Analyzing the Potential of Advanced Insulin Dosing Strategies in Patients With Type 2 Diabetes: Results From a Hybrid In Silico Study

Abstract

Background:

The ongoing improvement of continuous glucose monitoring (CGM) sensors and of insulin pumps are paving the way for a fast implementation of artificial pancreas (AP) for type 1 diabetes (T1D) patients. The case for type 2 diabetes (T2D) patients is less obvious since usually some residual beta cell function allows for simpler therapy approaches, and even multiple daily injections (MDI) therapy is not very widespread. However, the number of insulin dependent T2D patients is vastly increasing and therefore a need for understanding chances and challenges of an automated insulin therapy arises. Based on this background, this article analyzes conditions under which the use of more advanced therapeutic approaches, particularly AP, could bring a substantial improvement and should be considered as a viable therapy option.

Method:

Data of 14 insulin-treated T2D patients on MDI wearing a CGM device and deviation analysis methods were used to estimate the expected improvements in the clinical outcome by using self-monitoring of blood glucose (SMBG) with advanced carbohydrate counting, a full AP or intermediate approaches, either CGM measurements with MDI therapy or SMBG with insulin pump. HbA1C and time in range (70-140 mg/dl, 70-180 mg/dl, respectively) were used as a performance measure. Outcome measures beyond glycemic control (eg, compliance, patient acceptance) have not been analyzed in this study.

Results:

AP has the potential to improve the condition of many poorly controlled insulin-treated T2D patients. However, as the interpatient variability is much higher than in T1D, a prescreening is recommended to select suitable patients.

Conclusions:

Clinical criteria need to be developed for inclusion/exclusion of T2D patients for AP related therapies.

Artificial pancreas (AP) has been developing from an academic interest to a viable option for T1D patients over the years.^1-5 Clinical trials have proven the safety and effectiveness for AP in real-life settings (see, eg, Thabit et al).⁶ First commercial devices for T1D patients have recently become available (Medtronic has launched their commercial AP system in the US in 2017 and competitors are soon to follow).⁷ The rationale behind it is evident since all T1D patients require insulin and the correct dosage of insulin has an enormous impact on the risk for short-term and long-term complications. Continuous glucose monitoring (CGM) is also becoming more and more widespread among T1D patients, mainly due to its substantial increase in accuracy over the last couple of years and (as a consequence) its ability to accurately detect early or even predict hypoglycemia and to issue alarms. Once a CGM is in place, it is quite intuitive to connect it to an insulin pump for continuous subcutaneous insulin infusion (CSII). The simplest form of AP is the pump shut down approach, in which the insulin flow is suspended as soon as the glucose value measured by the CGM crosses a lower threshold.

Opposed to the multitude of clinical trials in T1D, there is few data available for advanced technological treatment interventions in T2D patients. In the Opt2mise trial it was shown that for insulin-treated T2D patients with unsatisfactory glycemic control on MDI therapy a significant improvement (in terms of HbA1c, but also time in range) can be achieved by using an insulin pump.^8-10 In the DIAMOND trial on the other hand it was found that CGM use can help to improve glycemic control (HbA1c and time in range) for insulin-treated T2D patients on MDI therapy.¹¹ However, regarding AP solutions for T2D there is so far a lack of clinical data with the exception of two studies by the Hovorka group conducted in a hospital setting^12,13 and a small Canadian pilot trial.¹⁴ In those studies was found that AP does indeed have the potential to significantly improve time in range and to reduce time in hyperglycemic for patients with T2D in hospital settings.

In reality, the clinical priorities for most insulin-treated T2D patients are slightly different from those for T1D patients. Although hypoglycemia is a problem in insulin-treated T2D patients as well, hyperglycemia is a much bigger problem (this can, eg, be seen based on the results for the T2D patients in the DIAMOND trial).¹¹ Furthermore, insulin administration is not the only therapeutic approach, since the treatment of T2D usually starts with oral antidiabetic drugs (OAD), in particular metformin, which is the first line drug according to international guidelines. Most oral drugs are usually continued even when insulin becomes necessary. When T2D patients need insulin, usually one to two daily injections of basal insulin are sufficient for an extended period. Behind that, there is the fact that T2D is a progressive disease, and some residual beta cell function is retained, so that the therapy is in some sense designed to support the natural regulatory system and not to replace it completely, as it is the case in T1D patients.

