Abstract:
Methods and apparatus for automatically detecting epileptic seizures by monitoring and analyzing brain wave (EEG or MEG) signals. Steps include: acquiring the brain wave data from the patient; digitizing the data; obtaining nonlinear measures of the data via chaotic time series analysis; obtaining time serial trends in the nonlinear measures; determining that one or more trends in the nonlinear measures indicate a seizure, and providing notification of seizure occurrence.

Description:
The United States Government has rights in this invention pursuant to contract no. DE-AC05-84OR21400 between the United States Department of Energy and Lockheed Martin Energy Systems, Inc. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to the application of chaotic time series analysis (CTSA) to electroencephalogram (EEG) data and magnetoencephalogram (MEG) data, and more particularly to the analysis of the data to detect epileptic seizures. 
     CROSS-REFERENCE TO RELATED APPLICATIONS 
     This invention is related to U.S. application Ser. No. 08/619,030 Epileptic Seizure Prediction by Nonlinear Methods by Lee M. Hively, Ned E. Clapp, C. Stuart Daw, and William F. Lawkins and to U.S. application Ser. No. 08/619,031 Method and Apparatus for Extraction of Low-Frequency Artifacts from Brain Waves for Alertness Detection by Ned E. Clapp and Lee M. Hively, both of which are filed on even date herewith, and both of which are assigned to the same entity. 
     BACKGROUND OF THE INVENTION 
     The theory of nonlinear dynamics provides a basis for understanding and potentially controlling many complex physical and engineering systems. An extensive literature exists for nonlinear dynamics in the brain and related work (18). It is well known that brain waves exhibit seemingly random, unpredictable behavior, that is characteristic of deterministic chaos (1, 20). Moreover, chaotic behavior is &#34;normal,&#34; while nonchaotic or periodic behavior is indicative of pathophysiology in experimental epilepsy (20). Schiff et al. (11 ) showed that chemically-induced seizures in rat-brain can be electrically controlled, leading to speculation (4) that human epilepsy may be controlled without drug or surgical intervention. However, effective use of chaos control for epilepsy requires definitive seizure detection. Thus, this invention diagnoses brain wave data via chaotic time series analysis (CTSA) methods to detect an epileptic seizure. 
     Nonlinear analysis of neurological diseases via EEG data is extensive. For example, see the 1994 review by Elbert et al. (18). Epilepsy can be recognized only with clear EEG manifestations, but even these seizures are not easy to detect because there is no stereotyped pattern characteristic of all seizures (5). Work by Olsen and colleagues (7) used various linear measures with autoregressive modeling, discriminant analysis, clustering, and artificial neural networks. Valuable nonlinear tools for studying EEG data include correlation dimension, mutual information function, Kolmogorov entropy, phase-space attractors, and largest Lyapunov exponent. 
     Very recent analysis by Theiler (16) studied correlation dimension and Lyapunov exponent, using a form of surrogate analysis on a single EEG time series during an epileptic seizure. The surrogate analysis involved a random shuffling of blocks of time serial data, each block containing one quasi-periodic spike-wave complex. The auto-correlation function for the original data is nearly indistinguishable from the surrogate data. The correlation dimension for the original data is significantly different from the surrogate data only at large scale sizes and large embedding dimensions. The maximum Lyapunov exponent (λ) was negative for both the original and surrogate data and not substantially different, contrary to previous work which found positive λ values. Theiler concluded that his analysis suggests a nonlinear oscillator with noise on the time scale of the spike-wave complex, but cannot indicate whether chaos exists on a shorter time scale. 
     Other patents for epileptic seizure detection have been granted. U.S. Pat. No. 5,311,876 &#34;Automatic Detection of Seizures Using Electroencephalograpic Signals&#34; by D. E. Olson et al. relies on linear analysis of EEG features for seizure detection. U.S. Pat. No. 5,349,962 &#34;Method and Apparatus for Detecting Epileptic Seizures&#34; by J. S. Lockard et al. detects seizures if the wavefom is within a predetermined threshold. These patents use linear methods, as distinguished from the nonlinear techniques of the present invention. No other work is known that applies several CTSA measures to EEG data or MEG data for systematic characterization of non-seizure, seizure, and transition-to-seizure. 
     DOCUMENT LIST 
     1. A. Babloyantz and A. Destexhe, &#34;Low-Dimensional Chaos in an Instance of Epilepsy,&#34; Proc. Natl. Acad. Sci. USA 83, 3513-3517 (1986). 
     2. D. F. Elliott and K. R. Rao, Fast Transforms, Analyses, Applications, Academic Press, 1982. 
     3. A. M. Fraser and H. L. Swinney, &#34;Independent Coordinates for Strange Attractors from Mutual Information&#34; Phys. Rev A 33, 1134-1140 (1986). 
