Electromyographic Signals Signals Research Articles

Phasor-Based Myoelectric Synergy Features: A Fast Hand-Crafted Feature Extraction Scheme for Boosting Performance in Gait Phase Recognition.

Gait phase recognition systems based on surface electromyographic signals (EMGs) are crucial for developing advanced myoelectric control schemes that enhance the interaction between humans and lower limb assistive devices. However, machine learning models used in this context, such as Linear Discriminant Analysis (LDA) and Support Vector Machine (SVM), typically experience performance degradation when modeling the gait cycle with more than just stance and swing phases. This study introduces a generalized phasor-based feature extraction approach (PHASOR) that captures spatial myoelectric features to improve the performance of LDA and SVM in gait phase recognition. A publicly available dataset of 40 subjects was used to evaluate PHASOR against state-of-the-art feature sets in a five-phase gait recognition problem. Additionally, fully data-driven deep learning architectures, such as Rocket and Mini-Rocket, were included for comparison. The separability index (SI) and mean semi-principal axis (MSA) analyses showed mean SI and MSA metrics of 7.7 and 0.5, respectively, indicating the proposed approach's ability to effectively decode gait phases through EMG activity. The SVM classifier demonstrated the highest accuracy of 82% using a five-fold leave-one-trial-out testing approach, outperforming Rocket and Mini-Rocket. This study confirms that in gait phase recognition based on EMG signals, novel and efficient muscle synergy information feature extraction schemes, such as PHASOR, can compete with deep learning approaches that require greater processing time for feature extraction and classification.

The relationship between asymmetry changes in the slope frequency of bioelectrical activity of the gluteus maximus muscles and experience in short track speed skating athletics

BACKGROUND: In short track speed skating, there is asymmetric fatigue of the gluteus maximus (GM) muscle resulting from the technique of skating. Scientific reports confirm the relationship between muscle fatigue and its change in the slope frequency of bioelectrical activity. OBJECTIVE: To investigate whether athletic experience in elite short track speed skating can distinguish the asymmetry change in slope frequency of the raw electromyographic signal (EMG) of the GM muscle, influenced by the disparity in experience between junior and senior athletes. METHODS: In the research, an elite group of short track speed skating national team athletes Junior and Senior, participated. Isometric tension GM muscle was tested using the Biering-Sorensen test. RESULTS: The study confirmed differences in the asymmetry of slope frequences EMG signal in GM muscle between juniors and seniors in short track speed skating (p⩽ 0.001). Senior athletes showed greater slope frequences in the right GM muscle (p⩽ 0.002), while juniors showed greater in the left GM muscle (p⩽ 0.008). Intergroup analysis revealed significantly meaningful differences (p⩽ 0.001) in the level of slope frequences of the right GM muscle (juniors vs. seniors), highlighting the asymmetry resulting from experience. CONCLUSIONS: Statistically significant differences in the level of slope frequences of the right gluteus maximus muscle juniors vs. seniors were demonstrated, suggesting asymmetry due to experience and skating technique.

Spectral characterization of human leg EMG signals from an open access dataset for the development of computational models.

Large-scale neuromusculoskeletal models have been used for predicting mechanisms underlying neuromuscular functions in humans. Simulations of such models provide several types of signals of practical interest, such as surface electromyographic signals (EMG), which are compared with experimental data for interpretations of neurophysiological phenomena under study. Specifically, realistic characterization of spectral properties of simulated EMG signals is important for achieving powerful inferences, whereas considerations should be taken for myoelectric signals of different muscles. In this study, we characterized spectral properties of surface interference pattern EMG signals and motor unit action potentials (MUAP) acquired from three plantar flexor muscles: Soleus (SO), Medial Gastrocnemius (MG), and Lateral Gastrocnemius (LG); and one dorsiflexor muscle: Tibialis Anterior (TA). Surface EMG signals were acquired from 20 participants using the same convention for electrode placement. Specifically, interference pattern EMG signals were obtained during isometric constant force contractions at 5%, 10% and 20% of maximum voluntary contraction (MVC), whereas surface MUAPs were decomposed from surface EMG signals obtained at low contraction forces. We compared the spectrum median frequency (MDF) estimated from interference pattern EMG signals across muscles and contraction intensities. Additionally, we compared MDF and durations of MUAPs between muscles. Our results showed that MDF of interference pattern EMG signals acquired from TA were higher compared to SO, MG, and LG for all contraction intensities i.e., 5%, 10%, and 20% MVC. Consistently, MUAPs acquired from TA also had higher MDF values and shorter durations compared to the other leg muscles. We provide herein a dataset with the surface MUAPs waveforms and interference pattern EMG signals obtained for this study, which should be useful for implementing and validating the simulation of myoelectrical signals of leg muscles. Importantly, these results indicate that spectral properties of myoelectrical signals should be considered for improving EMG modeling in large-scale neuromusculoskeletal models.

