Journal of Innovations in Pharmaceutical and Biological Sciences (JIPBS)
eISSN: 2349-2759 | pISSN: 2395-1095 | Vol. 4, Issue 4, 2017, pp. 65-72

A novel approach in adjustment of total daily insulin dosage for type 2 diabetes patients using a fuzzy logic based system

Ahmed Masud Chowdhury1, Rubayat Islam Khan2, Saif Shahriar Rahman Nirzhor2, Jafrina Jabin2, Arafat Islam Khan3

1Department of Electrical & Computer Engineering, North South University, Dhaka, Bangladesh
2Department of Pharmacy, BRAC University, Dhaka, Bangladesh
3Department of Aerospace Engineering, San Diego State University, San Diego, California, USA
DOI: 10.56511/JIPBS.2017.v4.i04.pp65-72 | Published: 2017-10-05 | Article page and PDF

Abstract

The aim of this study is to adjust the total daily insulin dosage for type 2 diabetes patients, who are already on an insulin treatment regimen, by using a fuzzy-based system. The dose is adjusted by taking into account three patient-related linguistic factors (PRFs) for 39 patients i.e. weight, body mass index (BMI), and average daily carbohydrate intake and utilizing this data to develop rules for a fuzzy-based system in MATLAB. The system was then made to generate an output which was compared to the prescribed doses of insulin by the patients’ respective physicians. The fuzzy based system was seen to bring a better regulation to the insulin treatment regimen for a particular patient as compared to the traditional non-fuzzy based methods which calculate total daily insulin dose based on each individual factor discretely. According to the output generated, the reasonable changes that this system suggested may evince better control on patient blood glucose levels. The usage of this system will allow fewer instances of hyperglycemic and hypoglycemic events among type 2 diabetes patients and may be further be translated to type 1 diabetics.

Keywords: Insulin; Fuzzy; MATLAB; Type 2 Diabetes; Dose Adjustment; Drug Dosing

Introduction

Type-2 diabetes is a condition that affects approximately half a billion people worldwide with a prevalence of 8.1% in adults according to the World Health Organization [1]. Its onset is due to the ineffective use of insulin by the human body and accounts for majority of diabetes cases around the world. It is estimated that about 80% of the people with Type-2 diabetes reside in low and middle income countries and in Bangladesh alone, it has a prevalence of 11%. [2,3]. Type-2 diabetes affects many major organs, including the kidneys, eyes, nerves, blood th vessels, and the heart. It currently ranks 6 in the top 10 causes of death around the world [1]. However, Type-2 diabetes could be managed better with the help of insulin therapy where patients can self-inject a prescribed dose by the physician in order to regulate their blood glucose levels. The success of this type of therapy is strictly dependent on careful monitoring of certain factors such as their height, weight, BMI, and carbohydrate intake. The prescribed insulin dose by the physician is contingent upon these various factors and mismanagement of blood sugar could often lead to life-threatening complicacies like hyperglycemia (dangerously high blood sugar) or hypoglycemia (extremely low blood sugar) [3]. In order to avoid such problems, a more accurate dosing system is required that takes into account patient-related factors such as weight, body mass index (BMI), and average daily carbohydrate intake, factoring them in determining the precise insulin dose needed for any particular patient. Such a personalized therapy is perfected using a fuzzylogic based system where a computer system is developed that takes in patient factor data to develop rules and membership functions between each factor, rendering a dosage output optimum for the patient [4, 5].

