- Research
- Open Access
Wavelet-based Gaussian-mixture hidden Markov model for the detection of multistage seizure dynamics: A proof-of-concept study
- Alan WL Chiu^{1}Email author,
- Miron Derchansky^{2},
- Marija Cotic^{2, 3},
- Peter L Carlen^{2},
- Steuart O Turner^{1} and
- Berj L Bardakjian^{3}
https://doi.org/10.1186/1475-925X-10-29
© Chiu et al; licensee BioMed Central Ltd. 2011
- Received: 26 October 2010
- Accepted: 19 April 2011
- Published: 19 April 2011
Abstract
Background
Epilepsy is a common neurological disorder characterized by recurrent electrophysiological activities, known as seizures. Without the appropriate detection strategies, these seizure episodes can dramatically affect the quality of life for those afflicted. The rationale of this study is to develop an unsupervised algorithm for the detection of seizure states so that it may be implemented along with potential intervention strategies.
Methods
Hidden Markov model (HMM) was developed to interpret the state transitions of the in vitro rat hippocampal slice local field potentials (LFPs) during seizure episodes. It can be used to estimate the probability of state transitions and the corresponding characteristics of each state. Wavelet features were clustered and used to differentiate the electrophysiological characteristics at each corresponding HMM states. Using unsupervised training method, the HMM and the clustering parameters were obtained simultaneously. The HMM states were then assigned to the electrophysiological data using expert guided technique. Minimum redundancy maximum relevance (mRMR) analysis and Akaike Information Criterion (AICc) were applied to reduce the effect of over-fitting. The sensitivity, specificity and optimality index of chronic seizure detection were compared for various HMM topologies. The ability of distinguishing early and late tonic firing patterns prior to chronic seizures were also evaluated.
Results
Significant improvement in state detection performance was achieved when additional wavelet coefficient rates of change information were used as features. The final HMM topology obtained using mRMR and AICc was able to detect non-ictal (interictal), early and late tonic firing, chronic seizures and postictal activities. A mean sensitivity of 95.7%, mean specificity of 98.9% and optimality index of 0.995 in the detection of chronic seizures was achieved. The detection of early and late tonic firing was validated with experimental intracellular electrical recordings of seizures.
Conclusions
The HMM implementation of a seizure dynamics detector is an improvement over existing approaches using visual detection and complexity measures. The subjectivity involved in partitioning the observed data prior to training can be eliminated. It can also decipher the probabilities of seizure state transitions using the magnitude and rate of change wavelet information of the LFPs.
Keywords
- Feature Space
- Hide Markov Model
- Wavelet Coefficient
- Seizure Detection
- Wavelet Feature
Background
Epilepsy is one of the most common neurological disorders, affecting over 50 million people worldwide. The disorder is characterized by spontaneous, recurrent, seemingly unpredictable symptoms called seizures [1, 2]. A seizure can be defined as the sudden manifestation of lowered complexity synchronized rhythmic activities across populations of neurons [3]. Epilepsy affects motor and speech, as well as other cognitive functions that, if untreated, can lead to permanent damage to the brain. Time-frequency representation (TFR) is an important marker for understanding the progression into seizure onsets [4]. The progression to the seizure onset is associated with the entrainment of neuronal population firing. In particular, the TFR of epileptiform oscillation has been suggested as a useful tool in localizing regions of seizure onsets and in understanding the mechanisms behind seizure generation [5]. The current methods for detecting the state transitions of seizure episodes based on TFR usually involve the computation of state-specific features through supervised learning techniques [6–10]. In general, supervised learning strategies require certain knowledge of the system so that the data can be separated into different states based on their known dynamics before the training process. To date, a great deal of subjectivity is required for the implementation of these algorithms since the desired solution for detection must be defined by the experimenter.