     4. J. Glanz, &#34;Do Chaos-Control Techniques Offer Hope for Epilepsy?&#34; Science 265, 1174 (1994). 
     5. J. Gotman, &#34;Seizure Recognition and Analysis&#34; Long-term Monitoring in Epilepsy (EEG Suppl. No. 37), pgs. 133-145 (1985). 
     6. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Company, New York, 1968. 
     7. D. E. Olsen, J. A. Cristion, and C. W. Spaur, &#34;Automatic Detection of Epileptic Seizures Using Electroencephalographic Signals,&#34; Johns Hopkins APL Techn. Digest 12, 182-191 (1991). 
     8. J. P. M. Pijn, &#34;Quantitative Evaluation of EEG Signals in Epilepsy--Nonlinear Associations, Time Delays, and Nonlinear Dynamics,&#34; Ph.D. Thesis, University of Amsterdam, 1990. 
     9. L. R. Rabiner and B. Gold, Theory and Application of Digital Signal Processing, Prentice Hall Inc., 1975. 
     10. S. M. Selby and B. Girling, Standard Mathematical Tables, page 390, The Chemical Rubber Co. ( 14 th edition, 1965). 
     11. S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto, &#34;Controlling Chaos in the Brain&#34; Nature 370, 615-620 (1994). 
     12. J. C. Schouten, F. Takens, and C. M. van den Bleek, &#34;Maximum-Likelihood Estimation of the Entropy of an Attractor,&#34; Phys. Rev. E 49, 126-129 (1994). 
     13. J. C. Schouten, F. Takens, and C. M. van den Bleek, &#34;Estimation of the Dimension of a Noisy Attractor,&#34; Phys. Rev. E 50, 1851-1861 (1994). 
     14. F. Takens, &#34;On the Numerical Determination of the Dimension of an Attractor,&#34; in Dynamical Systems and Bifurcations, ed. B. L. J. Braaksma, H. W. Broer, and F. Takens, Lecture Notes in Mathematics 1125, 99-106 (1984) Springer-Verlag, Berlin. 
     15. F. J. Taylor, Digital Filter Design Handbook,&#34; Marcel Dekker, Inc., Publ., New York and Basel, 1983 
     16. J. Theiler, &#34;On the Evidence for Low-Dimensional Chaos in an Epileptic Electroencephalogram,&#34; Phys. Lett. A 196, 335-341 (1995). 
     17. R. C. Watt and S. R. Hameroff, &#34;Phase Space Analysis of Human EEG during General Anesthesia,&#34; Ann. N.Y. Acad Sci. 504, 286-288 (1987). 
     18. T. Elbert, W. J. Ray, Z. J. Kowalik, J. E. Skinner, K. E. Graf, N. Birbaumer, &#34;Chaos and Physiology: Deterministic Chaos in Excitable Cell Assemblies,&#34; Physiological Reviews 74 (1994) 1-47. 
     19. S. Blanco, R. Quian Quiroga, 0. A. Rosso, and S. Kochen, &#34;Time-frequency analysis of electroencephalogram series,&#34; Physical Review E, The American Physical Society, Volume 51, Number 3, March 1995 
     20. S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto, &#34;Controlling Chaos in the Brain&#34; Nature 370, 615-620 (1994) 
     OBJECTS OF THE INVENTION 
     Accordingly, it is an object of the present invention to provide new and improved methods and apparatus for detecting epileptic seizures in a patient and providing notification to permit assistance to be given to the patient or to a person who can assist the patient. 
     Further and other objects of the present invention will become apparent from the description contained herein. 
     SUMMARY OF THE INVENTION 
     In accordance with one aspect of the present invention, the foregoing and other objects are achieved by a method for automatically detecting an epileptic seizure in a patient comprising the steps of: providing at least one channel of a patient&#39;s raw brain wave data, called e-data, selected from the group consisting of electroencephalogram data and magnetoencephalogram data; separating the e-data into artifact data, called f-data, and artifact-free data, called g-data, while preventing phase distortions in the data; processing g-data through a low-pass filter to produce a low-pass-filtered version of g-data, called h-data; applying at least one nonlinear measure selected from the group consisting of time steps per cycle, Kolmogorov entropy, first minimum in the mutual information function, and correlation dimension to at least one type of data selected from the group consisting of e-data, f-data, g-data, and h-data to provide at least one time serial sequence of nonlinear measures, from which at least one indicative trend selected from the group consisting of abrupt increases and abrupt decreases can be determined; comparing at least one indicative trend with at least one known seizure indicator; and determining from said comparison whether an epileptic seizure is occurring in the patient. 
