Development of a glucose prediction model and insulin-delivery algorithm for critically ill patients.

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Development of a glucose

prediction model and

insulin-delivery algorithm for critically ill

patients.

Scientific Research Project

Khalid Seddouki

10319808

OLVG Intensive Care

Oosterpark 9, 1091 AC Amsterdam

Tutor:

J.H. Leopold, Assistant Professor

Mentors:

M. van Boorn, MSc

V. Lagerburg, Dr. Ir.

P.H.J. van der Voort, Prof, MD, PhD, MSc

Period:

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Abstract

Introduction: Hyperglycemia is common in critically ill patients. The incidence of hyperglycemia

in intensive care patients varies from 40 to 90%, depending on the threshold used to define a hyperglycemia [1-3]. Hyperglycemia can increase morbidity and mortality in critically ill patients [9]. Therefore, glucose regulation is an important goal in the intensive care unit (ICU) [4]. Currently nurses manually measure the glucose at discrete time intervals and based on these results insulin or glucose is manually administered. With intermittent manual measurements intermediate fluctuations in glucose values, hypo- and hyperglycemias are often undetected. To improve the glucose control and reduce the workload for care givers, ICU care givers will need to be empowered with a closed loop glucose control system. This system, which continuously measures the blood glucose levels and based on the glucose prediction, administers intravenous insulin and glucose. The first goal of this study is to develop a glucose prediction model for critically ill patients, with insulin as a variable. The second objective is to develop an and insulin delivery algorithm which makes it possible to automate glucose management in a closed loop system.

Methods: The data used during this study has been collected in a previous study [5]. The dataset

contains 98 patients with a total of 125353 glucose measurements. The first goal is to gain insight into the effect of insulin on the glucose values and the factors that can influence this effect. The model consists of a mathematical part which uses historical data for prediction and a physiological part in which the effect of insulin on the glucose values will be modelled. The second goal is to develop an insulin delivery algorithm. Several outcomes measures have been used to evaluate the glucose prediction model and insulin delivery algorithm.

Results: The physiological model achieves the best accuracy with an insulin effectiveness of 0.01

mmol/L/min/IU. The MSE is 0.53, the R2 _{is 0.86 and the accuracy in the desired range is 85.7%.}

Furthermore, 99.8% of the predictions were in region A and B of the Clarke Error Grid. The insulin delivery algorithm performs the right action in all scenarios. The insulin boluses calculated by the model are higher compared to the insulin boluses in the dataset.

Conclusion The prediction model has a high accuracy but including insulin as a variable for

glucose prediction does not improve the prediction accuracy. In addition, an automated insulin delivery algorithm, which gives patient-specific doses and is based on predicted glucose values has been developed and gives the correct advice in all the scenarios.

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Samenvatting

Introductie: Hyperglykemie komt vaak voor bij patiënten op de intensive care unit (ICU). De

incidentie van hyperglykemie varieert tussen de 40 en 90%, afhankelijk van de glucosewaarde die wordt gebruikt om een hyperglykemie te definiëren [1-3]. Hyperglykemie verhoogt de morbiditeit en mortaliteit bij kritisch zieke patiënten [9]. Om deze reden is glucoseregulering een belangrijk doel op de ICU [4]. In de huidige situatie meten verpleegkundigen de glucosewaarden handmatig op gezette tijden en op basis van deze resultaten wordt insuline en glucose handmatig toegediend. Met handmatige metingen worden tussentijdse fluctuaties in glucosewaarden, hypo- en hyperglycemieën niet altijd waargenomen. Daarnaast zijn dit tijdsintensieve handelingen. Om de glucoseregulatie te verbeteren en de werkdruk voor zorgverleners te verlagen, kunnen zorgverleners op de ICU voorzien worden van een closed loop glucose controlesysteem. Dit systeem meet de bloedglucosewaarden continu en regelt de toediening van intraveneuze insuline en glucose automatisch. Het eerste doel van deze studie is het ontwikkelen van een glucosevoorspellingsmodel voor ICU-patiënten, met insuline als variabele. Het tweede doel is het ontwikkelen van een algoritme voor de toediening van insuline. Hiermee kan de glucoseregulering middels een Closed-loop systeem worden geautomatiseerd.

Methode: De data die tijdens deze studie zijn gebruikt, zijn verzameld in een eerdere studie [5].

De dataset bevat 98 patiënten met in totaal 125353 glucosemetingen. D eerste stap is om inzicht te krijgen in het effect van insuline op de glucosewaarden en de factoren die dit effect kunnen beïnvloeden. Het model zal bestaan uit een mathematische deel [23] en een fysiologisch deel waarin het effect van insuline op de glucosewaarden zal worden gemodelleerd. Verder zal een insuline toedieningsalgoritme worden ontwikkeld. Verschillende uitkomstmaten zijn gebruikt om het glucosevoorspellingsmodel en het insuline toedieningsalgoritme te evalueren.

Resultaten: Het fysiologische model presteert optimaal bij een insuline effectiviteit van 0,01

mmol/L/min/IU. Hierbij is de MSE 0,53, de R2_{is 0,86 en de nauwkeurigheid in de gewenste}

bandbreedte is 85,7%. Verder bevonden 99,8% van de voorspellingen zich in regio A en B van een Clarke Error Grid. Het glucose en insuline toedieningsalgoritme voert de juiste acties uit in alle scenario's. De insulinebolussen berekend door het algoritme zijn hoger in vergelijking met de insulinebolussen die in de dataset voorkomen.

