Advanced carbohydrate counting: An engineering perspective

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Advanced carbohydrate counting: An engineering perspective Florian Reiterer a,∗, Guido Freckmann b a b

Institute for Design and Control of Mechatronical Systems, Johannes Kepler University Linz, Austria Institut für Diabetes-Technologie Forschungs- und Entwicklungsgesellschaft mbH an der Universität Ulm, Germany

a r t i c l e

i n f o

Article history: Received 17 May 2019 Accepted 13 June 2019 Available online xxx Keywords: Diabetes Metabolic control Biomedical systems Insulin therapy

a b s t r a c t Since they lack insulin-producing β -cells, patients with type 1 diabetes mellitus (T1DM) need to supply their body with insulin from external sources to manage their blood glucose (BG) concentration and mitigate the long-term effects of chronically increased BG levels. The common way of dosing insulin in T1DM is basal bolus therapy. In this method, patients continuously supply their body with a small amount of insulin that is meant for keeping their BG level more or less constant in case no large disturbances occur. Bolus insulin (which makes up roughly 30–60% of the total insulin amount) on the other hand is used to counterbalance such disturbances. The biggest perturbation of BG is caused by meals that can lead to large postprandial glucose excursions. By far, the most common approach to determine bolus insulin requirements in T1DM is known as Advanced Carbohydrate Counting (ACC). In ACC the bolus insulin amount is determined proportional to the estimated carbohydrate content of the ingested meal. Even though this semi-heuristic approach has proven very valuable in daily practice, its use is not without pitfalls. In this paper we discuss the background, implicit assumptions and limitations of ACC from an engineering perspective and show how concepts from the fields of data-based modeling and control have been successfully used to facilitate the computation of bolus insulin requirements. © 2019 Elsevier Ltd. All rights reserved.

Contents 1.

2.

3.

4.

∗

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. The burden of diabetes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3. Insulin therapy in type 1 diabetes mellitus . . . . . . . . . . . . . . . . . . . . . . . Adjustment of bolus calculator settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Rules of thumb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Bolus calculator logic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Run-to-run control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Insulin sensitivity index-based optimization of CIR . . . . . . . . . . . . . . . . 2.5. Graybox modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6. Other types of insulin dosing algorithms. . . . . . . . . . . . . . . . . . . . . . . . . Estimating the carbohydrate content of meals. . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Food database systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Computer vision based systems for meal analysis . . . . . . . . . . . . . . . . . 3.3. Automatic meal detection from glucose traces . . . . . . . . . . . . . . . . . . . . Factors impacting glycemic outcomes with advanced carbohydrate counting. 4.1. Methods and data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1. Assessment strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2. Clinical data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Impact of carbohydrate counting errors. . . . . . . . . . . . . . . . . . . . . . . . . .

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Corresponding author. E-mail addresses: fl[email protected] (F. Reiterer), [email protected] (G. Freckmann).

https://doi.org/10.1016/j.arcontrol.2019.06.003 1367-5788/© 2019 Elsevier Ltd. All rights reserved.

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4.2.1. Impact of carbohydrate counting errors - introduction . . . . . . . . . 4.2.2. Impact of carbohydrate counting errors - data analysis . . . . . . . . 4.2.3. Impact of carbohydrate counting errors - results and discussion . 4.3. Mixed meal effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1. Mixed meal effects - introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2. Mixed meal effects - results and discussion. . . . . . . . . . . . . . . . . . 4.4. Other influencing factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1. Impact of glucose rate of change . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2. Impact of glucose measurement and insulin dosing errors. . . . . . 5. Conclusions and future challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Funding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Declaration of Competing Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction 1.1. Overview The current paper introduces the methods of advanced carbohydrate counting (ACC), which is standard in type 1 diabetes therapy, from an engineering perspective. It is organized as follows: In Section 1.2 the metabolic disease diabetes is introduced. Section 1.3 gives a short overview about insulin therapy in type 1 diabetes. In that subsection also the basic concepts of ACC are explained. In the subsequent Section 2 different approaches to obtain patient-specific therapy settings in ACC are discussed, including approaches proposed in control engineering literature. Section 3 introduces advanced tools to facilitate the task of estimating the carbohydrate content of meals, which is the core of ACC. In Section 4 other influencing factors apart from meal carbohydrates are reviewed, that also impact glycemic outcomes in ACC. Of those factors, two are explored in more detail presenting original data: The impact of errors in the estimated carbohydrate amount is introduced in Section 4.2, whereas Section 4.3 studies the impact of other macronutrients besides meal carbohydrates in mixed meals. Finally, Section 5 summarizes the main messages of the paper and brings forward some issues in the field of ACC, that require further study. 1.2. The burden of diabetes Diabetes is a chronic disease that is characterized by pathologically elevated blood glucose (BG) levels and abnormalities in carbohydrate, fat and protein metabolism. The vast majority of diabetic patients can be classified into one of the following two categories: • Type 1 diabetes mellitus (T1DM): In T1DM the β –cells of the pancreas are destroyed by an auto-immune reaction that leads to an absolute insulin insufficiency. Within a rather short amount of time patients suffering from T1DM depend on external supply of insulin for survival. Patients at time of diagnosis are usually lean and have experienced significant weight loss since the time of onset of the disease. T1DM accounts for approximately 10% of diabetes cases. • Type 2 diabetes mellitus (T2DM): T2DM is a chronic disease that is characterized by a reduced insulin sensitivity (“insulin resistance”) of liver, muscles and adipose tissue combined with an impairment of β –cell secretory function. Normally, the pancreas is still able to produce insulin, even in far advanced cases of T2DM, but is insufficient to keep the BG level in a healthy range. Patients suffering from T2DM can often spend several years after the diagnosis of the disease without external supply of insulin. T2DM and obesity are strongly interlinked. Roughly

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80–90% of patients diagnosed with T2DM are overweight or obese (The American Diabetes Association, 2008) and obesity is thought to be the highest risk factor for developing T2DM. Therapy depends very much on the stage of the disease. In early stages of T2DM the standard therapy with oral antidiabetics (usually: Metformin) is sufficient, whereas in advanced stages insulin injection is required. T2DM accounts for approximately 90% of diabetes cases.

Additionally, there exist less frequent forms like gestational diabetes and maturity onset diabetes of the young (MODY). The chronically elevated BG levels in diabetes cause severe disruptions in the human organism, resulting in grave long-term consequences like kidney failure or diabetic retinopathy. Leung, Pollack, Colditz, and Chang (2015) and Zhuo et al. (2014) showed that diabetes is associated with significant decreases in life expectancy and large increases in lifetime health care expenditures. The risk of diabetes-related complications is inevitably linked with the quality of BG control. Keeping the BG level within a relatively narrow range is therefore very important. Too high glucose levels (known as “hyperglycemia”) are typically not immediately life threatening (unless the glucose level is very elevated like in unmedicated T1DM). However, if such a condition persists over a longer period of time (months, years) this causes severe disruptions in the human organism and result in microvascular and macrovasuclar complications (Fowler, 2008). Microvascular complications include diabetic retinopathy (which can results in blindness), nephropathy (which can result in kidney failure) and neuropathy. Diabetic neuropathy is a reason why people with diabetes have a roughly 40 times higher risk of having to undergo a foot amputation. The main macrovascular complications on the other hand are connected to atherosclerosis, resulting in an elevated risk for developing cardiovascular disease and suffering a myocardial infarction. For people with diabetes the risk of suffering from a heart attack is 2 to 4 times that of people that do not have diabetes. The border between euglycemia and hyperglycemia is usually defined as 180 mg/dl, see e.g. Beck et al. (2019). On the other hand if due to diabetes medication (especially insulin) the BG concentration falls below roughly 60 mg/dl first symptoms, e.g. weakness and sweating, start to appear, in case of a further decrease this can cause a comatic state which should under all circumstances be avoided. Having the glucose level at a very low level for a prolonged period of time is thought to cause cardiac arrhythmias and is potentially life threatening (Novodvorsky et al., 2017). States of a too low glucose concentration are generally referred to as “hypoglycemia”. A threshold of 70 mg/dl is generally accepted to characterize the border between the safe glucose range (“euglycemia”) and the hypoglycemic range (Beck et al., 2019).

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1.3. Insulin therapy in type 1 diabetes mellitus The current paper focuses on the application of ACC in patients with T1DM. This is due to the fact that ACC is used almost exclusively in this subgroup of patients, while it is very uncommon in T2DM. Therefore, all further explanations given in subsequent sections are typically limited to T1DM patients. It was shown in the famous Diabetes Control and Complications Trial (DCCT) (The Diabetes Control And Complications Trial Research Group, 1993) that intensive insulin therapy can significantly reduce the risk of the long-term complication associated with chronically elevated BG levels for T1DM patients. Furthermore, it was found in the DCCT that having a good glycemic control, as expressed by an HbA1c1 level of ≤ 7.0%, is essential for this reduction of diabetes-associated microvascular and macrovascular complications. The threshold of HbA1c ≤ 7.0% is therefore often used as a therapeutic goal in diabetes (American Diabetes Association, 2018). Even though intensive insulin treatment is nowadays the standard method for treating T1DM, still only few patients actually achieve satisfying BG levels. In Casagrande, Fradkin, Saydah, Rust, and Cowie (2013) it was found that only 30.3% of insulin treated diabetes patients achieve an HbA1c lower than 7.0%, whereas 36.1% have HbA1c levels larger than 8.0%, which corresponds to a poor glycemic control. The main difficulty in insulin therapy for patients with T1DM is the correct dosing. Insulin requirements are known to vary significantly from patient to patient, but also within the same patient from one day to another and even within the same day. Patients therefore have to adjust their insulin doses on a daily basis depending on influencing factors like meal intakes, physical activity, daytime, etc. Doing so is difficult and requires a lot of effort. Furthermore, patients have to do most of this adjustment on their own and only get occasional assistance by their primary care provider, implying that patients need to be well-trained to be fit for this task. The challenge in correctly dosing insulin is associated with the dangers of overdosing. Injecting an excess of insulin leads to hypoglycemia, which is potentially life threatening, but rather common among diabetes patients on insulin treatment. In Leese et al. (2003) data collected during one year at a regional hospital in U.K. was analyzed. It was found that 7.1% of T1DM patients and 7.3% of insulin treated patients with T2DM living in that region had at least one episode of severe hypoglycemia within this one year that required emergency assistance in that hospital. The goal in insulin therapy is to keep the glucose levels as much as possible within the euglycemic range. To adjust therapy parameters and to check therapy success, the availability of reliable measurements of the glucose level are required. Most patients do so by means of several daily point measurements with a BG meter. Alternatively T1DM patients can use continuous glucose monitoring (CGM) devices. The devices used for insulin administration are either an insulin pen or (nowadays less common) a syringe for multiple daily injection (MDI) therapy or an insulin pump for continuous subcutaneous insulin infusion (CSII). In either case, insulin is administered subcutaneously, i.e. into the subcutaneous adipose tissue and diffuses from there into the blood stream which distributes it across to other body compartments. The most common way of dosing insulin in T1DM is the basal bolus therapy. Patients continuously supply their body with a small amount of insulin that is meant for keeping their BG level approximately constant in case of no large 1 HbA1c corresponds to the percentage of hemoglobin in the blood with a glucose molecule covalently bound to it. HbA1c is strongly correlated to the average BG concentration over the last weeks/months (see e.g. Nathan et al. (2008)).