Controlling blood glucose levels for a type 2 diabetic patient can be a complicated process especially since dosing of insulin based on one single patient related factor can often lead to irregular control of blood sugar. Thus, a variety of factors need to be considered when performing such administration. These factors may include to: age, gender, BMI, and certain diseased conditions a patient might be facing [7]. Often times the dosage of insulin is either overshot or undershot and the patient has to undergo diet and life style changes in order to achieve proper glucose control. Erroneous administration of insulin may cause significant harm to the patients; if insulin is given more than the required amount, the patient may suffer from hypoglycemia. The symptoms for these may include increased hunger, fatigue, frequent urination, blurred vision, etc. [2, 3]. Due to the aforementioned complexities in case of Type-2 diabetes management using insulin, the likelihood of dosage errors in prescription and administration is high. Therefore, it is of utmost interest to provide an effective solution to the above insulin therapy and thus a fuzzy based insulin delivery system is utilized. A precise dosage amount of insulin can be calculated using this system, taking into account the various patient related factors. The fuzzy-based computational system learns through the various inputs provided to it and using inter-factor and intra-factor relations, it derives the various membership functions. This novel personalized dosing approach overcomes the possibilities of hyperglycemic and hypoglycemic events as individual patient dose is calculated individually based on their respective PRFs. Thus exact number of units of insulin can be delivered to the patient, aiding efficient control of glucose level [8- 11].

Experimental

Materials and Methods

Patients population

39 type 2 diabetes patients undergoing insulin treatment were randomly selected from the population of the city of Dhaka, Bangladesh; a patient pool comprising of 20 males and 19 females. The patients provided the following individual information: weight, height, average carbohydrate intake per day over a period of a month and the respective prescribed insulin dose by the physician. In each of the cases, first, the physician(s) calculated a nominal insulin dose based on the patient’s body weight and then secondly proceeded to adjust the daily amount of insulin given in accordance to subsequent consultation sessions with the patients. The data was then used to calculate the BMI for each patient. Each patient was apprised about the specific method by which this data was to be used and consented to the usage and publication of the results obtained.

Calculation method for insulin dosage and computational tools

MATLAB was used for method development and analysis of the acquired data. The dosage of insulin was calculated by using the fuzzy-based interface developed in MATLAB. Each PRF (i.e. weight, BMI, average carbohydrate intake in a given month in grams)was used as input variables in the system and the resultant predicted insulin dose was the output. Three disparate non-fuzzy based traditional methods used for calculating insulin dose were integrated to one system to generate this output. These standard methods were: calculation of insulin dosage based on body weight, calculation of insulin dosage based on BMI and calculation of insulin dosage based on average carbohydrate consumption methods of insulin dosage and produce a fuzzy output, the patient's details were used to calculate insulin dosage separately using each method. These calculations are shown in tables 1, 2, and 3 and for added simplicity, the numerical values of insulin units are shown only for the first 10 patients that were studied. Table 1 shows the insulin dosage calculated when only the patient's weight is used as a determinant factor. In this case, the body weight is simply multiplied by a factor of 0.5 in order to determine the number of units of insulin [12-14].

Table 1. Total daily insulin dose calculation based on patients' body weight (patient number 1 through 10 only) Patient Number Weight (kg) Calculated Insulin
Table 1. Total daily insulin dose calculation based on patients' body weight (patient number 1 through 10 only) Patient Number Weight (kg) Calculated Insulin

Table 2 shows the insulin dosage calculated when only the patient's BMI is used as a determinant factor. In this case, if the patient has a BMI of less than 25 then the body weight is multiplied by a factor of 0.4 in order to determine the number of units of insulin. If the patient has a BMI in between 25-30 then the body weight is multiplied by a factor of 0.5. And finally, if the patient has a BMI of greater than 30 then the body weight is multiplied by a factor of 0.6 in order to determine the number of units of insulin [12-14].

Table 2. Total daily insulin dose calculation based on patients' body mass index (BMI) (patient number 1 through 10 only) Patient Number BMI Calculated Insulin
Table 2. Total daily insulin dose calculation based on patients' body mass index (BMI) (patient number 1 through 10 only) Patient Number BMI Calculated Insulin

Table 3 shows the insulin dosage calculated when the patient's average carbohydrate intake is used as a determinant factor. In this case, the standard 500 rule is for that patient [15]. Firstly, the patient's body weight is used to determine the number of daily insulin units required per day. Then the number 500 is divided by this number in order to calculate the number of grams of carbohydrates 1 unit of insulin will cover for that particular patient. Lastly the patients average daily carbohydrate intake is divided by this number in order to determine the number of units of insulin required on a daily basis. (Note: this method does not take correct for the average blood glucose levels of the patient) [15].

