FES and spasticity

A model of hemiplegic spasticity based on electromyographical and biomechanical parameters measured during passive muscle stretching is presented. Two components of spasticity can be distinguished--phasic and tonic. This classification depends on the pattern of stretch reflex activity which can be either phasic or tonic as well as on the muscle stretch/tension characteristic. Stretch reflex, as a control loop, is in phasic spasticity characterized by increased sensitivity to velocity of stretching. In tonic spasticity, sensitivity to length of stretching is increased. After the injury, phasic spasticity appears first and invokes monosynaptic reflex pathways. The intensity of tonic spasticity increases with the duration of disability and hence causes changes in muscle fiber biomechanical properties. The model mentioned above has been used to evaluate the effects of FES on spasticity. Hemiplegic patients with implanted peroneal nerve stimulator for gait correction were followed up for one year starting a week before implantation. Long-term use of FES resulted in decrease of tonic spasticity in both ankle joint antagonistic muscle groups. In stimulated tibialis anterior muscle, the phasic type of spasticity increased. To obtain the correlation between changes in spasticity and functional abilities of patients, the maximal voluntary isometric contraction of both muscle groups was also measured. An improvement in voluntary strength was also observed. This can be taken as additional evidence that tonic spasticity is of greater physiological and clinical significance than phasic spasticity. It may be concluded that use of FES can decrease tonic spasticity and, if applied early after the injury, can prevent the appearance of tonic spasticity.     

Simultaneous and nonlinear identification of mechanical and reflexproperties of human elbow joint muscles

The naturally coexisting intrinsic mechanical and reflex properties of the human elbow joint were identified simultaneously using nonlinear, time-delay, continuous-time, and dynamic models. Angular random perturbations of small amplitude and low bandwidth were applied to the joint using a computer-controlled servomotor, while the subject maintained various levels of mean background muscle torque. Joint neuromuscular dynamics were identified from the measured elbow angle and torque. Stretch reflexes were modeled nonlinearly with both dynamic and static reflex gains. A continuous-time system identification method was developed to estimate parameters of the nonlinear models directly from sampled data while retaining realistic physical or physiological interpretations. Results from six subjects showed that dynamic stretch reflex gains, joint stiffness, and viscosity generally increased with mean background muscle torque; and that dynamic stretch reflex gain was higher during muscle stretch than that during muscle shortening. More importantly, the study provided realistic simultaneous estimates of the relative contributions of intrinsic mechanical and reflex actions to net joint torque. In particular, reflexively-mediated stiffness generated a significant portion of the total joint stiffness and the percentage varied systematically with background muscle torque     

Stability and Parameter Studies of a Stretch Reflex Loop Model

A model of the arm muscle stretch reflex loop is considered. Investigations are carried out on a system consisting of models of the forearm, the muscle spindle in a feedback structure, and the arm muscle. Specifically, the forearm is modeled as an inverted pendulum, the experimentally derived fourth-order muscle spindle model is taken from the literature, and two linear muscle models are employed. The stability of the feedback structure is investigated as a function of various free parameters in the component models. Frequency response profiles are analyzed for the muscle/muscle spindle combination, and are compared to experimentally derived data available in the literature. Finally, digital computer simulations are exhibited for a system corresponding to a quick release experiment, and for a system in which a periodic force is applied to the forearm.     

Quantifying proprioceptive reflexes during position control of the human arm

This study aimed to analyse the dynamic properties of the muscle spindle feedback system of shoulder muscles during a posture task. External continuous force disturbances were applied at the hand while subjects had to minimize their hand displacements. The results were analysed using two frequency response functions (FRFs) from which the model parameters were derived, being 1) the mechanical admittance and 2) the reflexive impedance. These FRFs were analysed by a neuromusculoskeletal model that implicitly separates the reflexive feedback properties (position, velocity and acceleration feedback gains) from intrinsic muscle visco-elasticity. The results show substantial changes in estimated reflex gains under conditions of variable bandwidth of the applied force disturbance or variable degrees of external damping. Position and velocity feedback gains were relatively larger when the force disturbance contained only low frequencies. With increasing damping of the environment, acceleration feedback gain decreased, velocity feedback gain remained almost constant and position feedback gain increased. It is concluded that under the aforementioned circumstances, the reflex system increases its gains to maximize the mechanical resistance to external force disturbances while preserving sufficient stability.     

