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Multichannel EEGs were obtained from healthy participants in the eyes-closed no-task condition (where the alpha component is typically abolished). EEG dynamics in the two conditions were quantified with two related binary Lempel-Ziv measures of the first principal component and with three measures of integrated information including the more recently proposed integrated synergy. Both integrated information and integrated synergy with model order p=1 had greater values in the eyes closed condition. If the model order of integrated synergy was determined with the Bayesian Information Criterion, this pattern was reversed, and in common with other measures, integrated synergy was greater in the eyes open condition. Eyes open versus eyes closed separation was quantified by calculation of the between-condition effect size. Lempel-Ziv complexity of the first principal component showed greater separation than the measures of integrated information. The performance of the integrated information measures investigated here when distinguishing between indisputably different physiological states encourages caution when advocating for their use as measures of consciousness.

We present a generically applicable four-step process for quantifying information movement in complex networks. (1) Construction of local entropy rate and specific entropy rate. Local entropy rate is a continuous, time-dependent measure that quantifies the information gained at time t on observing x(t) given the recent past. There is a statistically responsible procedure for specifying “recent”. Specific entropy rate is a related time-dependent locally determined measure that gives an estimate of uncertainty at time t. (2) Construct specific transfer entropy (i.e., a time-dependent generalization of epoch-determined transfer entropy) that gives a state- and time-resolved quantification of the predictive input of a candidate input system on a candidate output system. (3) Construct a time-dependent network adjacency matrix. Specific transfer entropy can be used to populate the adjacency matrix characterizing a network. In the case of multichannel EEG/MEG recordings, the nodes are electrodes, and specific transfer entropy quantifies information movement between electrodes. In this analysis, the adjacency matrix is real, time-dependent and asymmetric. Any of a large number of measures commonly used to characterize an adjacency matrix can be used. The result \(\Lambda (t)\) is a scalar function of time. (4) Identify hierarchical transition chronometries in \(\Lambda (t)\). The simple directive “find transitions in \(\Lambda (t)\)” is unacceptably naive. Dynamically meaningful transitions are timescale-dependent. In this analysis, \(\Lambda (t)\) is embedded and the structure of this embedded object is examined by quadrant scans of the corresponding recurrence diagram. A hierarchy of transitions can be identified by manipulating the embedding dimension. We note that \(\Lambda (t)\) can serve as the order parameter in phase transition experiments in which time is the tuning parameter.

Using healthy adult participants, seven measures of heart rate variability were obtained simultaneously from four devices in five behavioral conditions. Two devices were ECG-based and two utilized photoplethysmography. The 140 numerical values (measure, condition, device) are presented. The comparative operational reliability of the four devices was assessed, and it was found that the two ECG-base devices were more reliable than the photoplethysmographic devices. The interchangeability of devices was assessed by determining the between-device Limits of Agreement. Intraclass correlation coefficients were determined and used to calculate the standard error of measurement and the Minimal Detectable Difference. The Minimal Detectable Difference, MDD, quantifies the smallest statistically significant change in a measure and is therefore critical when HRV measures are used longitudinally to assess treatment response or disease progression.

Military service members (SMs) returning from combat are at high risk of developing neuropsychiatric conditions such as posttraumatic stress disorder (PTSD) and major depression. Symptom dynamics following reintegration into civilian life may be magnified over time such that some SMs present with delayed onset and may not reach a diagnostic threshold for months to years. Monitoring the trajectory of mental health in the aftermath of combat trauma can therefore be particularly important in enhancing diagnosis. In this study, we investigated the possible utility of the P300 event-related potential (ERP) as an objective marker for monitoring post-trauma mental health. SMs recently returned from a combat deployment were recruited to undergo a baseline assessment, with subsequent follow-up assessment at 6 or 12 months later. At each assessment, ERPs were recorded using a conventional visual oddball task and a set of psychological scores assessing PTSD, depression, and psychosocial functioning were obtained. We observed that the individuals with overall improved psychological scores at follow-up had increased P300 amplitude and shortened P300 latency, and the individuals with overall worsened psychological scores at follow-up had prolonged P300 latency. The degree of change in aggregate psychological score was significantly correlated with the magnitude of change in P300 amplitude (r = -0.72, p 0.0001) and latency (r = 0.42, p = 0.0201). These findings suggest that the P300 may be utilized as a quantitative biomarker for tracking the changes of mental health longitudinally. It may offer clinicians an objective tool for the assessment of the dynamics of mental health following trauma, and perhaps also for monitoring recovery during treatment.