     In accordance with a second aspect of the present invention, the foregoing and other objects are achieved by apparatus for automatically detecting an epileptic seizure in a patient comprising: data provision means for providing at least one channel of a patient&#39;s raw brain wave data called e-data selected from the group consisting of electroencephalogram data and magnetoencephalogram data; separation means for separating e-data into artifact data, called f-data, and artifact-free data, called g-data, while preventing phase distortions in the data, communicably connected to the data provision means; low-pass filter means for filtering g-data to produce a low-pass filtered version of g-data, called h-data, communicably connected to the separation means; application means for applying at least one nonlinear measure selected from the group consisting of time steps per cycle, Kolmogorov entropy, first minimum in the mutual information function, and correlation dimension to at least one type of data selected from the group consisting of e-data, f-data, g-data, and h-data to provide at least one time serial sequence of nonlinear measures, from which at least one indicative trend selected from the group consisting of abrupt increases and abrupt decreases can be determined, communicably connected to the low-pass filter means; comparison means for comparing at least one indicative trend with known seizure indicators, communicably connected to the application means; and determination means for determining from the comparison whether an epileptic seizure is occurring in the patient, communicably connected to the comparison means. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the drawings: 
     FIG. 1 is a block diagram showing how, in accordance with the present invention, EEG data is obtained from the patient, digitized, processed, and analyzed by nonlinear methods to detect and/or predict epileptic seizures. 
     FIG. 2 shows standard EEG electrode positions on a patient&#39;s scalp for the bipolar montage, looking from above. 
     FIG. 3 shows sample plots of EEG data, to illustrate raw data (e-data as the dotted curve in FIG. 3a), and artifact-filtered data (g-data, shown in FIG. 3b), as an example of the method and apparatus of this invention. 
     FIGS. 4, 5, 6, and 7 show linear and nonlinear measures of time serial data for Example I. FIG. 4 shows linear and nonlinear measures of raw (e-data);FIG. 5 shows linear and nonlinear measures of artifact (f-data); FIG. 6 shows linear and nonlinear measures of artifact-filtered (g-data); and FIG. 7 shows linear and nonlinear measures of artifact- and low-pass filtered (h-data). Various mathematical properties and characteristics are shown for each data type, and are further shown in parts (a), (b), (c), (d), (e), (f), (g), (h), and (i) for each data type. 
     These measures are shown as curves, each curve representing a time serial sequence of linear or nonlinear measures. Within each curve, significant features such as abrupt increases and abrupt decreases may be viewed as indicative trends which are then compared to trends which have been shown to be seizure indicators. Thus from the comparison it can be determined whether a seizure is occurring in the patient. In parts (a), (b), (c), (d), and (e) for each data type, the solid line is the specific measure, the dashed line is the 11-point average, and the dotted line is the standard deviation for the measure. 
     FIGS. 8, 9, 10, and 11 show linear and nonlinear measures of time serial data for Example II. FIG. 8 shows linear and nonlinear measures of raw (e-data); FIG. 9 shows linear and nonlinear measures of artifact EEG (f-data); FIG. 10 shows linear and nonlinear measures of artifact-filtered (g-data); and FIG. 11 show linear and nonlinear measures of artifact- and low-pass filtered (h-data). Various mathematical properties and characteristics as computed for each data type are further shown in parts (a), (b), (c), (d), (e), (f), (g), (h), and (i) for each data type. These measures are shown as curves, each curve representing a time serial sequence of linear or nonlinear measures. Within each curve, significant features such as abrupt increases and abrupt decreases may be viewed as indicative trends which are then compared to to trends which have been shown to be seizure indicators. Thus from the comparison it can be determined whether a seizure is occurring in the patient. In parts (a), (b), (c), (d), and (e) for each data type, the solid line is the specific measure, the dashed line is the 11-point average, and the dotted line is the standard deviation for the measure. 
     For a better trader standing of the present invention, together with other and further objects, advantages and capabilities thereof, reference is made to the following disclosure and appended claims in connection with the above-described drawings. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Chaotic time series analysis (CTSA) is applied to human electroencephalogram (EEG) data. 
     For reference, equation numbers are shown at the right of each equation. 
     Three epochs were examined: epileptic seizure, non-seizure, and transition from non-seizure to seizure. The CTSA tools were applied to four forms of these data: raw EEG data (e-data), artifact data (f-data) via application of a quadratic zero-phase filter of the raw data, artifact-filtered data (g-data) that was the residual after subtracting f-data from e-data, and a low-pass-filtered version (h-data) of g-data. Several nonlinear measures uniquely indicate an epileptic seizure, including: an abrupt increase in the number of time steps per cycle for f-data; an abrupt increase in the number of timesteps per cycle for g-data; an abrupt increase in the number of timesteps per cycle for h-data; an abrupt increase in the entropy of e-data; an abrupt increase in the entropy of f-data; an abrupt increase in the entropy of g-data; an abrupt increase in the entropy of h-data; an abrupt decrease in the first minimum in the mutual information function for f-data; an abrupt decrease in the first minimum in the mutual information function for h-data; an abrupt increase in the correlation dimension of e-data; an abrupt increase in the correlation dimension of f-data; an abrupt increase in the correlation dimension of g-data; an abrupt increase in the correlation dimension of h-data; and combinations thereof. Analysis of e-data shows that statistically significant nonlinear structure is present during the non-seizure, transition, and seizure epochs. 