Description of constrained responses based on correction approaches of physical parameters

Physical parameters to be estimated based on measured data from dynamic or static tests of systems do not coincide with analytical parameters due to measurement noise, model inadequacies, and structural damages. Measured data can be regarded as constraints to explain the behavior of the dynamic or static systems. The existence of constraints requires the additional forces to satisfy the measured data. The variation in the responses by constraints is expressed by the changes of physical parameters. Minimizing a square function of the difference between the analytical and corrected parameter matrices, this study derives the analytical equations to describe the constrained static and dynamic responses and the corrected forms of physical parameter matrices. It is shown that the derived equations coincide with the equations provided by Udwadia and Kalaba for dynamic systems and by Eun et al. for static systems. The validity of the proposed method is illustrated in applications.     

Design of gain-clamped doped-fiber amplifiers for optimal dynamicperformance

This paper provides a detailed analysis of gain-clamped doped-fiber amplifiers and design guidelines in a wavelength division multiplexed (WDM) networking environment. A simple dynamic model of the doped-fiber amplifier allows us to derive explicit expressions for the small-signal response, which help identify and optimize the most critical parameters for best dynamic performance. The most important parameter is the pump power, which should be chosen 1-2 dB's above its required open-loop value, with all channels present, for the required signal gain. In an all-optical networking scenario with input power per channel as high as -3 dBm the required pump power may well exceed 20 dBm. Thus optimization of other parameters such as laser wavelength and loop loss are important. For best dynamic performance either the loop loss should be extremely small, implying a very large laser flux, or the laser gain variation in response to a perturbation should be large. Accordingly, the laser wavelength should be placed either close to the unity-gain region of the clamped gain profile, or at its peak. Finally, the small signal model for a chain of clamped amplifiers is provided, and it is shown that long chains are vulnerable to low-frequency input signal perturbations     

Distortion Suppression in Neuromuscular Information Transmission Due to Interchannel Dispersion in Muscle Spindle Firing Thresholds

A mathematical multipath model of the flow of information within the afferent limb of the myotatic stretch reflex is reviewed and evaluated, with emphasis being placed on its multi-channel structure. The system is simulated, and the resultant output (alpha motoneuron transmembrane potential) is analyzed spectrally, with one single-tone input (muscle stretch) and a set of variations of different system parameters: (i) When all the channels are identical, the characteristics of the input signal are unrecognizable at the output, and can only be extracted by an ``unphysiological' motoneuron. (ii) When the afferent conduction delays are distributed among the channels, the output is similarly distorted, and can only be improved by assuming an atypically long conduction path. (iii) When the muscle spindle firing thresholds are either varied among the channels or vary temporally within each channel, the distortion is dramatically reduced and the input signal is easily recoverable.     

一种数字式自动增益控制系统的统计分析

本文介绍了一种数字式相关接收机自动增益控制系统,文中分析了环路的性能,并推导了决定灵敏度和其它性能指标的公式,还给出了一些例子的静态和动态特性,本文还讨论了设计这类自动增益控制系统的主要步骤。     

全闭环同步带传动系统的建模与控制方法研究

同步带传动是一种常用的传动机构。在高速高精度设备中,其动态性能直接影响到设备的精度和效率。对同步带系统进行建模,对电机模型、同步带传动模型和控制模型进行耦合分析并采用Simulink仿真系统中电流、速度以及位移全闭环的PD参数整定过程,获得了良好的动静态特性和最优控制参数。通过试验表明,运用参数整定仿真方法可高效优化实际控制对象的PD参数。并有效缩短调试时间。     

