ISRN Biomathematics

Volume 2013 (2013), Article ID 342970, 11 pages

http://dx.doi.org/10.1155/2013/342970

Research Article

A Note on Hypertension Classification Scheme and Soft Computing Decision Making System

Pankaj Srivastava,¹ Amit Srivastava,² Anjali Burande,³ and Amit Khandelwal²

¹Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad 211004, India

²Applied Mechanics Department, Motilal Nehru National Institute of Technology, Allahabad 211004, India

³Department of Mathematics, Dayanand College of Commerce, Latur 413512, India

Received 22 July 2013; Accepted 28 August 2013

Academic Editors: V. P. Emerenciano and J. R. C. Piqueira

Copyright © 2013 Pankaj Srivastava et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

Nowadays young professionals are a soft target of hypertension due to the increased work pressure and poor tolerance. Many people have high blood pressure for years without knowing it. Most of the time, there are no symptoms, but when this condition goes untreated it damages arteries and vital organs throughout the body and that is why it is also termed as the silent killer. Complications arising from hypertension could lead to stroke and heart failure. Soft computing approach provides a sharper conclusion from vague, ambiguous, and imprecise data (generally found in medical field) using linguistic variables. In this study, a soft computing diagnostic support system for the risk assessment of hypertension is proposed.

1. Introduction

A human body is a complex system and there are a number of variables that affect its functioning. The abnormality in its functioning causes a number of symptoms in the form of primary stages of different diseases although the recognition of these symptoms and their mapping with the diseases precisely is not an easy one. Sometimes compications in human body may be caused by improper diagnosis or improper management of the disease or due to the inaccessibility of medical personnel [1]. The quickening speed of change and adoption of western lifestyles by people in developing countries have led to a sharp rise in the incidence of hypertension [2]. Hypertension is a medical term for high blood pressure which is a condition that occurs when the pressure in the arteries is above the normal range. According to one of the studies “Recession has had an adverse impact on jobs in India and perhaps this is one of the reasons why cases of Hypertension have gone up in past two years among young IT professionals”. Recent analysis has predicted that more than 1.56 billon people will be living with hypertension worldwide by the year 2025. It has been declared by a survey report that one of four adults in India has high BP which kills 7.5 million people worldwide each year; moreover, AIDS, diabetes, road accidents, and tuberculosis are put together. In India 23.1% men and 22.6% women have high BP a notch lower than the global prevalence of one in three adults says the World Health statistics 2012 released, 16 May 2012. Jain [3] established a decision making process phenomenon in the presence of fuzzy variables. Poli et al. [4] developed a neural network expert system for diagnosing and treating hypertension. Degani [5] discussed computerized electrocardiogram diagnosis using fuzzy approach. Charbonnier et al. [6] proposed the statistical and fuzzy models of ambulatory systolic blood pressure for hypertension diagnosis. Jena et al. [7] discussed the application of soft computing in medical science. Pandey et al. [8] proposed a rule based system for cardiac analysis based on electrocardiography. Further, Allahverdi et al. [9] proposed a fuzzy expert system for the determination of coronary heart disease risk (CHD) of patient for the next ten years. Nalayini and Wahidabanu [10] were of the view that most of the cardiac diseases are characterized by varied degrees of intricacy and the conventional procedures are not capable of dealing with these intricacies very efficiently. Djam and Kimbi [1] developed a fuzzy expert system for the management of hypertension. Recently, P. Srivastava and A. Srivastava [11] proposed a soft computing diagnostic system to evaluate the risk factor for coronary heart disease (CHD). Srivastava and Sharma [12] designed a soft computing diagnostic system that classifies ECG beats in different phases and enables us to identify the status of cardiac health as per available ECG graphs. The present paper introduces a new soft computing model that measures risk factor on the basis of newly designed algorithm; a number of cases have been discussed as per available database.

2. Methodology

For complex systems, fuzzy tools are quite suitable because of its tolerance to some imprecision. In the present study, the inputs consist of age, systolic blood pressure (SBP), diastolic blood pressure (DBP), body mass index (BMI), heart rate, low density lipoprotein (LDL), high density lipoprotein (HDL), triglyceride, smoking, and exercise, while the output is the risk grade of hypertension.