Seizure detection refers to the identification of seizure onsets a few seconds before the observable behavioral changes [11, 12]. Several effective supervised pattern recognition strategies have been developed for seizure detection. Multi-layered networks were first introduced to analyze EEG data pertaining to seizure phenomenon in the mid-1990s [13, 14]. Various methods such as autoregressive models [15, 16] to more advanced techniques such as support vector machines [17, 18] were also proposed. The feature space for these approaches ranged from spectrogram [19], dominant frequency, power and amplitude [20] to time frequency distribution [21] such as wavelet transform based approximate entropy [22, 23]. It has been reported that frequency content of neuronal electrical activity changed significantly during the progression of a seizure, both in the interspike interval and in the intraburst dynamics [8, 24]. The major disadvantage of these supervised methods is that their performances can only be as good as the initial data separation criteria. Therefore, it is essential to utilize an unsupervised learning paradigm that transcends these restrictions.
An unsupervised probabilistic approach for the detection of seizure-like events (SLEs) in vitro extracellular local field potentials (LFPs) seizures using hidden Markov model (HMM) [25, 26] along with clustering of wavelet features is proposed. The in vitro model, emulating human epilepsy, provides a platform for testing the seizure dynamics detection algorithm. The HMM is not meant to reproduce the exact electrophysiological recordings of the brain. Instead, it is used to capture the essential TFR characteristics in the progression of SLEs and to estimate the state transitions as a multi-stage process. The HMM has an advantage over the supervised approaches because it does not require prior manual separation of data into different dynamics. The current approach of detecting seizure events using Markov models involves the estimation of either two (seizure and interictal) [27] or three (baseline, detected and seizure) [28] distinct states. Even though these proposed methods appear to detect seizure onsets, they failed to address the possibility of having multiple distinctive dynamics between non-ictal (interictal) and chronic seizure events, which may be an important aspect for the development of seizure therapy techniques. The training process of the HMM is an unsupervised approach. However, a certain amount of bias can be achieved by making an informed choice on the assignment of the model states to the electrographical activities after the unsupervised training process is completed.
To determine the optimal HMM topology for seizure detection, two methods were proposed and compared. First, the performance of the trained HMM was evaluated on the validation set to determine the suitable HMM topology. Second, minimum redundancy maximum relevance (mRMR) analysis [29] and Akaike Information Criteria (AICc) [30, 31] were used to find a suitable feature space and optimum model by balancing the log-likelihood (LL) against the number of model parameters. Furthermore, the performances of HMMs were compared with the wavelet-based supervised machine learning techniques [6, 7] based on the sensitivity and specificity of chronic seizure detection, the detection delay and the optimality measure [32]. We hypothesized that using appropriate wavelet features, the HMM can detect the various stages of SLEs at least as well as, if not better than, the supervised machine learning algorithms. We also hypothesized that the optimal HMM topology can illuminate multiple transitional characteristics in the tonic firing phrase leading to the onsets of chronic seizure activities.
Methods
A. Tissue preparation and data acquisition
Hippocampal slice recordings were obtained from eight Wistar rats (17-25 days old). The animals were anaesthetized with halothane and decapitated in accordance with the Canadian Animal Care Guidelines. The brains were promptly dissected and maintained in ice-cold (4°C) artificial cerebrospinal fluid (aCSF) for four to five minutes. Each brain was incised in a horizontal manner in accordance with the procedure outlined by [33, 34]. The dorsal cortex of each hemisphere was cut parallel to the rostral/caudal axis and glued dorsal side down to an aluminium block, with caudal end towards the blade. The block was secured at a 12-14° angle, and brain slices of 400 μm thick were sectioned using a vibratome. Next, slices were maintained at room temperature in