3

disturbances. This amount of insulin is referred to as basal insulin and usually accounts for 30 to 60% of the total daily insulin requirements. Patients on MDI therapy typically use one or two injections per day of long acting insulin. After a couple of days at a constant injection scheme of basal insulin the concentration of the corresponding insulin in the blood stream is roughly at a certain equilibrium concentration and, as a result, the slow acting insulin is metabolized at a roughly constant rate. Patients using an insulin pump, on the other hand, use a rapid acting insulin analogue for supplying the required basal insulin which is infused according to a preprogrammed profile as a function of daytime. This diurnal profile is referred to as the basal rate. In an insulin pump the amount of basal insulin can be adjusted much more precisely as a function of daytime than when using injections of slow acting insulin. In basal bolus therapy T1DM patients additionally have to supply their body with insulin boluses. Whereas basal insulin is meant for keeping the BG more or less constant in the absence of major challenges, boluses are used to counteract the effect of those challenges on the BG level, as well as to correct the BG level in case it is found to be above the target zone (by injecting a so-called “correction bolus”). The main challenges that lead to a fast increases in BG are meals. The amount of required bolus insulin for a meal (referred to as “meal bolus”) is usually assumed to be proportional to the amount of ingested carbohydrates. It is therefore crucial for the patient to estimate the carbohydrate content of meals, which can be achieved through basic or advanced carbohydrate counting (Warshaw & Bolderman, 2008) or purely based on patient’s experience and habits. The essence of basic carbohydrate counting is for the patient to understand the relationship between meal intakes, physical activity and insulin injections on BG level in a qualitative sense (Kulkarni, 2005). People using basic carbohydrate counting are encouraged to ingest a consistent quantity of carbohydrates at similar times each day. The insulin dosing is then adjusted for such a “standard day”. In ACC on the other hand the insulin dosing at meal times is adjusted individually for each meal based on its carbohydrate content. This offers much more flexibility, but is associated with more effort for the patient. ACC corresponds to the most widespread technique for determining the bolus insulin requirements in T1DM. The basic rationale behind methods from ACC is that there is an approximately linear relationship between ingested carbohydrate amount and bolus insulin requirements (see e.g. Halfon, Belkhadir, & Slama, 1989, Rabasa-Lhoret, Garon, Langelier, Poisson, & Chiasson (1999)). In the literature Schmidt, Schelde, and Nørgaard (2014) and Bell, Barclay, Petocz, Colagiuri, and Brand-Miller (2014), there is evidence that methods from ACC can lead to a better glycemic control than simpler treatment regiments. Furthermore, newer research in adolescents found that using methods of ACC leads to a higher quality of life (Anderson et al., 2017). However, it needs to be considered that the linear relationship between carbohydrate intake and bolus insulin requirement is a simplification of the more complex reality (Bell et al., 2015) and that the positive outcomes using ACC 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. Accurately determining the carbohydrate content of meals is difficult and needs a lot of experience. Besides an estimate of the carbohydrate content of the meal, a measurement of the actual preprandial BG level also has to be available (usually measured with a BG meter). Using the carbohydrate estimate and the preprandial BG level, the required amount of bolus insulin can be determined using the following formula (Walsh & Roberts, 2013; Warshaw & Bolderman, 2008):

Bolus =

BGpre − BGtarget CHO + − IOB CIR ISF

(1 )

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In (1) “Bolus” corresponds to the bolus insulin needs, CHO is the carbohydrate content of the meal in grams, BGpre is the preprandial BG, BGtarget describes the target value for the postprandial BG and IOB stands for insulin-on-board. The formula for calculating the required bolus insulin amount corresponds thus of three terms: • The first term is used for counteracting the effect of the meal intake on BG. This term is usually significantly bigger than the other two terms. The proportionality factor CIR in this term is the Carbohydrate-to-Insulin Ratio, i.e. the amount of carbohydrates that are counteracted by 1 insulin unit (IU)2 • The second term is used for BG corrections. The injected insulin amount from this term is proportional to the difference between BGpre and BGtarget . The factor ISF, the Insulin Sensitivity Factor, describes by how many mg/dl the BG level will decrease per injected IU. • The third term, IOB, stands for insulin-on-board, i.e. the bolus insulin from previous injections that is still active in the body. Eq. (1) can either be used for calculating the required bolus insulin by hand / mentally or can be implemented in an automatic bolus calculators (BC) (Schmidt et al., 2014), which can be part of a cellphone app or integrated into a BG meter or an insulin pump. The use of automatic bolus calculators can facilitate determining the required bolus insulin amount since patients otherwise have to compute this amount mentally which is rather error-prone. Evidence for improved glycemic outcomes by using an automatic BC can e.g. be found in Ziegler et al. (2013). Another main advantage of automatic BCs is the easy assessment of the third term of (1), IOB, which is used to reduce the risk of overdosing insulin. Because it is more difficult to determine, IOB is usually not accounted for when manually calculating bolus needs, but only in automatic BCs. It should be noted that even fastacting insulin needs several hours to be fully metabolized (typically around 5 to 6). To determine IOB, the pharmacodynamic profile of the injected insulin analogue has to be known. Automatic BCs have an average insulin action curve saved. However, the time needed for the full metabolization of bolus insulin, known as duration of insulin action (DIA), has to be entered into the automatic BC by the patient or medical doctor (MD) and depends not only on the insulin analogue used, but also on patient characteristics. The value of DIA is then used to scale the average insulin action curve. 2. Adjustment of bolus calculator settings The optimum adjustment of basal bolus therapy settings is difficult. There is not only a large variability between individuals (which is referred to as “interpatient variability”), but also, due to the large amount factors influencing the glucose metabolism, within one individual (referred to as “intrapatient variability”). When MDs adjust a patient’s therapeutic settings, it is usually only possible to account for the interpatient variability, meaning that the parameters of the basal bolus therapy are adjusted to best fit the average daily requirements. To do so, a large amount of rules of thumb are available to obtain a first estimate of adequate therapy settings. The required total daily dose (TDD) of insulin (i.e. the average value for the sum of basal and bolus insulin requirements within a 24h period) can for example be estimated from the patients’ body weight using the following correlation (Davidson, Heb-

2 The measurement unit IU is used mainly due to historical reasons and corresponds to the biological equivalent of 34.7 μg of crystalline insulin. This corresponds to the amount that is needed to decrease the BG level of a healthy rabbit in fasting state to 45 mg/dl (Sinding 2002).

blewhite, Steed, & Bode, 2008):

TDD(IU) = 0.53 · Body Weight(kg)

(2)

The resulting number calculated according to (2) gives an estimate of the TDD in IU, which has to be further adjusted patientspecifically. Similar rules exist for the adjustment of the basal insulin requirements and bolus quantities. In the following the adjustment of basal rates and total daily dose is not further considered, but only the optimum adjustment of BC settings. Specifically, the tuning of CIR and ISF is explained using either simple rules of thumb or other, more advanced approaches. The tuning of DIA is not discussed. Further information about adjustment of DIA can be found in Walsh, Roberts, and Heinemann (2014). The factors CIR and ISF in (1) have to be adapted patientspecifically to allow for a good control of the BG level. Because of the huge effect of interpatient and intrapatient variability this is difficult and several methods have been proposed to facilitate the task. 2.1. Rules of thumb Over the last decades a wide range of formulas has been proposed that link CIR and ISF to easily measurable quantities like the patient’s weight or TDD of insulin. These formulas are often derived by diabetologists based on their experience and statistical analysis of large datasets of patients with T1DM. The formulas are basically rules of thumb that describe the relationship between some quantities and CIR and ISF for an average patient. The formulas are often used in practice to obtain first estimates of CIR and ISF that are later-on optimized to obtain patient- and mealtimespecific values. In this section only three examples of different sets of formulas proposed in the scientific literature are listed. The first set of equations are the formulas from King and Armstrong (2007). These calculate CIR and ISF based merely on the TDD in IU:

CIRKing (g CHO/IU ) = 3 + 217/TDD(IU ) ISFKing (mg/dl/IU ) = 12 + 1076/TDD(IU )

(3)

As a second set of equations the formulas introduced in Walsh, Roberts, and Bailey (2010) are shown in (4). These include not only the influence of the TDD, but also of the patient’s body weight (in pounds):

CIRWalsh (g CHO/IU ) = 2.6 ∗ W eight (lb)/TDD(IU ) ISFWalsh (mg/dl/IU ) = 1960/TDD(IU ) As a last set of equations Davidson et al. (2008) are shown here:

(4) the

formulas

from

CIRDavidson (g CHO/IU ) = 2.8 ∗ W eight (lb)/TDD(IU ) ISFDavidson (mg/dl/IU ) = 1700/TDD(IU )

(5)

It can be seen that (4) and (5) have the same structure, but use different parameter values. Using rules of thumb like the ones from equations (3) through (5) to supply patients with some initial estimates for CIR and ISF (that are then fine-tuned to get patient and mealtime specific values) is common practice among diabetologists (see e.g. Walsh & Roberts (2013)). 2.2. Bolus calculator logic Another way of determining CIR and ISF proposed in the scientific literature is to measure the difference between pre- and postprandial BG and to obtain their values from BC formula (1), replacing BGpre − BGtarget by BG = BGpreprandial − BGpostprandial . An example for such a method is given in Ginsberg (2012). There, the

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IOB term of (1) is omitted (assumption: pre- and postprandial BG values correspond to equilibrium) and CIR and ISF are calculated according to the following set of equations:

CIRGinsberg,i, j = CHOi, j /(BIi, j − BGi, j /ISFGinsberg, j ) CIRGinsberg, j =

N 

(Wi, j ∗ CIRGinsberg,i, j )/

i=1

n 

Wi, j

i=1

ISFGinsberg,i, j = BGi, j /(BIi, j − CHOi, j /CIRGinsberg, j ) ISFGinsberg, j =

N 

(Wi, j ∗ ISFGinsberg,i, j )/

i=1

n 

Wi, j

(6)

i=1

The estimates of CIR and ISF of each time period j (e.g. morning period, evening period, etc.) are updated according to (6) whenever new data becomes available. If no data is available, ISF is initialized using a simple rule of thumb (In Ginsberg, 2012 it is initialized as ISF0 = 1700/TDD which correspond to ISFDavidson from (5)). Then, CIR and ISF are updated after each day i based on all recorded data up that point in time. First, the CIR for day i and period j is calculated based on BG and carbohydrate and bolus insulin intakes, as well as on the estimated value of ISF. Then, the updated estimate of CIR of time period j is computed as a weighted sum of all available values CIRi,j (with weights Wi,j ). After that, the ISF for day i and period j is determined using BG, carbohydrate and bolus insulin intakes, as well as the updated value of CIRj . In a last step the new estimate of ISF for period j is calculated as a weighted average of all previous values. The choice of the weights Wi,j influences the final results significantly and is not straightforward. Additionally to the iterative method of Ginsberg as described above, one could also consider performing a simple linear regression for the BC formula (1) to obtain values of CIR and ISF in a single-shot-procedure. Values of 1/CIR and 1/ISF are found as the fitting parameters of the linear regression:

BI + IOB(t0 ) − IOB(tE ) =

CHO BG + CIRBCLinReg ISFBCLinReg

(7)

As for the Ginsberg method, values of CIR and ISF can be obtained for different periods of the day separately. The times t0 and tE correspond to the starting and end times of the prandial period, BI to the bolus insulin taken during the period, CHO to the corresponding carbohydrates and BG is the difference in BG between beginning and end of the period. Furthermore, IOB can be accounted for by adding previously injected, but still active bolus insulin to BI and by subtracting the insulin that was not yet metabolized at tE . To do so, a profile for the insulin action as a function of time has to be assumed. Alternatively, one could assume (as for the Ginsberg method) that the BG is in equilibrium at t0 and at tE . No explicit description of this method could be found in the scientific literature, however, since the underlying reasoning is rather straightforward, it has most probably already been applied. A very similar approach has recently been proposed in Rodbard (2018). A different iterative approach also relying on inverting the BC formula (1) has been proposed in Herrero et al. (2015a). This method relies on glucose measurements obtained with a CGM device. The values used for the iterative updating are the preprandial glucose G0 , as well as the minimum postprandial glucose value Gmin .