     Two sets of channel-13 EEG data from one patient are provided as examples. In FIG. 1 of the drawings, 11 shows the patient&#39;s head, looking from above. 13 shows EEG electrode positions on the patient&#39;s scalp. 15 shows a nonlinear measure of EEG data. In FIG. 2 of the drawings, C13 labels the position where the channel 13 data, which is used in this work, originates. Analysis of C13 data was chosen for these examples to demonstrate the robust removal of eye-blink artifact, which otherwise dominates channel 13 because of its proximity to the eye. This method and apparatus can be applied to data from other EEG channels, as well as to MEG data, as is apparent to those skilled in the art. Both sets of data included non-seizure, transition-to-seizure, and epileptic seizure data. The analysis included various linear measures (standard deviation, absolute average deviation, skewedness, kurtosis), plus nonlinear measures (time steps per cycle, Kolmogorov entropy, first minimum in the mutual information function, and correlation dimension). Four forms of the data were analyzed: raw EEG (e) data, artifact (f) data via application of a zero-phase quadratic filter, artifact-filtered (g) data that was the residual after subtracting f-data from g-data, and a low-pass-filtered version (h) of the g-data. The nonlinear measures clearly discerned the epileptic seizures in these examples, while none of the linear measures provided definitive seizure indication. Nonlinear tools identified seizure indicators with and without artifact removal, with and without low-pass filtering, demonstrating the robustness of these methods to noise and artifacts. Surrogate analysis of e-data showed that this data has significant nonlinear structure. 
     In the examples described herein, sixteen channels of EEG data were analyzed in the bipolar montage, as illustrated in FIG. 2. The data were retrieved in analog form from VHS tapes and converted to digital form with 12-bit precision, giving an integer between -2048 and +2047. The digital sampling rate (f s ) was 512 Hz over a total sample time of 10-23 minutes, corresponding to a total dataset size of 9.8-22.5 megabytes in binary form. Three epochs of data were examined: epileptic seizure and post-seizure, non-seizure, and transition from non-seizure state to seizure (transition). 
     It is acknowledged that to detect an epileptic seizure as it occurs, the brain wave data used would not be recorded data, but would be currently-occurring data. This data would be taken from the patient to the apparatus directly using standard EEG or MEG methods, or indirectly by transmitting the data to an apparatus remote from the patient by means such as telephone, radio, or other communications means well known to the skilled artisan. 
     Raw brain wave data contains not only signals associated with brain activity, but also contains artifacts (e.g., eye blinks, muscle twitches, chewing, etc.) that obscure the brain-wave signal. In order to observe artifact-free data and artifact data independently, the raw data must be separated into artifact data and artifact-free data. A zero-phase filter was developed and used to remove low-frequency artifacts, based on the following criterion. A zero-phase-shift filter was needed to prevent phase distortions when subtracting the filter output (the &#34;artifact&#34; data signal) from the raw data signal to yield an undistorted artifact-filtered or artifact-free data signal, because phase relationships are most important in the subsequent nonlinear analysis. Standard high-pass filter techniques do not meet this criterion. A computationally fast, simple, low-frequency signal follower was necessary to eventually apply the filter in real- or near-real time. Consequently, quadratic regression analysis was used, with the same number of data samples on either side of a central point. Other standard digital filtering methods (15) could not meet this requirement. 