oxygenated "standard" aCSF (95% O_{2}, 5% CO_{2}) for a minimum of one hour prior to recording. The composition of the "standard" aCSF was as follows (in mM), NaCl (125), KCl (5), NaH_{2}PO_{4} (1.25), MgSO_{4} (2), CaCl_{2} (2), NaHCO_{3} (25) and glucose (10). The pH was approximately 7.4, with osmolarity in the range of 300 ± 5 mOsm. During the data acquisition stage, slices were transferred to the fusion chamber maintained at 30°C (Medical Systems Corp., Model PDMI-2, Harvard Apparatus, St. Laurent, Quebec, Canada). The pyramidal cells were visualized with an upright microscope (BX51, Olympus, Melville, NY, USA) using infrared imaging with differential interference contrast (IR-DIC) under 40 × magnification (water-immersion objective) with an OLY-150IR camera-video monitor unit (Olympus) [35]. Pyramidal cells were identified based on their characteristic spike frequency of 15.0 ± 5 Hz, their morphological features and the general location of the electrode placement. At the time of recording, spontaneous SLEs were induced by perfusing the slice with low-Mg^{2+} ACSF (containing in mM: 123 NaCl, 5 KCl, 1.5 CaCl2, 0.25 MgSO4, 25 NaHCO3, 1.2 NaH2PO4 and 15 glucose), or by tetanic stimulation of the CA3 region in "standard" aCSF, once every 10 min (80 Hz, 1 second duration), using a Grass S44 stimulator (Grass Medical Instruments, West Warwick, Rhode Island). The reduction of extracellular Mg^{2+} concentration has long been known to enhance neuronal excitability by decreasing membrane surface charge screening and, thereby, facilitating the activation of inward currents in addition to increasing the synaptic excitation by unblocking the NMDA receptor [36]. The population dynamic of the LFPs were measured using an aCSF-filled borosilicate glass pipette located in stratus pyramidal of the CA1 region of the hippocampus. Data was acquired using a custom-made DC differential amplifier with a lowpass filter (corner frequency 400 Hz), digitized at 1 kHz by a Digidata 1322 (Axon Instruments, Union City, California). The whole-cell patch-clamp recordings were performed in the current clamp configuration using an Axopatch 200B amplifier (Axon Instruments, Union City, CA, USA). The whole-cell patch pipette solutions contained (contained in mM: 8 NaCl, 0.001 CaCl_{2}, 10 Na-Hepes, 5 KCl, 140 potassium gluconate, 1 MgCl_{2}, 0.3 Na-GTP and 2 Na-ATP). The perforated patch pipette solution (containing in mM: 50 KCl, 2 Hepes, 0.1 EGTA and ≤50 μg/ml gramicidin).
Characteristics of the data set
Characteristics | |
---|---|
Duration of EEG recording | 121 m |
Number of seizures | 50 |
Duration of non-ictal activity | 30 m |
Mean ± Stdev of tonic firing | 49.8 ± 48.0 s |
Mean ± Stdev of chronic seizure | 73.6 ± 32.4 s |
Sampling rate | 1024 Hz |
B. Wavelet-based hidden Markov model seizure detector
The HMM is a powerful technique for the estimation and analysis of state transitions in any potentially multi-stage process. It is particularly useful in describing the progression of time-varying phenomenon in which the observed signals are emitted from the underlying dynamical states whose detailed generating mechanism is unknown or hidden. This is also important because the underlying dynamics of the brain is still relatively unknown.
Feature space
Feature space for the HMM
Bands | Frequency Range (Hz) |
---|---|
Delta | <4 |
Theta | 4 - 8 |
Alpha | 8 - 15 |
Beta | 15 - 40 |
Gamma | 40 - 100 |
Super gamma | 100 - 250 |
Fast ripple | 250 - 400 |
HMM topology
The HMM topology is defined by the number of states (Q) in the HMM and the number of basis functions (M) used to represent the feature space. The value Q can be interpreted as the potential number of distinct dynamics that may exist within a SLE. The value M can loosely be interpreted as the complexity of the feature for each possible model state.
In this study, Q could go up to 10, allowing for the detection of potential multi-stage SLE processes. The transition of the model states was also assumed to follow a static probability distribution such that the transition probability was independent of time.
Training and validation
The EM algorithm would typically take only a few seconds to complete. From the learning process described above, it should be obvious that if the number of clusters (M) and the number of possible HMM states (Q) were allowed to increase unrestricted, the LL would continue to improve at the expense of over-fitting the data.
The model with ΔAICc < 0.25 while having the least number of model parameters (K) was then denoted as the optimal HMM (HMM_{AIC}).