Table 3. Total daily insulin dose calculation based on patients' average carbohydrate intake (patient number 1 through 10 only)
Table 3. Total daily insulin dose calculation based on patients' average carbohydrate intake (patient number 1 through 10 only)

Both input and output was made into membership functions according to set ranges and fed into the fuzzy system. The system was then made to generate an output for daily insulin units which incorporated all three patient related factors.

Defining the fuzzy membership functions

The MATLAB Fuzzy Logic Designer Toolbox has been used to determine the output, namely Insulin dosage (insulin dose), against the inputs, i.e. a subject’s Body Mass Index (BMI), Carbohydrate intake (CHO) and Weight. All the variables are fuzzified and the membership functions are set to be triangular, with different ranges. The BMI and CHO has membership functions with three fuzzy values- Low (L), Optimum (O), High (H); the WEIGHT, however, has six fuzzy values Very Low (VL), Low (L), Optimum 1 (O1), Optimum 2 (O2), High (H), Very High (VH). The output variable, insulin dose, has five fuzzy values- A, B, C, D and E. Table 4 shows the ranges of the INPUTS and the OUTPUT, considered for the system. Table 5 illustrates the fuzzy value breakdown and their ranges for BMI and CHO.

Table 4. Ranges of the INPUTS and OUTPUTS Inputs Output BMI CHO WEIGHT Insulin Dose

0 – 40 340 - 490 71 – 100 25 – 55

Table 5. Fuzzy value breakdown and their ranges for BMI and CHO. BMI CHO
Table 5. Fuzzy value breakdown and their ranges for BMI and CHO. BMI CHO

Unity membership point is the point where the membership function has a membership value of 1. The membership of CHO reaches unity at 340 for L, 415 for O and 490 for H; meaning an intake of 340 carbohydrate is Low, 415 is the optimum amount of carbohydrate for a subject and 490 implies a high amount of carbohydrate intake. Anything in the middle has a membership lower than 1.

The variable WEIGHT is fuzzified with six triangular membership functions. Table 6 delineates the breakdown of WEIGHT.

Table 6. Fuzzy value breakdown for WEIGHT. WEIGHT Range Unity membership point
Table 6. Fuzzy value breakdown for WEIGHT. WEIGHT Range Unity membership point

The output variable i.e. the insulin dose is also fuzzified with triangular function, but only five membership functions are made, as stated previously. The fuzzy values, their corresponding ranges, and their unity membership points are given in Table 7.

Table 7. Fuzzy value breakdown for insulin dose. Insulin Dose Range Unity membership point
Table 7. Fuzzy value breakdown for insulin dose. Insulin Dose Range Unity membership point

As stated previously, all the membership functions are chosen to be triangular. There is no region of overlapping membership in any of the variable. Figure 1 shows the

Figure 1. The membership functions of BMI
Figure 1. The membership functions of BMI

The three triangular membership functions (L, O, H) of

Figure 2.The membership functions of CHO
Figure 2.The membership functions of CHO

The last input variable is WEIGHT which has six triangular membership functions (VL, L, O1, O2, H, VH). Shown in Figure 3 are the memberships of the six fuzzy values of WEIGHT.

Figure 3. The membership functions of WEIGHT
Figure 3. The membership functions of WEIGHT

The last set of membership functions of the system is that of the output, i.e. insulin dose- which includes five membership functions (A, B, C, D, E). Figure 4 illustrates

Figure 4. The membership functions of insulin dose
Figure 4. The membership functions of insulin dose

To recapitulate, all of the above figures and tables illustrate that triangular functions were used in the fuzzification of all variables and nowhere in the memberships did any overlapping take place.