Mild traumatic brain injury (mTBI) and posttraumatic stress disorder (PTSD) may share common symptom and neuropsychological profiles in military service members (SMs) following deployment; while a connection between the two conditions is plausible, the relationship between them has been difficult to discern. The intent of this report is to enhance our understanding of the relationship between findings on structural and functional brain imaging and symptoms of PTSD. Within a cohort of SMs who did not meet criteria for PTSD but were willing to complete a comprehensive assessment within 2 months of their return from combat deployment, we conducted a nested case-control analysis comparing those with combat-related mTBI to age/gender-matched controls with diffusion tensor imaging, resting state functional magnetic resonance imaging and a range of psychological measures. We report degraded white matter integrity in those with a history of combat mTBI, and a positive correlation between the white matter microstructure and default mode network (DMN) connectivity. Higher clinician-administered and self-reported subthreshold PTSD symptoms were reported in those with combat mTBI. Our findings offer a potential mechanism through which mTBI may alter brain function, and in turn, contribute to PTSD symptoms.

Alterations of functional central nervous system networks occur as the result of traumatic brain injury. Characterization of functional network structure is therefore an essential element in the initial evaluation of these patients and in the longitudinal assessment of the response to treatment. Several methods of dynamical analysis have been used to quantify CNS reorganization during recovery. They include measures of inter-regional synchronization, analysis of network geometries (small world models) and the identification of causal networks. This project began with the identification of causal networks as its objective. This form of analysis moves beyond correlation by quantifying the direction and magnitude of information flow. An immediate difficulty presented itself. Consider a simple network consisting of two channels, Channel A and Channel B. Suppose that from time 0 t to 1 t Channel A is a strong causal driver of Channel B, and suppose further that from time 1 t to 2 t Channel B drives Channel A. If a causal analysis is constructed over the temporal epoch 0 t to 2 t , a failure to detect any causal relationships will probably result. It follows that an identification of transition chronometry is the first step in causality analysis. There are several classes of mathematical technologies for identifying transitions. Here we consider methods based on the examination of embedded data.

Information dynamics provides a broad set of measures for characterizing how a dynamical system stores, processes, and transmits information. While estimators for these measures are commonly used in applications, the statistical properties of these estimators for finite time series are not well understood. In particular, the precision of a given estimate is generally unknown. We develop confidence intervals for generic information-dynamic parameters using a bootstrap procedure. The bootstrap procedure uses an echo state network, a particular instance of a reservoir computer, as a simulator to generate bootstrap samples from a given time series. We perform a Monte Carlo analysis to investigate the performance of the bootstrap confidence intervals in terms of their coverage and expected lengths with two model systems and compare their performance to a simulator based on the random analog predictor. We find that our bootstrap procedure generates confidence intervals with nominal, or near nominal, coverage of the information-dynamic measures, with smaller expected length than the random analog predictor-based confidence intervals. Finally, we demonstrate the applicability of the confidence intervals for characterizing the information dynamics of a time series of sunspot counts.

The alterations of animal behavior after traumatic brain injury (TBI) can be subtle, and their quantitative characterization can present significant methodological challenges. Meeting these challenges is a critical need, because quantitative measures are required in studies that compare the efficacy of different clinical interventions. We developed a battery of assessments to quantify behavioral, motor, and cognitive changes in neonatal piglets with good sensitivity and specificity to the detection of persistent deficits that correlate with axonal injury severity after a rapid non-impact head rotation with a diffuse pattern of axonal injury. The battery of measures developed included open field behaviors of sniffing and moving a toy, locomotion measures of Lempel-Ziv complexity and the probability of remaining in the current location, and a novel metric for evaluating motor performance. Our composite porcine disability score was able to detect brain injury with a sensitivity of 100% and specificity of 85.7% at day +4 post-injury for n=8 injured and n=7 sham piglets and significantly correlated with the percent axonal injury in these animals (day +4: ρ=0.76, p=0.0011). A significant improvement over our previous assessments, this new porcine disability score has potential use in a wide variety of porcine disease and injury models.

