Fuzzy Techniques for Classification of Epilepsy risk level in Diabetic Patients Using Cerebral Blood Flow and Aggregation Operators

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1 Fuzzy Techniques for Classification of Epilepsy risk level in Diabetic Patients Using Cerebral Blood Flow and Aggregation Operators R.Harikumar, Dr. (Mrs).R.Sukanesh Research Scholar Assistant Professor Department of ECE, Thiagarajar College of Engineering, Madurai ABSTRACT The main objective of this paper is to classify the diabetic epilepsy risk level using cerebral blood flow (CBF) and Electroencephalogram (EEG) signals through fuzzy techniques. In our approach, the Mandani fuzzy system model uses two inputs such as measured CBF of a diabetic patient and derived epilepsy CBF which is obtained from EEG signal parameters and clinical parameters using aggregation operators. Four methods of aggregation operators are tested and one method with better performance is selected. The triangular membership is used for measured cerebral blood flow (CBF) input. The bell shaped membership function is used for derived epilepsy CBF whose slope is derived from aggregation operators. The output of fuzzy system is diabetic epilepsy risk level. This fuzzy system requires only five rules to classify the diabetic epilepsy risk levels with a confidence measure of 85% to 100%. This fuzzy system model is calibrated using seventy known diabetic patients. The performance obtained by this method is about 95% when compared to 76.8% obtained in rule base fuzzy system with twenty-five rules. The results correspond closely to the physician s diagnosis. Keywords: Cerebral blood flow, EEG, Epilepsy, Aggregation operator, Diabetes 1. INTRODUCTION This paper presents a novel approach to classify the diabetic epilepsy risk levels of from cerebral blood flow (CBF) measurements and electroencephalogram (EEG) signals, in association with the criteria decisions obtained from aggregation operators. In clinical neurological practice, detection of abnormal EEG activity plays an important role in diagnosis of epilepsy [1]. Analysis of EEG includes detection of patterns and features characteristic of abnormal conditions. Quantitative EEG studies are used in cerebro vascular disorders to improve diagnostic sensitivity. Reports indicate that the EEG may indicate abnormalities with a sensitivity of 90% to 100%. Quantitative EEG abnormalities are proved in correlation with clinical outcome to predict the severity of the disease. EEG easily detects the oxygen delivery and utilization in brain [2]. This indicates the correlation between cerebral blood flows with EEG signals. Fuzzy logic provides reasoning methods capable of making appropriate decisions. In clinical engineering where diagnosis and management are almost never decided based on individual criterion, a weighted combination of many criteria is used instead, each criterion may support various alternatives and the alternatives with the strongest support is selected as the decision. This is a typical problem of Multi Criteria Decision Making (MCDM). One important class of methods in MCDM is based on constructing a utility or value functions U(x), which represents the overall strength of support in favor of the alternative x. This approach is known as Multi Attribute Utility Theory (MAUT) [3]. In fuzzy set theory (FST), membership function of fuzzy sets plays a similar role to that of utility functions-the role of degrees of preference [4] and this problem takes the form as below MaximizeF µω (x) = Agg {µ A1 (x 1 ), µ A2 (x 2 ), µ An (x n )}.(1) where Agg stands for an appropriate aggregation operator. It combines the membership values in the set A1, A2 An into the membership value of the set Ω formed by some operations on the sets A1,A2,.An. All aggregation operators are equivalent to the distance of the ideal one or anti ideal zero in the relevant metric. 2. MATERIALS AND METHOD The methodology of our approach is shown in figure.1. The cerebral blood flow using tetra polar impedance method and EEG signals are measured from diabetic patients [5], [6]. The measured CBF will have five linguistic levels such as very low, low, medium, high and very high. Features such as energy, peaks, spikes and sharp waves and events are extracted from the EEG signals and are classified as more relevant variables Y. The clinical parameters such as index of convulsions, seizure timings and total body fatigue are less relevant variables by the set X. The X and Y variables are aggregated by a group of operators in order to find out the appropriate derived epilepsy CBF [5], [6] with

