Application of Artificial Intelligence in the Diagnosis of Eosinophilia

Eosinophils are a type of white blood cell. They contain particles filled with chemicals that fight off infections and play a role in your body’s immune response. Normally our blood doesn’t have a large number of eosinophils. Our body may produce more of them in response to allergic disorders, inflammation of the skin, and parasitic infections. They can also increase in response to some infections or to some bone marrow disorders [1]. In some conditions, the eosinophils can move outside the bloodstream and into organs and tissues. Treatment of the problem depends on the cause.


Introduction
Eosinophils are a type of white blood cell. They contain particles filled with chemicals that fight off infections and play a role in your body's immune response. Normally our blood doesn't have a large number of eosinophils. Our body may produce more of them in response to allergic disorders, inflammation of the skin, and parasitic infections. They can also increase in response to some infections or to some bone marrow disorders [1]. In some conditions, the eosinophils can move outside the bloodstream and into organs and tissues. Treatment of the problem depends on the cause.
Diagnosis of the condition of eosinophilia is via blood count, but diagnosis of the underlying cause varies depending on the suspected condition. Treatment is determined by the causative condition. Eosinophilia can be idiopathic (primary) or secondary to another disease [3]. In the United States, allergic or atopic diseases are the most common causes, especially those of the respiratory systems. In the developing world, parasites are the most common cause. A parasitic infection of nearly any bodily tissue can cause eosinophilia.
Hypereosinophilia is a subcategory of idiopathic eosinophilia; diagnosis requires documentation of both sustained eosinophilia (absolute eosinophil count ≥1500 cells/μL for at least 6 months. An increase in eosinophils, i.e., the presence of more than 500 eosinophils/ micro litre of blood is called an eosinophilia. The normal concentration is between 0 and 0.5 x 10 9 eosinophils per litre of blood. Eosinophilia can be reactive (in response to other stimuli such as allergy or infection) or non reactive [2]. The release of interleukin 5 by T cells, mast cells and macrophages stimulates the production of eosinophils.
Alternative knowledge acquisition approaches based on fuzzy logic have recently attracted considerable attention. It is essential to realize that fuzzy logic uses truth degrees as a mathematical model of the vagueness phenomenon. Fuzzy logic resembles human reasoning in its use of approximate information and uncertainty to generate decisions [4]. An approach to uncertainty that combines real values [0…1] and logic operations is based on the ideas of fuzzy set theory and fuzzy set membership function.
This work presents the application of fuzzy logic to automate knowledge acquisition for diagnosis of Eosinophilia. Fuzzy logic is applied for the diagnosis of eosinophilia on knowledge base which consists of a data base and a rule base. The advantage of these methods over other approaches is that they can produce good results in situations where data is imprecise, noisy and inconsistent.

Materials and Methods
Fuzzy logic controller (FLC), a successful application of Zadeh's fuzzy set theory; [5] is a potential tool for dealing with uncertainty and imprecision. Thus, the knowledge of a doctor can be modeled using an FLC [6]. The performance of an FLC depends on its knowledge base which consists of a data base and a rule base. It is observed that the performance of an FLC mainly depends on its rule base and optimizing the membership function distributions stored in the data base is a fine tuning process [7].
The process of knowledge acquisition has been long recognized as one of the most complex and laborious tasks in the construction of expert systems. In some situations, lack of available expertise can make development of such systems impossible. Eliciting knowledge from experts encounters numerous obstacles. Although the experts are highly skilled in solving problems in their domain, they often have difficulty in articulating their knowledge or sometimes even in understanding their own decision making processes.

Designing of fuzzy inference system
Fuzzy inference is a method that interprets the values in the input and based on user defined Rules, assigns values to the output. For developing diagnosing tool for Eosinophilia, data is required; the data should be capable of representing the whole disease and also the severity of the disease. Basically the data is sign and symptoms of patients, some medical report etc. Hence, data was collected from Jeyasekaran Medical Trust, Nagercoil from which 150 patients were analysed. By consulting doctor and by analysing the data of the patients four symptoms were finalised as the inputs for diagnosing the eosinophilia. The four symptoms which are relevant and mostly used for the diagnosis of eosinophilia were used as an input in fuzzy inference system as shown below. Based on these symptoms presence or absence of eosinophilia was predicted as an output.