Correlations between ten-channel EEGs obtained from thirteen healthy adult participants were investigated. Signals were obtained in two behavioral states: eyes open no task and eyes closed no task. Four time domain measures were compared: Pearson product moment correlation, Spearman rank order correlation, Kendall rank order correlation and mutual information. The psychophysiological utility of each measure was assessed by determining its ability to discriminate between conditions. The sensitivity to epoch length was assessed by repeating calculations with 1, 2, 3, …, 8 s epochs. The robustness to noise was assessed by performing calculations with noise corrupted versions of the original signals (SNRs of 0, 5 and 10 dB). Three results were obtained in these calculations. First, mutual information effectively discriminated between states with less data. Pearson, Spearman and Kendall failed to discriminate between states with a 1 s epoch, while a statistically significant separation was obtained with mutual information. Second, at all epoch durations tested, the measure of between-state discrimination was greater for mutual information. Third, discrimination based on mutual information was more robust to noise. The limitations of this study are discussed. Further comparisons should be made with frequency domain measures, with measures constructed with embedded data and with the maximal information coefficient.

OBJECTIVE: This article aims to explore the future of translational research and its physical design implications for community hospitals and hospitals not attached to large centralized research platforms. BACKGROUND: With a shift in medical services delivery focus to community wellness, continuum of care, and comparative effectiveness research, healthcare research will witness increasing pressure to include community-based practitioners. METHODS: The roundtable discussion group, comprising 14 invited experts from 10 institutions representing the fields of biomedical research, research administration, facility planning and design, facility management, finance, and environmental design research, examined the issue in a structured manner. The discussion was conducted at the Washington Hospital Center, MedStar Health, Washington, D.C. CONCLUSIONS: Institutions outside the AMCs will be increasingly targeted for future research. Three factors are crucial for successful research in non-AMC hospitals: operational culture, financial culture, and information culture. An operating culture geared towards creation, preservation, and protection of spaces needed for research; creative management of spaces for financial accountability; and a flexible information infrastructure at the system level that enables complete link of key programmatic areas to academic IT research infrastructure are critical to success of research endeavors.

BACKGROUND: Efforts to produce definitions and diagnostic standards for mild traumatic brain injury (TBI) have a long and complex history. The diagnosis of TBI must be considered in the larger context of neuropsychiatric diagnosis. A major reconceptualization of diagnosis is now underway in which the classical syndrome conceptualization is being discarded. We address the question, what are the implications of this revision of thinking in the specific context of TBI? METHODS: A recent literature on logical structures for neuropsychiatric disorders was reviewed. The symptom pattern of TBI was identified, and a literature survey determined the frequency of these symptom patterns in other disorders and in healthy control populations. RESULTS: The frequency of symptom endorsement in populations without a history of TBI can be equal to endorsement frequencies in populations with a history of mild TBI. In some studies, the frequency of symptom endorsement in healthy controls having no history of head injury actually exceeded the endorsement rates in a comparison group with a history mild TBI. CONCLUSION: The heterogeneity of this clinical population and their clinical presentations, the absence of a unitary etiology of postinjury deficits, and the complex idiosyncratic time course of the appearance of these deficits argue against the valid implementation of the classical model of diagnosis. In addition, the accepted criteria of diagnostic utility are not satisfied. TBI is not a disease; it is an event. More precisely, TBI is an event or a sequence of events that can, in some instances, lead to a diagnosable neurological or psychiatric disorder. Language: en

We investigate the pairwise mutual information and transfer entropy of ten-channel, free-running electroencephalographs measured from thirteen subjects under two behavioral conditions: eyes open resting and eyes closed resting. Mutual information measures nonlinear correlations; transfer entropy determines the directionality of information transfer. For all channel pairs, mutual information is generally lower with eyes open compared to eyes closed indicating that EEG signals at different scalp sites become more dissimilar as the visual system is engaged. On the other hand, transfer entropy increases on average by almost two-fold when the eyes are opened. The largest one-way transfer entropies are to and from the Oz site consistent with the involvement of the occipital lobe in vision. The largest net transfer entropies are from F3 and F4 to almost all the other scalp sites.

