Mathematical Foundation of Electroencephalography

Doschoris, Michael; Kariotou, Foteini

doi:10.5772/68021

Cited by 6 publications

(21 citation statements)

References 32 publications

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“…These studies have been used as a criterion for the evaluation of epileptic activity [43][44][45][46][47]. Today, many mathematical methods are used in the analysis of EEG data [48][49][50]. Data collection systems are constantly changing with the developing technology.…”

Section: Discussionmentioning

confidence: 99%

Detection of Epileptic Seizure Using STFT and Statistical Analysis

Kalin¹,

Akıncı²,

Türkpençe³

et al. 2020

Advances in Neural Signal Processing

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In this study, EEG data from two volunteer individuals, a healthy individual and a patient with epilepsy, were investigated with two different methods in order to distinguish healthy and patient individuals from each other. The data were obtained from a healthy individual and from a patient with epilepsy at the time of epileptic seizure and of seizure-free interval. The data are those of which validity and reliability were proven and were supplied from the data bank records of University Hospital of Bonn in Germany. In the study, the statistical parameters of the collected data were calculated, then the same data were analysed using short-time Fourier transform (STFT) method, and then they were compared. Both statistical parameter results and spectrum analysis results are compatible with each other, and they can successfully detect healthy individuals and epileptic patients at the time of epileptic seizure and seizure-free interval. In this sense, the results were mathematically highly compatible, which offers significant information for the diagnosis of the disease. In the analysis, the variance values were determined as 253.203 for the healthy individual, 806.939 for the patient at seizure-free interval and 6985.755 for that patient at the time of seizure. Accordingly, standard deviation can be said to be quite distinctive in the designation of values. The frequencies of all three cases resulted in 0, 0-5 and 0-20 Hz, respectively, as a result of conducted STFT analysis, which is quite consistent with the results of the statistical analysis parameters.

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Section: Discussionmentioning

confidence: 99%

Detection of Epileptic Seizure Using STFT and Statistical Analysis

Kalin¹,

Akıncı²,

Türkpençe³

et al. 2020

Advances in Neural Signal Processing

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“…The discriminant analysis framework is structured around the projection of high dimensional data into a lower dimensional representation which can preserve the data structure, and aims to achieve maximum separation between data classes [4,34]. The discriminant function for the LDA and QDA can be seen in Equations (14) and (15) respectively:…”

Section: Gesture Classification Methodsmentioning

confidence: 99%

“…Electromagnetic interactions can be modelled with Maxwell's equations, which hold the basic laws of electromagnetism, and can be represented using four key fields, namely: the electric field E , the electric displacement D , the magnetic field H , and the magnetic induction B . The tissues in the head can be approximated as linear, and as a result, we can establish the following linear relationship as seen in Equation () [13,14]:

D = ε E and B = μ H

where, ε and μ represent the electric and magnetic permeability. Assuming permeability in the head to be the same as the free space, Equation () can be reformulated as shown in Equations ():

\nabla . (ε E) = ρ

\nabla . B = 0

c u r l E = - \partial_{t} B

c u r l B = µ_{o} J + µ_{o} \partial_{t} (ε E)

where, ρ is the charge density, J is the current density, and E is linked to Ohm's law through J =

{bold-italicJ}^{p} + σ E

.…”

Section: Methodsmentioning

confidence: 99%

“…Acquired EEG measurements reflect the neurological potential signals from various cortical sections in the brain [13,14]. The acquired electrical signal is said to emanate from pyramidal neurons on the scale of billions, synchronously firing within the human skull [13,14]. EEG is a useful tool in the localisation of the region from which neural activities that generate the acquired EEG signals emanate [13,14].…”

Section: Electroencephalographymentioning

confidence: 99%

“…Electromagnetic interactions can be modelled with Maxwell's equations, which hold the basic laws of electromagnetism, and can be represented using four key fields, namely: the electric field E, the electric displacement D, the magnetic field H, and the magnetic induction B. The tissues in the head can be approximated as linear, and as a result, we can establish the following linear relationship as seen in Equation ( 6) [13,14]:…”

Section: Quasi Static Maxwell Equationmentioning

confidence: 99%

See 2 more Smart Citations

Phantom motion intent decoding for transhumeral prosthesis control with fused neuromuscular and brain wave signals

Nsugbe

Samuel

Asogbon

et al. 2021

IET Cyber-Syst and Robotics

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In recent years, the electroencephalography (EEG) brain-computer interface (BCI) has been researched in the area of upper-limb prosthesis control due to the promise of being able to record neurological signals which follow activation patterns in the cortex directly from the brain with non-invasive electrodes. This is seen as a way of bypassing the limitation posed by acquiring neuromuscular signals predominantly with electromyography (EMG) directly from the stump, which possesses residual limb anatomy post-amputation. In this study, the sequential forward selection algorithm to form a 10-optimal-channel representation, alongside an extended signal feature vector was applied, to investigate the motion intent decoding performance of EMG-only, EEG-only, and a fused EMG-EEG sensing configuration for four transhumeral amputees with varying stump lengths. The results showed a considerable improvement for the EMG-only configuration with the advanced feature vector, but only a small increase for the EEG-only, and thus a marginal improvement when information from both signals was fused together. This is likely due to the EEG requiring a greater number of channels spread across the skull to provide a reliable intent decoding. Further work will now involve optimisation studies to find a greater representation of electrode representation and parsimony, to minimise the number of channels while boosting motion intent decoding accuracy. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Contrast of multi‐resolution analysis approach to transhumeral phantom motion decoding

Nsugbe

Samuel

Asogbon

et al. 2021

CAAI Trans on Intel Tech

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In signal processing, multiresolution decomposition techniques allow for the separation of an acquired signal into sub levels, where the optimal level within the signal minimises redundancy, uncertainties, and contains the information required for the characterisation of the sensed phenomena. In the area of physiological signal processing for prosthesis control, scenarios where a signal decomposition analysis are required: the wavelet decomposition (WD) has been seen to be the favoured time-frequency approach for the decomposition of non-stationary signals. From a research perspective, the WD in certain cases has allowed for a more accurate motion intent decoding process following feature extraction and classification. Despite this, there is yet to be a widespread adaptation of the WD in a practical setting due to perceived computational complexity. Here, for neuromuscular (electromyography) and brainwave (electroencephalography) signals acquired from a transhumeral amputee, a computationally efficient time domain signal decomposition method based on a series of heuristics was applied to process the acquired signals before feature extraction. The results showed an improvement in motion intent decoding prowess for the proposed time-domain-based signal decomposition across four different classifiers for both the neuromuscular and brain wave signals when compared to the WD and the raw signal.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Mathematical Foundation of Electroencephalography

Cited by 6 publications

References 32 publications

Detection of Epileptic Seizure Using STFT and Statistical Analysis

Detection of Epileptic Seizure Using STFT and Statistical Analysis

Phantom motion intent decoding for transhumeral prosthesis control with fused neuromuscular and brain wave signals

Contrast of multi‐resolution analysis approach to transhumeral phantom motion decoding

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