     The zero-phase filter method and apparatus which may be embodied in various ways well known to one skilled in the art, such as a specially-programmed computer or a programmed integrated circuit, semi-conductor chip, or micro-processor, is as follows. For a specific channel, the EEG signal (e) at time (t) is sampled at regular intervals (t i  =i Δt) to yield a set of time serial data e i  =e(t i ). We choose a filter-window length of 2n+1 points from the time series, where n is the number of points on either side of the central point (e c ) as indicated in the sequence below. ##EQU1## 
     The data was fitted to a quadratic equation that takes the form: F i  =F(t i )=a 1  (t i  -t c )  2  +a 2  (t i  -t c )+a 3  =a 1  T i   2  +a 2  T i  +a 3 . Here, t c  =c Δt is the time at the central point, and T i  =t i  -t c . This approximation is fitted to the data, by minimizing the sum of squares of the differences between the quadratic equation, F(t), and the raw EEG data, e(t), corresponding to the minimum in the following function: ##EQU2## 
     The minimum in L is found from the condition ∂L/∂a k  =0, for k={1, 2, 3}, forming three simultaneous linear equations in three unknowns. The window-averaged artifact (F c ) is given by the fired value of the central point, F c  =F(0)=a 3 . Note that the sums over odd powers of T i  are zero and that symmetric sums over even powers of T i  (over i from -n to +n) can be converted to sums from 1 to n with T i  =iΔt, yielding a window-averaged solution for the artifact signal: ##EQU3## 
     Here, Σ i  indicates the sum over i from -n to +n. Sums over even powers of &#34;i&#34; were explicitly evaluated with standard formulae (10). The effort to evaluate F c  can be reduced substantially by computing the sums initially from Eq.2 (at c=n+1), and then using the following recursions thereafter: ##EQU4## 
     The right-hand sides of Eqs. 3-5 only involve the sums previously computed. Application of Eqs. 2-5 to the N-point set of original time serial EEG data (e i , illustrated as the dotted curve in FIG. 3a) yields an artifact dataset (f i  or f-data, illustrated as the solid curve in FIG. 3a) with (N-2n) points that contains the low frequency artifact signal. The residual signal (g i  or g-data, illustrated as the solid curve in FIG. 3b) is the difference, g i  =e i  -f i , and is a signal that is free of low-frequency artifacts. Subsequently, the g-data is processed through a standard fourth-order low-pass filter at 50 Hz (e.g., see Ref. 9) to yield artifact-filtered, low-pass-filtered data (h i  or h -data) that is free of both low- and high-frequency artifacts. Note that spike-wave phenomena at 100 Hz in h-data are attenuated by 28 db (a factor of 25), while the g-data retain the full spike-wave signals. A standard second-order, third-order, or fourth order filter at frequencies between about 35 Hz and about 60 Hz would also be effective as a low-pass filter. 
     The filter-window length (n=128) corresponds to a frequency of 2.0 Hz  =512 Hz/(2n 1)!. FIG. 3a shows an example of the application of this method, with (raw) e-data in light gray and a superimposed (dark line) artifact signal (f-data), which clearly follows the low-frequency trends. FIG. 3b shows the residual signal (g-data) for this example, as having little low-frequency component while retaining the higher frequency information. 
     For a specific EEG channel, a time history of the nonlinear measures was obtained by applying the CTSA tools to a series of 20-second analysis-windows of the four data types (e, f, g, h). These data are designated herein as x i . The length of the analysis window (w) was 10,240 points. Each analysis-window had a 5,120-point overlap with the previous (or next) analysis-window of data. This 50% overlap provides an optimal mix of new and old data for smooth time-history trend generation (2), as illustrated below. ##STR1## 
     The zero-phase quadratic filter provides artifact-filtered data with frequencies of ≧2 Hz. A heuristic for (linear) Fourier analysis is that ≧10 periods of data are required to faithfully recover cyclic information at a specific frequency. Thus,≧5 seconds of data are needed to obtain Fourier amplitude and phase information at a signal frequency of 2 Hz. However, this heuristic does not apply to nonlinear analysis. For example, 20 seconds of data are necessary to obtain consistent results for the Kolmogorov entropy. This need for longer dataset lengths (˜10,000 points) for consistent nonlinear measures conflicts with the need for shorter dataset lengths (≦5,000 points) to provide adequate resolution for the time history generation of trends. Consequently, a 20-second analysis window was used, as described above, with a 50% overlap for an effective time history resolution of 10 seconds. The nonlinear measures for each 20-second analysis window were associated with the time at the center of the analysis window, i.e., every ten seconds. Shorter or longer analysis window lengths can be used in proportion to higher or lower data sampling rates, as is obvious to those skilled in the art. 
     Many characterization tools exist for chaotic data analysis. A subset of the tools that were found in previous work to be good measures for EEG data were used in carrying out the present invention. These tools include the following: standard statistical measures (minimum, maximum, average, absolute average deviation, standard deviation, skewedness, kurtosis, time per cycle); Kolmogorov entropy and entropy spectrum; mutual information function; maximum likelihood correlation dimension and correlation dimension spectrum; surrogate generation and nonlinearity tests; and nonlinear digital filters (as discussed herein). 
     Entropy, correlation dimension, and mutual information were used in the present invention as nonlinear measures for seizure analysis. The first minimum in the mutual information defines the time scale for generating the return map for EEG dynamics. The return map underlies the correlation dimension (measure of dynamic complexity) and entropy (measure of dynamic predictability). We have applied these same measures successfully in analyzing other systems. 