Traumatic brain injury, depression and posttraumatic stress disorder (PTSD) are neurocognitive syndromes often associated with impairment of physical and mental health, as well as functional status. These syndromes are also frequent in military service members (SMs) after combat, although their presentation is often delayed until months after their return. The objective of this prospective cohort study was the identification of independent predictors of neurocognitive syndromes upon return from deployment could facilitate early intervention to prevent disability. We completed a comprehensive baseline assessment, followed by serial evaluations at three, six, and 12 months, to assess for new-onset PTSD, depression, or postconcussive syndrome (PCS) in order to identify baseline factors most strongly associated with subsequent neurocognitive syndromes. On serial follow-up, seven participants developed at least one neurocognitive syndrome: five with PTSD, one with depression and PTSD, and one with PCS. On univariate analysis, 60 items were associated with syndrome development at p < 0.15. Decision trees and ensemble tree multivariate models yielded four common independent predictors of PTSD: right superior longitudinal fasciculus tract volume on MRI; resting state connectivity between the right amygdala and left superior temporal gyrus (BA41/42) on functional MRI; and single nucleotide polymorphisms in the genes coding for myelin basic protein as well as brain-derived neurotrophic factor. Our findings require follow-up studies with greater sample size and suggest that neuroimaging and molecular biomarkers may help distinguish those at high risk for post-deployment neurocognitive syndromes.

Measuring neuronal activity with electrophysiological methods may be useful in detecting neurological dysfunctions, such as mild traumatic brain injury (mTBI). This approach may be particularly valuable for rapid detection in at-risk populations including military service members and athletes. Electrophysiological methods, such as quantitative electroencephalography (qEEG) and recording event-related potentials (ERPs) may be promising; however, the field is nascent and significant controversy exists on the efficacy and accuracy of the approaches as diagnostic tools. For example, the specific measures derived from an electroencephalogram (EEG) that are most suitable as markers of dysfunction have not been clearly established. A study was conducted to summarize and evaluate the statistical rigor of evidence on the overall utility of qEEG as an mTBI detection tool. The analysis evaluated qEEG measures/parameters that may be most suitable as fieldable diagnostic tools, identified other types of EEG measures and analysis methods of promise, recommended specific measures and analysis methods for further development as mTBI detection tools, identified research gaps in the field, and recommended future research and development thrust areas. The qEEG study group formed the following conclusions: (1) Individual qEEG measures provide limited diagnostic utility for mTBI. However, many measures can be important features of qEEG discriminant functions, which do show significant promise as mTBI detection tools. (2) ERPs offer utility in mTBI detection. In fact, evidence indicates that ERPs can identify abnormalities in cases where EEGs alone are non-disclosing. (3) The standard mathematical procedures used in the characterization of mTBI EEGs should be expanded to incorporate newer methods of analysis including non-linear dynamical analysis, complexity measures, analysis of causal interactions, graph theory, and information dynamics. (4) Reports of high specificity in qEEG evaluations of TBI must be interpreted with care. High specificities have been reported in carefully constructed clinical studies in which healthy controls were compared against a carefully selected TBI population. The published literature indicates, however, that similar abnormalities in qEEG measures are observed in other neuropsychiatric disorders. While it may be possible to distinguish a clinical patient from a healthy control participant with this technology, these measures are unlikely to discriminate between, for example, major depressive disorder, bipolar disorder, or TBI. The specificities observed in these clinical studies may well be lost in real world clinical practice. (5) The absence of specificity does not preclude clinical utility. The possibility of use as a longitudinal measure of treatment response remains. However, efficacy as a longitudinal clinical measure does require acceptable test–retest reliability. To date, very few test–retest reliability studies have been published with qEEG data obtained from TBI patients or from healthy controls. This is a particular concern because high variability is a known characteristic of the injured central nervous system.

This study examined hyperbaric oxygen seizures (seizures induced by breathing pure oxygen under pressure). In addition to the subject's importance to military diving, this preparation is of more generic interest because it provides an experimental model of chemically induced seizures that are generalized at onset. The object of this preliminary study was to find noise-robust numerical procedures that can identify the time of seizure onset. Several candidate methods were compared. They included a high order FIR filter, wavelet denoising and computation of the Hurst exponent. In these calculations, the original signal was corrupted with progressively larger amplitude additive noise. All three methods successfully identified seizure onset to an SNR of -10 dB. Of the methods considered, only the Hurst exponent was able to find the seizure when the SNR dropped to -20 dB.

The Integrated Neuropsychiatric Assessment System is a portable platform for cognitive neurodynamic research and for clinical evaluations. It provides simultaneous acquisition of heart rate variability, quantitative electroencephalography and event related potentials during a neuropsychological assessment. The analysis protocol includes measures derived from dynamical systems theory including analysis of causal networks, event-dependent interregional synchronization and small world modeling.