Robust neural network filtering in the tasks of building intelligent interfaces

Objectives. In recent years, there has been growing scientific interest in the creation of intelligent interfaces for computer control based on biometric data, such as electromyography signals (EMGs), which can be used to classify human hand gestures to form the basis for organizing an intuitive human-computer interface. However, problems arising when using EMG signals for this purpose include the presence of nonlinear noise in the signal and the significant influence of individual human characteristics. The aim of the present study is to investigate the possibility of using neural networks to filter individual components of the EMG signal.Methods. Mathematical signal processing techniques are used along with machine learning methods.Results. The overview of the literature on the topic of EMG signal processing is carried out. The concept of intelligent processing of biological signals is proposed. The signal filtering model using a convolutional neural network structure based on Python 3, TensorFlow and Keras technologies was developed. Results of an experiment carried out on an EMG data set to filter individual signal components are presented and discussed.Conclusions. The possibility of using artificial neural networks to identify and suppress individual human characteristics in biological signals is demonstrated. When training the network, the main emphasis was placed on individual features by testing the network on data received from subjects not involved in the learning process. The achieved average 5% reduction in individual noise will help to avoid retraining of the network when classifying EMG signals, as well as improving the accuracy of gesture classification for new users.

Wavelet analysis of the EMG signal to assess muscle fatigue in the lower extremities during symmetric movement on a rowing ergometer

Purpose The aim of this publication is to propose a methodology to determine changes in fatigue in selected muscle groups of the lower extremity during dynamic and cyclical motion performed on a rowing ergometer. The study aims to use the discrete wavelet transform (DWT) to analyze electromyographic signals (EMG) recorded during diagnostic assessment of muscle and peripheral nerve electrical activity (electroneurography) using an electromyography device (EMG). Methods The analysis involved implementing calculations such as mean frequency (MNF) and median frequency (MDF) using the reconstructed EMG signal through DWT. The study examined the efficacy of DWT analysis in assessing muscle fatigue after physical exertion. Results The study obtained a negative regression coefficient for DWT analysis in all muscles except for the right gastrocnemius (GAS). The results suggest that DWT analysis can be an effective tool for evaluating muscle fatigue after physical exertion. Conclusions The use of DWT in the analysis of EMG signals during rowing ergometer exercises has shown promising results in assessing muscle fatigue. However, additional investigations are necessary to confirm and expand these findings. This publication addresses the literature gap on the determination of muscle fatigue considering motion analysis on a rowing ergometer using the discrete wavelet transform. Previous studies have extensively compared and analyzed methods such as the Fourier transform (FFT), short-time Fourier transform (STFT), and wavelet transform (WT) for muscle fatigue analysis. However, no previous work has specifically examined the assessment of muscle fatigue by incorporating DWT analysis with motion analysis on a rowing ergometer.

Hand Gesture Recognition Using EMG-IMU Signals and Deep Q-Networks

Hand gesture recognition systems (HGR) based on electromyography signals (EMGs) and inertial measurement unit signals (IMUs) have been studied for different applications in recent years. Most commonly, cutting-edge HGR methods are based on supervised machine learning methods. However, the potential benefits of reinforcement learning (RL) techniques have shown that these techniques could be a viable option for classifying EMGs. Methods based on RL have several advantages such as promising classification performance and online learning from experience. In this work, we developed an HGR system made up of the following stages: pre-processing, feature extraction, classification, and post-processing. For the classification stage, we built an RL-based agent capable of learning to classify and recognize eleven hand gestures-five static and six dynamic-using a deep Q-network (DQN) algorithm based on EMG and IMU information. The proposed system uses a feed-forward artificial neural network (ANN) for the representation of the agent policy. We carried out the same experiments with two different types of sensors to compare their performance, which are the Myo armband sensor and the G-force sensor. We performed experiments using training, validation, and test set distributions, and the results were evaluated for user-specific HGR models. The final accuracy results demonstrated that the best model was able to reach up to 97.50%±1.13% and 88.15%±2.84% for the classification and recognition, respectively, with regard to static gestures, and 98.95%±0.62% and 90.47%±4.57% for the classification and recognition, respectively, with regard to dynamic gestures with the Myo armband sensor. The results obtained in this work demonstrated that RL methods such as the DQN are capable of learning a policy from online experience to classify and recognize static and dynamic gestures using EMG and IMU signals.