     The statistical measures for the present study are obtained by standard methods (6). The maximum and minimum are obtained as maximum and minimum (respectively) over the x i  values in a time-serial window of w points. The average (x) is given by: ##EQU5## The r-th order moment (m r ) of the x-data is: ##EQU6## The absolute average deviation (a) provides a robust indicator of the x i  variability (13) and is defined as: ##EQU7## An unbiased estimate of the standard deviation (σ) is: ##EQU8## An estimate for the skewedness (s) is: ##EQU9## An estimate for the kurtosis (k) is: ##EQU10## The average cycle time (T c ) is important as a characteristic time of the nonlinear system: ##EQU11## 
     The mutual information function (MIF) is a nonlinear version of the (linear) auto-correlation and cross-correlation functions, and was developed by Fraser and Swinney (3). Mutual information measures the certainty with which a measurement can be predicted, given the outcome of another related measurement. Examples of the later include the same EEG channel at a different time, and another EEG channel at the same (or different) time. The MIF indicates the average information (in bits) that can be inferred from one measurement about a second measurement, and is a function of the time delay (number of time steps) between the measurements. The mutual information function also measures the nonlinear time dependent correlation in the same signal. For EEG data, information decay in an individual channel (univariate MIF) indicates local time scale, as the average time lag (t j  -t i ) that makes x(t i ) independent of x(t j ), and corresponds to the first (local) minimum (M i  in timesteps) in the MIF (3). For use herein, a minimum is defined as two successive decreases in the signal value, followed by two successive increases in signal value. Other definitions were tested and found to yield less consistent results. The MIF, I(Q,S), and system entropy (H) for two measurements (Q and S) are defined by: ##EQU12## 
     S denotes the whole system that consists of a set of possible messages (measurements for the value of s), s i , s 2 , . . . , s n  with associated probabilities P s  (s 1 ), P s  (s 2 ), . . . , P s  (s n ). Q denotes a second system that consists of a set of possible messages (measured values with a time delay relative to the s i  values), q 1 , q 2 , . . . , q n  with associated probabilities P Q  (q 1 ), P Q  (q 2 ), . . . , P Q  (q n ). The function P SQ  (s i , q j ) denotes the joint probability of both states occurring simultaneously. If the logarithm is taken to the base two, then H is in units of bits. Fraser and Swinney (3) describe the details for evaluating I(Q,S), including a sequence of recursive partitions in (s i , q j ) space to achieve adequate accuracy with tailoring to the local data structure. 
     The maximum-likelihood correlation dimension (D) is based on the early work by Takens (14) with modifications for noise (13): ##EQU13## where M is the number of randomly sampled point pairs, r ij  is the normalized maximum-norm distance between the (randomly chosen) i-j point pairs as defined in Eq. 17 (below), and r n  is the normalized distance (scale length) associated with noise as measured from the time serial data. The distances are normalized with respect to some nominal scale length (L O ), i.e. r ij  =L ij  /L O  and r n  =L n  /L O  with L O  as a representative scale length (typically a multiple of the absolute average deviation). The choice of scale length is a balance between a small scale for sensitivity to local dynamics (typically at L O  &lt;5a) and avoidance of excessive noise (typically at L 0  ≧a). The distances (L ij ) are defined by: ##EQU14## where m is the average number of points per cycle from Eq. 12 (i.e., m =T c ). Schouten et al. (40) describe the details for evaluating Eqs 16-17 to measure of the number of degrees of freedom in a system (e.g., the number of coupled first-order differential equations to depict the dynamics). 
     The Kolmogorov entropy (K-entropy or simply entropy) measures the rate of information loss per unit time, or (alternatively) the degree of predictability. A positive, finite entropy generally is considered to be a clear demonstration that the time series and its underlying dynamics are chaotic. An infinite entropy indicates a stochastic, non-deterministic (totally unpredictable) phenomenon. For entropy determination, one begins with two orbits on a chaotic attractor that are initially very close together. The entropy then is estimated from the average divergence time for pairs of initially-close orbits. More precisely, the entropy is obtained from the average time for two points on an attractor to go from an initial separation (L &lt;L 0 ), to become separated by more than a specific distance (L ≦L 0 ). The maximum-likelihood entropy (K): ##EQU15## with b i  as the number of timesteps for two points, initially within L&lt;L 0 , to diverge to L&gt;L 0 . The work by Schouten et al. (12), and references therein, provide details of the method. Note that the entropy used here is the order-2 Kolmogorov entropy which hereafter is called simply entropy. 
     The entropy (K) and correlation dimension (D) usually are reported in the limit of zero scale length. However, EEG data (and all biomedical data) have substantial noise. Consequently, the nonlinear measures, K and D, are reported for a finite scale length (L 0 ) that is slightly larger than the noise. Thus, the values of K and D, that are reported here, do not capture the full complexity of brain dynamics, i.e., their values are smaller than expected for the zero-scale-length limit. K and D are interpreted as nonlinear statistical indices of finite-scale dynamic structure. 