Algorithm for the fuzzy inference system for diagnosis of eosinophilia
For the four symptoms four input variables and one output variable "Eosinophilia" was created. The four symptoms which are considered here as an input variable for diagnostic system are crucial and mainly considered for the detection and diagnosis of Eosinophilia. The four input variables (Symptoms) are divided into 4 Membership Functions based on the frequency and percentage value of the symptoms. The Membership Function and Membership Function plot for four input variables are shown in the following Tables (1)(2)(3)(4)(5) and Figures (1-5).          Based on the descriptions of the input and output variables 30 rules were constructed by selecting an item in each input and output variable box and one Connection (AND). None was chosen as one of the variable qualities to exclude any of the variables from a given rule. The weight was specified to unity (1). Table 6 shows the rule base for the Eosinophilia inference system.

Membership Function Type Params
Based on these rules the roadmap of the whole fuzzy inference   system is shown in Figure 6. Rule Viewer acts as a diagnostic, can show which rules is active, or how individual membership function shapes are influencing the results. It displays a roadmap of the whole fuzzy inference process. In Figure 6 the five plots across the top of the figure represent the antecedent and consequent of the first rule. Each rule is a row of plots, and each column is a variable. The rule numbers are displayed on the left of each row.
There are 226 plots nested in a single figure window. The four plots across the top of the figure represent the antecedent and consequent of the first rule. Each rule is a row of plots, and each column is a variable. The rule numbers are displayed on the left of each row. The first four columns of plots (the yellow plots) show the membership functions referenced by the antecedent, or the if-part of each rule. The fifth column of plots (the blue plots) shows the membership functions referenced by the consequent, or the then-part of each rule. The plots which are blank in the if-part of any rule correspond to the characterization of none for the variable in the rule. The last plot in the fifth column of plots represents the aggregate weighted decision for the given inference system. This decision will depend on the input values for the system. The defuzzified output is displayed as a bold vertical line on this plot. The variables and their current values are displayed on top of the columns. In the lower left, there is a text field Input for entering specific input values.

Results and Discussion
Based on the rules the inference system calculated the type and severity of Eosinophilia by following AND connection and then defuzzyfying the generated output using the centroid method. The  (Table 7). In fuzzy logic the truth of any statement is matter of degree so the AND connection performed a min operation, i.e. resolved the statement A AND B, where A and B are limited to the range (0, 1) by using the function min (A, B).
The truth table was converted to a plot of two fuzzy sets applied together to create one fuzzy set. Figure 7 displays how the operations work over a continuously varying range of truth values A and B according to the defined fuzzy operations.

Defuzzification of the output
As much as fuzziness helps the rule evaluation during the intermediate steps, the final desired output for each variable is generally a single number. However, the aggregate of a fuzzy set encompasses a range of output values, and so must be defuzzified in order to resolve a single output value from the set. The defuzzification method used here was the centroid calculation, which returns the centre of area under the curve (Figure 8).
The defuzzified value was calculated based on the following equation: Based on the AND operation every rule was examined for a given set of Input values and the rule which satisfied the operational logic was used to generate the output for the Inference system. The output given by each rule was aggregated and then defuzzified using centroid calculation to generate a single output which was a single number representing the severity of Arthritis.

Testing of the arthritis fuzzy inference system
The effectiveness of the developed Fuzzy Inference System was tested by providing ten sets of field data. Results of the manually constructed FLC was found to be correct when compared with the field data output. It happened because the rule base of the constructed FLC was designed after a careful study of the effects of different inputs on the output, i.e., grade of the disease. Based on the output of the FLC which is expressed on a scale of 0-100, decision can be taken on the severity of Eosinophilia for a particular set of input symptoms. Table 8 shows the testing data and the generated output by the Fuzzy Inference System.
The entire span of the output set based on the entire span of the input set is shown in Figure 9. It displays the dependency of one of the outputs on anyone or two of the inputs i.e., it shows the plot of an output surface map for the system based on the rules defined in rule base.

Conclusion
This work was undertaken with the aim to design a system for the diagnosis of Eosinophilia diagnosis and its severity using Fuzzy Logic so that common people who suspects little bit of pain in there joints, may use this system and get the result on the diagnosis and severity of Eosinophilia which will be helpful to guide him to take proper curative measures before the severity increases. The results obtained from the systems reveal that the diagnostic system for Eosinophilia is giving expected results. The efficacy of the system developed is to be endorsed by the doctors in the field observation. Hence, afterwards the system can be made open to all through Internet. With the consultation of the doctors, the curative measures suggested by them can be made available with the system.