Multi-user myoelectric pattern recognition for shoulder motion intent detection

Myoelectric interfaces have a large range of applications in rehabilitation and prosthetic fields. The electromyographic signal (EMG) generates different patterns of activations according to a specific motion activity allowing the extraction of task-discriminant features, and leading to an efficient external device control [1]. The application of such methodologies in the motion intention detection (MID) is challenging, since this requires to predict the subjects’ intentions while attempting to generate a certain movement [2]. Despite good results have been obtained for the intra-subject scenario [3], the inter- subject generalization still remains an issue. The aim of this work was to investigate myoelectric interfaces for multi-user application on data relative to the shoulder MID. The dataset was composed by eight subjects performing six shoulder movements [4]. The signals were segmented into 150 ms windows with an overlap of 75 ms and four time-domain features were extracted. The feature matrix was split into a calibration and testing subsets. The spectral regression (SR) was used to reduce the dimension of the feature space and with the canonical correlation analysis (CCA) the reduced feature set was projected into a new space, where data related to different subjects are maximally correlated. The obtained projection coefficients were then used on the testing subset. The SVM classifier was trained on the projected calibration subset of a user A and the projected testing subset of a user B was used for testing. In this way, the classifier was trained on data belonging to a certain subject, and then tested on unseen data of a different person. Outcomes demonstrated that the presented approach boosted the classification performance, even if only one trial was used for the training session, with respect to the case in which neither the SR nor the CCA were applied. Indeed, the F1-score increased from 28% up to 53%. It can be also appreciated that increasing the number of repetitions for the calibration subset, the F1-score was further improved, up to 70% already with two repetitions. The accuracy presented a similar behaviour (Fig. 1). The coupling between SR and CCA proved to be reliable for the multi-user oriented shoulder MID. In MID problems, the movement recognition is performed relying on features extracted from a very short time period and on a transient epoch of the EMG signal, before the movement was fully achieved. For this challenging task, the present architecture proved to be reliable in an inter-subject scenario. Indeed, it provided high classification performances training on one subject and then testing on an unseen one, hence supporting the use of CCA for the development of subject-independent myoelectric interfaces.

Assist-As-Needed Exoskeleton for Hand Joint Rehabilitation Based on Muscle Effort Detection.

Robotic-assisted systems have gained significant traction in post-stroke therapies to support rehabilitation, since these systems can provide high-intensity and high-frequency treatment while allowing accurate motion-control over the patient’s progress. In this paper, we tackle how to provide active support through a robotic-assisted exoskeleton by developing a novel closed-loop architecture that continually measures electromyographic signals (EMG), in order to adjust the assistance given by the exoskeleton. We used EMG signals acquired from four patients with post-stroke hand impairments for training machine learning models used to characterize muscle effort by classifying three muscular condition levels based on contraction strength, co-activation, and muscular activation measurements. The proposed closed-loop system takes into account the EMG muscle effort to modulate the exoskeleton velocity during the rehabilitation therapy. Experimental results indicate the maximum variation on velocity was 0.7 mm/s, while the proposed control system effectively modulated the movements of the exoskeleton based on the EMG readings, keeping a reference tracking error <5%.