C. Statistical test and optimality index
The HMM topologies were evaluated according to their abilities to detect non-seizure events, different stages in the tonic activities as well as chronic seizures. After the unsupervised training, the marginal posterior distribution γ _{ i } (t) for each state i was computed by evaluating the HMMs on the test data. The detection of distinct initiation and termination of seizure dynamics as they evolved with time [42] was also considered in the form of early and late tonic spikes. An expert-guided state assignment procedure was used to identify non-ictal to ictal transitions using short time maximum Lyapunov exponent estimator derived from Rosenstein's algorithm [43]. The dynamics of chronic seizure period was first assigned to the most probable HMM state after training. Based on the state progression in the transition matrix, the tonic firing and non-ictal states were assigned in reverse order to HMM states before chronic activities; the postictal activity was assigned to the appropriate state forward-in-time to the HMM state after chronic activities.
Results
Comparison of the performance of HMM_{opt7D} and HMM_{opt14D} was done using a five-fold cross-validation technique. The model parameters of the HMMs were identified such that the best statistics for seizure detection in terms of optimality index (O) can be produced in the validation data set.
Next, the HMM approach was also compared against the supervised approach using identical wavelet coefficient feature set, in the form of a fully-supervised wavelet artificial neural network (WANN) seizure detection method designed by our group [6, 7]. The training data for the WANN was created by first identifying the EcSOT, the data prior to the EcSOT was separated into 30 s intervals based on the assumption that there may be distinct changes in LFP leading to the EcSOT. Based on one-way ANOVA statistical analysis, the WANN and HMMopt7D did not show significant difference in their optimality index (0.756 ± 0.059 and 0.665 ± 0.260, respectively).
Performance measure for supervised and unsupervised seizure detection approach
WANN | HMM _{opt7D} | HMM _{opt14D} | |
---|---|---|---|
Sensitivity (TP) | 73.1 ± 3.7% | 69.8 ± 20.3% | 86.7 ± 27.2% |
Specificity (TN) | 91.7 ± 4.4% | 88.1 ± 20.9% | 98.6 ± 7.7% |
Detection delay (ΔT) | 3.95 ± 3.38 s | 8.30 ± 15.33 s | -0.68 ± 10.07 s |
Optimality index (O) | 0.756 ± 0.059 | 0.665 ± 0.260 | 0.915 ± 0.302 |
Feature selection using mRMR method
Order | V _{F} /W _{c} | Frequency Range (Hz) |
---|---|---|
1 | 0.497 | 8 - 15 |
2 | 0.436 | 15 - 40 |
3 | 0.400 | 100 - 250 |
4 | 0.331 | 4 - 8 |
5 | 0.308 | 40 - 100 |
6 | 0.308 | 250 - 400 |
7 | 0.266 | <4 |
A summary of HMM performance measures
Features | Wavelet Coefficients Only | Wavelet Coefficients + Rate of Change | ||
---|---|---|---|---|
Validation Set | mRMR and ΔAICc | Validation Set | mRMR and ΔAICc | |
7-D (Q = 5, M = 4) | 2-D (Q = 3, M = 2) | 14-D (Q = 8, M = 3) | 4-D (Q = 5, M = 3) | |
Sensitivity (TP) | 69.8 ± 20.3% | 80.9 ± 34.4% | 86.7 ± 27.2% | 95.7 ± 14.0% |
Specificity (TN) | 88.1 ± 20.9% | 94.8 ± 15.6% | 98.6 ± 7.7% | 98.9 ± 6.5% |
Detection delay (ΔT) | 8.30 ± 15.33 s | 3.79 ± 8.67 s | -0.68 ± 10.07 s | -2.03 ± 7.10 s |
Optimality index (O) | 0.665 ± 0.260 | 0.813 ± 0.247 | 0.915 ± 0.302 | 0.995 ± 0.129 |
Discussion
The administration of a therapeutic intervention, such as electrical stimulation, may be effective in preventing seizures before and during the early stages of the seizure onset [45]. The success of a real-time closed-loop seizure prevention method depends on the time available between the early seizure detection and the manifestation of ictal onset. Many early seizure detection algorithms have been proposed [9, 15, 23, 32, 46–50]. The application of HMM for seizure dynamics detection was inspired by the relatively poor objective criteria for identifying the precise period of preictal interval in supervised learning. Here, an unsupervised training strategy with expert guided state assignment of HMM is proposed where the best rule to represent the wavelet features of seizure progression can be identified. One of the major criteria for selecting an appropriate seizure detection algorithm for a real-time seizure intervention system is the available time for the detection of the impending ictal onset. In this paper, HMMs were created utilizing different feature vectors to characterize the dynamics of SLEs. A motivation behind this work is to determine whether an unsupervised method can produce an accurate seizure detector with a high optimality index. Furthermore, feature selection based on the mRMR criteria and topology selection based on ΔAICc were implemented to evaluate the ability of the HMM to detect multi-stage dynamics leading to chronic seizure onset by measuring the sensitivity, specificity, detection delay and the optimality index.