Conclusie: Het voorspellingsmodel heeft een hoge nauwkeurigheid, maar het includeren van

insuline als een variabele in het glucose voorspellingsmode verbetert de voorspellingen niet. Een geautomatiseerd insuline toedieningsalgoritme, die patient specifieke insuline doseringen geeft op basis van voorspelde glucosewaarden is ontwikkeld. Dit algoritme geeft het juiste advies in alle scenario's.

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Introduction

Hyperglycemia is common in critically ill patients and can increase morbidity and mortality. Glucose management is therefore a very important goal in the intensive care unit (ICU) [1]. It is difficult to determine the exact incidence of hyperglycemia, which may vary from 40-90%, depending on the threshold used to define a hyperglycemia [2-4]. Hormonal response of having stress, sepsis or trauma is often the cause of a hyperglycemia [5]. However, there are several other factors, such as diet, medication and insufficient insulin that can affect the glucose levels [6]. Insulin resistance is also an important factor and it has been observed in more than 80% of ICU patients [7]. Insulin resistance is a condition in which the cells are less sensitive to insulin then normally. Factors such as medication (corticosteroids), weight, body temperature and severity of the disease can have influence on insulin resistance [8].

Until the Leuven study in 2001 [9], not much attention has been paid to tight regulation of glucose in critically ill patients. The Leuven study made it clear that a strict regulation of glucose results in a reduced morbidity (reduction of septicemia by 46%), reduced mortality (reduction from 8.0% to 4.6%) and a decreased length of stay on the ICU [9]. Several other studies have addressed this question as well with different results [10-13]. The greatest disadvantage of tight glucose management is the increased risk of a hypoglycemia as a result of the intensive insulin therapy [11]. Prolonged and severe hypoglycemia can cause neurological damage, and in some cases, hypoglycemia can even lead to mortality [14]. Overall glucose levels should be kept within a defined range, but the exact upper and lower limit remains to be determined. ICU’s put a lot of effort into keeping the blood glucose values within the desired ranges. In the ICU in OLVG in Amsterdam the desired glucose levels are between 6 mmol/L and 9 mmol/L [15].

Currently nurses manually measure the glucose levels. The frequency of measurement varies between four times a day to once every hour, depending on the glucose values. Based on the results of the measurements the insulin or glucose is manually administered. Manual measurements by nurses have several disadvantages. Firstly, it does not provide insight into the trend of the glucose values. As a result, glucose fluctuations, but also hypo- and hyperglycemic events, can be missed. This is not desirable since high glycemic variability is associated with increased mortality [16]. Furthermore, manual measurements and the manual adjustments of the insulin pump are time consuming while nurses are already struggling with a high workload [17]. To improve overall glucose control, ICU care givers could be empowered with a closed loop glucose control system. This system continuously measures the glucose levels and guides the insulin and glucose delivery automatically based on predicted glucose levels. Such a system will consist of:

1. Continuous Glucose Monitor (CGM) 2. Glucose prediction model

3. Prediction model-based insulin delivery algorithm 4. Automated syringe pump for insulin and glucose delivery

A CGM system measures the blood glucose continuously or highly frequent, depending on the device. CGM is a technology that provides insight into glycemic fluctuations [18]. Gaining insight in these glucose fluctuations is important to reduce the glucose variability. Because of the high frequency of measuring when using a CGM, it is possible to develop glucose prediction models. To realize tight glucose regulation, glucose prediction could be useful.

Several glucose prediction algorithms have been described in literature [19-22]. These algorithms did not only use the historical glucose data for the prediction but also the effect of insulin has been used as a variable. However, those glucose prediction algorithms have often been developed for diabetes type 1 patients and not for ICU patients. Most of these prediction models require a variety of parameters, such as physical activity, insulin administration and carbohydrates intake.

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These algorithms cannot be used for ICU patients, because these patients differ from diabetic patients. Insulin resistance occurs often in critically ill patients, which is something that does not apply to diabetes type 1 patients. During a previous study, a glucose prediction models has been developed for ICU patients [23]. The model only used the historical glucose data for the glucose predictions. Several studies have shown that including insulin administration in a prediction model for diabetes type 1 patients increases the accuracy significantly [19,22]. The pharmacokinetic properties for insulin are described extensively in literature for subcutaneous administration [24]. However, insulin is administered intravenously in the ICU. The kinetic properties for intravenous administration differ from the subcutaneous administration [24]. The third part of a closed loop glucose control system is an algorithm that will guide the insulin and glucose delivery automatically. This algorithm will calculate and deliver the exact dose of insulin as needed automatically.

Objective

The objective of this research is to develop a glucose prediction model for ICU patients which includes insulin as a variable. The kinetic properties for intravenous administration of insulin will be studied. The prediction model will predict the glucose level in the blood based on results of the GCM and insulin administration. Furthermore, an insulin delivery algorithm will be developed to guide the insulin delivery. Eventually, the aim is to create a closed loop system for glucose control in critically ill patients. To achieve the desired goals, several research questions will be answered during this scientific research project:

1. What is the effect of insulin on blood glucose levels?

2. What is the difference in accuracy between the prediction model with and without insulin administration included?

3. Is it possible to develop an insulin-delivery algorithm which will use glucose predictions to act on?

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Preliminaries

This chapter provides background information on the physiology of hyperglycemia and some background information on CGM will be given. In addition, the statistical methods will be explained that were used during this study.

Glucose management

Hyperglycemia is a condition in which the blood glucose level is too high. A lack of insulin or the reduced effectiveness of the insulin causes the glucose to accumulate in the blood. Hormonal response of having stress, sepsis or a trauma can also cause a hyperglycemia [5]. The body is incapable of converting glucose into glycogen and as a result the excess glucose in the blood cannot be removed. This causes the liver to release even more glucose, which result in an increasing blood glucose level [25].

