Theta mediated dynamics of human hippocampal-neocortical learning systems in memory formation and retrieval

Episodic memory arises as a function of dynamic interactions between the hippocampus and the neocortex, yet the mechanisms have remained elusive. Here, using human intracranial recordings during a mnemonic discrimination task, we report that 4-5 Hz (theta) power is differentially recruited during discrimination vs. overgeneralization, and its phase supports hippocampal-neocortical when memories are being formed and correctly retrieved. Interactions were largely bidirectional, with small but significant net directional biases; a hippocampus-to-neocortex bias during acquisition of new information that was subsequently correctly discriminated, and a neocortex-to-hippocampus bias during accurate discrimination of new stimuli from similar previously learned stimuli. The 4-5 Hz rhythm may facilitate the initial stages of information acquisition by neocortex during learning and the recall of stored information from cortex during retrieval. Future work should further probe these dynamics across different types of tasks and stimuli and computational models may need to be expanded accordingly to accommodate these findings.

Theta mediated dynamics of human hippocampal-neocortical learning systems in memory formation and retrieval

Episodic memory arises as a function of dynamic interactions between the hippocampus and the neocortex, yet the mechanisms have remained elusive. Here, using human intracranial recordings during a mnemonic discrimination task, we report that 4-5 Hz (theta) power is differentially recruited during discrimination vs. overgeneralization, and its phase supports hippocampal-neocortical when memories are being formed and correctly retrieved. Interactions were largely bidirectional, with small but significant net directional biases; a hippocampus-to-neocortex bias during acquisition of new information that was subsequently correctly discriminated, and a neocortex-to-hippocampus bias during accurate discrimination of new stimuli from similar previously learned stimuli. The 4-5 Hz rhythm may facilitate the initial stages of information acquisition by neocortex during learning and the recall of stored information from cortex during retrieval. Future work should further probe these dynamics across different types of tasks and stimuli and computational models may need to be expanded accordingly to accommodate these findings.

Information dynamics with confidence: Using reservoir computing to construct confidence intervals for information-dynamic measures

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.

Disrupted Gamma Synchrony after Mild Traumatic Brain Injury and Its Correlation with White Matter Abnormality

Mild traumatic brain injury (mTBI) has been firmly associated with disrupted white matter integrity due to induced white matter damage and degeneration. However, comparatively less is known about the changes of the intrinsic functional connectivity mediated via neural synchronization in the brain after mTBI. Moreover, despite the presumed link between structural and functional connectivity, no existing studies in mTBI have demonstrated clear association between the structural abnormality of white matter axons and the disruption of neural synchronization. To investigate these questions, we recorded resting state EEG and diffusion tensor imaging (DTI) from a cohort of military service members. A newly developed synchronization measure, the weighted phase lag index was applied on the EEG data for estimating neural synchronization. Fractional anisotropy was computed from the DTI data for estimating white matter integrity. Fifteen service members with a history of mTBI within the past 3 years were compared to 22 demographically similar controls who reported no history of head injury. We observed that synchronization at low-gamma frequency band (25–40 Hz) across scalp regions was significantly decreased in mTBI cases compared with controls. The synchronization in theta (4–7 Hz), alpha (8–13 Hz), and beta (15–23 Hz) frequency bands were not significantly different between the two groups. In addition, we found that across mTBI cases, the disrupted synchronization at low-gamma frequency was significantly correlated with the white matter integrity of the inferior cerebellar peduncle, which was also significantly reduced in the mTBI group. These findings demonstrate an initial correlation between the impairment of white matter integrity and alterations in EEG synchronization in the brain after mTBI. The results also suggest that disruption of intrinsic neural synchronization at low-gamma frequency may be a characteristic functional pathology following mTBI and may prove useful for developing better methods of diagnosis and treatment.