In this contribution, eleven different measures of the complexity of multichannel EEGs are described, and their effectiveness in discriminating between two behavioral conditions (eyes open resting versus eyes closed resting) is compared. Ten of the methods were variants of the algorithmic complexity and the covariance complexity. The eleventh measure was a multivariate complexity measure proposed by Tononi and Edelman. The most significant between-condition change was observed with Tononi–Edelman complexity which decreased in the eyes open condition. Of the algorithmic complexity measures tested, the binary Lempel–Ziv complexity and the binary Lempel–Ziv redundancy of the first principal component following mean normalization and normalization against the standard deviation gave the most significant between-group discrimination. A time-dependent generalization of the covariance complexity that can be applied to nonstationary multichannel signals is also described.

We discuss key theoretical and practical issues related to the identification of transitions in dynamical systems in real-time. We focus on the choice of candidate measures and optimization of decision thresholds for candidate measures. To illustrate these issues we develop and test a procedure for identifying one particular transition, the end-point of seizures in two-channel electro-encephalographic data recorded during generalized tonic–clonic seizures. Data from twenty-eight seizures were available and used to develop and test the procedure in terms of the agreement between the computationally identified seizure end-point compared against the ratings of an expert clinical electroencephalographer. Generalizations to multivariate seizure onset detection and to seizure prediction are described.

In this contribution, we show that the incorporation of nonlinear dynamical measures into a multivariate discrimination provides a signal classification system that is robust to additive noise. The signal library was composed of nine groups of signals. Four groups were generated computationally from deterministic systems (van der Pol, Lorenz, Rössler and Hénon). Four groups were generated computationally from different stochastic systems. The ninth group contained inter-decay interval sequences from radioactive cobalt. Two classification criteria (minimum Mahalanobis distance and maximum Bayesian likelihood) were tested. In the absence of additive noise, no errors occurred in a within-library classification. Normally distributed random numbers were added to produce signal to noise ratios of 10, 5 and 0 dB. When the minimum Mahalanobis distance was used as the classification criterion, the corresponding error rates were 2.2%, 4.4% and 20% (Expected Error Rate = 89%). When Bayesian maximum likelihood was the criterion, the error rates were 1.1%, 4.4% and 21% respectively. Using nonlinear measures an effective discrimination can be achieved in cases where spectral measures are known to fail. Most classification errors occurred at low signal to noise ratios when a stochastic signal was misclassified into a different group of stochastic signals. When the within-library classification exercise is limited to the four groups of deterministic signals, no classification errors occurred with clean data, at SNR = 10 dB, or at SNR = 5 dB. A single classification error (Observed Error Rate = 2.5%, Expected Error Rate = 75%) occurred with both classification criteria at SNR = 0 dB.

It is shown that inappropriately constructed random phase surrogates can give false-positive rejections of the surrogate null hypothesis. Specifically, the procedure erroneously indicated the presence of deterministic, nonlinear structure in a time series that was constructed by linearly filtering normally distributed random numbers. It is shown that the erroneous identification was due to numerical errors in the estimation of the signal's Fourier transform. In the example examined here, the introduction of data windowing into the algorithm eliminated the false-positive rejection of the null hypothesis. Additional guidelines for the use of surrogates are considered, and the results of a comparison test of random phase surrogates, Gaussian scaled surrogates and iterative surrogates are presented.

We present three distinct concepts of what constitutes a scientific understanding of a dynamical system. The development of each of these paradigms has resulted in a significant expansion in the kind of system that can be investigated. In particular, the recently-developed ‘algorithmic modelling paradigm’ has allowed us to enlarge the domain of discourse to include complex real-world processes that cannot necessarily be described by conventional differential equations.

A numerical algorithm is presented for estimating whether, and roughly to what extent, a time series is noise corrupted. Using phase-randomized surrogates constructed from the original signal, metrics are defined which can be used to quantify the noise level. A saturation occurs in these metrics at signal to noise ratios (SNRs) of around 0 dB and below, and also at around 20 dB and above. In between these two regions there is a monotonic transition in the value of the metrics from one region to the other corresponding to changes in the SNR. (c) 1997 American Institute of Physics.