2 Diabetic Patient Clinical Para meters EEG Signal Feature Extraction Tetra Polar Method X Y Meas ured CBF Aggregation Operators Fuzzy System Figure.1: The functional Diagram of Diabetic Epilepsy Risk level Classifier Diabetic Derived Epilepsy CBF Confidence level of 85% to 100%. This confidence level of derived epilepsy CBF will act as near equivalent to membership function. This fuzzy system works with two inputs namely measured CBF and derived epilepsy CBF and one output which is the diabetic epilepsy risk level with only five rules in the rule base Definition of the problem Normally in any basic fuzzy system with two experimental inputs parameters with five linguistic levels per input need twenty- five fuzzy rules in the rule base. The performance of this fuzzy system will vary from 62.5% to 76.8%, which depends upon the gray area in the input levels. In our approach, as in [5], a basic fuzzy system with measured CBF as one input and epileptic CBF as another input, from the database of non-diabetic epileptic patients, a rule base with twenty five rules are used. The diabetic epilepsy risk level is the output of this fuzzy system. We identified that there were many gray area in the input levels and there is an urgent need to optimize the fuzzy rule base. Therefore we attempted to use aggregation operators for optimization of the fuzzy rule base. The purpose of this paper is to find out a good choice of aggregation operators that will be well suited for this kind of classification. The following sections of the paper are organized as fuzzy techniques, selection of appropriate aggregation operation and results and discussions. The results obtained from seventy well-defined test cases are used for calibration of the system. Acute diabetic stroke patients are excluded in this analysis. The system is tested with seventy unknown cases for validation. The diabetic epilepsy risk level classification performance is compared with the physician s diagnosis. Epilepsy Risk Level 2.2. Fuzzy Techniques Fuzzy systems are being used successfully in an increasing number of application areas. They are linguistic rules to describe a system. The rule based systems are more suitable for complex systems where it is very difficult, but not impossible to describe the system mathematically Data Collection The CBF is measured by tetra polar method [5] [6]. The normal blood flow through the brain tissue of adult averages ml/100 gm of brain per minute [7], [8]. For the entire brain, this comes out to 750 ml/min to 900 ml/min, or 15 percent of the total resting cardiac output [2]. Based on the well established theory of CBF mechanism, as it increases to 70%, the oxygen concentration of the blood is reduced by 30% [9]. This leads to the long lasting hypoxia and cerebral ischemia. Therefore the epileptic convulsions risk will be increased in the patients. Raw data of EEG signals of 16 bipolar channels are recorded. The EEG signal is broken down into section or epochs for the purpose of feature extraction. An epoch of 2 seconds with sampling rate of 200 Hz is used. The following features are extracted from EEG signals for each epoch N 1) Energy of the signal E = S 2 i Where S i i= 1 is the signal sample value in micro volts. The normalized energy is obtained by dividing the energy by ) The number of positive and negative peaks exceeding a threshold 3) The total number of spikes and sharp waves in all the channels together are recorded as events 4) Spikes and sharp waves are recorded when the zero crossing duration of predominantly high amplitude peaks in EEG waveform lies between 20ms to 70ms and from 70 ms to 200 ms respectively Fuzzy Membership Function. The Mamdani fuzzy system with two inputs and one output is the basic fuzzy model. The center of gravity defuzzification method is employed. Five fuzzy linguistic variables such as very low, low, medium, high, very high are constructed for the measured CBF input using triangular membership functions. The derived CBF input uses bell shaped membership functions with five linguistic variables. The slope of the bell function is derived from seventeen simulated test conditions using aggregation operators that are discussed in the following sections. This fuzzy system performs well with five rules in the rule base such as