自动增益控制环路方程的一种简化处理方法及环路稳定时间分析

基于一种典型的自动增益控制(AGC)环路的模型，采用对数表示方式，简化了AGC环路的静态微动方程和动态运动方程。用数学模型动态表示出AGC环路输出信号和增益控制信号的变化过程，定量定性分析了AGC环路的稳定时间。仿真结果及实际应用验证了本文方法的有效性。     

中频宽带接收机AGC电路的研究

从一种典型的AGC环路模型推导出环路的动静态特性与环路各元件参数的关系，定性定量地分析了环路的稳态误差、稳定时间以及动态范围，并利用Analog公司的AD8367和AD8361设计了符合要求的具有大动态范围、宽带放大能力的中频AGC环路，通过实际测量验证了理论分析的正确性。     

The analysis of a digital gain control loop

In this paper, an auto-gain-control (AGC) loop which operates in a digital correlating receiver is described. The properties of the loop is analyzed mathematically and the formulas to determine the sensibility and other parameters are derived. The static and dynamic features of some examples are shown. The procedure for designing such a gain control loop is discussed.     

Estimation of intrinsic and reflex contributions to muscle dynamics: a modeling study

This work evaluated system identification-based approaches for estimating stretch reflex contributions to muscle dynamics. Skeletal muscle resists externally imposed stretches via both intrinsic stiffness properties of the muscle and reflexively mediated changes in muscle activation. To separately estimate these intrinsic and reflex components, system identification approaches must make several assumptions. We examined the impact of making specific structural assumptions about the intrinsic and reflex systems on the system identification accuracy. In particular, we compared an approach that made specific parametric assumptions about the reflex and intrinsic subsystems to another that assumed more general nonparametric subsystems. A simulation-based approach was used so that the "true" characters of the intrinsic and reflex systems were known; the identification methods were judged on their abilities to retrieve these known system properties. Identification algorithms were tested on three experimentally based models describing the stretch reflex system. Results indicated that the assumed form of the intrinsic and reflex systems had a significant impact on the stiffness separation accuracy. In general, the algorithm incorporating nonparametric subsystems was more robust than the fully parametric algorithm because it had a more general structure and because it provided a better indication of the appropriateness of the assumed structure.     

A Discrete-Time Model of Electrcally Stimulated Muscle

A model describing the input/output properties of electrically stimulated isometric muscle is developed and experimentally tested. A discrete-time model gives the force output at the times of stimulation during pulse width modulation of recruitment at fixed stimulus amplitudes and periods. Two elements are necessary in the model: a static nonlinear element followed by a linear dynamic element. The static nonlinearity describes the relationship between pulse width and steady-state force. The dynamic properties are described with less than 10 percent error by a second-order discrete-time deterministic autoregressive moving average (DARMA) model. Exponentially weighted recursive least squares methods allow efficient parameter estimation. Model parameters are found to vary systematically with muscle length and stimulus frequency. Tests comparing actual and simulated feedback control of electrically stimulated muscle indicate that the model is adequate for digital controller design for applications in functional electrical stimulation.     

A Control System for Long-Term Ventilation of the Lungs

A respirator control system based on a variant process model and optimization of system performance is described. The system attempts to minimize the harmful effects of positive pressure ventilation while meeting the ventilatory requirement of the patient. As alveolar pressure is indicative of respiratory dynamics, it has been used as control parameter. Desired alveolar pressure is derived from a fixed parameter RC lung model while actual alveolar pressure is estimated from the variant lung model which is continuously updated through on-line computation of respiratory mechanical parameters. The controller gain is optimally adjusted so as to minimize error index. The system has been simulated on a digital computer and several representative cases of sudden and gradual parameter variation have been studied. It has been shown that in case of changes in the process, the error quickly damps out to zero.     