In order to design a user friendly informative system for evaluating risk percentage of hypertension, we propose fuzzy Algorithm 1.

(I)          Initial fuzzification mechanism

              BEGIN

      (1)    Input-Fuzzy system with suitable “” parameters

      (2)    Initialize

              DO UNTIL ()

              Categorize fuzzy sets in linguistic variables

              DO UNTIL ()

      (1)    Construction of suitable membership function

      (2)    Increment

              END DO UNTIL

              Increment

              END

(II)        Construction of Fuzzy Strings

              BEGIN

     (1)    Input: “” fuzzy sets in linguistic variables

              ; , and

      (2)    Input: output parameters , .

      (3)    Develop linguistic strings ;

              using AND operation on each linguistic term ;

      (4)    Initialize

              DO UNTIL ()

              Increment

              END DO UNTIL

              Increment

              END

(III)      Output Evaluation

              BEGIN

      (1)    Construct Utility matrix of pxq order.

      (2)    Construct utility fuzzy sets ;         

               using for each

      (3)    Initialize

              DO UNTIL ()

      (4)    Construct maximizing sets ,

              corresponding to each alternative.

      (5)    Develop optimal fuzzy utility sets , .         

              Each optimal fuzzy set is obtained by fuzzy

              intersection ⋀ on fuzzy utility set and maximizing

              set such that

               for each utility value .

      (6)    Take maximum membership value from each optimal utility fuzzy set.

      (7)    The optimal alternative with corresponding maximum

              membership grades obtained in step 10 such as

               for .

              END DO UNTIL

              Increment

              END

Algorithm 1

2.1. Input Variables

2.1.1. Blood Pressure

In this field we use systolic BP (SBP) and diastolic BP (DBP). The input variables for SBP and DBP were classified into seven fuzzy sets (see Table 1).

Table 1

Systolic BP in mm Hg
Diastolic BP in mm Hg

Desirable
90–120
60–80

Above desirable
120–130
80–85

Moderate
130–140
85–90

Above moderate
140–150
90–95

Little high
150–160
95–100

High
160–170
100–110

Very high
>168
>108

Systolic Blood Pressure (SBP). Consider

Diastolic Blood Pressure (DBP)

2.1.2. Cholesterol

In this study we have classified total cholesterol into low density lipoprotein (LDL) cholesterol and high density lipoprotein (HDL). HDL cholesterol level has been classified into four fuzzy sets. LDL cholesterol level has been classified into five fuzzy sets. High levels of LDL are associated with coronary artery disease, whereas high levels of HDL appear to protect against coronary artery disease. These fuzzy sets have been shown in Table 2.

Table 2

Cholesterol (mg/dL)

LDL
HDL

Normal
≤100
Very high
30

Above normal
100–130

Borderline high
130–160
High
30–50

High
160–190
Nearly normal
50–60

Very high
≥180
Normal
≥58

Low Density Lipoprotein (LDL). Consider

High Density Lipoprotein (HDL). Consider

2.1.3. Age

This input field is classified into six fuzzy sets. The fuzzy sets with their range are shown in Table 3. Consider

Table 3

Age (in years)

Young
<30

Adult
25–48

Midaged
45–60

Aged
58–72

Old
70–86

Very old
>80

2.1.4. BMI

Body mass index is defined as the individual’s body weight divided by square of his or her height. This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table 4. Consider

Table 4

Body mass index (kg/m²)

Low (underweight)
10–18

Medium (normal weight)
15–26

Above medium (overweight)
25–34

High (obese)
32–40

Very high (severe obese)
38–46

Very very high (super obese)
44–50

2.1.5. Heart Rate

This input field is classified into four linguistic variables.The fuzzy sets with their range are shown in Table 5. Consider

Table 5

Heart rate (beats/min)

Low
50–65

Normal
60–80

High
78–110

Very high
105–125

2.1.6. Triglyceride

Triglycerides have been identified to play a major role in heart disease and hypertension. This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table 6. Consider