3 1) If CBF is Very Low AND Epilepsy CBF is Very Low, the output is Normal. 2) If CBF is Low AND Epilepsy CBF is Low, the output is Low risk 3) If CBF is Medium AND Epilepsy CBF is Medium, the output is Medium risk 4) If CBF is High AND Epilepsy CBF is High, the output is High risk 5) If CBF is Very High AND Epilepsy CBF is Very High, the output is Very High risk The linguistic fuzzy membership functions are illustrated in figure 2. Figure 2: Input/ Output membership functions of the Fuzzy System 3. SELECTION OF APPROPRIATE AGGREGATION OPERATORS This section of the paper discusses how aggregation operators can be selected and adjusted to fit empirical data series of test case. We consider the situation where the experts have a clear idea about the form of the aggregation operators but are not sure about certain parameters such as the relative importance of rule antecedents. The analysis of aggregation operators of our case are given as variables x 1, x 2, x 3 and y 1, y 2, y 3, y 4, which are derived from the clinical parameters and EEG signals respectively. These variables are normalized in a non-linear fashion using secant function and sigmoid functions over the range of zero to one [3]. Now consider the general aggregation operator f(x) used in our approach f(x)= α 1 (x 1 +x 2 +x 3 )+ α 2 (y 1 +y 2 +y 3 +y 4 ) (2) Where x 1, x 2, x 3 are index of convulsions, seizure timings and total body fatigue. The variables y 1, y 2, y 3, y 4 are defined as energy, peaks, events and sharp waves of EEG signal. We select four different methods of aggregation operators with different values of α 1 and α 2 which is shown below Method 1: α 1 takes values 0.1, 0.25, 0.15; α 2 takes values 0.5, 0.45, 0.5 f 11 (x) = 0.1(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(3) f 12 (x) = 0.25(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(4) f 13 (x) = 0.15(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 ) (5) Method 2: α 1 and α 2 = 1- α 1 f 21 (x) = 0.1(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(6) f 22 (x) = 0.25(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(7) f 23 (x) = 0.15(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(8) Method 3: α 1 = exp (-β 1 ) and α 2 = exp (-(1- β 1 )) and β 1 takes values 0.1, 0.25, 0.15; f 31 (x) = 0.9(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(9) f 32 (x) = 0.77(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(10) f 33 (x) = 0.86(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(11) Method 4: α 1 = exp (β 1 ) and α 2 = exp (1- β 1 ) and β 1 takes values 0.1, 0.25, 0.15; f 41 (x) = 1.105(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(12) f 42 (x) = 1.28(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(13) f 43 (x) = 1.16(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(14) The test data analysis of f(x) is done as follows. The variables x and y are taken as minimum (min) in the range 0-0.3; medium (mid) in the range ; maximum (max) in the range in a non linear scale. Theoretically there are 4536 different test combinations are possible of which seventeen different test combinations (such as*) are selected and conditioned to obtained derived epilepsy CBF linguistic levels through the four groups of aggregation operators. * 1. x 1, x 2 min, x 3 max ; y 1, y 2, y 3 min, y 4 -max 2. x 1, x 3 min, x 2 max ; y 1, y 2 min, y 3, y 4 max 3. x 2, x 3 - min, x 1 - max ; y 1, y 2 max, y 3, y 4 -min 4. All minimum 5. All maximum

4 All medium is excluded from this analysis The conditions 1, 2, 4 and 5 are universal conditions and they never alter the derived epilepsy CBF level. These seventeen conditions are closely related to the clinical trials. The derived epilepsy CBF linguistic levels are coded as follows Derived Epilepsy CBF linguistic Level Very low Low Medium High Very High Code U W X Y Z The derived epilepsy CBF linguistic levels obtained from the appropriate aggregation operators fewer than seventeen test simulated conditions against the desired clinical state are depicted in table 1. Table.1: Derived Epilepsy CBF linguistic level based on Aggregation Operators for Seventeen test conditions Agg. Method Derived Epilepsy CBF level for Different conditions Conditions Desired state W X Y U Z X Y Y W Obtained state W X Y U Z X Y Y W f 11 (x) f 21 (x) W X Y U Z X Y Y W f 22 (x) W X Y U Z X Y Y W f 23 (x) W X Y U Z X Y Y W Agg. Method Derived Epilepsy CBF level for Different conditions Conditions Desired state Y W Y W Z W Y X Obtained Y W Y W Z W Y X state f 11 (x) f 21 (x) Y W Y W Z W Y X f 22 (x) Y X* Y W Z W Y X f 23 (x) Y W Y W Z W Y X The performance of the aggregation operators is defined as follows [10]. Performance = {(PI-MI-FI)/PI}*100...