Fuzzy Logic in Neurophysiology: A Case Study
Goran Trajkovski, Bojan Cukic Dept. of Computer Sci. and El. Eng. West Virginia University, PO Box 6109 Morgantown, WV 26506-6109, USA Email: {goran, cukic}@csee.wvu.edu
Georgi Stojanov Faculty of Electrical Engineering "Sv Kiril i Metodij" University, PO Box 574 Skopje, MK 91000, Republic of Macedonia Email:
[email protected]
Abstract The Contingent Negative Variation Potentials (CNV) feature slow shifts in brain potentials due to efferent stimuli. These waves are often considered to be a relevant measure of the learning capabilities of an individual.
µV
In order to be able to conduct a number of experiments whose crucial step is the detection of CNV in the brain waves (such as the Dynamic CNV experiment), fast, simple and reliable automatic classification algorithm for wave classification/CNV detection is needed. In this paper, fuzzy logic rules, motivated by an instance of an expert's colloquial explanation, are used to detect whether a given potential is a CNV wave. The results obtained using the fuzzy approach in detection are compared with the neural network approach.
1. Introduction
In many fields of the medical sciences (and in many others, especially in most social sciences), the definitions of certain phenomena are rather vague, if any. Most of the time the definitions are given in a form of assertions vaguely explaining selected features of the problem at hand.
se c Figure 1. A typical CNV waveform
Having seen lots of samples indicating existence/absence of an observed phenomenon (e.g. EEG, EKG etc), medical experts in the corresponding field develop ability to recognize certain patterns. They are able to tell the EKG from a healthy young man from the one of a post-stroke elderly woman, or to locate cancer by the means of X-ray only. They do that following some learned, implicit rules, despite the fact that there are not sharp definitions of the above notions in the sense that there are not well-defined parameters that can be measured and inferred upon. Using the experts in a certain field in order to be able to detect certain phenomena is usually a very costly and timeconsuming process. Engineers tend to ease the procedures,
where possible, and come up with algorithms that can minimize or even eliminate the presence of the expert in the detection process. That is of a great help to the medical procedures (treatments, experiments, etc), especially if they are time-critical. This paper discusses the problem of automatic detection of Contingent Negative Variation (CNV) potentials in planning the Dynamic CNV (DCNV) experimental procedure [2]. The experiment itself is a modification of the 1964 procedure that Walter developed in order to investigate some features of learning in humans [9]. His experiment consisted in filtering some low potentials from the EEG signal at humans while they were asked to press a button as soon as possible after the second stimulus in the stimulus-stimulus-response experimental setup. He discovered that these (so called CNV) potential appear after the subject of the experiment learns when to expect the second, imperative stimulus, since in the experiment it followed the first, warning signal in exactly 2 seconds.
One of the most important procedures needed to carry out the DCNV experiment in a timely manner is the automatic detection of the CNV in the waveform of the current run. This experiment is only one of the many that need simple, fast and reliable detection of CNV in order to study the learning phenomena in humans [5]. All of the above served as motivation to initiate an effort to contribute towards the fast, timely and reliable tool for CNV detection. Asked to comment whether a certain waveform in terms of the parameters of the ramp-model (shown in Fig 2. and explained in the next section), is a CNV, an CNV expert gave the following a statement: "If the angle ϕ, the difference a-reff0, and the amplitude A are large enough, then the wave is a CNV." Statements like this one are motivating a fuzzy approach in solving the problem of defining and classifying waveforms [3], since they account for the fuzziness of the natural language.
The paper is organized in the following way. Section 2 discusses the essential moments that motivated our approach. Section 3 gives a short survey of the background and the related work in the field. Section 4 presents the fuzzy approach in CNV detection, whereas the last section summarizes the results and the conclusions of the work done within the scope of this paper.