HYBRID CLASSIFICATION STRATEGY OF EMG SIGNALS FOR ROBOTIC HAND CONTROL

Among the different bio-signals modalities, Electromyographic signal (EMG) has been one of the frequently used signals in the bio-robotics applications field. This is due to the fact that the EMG reflects directly the muscle activity of the user following the human motion intention. Consequently, the decoding of this intention is an essential task for controlling devices such as prosthetic hands and exoskeletons, based on EMG signals. This paper deals with the processing of EMG signals of the forearm muscles, in order to control two degrees of freedom (2 DoFs) robotic hand. The main contribution of this paper is the proposal of a hybrid approach that combines a pattern and a non-pattern recognition-based strategy. The proposed approach aims to take advantage of both strategies and overcome their shortcomings leading to a better analysis of the user movement intention. The EMG recorded signals are processed for feature extraction based on a Wavelet Packet Decomposition (WPD) method and classification using an Artificial Neural Network (ANN). Furthermore, we investigate the effect of the various parameters such as the applied force level, the number of the EMG channels and the window length of the EMG signal. The proposed approach is validated experimentally under realistic conditions. Very interesting results have been obtained for user intention decoding.

Digital Evaluation Algorithm for Upper Limb Motor Function Rehabilitation Based on Micro Sensor

The electroencephalogram (EEG) of the cerebral cortex reflects the upper limb motion control information of the human body. The electro myographic signal (EMG) of the body muscle tissue reflects the response of the upper limb muscle to the brain control. The intersection of two physiological electrical signals has become a new hot field in artificial intelligence, medical rehabilitation and neuroscience. Firstly, starting with the analysis of the power consumption characteristics of the micro-sensor system, by studying the working principle and design scheme of the energy self-capture technology, various energy supply methods of the combined vibration energy harvesting system, the thermoelectric energy harvesting system and the RF energy harvesting system are proposed. Combined upper limb exercise rehabilitation energy is self-capture program. Secondly, the upper limb motor EEG and EMG signal acquisition experiments were designed to preprocess the acquired signals. Based on the wavelet threshold denoising method, an improved threshold algorithm is proposed to remove the noise in the EEG signal and improve the signal-to-noise ratio of the EEG signal. On the basis of the wavelet analysis method, the stratified threshold denoising method is applied to the collected EMG signals for denoising processing and digital evaluation of upper limb motor function rehabilitation. Finally, a digital evaluation method for upper limb motor function rehabilitation combined with wavelet low-frequency coefficients and significant information is proposed. The algorithm combines wavelet transform, motion estimation, and significant information to design a video quality evaluation algorithm. It can be seen from the experimental results that the performance of this algorithm is superior and maintains high consistency with the human motion system.

SEMG Motion Intention Recognition Based on Wavelet Time-Frequency Spectrum and ConvLSTM

The electromyographic signal (EMG) is a kind of bioelectrical signal, which can predict human motion intention through signal analysis. Multiple classification models are used to predict the motion intention. It has been found that the classification accuracy is closely related to the feature information extracted from the signal. Traditionally, features are designed manually through prior knowledge. In this paper, a kind of EMG signal classification method based on convolutional neural network and convolutional long-term memory network (CNN-ConvLSTM) is proposed. ConvLSTM, with its global feature extraction capability, is designed to extract the sEMG features of each channel, and due to its strong local feature extraction capability, CNN was designed to further extract the fused feature information and realize end-to-end classification. The experimental results show that this algorithm has better classification performance than the existing classification methods. The electromyographic signal (EMG) is a kind of bioelectrical signal to recognize human movement intention.

Deep learning-based classification using Cumulants and Bispectrum of EMG signals

Surface electromyographic signals (EMG) historically have been used to classify tasks in basis of a feature extraction scheme and low complexity classifiers. Deep networks, as Multilayer Perceptron and Convolutional Neural Network (MLP and CNN, respectively), avoid the traditional, complex and heuristic (handcrafted) process of feature extraction. Today, it is possible to face the computational cost that these automatic techniques require due to the technology advancement. This allowed deep learning techniques to be quickly generalized to countless applications. This paper proposes to use the third order cumulants and their 2D Fourier transform (Bispectrum) to directly feed CNN and MLP deep learning networks. The classifier is not user-dependent (same classifier for all users) and obtains better results than the classical scheme according to several metrics.

Support Vector Machine-Based EMG Signal Classification Techniques: A Review

This paper gives an overview of the different research works related to electromyographic signals (EMG) classification based on Support Vector Machines (SVM). The article summarizes the techniques used to make the classification in each reference. Furthermore, it includes the obtained accuracy, the number of signals or channels used, the way the authors made the feature vector, and the type of kernels used. Hence, this article also includes a compilation about the bands used to filter signals, the number of signals recommended, the most commonly used sampling frequencies, and certain features that can create the characteristics of the vector. This research gathers articles related to different kinds of SVM-based classification and other tools for signal processing in the field.