Badd =

(Gmin − BGtarget ) ISF

CIRHerrero,i, j = ISFHerrero,i, j

CHO +

(G0 −BGtarget ) 1960/2.6·Weight (kg)

BI + IOB + Badd 1960 · CIRHerrero,i, j = 2.6 · W eight (kg)

(8)

(9) (10)

5

In those equations Badd corresponds to th difference compared to the actually injected insulin amount that would have resulted in a Gmin equal to the BG setpoint BGtarget . In (9) CIR is updated by dividing some corrected carbohydrate amount by the total amount of insulin which would have been required for good control. The second term in the numerator corrects for the preprandial BG not coinciding with the BG setpoint. ISF is estimated based on the formulas by Walsh (4), expressing ISF as a function of CIR. 2.3. Run-to-run control In the last couple of years, effort has been made in the research community to take advantage of the clear 24-h patterns in diabetes management for iteratively learning an adequate BG control strategy. This approach, known as run-to-run control, has been used successfully in in silico and clinical trials. The first published works aimed at learning the right amount and timing of insulin doses (see e.g. Owens et al., 2006) and showed some limitations. Newer publications on the other hand use run-to-run control to learn estimates of CIR and are better at dealing with day-to-day variations in patient behavior (see e.g. Herrero et al., 2015b; Palerm, Zisser, Bevier, Jovanovic, & Doyle III, 2007). In the run-to-run control framework, CIR is iteratively updated on a day-to-day basis using the following formula:

CIRR2R,i+1 = CIRR2R,i + K · ( r − i )

(11)

In this formula index i refers to the corresponding day,  is a performance measure ( i is the value of  at day i and  r is the reference value that should be achieved) and K a linear gain factor. K is basically a tuning parameter that determines how aggressively the CIR is updated from one day to another. The choice of  varies between the three run-to-run methodologies cited here. In Palerm et al. (2007) (and later in Zisser, Palerm, Brevier, Doyle III, & Jovanovic, 2009)  was calculated based on one preprandial BG (G0 ) and two postprandial BG point measurements (G1 and G2 , taken T1 and T2 minutes after G0 ):

G60min = 60 ·

G1 − G0 T1

(12)

G60min = G60min − G0

(13)

GT2 = G2 − G0   = G260min + G2T2

(14) (15)

In Herrero et al. (2015b) on the other hand the area under the curve (AUC) calculated from CGM data is used:

=



5h

0min

(G(t ) − G0 )dt

(16)

with G0 again corresponding to the preprandial glucose value at time t = 0min. For updating CIR with run-to-run control, it is critical to determine a suitable postprandial reference BG profile and therefore a good  r . Whereas in Palerm et al. (2007) a reference profile is used that corresponds to the BG returning to the preprandial value two hours after the meal bolus (which results in a reference  r = 0), no explicit reference profile is given in Herrero et al. (2015b) (there it is written that the patient-specific reference profile has to be defined by a medical professional). In Herrero et al. (2015a) the minimum in the postprandial CGM profile is requested to correspond to the target glucose value. As for the method by Ginsberg, different CIR and ISF values can be used for different cases / applications j (e.g. different times of the day).

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2.4. Insulin sensitivity index-based optimization of CIR In Schiavon, Dalla Man, and Cobelli (2018), a method describes how to obtain an estimate of CIR in CSII therapy based on measured postprandial CGM data together with information about meal carbohydrates and insulin intakes. The first step consists in computing an estimate for the insulin sensitivity index SISP from this data using the methodology described in Schiavon, Dalla Man, Kudva, Basu, and Cobelli (2014). This estimate is calculated using the oral minimal model (Caumo, Bergman, & Cobelli, 20 0 0) parameterized with population mean parameter values as a basis. In a next step the direct link between insulin sensitivity and meal bolus insulin requirements is exploited (the more sensitive a person is to insulin, the less bolus insulin is required) by simply rearranging terms in the formula for computing SISP to end up with an estimated CIR. In order to assure patient safety, however, this estimate of CIR is not applied directly, but is compared to the value and the glycemic outcomes obtained with the previously used CIR of the patient. 2.5. Graybox modeling In the current subsection the graybox modeling approach from Reiterer, Kirchsteiger, Assalone, Freckmann, and del Re (2015); Reiterer, Kirchsteiger, Freckmann, and del Re (2015) is introduced, which uses routinely-collected T1DM data to obtain estimates for the patient-specific and daytime-specific settings of a BC. The data required for this purpose are recorded CGM traces together with information about bolus insulin injections and carbohydrates from ingested meals. As a basis for identifying CIR and ISF values from the measured glucose dynamics, the following third order transfer function including an integrator term is chosen to model the response of the BG to carbohydrate intakes as well as to bolus insulin injections:

BG(s ) =

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K1

(1 + sT1 ) s 2

· D (s ) +

K2

(1 + sT2 )2 s

· U (s )

(17)

In this formula, BG(s) describes the glucose level, D(s) the carbohydrates of meal intakes and U(s) the bolus insulin injections, all in the Laplace domain. Other influencing inputs like stress, sports, mixed meal composition etc. are not incorporated into this model structure. The model has already been used extensively (and successfully) in previous studies, see e.g. Kirchsteiger, Pölzer, Johansson, Renard, and del Re (2011) and Kirchsteiger, Johansson, Renard, and del Re (2014). The advantage of using model structure (17) is that the parameters of the model have a clear physiological meaning (see also Kirchsteiger & del Re, 2014). The constant K1 describes the effect of 1 g of carbohydrates on the BG, whereas K2 predicts the effect of 1 IU of bolus insulin (both for t → ∞). Please note that K1 is positive, whereas K2 corresponds to a negative value. The time constants T1 and T2 are proportional to the response time of the BG to carbohydrate and insulin inputs. Interestingly, the constant −K2 has the same physiological meaning as the factor ISF in the BC formula (1). Furthermore, the physiological interpretation of the mixed constant −K2 /K1 is identical to that of the CIR. As implicitly assumed by using the BC formula (1) for calculating the bolus insulin needs, carbohydrate and insulin inputs have a persistent effect on the BG in the model structure (17), which is caused by the fact that both transfer functions contain an integrator term (pole at s = 0). In this model structure only bolus insulin is treated as an input and has therefore an effect on the glucose dynamics. Basal insulin is assumed to be well adjusted and would therefore keep the BG at a constant level in the absence of challenges to the glucose metabolism.

Using such graybox model structures for identifying CIR and ISF values is not a new idea. The first attempt for doing so is reported in Percival et al. (2010), however, with only limited success. The model structure (17) was first reported in Kirchsteiger, Castillo Estrada, Pölzer, Renard, and Del Re (2011) as a tool for identifying interval models. In Kirchsteiger and del Re (2014) the same structure is then used in an in silico study for the identification of CIR values by fitting the model to data. These CIR values are then subsequently used (successfully) for glucose control. The advantageous properties of model structure (17) is shown by the fact that it has been reinvented independently for exactly the same purpose (Bock, François, & Gillet, 2015). However, in both cases Kirchsteiger, Castillo Estrada, et al. (2011) and Bock et al. (2015) the model was only able to describe the glucose dynamics after a single meal challenge (around 5 hours of data). The model was slightly enhanced in Magdelaine et al. (2015) by combining basal and bolus insulin to one input and by adding a constant term in the model that mimics the net glucose output of the body (hepatic glucose production minus insulin independent glucose utilization in the brain). However, this enhanced model structure can be applied for the case of CSII therapy, seen that only in CSII the same rapid-acting insulin is used for supplying the basal rate and the bolus requirements. It was shown in Magdelaine et al. (2015) that for selected patients the enhanced model structure was able to fit longer datasets (up to 4 days) considerably well. No validation of the obtained parameter values CIR and ISF has been reported though. Assuming constant, patient-specific factors for CIR and ISF is a strong simplification. The amount of insulin that has to be injected per gram of carbohydrates is in reality influenced by a myriad of different variables such as the levels of physical activity, and psychological and physical stress (Palerm et al., 2007). Specifically, it is nowadays a widely accepted fact that the insulin sensitivity is not the same for all meals of the day, but changes over the day. Based on results from a dedicated clinical study it could be shown in Hinshaw et al. (2013) that there are tremendous diurnal variation in insulin sensitivity SI (as assessed via the oral minimal model). Typically, a higher insulin dose per gram of carbohydrate has to be injected for breakfast than for a later meal (Van Cauter, Polonsky, & Scheen, 1997). Many patients account for this effect in practice by using different values of CIR and ISF for breakfast, lunch and dinner (see e.g. Nakamure et al., 2014). To accommodate for such diurnal variations, the model structure (17) has been modified in Reiterer, Kirchsteiger, Assalone, et al. (2015, Reiterer, Kirchsteiger, Freckmann, et al., 2015b) to model the effect of the daytime on insulin action and carbohydrate effects. The factors K1 and K2 are no longer assumed to be constant, but for each meal intake and insulin injection a specific value is calculated. However, the factors are assumed to change slowly and smoothly over time, therefore they were chosen to be described by a second-order polynomial of daytime:

K1,i = K11 + K12 ·ti + K13 ·ti2

(18a)

K2, j = K21 + K22 ·t j + K23 ·t 2j

(18b)

As can be seen in (18a) and (18b), for each input a separate value of K1 and K2 is calculated using the time of the corresponding carbohydrate intake (ti ) and insulin injection (tj ). The values are then kept constant for calculating the system response following a specific input. Assuming quadratic functions for both, K1 and K2 , proved to be a good compromise between keeping the simplicity of the model and having a good performance at fitting the data. Doing so increases the number of unknown parameters for the system

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identification problem from 4 as in the original model (K1 , K2 , T1 and T2 ) to 8 (θ = [K11 , K12 , K13 , K21 , K22 , K23 , T1 , T2 ]T ). The system identification therefore tries to find the optimum set of parameters that minimizes the quadratic error between the calculated BG as described by (17) and (18) and the measured CGM values. For each patient the parameters θ of one identification time frame are assumed to be constant. However, to limit the intrapatient variability of the model parameters, it proved to be crucial to limit the variability of the time constants T1 and T2 . Therefore, the parameters for all days are determined in one go, and the deviation of T1 and T2 from the mean value is limited by additional constraints in the optimization. Furthermore, to limit the search for optimum parameters to a physiologically relevant parameter space, minimum and maximum values for the model parameters are defined. The whole optimization problem therefore reads as stated in (19).