     EXAMPLE I 
     The method and apparatus of this invention are illustrated by the analysis of two datasets. Both datasets are from the same patient, who is a 20-year-old female with a lifelong history of seizures, beginning at age 4 months. The cause of the seizures is not established, although neuro-imaging studies (including computerized tomography and magnetic resonance) are normal. The seizures are poorly controlled despite treatment with various combinations of anti-epileptic drugs, which at the time of the recordings were Phenytoin, Phenobarbital, and Felbamate. The seizures are partial complex with some occasions of secondary generalization. During the seizure designated Example I, the patient was sitting up in bed, doing some neurophysiologic testing. Her EEG shows an activated pattern. She then showed automatisms with picking movements and staring, followed by vocalizations (several seconds of screams). Hyper-extended head and neck posturing followed. Her upper extremities became flexed, and then she showed clonic activity, involving abduction/adduction at the shoulders and hips. There was tonic posturing and clonic activity of all extremities. The convulsive movements were associated with high-amplitude EEG waves, involving spikes, polyspikes, and much artifact activity. As the clinical seizure spontaneously terminated, the subject was unresponsive and made loud snoring sounds. Then, the brain wave amplitudes became quite suppressed. The automatisms were associated with polyspike discharges from the left frontal region. After seizure termination, spike discharges occurred from this same region, followed by suppressed background waves. 
     The results from Example I involved four analyses (e-, f-, g-, and h-data) on the three epochs of channel 13 data (epileptic seizure and post-seizure, non-seizure, and transition from non-seizure to seizure). These three epochs of data were provided and analyzed as three separate, non-contiguous ten-minute data segments. The non-seizure data segment ended several hours before the transition data, which in turn ended ˜10 seconds before the start of the seizure data segment. The results are combined as one thirty-minute set of plots for the e-data (FIG. 4), f-data (FIG. 5), g-data (FIG. 6), and h-data (FIG. 7), with gaps in the analysis to indicate where one dataset ends and the next dataset begins. In particular, the data from 10-590 s is the non-seizure epoch with large amplitude signals at 520-600 s from chewing and drinking. The data from 610-1190 s is the (transition) period immediately before seizure. The data from 1210-1790 s includes the seizure and post-ictal phases. The various measures were obtained for every analysis-window, and the resulting values were plotted at the center of the 20-second analysis-window. 
     Each plot in FIGS. 4-7 for Example I displays the analysis-window-centered measure as a solid line. The dashed line (- - -) in each figure is the average value of the measure (from Eq. 6) over an 11-point averaging-window, plotted at the central (sixth) point of the averaging window. The dotted line (. . . ) in each figure is the corresponding sample standard deviation over this 11-point averaging-window (from Eq. 9), also plotted at the central point of the averaging-window. The scale length (L 0 ) was fixed at ˜1.4 times the absolute average deviation, as obtained by averaging over the complete non-seizure e-data, and was used in all the analyses as the reference scale length for all three data epochs. Smaller values for this scale length caused numerical problems in the determinations of the correlation dimension and the Kolmogorov entropy; larger values limited the resolution of the nonlinear measures. 
     The clinical seizure in Example I occurred from 53 to 95 s in the (third) seizure epoch (1253 to 1295s in FIGS. 4-7). Rhythmic convulsions began at 1295s, and post-ictal features appeared at 1314s. Table 1 shows features in the nonlinear measures that uniquely indicate the seizure; starred entries (*) denote no clear indicators. Two measures (the peak in Kolmogorov entropy of g-data and the peak in correlation dimension of h-data) show epilepsy onset beginning ˜30 seconds before the clinical seizure. 
     
                                           TABLE 1__________________________________________________________________________Summary of seizure indicators in Example ISpecific measure       e-data f-data  g-data h-data__________________________________________________________________________Time per cycle (T.sub.c)       *      abrupt decrease                      *      *(timesteps per cycle)              T.sub.c &lt; 200              1255-1300sEntropy (K) abrupt increase              abrupt increases                      abrupt increase                             abrupt increase(bits/second)       K &gt; 0.063              K &gt; 0.008                      K &gt; 0.056                             K &gt; 0.016       1230-1350s              1230-1240s                      1220-1340s                             1230-1320s              1270-1275s              1280-1300s1.sup.st Min. in MIF (M.sub.1)       *      abrupt decrease                      *      abrupt decrease(timesteps)        M.sub.1 &lt; 85   M.sub.1 &lt; 20              1290-1310s     1270-1280sCorrelation dimension (D)       abrupt increase              abrupt increase                      abrupt increase                             abrupt increase       D &gt; 5  D &gt; 5.6 D &gt; 3.2                             D &gt; 2       1270-1305s              1340-1345s                      1235-1340s                             1220-1325s__________________________________________________________________________ 
    
     EXAMPLE II 
     The dataset designated Example II is from the same patient as Example I, who is a 20-year-old female with a lifelong history of seizures as previously described in Example I. During the seizure designated Example II, the patient is lying in bed, awake with her right upper extremity in a flexed posture. The EEG shows spike-wave discharges in the left hemisphere, after which the brain waves become very sharp, dominated by high frequency activity and artifacts. The patient showed eye deviation to the right and some head turning to the right, with head jerking also to the right, but without any usual posturing of the right upper extremity. The eye/head turning is preceded by a high-frequency vocalization. After the clinical seizure spontaneously terminated, the EEG shows high amplitude wave slowing and subsequent amplitude suppression. The subject remained awake during the seizure but was poorly responsive. 