Pigs continue to grow in importance as a tool in neuroscience. However, behavioral tests that have been validated in the rodent model do not translate well to pigs because of their very different responses to behavioral stimuli. We refined metrics for assessing porcine open field behavior to detect a wide spectrum of clinically relevant behaviors in the piglet post-traumatic brain injury (TBI). Female neonatal piglets underwent a rapid non-impact head rotation in the sagittal plane (n=8 evaluable) or were instrumented shams (n=7 evaluable). Open field testing was conducted 1 day prior to injury (day −1) in order to establish an individual baseline for analysis, and at days +1 and +4 after injury. Animals were then killed on day +6 after injury for neuropathological assessment of axonal injury. Injured piglets were less interested in interacting with environmental stimuli and had a lower activity level than did shams. These data were compared with previously published data for axial rotational injuries in neonatal piglets. Acute behavioral outcomes post-TBI showed a dependence on the rotational plane of the brain injury, with animals with sagittal injuries demonstrating a greater level of inactivity and less random usage of the open field space than those with axial injuries. The persistence of axonal injury is also dependent on the rotational plane, with sagittal rotations causing more prolonged injuries than axial rotations. These results are consistent with animal studies, finite element models, and studies of concussions in football, which have all demonstrated differences in injury severity depending upon the direction of head impact rotation.

The identification and longitudinal assessment of traumatic brain injury presents several challenges. Because these injuries can have subtle effects, efforts to find quantitative physiological measures that can be used to characterize traumatic brain injury are receiving increased attention. The results of this research must be considered with care. Six reasons for cautious assessment are outlined in this paper. None of the issues raised here are new. They are standard elements in the technical literature that describes the mathematical analysis of clinical data. The purpose of this paper is to draw attention to these issues because they need to be considered when clinicians evaluate the usefulness of this research. In some instances these points are demonstrated by simulation studies of diagnostic processes. We take as an additional objective the explicit presentation of the mathematical methods used to reach these conclusions. This material is in the appendices. The following points are made: (1) A statistically significant separation of a clinical population from a control population does not ensure a successful diagnostic procedure. (2) Adding more variables to a diagnostic discrimination can, in some instances, actually reduce classification accuracy. (3) A high sensitivity and specificity in a TBI versus control population classification does not ensure diagnostic successes when the method is applied in a more general neuropsychiatric population. (4) Evaluation of treatment effectiveness must recognize that high variability is a pronounced characteristic of an injured central nervous system and that results can be confounded by either disease progression or spontaneous recovery. A large pre-treatment versus post-treatment effect size does not, of itself, establish a successful treatment. (5) A procedure for discriminating between treatment responders and non-responders requires, minimally, a two phase investigation. This procedure must include a mechanism to discriminate between treatment responders, placebo responders, and spontaneous recovery. (6) A search for prodromes of neuropsychiatric disorders following traumatic brain injury can be implemented with these procedures.

Psychophysiological investigations of traumatic brain injury (TBI) are being conducted for several reasons, including the objective of learning more about the underlying physiological mechanisms of the pathological processes that can be initiated by a head injury. Additional goals include the development of objective physiologically based measures that can be used to monitor the response to treatment and to identify minimally symptomatic individuals who are at risk of delayed onset neuropsychiatric disorders following injury. Research programs studying TBI search for relationships between psychophysiological measures, particularly ERP component properties (e.g. timing, amplitude, scalp distribution), and a participant’s clinical condition. Moreover, the complex relationships between brain injury and psychiatric disorders are receiving increased research attention, and ERP technologies are making contributions to this effort. This review has two objectives supporting such research efforts. The first is to review evidence indicating that traumatic brain injury is a significant risk factor for post-injury neuropsychiatric disorders. The second objective is to introduce ERP researchers who are not familiar with neuropsychiatric assessment to the instruments that are available for characterizing traumatic brain injury, post-concussion syndrome, and psychiatric disorders. Specific recommendations within this very large literature are made. We have proceeded on the assumption that, as is typically the case in an ERP laboratory, the investigators are not clinically qualified and that they will not have access to participant medical records.

We have re-examined single channel EEG data obtained from normal human subjects. In the original analysis, calculation of the correlation dimension with the Grassberger-Procaccia algorithm produced results consistent with an interpretation of low-dimensional behavior. The re-examination suggests that the previous indication of low-dimensional structure was an artifact of autocorrelation in the oversampled signal. Calculations with a variant of the Grassberger-Procaccia algorithm modified to be less sensitive to autocorrelations, and comparison with linear gaussian surrogate data, indicate that these data may be more appropriately modeled by linearly filtered noise. Discriminant analysis further indicates that the correlation dimension is a poor discriminator for distinguishing between EEGs recorded at rest and during periods of cognitive activity. It remains possible that the application of other nonlinear measures or the examination of multichannel EEG data may resolve structures not found in these calculations.

