Control of Blood Glucose Level for Type 1 Diabetes Mellitus using Improved Hovorka Equations: Comparison between Clinical and In-Silico Works

Background Type 1 diabetes mellitus (T1DM) occurs due to inability of the body to produce sufficient amount of insulin to regulate blood glucose level (BGL) at normoglycemic range between 4.0 to 7.0 mmol/L. Thus, T1DM patients require to do self-monitoring blood glucose (SMBG) via finger pricks and depend on exogenous insulin injection to maintain their BGL which is very painful and exasperating. Ongoing works on artificial pancreas device nowadays focus primarily on a computer algorithm which is programmed into the controller device. This study aims to simulate so-called improved equations from the Hovorka model using actual patients’ data through in-silico works and compare its findings with the clinical works. Methods The study mainly focuses on computer simulation in MATLAB using improved Hovorka equations in order to control the BGL in T1DM. The improved equations can be found in three subsystems namely; glucose, insulin and insulin action subsystems. CHO intakes were varied during breakfast, lunch and dinner times for three consecutive days. Simulated data are compared with the actual patients’ data from the clinical works. Results Result revealed that when the patient took 36.0g CHO during breakfast and lunch, the insulin administered was 0.1U/min in order to maintain the blood glucose level (BGL) in the safe range after meal; while during dinner time, 0.083U/min to 0.1 U/min of insulins were administered in order to regulate 45.0g CHO taken during meal. The basal insulin was also injected at 0.066U/min upon waking up time in the early morning. The BGL was able to remain at normal range after each meal during in-silico works compared to clinical works. Conclusions This study proved that the improved Hovorka equations via in-silico works can be employed to model the effect of meal disruptions on T1DM patients, as it demonstrated better control as compared to the clinical works.

An attempt also has been made by previous researchers to improve the existing 48 Hovorka equations [12][13][14][15]; however, as of to date, there are still no clinical data used in the 49 simulation work so as to prove the applicability and userability of the newly developed 50 control algorithm using the improved Hovorka equations. Furthermore, a comparative study 51 has to be made between the finding results from the clinical work and in-silico work 52 (simulated result via improved equations) using actual T1DM patients' data in order to compare their performances in regulating BGL for sustainable purposes in the future. 54 Therefore, the objectives of this study are; 1) to determine the amount of administered 55 exogenous insulin required to regulate the BGL in the normoglycemic range at all times for 56 T1DM patients, 2) to compare the findings between the clinical and in-silico works using 57 actual patient data in terms of its performance, and 3) to determine the userability and 58 applicability of the improved Hovorka equations for model verification. 59 The study is only limited to the effect of meal disturbances to the BGL without 60 considering other disturbances such as stress and physical activities. Apart from that, 61 hormone used is limited to insulin only and served in regulating the BGL for T1DM. T1DM Artificial pancreas is a device that closely imitates the function of actual pancreas in 72 regulating blood glucose level. In general, artificial pancreas device comprises the following 73 parts; continuous glucose monitoring (CGM) sensor, CGM receiver, control algorithm device 74 (CAD) and continuous subcutaneous insulin infusion (CSII) pump [16]. CGM sensor 75 measures the blood glucose level continuously via the sensor attached on the skin prior to 76 transmitting to the CGM receiver from which it displays the current readings and trends of blood glucose in the form of a graph. The readings are sent to the CAD such as smartphone 78 or personal computer (PC) whereby the algorithms analyse and calculate the insulin doses 79 required. The CAD then interacts with the insulin pump to deliver proper doses of insulin.

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Previous works related to managing diabetes had been done especially towards using 82 mathematical modelling in the past 50 years in which these works were developed to simulate 83 the glucose-insulin dynamic system [17][18][19][20][21][22][23][24]. For the purpose of this study, improved Hovorka 84 equations from Hovorka Model [21] are used to facilitate the simulation work. In improved 85 Hovorka equations, additional parameters have been added into the glucose subsystem, 86 insulin action subsystem and plasma insulin subsystem whilst the rest of the equations remain 87 the same [14]. This improvement of the equations is done due to lacks of interaction between 88 the parameters and variables in the insulin action subsystem and mass of glucose in 89 accessible compartment (Q 1 ) and non-accessible compartment (Q 2 ) [14]. The results had 90 caused a change in behaviour in Q 1 and Q 2 when compared to Hovorka model [21].