The reduced insulin effectiveness in ICU patients is a result of physiological stress. Hormones, such as cortisol, glucagon, catecholamines and growth hormone and acute-phase proteins are released to control and prevent further damage. These are all counter-regulatory to insulin and result in a higher insulin resistance [26]. Hyperglycemia can increase risks of infections, acute kidney injury, atrial fibrillation, low cardiac output syndrome, cerebrovascular accidents and cognitive impairment [26]. Additionally, prolonged hyperglycemia can result in ketoacidosis, which could be life threatening [27]. It is difficult to determine the exact incidence of hyperglycemia in ICU patients. This is because hyperglycemia can be defined using different thresholds. The American Diabetes Association (ADA) defines a hyperglycemia if the blood glucose level is above 11.1 mmol/L [3], while the NICE-SUGAR study proposes a threshold of 10 mmol/L [13].

A great deal of effort is put into managing the glucose levels by ICU’s. There are two types of insulin administration, basal insulin and bolus insulin are used to control the blood glucose level. Basal insulin regulates the glucose levels throughout the day to keep the glucose level stable [9]. This mimics the situation in healthy people in which the pancreas also constantly makes and releases a small amount of insulin into the blood to manage the regular release of stored glucose. An insulin bolus is administered when the blood glucose value is too high [11].

Two major studies regarding tight glucose management in the ICU have been conducted that have shown conflicting results. The Leuven study [9] made it clear that a strict regulation of glucose results in a reduced morbidity (reduction of septicemia by 46%), reduced mortality (reduction from 8.0% to 4.6%), decreased length of stay on the intensive care, decreased need for antibiotics, fewer blood transfusions and reduced organic failure. The NICE-SUGAR [13] study showed that the 90-day mortality was increased from 24.9% to 27.5%. Furthermore, they did not find a reduction in the frequency of organ failure, the length of ICU stay, and the time patients were on mechanical ventilation or renal replacement therapy. The greatest disadvantage of tight glucose management is the increased risk of a hypoglycemia because of the intensive insulin therapy [13]. Prolonged and severe hypoglycemia can cause neurological damage, and in some cases, hypoglycemia can even lead to mortality [12]. A meta-analysis, including the NICE-SUGAR data, found a 6-fold increase in hypoglycemia among patients treated with intensive insulin therapy to achieve tight glucose management [28].

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Continuous glucose monitoring

A CGM measures the blood glucose continuously or highly frequent, depending on which CGM system is used. There are different types of CGM’s. Firstly, CGM systems differ in terms of the body fluid used for the measurements. Overall four types of fluid are used for the measurements. This can be the plasma, whole blood, dialysate or the interstitial fluid [29]. Measuring in these body fluids can have several disadvantages. Glucose levels are higher in the plasma then in whole blood [30]. Glucose levels in dialysate are lower compared to the surrounding fluids from which the dialysate is created [31].When measuring the glucose in the interstitial fluid a delay occurs, this is the time it takes for glucose to move from the blood to the interstitial fluid [32] .

There are also various measurement methods. The glucose values can be measured based on an enzymatic reaction. When there is more glucose, more hydrogen peroxide will be released, which can be measured [33]. Fluorescence is also a method to measure the glucose levels. This method depends on the emission of light by a substance after absorbing light. When the glucose level increases, the fluorescent signal increases, which is detected [34]. Spectroscopy can also be used as a measuring method. Spectroscopy technique is based on the interaction between the molecules and electromagnetic radiation in term of absorption or scattering [35]. A disadvantage of any biosensor is the buildup of body fluid deposits on the sensor surfaces, therefore repeated calibrations and eventually sensor replacements are needed [29].

The number of studies assessing accuracy of CGM devices for ICU patients is still limited [29]. Most studies were small regarding the number of patients. In addition, accuracy was sometimes only tested in specific patients such as patients in the ICU after surgery. In general, the point accuracy of CGM’s is low, but the trend accuracy is high [29].

Mathematical model

In a previous study, a mathematical model was developed for predicting the glucose values of patients in the ICU of the OLVG [23]. The mathematical model uses the first and second derivative to predict the glucose values. With a first derivative, the degree of change in the glucose values is determined. The second derivative is used to calculate the change of the first derivative. The second derivative thus determines wheter the change in the glucose values is flattening or still increasing. By taking the average of the first derivative (dG/dT ) and the average of the second derivative (d2_{G/dT) and adding those two values to the measured value glucose value (G}_x_{), the}

mathematical model predicts the glucose value (BGmat). With an averaging time of 90 minutes the

best prediction result, with a mean squared error of 0.53 and a coefficient of determination (R2₎

of 0.86, was achieved with a prediction window of 30 minutes. Equation 1 is used to predict the glucose values. The definitions of the terms in the equation are as follows:

𝑩𝑮𝒎𝒂𝒕 (𝑻𝒙+𝟑𝟎) = 𝑮𝒙+ 𝟑𝟎 ∗ [𝒎𝒆𝒂𝒏 ( 𝒅𝑮

𝒅𝑻 )_𝒙] + 𝟑𝟎 ∗ [𝒎𝒆𝒂𝒏 ( 𝒅𝟐𝑮

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Statistics

Mean squared error

The extent to which the predicted glucose values (̂ŷ) deviate from the reference values (y) can be calculated with the MSE.The closer the MSE approaches zero, the less the predicted values deviate from the reference values. The MSE is calculated by Equation 2.

