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Quantitative electroencephalography (qEEG or QEEG) is a field concerned with the numerical analysis of electroencephalography (EEG) data and associated behavioral correlates.
Techniques used in digital signal analysis are extended to the analysis of electroencephalography (EEG). These include wavelet analysis and Fourier analysis, with new focus on shared activity between rhythms including phase synchrony (coherence, phase lag) and magnitude synchrony (comodulation/correlation, and asymmetry).
The analog signal comprises a microvoltage time series of the EEG, sampled digitally and sampling rates adequate to over-sample the signal (using the Nyquist principle of exceeding twice the highest frequency being detected). Modern EEG amplifiers use adequate sampling to resolve the EEG across the traditional medical band from DC to 70 or 100 Hz, using sample rates of 250/256, 500/512, to over 1000 samples per second, depending on the intended application.[ citation needed ] QEEG can be performed by open-source toolboxes such as EEGLAB or the Neurophysiological Biomarker Toolbox.
Several QEEG products have received Class 2 FDA medical device clearance and the method has received some medical acceptance for use in epilepsy patients. However QEEG has not been endorsed by the American Academy of Neurology or the American Clinical Neurophysiology Society. [1]
The Fourier decomposes the EEG time series into a voltage by frequency spectral graph commonly called the "power spectrum", with power being the square of the EEG magnitude, and magnitude being the integral average of the amplitude of the EEG signal, measured from(+) peak-to-(-)peak), across the time sampled, or epoch. The epoch length determines the frequency resolution of the Fourier, with a 1-second epoch providing a 1 Hz resolution (plus/minus 0.5 Hz resolution), and a 4-second epoch providing 0.25 Hz, or ±0.125 Hz resolution.
Where ξ = frequency
A wavelet is a time-frequency transformation that allows analysis of EEG signals in the time extension that is not possible with Fourier analysis.
Where a = scaling; b = time
QEEG has been accepted for diagnostic evaluation in some areas, such as cerebro-vascular disorders, encephalopathy, dementia and epilepsy, though it remains yet to be accepted in other clinical areas, such as diagnosing mild traumatic brain injury or psychiatric disorders. The use of qEEG techniques in investigations in clinical and research settings are ongoing. [2] QEEG has also been utilized to provide neurofeedback, which is a form of biofeedback, wherein electrical activity in the brain is monitored by a computer program, which is applied to modulate visual or auditory stimuli—these stimuli, in turn, are designed to be controlled by the user.
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing.
In physics, engineering and mathematics, the Fourier transform (FT) is an integral transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches.
Magnetoencephalography (MEG) is a functional neuroimaging technique for mapping brain activity by recording magnetic fields produced by electrical currents occurring naturally in the brain, using very sensitive magnetometers. Arrays of SQUIDs are currently the most common magnetometer, while the SERF magnetometer is being investigated for future machines. Applications of MEG include basic research into perceptual and cognitive brain processes, localizing regions affected by pathology before surgical removal, determining the function of various parts of the brain, and neurofeedback. This can be applied in a clinical setting to find locations of abnormalities as well as in an experimental setting to simply measure brain activity.
In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of systems, such as audio and control systems, where they simplify mathematical analysis by converting governing differential equations into algebraic equations. In an audio system, it may be used to minimize audible distortion by designing components so that the overall response is as flat (uniform) as possible across the system's bandwidth. In control systems, such as a vehicle's cruise control, it may be used to assess system stability, often through the use of Bode plots. Systems with a specific frequency response can be designed using analog and digital filters.
In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time, as in time series. Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how the signal is distributed within different frequency bands over a range of frequencies. A complex valued frequency-domain representation consists of both the magnitude and the phase of a set of sinusoids at the frequency components of the signal. Although it is common to refer to the magnitude portion as the frequency response of a signal, the phase portion is required to uniquely define the signal.
The short-time Fourier transform (STFT), is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practice, the procedure for computing STFTs is to divide a longer time signal into shorter segments of equal length and then compute the Fourier transform separately on each shorter segment. This reveals the Fourier spectrum on each shorter segment. One then usually plots the changing spectra as a function of time, known as a spectrogram or waterfall plot, such as commonly used in software defined radio (SDR) based spectrum displays. Full bandwidth displays covering the whole range of an SDR commonly use fast Fourier transforms (FFTs) with 2^24 points on desktop computers.
Neurofeedback is a form of biofeedback that uses electrical potentials in the brain to reinforce desired brain states through operant conditioning. This process is non-invasive and typically collects brain activity data using electroencephalography (EEG). Several neurofeedback protocols exist, with potential additional benefit from use of quantitative electroencephalography (QEEG) or functional magnetic resonance imaging (fMRI) to localize and personalize treatment. Related technologies include functional near-infrared spectroscopy-mediated (fNIRS) neurofeedback, hemoencephalography biofeedback (HEG), and fMRI biofeedback.
In mathematics, the continuous wavelet transform (CWT) is a formal tool that provides an overcomplete representation of a signal by letting the translation and scale parameter of the wavelets vary continuously.