Table 6

Triglyceride (mg/dL)

Normal
<150

A little bit high
150–200

High
200–500

Very high
≥500

2.1.7. Physical Exercise

This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table 7. If a person is not doing exercise, then input value is zero. Consider

Table 7

Exercise (in Min)

Low effective
5–30

medium effective
30–60

High effective
60–100

Very high effective
90–120

2.1.8. Smoking

This input field is classified into four fuzzy sets. The fuzzy sets with their range are shown in Table 8. If person is not smoking, then input value is zero. Consider

Table 8

Smoking (per day)

Low smoker
5–10 cigarettes

Medium smoker
8–20 cigarettes

High smoker
18–30 cigarettes

Very high smoker
28–35 cigarettes

2.2. Output Variable

The output contains risk grade of hypertension which is classified in five linguistic variables, very low, low, moderate, high, and very high. The output optimal alternatives indicate patient’s present grade of hypertension. These optimal alternatives have been graphically shown in the form of Sugeno’s spikes.

3. Result

Now we have developed various linguistic strings to represent the state of the patient using the input variables such as age, LDL, HDL, SBP, DBP, triglyceride, BMI, HR, exercise, and smoking. Some of the linguistic strings are given as follows.

J ₁ = YoungAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglycerideMBMINormalHRNoExcerciseNoSmoking

J ₂ = YoungAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglycerideMBMINormalHRLowExcerciseLowSmoking

J₃ = YoungAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglycerideMBMINormalHRMediumExcerciseLowSmoking

J ₄₀₀ = YoungAgeNormalLDLNormalHDLNormalSBPNormalDBPNormalTriglycerideAMBMINormalHRMediumExcerciseLowSmoking

J ₄₀₁ = YoungAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglycerideAMBMIHighHRMediumExcerciseMedSmoking

J ₂₅₀₀ = AdultAgeNormalLDLNormalHDLDesirableSBPADesirableDBPNormalTriglycerideMBMINormalHRNoExcerciseNoSmoking

J ₆₅₀₀ = AdultAgeHighLDLHighHDLDesirableSBPModerateDBPNormalTriglycerideAMBMIHighHRLowExcerciseLowSmoking

J ₁₀₀₀₁ = AdultAgeHighLDLHighHDLDesirableSBPModerateDBPNormalTriglycerideAMBMIHighHRLowExcerciseMediumSmoking

J ₁₇₀₀₉ = MidagedAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglycerideMBMINormalHRNoExcerciseNoSmoking

J₁₇₀₁₀ = MidagedAgeNormalLDLNormalHDLDesirableSBPDesirableDBPNormalTriglycerideMBMIHighHRNoExcerciseLowSmoking

J ₂₀₀₀₈₀ = AgedAgeNormalLDLNormalHDLDesirableSBPADesirableDBPNormalTriglycerideMBMINormalHRNoExcerciseNoSmoking

J ₄₀₅₀₀₁ = AgedAgeHighLDLHighHDLModerateSBPModerateDBPNormalTriglycerideVHBMIVHHRLowExcerciseMediumSmoking

J ₉₆₆₀₈₀ = AgedAgeVeryHighLDLNVeryhighHDLVeryhighSBPVeryhighDBPVeryhighTriglycerideVHBMINormalHRLowExcercisehighSmoking

J ₁₂₀₀₂₀₀ = OldAgeHighLDLNormalHDLAboveDesirableSBPModerateDBPNormalTriglycerideAMBMINormalHRLowExcercise NoSmoking

J ₂₃₄₄₅₆₉ = OldAgeVeryHighLDLNVeryhighHDLVeryhighSBPhighDBPVeryhighTriglycerideAMBMIHighHRNoExcerciseVery highSmoking

J ₅₆₇₆₈₈₀ = VeryOldAgeVeryhighLDLNormalHDLModerateSBPADesirableDBPNormalTriglycerideAMBMINormalHRLowExcercise LowSmoking