(K1∗k,l , K2∗k,l , T1∗,l , T2∗,l ) =

argmin K1k,l ,K2k,l ,T1,l ,T2,l

(BGmodel − BGmeas )

·(BGmodel − BGmeas )

(19)

subject to:

K1,min < K11,l + K12,l ·t + K13,l ·t 2 < K1,max for t ∈ [tmin , tmax ] K2,min < K21,l + K22,l ·t + K23,l ·t 2 < K2,max for t ∈ [tmin , tmax ] CIRmin < 1 − K <

K21,l + K22,l ·t + K23,l ·t 2 < CIRmax for t ∈ [tmin , tmax ] K11,l + K12,l ·t + K13,l ·t 2 1 N

N

K11,l + K12,l ·t + K13,l ·t 2

m=1

(K11,m + K12,m ·t + K13,m ·t 2 )

< 1 + K for t ∈ [tmin , tmax ] 1 − K <

1 N

N

K21,l + K22,l ·t + K23,l ·t 2

m=1

(K21,m + K22,m ·t + K23,m ·t 2 )

< 1 + K for t ∈ [tmin , tmax ] 1 − ISF <

K21,l + K22,l ·t + K23,l ·t 2 < 1 + ISF for t ∈ [tmin , tmax ] −ISFKing

T1,min < T1,l < T1,max ; T2,min < T2,l < T2,max ; T21,min < < T21,max T1,l 1 − T < N 1 N

m=1 T1,m

< 1 +  T ; 1 − T <

< 1 + T

1 N

T2,l T1,l

T2,l N

m=1 T2,m

with:

k = 1, 2, 3

l = 1, 2, . . . , N

In this optimization problem BGmeas is the vector of measured glucose values, whereas BGmodel corresponds to a vector of values calculated using equation (17) evaluated at the time points of the measurements, so the cost function is the sum of quadratic errors between measured and calculated values. The model output in vector BGmodel depends of course on the values of the model parameters K1k,l , K2k,l , T1,l and T2,l with indexes k (index to describe the three parameters in the quadratic equations for K1 and K2 ) and l (index describing each separate time frame for the system identification, N time frames in total). Minimum and maximum values are given for K1 , K2 , K2 /K1 , T1 and T2 to restrict the parameter space to a physiologically meaningful region. For K1 and K2 is has to be assured that the quadratic equations (18a) and (18b) stay within the search interval defined by minimum and maximum value for K1 and K2 . This is done by imposing the first two inequalities of (19) for specific time points within each identification time frame (defined by the corresponding tmin and tmax ). These inequalities are imposed at equidistant

7

Table 1 Maximum and minimum parameter values for the system identification as defined in the inequality constraints of (19).

K1 [mg/dl/g CHO] K2 [mg/dl/IU] −K2 /K1 [g CHO/IU] T1 [min] T2 [min] T2 /T1 [-]

Minimum

Maximum

2 −100 2 10 25 1

8 −10 100 60 150 10

time points separated by intervals of one hour. The same procedure is done to impose that −K2 /K1 should lie within a physiologically meaningful range (defined by CIRmin and CIRmax ). A compilation of the minimum and maximum values used in the system identification can be found in Table 1. These were chosen in accordance with scientific literature (see e.g. Walsh & Roberts, 2013) to represent a physiologically relevant parameter space. Additionally, a restriction was put to limit the intrapatient variability of T1 and T2 . An inequality constraint limits the maximum deviation from the corresponding mean value (average for all N days) to T . A maximum deviation of 25% is used for both, T1 and T2 (T = 0.25). This additional restriction proved to be necessary to be able to identify patient-specific diurnal profiles for −K2 /K1 . Furthermore, the resulting patterns of −K2 /K1 showed a much better resemblance with the diurnal variations of factor CIR as actually used by patients for calculating their insulin bolus needs. Additional constraints are introduced to limit the intrapatient variability of model parameters. The day-to-day variability of T1 and T2 was restricted to 25% (T = 0.25) and the day-to-day variations of the profiles of K1 and K2 were limited to 30% (K = 0.30) which were assumed to be reasonable values (see e.g. Heinemann (2002) for the intrapatient variability of insulin absorption and insulin action). The values of −K2 are furthermore imposed not to vary too much from some predefined reference ISF values. The maximum allowed deviation between −K2 and ISFKing (calculated according to (3)) is set to 25% (ISF = 0.25). By simply rearranging terms, the inequality constraints in (19) can be rewritten in the form A · θ < b (where θ corresponds to the parameter vector containing the unknown model parameters), which means that the problem boils down to an optimization problem subject to linear inequalities which can be solved by most standard optimization tools, like the MATLAB routine FMINCON. As a results of fitting the graybox model to recorded CGM data a patient-specific diurnal profile for CIR (i.e. −K2 /K1 ) and ISF (i.e. −K2 ) is obtained for each day of the system identification. An illustrative result for the identified graybox models using data from Zschornack et al. (2013) can be seen in Fig. 1 a and b for one patient and two days of data. The top panel of the two subfigures displays the CGM data from the clinical trial (as well as the recoded BG point measurements) together with the glucose dynamics as described by the fitted model. For this case a reasonable agreement between the measurements and the model output could be achieved for both analyzed days (FIT values between 63.81% and 69.93%). In the middle panel the carbohydrate intakes and insulin injections as recorded during the trial can be seen. These were used as inputs for the model. The bottom panel shows the evolution of K1 and K2 as described by Eqs. (18a) and (18b) with the values of the identified model parameters as well as the diurnal changes of the resulting −K2 /K1 . As already pointed out previously, it should be noted that K1 is positive, whereas K2 is negative. Furthermore, the numerical values of K1 are by about one order of magnitude smaller than K2 . The identified profiles for CIR and ISF for all days used in the system identification can then be combined

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200 150 100 50

−K2/K1 [g CHO/IU]

140 120 100 80 60 40 20 0 07:00

09:00

11:00

13:00

15:00

17:00

19:00

21:00

23:00

Daytime

09:00

11:00

13:00

15:00

17:00

19:00

21:00

23:00

14 12 10 8 6 4 2 0

Bolus Ins. [IU]

0 07:00

Carbs [g]

CGM measured Model output SMBG samples

250

Daytime 25 20 15 10 5 0 07:00

K2/K1 K1 K2 09:00

11:00

13:00

15:00

17:00

19:00

21:00

23:00

20 0 −20 −40 −60 −80

K [mg/dl/U)]

Glucose Concentration [mg/dl]

300

Daytime

(a) Patient 0013, day 2: Measured data and identified model, FIT=67.87 %.

250 200 150 100 50

−K2/K1 [g CHO/IU]

140 120 100 80 60 40 20 0 07:00

09:00

11:00

13:00

15:00

17:00

19:00

21:00

23:00

Daytime

09:00

11:00

13:00

15:00

17:00

19:00

21:00

23:00

14 12 10 8 6 4 2 0

Bolus Ins. [IU]

0 07:00

Carbs [g]

CGM measured Model output SMBG samples

300

Daytime 25 20 15 10 5 0 07:00

K2/K1 K1 K2 09:00

11:00

13:00

15:00

17:00

19:00

21:00

23:00

20 0 −20 −40 −60 −80

K [mg/dl/U)]

Glucose Concentration [mg/dl]

350

Daytime

(b) Patient 0013, day 3: Measured data and identified model, FIT=69.93 %. Fig. 1. ABC method for system identification - Illustrative results for measured data and model output (P0013, days 2 and 3 from Zschornack et al., 2013).

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−K 2 [mg/dl/IU]

−K2 / K1 [g CHO / IU]

F. Reiterer and G. Freckmann / Annual Reviews in Control xxx (xxxx) xxx

9

15 10 5 07:00

09:00

11:00

13:00 Daytime

15:00

17:00

19:00

09:00

11:00

13:00

15:00

17:00

19:00

50 40 30 20 07:00

Fig. 2. ABC method for system identification - Illustrative results for CIR and ISF profiles as a function of daytime (P0037 from Zschornack et al., 2013). (For interpretation of the references to color in the text, the reader is referred to the web version of this article.)

in as next step. An illustrative result for doing so for one patient and five days of data is shown in Fig. 2: The top panel shows the identified profiles for CIR vs. daytime, whereas the bottom panel displays the corresponding profiles for ISF. Each blue line corresponds to one day of data from the system identification, whereas the bold black lines indicate the average profile (average over all blue lines). Daytime-specific estimates for CIR and ISF can then be obtained from these average diurnal profiles. This approach of obtaining daytime specific BC settings is in the following referred to as “Adaptive Bolus Calculator” (ABC) approach. A validation of the method can be found in Reiterer, Kirchsteiger, Assalone, et al. (2015, Reiterer, Kirchsteiger, Freckmann, et al., 2015b) (comparison with BC settings adjusted by MDs) and Reiterer (2017) (validation in simulation studies). 2.6. Other types of insulin dosing algorithms Additionally, there is a wide variety of other insulin dosing algorithms for T1DM that are not using the rationale of the BC formula (1), but which optimize insulin based on differing assumptions, e.g. by optimizing the predicted glucose trajectory for a nonlinear physiological model. A literature review of all sorts of different insulin dosing algorithms for intensive insulin therapy can be found in chapter 6 of Garcia Jaramillo (2011). Newer algorithms not included there are e.g. Grosman et al. (2013), Tuo, Sun, Shen, Wang, and Wang (2015) and Boiroux et al. (2017). 3. Estimating the carbohydrate content of meals Whereas the standard approach in ACC consists of educating the patient to mentally estimate the carbohydrate content of meals, in the last years several advanced technological approaches have been proposed to facilitate this task. The current section aims at giving an overview about such methods. 3.1. Food database systems A relatively simple method to help patients with estimating the carb content of meals is to supply them with a database system, which contains information about the macronutient content of processed food. An example for such a database is e.g. Menard et al. (2011) and ANSES (2017). The positive effect of this method is long known (see e.g. Pithova & Kvapil, 2006) and T1DM patients are nowadays taught to use such additional resources if necessary (Warshaw & Bolderman, 2008). In recent years also attempts have been reported to directly link such food databases to

´ BCs (Diouri et al., 2015; Pankowska & Błazik, 2010). A more sophisticated version of such a system is the VoiceDiab app (Foltynski et al., 2018; Ladyzynski et al., 2018), which analyzes the voice description of meals, obtains the corresponding macronutrient composition from a food database and computes the required insulin amount with a BC. With the assistance of food databases though, patients still need to estimate the size of the meal by themselves. 3.2. Computer vision based systems for meal analysis A more advanced strategy consists of computer vision based approaches that try to analyze the carb content of food from pictures. The most prominent example is the GoCARB system developed by a research group at the University of Bern (Anthimopoulos et al., 2015). GoCARB is an app that analyzes pictures of a plate with food taken by a smartphone. To allow for an estimation of meal sizes, it is actually necessary to take two pictures of the plate from two different angles to allow for a 3D reconstruction of the food items on it. The food items on the plate should not be overlapping to avoid estimation biases. Different foods are recognized based on their color and texture by a machine learning algorithm and the food volume is estimated using a 3D reconstructed image. The carbohydrate content of the meal is then computed based on this information together with tabulated data from a food database (see Section 3.1). Besides GoCARB, there are also examples of computer-vision based software for automatic meal analysis, which have not been exclusively developed for this purpose. Examples are e.g. Zhang, Yu, Siddiquie, Divakaran, and Sawhney (2015), Meyers et al. (2015) and Merler, Wu, Uceda-Sosa, Nguyen, and Smith (2016). While such approaches are undoubtedly promising and interesting, there are still some problems though, which are difficult to solve and which limit their applicability. It is e.g. necessary in GoCARB that food items are separates on a plate, which is typically not the case for standard restaurant meals. Furthermore, it is impossible for such tools to recognize e.g. the hidden carbs in a salad dressing appropriately. 3.3. Automatic meal detection from glucose traces Besides aforementioned approaches for carbohydrate estimation, there is also a rich scientific literature on the topic of automatic meal detection, mainly in the context of Artificial Pancreas (AP) systems. Most AP systems under development are hybrid APs, meaning that the carbohydrate content of meals still has to be announced to the AP system to trigger an adequate bolus injection. For those systems the patients’ ability to estimate the carbohydrate

