 |
|
ISSN 1320-0682 | ||||
| Volume 3 | April 1996 | ||||
John Klopp, Valeriy I. Nenov & Cameron Jones
Klopp UCLA Interdepartmental Ph.D. Program for Neuroscience, Box 951761, Los Angeles, CA 90095-1761, USA
Nenov UCLA School of Medicine, Division of Neurosurgery, 10833 LeConte Ave. CHS 74-140, Los Angeles, CA 90095, USA
Jones Centre for Applied Colloid and BioColloid Science, Swinburne University of Technology, School of Chemical Sciences, GOP Box 218, Hawthorn, Victoria 3122, Australia
Email:jklopp@ucla.edu
Neuronal systems are capable of generating electroencephalographic (EEG) signals with high-dimensional nonlinear dynamics. Patients with complex partial epilepsy sometimes undergo depth EEG monitoring for pre-surgical localisation of seizure onset. Stroboscopic and coherence mapping, two novel approaches for EEG analysis, were applied to depth EEG seizure data from two patients. Multiple time-lagged one-dimensional strobomaps were derived from phase plots of seizure data. Negative correlation values between V(n) and V(n+1) in strobomaps reached -0.97 during seizure activity from the right amygdala of one patient. Although not indicative of deterministic chaos, this suggests non-random, low frequency modulation of neural group activity during seizures. Characteristic patterns of coherence fluctuation also occurred during seizure episodes. Further analysis that incorporates the full spatial distribution of all available data may uncover chaos hidden in the ensemble of electrical seizure activity within the human brain. Signature patterns of stroboscopic or coherence measures associated with specific seizure stages could aid in elucidating the neural substrates of epileptogenesis. However, the clinical value of this information has yet to be determined.
The human brain is the most complex information-processing structure known to science. We often take for granted its vast parallel multi-tasking, sensory-motor integration and context specific associational capabilities. As with any elaborate machine, malfunction is always a danger. One problem that electrically coupled neural networks confront is unrestrained recurrent excitation. In humans, hyper-synchronous activations of neural tissue that disrupt normal signal processes are known as seizures. Epilepsy is a generic term for the wide range of seizure disorders. The symptomatic severity of epilepsy ranges from stereotyped and involuntary alterations of behaviour from jerking movements, transient loss of awareness and memory impairment to massive convulsions and complete loss of consciousness. Approximately one out of two hundred people suffers from chronic epileptic seizures. Aside from direct physical trauma, seizure-induced behavioural alterations have a major psychological impact on the life of epilepsy patients. The underlying pathology may be structural or molecular, and it may be diffuse or localised. Known causes of seizure disorders include a variety of factors such as tumors, infection, trauma and oxygen deprivation. However, in about half of epilepsy patients no specific causative factor is ever pinpointed.
The EEG represents dynamics of electrical brain activity on a time scale of milliseconds. Neural systems are capable of generating complex EEG signals with highly nonlinear dynamics. Quantitative analysis of one-dimensional EEG time series can be performed with non-linear statistical methods. For example, EEG dimensional complexity (a measure of underlying degrees of freedom) increases during a mental task [1], and appears to decrease during stage II and IV sleep (but not REM) relative to the waking state [2]. Especially low dimensional complexity values occur during epileptic seizures [3]. More recent work employing Poincaré and stroboscopic mapping of hippocampal field potentials shows evidence of chaotic activity in an in vitro preparation of a biological neural network [4].
The process of neural entrainment that leads to seizure onset may involve a transient interaction between brain regions. Such interaction would appear as enhanced spectral coherence [5]. This coherence is interpreted as a measure of the functional relationship between brain areas [6]. A variety of studies has previously demonstrated the value of EEG coherence estimation [7], [8], [9]. Measurements of inter-channel EEG coherence can be used to study the distribution, spatial extent and timing relationship of electrical activity generated by different regions of the brain. Coherence measurements can also be used to extract clinically useful information about abnormal EEG recordings that would otherwise not be apparent from visual inspection alone [10].