J ₇₅₆₆₇₈₀ = VeryoldAgeHighLDLHighHDLVeryhighSBPVeryhighDBPVeryhighTriglycerideHighBMIVHHRNoExcerciseVeryhighSmoking

J ₈₅₄₅₂₀₀ = VeryoldAgeVeryHighLDLVeryhighHDLVeryhighSBPHighDBPV.highTriglycerideVHBMIHighHRNoExcercisehighSmoking

J ₉₀₃₁₆₇₈ = VeryoldAgeVeryHighLDLVeryhighHDLVeryhighSBPVeryhighDBPVeryhighTriglycerideVHBMIVHHRLowExcerciseVery highSmoking

J ₉₀₃₁₆₈₀ = VeryoldAgeVeryHighLDLVeryhighHDLVeryhighSBPVeryhighDBPVeryhighTriglycerideMVVHBMIVHHRNoExcerciseVery highSmoking.

On the basis of our proposed technique to investigate the health status of a person whose medical data is available, three different cases have been discussed as follows.

Case 1. The input variables of first patient are

(1)Age = {(0, young), (0.8, adult), (0, midaged), (0, aged), (0, old), (0, very old)}.(2)LDL = {(0.71, normal), (0, above normal), (0, borderline high), (0, high), (0, very high)}.(3)HDL = {(0, very high), (0, high), (0, nearly normal), (1, normal)}.(4)SBP = {(0, desirable), (0.8, above desirable), (0, moderate), (0, above moderate), (0, little high), (0, high), (0, very high)}.(5)DBP = {(0, desirable), (1, above desirable), (0, moderate), (0, above moderate), (0, little high), (0, high), (0, very high)}.(6)Triglyceride = {(0.72, normal), (0, a little bit high), (0, high), (0, very high)}.(7)BMI = {(0, low), (0.99, medium), (0, above medium), (0, high), (0, very high), (0, very very high)}.(8)HR = {(0, low), (0.86, normal), (0, high), (0, very high)}.(9)Exercise = {(1, low), (0, medium), (0, high), (0, very high)}.(10)Smoking = {(1, low), (0, medium), (0, high), (0, very high)}.

This is the fuzzy set which represents the state of concerned patient:

The utility matrixof order 59031680 by using the fuzzy rule base designed is as follows:

The five fuzzy utilities are

(1)₁ = {(0.71, 98)},(2)₂ = {(0.71, 68)},(3)₃ = {(0.71, 30)},(4)₄ = {(0.71, 20)},(5)₅ = {(0.71, 10)}.

The maximum sets corresponding to each alternative are

(1)1m = {(1, 98)},(2)2m = {(0.69, 68)},(3)3m = {(0.30, 30)},(4)4m = {(0.20, 20)},(5)5m = {(0.10, 10)}.

Now, the optimal fuzzy utilities using fuzzy utilities and maximizing sets are

(1)1o = {(0.71, 98)},(2)2o = {(0.69, 68)},(3)3o = {(0.30, 30)},(4)4o = {(0.20, 20)},(5)5o = {(0.10, 10)}.

Using these utilities, the optimal alternatives are given by

This optimal alternative indicates that the patient presently is in very low grade of hypertension. The optimal alternatives have been graphically shown in Figure 1 in the form of Sugeno’s spikes.

Figure 1: View of Sugeno’s spikes.

Case 2. The input variables of the second patient are as follows.

(1)Age = {(0, young), (0, adult), (1, midaged), (0, aged), (0, old), (0, very old)}.(2)LDL = {(1, normal), (0, above normal), (0, borderline high), (0, high), (0, very high)}.(3)HDL = {(0, very high), (0.6, high), (0, nearly normal), (0, normal)}.(4)SBP = {(0, desirable), (0.8, above desirable), (0, moderate), (0, above moderate), (0, little high), (0, high), (0, very high)}.(5)DBP = {(0, desirable), (0.66, above desirable), (0, moderate), (0, above moderate), (0, little high), (0, high), (0, very high)}.(6)Triglyceride = {(0.66, normal), (0, a little bit high), (0, high), (0, very high)}.(7)BMI = {(0, low), (0, medium), (0.86, above medium), (0, high), (0, very high), (0, very very high)}.(8)HR = {(0, low), (0.76, normal), (0, high), (0, very high)}.(9)Exercise = {(0, low), (0.79, medium), (0, high), (0, very high)}.(10)Smoking = {(1, low), (0, medium), (0, high), (0, very high)}.