Specific transfer entropy and other state-dependent transfer entropies for continuous-state input-output systems

Since its original formulation in 2000, transfer entropy has become an invaluable tool in the toolbox of nonlinear dynamicists working with empirical data. Transfer entropy and its generalizations provide a precise definition of uncertainty and information transfer that are central to the coupled systems studied in nonlinear science. However, a canonical definition of state-dependent transfer entropy has yet to be introduced. We introduce a candidate measure, the specific transfer entropy, and compare its properties to both total and local transfer entropy. Specific transfer entropy makes possible both state- and time-resolved analysis of the predictive impact of a candidate input system on a candidate output system. We also present principled methods for estimating total, local, and specific transfer entropies from empirical data. We demonstrate the utility of specific transfer entropy and our proposed estimation procedures with two model systems, and find that specific transfer entropy provides more, and more easily interpretable, information about an input-output system compared to currently existing methods.

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.

Advancing Translational Research through Facility Design in Non-AMC Hospitals

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.

KEYWORDS

Hospital, interdisciplinary, leadership, planning, work environment.

Procedures for the Comparative Testing of Noninvasive Neuroassessment Devices

A sequential process for comparison testing of noninvasive neuroassessment devices is presented. Comparison testing of devices in a clinical population should be preceded by computational research and reliability testing with healthy populations, as opposed to proceeding immediately to testing with clinical participants. A five-step process is outlined as follows: 1. Complete a preliminary literature review identifying candidate measures. 2. Conduct systematic simulation studies to determine the computational properties and data requirements of candidate measures. 3. Establish the test-retest reliability of each measure in a healthy comparison population and the clinical population of interest. 4. Investigate the clinical validity of reliable measures in appropriately defined clinical populations. 5. Complete device usability assessment (weight, simplicity of use, cost effectiveness, ruggedness) only for devices and measures that are promising after steps 1 through 4 are completed. Usability may be considered throughout the device evaluation process but such considerations are subordinate to the higher priorities addressed in steps 1 through 4.

Predictors of Neurocognitive Syndromes in Combat Veterans

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.

Traumatic brain injury detection using electrophysiological methods

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.

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.

Improved behavior, motor, and cognition assessments in neonatal piglets

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.

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.

Behavioral deficits and axonal injury persistence after rotational head injury are direction dependent

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.

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

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.

Fully optimized discrimination of physiological responses to auditory stimuli

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.

Statistical validation of mutual information calculations: comparison of alternative numerical algorithms

Given two time series X and Y , their mutual information, I (X,Y) = I (Y,X) , is the average number of bits of X that can be predicted by measuring Y and vice versa. In the analysis of observational data, calculation of mutual information occurs in three contexts: identification of nonlinear correlation, determination of an optimal sampling interval, particularly when embedding data, and in the investigation of causal relationships with directed mutual information. In this contribution a minimum description length argument is used to determine the optimal number of elements to use when characterizing the distributions of X and Y . However, even when using partitions of the X and Y axis indicated by minimum description length, mutual information calculations performed with a uniform partition of the XY plane can give misleading results. This motivated the construction of an algorithm for calculating mutual information that uses an adaptive partition. This algorithm also incorporates an explicit test of the statistical independence of X and Y in a calculation that returns an assessment of the corresponding null hypothesis. The previously published Fraser-Swinney algorithm for calculating mutual information includes a sophisticated procedure for local adaptive control of the partitioning process. When the Fraser and Swinney algorithm and the algorithm constructed here are compared, they give very similar numerical results (less than 4% difference in a typical application). Detailed comparisons are possible when X and Y are correlated jointly Gaussian distributed because an analytic expression for I (X,Y) can be derived for that case. Based on these tests, three conclusions can be drawn. First, the algorithm constructed here has an advantage over the Fraser-Swinney algorithm in providing an explicit calculation of the probability of the null hypothesis that X and Y are independent. Second, the Fraser-Swinney algorithm is marginally the more accurate of the two algorithms when large data sets are used. With smaller data sets, however, the Fraser-Swinney algorithm reports structures that disappear when more data are available. Third, the algorithm constructed here requires about 0.5% of the computation time required by the Fraser-Swinney algorithm.