A new method of diagnosing athlete's anterior cruciate ligament health status using surface electromyography and deep convolutional neural network

Anterior cruciate ligament (ACL) injury is one of the most common injuries in high-demand sports. Due to long-term treatment of this injury, diagnosing recovery of ACL becomes important, particularly six months postoperatively. The purpose of this research is to provide a cost-effective and intelligent method to diagnose ACL's health status. For this purpose, 11 healthy and 27 ACL-injured subjects have been selected. In the proposed method, the athlete performs a single-leg landing protocol and surface electromyographic signals (EMG) are taken from eight lower limb muscles. Then, time–frequency distributions of EMG signals in each landing are calculated as an image, using pseudo Wigner–Ville distribution (PWVD), which are the inputs of a deep convolutional neural network (DCNN). By time–frequency analysis, it has been made clear that any change in ACL's health status causes changes in the extent of energy spread in PWVD, distribution volume, frequency content, damping rate and the peak value of EMG signals. In this research, a new relationship between ACL's health status and lower limb muscles activity is introduced through monitoring of PWVD images. The result indicates that the designed expert system is able to diagnose ACL's health status with 95.8% accuracy. In this non-invasive method, PWVD images of EMG signals are chosen as the inputs of DCNN, instead of MRI images, which, in addition to their high accuracy in diagnosing, are safer and much cheaper. The presented method can play an important role in assessing the recovery process, six months postoperatively and after that.

MIMO human handwriting model in stochastic environment

The present paper deals with a multi inputs multi outputs (MIMO) human handwriting model to characterise the pen-tip displacement on the plan from two forearm muscles activities, called electromyography signals (EMG). The proposed model takes into account perturbations and incertitude whish can affect the handwriting process (instability of the writing support, psychical state of the writer, brusque movement, etc.). In this sense, an experimental approach was presented to record the displacements of a pen-tip moving on the plane and two EMG signals during the handwriting motion. The velocity of the writing and ARMAX structure are used to characterise this biological act. Recursive extended least square (RELS) algorithm is used to estimate the parameters of the proposed handwriting model. The obtained structure shows good concordance with the experimental recorded data.

Using lower extremity muscle activity to obtain human ankle impedance in the external–internal direction

The human ankle has a critical role in locomotion and estimating its impedance is essential for human gait rehabilitation. The ankle is the first major joint that regulates the contact forces between the human body and the environment, absorbing shocks during the stance, and providing propulsion during walking. Its impedance varies with the level of the muscle activation. Hence, characterizing the complex relation between the ankle impedance and the lower leg’s muscle activation levels may improve our understanding of the neuromuscular characteristics of the ankle. Most ankle–foot prostheses do not have a degree of freedom in the transverse plane, which can cause high amounts of shear stress to be applied to the socket and can lead to secondary injuries. Quantifying the ankle impedance in the transverse plane can guide the design for a variable impedance ankle–foot prosthesis that can significantly reduce the shear stress on the socket. This paper presents the results of applying artificial neural networks (ANN) to learn and estimate the relation between the ankle impedance in the transverse plane under non-load bearing condition using electromyography signals (EMG) from the lower leg muscles. The Anklebot was used to apply pseudorandom perturbations to the human ankle in the transverse plane while the other degrees of freedom (DOF) in the sagittal and frontal planes were constrained. The mechanical impedance of the ankle was estimated using a previously proposed stochastic identification method that describes the ankle impedance as a function of the applied disturbances torques and the ankle motion output. The ankle impedance with relaxed muscles and with the lower leg’s muscle activations at 10 and 20% of the maximum voluntary contraction were estimated. The proposed ANN effectively predicts the ankle impedance within 85% accuracy (±5 Nm/rad absolute) for nine out of ten subjects given the root-mean-squared (rms) of the EMG signals. The main contribution of this paper is to quantify the relationship between lower leg muscle EMG signals and the ankle impedance in the transverse plane to pave the way towards designing and controlling this degree of freedom in a future ankle–foot prosthesis.

Real-time muscle state estimation from EMG signals during isometric contractions using Kalman filters.

