Advancing biomedical engineering: Leveraging Hjorth features for electroencephalography signal analysis

The Activity parameter is the mean square value of the amplitude, representing the power of the EEG signal. It is calculated using equation 1 [16]: (1)Activity=Var(x)=1N∑i=1N(Xi−AMx)2$$Activity{\rm{ }} = Var(x) = {1 \over N}\sum\nolimits_{i = 1}^N {{{\left( {{X_i} - A{M_x}} \right)}^2}} $$ where X_i is the signal amplitude at the i^th sample, AM_x is the mean amplitude of the signal over N samples, N is the total number of samples. This parameter is indicative of the signal variance and is a direct measure of the signal’s power.

Mobility is a measure of the mean frequency or the rate of change in the signal, providing an estimate of the signal’s standard deviation. It is obtained from the variance of the first derivative of the signal as follows: First, the difference between consecutive signal amplitudes is calculated in equation 2 below: (2)di=xi+1−xi$${d_i} = {x_{i + 1}} - {x_i}$$

Then, the variance of these differences is calculated using equation 3 [17]: (3)Var(d)=1N−1∑i=1N(di−AMd)2$$Var(d) = {1 \over {N - 1}}\sum\nolimits_{i = 1}^N {{{\left( {{d_i} - A{M_d}} \right)}^2}} $$

Where d_i is the first derivative at the i^th sample, AM_d is the mean value of d over N samples. The Mobility is then computed as the square root of the ratio of the variance of the first derivative of the signal to that of the signal itself as written in equation 4 [18]: (4)Mobility=Var(d)Var(x)$$Mobility{\rm{ }} = \sqrt {{{Var(d)} \over {Var(x)}}} $$

This parameter reflects the frequency content of the signal by measuring the standard deviation of the power spectrum.

Complexity compares the signal’s pattern to the pattern of a pure sine wave, indicating the signal’s pattern changes. It is calculated as the Mobility of the first derivative of the signal divided by the Mobility of the signal as equation 5 states [19]: (5)Complexity=MobilityofdMobilityofx$$Complexity{\rm{ }} = {{{\rm{ }}Mobility{\rm{ }}of{\rm{ }}d} \over {{\rm{ }}Mobility{\rm{ }}of{\rm{ }}x}}$$

This dimensionless metric is indicative of the signal’s complexity, with higher values suggesting a more complex signal structure compared to a simple sine wave.

By integrating these parameters into the analysis, a rich feature set is derived that is capable of improving the performance of machine learning models in classifying and interpreting EEG signals, as will be stated in the following context.

The time-domain analysis of EEG signals provides the initial layer of understanding, showcasing the fluctuations of neural activities. Here, the section details the observed patterns within the EEG signals as they correspond to different limb movements and rest periods, establishing a baseline for the feature extraction process.

Randomly selected, Figures 4 and 5 depict the electrode responses in microvolts for an interval of 500 instances for two tasks, namely CRH and Resting, respectively. More intense fluctuations are noticed when analyzing Figure 4 due to the presence of a movement while slightly less amplitudes or fluctuations are observed in the resting task due to the absence of any movement by the subject. These values are chosen randomly to subject 10 and the features will be calculated to the same individual to understand the potential of these same patterns.

Fig.4:

Fig.5:

Moving deeper into the data, we dissect the Hjorth parameters extracted from the time-domain signals. The statistical significance of Activity, Mobility, and Complexity is evaluated to discern how these features can be correlated with specific motor tasks or mental states, revealing distinct behavioral clusters within the dataset.

In Figure 6, the Hjorth parameters for the Resting movement across all electrodes are depicted through a tripartite series of sub-figures. Each of these sub-figures is dedicated to one of the three dynamic statistical measures: activity, mobility, and complexity. These parameters provide insight into the signal’s variance, the frequency of the signal, and the similarity of the signal’s waveform to a pure sine wave, respectively. Notably, electrodes 14 and 15 exhibit markedly high amplitudes across all Hjorth parameters, suggesting a pronounced signal variability, frequency content, and waveform complexity at these locations. This could be indicative of localized neural dynamics or a heightened responsiveness to the resting state, to describe the unique patterns of neural activity captured by electrodes 14 and 15. Conversely, electrodes 7 and 13 are characterized by high fluctuation trends across all parameters, which may reflect a different neural mechanism or a response to physiological variables not captured by the other electrodes. The observed patterns in activity, mobility, and complexity could have significant implications for understanding the resting state’s neural underpinnings and call for a more nuanced analysis of electrode-specific activity.