Studies of human EEG genesis are complicated by the fact that the sources of EEG signals are embedded within the cortex whereas, except under rare conditions, human brain activity is sampled indirectly from the surface of the scalp. Comparisons of recordings from the skull with those from the cortical surface reveal many differences not limited to the significant decrease of voltage in scalp recordings [11], [5]. These differences are due to the complicated geometry of the generator layer of gyrated cortex and to differences in conductivity of the interposed layers, particularly the cerebrospinal fluid which has a high conductance [12]. The prevailing view is that principal generators of compound field potentials are microscopic and chiefly the product of membrane potentials. In contrast, the majority of EEG data, which is derived from scalp recordings, comes from EEG contacts at a distance of 4 centimeters apart. A conservative estimate predicts that such recordings are the vector sum of activity in about 15 million cells [13]. Depth implanted probes have a great advantage in this regard as they sample much smaller neural populations.
Epileptic seizures are broadly classified into partial and generalised forms. Partial seizures commence at a focal cortical site and are associated with preservation of consciousness. Generalised seizures entail widespread involvement of both cortical hemispheres [14]. Complex Partial Seizures (CPS), also known as psychomotor seizures, account for 40% of all cases of epilepsy [15] and are characterised by complex illusory phenomena and semi-purposeful elaborate motor acts. CPS often start in, or are spread through, limbic structures of the medial temporal lobe. As many as 50% of CPS patients are medically intractable. For this group, a final recourse lies in the surgical removal of neural tissue responsible for seizure onset. Recognition of propagated seizure activity and localisation of the germinal focus is vital for an attempt at curative resective neurosurgery.
Stroboscopic and coherence mapping techniques provide a new perspective on brain electrical activity during normal and pathological conditions. By applying novel analytical methods to these data we hoped to discover characteristic patterns that correspond with specific stages of seizure development, maintenance and termination. If stroboscopic or coherence measurements show such characteristic alterations they may potentially provide clinically useful information.
In some cases, pre-evaluation of epilepsy patients for surgical resection requires depth and or subdural electrode monitoring. Pre-operative magnetic resonance imaging allows accurate implantation of depth electrodes into target structures by stereotactic methods. Post-operative magnetic resonance images verify the placement of depth EEG probes (see Figure 1).
Figure 1: A post-operative MRI of depth implanted EEG probes
Recordings from the multi-contact probes (see Figure 2) during seizure onset assist the surgeon in pinpointing the focus of epileptogenesis.
Figure 2: Schematic diagram of a single depth EEG probe
In this study, coherence mapping and strobomap functions were applied to seizure episode data. Raw data was acquired at 12-bit resolution and digitised at 256 or 200 Hz with a bandpass filter of 0.3 to 70 Hz. Up to 80 EEG contacts were simultaneously recorded from depth implanted electrodes in patients with epilepsy. Bilateral implantation sites commonly include medial temporal lobe structures (amygdala, entorhinal cortex, hippocampus, and parahippocampal gyrus) as well as orbito-frontal areas. The 2 patients in this study each had medically intractable unilateral temporal lobe complex partial seizures. Patient DH's seizures started on the right side while patient MH had seizures initiated on the left side of the brain.
Stroboscopic and coherence mapping was based on bipolar derivations of adjacent-neighbor EEG contact pairs separated by approximately 5 mm. Although up to 80 depth EEG contacts may simultaneously be acquired, only 4 are taken into account in each coherence map and 2 in each strobomap function.