State-space control of myoelectric devices and real-time visualization of muscle forces in virtual rehabilitation require measuring or estimating muscle dynamic states: neuromuscular activation, tendon force and muscle length. This paper investigates whether regular (KF) and extended Kalman filters (eKF), derived directly from Hill-type muscle mechanics equations, can be used as real-time muscle state estimators for isometric contractions using raw electromyography signals (EMG) as the only available measurement. The estimators' amplitude error, computational cost, filtering lags and smoothness are compared with usual EMG-driven analysis, performed offline, by integrating the nonlinear Hill-type muscle model differential equations (offline simulations-OS). EMG activity of the three triceps surae components (soleus, gastrocnemius medialis and gastrocnemius lateralis), in three torque levels, was collected for ten subjects. The actualization interval (AI) between two updates of the KF and eKF was also varied. The results show that computational costs are significantly reduced (70x for KF and 17[Formula: see text] for eKF). The filtering lags presented sharp linear relationships with the AI (0-300ms), depending on the state and activation level. Under maximum excitation, amplitude errors varied in the range 10-24% for activation, 5-8% for tendon force and 1.4-1.8% for muscle length, reducing linearly with the excitation level. Smoothness, measured by the ratio between the average standard variations of KF/eKF and OS estimations, was greatly reduced for activation but converged exponentially to 1 for the other states by increasing AI. Compared to regular KF, extended KF does not seem to improve estimation accuracy significantly. Depending on the particular application requirements, the most appropriate KF actualization interval can be selected.

EFFECTS OF SADDLE HEIGHT ON PERFORMANCE AND MUSCULAR ACTIVITY DURING THE WINGATE TEST

This study aimed to analyze the anaerobic performance and muscle activation during a supramaximal cycling test at three different saddle positions. Twelve competitive cyclists completed an incremental cycling test and three 30-s Wingate tests in three different saddle heights (reference, downward, and upward), in a random order, on different days. The saddle height was individually shifted downward and upward (seeing 2.5% of the distance from the pubic symphysis to ground) from the reference position. The electromyographic signal (EMG) data was obtained from the rectus femoris, vastus lateralis, biceps femoris (long head), and gastrocnemius lateralis in order to assess muscle activation during the entire test. The anaerobic variables and the EMG data were divided into six consecutive windows of 5-s. The EMG signals were normalized by the first 5-s window of the reference position to provide the percentage changes throughout the test. The results suggest that during a 30-s Wingate test small changes in saddle height result in greater peak power output (reference=1380±241 W; downward=1497±175 W, p=0.036; upward=1491±225 W, p=0.049) and greater activation period for vastus lateralis (reference=33.6%, downward=33.2%, upward=35.0%; p=0.001) in comparision to rectus femoris (reference=24.5%, downward=25.2%, upward=23.7%), biceps femoris (reference=20.7%, downward=20.8%, upward=19.9%), and gastrocnemius lateralis (reference=21.2%, downward=20.8%, upward=19.9%). The results suggest that small adjustments in saddle height may affect the force-length relationship of the muscles of the lower limb, and consequently their recruitment pattern and their ability to generate force.

CNN architecture for robotic arm control in a 3D virtual environment by means of by means of EMG signals

This paper presents the development of a 3D virtual environment to validate the effectiveness of a Convolutional Neural Network (CNN) in a virtual application, controlling the movements of a manipulator or robotic arm through commands recognized by the network. The architecture of the CNN network was designed to recognize five (5) gestures by means of electromyography signals (EMGs) captured by surface electrodes located on the forearm and processed by the Wavelet Packet Transform (WPT). In addition to this, the environment consists of a manipulator of 3 degrees of freedom with a final effector type clamp and three objects to move from one place to another. Finally, the network reaches a degree of accuracy of 97.17% and the tests that were performed reached an average accuracy of 98.95%.

Multi-model approach to characterize human handwriting motion

This paper deals with characterization and modelling of human handwriting motion from two forearm muscle activity signals, called electromyography signals (EMG). In this work, an experimental approach was used to record the coordinates of a pen tip moving on the (x,y) plane and EMG signals during the handwriting act. The main purpose is to design a new mathematical model which characterizes this biological process. Based on a multi-model approach, this system was originally developed to generate letters and geometric forms written by different writers. A Recursive Least Squares algorithm is used to estimate the parameters of each sub-model of the multi-model basis. Simulations show good agreement between predicted results and the recorded data.