𝑴𝑺𝑬 =

𝟏 𝒏

∑(𝒚 − ŷ)

𝟐 𝒏 𝒊=𝟏

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Coefficient of determination

R2_{is the proportion of the variance in the dependent variable that is predictable from the} independent variable. An R2_{between 0 and 1 indicates the extent to which the dependent variable}

is predictable. An R2_{of 0.10 means that 10 percent of the variance in is predictable, an R}2_{of 0.20}

means that 20 percent is predictable; and so on.

Clarke Error Gird analysis

The Clarke Error Grid Analysis (CEGA) has been developed in 1987 to determine the clinical accuracy of blood glucose meters [36]. Since then, CEGA has been one of the gold standards for determining the clinical accuracy of blood glucose meters. An CEGA can also be used for prediction models. In an CEGA the predicted values are compared with the reference values and are classified in five different regions in a scatter plot, see figure 1.

According to ISO criteria, at least 95% of the values should be in region A and no more than 5% of the values in region B.

• Region A: values within 20% of the observed values.

• Region B: values outside of 20% but without inappropriate treatment.

• Region C: values lead to unnecessary treatment. • Region D: values indicating a potentially dangerous failure to detect hypoglycemia or hyperglycemia.

• Region E: values confuse treatment of

hypoglycemia for hyperglycemia and vice versa.

Figure 1: different regions in the Clarke Error Grid Analysis

Accuracy

Sensitivity measures the proportion of actual positives (tp) that are correctly identified as positive. The sensitivity can be calculated with equation 3, in which false negative is abbreviated

as fn: 𝒔𝒆𝒏𝒔𝒊𝒕𝒊𝒗𝒊𝒕𝒚 = 𝒕𝒑

𝒕𝒑+𝒇𝒏 (𝟑)

Specificity measures the proportion of actual negatives (tn) that are correctly identified as negatives. The specificity can be calculated with equation 4: in which false positive is abbreviated

as fp: 𝒔𝒑𝒆𝒄𝒊𝒇𝒊𝒄𝒊𝒕𝒚 = 𝒕𝒏

𝒕𝒏+𝒇𝒑 (𝟒)

The sensitivity and specificity will be calculated to determine the accuracy, see equation 5. 𝒂𝒄𝒄𝒖𝒓𝒂𝒄𝒚 = 𝒕𝒏 + 𝒕𝒑

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Methods and Materials

Data

The dataset used in this study has been collected in a previous study [37]. For the data in this study, the Freestyle Navigator II of Abbott Laboratories has been used to perform the continuous glucose measurements. The sensor measures glucose at 1- and 10-minutes intervals and measures the glucose levels in the interstitial fluid. Calibration of the sensor is needed at 10, 12, 24 and 72 hours after insertion.

Physiological prediction model

The physiological model will add the effect of insulin on glucose levels as a variable to the mathematical model [23]. Modelling the effect of insulin on glucose will be based on pharmacokinetics properties of the insulin type NovoRapid, which is being used in the ICU. Table 1 shows the pharmacokinetics properties of intravenously administered insulin. These parameters will be used in the physiological model.

Table 1: pharmacokinetic properties of insulin (Novo Rapid)

Insulin effectiveness is a patient-specific value. Therefore, an average insulin effectiveness must be obtained in a different way. To determine insulin effectiveness, this parameter will be adjusted in the model until the model performs optimally. The insulin effectiveness in the model will be incrementally increased with steps of 0.01 mmol/L per IU per minute, starting with an insulin effectiveness of 0.01 mmol/L /min/IU.

Model for determining insulin effectiveness

To properly predict the glucose values, the calculations in the prediction model should be made with the correct insulin concentration. Equation 6 is used to determine the decrease (cdecr (t)) in the insulin concentration over time.

𝒄𝒅𝒆𝒄𝒓(𝒕) = 𝒄𝒐𝒏𝒄(𝒕) ∗ 𝟎. 𝟓𝒕/𝒕𝟏/𝟐(6)

When the insulin concentration is known at a certain time, it is possible to determine the effect of the insulin on the glucose values. Equation 7 shows how the decrease of the glucose (gdecr (t)) value due to the administered insulin is calculated. In this equation (t) is the time in minutes for which the insulin effect (effect) must be calculated. The effect in this case is a decrease in glucose mmol/L/min/IU.

𝒈𝒅𝒆𝒄𝒓(𝒕) = 𝒆𝒇𝒇𝒆𝒄𝒕 ∗ (𝒄𝒐𝒏𝒄(𝒕) − 𝒄𝒅𝒆𝒄𝒓(𝒕)) (7)

In order to predict the glucose values (pval (t)) at a prediction time of 30 minutes, the calculated glucose decreases for half an hour will be added together. See equation 8.

𝒑𝒗𝒂𝒍(𝒕) = 𝒈𝒗𝒂𝒍(𝒕) − ∑ 𝒈𝒅𝒆𝒄𝒓

𝟑𝟎

𝒙=𝟎

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Kinetic properties Explanation Value

Onset of action Time in minutes before insulin starts to have effect 0 minutes

Half-life Time in minutes needed to reduce the doses by 50% 5 minutes

Insulin effectiveness

Decrease of blood glucose in mmol/L per minute per Insulin Unit (IU)

Patient-specific Start value= 0.01

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Insulin delivery algorithm

An algorithm for guiding the insulin delivery will be developed. The algorithm will adjust the insulin delivery based on the glucose values predicted with the mathematical prediction model. The algorithm determines the pump value and calculates the dose for the insulin boluses. It has been decided that a bolus should not be higher than 10 IU to prevent a hypoglycemia. The algorithm divides glucose values into different ranges. A different insulin administration policy will be implemented for each range, see appendix I. These different ranges will be the same ranges as they are now in the protocol that is used in the ICU [15], see table 2.