Poincaré mapping is a common method used to investigate deterministic features of time series (for a good introduction to this topic see [16]. Plotting V(t) versus V(t+tau), where tau equals the first zero crossing of the auto-correlation function and V is the bipolar voltage potential difference between 2 depth EEG contacts yields phase plots of raw EEG data. Strobomaps are computed by sampling the phase plot at constant time intervals. They are similar to return maps with the main difference being that return maps slice across a reference plane of the phase plot whereas strobomapping uses a constant time interval. A fixed time interval (approximately 150 milliseconds) was used to derive one-dimensional strobomaps from phase plots. Deterministic chaos is reflected in both stroboscopic and return maps as a non-invertible function [4]. A high correlation value in the stroboscopic map where V(n) correlated with V(n+1), is indicative of a linear relationship and would suggest non-random modulation but not chaos. Standard correlation values (Pearson product-moment correlation coefficient) are calculated from 2 signals using the formula:
The result of this calculation gives the correlation coefficient which is a measure of the linear association between two variables. A correlation coefficient of 1 indicates that the two time series are perfectly correlated, (that is, an increase in x is always associated with an increase in y) and a value of -1 indicates perfect negative correlation (that is, when x increases, y always decreases). Measurements of correlation coefficients were chosen because initial Poincaré mapping did not indicate clear non-linear relationships but did hint at linear associations that could be detected by correlation analysis.
Correlation analysis of consecutive overlapping stroboscopic map values was performed on 4 seizure episodes. Each strobomap was constructed from approximately 8 seconds of data. Consecutive strobomaps overlapped by 99% with more than 1300 maps covering each seizure recording.
Coherence is a quantitative measurement that reflects the extent to which two time series are synchronous within a given frequency range. It is analogous to the square of a Pearson's product correlation coefficient between two channels of EEG. Coherence, like correlation, is independent of amplitude. High coherence values approach a maximum of 1 while low coherence values approach 0. Thus, a coherence value of 1 indicates perfectly coincident activity and a coherence value of 0 indicates a complete absence of synchronicity. Coherence is defined as a function of the power spectral outputs from 2 channels at any given frequency f:
Spectral coherence can be calculated from either referential or bipolar pairs of EEG channels. There is a danger in using common reference data in coherence calculation [17]. This danger mainly arises from activity at the common reference electrode. Such contamination would bias coherence estimates toward inflated values.
In this study, coherence mapping was performed on pairs of bipolar EEG derivations during the same 4 seizure episodes as used in the strobomapping function. For coherence estimation, medial pairs from depth probes were matched with lateral pairs in the overlying neocortex. Spectral analysis was performed on sliding time windows of 4 second duration. Consecutive windows overlapped by 3 seconds. Coherence values were produced for the frequency range of 0 to 100 Hz.
Both stroboscopic and coherence analytical methods showed characteristic
patterns that corresponded with specific stages of seizure development,
maintenance and termination.
The right amygdala from patient DH displayed a mean pre-seizure stroboscopic correlation of -0.28 with a standard deviation of 0.16 (see Figure 3).
Figure 3: Result of a stroboscopic map analysis during a
seizure event
Seizure onset was marked by a rapid and persistent decrease in correlation values derived from stroboscopic maps. The first 15 seconds of the seizure showed the maximal negative correlation of -0.97. About 15 seconds into the seizure, correlation values increased. This trend continued for 15 seconds until correlation values reach beyond pre-seizure levels to 0.4. This was followed by another decrease of correlation which appeared to stabilise just below pre-seizure levels at the end of the seizure.
Results for patient MH displayed a similar trend for stroboscopic map correlation values. An initial decrease of correlation values occurred at seizure onset and persisted until the seizure episode terminated. One difference between the two patients was DH's transient mid-seizure increase in correlation coefficient values.
Seizure coherence maps, like the strobomaps, show distinct phases. For a 65 second seizure episode from patient DH's right amygdala, onset (0 to 15 seconds post-onset) is characterised by a broad frequency coherence increase, most prominent in alpha (8-12 Hz) and low frequency (0-4 Hz) bands (see Figure 4). The vertical axis shows the frequency (divide by 3 for the true frequency). The horizontal axis shows time in seconds. Seizure onset occurs at about the 76th second. The coherence scale is continuous in intensity from bright yellow (approaching 1) to black (approaching a value of 0).