The unsupervised learning strategy of the HMM involves the estimation of the model parameters through the maximization of the LL function. The training data consists of the wavelet-based features from 20 SLEs. Unlike other recent approaches that assumed a fixed number of states (such as interictal, preictal and ictal) in the model [28], the total number of hidden states in the HMM in this study was allowed to vary in an unsupervised manner. It is logical to expect that if more states are allowed, the better the model would match the observations. However, increasing the possible number of hidden states would lead to over-fitting, hence reducing its ability to generalize. To alleviate this problem, we need to find out the optimal HMM topology defined by the number of states (Q) and the number clusters in the feature space (M) that would be able to generalize well.
The first method we tried was to set aside a portion of the data for validation purpose. The objective was to get the Q and M combination that would give the highest optimality index in the validation set. The optimal HMM (HMM_{opt7D}) created using only wavelet coefficient features had five states (Q = 5) with each feature space modeled by four clusters (M = 4). If the rate of change of the wavelet coefficients was also included in the feature space, the optimal HMM (HMM_{opt14D}) would consist of eight states (Q = 8) with the feature space modeled using three clusters (M = 3). The HMM_{opt14D} is superior to the HMM_{opt7D} not only because it has a higher optimality index (0.915 ± 0.129, compared to 0.665 ± 0.260), but also because it is more robust in identifying multiple distinct dynamics between non-ictal and ictal events. The detection of early and late tonic firing activities prior to the chronic onset in vitro also became possible. While the training process of the HMM was not constrained to follow a unidirectional state transition, the state transitions leading to the ictal onset often possessed some unidirectional progress. Once the HMM_{opt7D} output moved away from the interictal state, it must go through the whole seizure progression before returning to interictal. This would then increase the number of false detection in HMM_{opt7D}, as indicated by the results shown in Table 3. On the other hand, some early tonic firing state in the HMM_{opt14D} was allowed to revert back to interictal directly. However, once it had advanced past the early tonic state, it could not revert back to non-ictal activities. The HMM_{opt14D} was successfully tested on non-seizure or interictal burst data, demonstrating a mean accuracy of over 97%. Next, the unsupervised HMM and supervised WANN approaches [6] were compared. The two methods differ in the way that the parameters are obtained. The parameters of the HMM were updated in an iterative manner until no significant improvement in LL was achieved. The supervised WANN approach, on the other hand, required that the human user separated the data into different training groups. The WANN parameters were updated iteratively based on the partial derivative of error with respect to the weights. By definition, the performance of any supervised learning algorithm can be no better than the initial separation of seizure states by the human expert's "Gold Standard". Since the human user has access to the entire observation before marking the chronic onsets, retrospective bias exists in any supervised learning algorithm [28]. This retrospective bias can be eliminated with an unsupervised algorithm such as HMM. The HMM implementation is superior to the WANN because it can distinguish between the early and late tonic firing without having to define them before training.