Setting the rules for fuzzy inference

Setting the rules for the input/output relationship succeeds after the definition of membership functions, for fuzzy inference. This is where the decision making is outlined. The if/then relationships are used to set the rules for the inference. The system presented in this paper has 54 if/then the three input variables (BMI, CHO, WEIGHT) to give an output (insulin dose). The decision matrices, used in setting the if/then rules, for insulin dose are shown in the Table 8 to

Table13.
Table13.
Table 8. The decision matrix, considering WEIGHT = VL CHO L O H L A C C
Table 8. The decision matrix, considering WEIGHT = VL CHO L O H L A C C
Table 9. The decision matrix, considering WEIGHT = L CHO L O H L B C C
Table 9. The decision matrix, considering WEIGHT = L CHO L O H L B C C
Table 10. The decision matrix, considering WEIGHT = O1 CHO L O H L A B C
Table 10. The decision matrix, considering WEIGHT = O1 CHO L O H L A B C
Table 11. The decision matrix, considering WEIGHT = O2 CHO L O H L A B C
Table 11. The decision matrix, considering WEIGHT = O2 CHO L O H L A B C
Table 12. The decision matrix, considering WEIGHT = H CHO L O H L B C C
Table 12. The decision matrix, considering WEIGHT = H CHO L O H L B C C
Table 13. The decision matrix, considering WEIGHT = VH CHO L O H L B C D
Table 13. The decision matrix, considering WEIGHT = VH CHO L O H L B C D

From Table 13, it can be inferred from the decision matrix that, when WEIGHT = VH (95 - 100), BMI = O (25 - 30), CHO = L (340 - 390), the preferred insulin dosage will be, insulin dose = D (43.5 – 49.5). The above contention can be read linguistically as “when a subject’s weight is very high (95kg - 100 kg), BMI is optimum (25 - 30), and carbohydrate intake is low (340g – 390g) – his/her insulin dosage should be between 43.5 and 49.5. The fuzzy if/then rules for the inference are set from the decision tables and are depicted as follows:

1. If (BMI is L) and (CHO is L) and (WEIGHT is VL) then (insulindose is A) 2. If (BMI is L) and (CHO is O) and (WEIGHT is VL) then (insulindose is C) 3. If (BMI is L) and (CHO is H) and (WEIGHT is VL) then (insulindose is C) 4. If (BMI is O) and (CHO is L) and (WEIGHT is VL) then (insulindose is B) 5. If (BMI is O) and (CHO is O) and (WEIGHT is VL) then (insulindose is C) 6. If (BMI is O) and (CHO is H) and (WEIGHT is VL) then (insulindose is C) 7. If (BMI is H) and (CHO is L) and (WEIGHT is VL) then (insulindose is C) 8. If (BMI is H) and (CHO is O) and (WEIGHT is VL) then (insulindose is C) 9. If (BMI is H) and (CHO is H) and (WEIGHT is VL) then (insulindose is D) 10. If (BMI is L) and (CHO is L) and (WEIGHT is L) then (insulindose is B) 11. If (BMI is L) and (CHO is O) and (WEIGHT is L) then (insulindose is C) 12. If (BMI is L) and (CHO is H) and (WEIGHT is L) then (insulindose is C) 13. If (BMI is O) and (CHO is L) and (WEIGHT is L) then (insulindose is C) 14. If (BMI is O) and (CHO is O) and (WEIGHT is L) then (insulindose is C) 15. If (BMI is O) and (CHO is H) and (WEIGHT is L) then (insulindose is D) 16. If (BMI is H) and (CHO is L) and (WEIGHT is L) then (insulindose is C) 17. If (BMI is H) and (CHO is O) and (WEIGHT is L) then (insulindose is D) 18. If (BMI is H) and (CHO is H) and (WEIGHT is L) then (insulindose is D) 19. If (BMI is L) and (CHO is L) and (WEIGHT is O1) then (insulindose is A) 20. If (BMI is L) and (CHO is O) and (WEIGHT is O1) then (insulindose is B) 21. If (BMI is L) and (CHO is H) and (WEIGHT is O1) then (insulindose is C) 22. If (BMI is O) and (CHO is L) and (WEIGHT is O1) then (insulindose is B) 23. If (BMI is O) and (CHO is O) and (WEIGHT is O1) then (insulindose is B) 24. If (BMI is O) and (CHO is H) and (WEIGHT is O1) then (insulindose is D) 25. If (BMI is H) and (CHO is L) and (WEIGHT is O1) then (insulindose is C) 26. If (BMI is H) and (CHO is O) and (WEIGHT is O1) then (insulindose is D) 27. If (BMI is H) and (CHO is H) and (WEIGHT is O1) then (insulindose is E) 28. If (BMI is L) and (CHO is L) and (WEIGHT is O2) then (insulindose is A) 29. If (BMI is L) and (CHO is O) and (WEIGHT is O2) then (insulindose is B) 30. If (BMI is L) and (CHO is H) and (WEIGHT is O2) then (insulindose is C) 31. If (BMI is O) and (CHO is L) and (WEIGHT is O2) then (insulindose is B) 32. If (BMI is O) and (CHO is O) and (WEIGHT is O2) then (insulindose is C) 33. If (BMI is O) and (CHO is H) and (WEIGHT is O2) then (insulindose is D) 34. If (BMI is H) and (CHO is L) and (WEIGHT is O2) then (insulindose is C) 35. If (BMI is H) and (CHO is O) and (WEIGHT is O2) then (insulindose is D) 36. If (BMI is H) and (CHO is H) and (WEIGHT is O2) then (insulindose is E) 37. If (BMI is L) and (CHO is L) and (WEIGHT is H) then (insulindose is B) 38. If (BMI is L) and (CHO is O) and (WEIGHT is H) then (insulindose is C) 39. If (BMI is L) and (CHO is H) and (WEIGHT is H) then (insulindose is C) 40. If (BMI is O) and (CHO is L) and (WEIGHT is H) then (insulindose is B) 41. If (BMI is O) and (CHO is O) and (WEIGHT is H) then (insulindose is D) 42. If (BMI is O) and (CHO is H) and (WEIGHT is H) then (insulindose is D) 43. If (BMI is H) and (CHO is L) and (WEIGHT is H) then (insulindose is C) 44. If (BMI is H) and (CHO is O) and (WEIGHT is H) then (insulindose is D) 45. If (BMI is H) and (CHO is H) and (WEIGHT is H) then (insulindose is E) 46. If (BMI is L) and (CHO is L) and (WEIGHT is VH) then (insulindose is B) 47. If (BMI is L) and (CHO is O) and (WEIGHT is VH) then (insulindose is C) 48. If (BMI is L) and (CHO is H) and (WEIGHT is VH) then (insulindose is D) 49. If (BMI is O) and (CHO is L) and (WEIGHT is VH) then (insulindose is D) 50. If (BMI is O) and (CHO is O) and (WEIGHT is VH) then (insulindose is D) 51. If (BMI is O) and (CHO is H) and (WEIGHT is VH) then (insulindose is E) 52. If (BMI is H) and (CHO is L) and (WEIGHT is VH) then (insulindose is D) 53. If (BMI is H) and (CHO is O) and (WEIGHT is VH) then (insulindose is E) 54. If (BMI is H) and (CHO is H) and (WEIGHT is VH)