A time–frequency representation (TFR) is a view of a signal represented over both time and frequency. Time–frequency analysis means analysis into the time–frequency domain provided by a TFR. This is achieved by using a formulation often called "Time–Frequency Distribution", abbreviated as TFD.
In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations. Rather than viewing a 1-dimensional signal and some transform, time–frequency analysis studies a two-dimensional signal – a function whose domain is the two-dimensional real plane, obtained from the signal via a time–frequency transform.
A gamma wave or gamma rhythm is a pattern of neural oscillation in humans with a frequency between 25 and 140 Hz, the 40 Hz point being of particular interest. Gamma rhythms are correlated with large-scale brain network activity and cognitive phenomena such as working memory, attention, and perceptual grouping, and can be increased in amplitude via meditation or neurostimulation. Altered gamma activity has been observed in many mood and cognitive disorders such as Alzheimer's disease, epilepsy, and schizophrenia.
The sensorimotor rhythm (SMR) is a brain wave. It is an oscillatory idle rhythm of synchronized electric brain activity. It appears in spindles in recordings of EEG, MEG, and ECoG over the sensorimotor cortex. For most individuals, the frequency of the SMR is in the range of 7 to 11 Hz.
In mathematics and statistical analysis, bicoherence is a squared normalised version of the bispectrum. The bicoherence takes values bounded between 0 and 1, which make it a convenient measure for quantifying the extent of phase coupling in a signal. The prefix bi- in bispectrum and bicoherence refers not to two time series xt, yt but rather to two frequencies of a single signal.
Electrocorticography (ECoG), a type of intracranial electroencephalography (iEEG), is a type of electrophysiological monitoring that uses electrodes placed directly on the exposed surface of the brain to record electrical activity from the cerebral cortex. In contrast, conventional electroencephalography (EEG) electrodes monitor this activity from outside the skull. ECoG may be performed either in the operating room during surgery or outside of surgery. Because a craniotomy is required to implant the electrode grid, ECoG is an invasive procedure.
The Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform. It is used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. The function to be transformed is first multiplied by a Gaussian function, which can be regarded as a window function, and the resulting function is then transformed with a Fourier transform to derive the time-frequency analysis. The window function means that the signal near the time being analyzed will have higher weight. The Gabor transform of a signal x(t) is defined by this formula:
Geophysical survey is the systematic collection of geophysical data for spatial studies. Detection and analysis of the geophysical signals forms the core of Geophysical signal processing. The magnetic and gravitational fields emanating from the Earth's interior hold essential information concerning seismic activities and the internal structure. Hence, detection and analysis of the electric and Magnetic fields is very crucial. As the Electromagnetic and gravitational waves are multi-dimensional signals, all the 1-D transformation techniques can be extended for the analysis of these signals as well. Hence this article also discusses multi-dimensional signal processing techniques.
Electroencephalography (EEG) is a method to record an electrogram of the spontaneous electrical activity of the brain. The biosignals detected by EEG have been shown to represent the postsynaptic potentials of pyramidal neurons in the neocortex and allocortex. It is typically non-invasive, with the EEG electrodes placed along the scalp using the International 10–20 system, or variations of it. Electrocorticography, involving surgical placement of electrodes, is sometimes called "intracranial EEG". Clinical interpretation of EEG recordings is most often performed by visual inspection of the tracing or quantitative EEG analysis.
Clinical Electrophysiological Testing is based on techniques derived from electrophysiology used for the clinical diagnosis of patients. There are many processes that occur in the body which produce electrical signals that can be detected. Depending on the location and the source of these signals, distinct methods and techniques have been developed to properly target them.
Hjorth parameters are indicators of statistical properties used in signal processing in the time domain introduced by Bo Hjorth in 1970. The parameters are Activity, Mobility, and Complexity. They are commonly used in the analysis of electroencephalography signals for feature extraction. The parameters are normalised slope descriptors (NSDs) used in EEG. Moreover, in the robotic area, the Hjorth parameters are used for tactile signal processing for the physical object properties detection such as surface textures/material detection and touch modality classification via artificial robotic skin.
EEG analysis is exploiting mathematical signal analysis methods and computer technology to extract information from electroencephalography (EEG) signals. The targets of EEG analysis are to help researchers gain a better understanding of the brain; assist physicians in diagnosis and treatment choices; and to boost brain-computer interface (BCI) technology. There are many ways to roughly categorize EEG analysis methods. If a mathematical model is exploited to fit the sampled EEG signals, the method can be categorized as parametric, otherwise, it is a non-parametric method. Traditionally, most EEG analysis methods fall into four categories: time domain, frequency domain, time-frequency domain, and nonlinear methods. There are also later methods including deep neural networks (DNNs).
Quantitative spectral analysis of EEG in psychiatry revisited: drawing signs out of numbers in a clinical setting. Clin Neurophysiol. 2003 Dec;114(12):2294-306.
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CFC delta-beta is related with mixed features and response to treatment in bipolar II depression. Heliyon. 2019 Jun 13;5(6):e01898.
