and common drive

Concurrently active motor units (MUs) of a given muscle can exhibit a certain degree of synchronous firings, and a certain degree of common variation in their firing rates. The former property is referred to as motor unit synchrony in the literature, which is termed motor unit innervation process (MUIP) correlation in this study. The latter is referred to as motor unit common drive and can be quantified by the common drive coefficient, which is the correlation coefficient between the smoothed firing rates of the two MUs. Both properties have important roles and implications in the generation and resulting characteristics of the myoelectric signal and for the development of signal processing algorithms in myoelectric signal (MES) applications. In order to study these implications and characteristics, in this paper estimation procedures are developed to quantify the degree of MUIP correlation and common drive as functions of physiological parameters. Also, the interaction between MUIP correlation and motor unit common drive is studied in a physiologically realistic simulation model. Neurons modeled by Hodgkin-Huxley systems form the framework of the simulation model in which excitation and synaptic characteristics can be modified. MUIP correlation and common drive degree and interaction are studied through a number of simulations. To support the simulation results, experimental in vivo motor unit trains were collected at low levels of contraction from 11 subjects, and decomposed into the constituent unit trains giving 50 concurrently active motor unit pairs. The simulation demonstrated that the innervation process correlation coefficient is controlled primarily by the postsynaptic conductance, gsyn, and was less than 0.05 mS/cm2 for realistic values of gsyn. The common drive was found to be controlled by the exciting neuron input with no statistically significant interaction between it and the MUIP correlation. The experimental data gave results in close agreement with those of the simulation.     

A Procedure for Decomposing the Myoelectric Signal Into Its Constituent Action Potentials?Part I: Technique, Theory, and Implementation

A technique has been developed which enables the decomposition (separation) of a myoelectric signal into its constituent motor unit action potential trains. It consists of a multichannel (via one electrode) myoelectric signal recording procedure, a data compression algorithm, a digital filtering algorithm, and a hybrid visual-computer decomposition scheme. The algorithms have been implemented on a PDP 11/34 computer. Of the four major segments of the technique, the decomposition scheme is by far the most involved. The decomposition algorithm uses a-sophisticated template matching routine and details of the firing statistics of the motor units to identify motor unit action potentials in the myoelectric signal, even when they are super-imposed with other motor unit action potentials. In general, the algorithms of the decomposition scheme do not run automatically. They require input from the human operator to maintain reliability and accuracy during a decomposition.     

The dynamic response model of nine different skeletal muscles

The frequency response model of nine different skeletal muscles in the hindlimb of the cat was determined with the aide of electrical nerve stimulation which allows orderly stimulation of motor units concurrently with firing rate increase. It was shown that the general model consists of a linear second-order system with double real poles and a pure time delay. The pole values were different for the different muscles, ranging from 1.55 to 2.8 Hz. Similarly, the pure time delay varied from muscle to muscle, ranging from 8 to 17 ms. Statistical analysis demonstrates that under isometric contraction with force oscillations in the range of 10-90% of maximal the model poles are determined, and could be predicted, from the muscles functional and anatomical location in the limb and from its pennation pattern.     

Motor Unit Firing Rate During Static Contraction Indicated by the Surface EMG Power Spectrum

In this study, power spectral density functions (PSDF's) were computed of interference EMG of various facial and jaw-elevator muscles during nonfatiguing submaximal static contractions, recorded with surface electrodes. A distinct peak was found in the PSDF's in the frequency region below 40 Hz. It was shown that the peak was due to genuine EMG activity and that it could not be considered as an artifact, which was caused by electrode displacements during contraction. An increase of contraction strength resulted in a shift of the peak to higher frequencies and a decrease of peak amplitude relative to the power spectral estimates above 40 Hz, which were shown to be determined by the shape of the motor unit (MU) action potentials. In accordance with mathematical models of the EMG PSDF, it was demonstrated that the peak indicates the dominant firing rate of the sampled MU's. Our results suggest that this can be defined as the firing rate of the first recruited low-threshold MU's, which may be expected to dominate the interference EMG signal because of their preponderance in number. The data further suggest that the peak can be more readily observed in PSDF's of facial and jaw-elevator muscles than in PSDF's of limb muscles. This might be related to differences in MU firing statistics.     

直线电机往复泵采油控制技术的研究

目前各油田的抽油设备多为游梁式抽油机,其存在的主要问题是能耗大、效率低.而直线电机抽油机采用直线电机驱动,舍弃了大部分变速传动环节,将传统的旋转驱动变为直线往复驱动,使直线电机抽油机具有更加完善的运动性能、动力性能和平衡性能.论文首先探讨了低渗透油田采油机理,进而分析了直线电机等效电路和机械特性,在此基础上提出了直线电机往复泵采油工艺方案.试验结果证明,该工艺解决了杆管偏磨问题,提高了能源利用率,延长了检泵修井周期,是采油厂降本增效行之有效的采油工艺.     