(15) PI= Perfect Classification MI= Missed Classification, FI= False alarm Missed classification represents high level as low level, false alarm represents low level as high level. The comparison of performance for different aggregation operators are shown in table.2 Table.2: Performance of Different Aggregation Operators Type % classification of Derived CBF Linguistic level against desired clinical state Missed False Perfect Perfor mance (%) Level Level Level Method Method Method Method Based on the observation from table.2, we come to a decision that x variables namely the clinical parameters need less weight and the y variables require higher weight. Therefore Method-2 aggregation operators are selected as a good choice to obtain the derived epilepsy CBF. Except for the test condition number 11 ( x 1, x 3 - mid, x 2 -max ; y 1, y 2 -mid, y 3, y 4 -min), in all the other 16 out of 17 conditions the output settles to identical derived epilepsy CBF levels along column-wise. The aggregation operator f 11 (x) also provides the same result as in method 2. Therefore f 11 (x) is also included as a good class of aggregation operators. The following aggregation operators are selected to obtain the derived epilepsy CBF level with Confidence Level of 85% to 100%. f 11 (x) = 0.1(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(16) f 21 (x) = 0.1(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(17) f 22 (x) = 0.25(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(18) f 23 (x) = 0.15(x 1 +x 2 +x 3 ) (y 1 +y 2 +y 3 +y 4 )...(19) To obtain the numerical values of aggregation operators output in the five linguistic sets, we assigned the following values for minimum (min) = 0.1, medium (med) = 0.5 and maximum (max) = 0.8. These numerical values are substituted in the equations 3 to 12 and seventeen test conditions are simulated to produce 204 numerical values. These values are clustered by the R.Yager s ordered weighted aggregation (OWA) [11] method. The obtained numerical values of aggregation operators outputs in the five linguistic levels through Yager s method [11] are given in table 3. Table 3: Numerical values of aggregation operator s output aggregated for seventeen stimulated test condition for selected methods Aggreg ation Aggregation Operators Output at Five Linguist Levels Type Very Low Low Mediu m High Very High f 11 (x) f 21 (x) f 22 (x) f 23 (x)

5 In [11], Yager introduced the OWA operators, which is defined as follows. Definition: An OWA operator of dimension n is a mapping. F: R n R, Which has an associated weighting vector, W= [w 1, w 2, w 3, w n ] in which w j ε[0,1], n j = 1 n j = 1 w w j j b = j 1 Where F (a 1, a2, a3... a n ) = with b j being the jth largest of the a i. A key feature of this operator is the ordering of arguments by values, a process that introduces nonlinearity into the operation. It can be shown that this operator is in the class of mean operator as it is commutative, monotonic and idem potent. Its generality lies in the fact that by selecting the weights it can implement different aggregation operators. Specifically by appropriately selecting the weights in W, we can emphasis different arguments based upon their position in the order. Thus if we place most of the weights near the top of W we can emphasize the higher scores, while placing the weights near the bottom of W emphasizes the lower scores in the aggregation [12]. A fundamental aspect of the OWA operator is the reordering step, in particular an aggregate a i is not associated with a particular weight w i but a weight w i is associated with a particular reordered position [13]. The OWA operators can model the Max, Min and Arithmetic mean operators for certain vector of weights W. From above table.3 we obtained single numerical aggregation value f 2 (x) in the five linguistic levels from f 21 (x), f 22 (x) & f 23 (x) through better aggregation. The selected weights are W=[0.4,0.3,0.3]. For example in the very high-risk level case the obtained single numerical value of aggregation output is Very high risk f 2 (x) = 0.4 (3.1814) (3.0497) (3.1375) = Likewise other linguistic levels numerical values are obtained which is shown in table.4 Table.4: Numerical Values of Aggregation operator s output averaged for seventeen stimulated conditions Aggregation Operators output Method Very Low Medium High Very High Low f 11 (x) f 2 (x) of bell shaped membership function are shown in table 5. Table.5: Derived Epilepsy CBF level and slope function from aggregation operators Fuzzy linguistic levels Derived Epilepsy CBF level (Median) Normalized slope function (γ) Very Low Low Medium High Very High RESULTS AND DISCUSSIONS This fuzzy system model is calibrated with seventy well defined diabetic cases and another seventy are taken for comparison purpose. For example we will take up a sample case for analysis. Let the measured CBF of the patient be 83 ml/100gm/min (Medium). Based on the EEG signal parameters and clinical parameters the derived epilepsy CBF is obtained as 81ml/100gm/min, which is also at medium risk level. The output