Range Glucose Values

1 < 3.5 mmol/L

2 3.5 mmol/L < & < 4.6 mmol/L

3 4.6 mmol/L < & < 7.0 mmol/L

4 7.0 mmol/L < & < 8.5 mmol/L

5 8.5 mmol/L < & < 12.0 mmol/L

6 12.0 mmol/L < Table 2: different glucose ranges

The algorithm will evaluate every twenty minutes whether a change in the insulin administration should take place.The rate of change is determined by looking at the change in the predicted glucose values between the evaluation moments. The classification for degree of change can be seen in table 3.

Change in percentages Classification

≤ 5% Slow

> 5% and < 10% Average

≥ 10% Fast

Table 3: classification for degree of change

Figure 2 shows how the insulin-delivery algorithm works. First, the algorithm determines the glucose range in which the predicted value is. The value is then compared to the previous predicted value to determine the rate of change of the glucose value. Based on these two conditions an insulin administration policy will be executed. After the evaluation time of twenty minutes, the model will predict the glucose value 30 minutes ahead and evaluates whether a change in the insulin administration is needed.

Figure 2: flowchart of the insulin delivery algorithm without an insulin bolus

Care givers could decide to administer insulin manually between the evaluations. The time (the number of minutes from the previous evaluation) and the height of the bolus will be used to calculate the effect of the bolus. The algorithm will then include the effect of this extra bolus in the evaluation.

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Insulin boluses

A glucose value of 8 mmol/L will be the target value after an insulin bolus is administered. The desired glucose decrease is the difference between the current glucose value and 8 mmol/L. The effect of insulin is known. The algorithm will solve equation 9 and thereby calculate the required bolus. The first bolus is based on the insulin effectiveness obtained with the physiological model.

∑ 𝒆𝒇𝒇𝒆𝒄𝒕 ∗ (𝒃𝒐𝒍𝒖𝒔 ∗ 𝟎. 𝟓𝒕/𝟓 ₎ 𝟐𝟎

𝒊=𝟎

− 𝒅𝒆𝒔𝒊𝒓𝒆𝒅 𝒅𝒆𝒄𝒓𝒆𝒂𝒔𝒆 = 𝟎 (9)

Varying insulin effectiveness

Insulin effectiveness is a patient-specific value because insulin resistance can vary per patient. To solve this problem, the algorithm contains a function that evaluates whether a patient has a different insulin effectiveness. The difference between the expected decrease in glucose value and the actual decrease in glucose value will be determined. See equation 10.

𝒓𝒆𝒂𝒍𝒊𝒔𝒆𝒅 𝒅𝒆𝒄𝒓𝒆𝒂𝒔𝒆

𝒆𝒙𝒑𝒆𝒄𝒕𝒆𝒅 𝒅𝒆𝒄𝒓𝒆𝒂𝒔𝒆− 𝟏 ∗ 𝟏𝟎𝟎 = 𝒅𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏 (10)

The algorithm will then correct the insulin boluses and adjustments to the pump value for this deviation. See figure 3.

Figure 3: Flowchart of the function to correct for varying insulin effectiveness

Statistics

To evaluate the physiological model several outcomes will be used. The mean squared error (MSE) and coefficient of determination (R2_{) will be calculated. The clinical accuracy will be calculated}

with a Clarke Error Grid analysis. The reference values for all these outcomes will be the measured glucose values with the CGM. For more information about the outcome measures used, see the statistics section in the preliminaries. All analyses were performed using Python 3.

In addition, the accuracy for 3 different ranges will be examined, see table 4 for the ranges. These ranges have been taken from the previous study [23] to be able to compare the physiological model with the mathematical model.

Range Glucose values

Hypoglycemia < 3.5 mmol/L

Desired Range 6 mmol/L ≤ ≤ 9 mmol/L Hyperglycemia > 15 mmol/L

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The glucose predictions will be analyzed to assess whether the prediction is a false positive (FP), false negative (FN), true positive (TP) or true negative (TN). See table 5.

Glucose value out of range Glucose value within range

TP FP

Model

Positive ref. value < 6 mmol/L & predicted value< 6 mmol/L OR

ref. value > 9 mmol/L & predicted value > 9 mmol/L

6 mmol/L ≤ ref. value ≤ 9 mmol/L & 6 mmol/L < predicted value OR predicted value > 9 mmol/L

FN TN

Model Negative

ref. value < 6 mmol/L OR ref. value > 9 mmol/L &

6 mmol/L ≤ predicted value ≤ 9 mmol/L

6 mmol/L ≤ ref. value ≤ 9 mmol/L & 6 mmol/L ≤ predicted value ≤ 9 mmol/L Table 5: Classification of TP, FP, FN and TN

Verification of the insulin-delivery algorithm

A dummy dataset has been created to verify whether the algorithm recommend the correct actions. Analysis of six scenarios with corresponding actions are described in table 6. This dataset includes glucose values from all ranges listed in table 2. Furthermore, all different rates of change as mentioned in table 3 are also present in the data set. The dataset will also contain scenario’s in which the actual decrease deviates from the expected decrease. The algorithm should respond correctly in every scenario. Verification of the algorithm will be performed by assessing whether the correct actions have been advised by the algorithm in all scenarios. The algorithm must provide the correct advice in 100% of the cases.