S1
S2
µV
A
ϕ a
b = tan ϕ
reff0
2. Motivation
|S| sec
This section discusses the motivations underlying our investigation in the implementation of the fuzzy paradigm in the area of detection of CNV. The DCNV experiment [2, 4, 6] consists of a series of "Walter"-like stimuli setups, which consist of warning and imperative stimuli if the brainwaves do not contain CNV, or of a warning stimulus if they do. The idea underlying the experiment is fairly simple: until the subject learns when to expect the second stimulus (until the potentials that are filtered do not contain CNV), the second stimulus is produced 2 seconds after the first one. When he learns the pattern, the second signal is omitted until he forgets the pattern (until there is no CNV in the waveform). After that, the imperative stimulus is produced again by the experimentator's setup and so on till the end of the experiment (usually 50 trials in a row).
Figure 2. The ramp-like model of a CNV wave.
3. Background and related work
This section surveys the most important moments and facts in the area of the ERP (Evoked Response Potentials). Brain potentials can be classified into two groups according to the cause of their appearance: spontaneous and eventrelated [5]. The event-related potentials appear due outer stimuli, and can be anticipatory or evoked. The anticipatory potentials appear before the correspondent event, thus
representing the individual's expectation and/or motor preparation process in the brain. The ERPs, on the other hand, are due to some efferent or afferent stimuli or psycho-physiological event. A large subclass of the ERP potentials is formed by the slow brain waves, which are said to be the manifestations of various psychological states due to somatosensory, mental, auditory, or visual stimuli. CNV waves have been initially reported in [9], using the so-called classical CNV paradigm experimental setup explained in the introductory section. Negative variation in the brain potential between the two stimuli is a relevant indicator that the subject learned when to expect the imperative signal [1, 6]. The CNV is usually defined as a negative shift of the cortex potential between the two stimuli. Therefore, the stimuli are also referred to as expectation waves. If the wave is CNV, then the negative shift in the potential appears between the stimuli. The wave increases monotonically, and the shift vanishes after the second signal [8]. The CNV classification problem requires setting the relation between the parameters, so that it can be detected whether a wave is CNV. The parameters taken into consideration in the ramp-like model are shown in Fig. 2. The reference zero reff0 represents the mean potential before the warning stimulus occurs. The initial shift a represents the change in the potential immediately following the warning stimulus. b is the slope of the wave in the inter-stimulus interval, and it is equal to the tangent of the angle ϕ. Finally, A is the amplitude of the wave in the moment when the imperative stimulus occurs [7]. The parameters a and b are obtained by linear regressive interpolation in the inter-stimulus interval of length |S|. The proposed method uses the above parameters, their ranks (as referred in the literature), and suitably defined fuzzy membership functions to approach the problem of determining whether a wave is CNV.
4. The fuzzy approach and its uniqueness
Here we present the details of our fuzzy based system for CNV detection. In the DCNV experimental setup a feedback makes the occurrence of the imperative stimulus dependent on the
current status of the CNV waveform. Various parameters can be measured during these experiments. Among them, the most relevant seem to be: • the number of runs until the subject learns the interconnectedness of the stimuli, • the average number of runs needed for the subject to learn the procedure, and • the average number of runs without the imperative stimuli to forget the relation. Taking into account the CNV expert's 'definition' of the CNV waveform (italicized text in Section 2), we define the fuzzy memberships for ϕ, a-reff0 and A to be continuous functions. These consist of three linear segments. Two constant segments are equal to 0 and 1, and the third segment 'connects' them, thus forming an angle α with the positive part of the variable range axis. Parameter δ is the value that maps to 0.5. Since the membership functions are piece-wise linear, the membership values are easy to compute. For the universes of discourse of each of the variables, we use the range of all the values that parameters can assume. The values α and δ (see Fig. 3) for each of the variables are set to the values that CNV expert suggested as minimal in all the observed waveforms (with and without CNV). They are given in Table 1 of the appendix.