At first glance the problem of regulating BG for T2D patients may seem easier compared to T1D due to the residual beta-cell function and lower degree of glycemic variability.^15-17 However, there are good reasons for having a closer look at possible advanced insulin treatment options for this group of patients as well. First of all, the T2D population is approximately 10 times larger than the T1D population with a fast growth rate. In addition, the life expectancy of T2D patients has been significantly increasing during the last decades. Therefore the number of insulin-treated T2D patients is increasing as well. Unfortunately, T2D patients also represent the largest group of diabetes patients affected by many diabetic complications. A large number of T2D patients do not achieve an optimal HbA1C level.

Besides the clinical outcome other aspects need to be considered, in particular the costs that come with the complex technology of an AP, as it requires using both CSII and a CGM device. The complexity of such a system might also cause a significant burden for some groups of patients, as detected in T1D patients using AP systems.¹⁸ Based on this evidence, it is legitimate to ask whether the additional complexity and costs of AP are justified for T2D patients.

The answer to this question, roughly speaking, is that AP is not a sensible choice for every insulin-treated T2D patient. However it can be for patients who do not achieve good results otherwise, especially for those who also exhibit a significant number of hypoglycemic events. For those patients using AP can potentially increase the quality of life and reduce long-term effects, such as kidney failure, retinopathy, neuropathy, and so on.

In this article, the potential of improving glycemic control by using advanced insulin dosing strategies is analyzed based on outpatient data collected at the Hvidovre University Hospital for a small group of autoantibody negative, multiple daily injections (MDI), insulin-treated T2D patients.The article studies the potential difference of advanced options for insulin treatment (including AP) in lowering the patients’ HbA1c, but also to increase time in range and decrease time in hypoglycemia and hyperglycemia. For this purpose a method called deviation analysis¹⁹ (which is also known under different names)^20-22 has been used, which allows a sensible prediction of the clinical outcome for the case of a variation of the used insulin dosage.

Data

For the simulation studies presented in this article the data of 14 MDI, insulin-treated T2D patients were used. Some key figures for those 14 patients are listed in Table 1. The patients underwent an outpatient study organized at the Hvidovre University Hospital.

Table 1.

Data of the T2D Patients Used in the Calculations.

Patient	Sex	Age (years)	Diabetes duration (year)	Height (cm)	Weight (kg)	BMI (kg/m²)	TDD basal (IU)	TDD bolus (IU)	HbA1c (%)	Avg. daily CHO intake (g)
1	Male	73	22	190	92	26	22	13	7.18	170
2	Male	54	9	188	110	31	32	22	7.73	202
3	Female	65	10	161	93	36	74	6	6.73	135
4	Female	62	14	153	65	28	38	19	7.82	94
5	Male	60	26	163	63	24	12	12	8.10	62
6	Male	67	23	175	89	29	26	40	8.65	91
7	Male	65	28	178	101	32	100	10	7.73	185
8	Male	68	15	183	124	37	100	100	8.56	140
9	Male	50	11	166	88	32	32	24	10.29	162
10	Male	73	16	180	100	31	28	30	8.56	67
11	Male	60	26	163	103	39	46	45	8.28	173
12	Male	70	18	176	84	27	28	11	8.01	151
13	Female	72	28	174	103	34	100	105	11.12	142
14	Female	65	17	159	88	35	116	12	10.75	67

The patients included in this analysis are well defined in terms of age, BMI and treatment duration, were treated with a basal-bolus insulin regimen and almost none of them were well controlled. The patients were equipped with a CGM device during their visit to Hvidovre University Hospital at the start of the trial and spent the subsequent four days at home during which they were asked to continue with their daily routines and inject their required insulin as usual. In addition, they were asked to keep a diary of their carbohydrate intake. During this time the patients used either Dexcom G4 Platinum (patients 1-4) or Medtronic iPro2 CGM sensors (patients 4-14) and their custom insulin pen. Both diary information and CGM data were collected for this analysis.

Figure 1 shows an example of a CGM measurement with the units of bolus insulin and the carbohydrate (CHO) amount of meals according to the diary. The analysis of the results of the combined BG data is illustrated in Table 2.

Figure 1.

Illustrative section of a typical dataset based on diary and CGM values as used for the current work (patient 1, day 2).