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content of meals is still indispensable. However, for the case of fully closed loop APs (i.e. AP systems, which do not use any manual meal announcements) as well as for safety modules in hybrid AP (designed for the detection fo missed meal boluses) it is necessary to detect meals automatically and online from glucose measurements via CGM. Several algorithms have been proposed for this purpose. In general, (most of) those algorithms can be subdivided into two big groups: The first group of algorithms is based on heuristics and tries to detect meals based on CGM features like rate-of-change (see e.g. Dassau, Bequette, Buckingham, & Doyle, 2008; Harvey, Dassau, Zisser, Seborg, & Doyle III, 2014), whereas the second group relies on a model in order to draw conclusions about meal effects in glucose readings (see e.g. Ramkissoon, Herrero, Bondia, & Vehi, 2018; Turksoy et al., 2016). Whereas many of the proposed meal detection algorithm only give binary information about meals (meal or no meal), there are also examples in the literature for algorithms which are capable to estimate the carb content of meals online based on CGM readings. These are e.g. Lee and Bequette (2009), Turksoy et al. (2016), Samadi et al. (2018, 2017) and Mahmoudi et al. (2019). In Lee and Bequette (2009), Turksoy et al. (2016) and Mahmoudi et al. (2019) the strategy for estimating the meal size is very similar: A physiological model of the human glucose metabolism is used together with a filtering approach to estimate the effect of meals on glucose levels. In Samadi et al. (2018, 2017) on the other hand the carbohydrate estimate is compute based on a fuzzy logic approach. Besides the meal detection algorithms for AP systems, there have also been other attempts to automatically estimate the carbohydrate content of meals based on glucose measurements. In Boiroux et al. (2017) a bolus calculator algorithm is proposed that combines a physiological model with a filtering algorithm in order to estimate the size of ingested meals online. In Patek et al. (2016) on the other hand a physiological model is used to retrospectively compute a so-called “net effects” vector using regularized deconvolution techniques. The identified net effects vector combines information about meal timing and size and could potentially be useful for the analysis of meal sizes. The proposed identification method from Patek et al. (2016), however, is only designed for retrospective analysis of glucose traces and is (in its current form) not suitable for the online estimation of meal sizes. Besides CGM data, meals could potentially also be detected using other wearable sensors. Examples include the acoustic detection of ingested meals via chewing sounds or the optical detection via smart glasses. Over the last years a rich literature on the topic of automatic dietary monitoring by means of wearable sensors has been written, see e.g. Schiboni and Amft (2018) for an overview. The use of such technology for the diabetes-specific applications is still at a rather early stage, though. 4. Factors impacting glycemic outcomes with advanced carbohydrate counting In ACC, when determining bolus insulin requirements according to (1), the only variables routinely taken into account are the to-

tal amount of carbohydrates, the preprandial glucose concentration and, in an implicit manner, daytime (by using a different CIR and ISF for breakfast, lunch and dinner). In this section the effect of additional influencing factors that also impact glycemic outcomes in ACC are reviewed based on findings from the literature. Of those factors, two are further discussed in more detail presenting original data, namely the impact of errors in the estimated carbohydrate amount and the impact of other macronutrients besides meal carbohydrates in mixed meals. For analyzing the impact of carbohydrate counting errors and mixed meal effects findings recently presented in Reiterer, Freckmann, and del Re (2018a,b) are used. Both works use the data from a recent clinical trial (Zschornack et al., 2013) as their basis and show results of simulation studies via Deviation Analysis. Therefore, in the following the clinical data used for those studies and the basic concept of Deviation Analysis is introduced first, before discussing the additional factors influencing glycemic outcomes in ACC. 4.1. Methods and data 4.1.1. Assessment strategy Over the last decades in silico evaluations using simulation models of the human glucose metabolism have proven to be very valuable tools for the assessment of new therapy interventions for diabetes. The most prominent example in this context is definitely the UVA/Padova (Dalla Man et al., 2014; Kovatchev, Breton, Cobelli, & Dalla Man, 2010) simulator. Even though these detailed physiological models have proven to be very valuable, there remain some drawbacks. Most models show a time-invariant behavior and are (usually) restricted to insulin and meal carbohydrates as only system inputs. As a result, the models are able to accurately capture interpatient variability, but lack a realistic description of intrapatient variability. Recently (see e.g. Reiterer, Reiter, Freckmann, & del Re, 2016), several new methodologies for the testing of insulin dosing strategies have been proposed that try to combine real measurement data, i.e. continuous glucose monitoring (CGM) data and information about insulin injections (dose and timing) with simple (often linear) models to create a test environment that also incorporates the complex phenomena of real-life glucose dynamics in diabetic patients. The methodologies differ slightly, however, the basic idea is always the same: A simple model of insulin action is used together with the assumption that the effect of insulin on the glucose level can be separated from all other effects. The basic workflow for Deviation Analysis is displayed in Fig. 3. The rough idea is to assume a model of insulin action, a transfer function model G2 (s) in the case of Fig. 3, and then subtract the effect of the measured insulin (Ins) and add the effect of the proposed insulin dosing (Insmod ) to measured CGM traces. The estimated effect of a new insulin dosing strategy is thus extrapolated using the real clinical data as a baseline. Several methods for performing Deviation Analysis simulations have been proposed over the last couple of years which are all very similar, but differ in the model that is used for describing insulin action (see Reiterer, Reiter, Freckmann, & del Re, 2016; Reiterer, Schauer, Reiter, & del Re, 2019 for an overview). For the current paper the slightly

Fig. 3. Workflow for assessing a control strategy in Deviation Analysis.

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more complex, nonlinear Deviation Analysis approach presented in Reiterer, Reiter, and del Re (2017) is used for the simulations. 4.1.2. Clinical data For the work presented in Sections 4.2 and 4.3 data from a recent clinical trial (Zschornack et al., 2013) performed at the Institute for Diabetes Technology, Germany is used. In this clinical trial 37 subjects with T1DM spent seven days hospitalized. During this time period each of them wore either two (28 individuals) or four (9 individuals) CGM systems in parallel. During the entire period of the study all CGM signals have been recorded, together with frequent BG point measurements by means of a BG meter (at least one measurement per hour during the day) and documentation about meal intakes, bolus insulin injections and basal insulin rates. During the study the patients calculated their bolus needs based on the self-estimated carbohydrate content of the meals using ACC and pre-adjusted patient- and mealtime-specific CIR and ISF values. Seen that the general BG management of the individuals in the study is acceptable (Patient HbA1C: 7.8 +/− 1.2%), it can be assumed that these patients were in general using suitable basal rates and well adjusted CIR and ISF settings. However, it should also be mentioned that no systematic verification of the patients’ therapy settings has been performed during the trial. Most ingested meals have been analyzed by a trained dietitian who retrospectively calculated the composition of those meals (carbohydrate, fat and protein content; both in terms of total grams and calories). On two days of the trial (first 28 patients: days 3 and 4; remaining 9 patients: days 3 and 6) glucose excursions have been induced by serving fast-absorbing breakfast meals with a high carbohydrate content (approx. 80% carbs) and by delaying the insulin injections by 15 minutes, leading to considerable temporary peaks in the BG values. Furthermore, the injected insulin quantities have been increased by 15% compared to the recommended values, often leading to a subsequent hypoglycemia which is then treated with rescue carbohydrates. 4.2. Impact of carbohydrate counting errors 4.2.1. Impact of carbohydrate counting errors - introduction The quality of the BG control with ACC is directly linked to the correctness of carbohydrate estimation by patients. However, many patients fail to do estimations accurately. There exist a variety of scientific publications investigating size and (to a lesser extent) effect of carbohydrate counting errors: In Brazeau et al. (2013) the systematic and random estimation errors when calculating the carbohydrates of meals have been investigated in an adult population with T1DM. It was found that in average an error of 15.4 ± 7.8 g or 20.9 ± 9.7% was made for each meal (with average meal CHO contents of 72.4 ± 34.7 g). Usually patients had a pronounced negative estimation bias, with 63% of the 448 analyzed meals being underestimated. It was furthermore found that larger carb counting inaccuracies were associated with lower time in the euglycemic range and higher glycemic variability. In Deeb, Al Hajeri, Alhmoudi, and Nagelkerke (2017) the carb counting errors in a T1DM population of children and adolescents have been studied. It was found that for 67% of meals the carbohydrate estimates were within ± 20% of the real amount. It was furthermore found that patients were more likely to underestimate the carbohydrate content of meals than to overestimate it. For 36% of meals a carbohydrate amount was estimated that was more than 20% lower than the true amount, whereas for only 8% of meals the estimated carbohydrate amount was more than 20% higher than the true amount. Additionally, it was found that underestimated meals tend to lead to above-target glucose values (in

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87% of those cases), whereas overestimated meals tend to give too low postprandial glucose values (in 63% of those cases). Having a good carbohydrate estimate (error smaller 20%) led to postprandial glucose values in the target range in 55% of the cases. In Smart et al. (2010) the carb counting errors have been investigated for children with T1DM, as well as for their caregivers. In average the children were able to estimate the carbohydrate content of meals relatively accurately, 73% of the estimates were within 10–15 g of the real carbohydrate quantity. Additionally, it was found that patients tend to overestimate carbs in small meals and underestimate them in big meals. Regarding the effect of carbohydrate counting errors on the quality of glycemic control it was found in Smart et al. (2009) that errors of within ± 10 g of the real carbohydrate quantity do not have a significant effect on the postprandial glucose levels or the glucose area under the curve (AUC), whereas in Smart, King, McElduff, and Collins (2012) it is stated that carbohydrate counting errors of ± 20 g lead to a significant deterioration in glycemic control. In Smart et al. (2012) an insulin bolus calculated for 60 g of carbohydrates was applied for meals containing 40, 50, 60, 70 and 80 g of carbohydrates. These tests led to postprandial hypoglycemia for the 40 g meals, as well as to postprandial hyperglycemia for 80 g meals, but resulted in no statistically significant differences among the other meal responses. Additionally, there are several in silico studies in which the performance of a specific (often closed-loop) insulin dosing algorithm is studied, considering carbohydrate counting errors as one of the disturbing factors. However, there are only few publications that explicitly analyze the impact of carbohydrate counting errors during standard basal-bolus-therapy. 4.2.2. Impact of carbohydrate counting errors - data analysis The analyses in the current section are based on the data from the clinical trial (Zschornack et al., 2013) described in Section 4.1.2. As already stated, in this study most meals have been analyzed by a trained dietitian who retrospectively calculated the composition of those meals (carbohydrate, fat and protein content). The corresponding values for the calculated carbohydrate contents of the meals, which are deemed much more accurate than the estimates by the patients, are used for the retrospective analyses presented in this section. In total detailed data for 897 meals are available. To gain an insight into the extent of carb counting errors in this trial, a detailed data analysis is performed similar to the ones from the literature presented in Section 4.2.1. For all analyzed quantities values of all patients and meals are pooled and statistics are given as median [interquantile range]. Since, however, in most publications on the topic only mean ± standard deviation is given, these values are also reported here in brackets for easier comparison. It should be noted though that some of the subsequently reported quantities do not follow a normal distribution. In such cases mean ± standard deviation is not very informative regarding the overall distribution of the data. The carbohydrate content of the analyzed meals in the trial was 56.1 g [32.6 g 75.1 g] (54.9 ± 27.6 g). In Fig. 4 the calculated carbohydrate content (from the dietitian) is plotted against the estimated carbohydrate content (estimated by the patients during the trial) for all meals combined. Each circle corresponds to one meal and the face color of the circle indicates the patient. As for the subsequent figures in this section, a distinct face color is used for each of the 37 patients of the trial. It can be seen that the difference between calculated and estimated carbohydrate content is bigger for bigger meals. Furthermore, based on a linear regression of the data it can be seen that there is a tendency to underestimate the carbohydrate content of meals as is clearly visible from the red line. In green, additionally the boundaries of a symmetrical tolerance interval are shown that corresponds to the mean value

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Fig. 5. Estimated divided by calculated carbohydrate amount: distribution and fit.