Scenario Corresponding action

1 Glucose value < 3.5 mmol/L glucose bolus + pump value to zero

2 Glucose value > 12 mmol/L insulin bolus + increase pump value

3 Lower insulin effectiveness adjust boluses and pump values for deviation

4 Higher insulin effectiveness adjust boluses and pump values for deviation

5 Glucose value remains outside of

the desired range despite of administered insulin

increase pump value after every evaluation

6 Glucose value stays unchanged in

the desired range no changes to pump value Table 6: scenarios and corresponding actions

Evaluation of the advised insulin boluses

To determine how the algorithm performs regarding insulin boluses all the present insulin boluses in the dataset will be evaluated. The absolute difference between the given bolus and the bolus advised by the algorithm will be calculated.

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Results

Dataset

The dataset contains 98 ICU patients with a total of 125353 glucose measurement. The data has been divided into a validation and training set with almost similar patient characteristics. The dataset contains a total of 57 insulin boluses. Table 7 provides an overview of how the training and validation groups have been divided.

Table 7: an overview of the patient characteristics

Validation of physiological prediction model

An insulin effectiveness of 0.01 resulted in the lowest MSE. In table 8, different outcome measures are listed for the mathematical and physiological model.

Outcome measure Mathematical

prediction model Physiological prediction model MSE 0.54 0.53 Desired range 86.06% 85.72% Hypoglycemia 91.42% 89.12% Hyperglycemia 47.86% 47.56% R2 _0.86 _0.86

Table 8: Overview of outcome measures per model

Clarke Error Grid Analysis

In the mathematical model, 94.49% and 5.29% of the predictions were in respectively region A and B. This was 94.47% and 5.30% of the glucose predictions for the physiological model. Table 9 gives an overview of the distribution among the different regions. Figure 5 is the scatterplot of the CEGA with the glucose values in the five different regions.

Region Mathematical model

n=59323 Physiological Model n=59323 A 94.49% 94.47% B 5.29% 5.30% C 0.02% 0.02% D 0.19% 0.19% E 0.005% 0.005%

Table 9: overview of occurrence in each region

Variable Training set

(n=49) Validation set (n=49) Total Cohort

Age (years) 69.35 ± 10.98 68.33 ± 12.17 68.89 ± 11.60 Sex, male 23 (46.9%) 32 (65.3%) 55 (56.1%) History of diabetes 10 (20.4%) 10 (20.4%) 20 (20.4%) BMI (kg/m2) 27.44 ± 5.26 27.77 ± 4.44 27.6 ± 4.87 APACHE IV (%) 40.77 ± 30.17 38.52 ± 28.14 39.47 ± 29.34 Died at ICU 11 (22.45%) 9 (18.37%) 20 (20.41%)

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Mathematical model Physiological Model

Figure 4: Clare Error Grid Analysis

Figure 5 shows the total insulin delivery algorithm with the function to evaluate the insulin effectiveness and the function to calculate and include the effect of a manual insulin bolus.

Figure 5: flowchart of the total insulin delivery algorithm

Verification of insulin delivery algorithm

All scenarios with the corresponding action are included in table 10. The algorithm advises for all mentioned scenarios the correct action.

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Scenario Action performed by the algorithm

1 Glucose value < 3.5 mmol/L

(Hypoglycemia)

2 Glucose value > 12 mmol/L

3 Lower insulin effectiveness

4 Higher insulin effectiveness

5 Glucose value remains outside of the desired range despite

of administered insulin

6 Glucose value stays within the desired range

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Validation of insulin bolus dosages

The boluses that have been administered in the patient data are compared to the boluses that the algorithm calculates. Table 11 shows typical administered insulin boluses, the glucose value when the insulin is administered and the glucose value half an hour after administration of the insulin. For a total list of boluses see appendix II. In all cases the insulin boluses calculated by the algorithm have a higher dose.

…………. Table 11: administered insulin boluses versus the calculated bolus by the algorithm

Patient Glucose Value (mmol/L) t=0 Bolus administered (IU) Glucose Value (mmol/L) t=30 Algorithm bolus(IU) Difference in bolus (IU) 6 10.7 9 15.4 11.5 2.5 11 10 7 9.9 8.5 1.5 43 10 4 10.1 8.5 4.5 58 11.9 8 12.1 16.7 8.7 59 11.2 16.1 4 7 10.7 15.2 13.7 34.6 9.7 27.6 80 12.3 7 11.9 18.4 11.4 86 12.6 12.1 13.4 7 8 7 12.3 11.8 12.7 19.6 17.5 23.1 12.6 9.5 16.1

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Discussion

Physiological model

The physiological prediction model achieved a high accuracy in which 94.5% of the predicted values were in region A and 5% of the values were in region B of the CEG. This nearly meets the ISO guideline that 95% of the values must be in region A and no more than 5% of the values can be in region B. The addition of insulin as a variable did not improve the prediction accuracy of the physiological prediction model compared to the mathematical model [23] which had an MSE of 0.54 and an R2 _{of 0.86.}

There are several studies that have developed a prediction model for ICU patients that includes insulin as a variable [38,39]. These studies did not describe the independent effect of insulin on the prediction accuracy. Therefore, it is not possible to determine whether the lack of improvement in the prediction model would also be visible in other studies. Prediction models developed for diabetes patients did show improvement of the prediction accuracy by including insulin as a variable [19-22]. This can be explained by the fact that in diabetic patients, insulin administration goes via the subcutaneous route [19,21]. This causes a delay in the effectiveness of the insulin. On the ICU insulin is administered intravenously. This means that insulin has an immediate effect on the glucose concentrations in the blood. This change in glucose will therefore also affect the 1st_{and 2}nd_{derivative in the mathematical model. The 1}st_{derivative is the degree of}

change in the glucose values, since the insulin has immediate effect on the glucose values, the 1st

derivative will change directly. This means that the decrease of the glucose value as a result of insulin administration is already included in the predictions of the mathematical model. Including the effect of insulin on the glucose values in the physiological mode would mean that the effect of insulin is included twice. That could also the explanation that the best results were achieved with a very low insulin effectiveness of 0.01 mmol/L/min/IU.