Table 2.

Analysis of the Patients’ Sensor Glucose Values for the T2D Data Used in This Work: Euglycemia 70-180 mg/dl, Hypoglycemia <70 mg/dl, Hyperglycemia >180 mg/dl.

Patient	Percentage of time in euglycemia (%)	Percentage of time in hypoglycemia (%)	Percentage of time in hyperglycemia (%)	Measured HbA1c (baseline) (%)	Calc. HbA1c from CGM data of Nathan et al23 (%)
1	68.69	0.00	31.31	7.18	7.42
2	79.44	0.43	20.12	7.73	6.99
3	81.18	0.87	17.95	6.73	6.99
4	65.13	2.26	32.61	7.82	7.28
5	94.38	0.00	5.63	8.10	6.12
6	65.90	3.70	30.40	8.65	6.99
7	91.33	8.67	0.00	7.73	5.43
8	71.68	1.39	26.94	8.56	7.02
9	26.37	0.00	73.63	10.29	8.99
10	34.64	1.43	63.93	8.56	8.53
11	42.31	0.00	57.69	8.28	8.69
12	73.64	0.00	26.36	8.01	7.36
13	0.58	0.00	99.42	11.12	10.66
14	22.43	0.00	77.57	10.75	9.30
ø	58.41	1.34	40.25	8.54	7.70

It is interesting to compare the clinical parameters of these patients with a cohort of 37 T1D patients from a different clinical trial as shown in Table 3 (data from Zschornack et al).²⁴

Table 3.

Analysis of the Patients’ Sensor Glucose Values for the T1D Patients from Zschornack et al:²⁴ Euglycemia 70-180 mg/dl, Hypoglycemia <70 mg/dl, Hyperglycemia >180 mg/dl.

Patient	Percentage of time in euglycemia (%)	Percentage of time in hypoglycemia (%)	Percentage of time in hyperglycemia (%)	Measured HbA1c (baseline) (%)	Calc. HbA1c from CGM data of Nathan et al23 (%)
37 patients with T1D	71.20 ± 10.67	6.25 ± 4.77	22.55 ± 12.68	7.75 ± 1.24	6.68 ± 0.65

It can be seen that hypoglycemia (defined as a CGM value lower than 70 mg/dl) is much less frequent in our selected T2D patient cohort compared to our selected cohort of T1D patients (percentage of time in hypoglycemia: 1.34% vs 6.25%). This corresponds to the general clinical experience that hypoglycemia is of more concern in T1D than in T2D (compare, eg, also the time in hypoglycemia between T2D and T1D patients in the DIAMOND trial).^11,25 The measured HbA1c value on the other hand was higher for the group of T2D patients (average HbA1c: 8.54% vs 7.75%).

It is interesting to see that for both groups of patients there is a significant discrepancy between the HbA1c measured at entry to the trial and an estimated HbA1c calculated from the glucose values recorded at the start of the clinical trial. Such a study HbA1c can be computed from the CGM data of the trial using the method of Nathan et al:²³

$$HbA1c=\frac{\frac{1}{N}{{\displaystyle \sum }}_{i=1}^{N}B{G}_i+68.8}{31.5}$$

The corresponding values (determined using this formula) are reported in the last column of Table 2 and Table 3, whereas the HbA1c values actually measured at the start of the trial can be found in the fifth column. The differences between those numbers can most probably be explained by the patients being especially motivated when participating in a clinical trial.

The previously mentioned difference in glycemic variability between T2D and T1D patients (see Kohnert et al,¹⁵ Satore et al,¹⁶ Greven et al¹⁷) is also illustrated in Figure 2. In that figure a CGM dataset of 90 patients from another clinical study, the DAQ trial performed in the framework of the DIAdvisor project²⁶ (see Cescon²⁷ for details on the study protocol), compromised of both patients with T1DM and T2DM, is visualized after transforming the data to the frequency domain by means of discrete Fourier transformation (see, eg, Fico et al²⁸ for details on the methodology; an explanation of discrete Fourier transformation and visualization of data in the frequency domain can also be found in the Supplementary Material). For convenience, results are displayed as function of time period. Each colored line corresponds to the data of one patient, whereas the bold black line shows the average profile and the gray area marks mean ± standard deviation. Whereas the top panel shows the combined results for all 76 patients with T1D, the bottom panel does the same for all of the 14 patients with T2D from the DAQ trial. As Figure 2 shows, the data of T2D patients exhibit both lower interpatient variability and a lower high frequency (=smaller time period) content.