± one standard deviation and that contains roughly 68.3% of all points. These boundaries are at:

carbsest. = (0.92 ± 0.19 ) · carbscalc.

(20)

In Fig. 5 the comparison between estimated and calculated carbohydrate content is plotted as probability density function (PDF) where the quantity on the x-axis corresponds to the estimated divided by the calculated carbohydrate amount. Again, the negative estimation bias becomes obvious (peak of the distribution at <1.0). Additionally, it can be seen that this distribution can be approximated reasonably well by a normal distribution which is plotted in magenta. Additionally the results of the linear regression as from Fig. 4 are shown (red: mean, green: mean ± 1σ ). In Fig. 6 the error in the estimated carbohydrate amount in g CHO is plotted as a function of the calculated carbohydrate amount. It can be seen that the tendency to underestimating the carbohydrate content is especially pronounced for large meals, whereas for small meals there seems to be even a slight trend to overestimating the carb content. This is quite in line with the findings from Smart et al. (2010). As in Smart et al. (2010) the data can be fitted with a quadratic model. However, contrary to that

publication no statistically significant axis intercept different from zero is found (p > 0.5). Analyzing the data displayed in Fig. 6 it is found that the median absolute estimation error in the data corresponds to 6.4 g [2.7 g 13.0 g] (mean ± standard deviation: 8.78 ± 8.39 g) which is significantly lower than the errors listed e.g. in Brazeau et al. (2013), indicating that the study population in the clinical trial considered here is rather well educated in carbohydrate counting. In 66.4% of the cases the estimates are within ± 10 g of the calculated carb amounts, whereas in 90.6% of the cases they are within ± 20 g, which is comparable to the findings in Smart et al. (2010). Patients tended to have a negative estimation bias: For 61.7% of the meals the estimated carbohydrate content was lower than the calculated one. In Fig. 7 the same analysis is performed for the error in the estimated carbohydrate amount in %. This plot looks also rather comparable to an analogous one in Smart et al. (2010). It is found that the median absolute estimation error corresponds to 13.8% [5.5% 24.4%] (mean ± standard deviation: 21.2 ± 71.5%). The mean value is comparable to the results reported in Brazeau et al. (2013), but the standard deviation is much higher. This, however, can easily be explained by the very high estimation errors for small meals. If only meals with a carbohydrate content larger than 40 g are

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considered the standard deviation computed from the absolute estimation errors decreases to 11.3% (median [interquantile range]: 12.7% [5.5% 20.8%]; mean ± standard deviation: 14.7 ± 11.3%). In 39.8% of the meals the estimation error is within ± 10%, whereas 66.4% of meals have an estimation error within ± 20%. These numbers are in line with the findings from Deeb et al. (2017). 4.2.3. Impact of carbohydrate counting errors - results and discussion The effect of carb counting errors on glycemic control during basal-bolus-therapy is studied by means of computer simulations via Deviation Analysis, as explained in Section 4.1.1 using the data from the clinical trial (Zschornack et al., 2013) as a basis. Furthermore, it is analyzed how inaccuracies in the carbohydrate estimates affect the insulin therapy settings. This is done using the ABC approach described in Section 2.5 which can retrospectively identify estimates for CIR and ISF from recorded data. As a first analysis the effect of the carb counting errors actually occurring during the trial on the glycemic control are studied in Deviation Analysis. The days 2 through 5 of the trial are used to identify adequate CIR and ISF settings with the ABC approach described in Section 2.5, whereas day 6 was used for the testing. The data from day 1 is omitted since the recording of data just started in the middle of the day. The same is done for the data of day 7 because the calculated carbohydrate amounts are missing for many of the meals on that day. In total 6 scenarios are analyzed: • Using the calculated carbohydrate content for identifying the CIR and ISF settings with the ABC approach, as well as for calculating the bolus needs on day 6 according to (1). • Using the calculated carbohydrate content for identifying the CIR and ISF settings with the ABC approach, but the estimated carbohydrates for calculating the bolus needs on day 6. This scenario would correspond to having the BC settings adjusted under controlled conditions (e.g. in a hospital). • Using the estimated carbohydrate content for identifying the CIR and ISF settings with the ABC approach, but the calculated carbohydrate amount for calculating the bolus needs on day 6. This scenario would correspond to having the BC settings tested under controlled conditions. • Using the estimated carbohydrate content for both, identifying the CIR and ISF settings with the ABC approach and calculating the bolus needs on day 6. This scenario would correspond to patients using the ABC method in an at-home setting for both, automatically adjusting their BC settings and calculating their bolus insulin needs. • Computing the insulin needs based on calculated carbohydrate content and the same CIR and ISF settings that the patients actually used during the trial for calculating their bolus insulin needs. • Computing the insulin needs based on estimated carbohydrate content and the same CIR and ISF settings that the patients actually used during the trial for calculating their bolus insulin needs. The last two cases, in which the insulin needs are computed based the same bolus calculator settings that the patients actually used during the trial, are in the following referred to as standard bolus calculator cases (StdBC). As performance measures the percentage of time in hypoglycemia (BG < 70 mg/dl), the percentage of time in hyperglycemia (BG > 180 mg/dl) and the following cost function V are used:

V = thyper /ttot + W · thypo /ttot

(21)

V is used to condense the information about glycemic control into one single number and is defined as the weighted sum (with weighting factor W) of time in hypoglycemia (thypo ) and hyperglycemia (thyper ), both normalized by the total time frame of the performance assessment (ttot ).

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0.417 ± 0.264 0.363 ± 0.236 0.358 ± 0.263

The results of the analysis are summarized in Table 2. The table shows mean value and standard deviation for the selected performance criteria for all 6 analyzed scenarios as calculated from the results of all 37 patients of the trial combined. The scenarios with CIR and ISF settings identified with the ABC approach based on the calculated carbohydrate amount are marked as “ABC, case1”, whereas those with BC settings identified based on the estimated carbohydrate amount are marked as “ABC, case2”. The first column of results (“Dev.Anal., calc. carbs”) corresponds to using the calculated carbohydrate amount for computing the bolus insulin in the Deviation Analysis, whereas the results in the second column (“Dev.Anal., est. carbs”) are for the case of using the estimated carbohydrate amount in the Deviation Analysis. It is interesting to see in Table 2 that all of the four analyzed scenarios with CIR and ISF values identified from data lead to a significantly lower value of cost function V (as from (21) with W = 5, same weighting factor as in Reiterer et al. (2016)) than the two scenarios with the StdBC settings. This is due to the higher level of hypoglycemia for the StdBC settings, which is an indication for a suboptimal adjustment of the clinically used CIR and ISF values. In general it can be seen that the differences between the four scenarios with CIR and ISF identified from data are rather small. However, both scenarios that use the calculated carbohydrate content lead to a lower value of V than the two corresponding scenarios with estimated carbohydrate content. This is due to a reduced time in hyperglycemia. Surprisingly, the scenario of using the estimated carbohydrate content for identifying the BC settings and the calculated carbs for bolus dosing on day 6 leads to a lower value of V than the scenario with calculated carbs for both, identifying the BC settings and later bolus dosing. This is due to the lower time in hyperglycemia for this scenario. As discussed earlier, the patients tend to have a negative estimation bias, which leads to lower values of CIR and ISF in the system identification and afterwards to higher insulin doses when calculating the bolus needs with the identified BC settings and the real carbohydrate amount. This can also be seen by the fact that this settings leads to higher values for the time in hypoglycemia than the other three scenarios with identified BC settings. To better understand the effect of carb counting errors on the glycemic control in ACC, an additional analysis is performed in which bias and random errors in the carb estimates are analyzed separately. For this analysis the calculated carbohydrates are used as a basis and are manipulated according to the following formula:

carbsest.,i = carbscalc.,i · (1 + bias + ei )

(22)

with

ei ∼ N (0, (uncertainty/1.96 ) ) 2

(23)

So, the estimated carb content of each meal i is computed by taking the calculated carbohydrate content, subtracting or adding a

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bias (between −20% and +10%) and then adding a random estimation error which is assumed to be normally distributed with zero mean and a standard deviation between 0% and 30%. To better understand the extent of the random errors, the values of the standard deviation are transformed to an “uncertainty”, which corresponds to the boundaries that enclose 95% of the errors and can easily be calculated as 1.96 · σ . The corresponding uncertainties are thus between 0% and roughly 60%. The basic setup of the performance assessment is chosen as for the first set of analyses described earlier in this section. Two scenarios are analyzed: In the first one (from now on referred to as “case A”) the calculated carbohydrates are used for identifying the BC settings with the ABC approach, and the estimated carbs are used only afterwards for calculating the bolus needs, whereas in the second scenario (from now on referred to as “case B”) the estimated carbohydrate amounts are used for both, identifying the BC settings and calculating the bolus needs afterwards. The combined results with all combinations of bias and uncertainty in the carbohydrate estimates are shown in Fig. 8. The left plots show the results for case A, whereas the right ones show the results for case B. The first row of plots displays the percentage of time in hypoglycemia, the center ones the percentage of time in hyperglycemia and the bottom ones the value for cost function V with W=5. Each point in the plot visualizes the corresponding value of the average over all 37 patients. It is interesting to see that for case A the time in hypoglycemia and hyperglycemia is determined almost entirely by the bias in the carb estimate, whereas for case B the bias has basically no effect on the time in hypoglycemia and hyperglycemia. This is due to the fact that in case B the same bias is used also in the identification step, which means that the identified CIR and ISF values implicitly contain the same bias which allows to compensate for it when using the factors af-

terwards for glucose control. It can be assumed that patients with well adjusted BC settings have their estimation bias counterbalanced by their CIR and ISF. When analyzing the effect of the random estimation errors on the glycemic control it is evident that a higher uncertainty in the estimated carbohydrates leads to a worse glycemic control, both in terms of time in hypoglycemia, as well as for time in hyperglycemia, which holds for case A, as well as for case B. When analyzing the values of V the results for case A and case B look somewhat similar. For the value of V the bias in the estimation has a smaller impact than the uncertainty in the estimates. For case B this is expected since the bias has basically no impact on the time in hypoglycmia and the time in hyperglycemia. For case A on the other hand this can be explained by the fact that a bias will have opposing effects on time in hypoglycemia and time in hyperglycemia. When adding up those effects for calculating V according to (21) they counterbalance each other to a certain degree. For the case of W = 5 the cost V is slightly more favorable for negative estimation biases since these lead to a reduced time in hypoglycemia. For other values of W this will of course look differently. In summary it is found in the analyses presented in the current section that systematic estimation biases in the carbohydrate counting hardly affect the results since the same biases are usually implicitly accounted for in the therapy settings if CIR and ISF are well adjusted. Random carb counting inaccuracies on the other hand do lead to a certain deterioration of glycemic control, but ACC is relatively robust towards this type of inaccuracies. Still, an improved performance should be possible by decreasing the level of random estimation errors. This could potentially be achieved by assisting the patients in their efforts of carb counting, e.g. using a