risk level obtained from the fuzzy system is also Medium risk. The surface view of this fuzzy system is shown in Figure3. Figure.3: Fuzzy Surface view The results of 70 cases with CBF and EEG findings are compared with physician s diagnosis as shown in figure 4. By using aggregation operators the effect of missed classification is nullified. At the same time the process of false classification or false alarm is not removed. Due to this there is a gray area in the low risk range and requires more research work in that direction. It is observed that, low values occur for f 11 (x) and a distinct high value for f 2 (x). These numerical values have a confidence level of 95% on either side. The slope function of bell shaped membership function is obtained by normalized numerical values from the aggregation operators output. The derived epilepsy CBF levels and slope function (γ)

6 Figure 4: Comparison of Aggregation Fuzzy Diagnosis with Physician s Diagnosis 5. CONCLUSION Aggregation operator based fuzzy classification of epilepsy risk level in diabetic patients is discussed in this paper based on CBF and EEG signals. The selection of aggregation operators plays a vital role in the decision making process. With good selection of aggregation operators we achieve performance levels of 98%. Since f 11 (x) and f 2 (x) are two different groups performing at two different numerical levels. Therefore there is a gray area in the low risk classification state. Due to this property, the confidence level comes down to 85%, to improve confidence levels; a special group of learning weight aggregation operators of Yager s is to be studied. The control limits and the slope function for the bell shaped membership functions in the derived epilepsy CBF can be standardized with more sample patients. After this standardization, the measured CBF will be transformed into a bell shaped membership function instead of triangular one. Then the fuzzy system will be converted into a one input (measured CBF) and one output (epilepsy risk level) system with the five rules in the rule base. This work may also be extended to predict Cardiac risk index of diabetic patients. 6. ACKNOWLEDGEMENT The authors thank the Management and the Principal of Thiagarajar College of Engineering, Madurai for providing necessary facilities and encouragement. 7. REFERENCES [1] Clement.C.C Pang et al, A Comparison of Algorithms for detection of Spikes in the EEG, IEEE Transactions on Bio-Medical Engineering, vol 50, No:4, pp , April [2] Muro et al, A mathematical Model of Cerebral Blood Flow Chemical Regulationpart II, IEEE Transactions on Bio-medical Engineering, vol 36, pp ,February [3] Gleb Beliakov and Jim Warren, Appropriate choice of Aggregation operators in Fuzzy Decision Systems, IEEE transactions on Fuzzy systems, vol 9, No:6,pp , December [4] Javier.G.Marin.Band Qiang Shen, From Approximate to Descriptive Fuzzy Classifiers, IEEE Transactions on Fuzzy Sytems, vol 10, No:4 pp , August [5] R.Harikumar, Sabarish Narayanan.B Prof.R. Sundararajan, Fuzzy based risk level analysis of epilepsy in diabetic patients using EEG signals and Cerebral Blood Flow, Proceedings of VIROHA 2K2, Vellore Institute of Technology-Vellore, pp 95-99, December [6] K.Paramasivam, R.Harikumar and Prof. R. Sundararajan, Simulation of VLSI Design Using Parallel Architecture for epilepsy risk level diagnosis in Diabetic Neuropathy, IETE Journal of Research, vol 50,No:4,pp , July-August [7] Celsis P.Goldman T. Henrik sen.l etal, A method for calculating regional cerebral blood flow from emission computed tomography of inert gas concentration, J.Computer Assist Tomography, vol 5, pp , [8] Mathews J.N.S.etal, Statistical method for the estimation of cerebral blood flow using the kety-schmidt technique, Clinical Science, vol 97, pp , [9] R.Harikumar and S.Selvan, Fuzzy based classification of patient state in diabetic neuropathy using cerebral blood flow, J. Systems Society of India, Paritantra vol 7, No:1, pp 37 41, August [10] Hauqn and Jean Gotman, A patient specific algorithm for detection and onset in long term EEG monitoring-possible use as a warning device, IEEE Transactions on Bio medical Engineering, vol 44, No:2, pp , February [11] Ronald R.Yager, On Ordered Weighted Averaging Aggregation operators in Multi criteria decision making, IEEE transactions on Sys,Man,Cybern, vol 18, No:1, pp , January/February [12] R.R.Yager, Including Importances in OWA Aggregations Using Fuzzy Systems Modeling, IEEE Trans. on Fuzzy Systems vol 6,No:2,pp ,1996. [13] P.Filev and R.R.Yager, Context dependent information aggregation, Proceedings of IEEE International Conference on Fuzzy Systems, , 2003.