Figure 2.

Comparison of T1D and T2D frequency plots for T1D patients (76 patients, top panel) and T2D patients (14 patients, bottom panel) from the same study (DAQ trial performed in the framework of the DIAdvisor project;²⁶ see Cescon²⁷ for details on the study protocol).

All this confirms the general clinical experience in the treatment of T2D patients, but also makes it clear that the main advantage of using a CGM—the ability to cope with impending hypoglycemia, in particular during the night—is less important for T2D as it is for T1D.

All this suggests that AP could only be beneficial for a proportion of T2D patients. Still, considering the large and rising number of insulin-treated T2D patients, its relevancy should not be ignored. In addition, there is reason to believe that keeping the BG in the euglycemic range by AP will help slow the progress of this disease.²⁹

Methods

Evaluation Criteria

In the previous years it has become an understanding that besides HbA1c, an indicator for the long-term average BG value,³⁰ also the time in specific glycemic ranges, is a good indicator for the quality of BG regulation.^31,32 Three of these measures are used in this report (definitions taken from Maahs et al):³³

• Percentage of time in low BG range is defined as t_hypo/t_tot * 100 and hypoglycemia is considered when BG < 70 mg/dl.

• Percentage of time in euglycemic range is defined as t_range/t_tot * 100 and the euglycemic range is considered when 70 mg/dl < BG < 140 mg/dl.

• Percentage of time in high BG range is defined as t_hyper/t_tot * 100 and hyperglycemia is considered when BG > 180 mg/dl.

The euglycemic range is defined to correspond to the tight range of 70 mg/dl < BG < 140 mg/dl to be able to better distinguish between the performance of the different treatment options. For the common definition of 70 mg/dl < BG < 180 mg/dl for euglycemia, the differences in time ranges are smaller between the considered insulin therapies.

To estimate the change in HbA1c, resulting from a change in therapy, the HbA1c is estimated from the calculated glucose traces of the simulations using the methodology from Nathan et al.²³

Performance Assessment With Deviation Analyses

To conclusively evaluate the performance of any therapeutic intervention clinical trials are indispensable. However, clinical trials are expensive and for a certain therapeutic intervention only a limited amount of settings can be tested. In addition, it can be unethical to evaluate a therapeutic intervention in real patients without any previous data on its efficacy or safety. For the case of insulin dosing algorithms simulation studies with physiological models of the human glucose metabolism—so-called in silico evaluations—were found to be a useful tool to obtain a first impression about the possible performance of a newly proposed algorithm, as well as for some tentative fine-tuning. The most well-known step in this direction is certainly the UVA/Padova simulator³⁴ which has been accepted by the FDA as a replacement for some preliminary animal tests.³⁵ The UVA/Padova simulator uses a set of 300 virtual patients, taking the interpatient variability into account. Disturbances can be added as well, yielding a more realistic setup. However, this simulator is essentially focused on reference cases.

As a complement to conventional in silico studies, several authors^19-22 have proposed variation methods to estimate the effect of a modified therapy using recorded clinical data. The key idea is to assume that the measured BG values are a combination of the effect of CHO and insulin intake and from unknown random disturbances. Assuming that a different insulin bolus was used, the theoretical outcome of the modified insulin dosage can be predicted. This methodology is illustrated in Figure 3, where it is assumed that the CHO and insulin effect can be described by linear time-invariant (LTI) models. Because in deviation analyses real clinical data are used as a baseline and only parts of the influencing factors are described by models, the resulting glucose trajectories computed in the simulations still include the same type of disturbances and difficult to quantity impacts as the real glucose data.

Figure 3.

The basic workflow for performing deviation analyses.