In addition, insulin boluses are much more common in diabetes patients than in ICU patients. Diabetes patients administer an insulin bolus with every meal. The dataset however, contains only a limited amount of 57 boluses. As described earlier in the preliminaries, insulin boluses are administered to lower glucose levels. The physiological model can therefore only calculate the effect of the insulin in 57 cases. As a result, it is not possible to calculate a value for the effectiveness of insulin.

Another possible explanation for a lack of improvement in the prediction model may be that there is no standard value for insulin effectiveness in all patients. Nonetheless insulin effectiveness has been included as a standard value in the model because it is not possible to include all variables that influence insulin effectiveness in the model. The insulin effectiveness varies per patient. There are patients in which the physiological model achieves a lower MSE for a certain insulin effectiveness while in other patients the result is an increase in the MSE. Insulin effectiveness is partly determined by the insulin resistance. The higher the insulin resistance is, the lower the insulin effectiveness becomes. The degree of insulin resistance depends on many factors. There is a difference in insulin resistance between surgical and medical patients. Surgical patients often have a temporarily increased insulin resistance after surgery [40]. Furthermore, patients which are already known with type 2 diabetes have an increased insulin resistance. The use of corticosteroids also increases insulin resistance [41]. The factors that influence insulin resistance are known. However, it is not known to what extent each of these factors influence insulin resistance. Therefore, it is not possible to include the effect of insulin resistance in the glucose predictions. This makes it difficult to determine the correct insulin effectiveness for every patient.

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The algorithm advises for all mentioned scenarios the correct action. The insulin boluses calculated by the algorithm are higher than the insulin boluses administered in the dataset. The algorithm evaluates whether an insulin bolus achieves the desired decrease and adjust for an increased or reduced insulin effectiveness.

Several researchers in the field of diabetes have examined the possibility of automation of insulin delivery [42-46]. In addition, there have also been studies into automated insulin delivery algorithms for intensive care patients [47,48]. These studies indicate that patients have a better average glucose value and that these patients achieve normoglycemia earlier. However, there are some differences. Firstly, these algorithms were not based on predicted values, but with measured values which often are not continuously measured. Furthermore, the developed insulin delivery algorithm during this study takes the varying insulin effectiveness among different patients into account. As a result, the algorithm developed during this study provides a personalized insulin delivery policy. This solves the problem of varying insulin effectiveness between patients.

It has been decided that a bolus should not be higher than 10 IU. This is done to prevent the risk of a hypoglycemia, which could be life threatening [12]. In all the cases the model recommends higher insulin boluses compared to the insulin boluses that have been administered to the patients in the dataset. These recommended insulin boluses by the algorithm are in most cases above 10 IU. All the boluses that have been administered in the dataset seem to be too low because the glucose values did not get into the desired range. Given the limited effect of the insulin boluses delivered in practice it might be better to raise the insulin bolus maximum. However, this could increase the risk of a hypoglycemia, so the increase in the maximum bolus should only be done if it appears in practice that boluses of a maximum of 10 IU are indeed not high enough. The risk of a hypoglycemia was also the reason to set the target value at 8 mmol/L after an insulin bolus. The target value is at the top of the desired range (6-9 mmol/L) which means that the risk of a hypoglycemia is limited if a bolus is too high.

Because of the shorter evaluation time, the developed insulin delivery algorithm evaluates the glucose values far more often than ICU care givers currently do in the ICU. Glucose fluctuations will be observed in time, making it possible to respond quicker to glucose fluctuations. The algorithm acts on predicted glucose values. This makes it even possible to act before an event, such as a hypoglycemia or hyperglycemia occurs. The expectation is that this will reduce the risk of a hypoglycemia or hyperglycemia and therefore will also reduce the need of insulin and glucose boluses. The algorithm has been set to evaluate the predicted glucose values every twenty minutes. It could have been better if the model could already evaluate after 15 minutes. The insulin concentration is reduced to such an extent after fifteen minutes already that the remaining concentration insulin will not have any significant effect on the glucose values. More time between evaluations could cause a delay in observing glucose fluctuations. However, the glucose measurements in the dataset had often ten-minute intervals between measurements making it impossible to have an evaluation time of fifteen minutes. An evaluation time of 10 minutes was possible with this dataset but is not desirable because insulin still has effect on the glucose levels after 10 minutes.

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Lastly it was not possible to evaluate the insulin delivery algorithm with patient data. The glucose values in the data set are static. Therefore, these values will not respond to any recommended insulin doses. By simulating glucose values and the effect of the insulin on the glucose values and creating a dummy dataset it became possible to verify the algorithm. However, evaluation of the algorithm is still not possible with this data. Therefore, it is still unclear how the algorithm will perform in patients.