Dynamical analysis reveals individuality of locomotion in goldfish

Goldfish swimming was analysed quantitatively to determine if it exhibits distinctive individual spatio-temporal patterns. Due to the inherent variability in fish locomotion, this hypothesis was tested using five nonlinear measures, complemented by mean velocity. A library was constructed of 75 trajectories, each of 5 min duration, acquired from five fish swimming in a constant and relatively homogeneous environment. Three nonlinear measures, the `characteristic fractal dimension' and `Richardson dimension',both quantifying the degree to which a trajectory departs from a straight line, and `relative dispersion', characterizing the variance as a function of the duration, have coefficients of variation less than 7%, in contrast to mean velocity (30%). A discriminant analysis, or classification system, based on all six measures revealed that trajectories are indeed highly individualistic,with the probability that any two trajectories generated from different fish are equivalent being less than 1%. That is, the combination of these measures allows a given trajectory to be assigned to its source with a high degree of confidence. The Richardson dimension and the `Hurst exponent', which quantifies persistence, were the most effective measures.

Comparative study of embedding methods

Embedding experimental data is a common first step in many forms of dynamical analysis. The choice of appropriate embedding parameters (dimension and lag) is crucial to the success of the subsequent analysis. We argue here that the optimal embedding of a time series cannot be determined by criteria based solely on the time series itself. Therefore we base our analysis on an examination of systems that have explicit analytic representations. A comparison of analytically obtained results with those obtained by an examination of the corresponding time series provides a means of assessing the comparative success of different embedding criteria. The assessment also includes measures of robustness to noise. The limitations of this study are explicitly delineated. While bearing these limitations in mind, we conclude that for the examples considered here, the best identification of the embedding dimension was achieved with a global false nearest neighbors argument, and the best value of lag was identified by the mutual information function.

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 Shannon's 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 subject's 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.

Entropy and complexity of finite sequences as fluctuating quantities

The paper is devoted to the analysis of digitized sequences of real numbers and discrete strings, by means of the concepts of entropy and complexity. Special attention is paid to the random character of these quantities and their fluctuation spectrum. As applications, we discuss neural spike-trains and DNA sequences. We consider a given sequence as one realization of finite length of certain random process. The other members of the ensemble are defined by appropriate surrogate sequences and surrogate processes. We show that n-gram entropies and the context-free grammatical complexity have to be considered as fluctuating quantities and study the corresponding distributions. Different complexity measures reveal different aspects of a sequence. Finally, we show that the diversity of the entropy (that takes small values for pseudorandom strings) and the context-free grammatical complexity (which takes large values for pseudorandom strings) give, nonetheless, consistent results by comparison of the ranking of sample sequences taken from molecular biology, neuroscience, and artificial control sequences.

Effective normalization of complexity measurements for epoch length and sampling frequency

The algorithmic complexity of a symbol sequence is sensitive to the length of the message. Additionally, in those cases where the sequence is constructed by the symbolic reduction of an experimentally observed wave form, the corresponding value of algorithmic complexity is also sensitive to the sampling frequency. In this contribution, we present definitions of algorithmic redundancy that are sequence-sensitive generalizations of Shannon's original definition of information redundancy. In contrast with algorithmic complexity, we demonstrate that algorithmic redundancy is not sensitive to message length or to observation scale (sampling frequency) when stationary systems are examined.

Complexity measures in molecular psychiatry

The most frequently used measures in behavioral research are distribution-determined measures that provide a quantitative determination of the relative frequency of a specified behavior. These measures are, however, insensitive to the sequence of behaviors. Complexity measures address this deficiency. Several sequence-sensitive measures including the topological entropy, metric entropy, algorithmic complexity and stochastic model complexity will be described. Several applications to psychiatric research will also be discussed. These applications include the characterization of changes in animal behavior in response to CNS-active drugs and the analysis of single-unit interspike interval spike trains. Clinical applications include the analysis of electromyographic and electroencephalographic signals, the examination of choice task behavior in clinical populations, and protocol analysis.

Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram

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 and 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.

The algorithmic complexity of neural spike trains increases during focal seizures

The interspike interval spike trains of spontaneously active cortical neurons can display nonrandom internal structure. The degree of nonrandom structure can be quantified and was found to decrease during focal epileptic seizures. Greater statistical discrimination between the two physiological conditions (normal vs seizure) was obtained with measurements of context-free grammar complexity than by measures of the distribution of the interspike intervals such as the mean interval, its standard deviation, skewness, or kurtosis. An examination of fixed epoch data sets showed that two factors contribute to the complexity: the firing rate and the internal structure of the spike train. However, calculations with randomly shuffled surrogates of the original data sets showed that the complexity is not completely determined by the firing rate. The sequence-sensitive structure of the spike train is a significant contributor. By combining complexity measurements with statistically related surrogate data sets, it is possible to classify neurons according to the dynamical structure of their spike trains. This classification could not have been made on the basis of conventional distribution-determined measures. Computations with more sophisticated kinds of surrogate data show that the structure observed using complexity measures cannot be attributed to linearly correlated noise or to linearly correlated noise transformed by a static monotonic nonlinearity. The patterns in spike trains appear to reflect genuine nonlinear structure. The limitations of these results are also discussed. The results presented in this article do not, of themselves, establish the presence of a fine-structure encoding of neural information.

A guide to dynamical analysis

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.

Optimal digital filters for long-latency components of the event-related brain potential

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.

Three quantitative studies of gender and identity in psychotherapy consultations

This paper details the application of three distinctive approaches to the analysis of line-by-line scores for themes of gender and identity in recorded psychotherapy consultations conducted by three male analysts with a female patient. The first method involved commonly used statistical comparisons of the frequency with which gender subthemes and allusions to identity appeared in each consultation session. The results of this study indicate three significantly different patterns of gender material in the communications from the patient with each of the analysts who interviewed her--and from each analyst and patient/analyst system as well. Therapist dominance in this area appeared to be quite strong. The second study involved measures of overall informational complexity for various aspects of the gender/identity sequence of communications. Here too, individual differences emerged. They not only add to the evidence for therapist dominance in these protocols, but also provide indications that sessions differ in respect to the extent to which the information they contain is ordered and repetitive or redundant, as compared to disordered, complex, and varied. The third study availed itself of stochastic methods in which the Box-Jenkins models were used to define mathematically and post hoc, the deeper structure of aspects of the vicissitudes of gender/identity expressions in the course of these consultations. The main finding was that change in speaker role in respect to these themes accelerated in response to random interventional shocks to the system that occurred at the time of measurement and inversely with shocks to the system sustained the previous second. This look into the deeper structure of these sequences revealed considerable sensitivity to recent shocks to the patient/therapist system, much underlying instability, and strong tendencies toward establishing stability or equilibrium when the system destabilized. Of note is the finding that all three consultations, by and large, followed the same configuration--itself a rarely seen model. The implications and promise of these methods are discussed.

Toward a quantitative characterization of patient-therapist communication

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.

Dynamics of brain electrical activity

In addition to providing important theoretical insights into chaotic deterministic systems, dynamical systems theory has provided techniques for analyzing experimental data. These methods have been applied to a variety of physical and chemical systems. More recently, biological applications have become important. In this paper, we report applications of one of these techniques, estimation of a signal's correlation dimension, to the characterization of human electroencephalographic (EEG) signals and event-related brain potentials (ERPs). These calculations demonstrate that the magnitude of the technical difficulties encountered when attempting to estimate dimensions from noisy biological signals are substantial. However, these results also suggest that this procedure can provide a partial characterization of changes in cerebral electrical activity associated with changes in cognitive behavior that complements classical analytic procedures.