As mentioned above, the utilization of deviation analyses requires the specification of an assumed insulin action. For the current article the methodology described in Cameron et al³⁶ was applied where a population mean pharmacodynamic profile, scaled by a patient-specific insulin sensitivity factor (ISF), is used. The empirically obtained pharmacodynamic profile can be approximated by a linear transfer function of third order

$$G_2\left(s\right)=\frac{-\exp \left(2\right)*ISF*T}{2*{\left(1+T*s\right)}^3}$$

where $T=38$ min and the ISF is obtained from the total daily dose (TDD) by the standard 1800-rule

$$ISF\left(\mathrm{in}\mathrm{mg}/\mathrm{dl}/\mathrm{IU}\right)=\frac{1800}{TDD}.$$

As the name suggests, the deviation analysis examines perturbations around the measured BG/insulin values. Therefore, more confident conclusions can be made for smaller deviations, that is, small changes of the insulin dosage, independently from the reason for it. This also means that the results allow a qualitative comparison of different choices, but not for an exact prediction.

In this article deviation analyses are used to be able to test several advanced options for insulin dosing in the same patient to have a virtual head-to-head trial for those options and to be able to compare, for example, the relative impact of an insulin pump compared to that of a CGM in T2D patients. However, it must not be forgotten that the current work is a hybrid in silico evaluations that rely upon assumptions and simplifications chosen by the authors and therefore has its limitations (see the Supplemental Materials for details).

Treatment Options

The focus of this study is on methods of insulin administration, characterized by different complexity of medical devices and dosing strategies. The purpose of any automated dosing strategy, such as an AP, is not to change the strategy or to overcome physiological limitations: it will just try to provide the right dosing decision at every instant requiring as little input as possible from the patient.

Baseline

The simplest basal-bolus-therapy is a fixed insulin dosing scheme. The amount of administered basal and bolus insulin is determined by a medical doctor and only occasionally modified when glycemic control is unsatisfactory. For this treatment option only an insulin pen is needed to inject the hormone, and a BG meter to monitor the success of the treatment. This setting was used by the 14 patients whose data were collected in the outpatient study. Their data is used to perform the deviation analyses and can therefore be considered as the baseline case. Due to the inflexible dosing scheme, it is expected that the recorded BG traces offer room for improvement, which can be exploited by more advanced dosing regiments.

Pen & SMBG

A frequently used option in T1D but less frequently in T2D is the basal-bolus-therapy, using a bolus calculator and advanced carbohydrate counting. The basic rationale behind methods from advanced carbohydrate counting is the fact that there is an approximately linear relationship between ingested carbohydrate amount and bolus insulin requirements (see, eg, Halfon et al,³⁷ Rabasa-Lhoret et al³⁸). In the literature,^39,40 there is evidence that methods from advanced carbohydrate counting can lead to a better glycemic control than simpler treatment regiments. However, it needs to be considered that the linear relationship between carbohydrate intake and bolus insulin requirement is a simplification of the more complex reality⁴¹ and that the positive outcomes using advanced carbohydrate counting strongly depend on a patient’s adherence, the patient’s ability to estimate the carbohydrate content of meals and the correct adjustment of treatment parameters.

To test advanced carbohydrate counting in simulation, the actual BG value at mealtime is assumed to be determined by means of self-monitoring of blood glucose (SMBG). The required amount of bolus insulin at a mealtime is determined by the formula

$$BI=\frac{CHO}{CIR}+\frac{BG-B{G}_{target}}{ISF}-IOB$$

where BI is bolus insulin, CHO is the amount of carbohydrates ingested, CIR is the patient-specific carbohydrate to insulin ratio, BG is the measured BG value, BG_target is the glucose setpoint, ISF is the insulin sensitivity factor and IOB is insulin on board.

In this study CIR and ISF are tuned patient-specifically and daytime-specifically using the adaptive bolus calculator (ABC) method.^42,43 The ABC uses a simple mathematical model to identify the correlation between insulin amounts and BG values, as well as between carbohydrate amounts and BG values from data and derives estimates of CIR and ISF from those mathematical descriptions. The resulting estimates for CIR and ISF are further used in the standard bolus calculator formula. A detailed description of the ABC method can be found in the Supplementary Material.

Pen & CGM

The third option is similar to the previous one. However, in addition to the bolus administration using an insulin pen and the bolus calculator, a CGM is used for BG surveillance. The real time feedback on the actual BG values enables the patients to administer additional insulin dosages at very high BG levels and to avoid hypoglycemia by small carbohydrate interventions, that is, snacks (see the Supplementary Material for how exactly this has been considered in the deviation analyses).