Insulin dosage recommendation by defuzzification and surface diagrams

After the inputs/outputs are defined and the rules are set, the last step is the defuzzification of the system, where the system will return a crisp value for the output, in this caseinsulin dose. There are different methods of defuzzification available in MATLAB. For this paper, the ‘Centroid’ method is used, as this method gives close approximate results for the subject under consideration. After defuzzification, a single crisp number recommendation, for insulin dosage, is obtained. Figure 5 shows a recommendation for an insulin dose of 39.5, returned by the fuzzy logic system after defuzzification, for a subject with a BMI of 28, a carbohydrate intake of 466gm, and a weight of

Figure 5. A recommendation of insulin dosage returned by the fuzzy logic system
Figure 5. A recommendation of insulin dosage returned by the fuzzy logic system

The surface diagrams, provided in Figure 6 through Figure 8, illustrate the relationships among BMI, CHO, WEIGHT

Figure 6. Surface diagram of insulin dose against CHO and
Figure 6. Surface diagram of insulin dose against CHO and
Figure 7: Surface diagram of insulin dose against WEIGHT and BMI
Figure 7: Surface diagram of insulin dose against WEIGHT and BMI
Figure 8: Surface diagram of insulin dose against WEIGHT and CHO
Figure 8: Surface diagram of insulin dose against WEIGHT and CHO

The surface diagram visualizes the relationships between variables, in this case BMI, CHO, WEIGHT and the output insulin dose.

Results and Discussion

All of the patents in the sample population were chosen at random and are residents of Dhaka, Bangladesh. These patients were already undergoing insulin treatment on a regular basis hence they all had prescription knowledge beforehand. The predicted doses for all 39 patients were then compared to the actual prescribed doses by the physicians in Table 14. Table 14 also shows the numerical differences between the two doses for each patient.

The numerical differences between the predicted and the prescribed insulin doses suggest that there was a correction based on the three patient related factors (PRFs) provided. Some doses were significantly different in comparison to the prescribed doses; for example in the case of patient 6. Here the numerical difference in dose was +22.6 units; as in the prescribed dose was significantly lower compared to the predicted dose. This dose was suggested to the patient as a better fit, especially considering the fact that the patient experienced hyperglycemic events on a regular basis.

Table 14. Predicted dose vs. prescribed dose of daily insulin units for each of the 39 patients
Table 14. Predicted dose vs. prescribed dose of daily insulin units for each of the 39 patients

Patient 6 was then observed for one full week with the adjusted dose and the number of hyperglycemic events reduced significantly. Thus, for this one case the higher dose of insulin led to better blood glucose regulation. Only in the cases of six patients was the numerical difference a negative number. This meant that the prescribed dose was higher than the dose predicted by the fuzzy system. Among the patient population, a common trend was observed in terms of the frequency of occurrences of hyperglycemic events. This is the reason why for a number of patients, the numerical differences were in excess of +10. For these patients, a higher dose of insulin may reduce the chances of these events and increase the quality of life. However, it is important to realize that if the insulin dosage is too high, then hypoglycemic events may start to exude. For example, Rubin et al. conducted a study on insulin related hypoglycemic events on 1990 hospital patients and concluded that chances of these events were low at a threshold below 0.6 units/kg [13]. Table 15 shows the values of units/kg for each patient for the daily insulin doses calculated by the fuzzy system. The fact that all of these values were below 0.6 units/kg may be a key factor in reducing hypoglycemic events for the patient population used in this study.

Table 15. Units/kg values for predicted dose using fuzzy system of daily insulin units for 39 patients
Table 15. Units/kg values for predicted dose using fuzzy system of daily insulin units for 39 patients

Conclusion

Since the fuzzy based system provides a more personalized calculation for daily insulin doses, it may create better regulation for blood glucose levels for type 2 diabetes patients. This fact should eventuate once the patient blood glucose levels are monitored over long periods of time. For patient 6 in particular, the benefits were apparent after a week of observation. For this one case, the fuzzy-based system was able to predict a more accurate dose leading to better blood glucose control. It is conceivable that these adjusted doses might translate to better glucose control for other patients as well but further observations need to be made in order for that claim to be conclusive.

References

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