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4.3. Mixed meal effects 4.3.1. Mixed meal effects - introduction In standard ACC only the carbohydrate content of meals are considered for the calculation of bolus insulin needs. In reality, however, it is already long known that also the other macronutrients of meals play an essential role. Additionally, the glycemic index (GI) of the meal, which is an indicator for how fast the carbohydrates of the meal is absorbed (high GI meals correspond to fast absorbing carbohydrates, e.g. sugar, whereas low GI meals contain carbohydrates that are slowly absorbed, e.g. wholewheat flour), plays a role. It was e.g. shown in Wolever and Mullan (2011) that meals high in sugar lead to a quick and pronounced peak in BG compared to meals with lower GI carbohydrates. Additionally, the fat content in mixed meals was shown to have a strong impact on the glycemic response after meal ingestion. Meals with a high fat content were found to lead to a slower increase in BG and a longer time till reaching the peak value in BG. This can be explained by the effect that fat in meals slows down the gastric emptying. Additionally, in Wolpert, Atakov-Castillo, Smith, and Steil (2013) it was found in closed-loop experiments that meals high in fat lead to increased insulin requirements. This could be explained in Laxminarayan, Reifman, Edwards, Wolpert, and Steil (2015) by a model-based analysis of the data of these experiments. It was shown there that for high fat meals not only the absorption time is prolonged, but also the insulin sensitivity is decreased which leads to an increase in insulin needs. Possibly, this is due to an increase in free fatty acids (FFAs) in the blood after high fat meals (see e.g. Roy & Parker, 2006 for this impact). But not only high fat meals lead to increased insulin requirements. Meals with a high protein content are also said to require additional bolus insulin. It was e.g. shown in Paterson et al. (2016) that meals containing 75 g or more of protein but no other macronutrients, i.e. also no carbohydrates, still do have a significant impact on the BG level. The effect, however, is significantly slower than for the ingestion of high GI carbohydrates. In Bell et al. (2015) a meta-analysis is presented using published data from clinical trials that investigated the effect of fat, protein, as well as GI on the postprandial glucose response in T1DM, as well as on the insulin requirements. Additionally, pragmatic recommendations are given on how to adjust the insulin dosing in mixed meal situations. It is recommended there to use additional insulin for meals that are high in fat and protein. There also exist other recommendations and algorithms for computing the bolus insulin needs in mixed meal situations. Especially in Poland patients with T1DM are educated on how to estimate the fat and protein content of meals and how to adjust the bolus needs accordingly. A basic algorithm for doing so is pre´ ´ sented e.g. in Pankowska and Błazik (2010) and Pankowska, Błazik, and Groele (2012): The amount of fat and protein is estimated in terms of fat-protein-units (FPUs) which can then be used in the standard BC formula (1) applying the standard CIR in the calculation, implying that the required amount of insulin per g of fat and protein is proportional to the required amount of insulin per g of carbohydrates. Additionally, there also exists work in the literature in which it is tried to optimize the insulin dosing in mixed meal situations based on models of the human glucose metabolism. In Srinivasan, Bok Lee, Dassau, and Doyle III (2014) the insulin delivery profiles for high-fat meals are optimized without taking into consideration the effect of mixed meal composition on in-

100 Breakfast Composition [%] (of Calories)

computer vision based tool that tries to estimate the carb content in meals based on pictures (see Section 3.2).

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Fig. 9. Breakfast composition for standard meals and induced glucose swings. Error bars indicate the variability in macronutrient composition.

sulin requirements. It was found that, contrary to low-fat meals (for which injecting the entire bolus insulin at the time of the meal gives the best results), high-fat meals are better controlled with more sophisticated injection strategies like a biphasic profile. In Bell, Toschi, Steil, and Wolpert (2016) an algorithm for model-based bolusing in mixed-meal situations is tested. The strategy consists of adjusting the parameters of a relatively simple physiological model to the postprandial responses after two different mixed meals with identical carbohydrate content, where one is high in fat and protein, whereas the other one is low in fat and protein. In a next step the adjusted models are used to optimize the insulin delivery profiles for such mixed meals. As a result, the algorithm suggested an additional 65% of bolus insulin for the meal high in fat and protein compared to the meal low in fat and protein. 4.3.2. Mixed meal effects - results and discussion In the current section the effect of the mixed meal composition on bolus insulin requirements and glycemic control is studied by means of the ABC algorithm described in Section 2.5. The corresponding analysis relies on the data presented in Section 4.1.2. To see retrospectively how a difference in insulin dosing would have affected glycemic control, Deviation Analysis simulations are performed (introduced in Section 4.1.1). For the dataset used in this work, the impact of the mixed meal composition on the CIR and ISF values can be studied especially well for the breakfasts. During two days of the trial the patients ingested a breakfast consisting almost exclusively of high GI carbohydrates (in the following referred to as “high carb breakfast”), whereas for the other days the patients could choose their breakfast compositions freely. A comparison of composition of high carb and standard breakfasts can be seen in Fig. 9 in terms of calories. The colored bars show the average composition for all patients and all breakfasts combined, and the error bars indicate the standard deviation of the composition. Not only do the standard breakfasts contain a significantly higher fraction of fat and protein, also the variability is much higher. A strong difference in CIR values can be observed between standard or high carb breakfasts. For each patient an average CIR is calculated for the standard and the high carb breakfasts from the identified values for the corresponding days. A ratio is then calculated between those two CIR values (CIRHigh Carb Breakfast /CIRStandard Breakfast ). Fig. 10 shows the distribution of these ratios for all patients combined. It can be seen that

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CIRHigh Carb Breakfast / CIR

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CIRHigh Carb Breakfast is considerably bigger than CIRStandard Breakfast which indicates that for the same carbohydrate amount a larger quantity of bolus insulin is required for the standard breakfasts. The difference between the two CIRs is found to be statistically highly significant (p = 0.0 0 08 as tested with a t-test). This finding is in line with the statements from the literature which indicate that the protein and fat in mixed meals lead to an increase in bolus insulin needs. Additionally, the identified parameters of model structure (17) are compared separately. The K1 and K2 values of the ABC for high carb and standard breakfasts are compared separately, as is done for the identified T1 and T2 values for the corresponding days. This comparison is shown in Fig. 11. It is found that the K2 values for the high carb breakfasts are significantly larger than the corresponding values for the standard breakfasts (p = 0.0 0 06). For K1 on the other hand no significant difference between the values for the two different breakfasts is found. The findings indicate that the insulin sensitivity is lower for the breakfasts with a higher fat and protein content, whereas the total amount of glucose appearing in the blood after the meal is identical for both meal types. When analyzing the T1 and T2 values a significantly higher T1 is found for the standard breakfasts (p < 0.0 0 01) indicating a slower meal absorption, whereas there is no significant difference in the T2 values (i.e. no difference in the time needed for subcutaneous insulin absorption). These results mirror surprisingly well the findings stated in Laxminarayan et al. (2015) regarding the mechanisms of mixed meal effects on the human glucose metabolism. Seen that the mixed meal composition does have a significant impact on the CIR and ISF factors identified in the ABC approach, the question is how these effects impact the glycemic control and how to possibly account for mixed meal effects when calculating the bolus insulin needs. In the current section a strategy similar to the case-based reasoning approach proposed in Herrero et al. (2015b) is tested for this purpose: The identification of CIR and ISF values is performed using only the carbohydrate content as an input to the model, as described in Section 2.5. However, besides saving the identified CIRs and ISFs as a function of daytime, also the corresponding meal composition of each breakfast, lunch and dinner are saved to the ABC internal database. When calculating the bolus insulin needs, the database will serve as a standard reference. First, the meal composition of the meal to be ingested is compared to previous records in database. The most similar meal ingested around the same daytime (measured by the Euclidian distance) is identified in the database, and the CIR and ISF values of this most similar

Fig. 11. Effect of breakfast composition on identified parameter values in the system identification.

meal are used. This strategy will in the following be referred to as “ABC with Meal Matching”. In contrast, for the baseline case, in the following referred to as “baseline ABC” strategy, only the identified CIRs and ISFs as a function of daytime are stored in the database for each dataset (i.e. for each day of data used in the system identification) and the bolus insulin needs are calculated based on the average profiles (see e.g. the bold black lines in Fig. 2). For the test calculations four days of trial are used for the identification of CIR and ISF values using the standard ABC strategy, whereas the remaining two days (one is a standard day, the other one contains an induced glucose swing in the morning caused by a high carb breakfast) are used for the performance assessment in the Deviation Analysis. For those two days the performance of the Baseline ABC is compared to the performance of the ABC with Meal Matching. Additionally, the performance is also compared to the one achieved with the Standard BC settings that the patients used during the trial (i.e. applying the clinically used CIR and ISF values). For the performance assessment the nonlinear Deviation Analysis strategy presented in Reiterer, Reiter, et al. (2017) is used. In Fig. 12 two examples for calculated glucose trajectories of above three strategies are shown. Both plots show a standard day without induced glucose excursions. In the example shown in Fig. 12 a the Standard BC settings and Baseline ABC give a very similar result for the calculated glucose trajectory and both lead to hypoglycemia around 16:00. The ABC with Meal Matching on the other hand leads to a a calculated trajectory that stays within the target BG range (i.e. between 70 mg/dl and 180 mg/dl) for the entire analysis period. In Fig. 12 b a second example is shown in which Baseline ABC and ABC with Meal Matching show

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Of course, there are a lot of more complicated issues regarding application of ACC for mixed meals that have not been treated explicitly in this section. One of those complications that are difficult to quantify and deal with is mentioned in Shukla, Iliescu, Thomas, and Aronne (2015): Not only the mixed meal composition and the GI play an important role for the postprandial glucose response, also the order in which a mixed meal is ingested has a significant impact. In case the carbohydrates are ingested first (in the trial described in Famulla et al. (2016): bread, orange juice) and the protein (chicken breast) and vegetables of the meal afterwards, this led to a significantly larger postprandial peak than the case of eating the protein and the vegetables first and the carbohydrates afterwards. It can thus be seen that a small, but statistically significant improvement can potentially be achieved by considering information about the mixed meal composition. However, it is still not clear whether the extra effort of estimating the exact mixed meal composition leads to a sufficiently high performance gain that would justify this extra effort. Probably it would be more efficient to classify meals according to their macronutrient content and to estimate a specific CIR and ISF for each case. This would correspond to the case-based reasoning approach as proposed in Herrero et al. (2015b). Doing so would vastly reduce the patients’ burdens. For testing such a strategy in Deviation Analysis, however, a dataset significantly bigger and more diverse than the one from Zschornack et al. (2013) would be required. 4.4. Other influencing factors

Fig. 12. Illustrative Deviation Analysis results – Baseline ABC and ABC with Meal Matching vs Standard BC.

very similar trajectories that both stay within the target zone most of the time, whereas in the case of the Standard BC settings hypoglycemia occurs around 12:00 and around 16:00. When analyzing the calculated glucose trajectories for the day with the induced glucose swings for all patients combined, the results for Baseline ABC and ABC with Meal Matching are almost identical (see Fig. 13). No statistically significant differences are found between them, neither for time in hypoglycemia, nor for time in hyperglycemia. This might be due to the delayed bolus timing at breakfast (the bolus insulin is injected 15 minutes after the meal) which blurs the effect of having somewhat different bolus insulin amounts. However, for the standard day, some differences between these two methods become apparent. The corresponding results for all patients combined are displayed in Fig. 13 b. It can be seen that the ABC with Meal Matching leads to a small, but statistically significant reduction of the percentage of time in hyperglycemia from 24.7% to 22.6% (p = 0.003, checked with the Wilcoxon signed-rank test) with virtually no change for the percentage of time in hypoglycemia (1.7% vs 1.8%, p = 0.910). Interesting is also the comparison with the Standard BC settings. Whereas the Baseline ABC leads a significantly lower time in hypoglycemia (p = 0.007), it also leads to a significantly higher time in hyperglycemia (p = 0.003). The ABC with Meal Matching on the other hand leads to a significantly lower time in hypoglycemia (p = 0.039), but with no statistically significant change for the time in hyperglycemia (p = 0.274).