Pump & SMBG

The fourth treatment strategy considered is an optimized basal rate provided by CSII. In this case, it is assumed that meal boluses are unchanged and only the time profile of the basal rate (in the form of micro-boluses) is optimized. To do so, a CGM has to be worn at intervals (eg, every few months) to readjust the basal profile. The infusion rate can be independently set for each time of the day: overnight, morning, during day and evening. A run-to-run algorithm finds the appropriate value for each time of the day by minimizing a cost function (see, eg, Palerm et al).⁴⁴

$$\begin{array}{c}BasalRat{e}_{k+1}=BasalRat{e}_k+{\mathrm{K}}_1\left(\overline{\mathrm{BG}}-{\overline{BG}}_{target}\right)\\ +{\mathrm{K}}_2\left(T_{Hypo}\right)\end{array}$$

Specifically, the cost function incorporates a term for the deviation of the mean BG value to some set-point and a term for the time in hypoglycemia. After some iteration of deviation analyses, an optimal basal profile is found (see the Supplementary Material for some additional details). This method is very similar to the approach presented in Patek et al.⁴⁵

AP

The technologically most complex setup is the classical AP, where an insulin pump, a CGM and a smart device for hosting the control algorithm is needed. An ordinary model predictive control (MPC) setup with asymmetric cost function (see, eg, Parker et al)⁴⁶ and measured disturbance input for the incorporation of meal announcements is used in the current article. The internal model is of fourth order and its states are estimated by a Kalman filter, which accounts for the measurement discrepancies inevitable in CGM readings. This option is the only one with permanent feedback and it is therefore expected to give the best results. Details about the used MPC algorithm and its implementation into the deviation analysis framework can be found in the Supplementary Material.

Results

In all patients, each option was tested, using the deviation analysis method described above, leading to alternative insulin dosing and a differing BG trace.

Detailed numerical results for all options and for all 14 patients, as well as the mean values for all patients are summarized in Table 4. In addition, a visual representation of the average results (average over all 14 patients) is given in Figure 4. Each bar in this figure has a red section visualizing the time in hypoglycemia, a yellow one visualizing the time in hyperglycemia and a green one representing the time in the target range between 70 mg/dl and 140 mg/dl. In addition, to avoid confusion, a violet bar depicts the percentage of time between 140 mg/dl and 180 mg/dl (the corresponding numbers, however, are not considered here as a performance criterion). Whereas the first bar represents the data recorded during the study (“Baseline”), the second and third bar represent the use of methods from advanced carbohydrate counting for calculating bolus insulin, once with SMBG (“Pen & SMBG”) and once with CGM (“Pen & CGM”). In the fourth bar the results for the use of CSII with an optimized basal rate, but without any adjustments for the bolus insulin, are displayed (“Pump & SMBG”). The last bar represents the results for the AP with MPC algorithm (“AP”).

Table 4.

Comparison of All Treatment Options: Overall Results.