µϕ 1
.5
30 -90o
O
200
900
ϕ(deg)
Figure 3. Graph of the membership function for the variable ϕ (α α=30 and δ=200)
Based on the defined membership functions for all the variables, we construct a membership function µ over the Cartesian product of the universes of ϕ, a-reff0 and A, as given below:
µ(x,y,z)=max{min{µϕ(x), µa-reff0(y)}, min{µϕ(x),µA(z)}, min{µa-reff0(y), µA(z)}},
where x, y, and z are the measured parameters of the waveform. After a given input triplet is evaluated, we take its 0.5-cut to be the CNV waves.
5. Results and conclusion
The results of the implementation of the fuzzy detection system are presented in this section. These results are compared with the results obtained by using a neural network approach towards the same goal. For the purposes of testing the automatic CNV detection system, a CNV expert was asked to evaluate 50 waveforms that were filtered from the subject’s EEG. The expert was making decisions upon the waves on the basis of their waveform, instead of using the wave parameters. The fuzzy decision algorithm guided the experiment itself. Upon comparing the results of the fuzzy approach with expert’s classification, a mismatch was detected in 5 (10%) of the cases. This is two times better than in the case when artificial neural networks are used (see Table 1) [8]. By lowering the cut-level of the fuzzy decision module to 0.45, mismatch occurs in two of the cases (4%). However, we should not take for granted the fact that for this data set the fuzzy approach work better. It is a static, and a result of minor calibrations done in order to improve the good–guess ratio. It is easy to implement, and promising, from what can be seen in Table 2 in the appendix. The neural network performance is also satisfactory. Trained with larger data sets, the neural network is expected to provide with better results, since the implicit interpolation it performs is certainly a better approximation to the human expertise then the piece-wise linear membership functions of the fuzzy system. Therefore, various trade-offs should be made when designing the experiment. We attribute the satisfactory results of the fuzzy system to the soft-threshold feature of the CNV phenomenon. They vary from human to human, from situation to situation, and therefore cannot be crisply defined. The other issue that should be addressed is the reliability of the expert that provides the evaluations for the comparison of the results and performance of the soft computing techniques (and for training the neural networks). Different CNV experts are likely to give sometimes different estimations on the brainwaves,
especially in the cases that are referred to as "boundary cases." However, we cannot come with a better criterion for assessing our approaches than the knowledge of the experts, and therefore we should always tend to increase the similarity between the 'outputs' we get from an experts and from our classification engine. From all what was stated above, we can conclude that the proposed fuzzy approach is good, applicable, and fast for practical use. It eliminates the active role of the CNV expert in conducting the experiments, accelerates the experimental process and, hence, diminishes the impact of the inter-run latency time on the learning performance of the subject.
6. References [1] L. Bozinovska: Analysis of the learning Process with Dynamic CNV Experiment, Ph. D. thesis, faculty of Medicine, Skopje, Macedonia, 1991 (in Macedonian). [2] L. Bozinovska, T. Prevec, G. Stojanov, S. Bozinovski: "Dynamic CNV psaradigm," Proc. 1st European Psychology Conf., Tilburg, Germany (1991). [3] G.J. Klir, B. Yuan: Fuzzy Sets and Fuzzy Logic, Prentice Hall, Upper Saddle River, NJ, 1995. [4] M. Setstakov: Digital Processing of Preparatory and Evoked Bio-electrical Signals, Ms.C. Thesis, ETF, Skopje, Macedonia, 1988 (in Macedonian). [5] G. Stojanov: Theory of Expectation and Interpretation of EXG curves in the Context of Biological and Machine Intelligence, Ph.D. Thesis, "St. Cyril and Methodius" University, Skopje, Macedonia, 1997. [6] G. Trajkovski: Fuzzy Relations and Fuzzy Lattices, M. Sc. Thesis, "St. Cyril and Methodius" University, Skopje, Macedonia, 1997. [7] G. Trajkovski, G. Stojanov, S. Bozinovski: "Application of fuzzy sets in CNV detection during the DCNV paradigm experiment," Proc. 7th IFSA World Congress, Prague, Czech Republic (1997) 249-252. [8] G. Trajkovski, G. Stojanov, S. Bozinovski, L. Bozinovska, B. Janeva: "Fuzzy sets and neural networks in CNV detection," Proc. ITI'97, Pula, Croatia (1997) 153158. [9] G. Walter, R. Cooper, W. McCallum: "Contingent negative variation: An electric sign of sensory-motor association and expectancy in human brain," Nature, 203 (1964) 380-384.
