The fundamental design concept of Z score biofeedback [also known as Z-Score neurofeedback] was first introduced in 1998 (Thatcher, 1998; 1999; 2000a; 2000b). The central idea of the instantaneous Z score is the application of the mathematical Gaussian curve or ‘Bell Shaped’ curve by which probabilities can be estimated using the auto and cross-spectrum of the electroencephalogram (EEG) in order to identify brain regions that are de-regulated and depart from expected values in real-time. Linkage of symptoms and complaints to functional localization in the brain is best achieved by the use of a minimum of 19 channels of EEG evaluation so that current source density and LORETA source localization can be computed. Once the linkage is made, then an individualized Z score protocol can be devised. However, in order to make a linkage to symptoms an accurate statistical inference must be made using the Gaussian distribution.

The Gaussian distribution is a fundamental distribution that is used throughout science, for example, the Schrodinger wave equation in Quantum mechanics uses the Gaussian distribution as a basis function without which there would be no microwave ovens or computers, etc. (Robinett, 1997). The application of the EEG to the concept of the Gaussian distribution requires the use of standard mathematical transforms by which all statistical distributions can be transformed to a Gaussian distribution (Box & Cox, 1964). In the case of the EEG, transforms such as the square root, cube root, log10, Box-Cox, etc. are applied to the power spectrum of the digital time series in order to approximate a normal distribution. The choice of the exact transform depends on the accuracy of the approximate match to a Gaussian distribution. The fact that accuracies of 95% to 99% match to a Gaussian are commonly published in the EEG literature encouraged me and colleagues to develop and test the Z score biofeedback program.

The second design concept is the application of the Gaussian distribution to averaged “instantaneous” time domain spectral measures from groups of normal subjects and then to cross-validate the means and standard deviations for each subject for each instant of time (Thatcher, 1998; 1999; 2000a; 2000b). The cross-validation is directly related to the variance of the distribution. However, in order to achieve a representative Gaussian distribution it is necessary to include two major categories of statistical variance: 1- the moment-to-moment variance or within session variance, and 2- between subject variance across an age group. In the case of the Fast Fourier Transform (FFT) there is a single “integral” of the power spectrum for each subject and each frequency and, therefore, there is only between-subject variance in normative databases that use non-instantaneous analyses such as the FFT. Thus, there is a fundamental and important difference between an instantaneous Z score and an integrated FFT Z score with the former having two sources of variance while the latter has only one source of variance. Figure 1 illustrates the relationship between an FFT based normative database versus an “instantaneous” or Joint Time Frequency Analysis (JTFA) database such as used for the computation of instantaneous Z scores.

The third design concept is simplification and standardization of EEG biofeedback by the application of basic science. Simplification is achieved by the use of a single metric, namely, the metric of the “Z Score” for widely diverse measures such as power, amplitude asymmetry, power ratios, coherence and phase delays. Standardization is also achieved by EEG amplifier matching of the frequency response of the normative database amplifiers to the frequency characteristics of the EEG amplifiers used to acquire a comparison subject’s EEG time series.

A fourth and intertwined clinical concept in the design of Z score biofeedback is “individualized” EEG biofeedback and non-protocol EEG biofeedback. The idea of linking patient symptoms and complaints to functional localization in the brain as evidenced by “de-regulation” of neural populations is fundamental to individualized biofeedback. For example, de-regulation is recognized by significantly elevated or reduced power or network measures such as coherence and phase within regions of the brain that sub-serve particular functions that can be linked to the patient’s symptoms and complaints. The use of Z scores for biofeedback is designed to “re-regulate” or “optimize” the homeostasis, neural excitability and network connectivity in particular regions of the brain. The functional localization and linkage to symptoms is based on modern knowledge of brain function as measured by fMRI, PET, penetrating head wounds, strokes and other neurological evidence acquired over the last two centuries (Heilman & Valenstein, 1993; Braxis et al, 2007; the Human Brain Mapping database of functional localization). Thus, the false concern that Z score biofeedback will make exceptional people dull and an average individual a genius is misplaced. The concept is to link symptoms and complaints and then monitor improvement or symptom reduction during the course of treatment. For peak performance applications, a careful inventory of the client’s personality style, self assessment of weaknesses and strengths and identification of the client’s specific areas that he/she wishes to improve must be obtained before application of Z score biofeedback. Then, the practitioner attempts to link the client’s identification of areas of weakness that he/she wants improved to functional localization as expressed by “de-regulation” of deviant neural activity that may be subject to change.