		Baseline	Pen & SMBG	Pen & CGM	Pump & SMBG	AP
% of time BG < 70 mg/dl	1	0.0	0.0	0.1	0.6	1.2
	2	0.4	4.6	4.2	0.1	2.9
	3	0.9	1.3	0.0	0.0	2.3
	4	2.3	3.3	0.6	0.3	3.1
	5	0.0	2.5	6.4	0.0	3.3
	6	3.7	0.0	3.2	0.0	2.5
	7	8.7	9.5	6.9	0.4	22.3
	8	1.4	0.0	1.6	0.8	7.3
	9	0.0	1.0	1.2	1.4	1.3
	10	1.4	0.9	2.9	2.2	2.3
	11	0.0	7.2	6.6	1.2	1.7
	12	0.0	3.2	4.4	0.2	0.0
	13	0.0	1.7	0.8	1.2	0.0
	14	0.0	0.3	1.7	2.3	2.1
	ø	1.3	2.5	2.9	0.8	3.7
% of time 70 < BG < 140 mg/dl	1	29.1	37.8	42.0	47.1	60.0
	2	36.9	33.7	34.3	56.3	64.7
	3	36.9	51.3	56.4	57.0	81.8
	4	41.7	43.6	55.8	37.7	61.2
	5	75.9	74.6	77.1	79.9	89.3
	6	43.6	38.4	43.4	51.1	64.5
	7	80.8	76.7	81.2	39.3	75.1
	8	39.3	25.5	37.7	36.6	62.5
	9	9.6	10.1	21.4	32.2	28.2
	10	12.5	17.3	22.5	24.3	39.8
	11	19.5	11.1	19.7	24.6	42.0
	12	24.2	31.2	39.2	65.9	69.7
	13	0.0	6.8	7.1	39.5	4.3
	14	3.9	14.7	14.3	36.6	41.7
	ø	32.4	33.8	39.4	44.9	56.1
% of time BG >180 mg/dl	1	31.3	30.7	24.7	18.9	17.9
	2	20.1	28.7	18.6	13.4	16.8
	3	18.0	11.1	9.5	15.2	1.5
	4	32.6	28.7	22.9	37.6	23.3
	5	5.6	10.5	6.4	4.3	4.4
	6	30.4	39.2	24.9	23.2	14.1
	7	0.0	6.9	5.2	34.0	0.6
	8	26.9	42.9	33.3	31.9	15.5
	9	73.6	72.8	53.9	40.8	38.5
	10	63.9	60.2	38.5	47.1	21.4
	11	57.7	59.9	45.5	49.8	31.2
	12	26.4	27.6	15.0	10.4	10.9
	13	99.4	85.3	85.3	28.7	63.4
	14	77.6	61.2	47.9	32.5	11.9
	ø	40.3	40.4	30.8	27.7	19.4
ΔHbA1c (compared to baseline)	1	0.0	−0.1	−0.4	−0.6	−0.6
	2	0.0	+0.2	+0.0	−0.4	−0.3
	3	0.0	−0.3	−0.4	−0.5	−1.1
	4	0.0	−0.1	−0.3	+0.1	−0.4
	5	0.0	+0.2	−0.2	−0.2	−0.5
	6	0.0	+0.8	+0.2	−0.1	−0.3
	7	0.0	+0.2	+0.1	+1.8	−0.4
	8	0.0	+1.3	+0.6	+0.1	−0.5
	9	0.0	+0.4	−0.8	−1.4	−1.4
	10	0.0	−0.2	−1.1	−0.8	−1.2
	11	0.0	+0.9	−0.2	−0.5	−1.2
	12	0.0	−0.1	−0.6	−1.0	−0.8
	13	0.0	−0.6	−1.1	−3.6	−1.7
	14	0.0	−0.7	−1.4	−2.0	−2.4
	ø	0.0	+0.1	−0.4	−0.6	−0.9

Figure 4.

Comparison of mean performance of all considered treatment options (average over all 14 patients).

Discussion

Our analysis showed that on average the best results can be achieved by using a pump and CGM combined to an AP. Especially, the time in the tight euglycemic range can be increased drastically. Also, the reduction of hyperglycemia is very well accomplished by the control algorithm, despite the fact that temporally high BG values can occur. The time in the low BG range can typically still be held at very low values. The only exceptions are patients 7 and 8 which both show a relatively high level of hypoglycemia. For those patients the MPC algorithm is too aggressive and would have to be retuned to obtain better results. However, the HbA1c estimated from the recorded glucose traces (see Table 2) indicates that for those two patients the combination Pen & SMBG with fixed bolus quantities is basically sufficient to achieve a satisfactory glycemic control, meaning that those two patients are anyway not the ideal candidates for an AP. Regarding the increased time in hypoglycemia with AP for some of the 14 patients in our cohort it should furthermore be mentioned that an adapted AP algorithm with patient-specific settings might be able to show a better performance with this respect. In future works tailoring an AP algorithm specifically for the needs of T2D patients should therefore be envisioned.

The results in Table 4 and Figure 4 show that advanced carbohydrate counting not necessarily leads to better results than fixed meal boluses. On the contrary, the application of fixed bolus amounts could be a more robust option. The method of adjusting insulin dosages based on ingested carbohydrates and actual BG value is well established in T1D, but does not seem to lead to the same benefits for patients with T2D in this study.

The clear advantage of using a CGM can be seen when comparing the options Pen & SMBG and Pen & CGM. In Figure 5, it can be seen that the proactive use of CGM information (as described in the Supplementary Material) decreases the time in hyperglycemia and increases the time in the target range for 13 out of the 14 patients. Due to the fact that hyperglycemia can be detected early by using a CGM, too high BG values can quickly be counterbalanced by a correction bolus.