Calculations with surrogate variants of original data are used to validate results obtained in dynamical analysis. Three classes of surrogates are now in use: random-shuffle surrogates, random-phase surrogates and Gaussian-scaled random-phase surrogates. In this paper we present an example based on a natural source of random numbers (radioactive decay) in which random-shuffle and Gaussian-scaled random-phase surrogates both correctly identify the random nature of the data while random-phase surrogates give a dramatic, and totally spurious, identification of non-random structure. The application of random-phase surrogates by themselves, without confirmatory calculations using Gaussian-scaled random-phase surrogates, is becoming increasingly common. The results presented here argue against this practice. The first step in the application of symbolic analysis to dynamical data is the partitioning of the data into a finite symbol alphabet. These results also show that appropriately constructed surrogates can be used as a protection against spurious results caused by defective partitioning.

The number and variety of methods used in dynamical analysis has increased dramatically during the last fifteen years, and the limitations of these methods, especially when applied to noisy biological data, are now becoming apparent. Their misapplication can easily produce fallacious results. The purpose of this introduction is to identify promising new methods and to describe safeguards that can be used to protect against false conclusions.

Human electromyograms were obtained from normal muscle and from spontaneously fibrillating, denervated muscle, and the time intervals between spikes in electrical activity were measured. The entropy and measures related to the entropy were used to examine these data. We have achieved a statistically significant discrimination between normal and denervated muscle (p In this review we also establish the relationships between conventional statistical measures and the limiting values of coarse grained measures obtained as the number of elements in the partition approaches infinity.

A fundamentally important problem for cognitive psychophysiologists is selection of the appropriate off-line digital filter to extract signal from noise in the event-related brain potential (ERP) recorded at the scalp. Investigators in the field typically use a type of finite impulse response (FIR) filter known as moving average or boxcar filter to achieve this end. However, this type of filter can produce significant amplitude diminution and distortion of the shape of the ERP waveform. Thus, there is a need to identify more appropriate filters. In this paper, we compare the performance of another type of FIR filter that, unlike the boxcar filter, is designed with an optimizing algorithm that reduces signal distortion and maximizes signal extraction (referred to here as an optimal FIR filter). We applied several different filters of both types to ERP data containing the P300 component. This comparison revealed that boxcar filters reduced the contribution of high-frequency noise to the ERP but in so doing produced a substantial attenuation of P300 amplitude and, in some cases, substantial distortions of the shape of the waveform, resulting in significant errors in latency estimation. In contrast, the optimal FIR filters preserved P300 amplitude, morphology, and latency and also eliminated high-frequency noise more effectively than did the boxcar filters. The implications of these results for data acquisition and analysis are discussed.

This contribution presents four results. First, calculations indicate that when examined by the Grassberger-Procaccia algorithm alone, filtered noise can mimic low-dimensional chaotic attractors. Given the ubiquity of signal filtering in experimental investigations, this is potentially important. Second, a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor. Third, it is shown that a criterion derived by Eckmann and Ruelle [Physica D 56, 185 (1992)] to estimate the minimum number of data points required in a Grassberger-Procaccia calculation can be used to provide a further check on these dimension estimates. Fourth, it is shown that surrogate data techniques recently published by Theiler and his colleagues [in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubanks (Addison Wesley, Reading, MA, 1992)] can successfully distinguish between linearly correlated noise and nonlinear structure. These results, and most particularly the first, indicate that Grassberger-Procaccia results must be interpreted with far greater circumspection than has previously been the case, and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data. When filtered signals are examined by this algorithm alone, a finite noninteger value of ${\mathit{D}}_{2}$ is consistent with low-dimensional chaotic behavior, but it is certainly not a definitive diagnostic of chaos.

