Comparative Study between In-silico and Clinical Works on the Control of Blood Glucose Level in People with Type 1 Diabetes using Improved Hovorka Equations

Background Hovorka model is one of the diabetic models which is widely used in the artificial pancreas device (APD) also known as closed loop system, meant for people with type 1 diabetes (T1D). Previous workers had modified some equations in the sub-sections of the Hovorka model, which is also known as improved Hovorka equations, in regulating the blood glucose level (BGL) within normoglycemic range (4.0 to 7.0 mmol/L). However, the improved Hovorka equations have not been tested yet in terms of its usability to regulate and control the BGL in safe range for two or more people with T1D. This study aims to simulate their BGL with meal disturbances for 24 hours using the improved Hovorka equations. Methods Data for people with T1D were obtained from Clinic 1, Clinical Training Centre (CTC), UiTM Medical Specialist Centre, Sungai Buloh, Selangor. Data collected include gender, age, body weight, mealtimes, meal amount, and duration. Three patients whose ages range from 11 to 14 years old were selected. All patients consumed three meals daily: breakfast, lunch, and dinner. The simulation (in-silico work) was done using MATLAB software, and the BGL profile from both in-silico and clinical works were compared and analysed. Results It was revealed that the BGLs for all three people with T1D were far better in the in-silico work compared to the clinical work. The BGL for patient 1 was able to achieve normoglycaemia 73% of the time in the in-silico work. Meanwhile, patient 2 managed to stay in the normoglycemic range for 85% of the time in the in-silico work compared to clinical work, which was merely 31%. For Patient 3, the time duration spent in the normoglycemic range was only 16% in the in-silico work compared to none as in the clinical work. The p-values obtained in the study were less than 0.05, indicating that the in-silico work using the improved Hovorka equations was acceptable for predicting the BGL for people with T1D. Conclusions It can be concluded that the improved Hovorka equations are reliable in simulating the meal disturbances effect on BGL and increasing people in T1D times’ duration in the normoglycemic range compared to the clinical work.

18 in delivering the proper insulin dosage to people with T1D. Previous workers had modified 19 some equations in the sub-sections of the Hovorka model [4], which is also known as improved 20 Hovorka equations, in regulating the blood glucose level (BGL) within normoglycemic range 21 (4.0 to 7.0 mmol/L) [5][6]. However, the improved Hovorka equations have not been tested yet 22 in terms of its usability to regulate and control the BGL in safe range for two or more people 23 with T1D. This study aims to simulate their BGL with meal disturbances for 24 hours using 24 the improved Hovorka equations. Then, the patients' BGL from the simulation (in-silico work) 25 are compared with the clinical work. This study is a continuation of work from the previous 26 studies [7][8][9].

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Ethical approval for this study was granted by the UiTM Ethics Committee before data 30 collection was commenced. Information sheets were provided, and formal consent for 31 participation was obtained from parents or guidance of the focus groups, i.e., three people with 32 T1D ages range from 11 to 14 years old. Data collected include name, age, gender, body 33 weight, meal times, amounts of meals consumed, and meal duration. Tables 1 to 3 summarise 34 the amounts of meals consumed in 24 hours for the three people with T1D. Detailed meal 35 contents for the study were adopted from the previous work [10]. All the three people with 36 T1D were on self-monitoring of blood glucose (SMBG) via finger pricks and their BGLs were 37 taken before and after each meal intake namely: during breakfast, lunch, and dinner.

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The improved Hovorka model based on Hovorka model [4] is specifically designed for 41 of three subsystems: the glucose subsystem, insulin subsystem, and insulin action subsystem.
42 Equations for glucose subsystem are as shown in Eq. (1) and (2): 48 where: Q 1 (mmol) is mass of glucose in accessible compartment, Q 2 (mmol) is mass of glucose 49 in non-accessible compartment, k w1 , k w11, k w2 , k w22 , k w3 , and k w33 (min -1 ) are activation rates, 50 k 12 (min -1 ) is transfer rate, EGP 0 is endogenous glucose production (EGP) extrapolated to zero 51 insulin concentration, V G (L/kg) is glucose distribution volume, G (mmol/L) is glucose 52 concentration, x 1 , x 2 , and x 3 are the effects of insulin on glucose transport and distribution, 53 glucose disposal, and EGP respectively, F 01 c (mmol min -1 kg -1 ) is total non-insulin dependent 54 glucose flux, and F R (mmol/min) is renal glucose clearance.

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When a meal is consumed, the carbohydrate (CHO) content will be broken down into 56 glucose prior to being converted into energy. Thus, increasing the BGL. The equation to 57 observe the effect of meal disturbances on BGL is shown in Eq. (5). Where,

D G = amount of carbohydrate (CHO) digested (mmol)
A G = carbohydrate bioavailability t max,G = time-to-maximum of CHO absorption (min) 59 Eq. (6) to (8) show the insulin subsystem. Insulin is administered subcutaneously. This method 60 is less invasive than the intravenous method, in which insulin is injected directly into the 61 bloodstream. 62 63 64 The insulin absorption rate in the bloodstream is given by Eq. (9).
65 where: S 1 and S 2 (mU) are insulin sensitivity in accessible and non-accessible compartments 66 respectively, u(t) (mU/min) is bolus insulin, t max,I (min) is time-to-maximum of insulin 67 absorption, U I (mU/min) is insulin absorption rate, V I (L/kg) is insulin distribution volume, 68 and k e (min -1 ) is fractional elimination rate.

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The in-silico work was performed based on the estimated meal disturbances on the 74 people with T1D as adopted from [10]. The amounts of insulin administered (U t ) selected for 75 this study were namely: 0.100 U/min for high dosages, 0.050 U/min for medium dosage and 76 0.0167 U/min for low dosage as also adopted from [10]. The simulation (in-silico work) using 77 the improved Hovorka equations was done in MATLAB and data obtained were then collected 78 for further analysis and evaluation.