Apart from aforementioned points, there is a myriad of other influencing factors that do have an impact on bolus insulin requirements and therefore also on glycemic outcomes when using ACC. Based on the data of a pilot trial (Pesl et al., 2017) it was e.g. found for the bolus calculator algorithm developed at Imperial College (Herrero et al., 2015a; 2015b) that CIR tends to be decreased in the case of alcohol intake or exercise (leading to smaller bolus doses), whereas it tends to be increased for the case of hyperglycemia (leading to a decrease in insulin doses). Other influencing factors that certainly impact glycemic outcomes in ACC are, among others, the circadian rhythm (as already discussed in Section 2.5), the initial state of the patient at the time of bolusing, glucose measurement and insulin dosing errors, but also less obvious factors like the menstrual cycle influence insulin requirements. It has e.g. been reported in Lunt and Brown (1996) that more than thirty percent of the women participating in a survey reported performing adjustments in their insulin dosing according to the menstrual cycle. Typically insulin doses are increased in the days before menstruation to counteract the effect of an increase in glucose levels experienced in that time. Furthermore, also the tissue properties around the injection/infusion site have a significant impact on glycemic outcomes in ACC. There is e.g. a much larger intrapatient variability of insulin kinetics reported if insulin is injected into lipohypertrophic tissue (Famulla et al., 2016). In the following the topics of patient initial state at the time of bolusing (more specifically: how information about it that is useful for bolusing can inferred from the glucose rate of change indicated by a CGM), as well as of glucose measurement and insulin dosing errors are discussed in a bit more detail based on data from the literature. 4.4.1. Impact of glucose rate of change With the increasing performance of CGM devices, the question of non-adjunct CGM use is widely discussed (Castle & Jacobs, 2016). In most European countries so far four CGM devices have been approved for non-adjunct use, the Dexcom G5 and G6, as well as the Abbott Freestyle Libre and Libre 2. The general

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Fig. 13. Combined Deviation Analysis results for Standard BC, Baseline ABC and ABC with Meal Matching.

criteria that have to be met by the device to be safe for nonadjunct use are not very clear. In Kovatchev, Patek, Ortiz, and Breton (2015) it is e.g. proposed that the Mean Absolute Relative Difference (MARD) of the corresponding CGM device, an indicator for CGM measurement performance (Reiterer, Polterauer, et al., 2017), should be lower than 10%. Additionally, in the meantime patients using CGM devices have themselves understood the benefit of the additional information from CGM data for insulin bolusing and many have changed the way they dose insulin based on the rateof-change (ROC) arrows displayed to the user by the CGM device (Pettus & Edelman, 2016a; 2016b). Non-adjunct CGM use is thus already ongoing among T1DM patients, irrespective of manufacturer labeling of devices. It can thus be assumed that sooner or later non-adjunct insulin therapy will become the new standard of care in T1DM, at least in the western hemisphere. It is, however, not very clear how to best use CGM information for bolusing. The most straightforward way is to merely compute the required bolus amount according to (1) and replacing the

preprandial BG point measurement by the corresponding glucose value indicated by the CGM. This, however, ignores the additional trend information available in the device. Potentially, the additional ROC information should lead to an improved gycemic control as compared to bolusing based merely on BG point measurements, since it gives some information about the patient state at the time of bolusing. Using (1) the only information about the initial state corresponds to the term IOB. So far literature is scarce on how to include information about the initial state for bolus computation. The are some first publications with simple guidelines (Cappon, Marturano, Vettoretti, Facchinetti, & Sparacino, 2018; Pettus & Edelman, 2017; Scheiner, 2015). These usually recommend some adjustments in bolus insulin based on the ROC indicated by the CGM device, but typically not explicitly take into account IOB. The only exception so far corresponds to Cappon, Vettoretti, Marturano, Facchinetti, and Sparacino (2018) which computes the optimum meal bolus amount via Artificial Neural Networks, taking into account not only glucose ROC, but also, among other variables, IOB.

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4.4.2. Impact of glucose measurement and insulin dosing errors It seems clear that the quality of the glucose measurements has a significant impact on glycemic outcomes in ACC. Whereas there is plenty of data on device accuracy and the glucose measurement errors (see e.g. Facchinetti, Favero, Sparacino, and Cobelli (2015) and Breton and Kovatchev (2008) presenting models for the errors of CGM devices, and Vettoretti, Facchinetti, Sparacino, and Cobelli (2017) introducing a model for the error of a BG meter), data is rather scarce that explicitly quantifies the impact on glycemic outcomes during basal-bolus therapy. Studying the effect of sensor errors on dosing errors and glycemic control in basal-bolus therapy is a complex research topic, with many device-specific influencing variables and is difficult to assess in in vivo clinical trial. Most publications on the topic are therefore simulation studies, see e.g. Kovatchev et al. (2015), Vettoretti, Facchinetti, Del Favero, Sparacino, and Cobelli (2016), Virdi and Mahoney (2012), Campos-Náñez, Fortwaengler, and Breton (2017) and Campos-Náñez and Breton (2017). Even though often not considered, just as glucose measurement devices, also insulin dosing devices like insulin pens and pumps have only a limited accuracy. Again, there is some data regarding dosing accuracy of devices (see e.g. Borot et al., 2014; Jahn, Capurro, & Levy, 2013), but very little information regarding the impact of such dosing errors on glycemic outcomes. 5. Conclusions and future challenges This paper presents an overview about ACC from an engineering perspective. The main idea of ACC corresponds in injecting a bolus insulin quantity at mealtimes that is proportional to the amount of meal carbohydrates. ACC is nowadays the standard of care in insulin therapy for T1DM and gives patients better flexibility regarding meal intakes and other day-to-day habits. The efficacy of ACC has been proven in clinical studies, but it should be mentioned that in general the evidence for the advantage of ACC over simpler insulin dosing schemes is not overwhelmingly high (see Bell et al., 2014; Schmidt et al., 2014). The main factor lowering the therapeutic performance with ACC, however, seems to be connected not so much with the simple assumptions behind it, but with a lack of patient adherence. The paper introduces methods that facilitate the patient and daytime-specific parametrization of BC formula (1). Furthermore, the impact of other influencing factors typically not accounted for in ACC are presented and their impact are quantified. Subsequently, additional limitations, challenges and open issues in ACC not touched upon so far in this paper shall be discussed. The main assumption in ACC about a linear relationship between carbohydrate amount and required bolus insulin quantity has been confirmed experimentally e.g. in Halfon et al. (1989) and Rabasa-Lhoret et al. (1999). In several papers, however, nonlinear relationships are suggested instead. In Slama et al. (1981) e.g. a slightly nonlinear relationship between delivered insulin amount and glucose load was found in closed-loop experiments. In Goodwin, Carrasco, Medioli, King, and Stephen (2015) a nonlinear rule for the calculation of bolus insulin is derived based on a physiological model. It was found that for big meals a smaller insulin amount per g of carbohydrates should be injected than for small meals. Contrary to that, in Marran, Davey, Lang, and Segal (2013) it is concluded based on clinical data that the amount of injected bolus insulin should be increased exponentially as a function of the carbohydrates in the meal. As a result, more IU should be injected per g of carbohydrates for big meals than for small meals. These controversies basically indicate that there is still a need for additional clinical data regarding this question. Furthermore, it should be recapitulated that many T1DM patients are not able to achieve their glycemic targets, even with

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ACC. This can often be explained by fear of hypoglycemia (and, as a consequence, underdosing of insulin), lack of diabetes education or poor adherence, but also the physiological limits of standard basal bolus therapy make it difficult to keep the glucose level in the euglycemic range during all time. Indeed, by injecting insulin at mealtimes according to (1) it is often found very difficult or impossible to simultaneously avoid hypoglycemia and hyperglycemia after a meal. This also is mirrored in the findings from Goodwin, Medioli, Carrasco, King, and Fu (2015): Since the insulin action time is in most cases significantly longer than the time needed for meal absorption, a postprandial excursion in BG will appear first, then followed by a pronounced minimum in BG. As a result, the large amount of insulin needed for limiting the postprandial BG excursion and for avoiding hyperglycemia will afterwards inevitably lead to hypoglycemia. This holds especially for the case of injecting a bolus without altering the basal insulin infusion. It was indeed shown in Bondia et al. (2009) that it is advantageous to inject basal and bolus insulin around meals in a coordinated manner. This can be done by injecting the insulin as a “superbolus” (Walsh & Roberts, 2013) which means that the bolus quantity is increased by the basal amount for the next e.g. 60 minutes and the basal rate of the insulin pump is then turned off for this amount of time. Other advanced algorithms for bolus dosing around mealtime that advocate a temporal adjustment of basal rates around the time of a meal bolus are e.g. Revert, Calm, Vehí, and Bondia (2011) and Rosales, De Battista, Vehí, and Garelli (2018). It should also be pointed out that in the current work ACC has only been discussed as part of standard basal-bolus therapy. However, also for most hybrid closed-loop systems under development and entering the market (Stone, Haviland, & Bailey, 2018) it is recommended to manually inject an insulin bolus at meals that is proportional to the carbohydrate content, thus still relying on methods from ACC. There is only limited data available though that shows whether or not the use of ACC during closed loop insulin delivery does improve glycemic control or whether simpler approaches for meal bolusing would lead to comparable outcomes. There is furthermore only limited data available that analyzes how methods of ACC and closed loop insulin delivery are best combined. A first attempt for integrating an advanced BC into an artificial pancreas system was done by Imperial College for their BC algorithm based on run-to-run control and case-based reasoning (Herrero et al., 2017). Another open point is the use of ACC in T2DM. Whereas most patients with T1DM rely on ACC for determining their bolus insulin needs, only a small fraction of insulin-treated T2DM patients use such methods. Instead, T2DM patients on MDI therapy typically use fixed meal bolus quantities (i.e. they inject the same mealtime-specific bolus insulin quantity on every day and do limited adjustments as a function of meal size or BG level). Potentially, a subgroup of insulin-treated T2DM patients would be able to improve their glycemic outcomes significantly using ACC for computing their bolus insulin needs. However, in general the efficacy of ACC in T2DM is an unresolved issue with very limited data available and unclear results (see e.g. Bergenstal et al., 2008; Christensen et al., 2018; Zipp, Roehr, Weiss, & Filipetto, 2011). Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Declaration of Competing Interest Both authors declare that they have no conflicts of interest with respect to the current manuscript.

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Acknowledgment The authors would like to thank Luigi del Re for his consultancies and ideas on the topic and the fruitful discussions. Furthermore, the authors are grateful to Junpeng Deng for proofreading the manuscript and her critical comments, as well as to Daniel Adelberger for his help in revising the paper.

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Please cite this article as: F. Reiterer and G. Freckmann, Advanced carbohydrate counting: An engineering perspective, Annual Reviews in Control, https://doi.org/10.1016/j.arcontrol.2019.06.003