Glucose profiles from fifteen subjects, including five subjects without DM (control group), four subjects with T1D and six subjects with T2D, were collected by our clinical col- laborator from the University of Oxford, Dr. Tim A. Holt, and were available for the study [144]. The recruitment ensured a diverse sample of ages and treatment regimens. Baseline biographical data were obtained on age, sex, body mass index, type of DM,
treatment regimen listed in Table3.1 is assumed to be consistent throughout the whole experimental period, and does not affect the modelling development in this study, be- cause the main focus of this research is the dynamics of the glucose response following food intake. Medtronic Minimed CGM devices were used to obtain blood glucose values every 5 minutes over 72 hours, and one participant in the T1D group voluntarily (on the independent advice of their clinician) kept the device on for more than 6 days. The CGM devices use enzymatic sensors that are inserted subcutaneously in the abdomen to measure the interstitial fluid glucose concentration. There are 3 – 12 minutes of time lag between the interstitial fluid glucose concentration and the plasma glucose concentration due to the diffusion of glucose across the capillary endothelial barrier [137]. Measurement time seriesG(ti) are available for each subject, and comprise the glucose concentrations
(in mmol/L) at time points ti =ih, whereh = 5 minutes is the sampling interval and i= 1,2, . . . , N (N is the number of measurement points). The measurements were taken in ‘free living’ conditions, i.e. no restrictions were placed on the subjects’ daily activities or food intake. The types of meals taken and the calorific intake are not available. Several example time series are presented in Fig.3.2. The dotted peaks in the time series represent the postprandial blood glucose excursions. To avoid mistaking measurement noise for genuine postprandial peaks, only distinguishable peaks with height more than 1.1 mmol/L during the daytime from 6 am to midnight were selected. The highest peak value for the subjects in the control group is just below 8 mmol/L, whereas the highest values for the T1D and T2D patients are greater than 15 mmol/L. Because the CGM devices need calibration at the beginning of each experiment and all the subjects started wearing the device during the evening time of the first day, the first peak for all the participants is selected as the first peak of the second day, which can be seen in Fig. 3.2. Since there are no restrictions on the time and the number of meals (food intake), the subjects have various numbers of distinguishable peaks corresponding to food intake events (between five to fourteen peaks for each individual).
There was no detailed information about the time of the food intake. The glucose concentration time series measured in the interstitial fluid by the CGM device was known to have a lag behind the blood glucose concentration. Therefore, the beginnings of the transient responses to each food intake needed to be determined by the modeller. After the transient response, the glucose concentration settled to a steady state. It was common in the fifteen time series that another external excitation (such as food
Table 3.1: Biometric indices, treatment regimens, HbA1c values and corresponding
estimated average blood glucose levels of participants.
No. Age Sex BMI Diabetes Treatment HbA1c Glucose level
kg/m2 status regimen mmol/mol mmol/L
1 57 F 20.5 T1D Basal bolus 63 10.0
(glargine plus aspart)
2 27 F 19.2 Control N/A N/A N/A
3 59 F 27.3 Control N/A N/A N/A
4 49 F 21.9 Control N/A N/A N/A
5 32 F 29.4 T1D Insulin pump 55 9.0 6 74 M 20.5 T2D Metformin, 61 9.7 gliclazide, rosiglitazone 7 66 F 25.9 T1D Insulin pump 38 6.3 8 75 M 23.4 T2D Metformin 46 7.6 9 68 F 32.7 T1D Basal bolus 48 7.8 (glargine plus aspart)
10 39 F 21.3 Control N/A N/A N/A
11 61 F 32.6 T2D Metformin 52 8.4
12 56 M 30.0 T2D Metformin 68 10.8
13 52 F 44.5 T2D Metformin, 89 13.8
glargine
14 22 F 19.6 Control N/A N/A N/A
15 63 F 27.0 T2D Newly diagnosed 42 7.0
intake, exercise, etc.) occurred before the glucose concentration had the chance to settle. In these cases, the response to the first food intake was interrupted and the steady state, which was the basal level Gb, remained unknown. The basal glucose level
usually demonstrates slow nonstationary dynamics [144]. Therefore, the basal level for each individual peak was considered different. Compared with the baseline differences from peak to peak, the baseline variations within the duration time of a single peak could be neglected and the baselines were considered as constant during the transient response to one food intake.
Figure 3.2: Example subcutaneous glucose time seriesGof a participant from (a) the control group (b) the T1D group (c) the T2D group. The solid grey curves represent the measured glucose values and the dots are the values used for modelling of single postprandial peaks. The solid and dashed vertical lines correspond to midnight (0 hours) and 6 am respectively. The first several hours of data in Day 1 (to the left from the first solid vertical lines) were excluded from the modelling due to the adjustment period of the CGM system. ‘B’ indicates breakfast, ‘S’ indicates snack, ‘L’ indicates
lunch, ‘D’ indicates dinner.
common patterns are as follows: 1) peaks with a clear and almost symmetrical rise and fall, such as the first peak in Fig.3.2 (c); 2) peaks with a steep rise followed by a slow fall and then a rapid fall, such as four peaks marked with ‘∗’ in Fig. 3.2 (b); 3) peaks with a distinguishable secondary peak indicated with ‘×’, or with multiple subpeaks
indicated with ‘o’ in Fig. 3.2 (a) and (b). According to [146], the glucose variations after food intake (and therefore the shape of the curves) can be influenced by different macro-nutrients of the meal, the time of the meal, the gender of the subjects and the diurnal cycling of hormones [146]. The peak shape variation is most likely due to erratic gastric emptying. The appearance of glucose in plasma depends on the gastric emptying rate. Liquids display exponential gastric emptying without an initial lag, while solids show biphasic gastric emptying with a lag [147]. When there are multiple peaks existing within a short period of time (within 3 hours), they may be caused by various emptying rate for different meal compositions or a pulsation secretion of insulin for the same food intake event, but can also be caused by two separate food intake events within a short interval of time. The complex patterns and the varieties in peak dynamics, as well as the lack of information on the precise food intake (including time, quantity and the constitution of macro-nutrients) make the task of finding a universal model difficult. Observing the time series in Fig.3.2can provide valuable information about the subjects’ food routines. For example, the peaks representing breakfasts for the subject in Fig. 3.2(c) are similar suggesting the subject has a daily breakfast routine. The small peaks between the breakfast and lunch in both days suggest that the subject also has a routine of eating a snack before lunch. Other subjects, such as the time series shown in Fig.3.2 (b), have less fixed meal times and more varieties of features in peaks that represent the same meal in different days.