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Therefore, the improved Hovorka equations are expected to be more precise and highly 92 efficient in stabilizing glucose-insulin regulatory system for T1DM. More details on the 93 improved Hovorka equations can be found in the methodology section.  proportional-integral-derivatives (PID) control, neural network control, fuzzy logic control, 99 and model predictive control (MPC) as can be encountered in the literature [25][26][27][28][29]. This  [30]. Some of the 107 applications of mp-MPC include automotive (catalytic converters), biomedical (artificial 108 organs and drug delivery) and industrial (robotics and process control) [30]. Past work using 109 eMPC as control strategy can be seen in the literature [31]. clinical and in-silico works were then compared, accordingly. Figure 1 shows the schematic flow diagram of the methodology, and Table 1 shows brief information of patient 1.
As mentioned above, data from the clinical works were used to simulate the improved 128 Hovorka equations in the in-silico works. The improved Hovorka equations were adopted 129 from Yusof et al. [14] The glucose subsystem, plasma insulin subsystem and insulin action 130 subsystem equations in the original Hovorka method have been modified while other 131 formulas remain unchanged. Figure 2 shows the schematic flow diagram of the improved 132 equations adapted from [24]. The improved equations are described as follows:

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Glucose subsystem 134 In the improved Hovorka equations, the glucose subsystem can be represented by the 135 following equations:

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Where the total non-insulin dependent glucose flux, F 01 c (mmol/min), and renal glucose 139 clearance, F R (mmol/min), can be found as in equations (3) and (4).
Where, Q 1 (t) = mass of glucose in accessible compartment (mmol) Q 2 (t) = mass of glucose in non-accessible compartments (mmol) U G = gut absorption rate (mmol/min)

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Equation for meal disturbances is represented by equation (5)

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Where, Plasma insulin subsystem 146 The insulin subsystem can be represented by the following equations: 149  (6).

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Constants and parameters involved in the equations are shown in the Tables 2 and 3.

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The simulation work on the meal disturbances was based on the actual patients' daily 160 meals intake. Table 4 shows an example of amount of daily meals intake specifically 161 carbohydrate (CHO) suggested for a male patient aged 13 years old (Patient 1). The 162 suggested meal intake is based on total daily calorie requirement which varies according to 163 age and gender as shown in Table 5. It consists of breakfast, lunch and dinner at which this 164 information is adopted into the simulation work using the improved Hovorka equations.

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Initial values for S 1 , S 2 , x 1 , x 2 , and x 3 were set at zero since the insulin had not been 196 injected into the patient's body and the insulin being administered which caused glucose 197 transport/distribution, glucose disposal and EGP had not yet occurred [24]. The bolus insulin    The BGL rose from 4.50 to 9.13 mmol/min after 30 minutes of the meal time, the highest normoglycemic range of 6.93 mmol/L at t = 965 min. Figures 5 to 7 show the detailed day 1 242 simulation work profiles of BGL versus time for breakfast, lunch and dinner, respectively. 243 Table 6 shows the comparison of BGL (at peak) between clinical and simulation 244 works for patient 1 on day 1. The BGL for clinical work was significantly higher than the   Table 9 shows the comparison of BGL at peak condition between clinical and   Figure 12 shows the profile of BGL versus time for clinical work (blue line) and 293 simulation work (yellow line) for 24-hours of patient 1 on day 3. Based on Figure 12 the BGL recorded an increase from 4.50 to 9.14 mmol/L prior to gradually descending upon reaching the normoglycemic range at t = 1100 min. Figures 14 to 16 show the detailed day 3 Table 12 shows the comparison of peak BGL between clinical and simulation works 317 on day 3. The BGL for clinical work was apparently higher than the simulation work. The 318 highest BGL was recorded at 17.40 mmol/L during breakfast in the clinical work, while it 319 was registered only at 9.74 mmol/L in the simulation. Table 13 shows that p value of x-320 variable 1 for clinical data was higher than 0.05 which indicated the data was not statistically were below 0.05 which indicated that the data were statistically reliable and very strong as 324 shown in Table 14. It has proven again that simulation work is better at controlling BGL than 325 the clinical work.