C. J. Cellucci

The algorithmic complexity of multichannel EEGs is sensitive to changes in behavior

Symbolic measures of complexity provide a quantitative characterization of the sequential structure of symbol sequences. Promising results from the application of these methods to the analysis of electroencephalographic (EEG) and event-related brain potential (ERP) activity have been reported. Symbolic measures used thus far have two limitations, however. First, because the value of complexity increases with the length of the message, it is difficult to compare signals of different epoch lengths. Second, these symbolic measures do not generalize easily to the multichannel case. We address these issues in studies in which both single and multichannel EEGs were analyzed using measures of signal complexity and algorithmic redundancy, the latter being defined as a sequence-sensitive generalization of Shannons redundancy. Using a binary partition of EEG activity about the median, redundancy was shown to be insensitive to the size of the data set while being sensitive to changes in the subjects behavioral state (eyes open vs. eyes closed). The covariance complexity, calculated from the singular value spectrum of a multichannel signal, was also found to be sensitive to changes in behavioral state. Statistical separations between the eyes open and eyes closed conditions were found to decrease following removal of the 8- to 12-Hz content in the EEG, but still remained statistically significant. Use of symbolic measures in multivariate signal classification is described.

Detecting noise in a time series.

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.

SURROGATE DATA PATHOLOGIES AND THE FALSE-POSITIVE REJECTION OF THE NULL HYPOTHESIS

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 signals 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.

NONLINEAR SIGNAL CLASSIFICATION

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, Rossler and Henon). 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.

Optimization of Embedding Parameters for Prediction of Seizure Onset with Mutual Information

Normal neurological function is characterized by a high volume of information transferred between different parts of the central nervous system. An imperfect, but nonetheless useful, assessment of this spatially distributed transfer process can be obtained by examining multichannel EEG records that are measured with an array of scalp electrodes. A nonlinear quantitative measure of the transfer can be obtained by calculating the pairwise mutual information of each electrode pair. The average mutual information of two time series is the amount of information of one that can be predicted by measuring the other. As suggested in our previous work, a reduction in information transfer, as estimated by this metric, can occur prior to clinically discernible seizure onset. In the case of the focal seizure examined here, this reduction first occurred in the area of the brain that was subsequently shown to contain the epileptogenic focus. Thus, the calculation contains two clinically valuable elements: a prediction of seizure onset and a preliminary localization of the epileptogenic focus. We predict that in the case of seizures that are generalized at onset, the initiation of a seizure will be preceded by a near-simultaneous reduction in cross-channel average mutual information for several electrode pairs.

Patient Characterization Protocols for Psychophysiological Studies of Traumatic Brain Injury and Post-TBI Psychiatric Disorders

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 (event-related potential) 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 TBI 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 TBI, 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.

QUANTITATIVE CHARACTERIZATION OF THE COMPLEXITY OF MULTICHANNEL HUMAN EEGS

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.

Statistical Issues in TBI Clinical Studies

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.

Communication patterns in a psychotherapy following traumatic brain injury: A quantitative case study based on symbolic dynamics

BackgroundThe 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.MethodsThe 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.ResultsThe 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).ConclusionsWhile 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.

Identifying Electrophysiological Prodromes of Post-traumatic Stress Disorder: Results from a Pilot Study

The objective of this research project is the identification of a physiological prodrome of post-traumatic stress disorder (PTSD) that has a reliability that could justify preemptive treatment in the sub-syndromal state. Because abnormalities in event-related potentials (ERPs) have been observed in fully expressed PTSD, the possible utility of abnormal ERPs in predicting delayed-onset PTSD was investigated. ERPs were recorded from military service members recently returned from Iraq or Afghanistan who did not meet PTSD diagnostic criteria at the time of ERP acquisition. Participants (n = 65) were followed for up to 1 year, and 7.7% of the cohorts (n = 5) were PTSD-positive at follow-up. The initial analysis of the receiver operating characteristic (ROC) curve constructed using ERP metrics was encouraging. The average amplitude to target stimuli gave an area under the ROC curve of greater than 0.8. Classification based on the Youden index, which is determined from the ROC, gave positive results. Using average target amplitude at electrode Cz yielded Sensitivity = 0.80 and Specificity = 0.87. A more systematic statistical analysis of the ERP data indicated that the ROC results may simply represent a fortuitous consequence of small sample size. Predicted error rates based on the distribution of target ERP amplitudes approached those of random classification. A leave-one-out cross validation using a Gaussian likelihood classifier with Bayesian priors gave lower values of sensitivity and specificity. In contrast with the ROC results, the leave-one-out classification at Cz gave Sensitivity = 0.65 and Specificity = 0.60. A bootstrap calculation, again using the Gaussian likelihood classifier at Cz, gave Sensitivity = 0.59 and Specificity = 0.68. Two provisional conclusions can be offered. First, the results can only be considered preliminary due to the small sample size, and a much larger study will be required to assess definitively the utility of ERP prodromes of PTSD. Second, it may be necessary to combine ERPs with other biomarkers in a multivariate metric to produce a prodrome that can justify preemptive treatment.