Z Score Neurofeedback: Clinical Applications

Neurofeedback is utilized by over 10,000 clinicians worldwide with new techniques and uses being found regularly. Z Score Neurofeedback is a new technique using a normative database to identify and target a specific individual’s area of dysregulation allowing for faster and more effective treatment. The book describes how to perform z Score Neurofeedback, as well as research indicating its effectiveness for a variety of disorders including pain, depression, anxiety, substance abuse, PTSD, ADHD, TBI, headache, frontal lobe disorders, or for cognitive enhancement. Suitable for clinicians as well as researchers this book is a one stop shop for those looking to understand and use this new technique.

• Contains protocols to implement Z score neurofeedback
• Reviews research on disorders for which this is effective treatment
• Describes advanced techniques and applications

• Language: English
• Publisher: Academic Press
• Release date: Sep 20, 2014
• ISBN: 9780128014646

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Chapter 1

History and Technical Foundations of Z Score EEG Biofeedback

Robert W. Thatcher, Carl J. Biver and Duane M. North,    NeuroImaging Laboratory, Applied Neuroscience, Inc., Seminole, FL, USA

The history and technical foundations of Z score electroencephalogram (EEG) biofeedback, including LORETA Z score biofeedback, is reviewed. The statistical standards are discussed and the step-by-step conceptual foundations of Z score biofeedback are explained. The central concept is linking symptoms to dysregulated nodes and connections between nodes in networks in the brain. The goal is to reinforce increased stability and efficiency in neural networks by reinforcing toward the center of a normal reference population. The use of Z scores for real-time or live biofeedback unifies different EEG metrics (e.g., power, amplitude, coherence, phase) to a single metric, i.e., the metric of the Z score with a mean=0 and a standard deviation=1 in the ideal case. Z score biofeedback also simplifies the EEG biofeedback process by providing clinicians with a guide or reference to determine threshold setting for biofeedback. For example, with raw score biofeedback, clinicians must guess at a threshold setting to trigger biofeedback. With Z score biofeedback, the guess work is removed since all metrics are treated the same in which the direction of biofeedback is toward Z=0.

Keywords

LORETA Z scores; real-time Z score biofeedback; symptom checklist

Introduction

The statistical foundations of Z score electroencephalogram (EEG) biofeedback are based on the fact that after the appropriate transform, all EEG variables are Gaussian distributed with sample sizes equal to or greater than about 20 subjects per age group. A review of the statistical foundations is in the paper History of the Scientific Standards of QEEG Normative Databases (Thatcher & Lubar, 2008). The Z score is a statistic of distance from the mean adjusted for variance or Z=mean–measure divided by the standard deviation where at infinity with a random sampling the ideal Gaussian mean=0 and the standard deviation=1. This is a powerful statistic that also has a multivariate expression called the Mahalanobis distance (Cooley & Lohnes, 1971). The interpretation of a Z score depends on the assumptions of (1) a Gaussian distribution (>0.95) after transform of the raw digital data, (2) a N>20 of a representative sample of the measure of interest, (3) the measures to compute the mean must be the same variables used to compute a Z score (e.g., FFT means cannot be used to compute joint time–frequency analysis (JTFA) Z scores or vice versa). The reason there is a violation of statistical sampling theory if one uses the FFT to compute a JTFA Z scores is because the FFT multiplies sine/cosine waves over a discrete interval of time (e.g., 1–2 s) as well as windowing to approximate infinity, whereas JTFA methods like Wavelets or Complex Demodulation do not use windowing or the convolution of sine waves over a discrete window of time. Although the FFT and digital filters can converge at infinity, the fact is that the same group of subjects produce different means when comparing the FFT to JTFA and therefore, standard #3 is violated. It is easy to show that the FFT produces different means than the JTFA on the same data samples, e.g., we find over 14% differences and Brainmaster 8% difference in means between the FFT and filter means which is a significant error and is in violation of statistical sampling theory.

The remainder of this chapter will review and integrate the statistical and technical methods used and described in various forums. In the sections to follow, steps are taken to adhere to the basic statistical foundations in which there is no violation of statistical sampling theory because only complex demodulation means are used to compute complex demodulation Z scores in all Neuroguide analyses of Z score biofeedback measures presented in this chapter.

