Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle

To restore functional use of paralyzed muscles by automatically controlled stimulation, an accurate quantitative model of the stimulated muscles is desirable. The most commonly used model for isometric muscle has had a Hammerstein structure, in which a linear dynamic block is preceded by a static nonlinear function, To investigate the accuracy of the Hammerstein model, the responses to a pseudo-random binary sequence (PRBS) excitation of normal human plantarflexors, stimulated with surface electrodes, were used to identify a Hammerstein model but also four local models which describe the responses to small signals at different mean levels of activation. Comparison of the local models with the Linearized Hammerstein model showed that the Hammerstein model concealed a fivefold variation in the speed of response. Also, the small-signal gain of the Hammerstein model was in error by factors up to three. We conclude that, despite the past widespread use of the Hammerstein model, it is not an accurate representation of isometric muscle. On the other hand, local models, which are more accurate predictors, can be identified from the responses to short PRBS sequences. The utility of local models for controller design is discussed

System Identification of Wrist Stiffness in Parkinson's Disease Patients

The purpose of this work is to investigate the characteristics of motor control systems in Parkinson's disease patients. ARMAX system identification was performed to identify the intrinsic and reflexive, the non-controllable and controllable, components of wrist stiffness, enabling a better understanding of the problems associated with Parkinson's disease. The results show that the intrinsic stiffness dynamics represent the vast majority of the total stiffness in the wrist joint and that the reflexive stiffness dynamics are attributable to a tremor commonly found in Parkinson's disease patients. It was found that Parkinsonian rigidity, a symptom of Parkinson's disease, interferes with the known and traditional methods for separating intrinsic and reflexive components. Resolving this problem could lead to early detection of Parkinson's disease in patients not exhibiting typical symptoms, analytical measurement of the severity of the disease, and as a testing mechanism for the effectiveness of new medicines

ESTIMATION OF STRETCH REFLEX CONTRIBUTIONS OF WRIST USING SYSTEM IDENTIFICATION AND QUANTIFICATION OF TREMOR IN PARKINSON'S DISEASE PATIENTS

"The brain's motor control can be studied by characterizing the activity of spinal motor nuclei to brain control, expressed as motor unit activity recordable by surface electrodes". When a specific area is under consideration, the first step in investigation of the motor control system pertinent to it is the system identification of that specific body part or area. The aim of this research is to characterize the working of the brain's motor control system by carrying out system identification of the wrist joint area and quantifying tremor observed in Parkinson's disease patients. We employ the ARMAX system identification technique to gauge the intrinsic and reflexive components of wrist stiffness, in order to facilitate analysis of problems associated with Parkinson's disease. The intrinsic stiffness dynamics comprise majority of the total stiffness in the wrist joint and the reflexive stiffness dynamics contribute to the tremor characteristic commonly found in Parkinson's disease patients. The quantification of PD tremor entails using blind source separation of convolutive mixtures to obtain sources of tremor in patients suffering from movement disorders. The experimental data when treated with blind source separation reveals sources exhibiting the tremor frequency components of 3-8 Hz. System identification of stiffness dynamics and assessment of tremor can reveal the presence of additional abnormal neurological signs and early identification or diagnosis of these symptoms would be very advantageous for clinicians and will be instrumental to pave the way for better treatment of the disease

Application of Linear Stochastic Models in the Investigation of the Effects of Parkinson’s Disease on the Cop Time Series