The most commonly used method for detecting deception is based on the assumption that lies given by a person in response to critical questions posed during a polygraph examination will elicit an identifiable pattern of autonomic reactivity. Critics of this method argue that a polygraph examination cannot detect lying because lying does not produce a distinct physiological response. They assert that the possession of information only the guilty person would be expected to have can be revealed in a polygraph examination, however, by the pattern of autonomic arousal presentation of this information elicits in a person who possesses it. In this article, the position is taken that the dependence of both procedures on autonomic measures diminishes their effectiveness and inhibits the development of alternatives. A few studies are reviewed that suggest that measures of brain electrical activity can be used to infer the possession of information in persons attempting to conceal it

Background The role of psychotherapy in the treatment of traumatic brain injury is receiving increased attention. The evaluation of psychotherapy with these patients has been conducted largely in the absence of quantitative data concerning the therapy itself. Quantitative methods for characterizing the sequence-sensitive structure of patient-therapist communication are now being developed with the objective of improving the effectiveness of psychotherapy following traumatic brain injury. Methods The content of three therapy session transcripts (sessions were separated by four months) obtained from a patient with a history of several motor vehicle accidents who was receiving dialectical behavior therapy was scored and analyzed using methods derived from the mathematical theory of symbolic dynamics. Results The analysis of symbol frequencies was largely uninformative. When repeated triples were examined a marked pattern of change in content was observed over the three sessions. The context free grammar complexity and the Lempel-Ziv complexity were calculated for each therapy session. For both measures, the rate of complexity generation, expressed as bits per minute, increased longitudinally during the course of therapy. The between-session increases in complexity generation rates are consistent with calculations of mutual information. Taken together these results indicate that there was a quantifiable increase in the variability of patient-therapist verbal behavior during the course of therapy. Comparison of complexity values against values obtained from equiprobable random surrogates established the presence of a nonrandom structure in patient-therapist dialog (P = .002). Conclusions While recognizing that only limited conclusions can be based on a case history, it can be noted that these quantitative observations are consistent with qualitative clinical observations of increases in the flexibility of discourse during therapy. These procedures can be of particular value in the examination of therapies following traumatic brain injury because, in some presentations, these therapies are complicated by deficits that result in subtle distortions of language that produce significant post-injury social impairment. Independently of the mathematical analysis applied to the investigation of therapy-generated symbol sequences, our experience suggests that the procedures presented here are of value in training therapists.

The efficacy of psychotherapy, in its many and varied forms, is one of the most intensely contested issues in clinical practice. Though many theories have been advanced, quantitative evidence in their defense is limited. This contribution is directed to relatively unambitious objectives. Rather than establish yet another qualitative theory of psychotherapeutic practice, we wish to contribute to the construction of research methodologies that can quantitatively characterize the dynamic patterns of patient-therapist communication. It is hoped that a theoretical understanding of psychotherapy might eventually emerge naturally from a growing body of quantitative data.

Direct application of a drop of penicillin to the brain's surface can elicit brain electrical activity similar to that seen in some forms of epilepsy. The procedure has therefore become one of the standard techniques in the experimental investigation of epilepsy. The time intervals between action potentials, called the interspike intervals, were measured from single nerve cells in the cerebral cortex of the rat before and after local administration of penicillin. The resulting interspike interval data were examined by elementary statistical procedures and by embedding the data in two- and three-dimensional spaces. The mean interspike interval did not change significantly in response to penicillin. In contrast, the geometrical characterization displayed a dramatic sensitivity to the drug.

We investigate whether causal relationships in coupled Van der Pol oscillators can be determined. Using the instantaneous phase of computer generated time series, which are unidirectionally and time dependently coupled, the technique of lagged mutual information is tested to determine its usefulness in detecting information transmission. If successful, it could assist in improving our understanding of the role of information transmission in organizing CNS activity.

The use of multivariate measurements to characterize brain activity (electrical, magnetic, optical) is widespread. The most common approaches to reduce the complexity of such observations include principal and independent component analyses (PCA and ICA), which are not well suited for discrimination tasks. We addressed two questions: first, how do the neurophysiological responses to elongated phonemes relate to tone and phoneme responses in normal children, and, second, how discriminable are these responses. We employed fully optimized linear discrimination analysis to maximally separate the multi-electrode responses to tones and phonemes, and classified the response to elongated phonemes. We find that discrimination between tones and phonemes is dependent upon responses from associative regions of the brain apparently distinct from the primary sensory cortices typically emphasized by PCA or ICA, and that the neuronal correlates corresponding to elongated phonemes are highly variable in normal children (about half respond with neural correlates of tones and half as phonemes). Our approach is made feasible by the increase in computational power of ordinary personal computers and has significant advantages for a wide range of neuronal imaging modalities.