Fig.6:

Figure 7 delineates the Hjorth parameters of the CRH movement, where the data present a stark contrast to the resting state. This figure illustrates an overall increase in fluctuation and amplitude across all electrodes. The activity parameter values range broadly from 0 to 600, indicating a wide variance in signal power during the CRH movement, which may be associated with the diverse motor and cognitive demands of this task. Mobility values extend from 0.3 to 1.4, suggesting variability in the frequency content of the signals that could be reflective of the complex motor control strategies employed during CRH movement. Complexity values between 1.1 and 3 indicate a range of waveform shapes, from simple oscillatory patterns to more irregular and complex forms. These variations can be attributed to the intricate neural coordination required for the CRH movement, highlighting the sophisticated interplay between different brain regions during this task.

Fig.7:

A comparison between Figures 6 and 7 reveals distinct patterns of neural activity associated with the different movements. While high amplitude in Hjorth parameters in the Resting movement is localized mainly to electrodes 14 and 15, the CRH movement is characterized by a universal elevation in fluctuation and amplitude across all parameters and electrodes. This suggests that the CRH movement engages a more extensive network of brain regions than the resting state, leading to increased variance, frequency content, and waveform complexity. The differential patterns observed in activity, mobility, and complexity between the two figures underscore the dynamism of the brain’s response to varying cognitive and motor demands. The marked contrasts between the resting and CRH states may provide valuable insights into the neural correlates of task-specific activities and the adaptability of the neural networks involved. These distinctions could pave the way for further research into the electrophysiological signatures of different brain states and movements, potentially contributing to the development of targeted interventions or diagnostic criteria for neurological conditions.

Figure 8 elucidates the behavior of Hjorth parameters for electrode 14 during Resting and CRH tasks, revealing distinct patterns of neural activity. During the Resting task, activity levels varied substantially, with a peak value suggesting intermittent spikes in neural activity, which could be indicative of spontaneous brain activity or external noise. Mobility remained relatively stable, suggesting a consistent frequency change, while complexity fluctuated, pointing to varying degrees of signal irregularity, perhaps reflecting the natural ebb and flow of resting brain dynamics. In contrast, the CRH task manifested higher overall activity levels with a broader range, implying increased neural engagement necessary for motor function. Mobility displayed greater variation, indicating more dynamic changes in frequency content, which aligns with the complex coordination required for hand movement. Complexity reached higher levels compared to the Resting task, suggesting a more intricate neural pattern during active movement. These fluctuations highlight electrode 15’s potential proximity to brain regions responsible for motor control, underscoring its significance in studies of neural dynamics and motor activity. To elaborate more, Figure 9 presents the instances of electrode 15 as well in comparison with those of figure 8.

Fig.8:

Fig.9:

Finally, the extracted features serve as inputs to machine learning models, aiming to classify tasks and diagnose conditions with greater accuracy. We discuss the integration of these features into various algorithmic frameworks, their impact on model performance, and the prospects they hold for the future of automated EEG analysis and biomedical applications.

Machine learning models have increasingly incorporated statistical features from EEG data to enhance classification and diagnostic capabilities. Deep Neural Networks (DNN) [20, 21], with their capacity for feature learning, have shown promise in deciphering complex patterns from Hjorth parameters and similar statistics. The hierarchical nature of DNNs allows them to distill high-level abstractions from raw data, which is particularly beneficial for identifying subtle neurological differences between various cognitive tasks or pathological states. Stacking models [22, 23], which combine the predictions of multiple machine learning algorithms to produce an ensemble, have also been utilized to capitalize on the strengths of individual models. This approach can yield more robust predictions, as it leverages the diverse perspectives of different models. Stochastic Gradient Descent (SGD) [24, 25], a cornerstone of many learning algorithms due to its efficiency in handling large datasets, has been adapted for EEG data to optimize performance in real-time applications, enhancing the potential for on-the-fly analyses in clinical settings.

Looking forward, the integration of statistical EEG features into machine learning models holds substantial promise for advancing the field of biomedical engineering. The next frontier includes refining these models to cope with the high dimensionality and variability inherent in EEG data. For instance, previous works have achieved a high classification accuracy while advancing machine learning-based algorithms with Hjorth parameters to optimize the models in the domain of EEG signals [26, 27]. As computational power and algorithmic sophistication advance, there is potential for developing real-time diagnostic systems and personalized medicine applications. This could lead to breakthroughs in understanding and treating neurological conditions, as well as in deploying brain-computer interfaces (BCIs) with unprecedented precision. Moreover, the fusion of EEG data with other biomarkers and the application of transfer learning to leverage pre-trained models on extensive datasets may unlock new pathways for comprehensive, cross-modal diagnostics. The continuous evolution of machine learning methodologies is poised to play a pivotal role in the translation of EEG analysis from research laboratories to clinical practice, heralding a new era of data-driven neuroscience.