Appendix Tables Table 1. The parameters of the membership functions for ϕ, a-reff0 and A
Variable ϕ a-reff0 A
α[deg] 3 5 2
Universe [units] [-90,90][deg] [-30,30][µV] [0,30][µV]
δ[units] 20 9 11
Table 2. Comparison of the results of waveform evaluation done by the CNV expert (EX) , the neural network (NN), and the fuzzy approach (µ µ). #
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36.
Measured parameters of the wave ϕ a-reff0 A 9 22 31 33 29 33 33 35 33 9 11 17 24 31 37 39 37 29 24 19 17 6 -9 -22 -17 -11 -17 -6 14 19 9 9 9 9 9 11
-3 -3 -2 -2 -2 -2 0 1 1 4 4 3 5 5 6 8 8 9 11 11 11 9 12 13 14 13 14 13 7 6 8 7 7 6 4 4
2 4 6 7 7 9 11 13 14 4 3 4 9 9 13 15 15 12 11 11 11 7 5 2 4 4 4 6 7 9 7 5 4 4 2 3
CNV EX
1 1 1
1 1 1 1 1 1 1 1 1
ΝΝ .05 .14 .29 .37 .35 .54 .65 .77 .81 .06 .04 .08 .35 .39 .71 .80 .79 .54 .39 .37 .36 .10 .02 .00 .01 .02 .01 .04 .14 .30 .12 .07 .05 .05 .03 .04
NN cut ≥.45
1 1 1 1
1 1 1 1
µϕ
µa
µA
µ
µϕ
µa
µA
µ
.00 .60 1.00 1.00 .96 1.00 1.00 1.00 1.00 .00 .05 .30 .65 1.00 1.00 1.00 1.00 .96 .65 .40 .30 .00 .00 .00 .00 .00 .00 .00 .15 .40 .00 .00 .00 .00 .00 .05
.00 .00 .00 .00 .00 .00 .00 .00 .00 .06 .06 .00 .14 .14 .24 .41 .41 .50 .67 .67 .67 .50 .76 .84 .93 .84 .93 .84 .32 .24 .41 .32 .32 .24 .06 .06
.20 .27 .34 .38 .38 .45 .52 .59 .62 .27 .24 .27 .45 .45 .59 .66 .66 .55 .52 .52 .52 .38 .31 .20 .27 .27 .27 .34 .38 .45 .38 .31 .27 .27 .20 .24
.00 .00 .34 .38 .38 .45 .52 .59 .62 .06 .06 .27 .45 .45 .59 .66 .66 .55 .65 .52 .52 .38 .31 .20 .27 .27 .27 .34 .32 .40 .38 .31 .27 .24 .06 .06
µ cut ≥.45
1 1 1 1
1 1 1 1 1 1 1 1 1
37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.
17 22 24 22 17 11 -3 -9 -3 6 11 22 22 31
5 5 5 6 7 7 8 9 7 8 7 6 7 8
7 9 10 12 13 12 9 9 10 12 14 16 17 18
1 1 1
1 1 1
.18 .34 .43 .56 .59 .48 .17 .14 .24 .43 .63 .81 .84 .88
1 1 1
1 1 1 1
.30 .60 .65 .60 .30 .05 .00 .00 .00 .00 .05 .60 .60 1.00
.14 .14 .14 .24 .32 .32 .41 .50 .32 .41 .32 .24 .32 .41
.38 .45 .48 .55 .59 .55 .45 .45 .48 .55 .62 .69 .73 .76
.30 .45 .48 .32 .32 .32 .41 .45 .32 .41 .32 .60 .60 .76
1 1
1
1 1 1