This is the fuzzy set which represents the state of concerned patient:

The utility matrix is the same as in Case 1.

The five fuzzy utilities are

(1)₁ = {(0.6, 55)},(2)₂ = {(0.6, 92)},(3)₃ = {(0.6, 40)},(4)₄ = {(0.6, 24)},(5)₅ = {(0.6, 10)}.

The maximum sets corresponding to each alternative are

(1)1m = {(0.59, 55)},(2)2m = {(1, 92)},(3)3m = {(0.43, 35)},(4)4m = {(0.26, 24)},(5)5m = {(0.10, 10)}.

Now, the optimal fuzzy utilities using fuzzy utilities and maximizing sets are

(1)1o = {(0.59, 55)},(2)2o = {(0.6, 92)},(3)3o = {(0.43, 35)},(4)4o = {(0.26, 24)},(5)5o = {(0.10, 10)}.

Using these utilities, the optimal alternatives are given by

This optimal alternative indicates that the patient presently is in low grade of hypertension. The optimal alternatives have been graphically shown in Figure 2 in the form of Sugeno’s spikes.

Figure 2: View of Sugeno’s spikes.

Case 3. The input variables of the third patient are as follows.

(1)Age = {(0, young), (0, adult), (0, midaged), (0, aged), (0.75, old), (0, very old)}.(2)LDL = {(0, normal), (0, above normal), (0, borderline high), (0.8, high), (0, very high)}.(3)HDL = {(0, very high), (1, high), (0, nearly normal), (0, normal)}.(4)SBP = {(0, desirable), (0, above desirable), (0.8, moderate), (0, above moderate), (0, little high), (0, high), (0, very high)}.(5)DBP = {(0, desirable), (1, above desirable), (0, moderate), (0, above moderate), (0, little high), (0, high), (0, very high)}.(6)Triglyceride = {(1, normal), (0.66, a little bit high), (0, high), (0, very high)}.(7)BMI = {(0, low), (0, medium), (0, above medium), (0.78, high), (0, very high), (0, very very high)}.(8)HR = {(0, low), (0, normal), (0.96, high), (0, very high)}.(9)Exercise = {(0, low), (1, medium), (0, high), (0, very high)}.(10)Smoking = {(1, low), (0, medium), (0, high), (0, very high)}.

This is the fuzzy set which represents the state of concerned patient:

The utility matrixis the same as in Case 1.

The five fuzzy utilities are

(1)₁ = {(0.66, 15)},(2)₂ = {(0.66, 30)},(3)₃ = {(0.66, 45)},(4)₄ = {(0.66, 80)},(5)₅ = {(0.66, 50)}.

The maximum sets corresponding to each alternative are

(1)1m = {(0.187, 15)},(2)2m = {(0.375, 30)},(3)3m = {(0.562, 45)},(4)4m = {(1, 80)},(5)5m = {(0.62, 50)}.

Now, the optimal fuzzy utilities using fuzzy utilities and maximizing sets are

(1)1o = {(0.187, 15)},(2)2o = {(0.375, 30)},(3)3o = {(0.562, 45)},(4)4o = {(0.66, 80)},(5)5o = {(0.62, 50)}.

Using these utilities, the optimal alternatives are given by

This optimal alternative indicates that the patient is presently in high grade of hypertension.

The optimal alternatives have been graphically shown in the form of Sugeno’s spikes in Figure 3.

Figure 3: View of Sugeno’s spikes.

4. Conclusion

The present research paper confirms that the soft computing diagnostic system can represent the expert’s thinking in an efficient manner to handle complex cases. The design and development of soft computing risk assessment system on the basis of the proposed technique will assist medical experts to measure grade classification of hypertension efficiently.

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