The primary objective of this study was to use linear stochastic modeling approach to investigate parameters which may be sensitive enough to detect and quantify the changes in postural instability (PI) related to the progression in Parkinson’s disease (PD). Data collected in a previous study were analyzed in the current study. Participants with mild PD (n=13), moderate PD (n=10) and age range match healthy controls (HC, n=21) were instructed to stand in a comfortable self-selected natural stance on a force platform in both eyes open (EO) and eyes closed (EC) conditions. The foot-floor reaction forces were used to calculate the center of pressure (COP) time series. This COP time series was fitted by two different linear stochastic models: 1) an autoregressive (AR), and 2) an autoregressive moving average (ARMA) model. The postural control system was modeled as an inverted pendulum to describe pure body mechanics and a proportional, derivative and integral (PID) strategy was assumed for balance regulation. Swiftness, damping and stiffness parameters were extracted from the AR model. Natural frequency and damping ratio were extracted from the ARMA model. The statistical analysis (ANOVA) of these parameters revealed significant differences in stiffness and swiftness parameters between the HC and moderate PD population in the EO condition. These three parameters showed trends with progression of PD. The swiftness parameter showed decreasing mean values as PD severity increased, indicating that PD caused slower reactions to small deviations from equilibrium when compared to healthy controls. The mild and moderate PD, compared to HC, demonstrated by higher mean values of stiffness, suggesting a more rigid control strategy. The analysis of damping parameter revealed that the PD, compared to HC, may have a reduced ability to attenuate sway velocity during quiet stance as indicated by lower mean values of damping parameter and damping ratio. The natural frequency did not show significant trends in EO condition, but revealed an increasing trend with progression of PD. This could indicate that the PD could have larger number of deviations of COP from equilibrium. The analysis of effect of condition (EO, EC) revealed significant differences in all the five parameters. The stiffness, damping parameter and damping ratio had higher mean values for EO, compared to the EC condition, indicating the vital role that the visual feedback plays in detecting small perturbations from equilibrium leading to a better posture regulation in EO condition. The swiftness parameter and natural frequency indicated higher mean values in EC, compared to the EO condition, suggesting that the various sensory cues might be weighted differently in EO and EC conditions. Future studies should investigate the sensitivity of these calculated parameters to changes in PI in PD using a larger sample size and longer duration of trials. Also the variations in these parameters in response to dynamic tasks such as gait initiation and balance recovery should be considered in future studies

Estimation of the parameters of continuous-time systems using data compression

This chapter provides a unified introductory account of the estimation of the parameters of continuous-time systems using data compression based on a number of previous publication

Estimation of Impedance About the

In performing manual tasks, muscles are voluntarily contracted in order to produce force and orient the limb in the desired direction. Many occupational tasks are associated with frequent musculoskeletal disorders. In tasks involving skilful manipulation, very frequently the forces are focused on the upper limb and neck. Upper extremity cumulative trauma disorders are among the more common worker related injuries. These muscle disorders may be related to repetitive exertions, excessive muscle loads and extreme postures. One of the major challenges is to quantify the muscle load and researchers have tried various measures to quantify muscle load. Joint mechanical impedance can be a robust method to quantify muscle load. Joint mechanical impedance characterizes the dynamic torque-angle relationship of the joint. Joint impedance has been measured by earlier researchers, for limited tasks, by imparting force (or angle) perturbations on the joint and relating resultant angular (or force) changes. The joint impedance gives a quantitative measure related to muscle co-contraction level. Measurement of the mechanical impedance at the workplace may provide useful information relevant to the understanding of upper limb disorders. Electromyogram (EMG) is the electrical activity of the muscle. Usually, an estimate of the EMG amplitude is obtained from the raw waveform recorded from the surface of the skin. EMG amplitude estimates can be used to non-invasively estimate torque about joints. Presently, there exists no means by which mechanical impedance can be estimated non-invasively (i.e., without external perturbations). Therefore, we proposed the use of EMG to noninvasively estimate the joint mechanical impedance. Our objective in this project was to determine the extent to which surface EMG can be used to estimate mechanical impedance. Simulation studies were first performed to understand the extent to which this tool could be useful and to determine methods to be used for the experiment. The simulations were followed by evaluating and estimating mechanical impedance using data collected from one experimental subject. Simulations helped to devise processing techniques for the measured signals and also to determine the length of data to be collected. Low pass filters for derivatives (used in the development of impedance estimates) were designed. Subtracting out a polynomial was the best approach to attenuate a low frequency drift (artifact) that occurs in torque measurements. Thirty seconds of data provided impedance estimates with a relative error of 5% when EMG amplitude estimates with SNR of 15 were used. Experimental data from constant-posture, slowly force-varying background torque level showed that the elbow joint system behaved like a second order linear system between 2 Hz and 10 Hz. Co-contraction by subjects during experiments caused impedance estimates to be unexpectedly high even at low background torque. Further experiments would need to be conducted with the subjects being instructed to avoid co-contraction