The second method to reduce the complexity of the HMM based on mRMR feature selection criteria and ΔAICc topology selection was evaluated. The mRMR analysis showed that activity in the alpha (8 - 15 Hz) and beta (15 - 40 Hz) range has the largest mutual information quotient (V _{ F } /W _{ c }) of 0.497 and 0.436 respectively. This result is consistent with the existing literature showing that the alpha and beta frequency bands exhibit considerable difference in the signal complexity between healthy subjects, epileptic subjects during a seizure-free interval, and during seizure [8]. Two new feature spaces were constructed: One consisted of 2-D wavelet coefficients and one consisted of 4-D wavelet coefficient with rate of change information. Using these new feature spaces, HMMs with different topologies were created using unsupervised learning. Since having large number of Q and M often lead to the curse of dimensionality resulting in over-fitting, AICc was used to select the appropriate model topology by balancing the goodness of fit with the number of parameters used. We found that many Q and M combinations were able to achieve similar levels of AICc; the optimal HMM was selected as the model with the smallest number of parameters while maintaining a difference of <0.25 from the minimum AICc. The HMM of 2-D reduced features consists of three states (Q = 3) with two clusters (M = 2). One of these three states reflects the dynamics of both tonic firing and postictal activities (Figure 8a). Because of the small transition probability (a _{ ij }= 0.001) from the tonic/postictal back to interictal state, it typically would take a much longer time for the model to return to the proper interictal state after chronic seizure. This has been the source for most of the misclassification in the non-ictal activity using this model. The HMM model of 4-D reduced features consists of five states (Q = 5) with three clusters (M = 3). Again, by including the wavelet rate of change information, this model gave the best overall performance with O = 0.995 ± 0.129, even though the use of AICc does not warrant an improvement in seizure detection performance. The AICc simply offers a much simpler alternative to selecting the optimal HMM topology. We were able to more easily and more quickly create a HMM seizure detector with fewer number of model states and feature clusters with similar performance level.
The interpretation of early and late tonic firing state detected using HMM_{AIC} in terms of the underlying intracellular whole-cell measurement was investigated. When the model posterior probabilities were plotted against the corresponding intracellular whole-cell recording, we found a significant overlap (>85%) between the late tonic state and the intracellular pre_{d} activity. It was also observed that the early hyperpolarizing activity (pre_{h}) could not be distinguished from the interictal activities.
The application of HMM is based on the assumption that state transitions in seizure generation follow first-order Markov processes. Depending on the sampling period of the signal and the available history of HMM output, it is likely that neurodynamic would depend on more than one previous sample in time. This work can be extended to incorporate additional states in the past for the estimation of state transitions, which can be achieved through modification of the conditional state transition probability equation such as the hidden semi-Markov model [51] where state transition depends on the lapsed time since entering the current state. This model is also appropriate because the underlying process of seizure generation may not have a geometrically distributed duration. Another possible improvement is to include other types of features such as multi-site coherence in the feature space, since the manifestation of epilepsy typically involved progressive global entrainment. Preliminary analysis on the analysis of clinical seizure data from intracranial EEG measurement using HMM also showed promising results [52].
Conclusions
Based on the analysis of optimality index, the implementation of hidden Markov model as a seizure dynamics detector offers significant improvement over existing approaches based on human visual classification and supervised connectionist perspectives. The subjectivity involved in partitioning the observed data into target states prior to training is eliminated. This model is able to estimate the parameters needed to best fit the observed data depending on its specified topology. Once the unsupervised training is completed, the assignment of the model state to the electrophysiology data is guided by a human expert. To alleviate the curse of dimensionality, feature selection based on minimum redundancy maximum relevance and topology selection based on Akaike information criteria are implemented without jeopardizing the sensitivity, specificity and early detection time of the final model. A five-state hidden Markov model was created, capable of detecting chronic seizures with 95.7% sensitivity and 98.9% specificity. It was also able to detect early and late tonic firing activities that correlate with the intracellular whole-cell dynamics prior to chronic seizure onset. Such a model would potentially allow the researchers to decipher possible sequence of distinct dynamic modes leading to seizure onsets.
Declarations
Acknowledgements
The project described was supported by Grant Number P20RR016456 from the National Center for Research Resources. The authors would also like to acknowledge the Canadian Institutes of Health Research (CIHR), the Natural Science and Engineering Research Council (NSERC) of Canada and the Louisiana Board of Regents (LEQSF(2007-10)-RD-A-20) for their financial support, as well as Dr. Geoffrey Hinton from the University of Toronto for his insightful feedbacks.
Authors’ Affiliations
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