First Use of Gaussian Probabilities to Identify Dysregulation in the Brain

The fundamental design concepts of Z score biofeedback were first introduced by Thatcher (1998, 1999, 2000a,b,c). 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 EEG in order to identify brain regions that are deregulated and depart from expected values. Linkage of symptoms and complaints to functional localization in the brain is best achieved by the use of a minimum of 19 channel 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, e.g., the Schrodinger wave equation in Quantum mechanics uses the Gaussian distribution as basis functions (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, and hyperbolic sine are applied to the power spectrum of the digital time series in order to approximate a normal distribution (Duffy, Hughes, Miranda, Bernad, & Cook, 1994; Gasser, Jennen-Steinmetz, Sroka, Verleger, & Mocks, 1988; John, Prichep, & Easton, 1987; John, Prichep, Fridman, & Easton, 1988; Thatcher, North, & Biver, 2005a,b; Thatcher, Walker, Biver, North, & Curtin, 2003). The choice of the exact transform depends on the accuracy of the approximate match to a Gaussian distribution. The fact that accuracies of 95–99% match to a Gaussian are commonly published in the EEG literature encouraged by Thatcher and colleagues to develop and test the Z score biofeedback program.

The majority of cortical pyramidal neurons resonate at specific center frequencies depending on the membrane potential and ionic conductances and behave like band pass filters that gate action potentials. The pyramidal neuron resonances wax and wane and exhibit rhythmic bursts and periods of asynchrony in a non-Gaussian distribution as a function of time. It is necessary to mathematically transform EEG digital data to approximate a Gaussian in shape and then the EEG normative database can be cross-validated and estimates of error can be made. Z score biofeedback using the target of reinforcing toward Z=0 with respect to the center of an age matched group of healthy individuals is designed to reinforce increased information processing in networks of the brain. The real-time EEG Z score utilizes a representative sample of normal and healthy subjects with no history of neurological psychological disorders with normal performance on neuropsychological tests measured while the first author (Thatcher) was the principal investigator and professor at the University of Maryland. Initially a sample of 625 normal subjects constituted the reference normal database and then the number was expanded to today with a total of 860 subjects. Standard equilibration of the amplifier frequency and gain characteristics was used to exactly match the amplifiers used to measure EEG from a patient to the frequency characteristics of the normative database amplifiers. The normative database includes clinical selection criteria, age range (2 months to 82 years), cross-validation tests, demographics, and other details of the Z score normative database have been published and are recommended reading for those interested in deeper details than is briefly reviewed in this document (see Thatcher, 1998, 1999, 2000a; Thatcher & Lubar, 2008; Thatcher et al., 2003).

In 2009, a method to aid in reinforcing extreme Z scores or outliers to move toward Z=0 was called "Z Tunes." This real-time Z score biofeedback method was implemented in recognition of the neurophysiological linkage to resonant cortical pyramidal neurons that operate by reinforcing outliers over a 10 s history if the slope of the time history of the outliers is in the direction of Z=0. That is, not reinforce outliers if they are diverging or becoming more extreme and only reinforce outliers if they are moving in the direction of increased stability in the direction of Z=0.

Application of Gaussian Probability Distributions to Instantaneous Z Score Biofeedback and Why JTFA Z Scores Are Smaller than FFT Z Scores

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,b). The cross-validation is directly related to the variance of the distribution (Thatcher et al., 2003, 2005a,b). 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 noninstantaneous 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 1.1 illustrates the relationship between an FFT-based normative database versus an instantaneous or JTFA database such as used for the computation of instantaneous Z scores.

Figure 1.1 JTFA normative databases are instantaneous and include within session variance plus between subject variance. In contrast, FFT normative data only contains between subject variance. t=time, s=subjects, and SDt=standard deviation for the within session and SDs=standard deviation between subjects. Thus, FFT Z scores are larger than JTFA Z scores and a ratio of 2:1 is not uncommon.

Simplification and Standardization

Another 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, 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.

Once a quantitative (QEEG) normative database analysis is completed, then one can use a Z score biofeedback program to train patient’s to move their instantaneous Z scores toward zero or the center of the age matched normal population. The absolute value and range of the instantaneous Z scores while smaller than those obtained using the offline QEEG normative database are nonetheless valid and capable of being minimized toward zero. An advantage of a Z score biofeedback program is simplification by reducing diverse measures to a single metric, i.e., the metric of a Z score. Thus, there is greater standardization and less guess work about whether to reinforce or suppress coherence or phase differences or power, etc., at a particular location and particular frequency band. The difference between standard and conventional EEG biofeedback versus Z score biofeedback is shown in Figure 1.2.