Why are so many biological systems periodic?

The ubiquity of oscillations in biological systems is well established. Oscillations are observed in all types of organisms from the simplest to the most complex. Periods can range from fractions of a second to months or years. From time to time, it has been suggested that many biological oscillations are the result of the breakdown of effective self-regulation. The opposite view is defended here. It is argued that most periodic behavior is not pathological but rather constitutes the normal operation for these systems. They are present because they confer positive functional advantages for the organism. The advantages fall into five general categories: temporal organization, spatial organization, prediction of repetitive events, efficiency and precision of control.

The bidirectional flux of cholesterol between cells and lipoproteins. Effects of phospholipid depletion of high density lipoprotein

The bidirectional surface transfer of free cholesterol (FC) between Fu5AH rat hepatoma cells and human high density lipoprotein (HDL) was studied. Cells and HDL were prelabeled with [4-14C]FC and [7-3H]FC, respectively. Influx and efflux of FC were measured simultaneously from the appearance of 3H counts in cells and 14C counts in medium. Results were analyzed by a computerized procedure which fitted sets of kinetic data to a model assuming that cell and HDL FC populations each formed a single homogeneous pool and that together the pools formed a closed system. This analysis yielded values for the first-order rate constants of FC influx and efflux (ki and ke), from which influx and efflux of FC mass (Fi and Fe) could be calculated. With normal HDL, the uptake and release of FC tracers conformed well to the above-described model; Fi and Fe were approximately equal, suggesting an exchange of FC between cells and HDL. HDL was depleted of phospholipid (PL) by treatment with either phospholipase A2 or heparin-releasable rat hepatic lipase, followed by incubation with bovine serum albumin. PL depletion of HDL had little or no effect on ki, but reduced ke, indicating that PL-deficient HDL is a relatively poor acceptor of cell cholesterol. The reduction in ke resulted in initial Fi greater than Fe and, thus, in net uptake of FC by the cells. This result explained previous results demonstrating net uptake of FC from PL-depleted HDL. In the presence of an inhibitor of acyl coenzyme A:cholesterol acyltransferase, the steady state distribution of FC mass between cells and HDL was accurately predicted by the ratio of rate constants for FC flux. This result provided additional validation for describing FC flux in terms of first-order rate constants and homogeneous cell and HDL FC pools.

Communication and control in reproduction: the ubiquity of periodic phenomena

Two statements will be presented and defended in this paper. First, it is claimed that oscillations are common in all biological systems. From the subcellular to the organismic levels of organization, oscillations are the normal operational mode for many biochemical and physiological control networks. Second, it will be demonstrated that periodic control offers several functional advantages over steady-state control.

A comparative survey of the function, mechanism and control of cellular oscillators

This review attempts to survey in a uniform manner the available evidence concerning the generation and behaviour of several well-investigated cellular oscillators. Members of two broad classifications are contrasted: (i) cytoplasmic oscillations, where the periodic phenomena is generated by an instability pathway and (ii) membrane oscillators in which a membrane potential rhythm is generated at the membrane. Interactions between the cytoplasmic and membrane compartments are considered and the effects of these interactions on oscillatory behaviour is discussed. Because of their biological importance and the greater body of experimental results, particular attention is directed to a study of membrane potential oscillations. These systems can be approximately classified in two groups: (i) systems in which a periodic potential results from oscillatory changes in permeability and (ii) systems in which potential oscillations result from the periodic activity of an electrogenic pump. The examples considered include the glycolytic oscillator, oscillations in vein contraction in the slime mould Physarum polycephalum, rhythmic aggregation in Dictyostelium discoideum, neural oscillators, the periodic potential in Purkinje fibres and the sino-atrial node and rhythmic behaviour in smooth muscle. Questions considered include the generation of periodic activity, the modulation of the oscillation by drugs and other metabolic and membrane effectors and the question of the functional role of these oscillations.