As mentioned previously, the instantaneous Z scores are much smaller than the FFT Z scores in the NeuroGuide software program which uses the same subjects for the normative database. Smaller Z scores when using the instantaneous Z scores is expected. One should not be surprised by a 50% reduction in JTFA Z scores in comparison to FFT Z scores and this is why it is best to first use 19 channel EEG measures and the highly stable FFT Z scores to link symptoms to functional localization in the brain to the extent possible. Then use the Z Score program inside of NeuroGuide to evaluate the patient’s instantaneous Z scores as a therapy design process before the biofeedback procedure begins (www.appliedneuroscience.com). This will allow one to obtain a unique picture of the EEG instantaneous Z scores of each unique patient prior to beginning Z score biofeedback. The clinician must be trained to select which Z scores best match the patient’s symptoms and complaints. A general rule for the choice of Z scores to use for biofeedback depends on two factors obtained using a full 19 channel EEG analysis: 1- scalp location(s) linked to the patient’s symptoms and complaints and, 2- magnitude of the Z scores. De-regulation by hyperpolarization produces slowing in the EEG and de-regulation due to changes in inhibition produces deviations at higher frequencies. The direction of the Z score is much less important than the location(s) of the deviant Z scores and the linkage to the patient’s symptoms and complaints.

Figure 2 is an example of the instantaneous Z score screen inside of NeuroGuide(TM) while the instantaneous Z scores are being reviewed. A free demo of instantaneous Z scores that are used for real-time Z score biofeedback can be downloaded and evaluated at Applied Neuroscience.

A P4 and C4 theta and delta deviation from normal is evident as well as bilateral occipital delta deviations from normal. There is diminished alpha and theta in the instantaneous Z scores but on the average the dynamic FFT provides a much clearer picture of the right parietal and right central Z scores. For illustration purposes only, a biofeedback protocol would be to reward Z score values less than and greater than 2 standard deviations in the theta frequency band in P4 and C4 and most of the feedback rewards will automatically occur in the delta and theta frequency band. As mentioned previously, the above is an example of an individualized Z score biofeedback procedure after reviewing the patent’s EEG using the same instantaneous Z score program running in BrainMaster, Thought Technology, EEG Spectrum and Deymed.

Members of the International Society for Neurofeedback and Research (ISNR) receive NeuroConnections as a free benefit of membership. Healthcare professionals who specialize in neurofeedback, biofeedback or QEEG are encouraged to join ISNR to receive the full edition (in a full color printed format) of NeuroConnections and other member benefits. The above article was reprinted from NeuroConnections with permission from ISNR.

**References:**

Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society, 211-243, discussion 244-252.

Brazis et al (2007). Localization in clinical neurology. Williams and Wilkins. Philadelphia, PA.

Heilman, K.M. & Valenstein, E. (1993). Clinical Neuropsychology (3rd ed.). Oxford University Press, New York.

Robinett, R.W. (1997). Quantum mechanics: classical results, modern systems and visualized examples. Oxford University Press, New York.

Thatcher, R.W. (1998) EEG normative databases and EEG biofeedback. Journal of Neurotherapy, 2(4): 8-39.

Thatcher, R.W. (1999). EEG database guided neurotherapy. In: J.R. Evans and A. Abarbanel Editors, Introduction to Quantitative EEG and Neurofeedback. Academic Press. San Diego.

Thatcher, R.W. (2000a). EEG operant conditioning (Biofeedback) and traumatic brain injury. Clinical EEG, 31(1): 38-44.

Thatcher, R.W. (2000b). An EEG Least Action Model of Biofeedback. 8th Annual ISNR conference, St. Paul, MN.

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