Figure 1.2 Top row is conventional or standard EEG biofeedback in which different units of measurement are used in an EEG analysis (e.g., µV for amplitude, theta/beta ratios, relative power 0–100%, coherence 0–1, phase in degrees or radians) and the clinician must guess at a threshold for a particular electrode location and frequency and age as to when to reinforce or inhibit a give measure. The bottom row is Z score biofeedback in which different metrics are represented by a single and common metric, i.e., the metric of a Z score and the guess work is removed because all measures are reinforced to move Z scores toward Z=0 which is the approximate center of an average healthy brain state based on a reference age matched normative database in real time.

Individualized EEG Biofeedback Protocols

An intertwined clinical concept in the design of Z score biofeedback is individualized EEG biofeedback and nonprotocol-driven EEG biofeedback based on a symptom checklist. The idea of linking patient symptoms and complaints to functional localization in the brain and resonant frequencies of the EEG as evidenced by dysregulation of neural populations is fundamental to individualized biofeedback. For example, dysregulation is recognized by significantly elevated or reduced power or network measures such as coherence and phase within regions of the brain that subserve 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 (see Brazis et al., 2007; Heilman & Valenstein, 1993; Thatcher, 2011a,b, 2012). 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 reinforce stability and not periods of chaos in networks linked to symptoms and complaints and then monitor improvement or symptom reduction during the course of treatment using a single metric for all measures, i.e., the Z score. 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 to improve to functional localization as expressed by deregulation 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 Neuroguide™ which uses the same subjects for the normative database. Smaller Z scores when using the instantaneous Z scores is expected because of the necessary inclusion of the moment-to-moment within session variance. 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 in preparation before the biofeedback procedure begins. 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 is 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) and (2) magnitude of the Z scores. Dysregulation by hyperpolarization produces slowing in the EEG and deregulation due to reduced 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.

Implementation of the Z Score Biofeedback

Step one is to compute means and standard deviations of instantaneous absolute power, relative power, power ratios, coherence, phase differences and amplitude asymmetries, phase reset, etc., on selected age groups of normal subjects from the 19 channel 10/20 electrode locations using the within session and between session variance as described previously. The inclusion/exclusion criteria, number of subjects, number of subjects per age group, cross-validation procedures, and other details of the means and standard deviation computations have been published (Thatcher et al., 2003; Thatcher, Walker, & Guidice, 1987). Step two is to develop a Dynamic Link Library or DLL that can be distributed to EEG biofeedback manufacturers such as BrainMaster, EEG Spectrum, Thought Technology, Mind Media BV (NeXus), EEG Spectrum, and Deymed which allows the manufacturers to integrate the instantaneous Z scores inside of their already existing software environments. The DLL involves only four command lines of code and is designed for software developers to easily implement the instantaneous Z scores by passing raw digital data to the DLL and then organizing the Z scores that are returned in less than 1 µs. This rapid analysis and return of Z scores is essential for timely feedback when specific EEG features are measured by the Complex Demodulation JTFA operating inside of the DLL.

JTFA Complex Demodulation Computations

The mathematical details of complex demodulation used to compute the instantaneous Z scores as contained in the Applied Neuroscience, Inc. DLL are provided in the Appendix section and are described in Otnes and Enochson (1977), Bloomfield (2000), Granger and Hatanka (1964), and Thatcher, North, and Biver (2009). Complex demodulation is a time/frequency domain digital method of spectral analysis, whereas the FFT is a frequency domain method. These two methods are related by the fact that they both involve sines and cosines and both operate in the complex domain and in this way represent the same mathematical descriptions of the power spectrum. The advantage of complex demodulation is that it is a time/frequency domain method and is less sensitive to artifact and does not require windowing nor even integers of the power of 2 as does the FFT. The FFT integrates power in a frequency band over the entire epoch length and requires windowing functions which can dramatically affect the power values whereas, as mentioned previously, complex demodulation does not require windowing (Otnes & Enochson, 1972). Complex demodulation was computed for the linked ears and eyes open and eyes closed conditions for all 625 subjects in the normative database.

Table 1.1 gives the center frequencies and bandwidths used by the Neuroguide DLL as well as the temporal equivalent of frequency in the right column.

Table 1.1

Time Domain Conversion of Frequencies to Time of the Z Score Biofeedback DLL and Neuroguide

*Neuroguide only.

Figure 1.3 is an illustration of the method of complex demodulation for the computation of power, coherence, and phase. The mathematical details are given in the