Universal low cost controller for electric motors with programmablecharacteristic curves

The realization of a universal low-cost controller for electric motors in CMOS technology with programmable characteristic curves is presented. With regard to the required chip area of 2.7 mm² in a 1.6 μm, 40 nm technology, the general advantage in comparison to microcontroller-based solutions lies in the low factory costs. The analog dc power supply is generated directly from the 230 V ac power line. An on-chip functional unit controls the firing current for the off-chip motor driving triac. Features of this functional unit are torque control and overload protection, firing, and post firing control. A new method was used to implement programmable multidimensional characteristic curves which are temperature and technology insensitive. In the actual controller application for a drilling machine motor, the mask-programmed curve shapes have been generated with the help of fuzzy algorithms. An impression of the reproducibility of multidimensional characteristic curves in manufacturing, as well as the accuracy of their precalculation, is given by introducing simulated and measured statistics of the actual design     

Single motor unit myoelectric signal analysis with nonstationarydata

The information content of the myoelectric signal (MES) is commonly revealed by statistical measures in the time or frequency domain. Empirical analyses of the MES from a single motor unit have generally assumed that features are invariant with time. Theoretical and experimental work has been done to demonstrate how nonstationary behavior in the discharge statistics of a motor neuron may affect estimates of features extracted from the motor unit's contribution to the MES. Specifically, it has been shown that nonstationary behavior can markedly influence estimates of features describing motor neuron firing behavior and consequently, the low-frequency portion of the MES power spectral density. These results may help to explain the discrepancies in the literature which report empirical models of motor neuron firing statistics     

A sliding mode current control scheme for PWM brushless DC motordrives

This paper proposes a sliding mode current control scheme for pulsewidth modulation (PWM) brushless DC motor drives. An improved “equivalent control” method is used in this scheme. A simple algorithm is proposed that differs from the original equivalent control method, which requires extensive calculation to estimate the load parameters. This algorithm can be implemented using logic circuits. Moreover, using autotuning, the proposed algorithm can be applied without load information. An operating principle for the power stage switching devices called single-side firing is also proposed. Single-side firing solves the dead-time problem, allowing the PWM frequency to be increased and the sampling rate to be raised. This paper explains the current control algorithm, single-side firing principle, and implementation of the proposed scheme in detail. Simulations and experimental results are given to show the validity of this scheme     

Estimation of motor unit twitches

This study deals with estimation of the mechanical twitch of a single motor unit in human muscle during voluntary contraction. The existing estimation method is based on averaging of the force produced by the whole muscle, using the motor unit action potential for triggering. This method leads to underestimation of twitch amplitude and rise time due to partial fusion of the twitches, even at the lowest firing rates which can be maintained during voluntary contraction. To obtain unbiased twitch estimates, even when the twitches partially fuse, three versions of a nonparametric system identification method are explored: averaging plus least squares estimation; least squares estimation; and Markov estimation. Averaging plus least squares estimation give poorer noise reduction than least squares estimation. The noise reduction obtained by least squares estimation is about the same as the noise reduction obtained by averaging alone. The noise is mainly due to the contraction of all active motor units, except the unit being studied. This noise has dominating low-frequency components. Markov estimation takes the spectrum of the noise into account, and thus in most cases provides a better estimate than least squares estimation.     

A model for the generation of synthetic intramuscular EMG signals to test decomposition algorithms

As more and more intramuscular electromyogram (EMG) decomposition programs are being developed, there is a growing need for evaluating and comparing their performances. One way to achieve this goal is to generate synthetic EMG signals having known features. Features of interest are: the number of channels acquired (number of detection surfaces), the number of detected motor unit action potential (MUAP) trains, their time-varying firing rates, the degree of shape similarity among MUAPs belonging to the same motor unit (MU) or to different MUs, the degree of MUAP superposition, the MU activation intervals, the amount and type of additive noise. A model is proposed to generate one or more channels of intramuscular EMG starting from a library of real MUAPs represented in a 16-dimensional space using their Associated Hermite expansion. The MUAP shapes, regularity of repetition rate, degree of superposition, activation intervals, etc. may be time variable and are described quantitatively by a number of parameters which define a stochastic process (the model) with known statistical features. The desired amount of noise may be added to the synthetic signal which may then be processed by the decomposition algorithm under test to evaluate its capability of recovering the signal features.     

表面放电AC—PDP放电特性的数值模拟

给出一种数值模拟的方法,来研究表明放电型AC－PDP的放电单元结构参数对着火电压的影响。通过这种方法,研究了放电单元结构参数,如放电间隙宽度、电极宽度、障壁高度、绝缘介质层厚度、介质层的介电常数以及寻直电极偏压等对着火电压的影响。所得结果有助于优化表面放电AC－PDP放电单元的结构设计。