Figure 5.

Comparison of the performance of the different considered treatment options for patient 4. Each axis shows the result for one performance criterion; each treatment option is shown in a different color; the treatment option leading to the best outcome is indicated by an enlarged circle for each of the four performance criteria.

For the Pump & SMBG option the meal boluses were kept the same as they were in the recorded datasets. Therefore, only small deviations from the measured CGM traces occurred. Basal rates were calculated retrospectively according to a cost function, which incorporates a term for time in hypoglycemia (see the Supplementary Material for details). This is the reason why this option performs so well in terms of hypoglycemia (see Figure 4). The results show that the flexibility to increase or decrease the basal rate at specific daytimes is also beneficial for T2D patients, especially if they have constant daily routines and experience repeated high or low BG values at certain times of the day (see also Reznik et al).⁸

To grasp the large amount of data given in Table 4 in an easier way and to facilitate drawing conclusions from those numbers, an additional way of visualizing the patient-specific results has been chosen. An example for such a plot for patient 4 can be seen in Figure 5. Each of the four axes corresponds to one of the four performance indices from Table 4 and is oriented in such a way that a small value on the axis corresponds to higher performance, whereas a large value indicates lower performance. The four indices for each of the considered treatment options span a tetragon whose area is an indicator for the overall performance of a specific treatment option. Ideally the area of the tetragon should be as small as possible. In addition, the treatment option with the most favorable outcome is marked in the plot with a bigger circle for each of the four performance indices.

Analyzing Figure 5 it can be seen that for patient 4 advanced carbohydrate counting in combination with a CGM for glucose monitoring leads to almost identical performance for time in hyperglycemia, time in range and HbA1c reduction as an AP, but with a significantly lower time in hypoglycemia. This therefore seems a very good option for patient 4. For patient 10 displayed in Figure 6 on the other hand, an AP leads by far to the best results in terms of time in hyperglycemia, time in the target range and HbA1c reduction and still remains in the acceptable region for time in hypoglycemia. All other treatment options lead to an unacceptably high time in hyperglycemia. Therefore, AP could be the best treatment option for this patient. Finally, Figure 7 shows the results for patient 12. This patient seems to benefit substantially from using CSII, whereas a full AP leads to almost no additional benefits in terms of glycemic control.

Figure 6.

Comparison of the performance of the different considered treatment options for patient 10. Each axis shows the result for one performance criterion; each treatment option is shown in a different color; the treatment option leading to the best outcome is indicated by an enlarged circle for each of the four performance criteria.

Figure 7.

Comparison of the performance of the different considered treatment options for patient 12. Each axis shows the result for one performance criterion; each treatment option is shown in a different color; the treatment option leading to the best outcome is indicated by an enlarged circle for each of the four performance criteria.

The outcomes of the deviation analyses suggest that a full AP is probably not the optimum solution in terms of glycemic control for all patients and sometimes simpler treatment options could achieve comparable results. For patients 2, 3, 5, 6, 7, and 8 the HbA1c values estimated from the recorded glucose traces (see Table 2) even indicate that those patients can basically be well controlled on a very simple treatment regimen, using just Pen & SMBG with fixed bolus quantities.

However, as already previously mentioned, it must not be forgotten that the current work is a hybrid in silico evaluations that rely upon assumptions and simplifications chosen by the authors and therefore has its limitations. Final conclusions can of course be derived only from real clinical trials. The simulation results presented in this article serve more as a first estimate of the achievable performance for advanced treatment options in insulin-treated T2D patients and as an inspiration for possible future clinical trials.

Conclusion

The main result of this analysis is that for many T2D patients on basal-bolus insulin treatment, even for rather well controlled ones, the BG regulation performance can be improved using more advanced insulin dosing regiments and additional or more complex devices.

However, it also illustrates that each treatment option leads to a different performance gain for each of the different patients. This confirms that whether it is beneficial or not to use an AP for T2D, differs from patient to patient and individually adjusted treatment options should be sought after. Therefore, clinical criteria for the identification of suitable subgroups need to be developed.

In addition, it is also crucial to take into account the technical awareness of patients, for example, whether they are able to operate an insulin pump or to estimate the carbohydrate amount of ingested meals. This is more relevant for T2D than for T1D patients, as they are often older and may have less technical awareness.