Nonlinear dynamic modeling of neuron action potential threshold during synaptically driven broadband intracellular activity

Activity-dependent variation of neuronal thresholds for action potential (AP) generation is one of the key determinants of spike-train temporal-pattern transformations from presynaptic to postsynaptic spike trains. In this study, we model the nonlinear dynamics of the threshold variation during synaptically driven broadband intracellular activity. First, membrane potentials of single CA1 pyramidal cells were recorded under physiologically plausible broadband stimulation conditions. Second, a method was developed to measure AP thresholds from the continuous recordings of membrane potentials. It involves measuring the turning points of APs by analyzing the third-order derivatives of the membrane potentials. Four stimulation paradigms with different temporal patterns were applied to validate this method by comparing the measured AP turning points and the actual AP thresholds estimated with varying stimulation intensities. Results show that the AP turning points provide consistent measurement of the AP thresholds, except for a constant offset. It indicates that 1) the variation of AP turning points represents the nonlinearities of threshold dynamics; and 2) an optimization of the constant offset is required to achieve accurate spike prediction. Third, a nonlinear dynamical third-order Volterra model was built to describe the relations between the threshold dynamics and the AP activities. Results show that the model can predict threshold accurately based on the preceding APs. Finally, the dynamic threshold model was integrated into a previously developed single neuron model and resulted in a 33% improvement in spike prediction.     

Sensitivity analysis of relative accommodation and vergence

A sensitivity analysis was performed to determine the variation in response to changes in parameter values of a previously developed nonlinear static model of accommodation and vergence. To determine normal behavior, model simulation responses were computed using previously obtained parameter values in 4 subjects under 2 conditions. In the first, relative accommodation was evaluated by maintaining the vergence stimulus constant at 2.5 meter angles (MA) and varying the accommodative stimulus from -2.5 to 2.5 diopters (D) in 0.25-D steps. In the second, relative vergence was evaluated by maintaining the accommodative stimulus constant at 2.5 D and varying the vergence stimulus from 25 prism diopters (PD) base-in to 25 PD base-out in 5-PD steps. Sensitivity of the model parameters, consisting of controller gains for accommodation (ACG) and vergence (VCG), crosslink gains for accommodation-to-vergence (AC) and vergence-to-accommodation (CA), deadspace operators for accommodation (AE±AD) and vergence (VE±VD), and the tonic levels for accommodation (ABIAS) and vergence (VBIAS) were assessed by varying them at 50% and 150% of their normal values. It was found that the accommodation and vergence systems mere most sensitive to variation in crosslink gain, moderately sensitive to variation in controller gain and tonic level, and least sensitive to variation in size of the deadspace. These results may provide a quantitative basis for the occurrence of ocular dysfunctions associated with abnormal crosslink gains, such as strabismus, in clinical patients     

Analysis of switched diversity systems on generalized-fadingchannels

The performances of switched diversity systems operating on generalized (Nakagami)-fading channels are analyzed using a discrete-time model. The average bit error rate (BER) of binary noncoherent frequency shift keying (NCFSK) on slow, nonselective Nakagami-fading channels is derived. Closed-form expressions that can be used to determine optimum switching thresholds (in a minimum error rate sense) are also derived. In addition, the use of optimum fixed thresholds is considered. It is found that a considerable amount of diversity gain can be obtained using an optimum fixed (rather than adaptive) switching threshold. Results are obtained for both independent and correlated Nakagami-fading branch signals. The effects of fading severity and the correlation coefficient on both the BER and on the optimum switching threshold are investigated. It is shown that useful diversity gain can be obtained with power correlation coefficients as high as 0.9 when the fading is strong. The results for a Rayleigh channel are obtained and presented as a special case of generalized-fading model     

综合孔径射电望远镜中锁幅环的增益抖动

本文介绍了一种综合孔径射电望远镜上的增益控制环路,并详细讨论了噪声对增益起伏的影响。文章介绍了锁幅环的基本性质,推导了噪声功率与增益均方抖动之间的关系式。推导了环路失锁门限,并画出了实验验证的结果。最后讨论了减少噪声影响的一些措施。