Future research

More research needs to be done into insulin resistance. The various factors that influence this must be analyzed. The effect of these various factors on insulin resistance should be quantified. Doing this will most likely improve the predictions of the effect of insulin. This would make it possible to calculate the needed insulin bolus more accurately. This is important because the mathematical model has a warm-up time of 90 minutes. With a 30-minute prediction window, this means that glucose predictions cannot be made during the first two hours of a patient admission. If available, simulation models for glucose regulation on the ICU could be used to evaluate the insulin and glucose delivery algorithm before testing with real patients. Another way to evaluate the model could be carried out if data is available with more insulin boluses. The evaluation can be performed by looking at the effect of an action advised by the algorithm. The effect of such insulin administration must be sought in another patient in the dataset with similar patient characteristics. This patient must be comparable to the other patient in terms of patient characteristics such as age, gender, BMI, APACHE IV score and whether a patient has diabetes. Eventually the insulin delivery algorithm should be evaluated in the ICU. To compare the current situation with the developed insulin delivery algorithm the time spent within the desired range, the number of hypoglycemic events and hyperglycemic should be used as outcome measures.

Conclusion

The prediction model has a high accuracy but including insulin as a variable for glucose prediction does not improve the prediction accuracy. In addition, an automated insulin delivery algorithm, which gives patient-specific doses and is based on predicted glucose values has been developed and gives the correct advice in all the scenarios.

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Appendix I

Range Situation Administration policy

< 3.5 mmol/L 6 gram glucose bolus

Set insulin pump rate to IU/h

3.5 mmol/L < &

< 4.6 mmol/L

Increase ≤ 5% No change to the insulin pump rate

Increase > 5% and < 10% No change to the insulin pump rate

Increase ≥ 10% No change to the insulin pump rate

Decrease ≤ 5% Lower the insulin pump rate with the

percentage change in the glucose value Decrease > 5% and < 10% Lower the insulin pump rate with the

percentage change in the glucose value

Decrease ≥ 10% Set insulin pump rate to 0 IU/h

4.6 mmol/L < &

< 7.0 mmol/L

Increase ≤ 5% No change to the insulin pump rate

Increase > 5% Increase the insulin pump rate with the

Decrease ≤ 5% Lower the insulin pump rate with the

percentage change in the glucose value Decrease > 5% and < 10% Lower the insulin pump rate with the

Decrease ≥ 10% Set insulin pump rate to 0 IU/h

7.0 mmol/L < &

< 8.5 mmol/L

If insulin pump rate =0 Set insulin pump rate to 2 IU/h

Increase ≤ 5% Increase insulin pump rate with 20%

Increase > 5% Increase the insulin pump rate with the

percentage change in the glucose value Maximum of 4 IU/h

Decrease ≤ 5% Increase the insulin pump rate with 0.5

IU/h

Decrease > 5% and < 10% Set insulin pump rate to 0 IU/h

Decrease ≥ 10% Lower the insulin pump rate with the

8.5 mmol/L < &

< 12.0 mmol/L

If insulin pump rate =0 Set insulin pump rate to 2 IU/h

Increase ≤ 5% Increase insulin pump rate with 20%

Increase > 5% Increase the insulin pump rate with 2 IU/h

Administer insulin bolus

Decrease ≤ 5% No change to the insulin pump rate

Decrease > 5% Set insulin pump rate to 2 IU/h

12.0 mmol/L < If insulin pump rate =0 Set insulin pump rate to 2 IU/h

Increased Increase insulin pump rate with 2 IU/h

Decrease < 10% No change to the insulin pump rate

Decrease ≥ 10% Increase the insulin pump rate with 2 IU/h

Administer insulin bolus Table 1: all the different situations and the needed insulin administration policy

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Appendix II

Table 1: administered insulin boluses versus the calculated bolus by the algorithm

Patient Glucose Value (mmol/L) t=0 Bolus administered (IU) Glucose Value (mmol/L) t=30 Algorith m bolus(IU) Difference in bolus (IU) 6 10.7 9 15.4 11.5 2.5 11 10 7 9.9 8.5 1.5 43 10 4 10.1 8.5 4.5 23 9.2 10.6 10.6 9.5 6 6 6 6 9.1 10.1 10.9 8.6 5.1 11.1 11.1 6.4 -0.9 5.1 5.1 0.4 25 9.4 5 9.1 6 1 26 7.7 4 8 - - 29 6.4 9.7 11.1 15.8 15.3 11.9 13.6 7 6 5 12 9 4 7 7.2 8.6 11.2 15.6 13.1 11.9 12.9 - 7.2 13.3 33.3 31.2 16.7 23.9 - 1.2 8.3 21.3 22.2 12.7 58 11.9 8 12.1 16.7 8.7 59 11.2 16.1 4 7 10.7 15.2 13.7 34.6 9.7 27.6 72 12.1 7 12.7 17.5 10.5 74 10.6 11.9 6 7 9.6 10.7 11.1 16.7 5.1 9.7 80 12.3 7 11.9 18.4 11.4 83 10.7 6 11.3 11.5 5.5 86 12.6 12.1 13.4 7 8 7 12.3 11.8 12.7 19.6 17.5 23.1 12.6 9.5 16.1 87 9.8 5 14.8 7.6 2.6 88 10.2 11.2 11.4 7 7 14 11.1 10.9 10.3 9.4 13.7 14.5 2.4 6.7 0.5 89 13.3 7.1 9.6 10.1 8 10 3 3 13.8 6.3 10.2 10.1 22.6 - 6.8 9 14.6 - 3.8 6 92 11.3 8 11.6 14.8 6.8 98 13.9 12.2 12.8 18.6 17.3 8 7 9 10 9 13.2 11.5 15.4 19.9 16.7 25.2 18 20.5 45.3 37.2 17.2 11 11.5 35.3 28.2

Development of a glucose prediction model and insulin-delivery algorithm for critically ill patients.