Figure 4: Coherence mapping of seizure data from EEG contacts
of patient DH
Elevated alpha band coherence remains throughout the seizure. From 15 to 34 seconds post-onset, high frequency coherence returns to pre-seizure levels while low frequency coherence abates after 20 seconds. In the second half of the seizure episode, a dramatic increase in coherence appears almost simultaneously in multiple frequency bands (maximum coherence of 0.99). At least 10 distinct, highly coherent frequency bands spaced by intervals of 1-2 Hz appear in the map between 0-60 Hz. The coherence bands show a general decrease in frequency over time while maintaining high coherence. A similar banding pattern was observed in spectral power maps.
Coherence maps of seizures from MH showed less characteristic, although distinct, patterns (see Figure 5). The vertical axis shows frequency as in Figure 4. The horizontal axis shows time in seconds. Seizure onset occurs at about the 145th second and the seizure termination occurs at about the 220th second. The coherence scale is continuous as in Figure 4.
Figure 5: Coherence mapping of seizure data from EEG contacts
in the left entorhinal cortex of patient MH
Seizure onset in the left entorhinal cortex was typically marked by a short duration increase in 10-25 Hz coherence followed by sporadic increases in high 40-100 Hz coherence. Seizure termination was marked by a more intense increase in the 1-30 Hz range coherence that persisted for about 25 seconds post-seizure.
Changes in the stroboscopic and coherence maps appear to occur in conjunction both with each other and with onset and termination of seizure activity as diagnosed from raw EEG records. Although not indicative of deterministic chaos, large negative correlation values from strobomaps during seizure activity indicates a non-random, low frequency modulation of neural group activity. One critical question to be addressed is how the system initiates and sustains this modulation during a seizure. Is the modulation in response to impinging excitation/inhibition from other neural structures or is it the result of altered membrane properties of the cells constituting the epileptic tissue? Further analysis employing the full range of spatial and time data (perhaps using principal component analysis to extract the proportion of signal variance contributed by each depth EEG contact) may uncover chaos in the ensemble code of neural activity and thereby suggest a mathematical model of seizure EEG genesis. Given the striking appearance of the descending coherence bands seen in patient DH, we feel that they may be the result of harmonic decomposition of decelerating spike-wave complexes. Epilepsy patients often exhibit multiple kinds of seizures in different seizure episodes. It would be interesting to understand the circumstances necessary for emergence of the spectral coherence banding patterns that occurred in patient DH as opposed to the less distinguished pattern from patient MH.
Our findings are based upon a limited set of EEG contacts during only a few complex partial seizure episodes with unilateral temporal lobe onset. By projecting the data into multiple exploratory analyses, we hope to attain a new understanding of the seizure state. In addition, these measures can be extended to non-seizure data (for example while the patient performs a memory task) to investigate the possible coupling of chaos (or lack thereof as measured by stroboscopic mapping) with normal transient fluctuation of coherence values. Further seizure episode coherence and stroboscopic mapping will indicate whether the observed changes are common seizure signatures. The existence of such signature patterns within the depth EEG records may provide important clues to the mechanisms of endogenous seizure onset and termination. Signature patterns described by these analytical methods provide a new perspective for understanding the dynamics of seizure activity. Whether or not this type of analysis will lend to predictive diagnostics in determining the efficacy of resective surgery for individual patients remains to be investigated.
One-Dimensional Strobomaps and Coherence Analysis of Human Depth EEG During Seizure Activity.
This document was generated using the LaTeX2HTML translator Version 96.1 (Feb 5, 1996) Copyright © 1993, 1994, 1995, 1996, Nikos Drakos, Computer Based Learning Unit, University of Leeds.
The command line arguments were:
latex2html kloppcs96.
The translation was initiated by Pam Milliken on Mon Dec 23 14:48:50 EST 1996