     The results from Example II for channel 13 involved four analyses (e-, f-, g-, and h-data) on one 23-minute dataset that included all three epochs of channel 13 data (epileptic seizure, non-seizure, and transition from non-seizure to seizure). The non-seizure period spanned 10-400s. The transition period occurred over 410-1200s. The seizure began at 1245s and ended at 1290s. The patient was aphasic at 1300s, with head movements and verbalization at 1315s. 
     The scale length (L O ) was fixed at ˜1.0 times the absolute average deviation, as obtained by averaging over the non-seizure e-data, and was used in all the analyses as the reference scale length for all three data epochs. The results were obtained as before, and arc plotted for e-data (FIG. 8), f-data, (FIG. 9), g-data (FIG. 10), and h-data (FIG. 11). The seizure is indicated clearly by several unique features in the nonlinear measures, as shown in Table 2; starred entries (*) denote no clear indicators. None of these measures show the epilepsy onset before the clinical seizure. 
     
                                           TABLE 2__________________________________________________________________________Summary of seizure indicators in Example IISpecific measure       e-data f-data g-data  h-data__________________________________________________________________________Time per cycle (T.sub.c)       *      *      abrupt increases                             abrupt increases(timesteps/cycle)         T.sub.c &gt; 24                             T.sub.c &gt; 62                     1255-1275s                             1250-1275s                     1290-1300s                             1290-1300sEntropy (K) abrupt increase              abrupt increase                     abrupt increase                             abrupt increase(bits/second)       K &gt; 0.089              K &gt; 0.006                     K &gt; 0.1 K &gt; 0.014       1255-1290s              1270-1330s                     1255-1290s                             1250-1320sl.sup.st Min. in MIF (M.sub.1)       *      abrupt decrease                     *       *(timesteps)        M.sub.1 &lt; 80              1250-1300sCorrelation dimension (D)       abrupt increase              abrupt increase                     abrupt increase                             abrupt increase       D &gt; 4  D &gt; 4.5                     D &gt; 3   D &gt; 2.5       1250-1300s              1280-1300s                     1240-1310s                             1240-1315s__________________________________________________________________________ 
    
     In Example I and Example II, abrupt increases in both the Kolmogorov entropy and correlation dimension indicate both epileptic seizures, although the seizures are clinically very different, as described further herein. Abrupt decreases in (T c )number of timesteps per cycle (for f-data) and in (M 1 ) the first minimum in the mutual information function (for f- and h-data) also indicate the first seizure (Example I). An abrupt decrease in M 1  (f-data) and abrupt increases in T c  (g- and h-data) mark the second seizure (Example II). These indicators of seizure are summarized in Tables 1 and 2. The difference in seizure indication (T c ) for the two seizures implies that care is needed in cataloging such features. 
     It has been shown by the foregoing that certain indicative trends such as sudden increases and sudden decreases in time serial sequences of nonlinear measures hereinbefore described are seizure indicators. 
     By comparing indicative trends in non-linear measures of the patient&#39;s brain wave data with known seizure indicators, it can be clearly determined by whether the indicative trends correspond with known seizure indicators whether a seizure is occurring in the patient. 
     Tables 1 and 2 and FIGS. 4 -11 clearly show that epileptic seizures are indicated by a number of trends in nonlinear measures of brain-wave data including the following: an abrupt decrease in the number of timesteps per cycle for f-data 101; an abrupt increase in the number of timesteps per cycle for g-data 103; an abrupt increase in the number of timesteps per cycle for h-data 105; an abrupt increase in the entropy of e-data 107; an abrupt increase in the entropy of f-data 109; an abrupt increase in the entropy of g-data 111; an abrupt increase in the entropy of h-data 113; an abrupt decrease in the first minimum in the mutual information function for f-data 115; an abrupt decrease in the first minimum in the mutual information function for h-data 117; an abrupt increase in the correlation dimension of e-data 119; an abrupt increase in the correlation dimension of f-data 121; an abrupt increase in the correlation dimension of g-data 123; an abrupt increase in the correlation dimension of h-data 125; and combinations thereof. 
     While there has been shown and described what are presently considered the preferred embodiments of the invention, it will be obvious to those skilled in the art that various changes and modifications can be made therein without departing from the scope of the inventions defined by the appended claims.