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Comput Methods Programs Biomed. Author manuscript; available in PMC 2014 February 1.

Published in final edited form as:

Published online 2012 February 17. doi: 10.1016/j.cmpb.2011.12.016

PMCID: PMC3369012

NIHMSID: NIHMS358249

Colleen Hughes-Karvetski,^{a} Stephen D. Patek,^{a} Marc D. Breton,^{b} and Boris P. Kovatchev^{a,}^{b}

The publisher's final edited version of this article is available at Comput Methods Programs Biomed

See other articles in PMC that cite the published article.

Safety measures to prevent or mitigate hypoglycemia are an important component of open loop, closed loop, and advisory mode insulin therapy control settings in type 1 diabetes. In recent work, we introduce a method for the automatic, gradual attenuation of the insulin pump delivery rate when a risk of hypoglycemia is detected, a method that we refer to as *brakes*. In the methods presented here, we demonstrate the use of historical glucose measurement data to inform and enhance the ability of the brakes to prevent hypoglycemia in real-time. The updated *brakes* are based on a patient-specific, time-varying model that reflects the typical trajectory of glycemic fluctuations throughout the day. Historical heightened risk of hypoglycemia throughout the day prompts an increase in the aggressiveness of insulin attenuation as compared to the original *brakes* that are based on real-time data alone. Through the use of available real-time data supplemented with historical glucose information to assess hypoglycemic risk, we are able to better anticipate and prevent hypoglycemia.

Hypoglycemia has been identified as the limiting factor in the optimal management of type 1 and type 2 diabetes [1]. In healthy human subjects, insulin secretion decreases and glucagon and epinepherine (counterregulatory hormones) secretion increases so that hypoglycemia can be avoided. In type 1 diabetes (T1DM), where insulin secretion is nearly if not totally absent, insulin must be delivered exogenously to maintain normoglycemia. Hypoglycemia in diabetes is most commonly the result of the combination of overinsulinization or an increased sensitivity to insulin and a weakened or absent counter-regulatory response to low blood glucose (BG) levels that is characteristic of patients with type 1 diabetes. To further complicate the situation in type 1 diabetes, hypoglycemia-associated autonomic failure (HAAF) assumes that glucose counterregulation is further impaired given recent hypoglycemic events.

Recent advancements in T1DM treatment technology offer the opportunity to inform the insulin pump delivery rate with glucose measurement feedback from a continuous glucose monitor (CGM) that provides subcutaneous glucose concentration data every 5–10 minutes. The present work proposes a method for prevention of hypoglycemia through an algorithm that automatically attenuates the insulin pump delivery rate. The novelty of the algorithm is that it is informed not only with real-time glucose measurement *and* insulin delivery data, but with historical information that allows us to assess hypoglycemic risk attributed to routine events that affect glycemic fluctuation in a temporal and patient-specific way.

Models that provide information regarding the metabolic state of the patient serve as useful tools in the design of insulin delivery strategies for treatment of T1DM. For patients with T1DM, transient increases (e.g. dawn phenomenon) or decreases (e.g. exercise, see [2]) in insulin requirements are required to respond to the decrease or increase in sensitivity to insulin in an effort to maintain normoglycemia. Most metabolic models are not equipped to *anticipate* behavioral events or even some routine metabolic processes that may influence the glycemic state of the patient or the trajectory of the patient’s glycemic state in the near future. Arguably, even the most routine of daily behaviors, meals, challenge models to generate accurate estimates and predictions of the patient’s metabolic state even with certainty regarding timing and size of upcoming meals.

Insulin dosing control algorithms account for time-varying, patient-specific changes in insulin requirements using Bayesian parameter estimation methods that identify model parameters in real-time [3], by forecasting likely changes in insulin sensitivity parameters in the next 1–3 hours using an integration-based parameter identification method [4], or using run-to-run control methods to adjust the basal insulin infusion rate [5]. Other work incorporates dawn phenomenon or diurnal cycles in simulation in an effort to build and evaluate insulin dosing strategies that can account for routine metabolic events [6]. The insulin delivery strategies for patients with T1DM undergoing an exercise regimen include preventing accelerated insulin absorption, mimicking insulin secretion during exercise, supplying additional carbohydrates during exercise, and providing patients with diabetes education [7].

In [8], we introduce an algorithm referred to as *brakes* that works by automatically attenuating the insulin delivery rate when a risk of hypoglycemia is detected based on CGM measurement and insulin delivery information. The algorithm uses an estimate and projection of the BG concentration obtained through a metabolic state observer. The observer is used to formally assess *risk* of hypoglycemia based on a symmetrization of the BG scale as described in [9]. In the present work, we propose a method for employing historical CGM data to inform an assessment of hypoglycemic risk in real-time that can be employed to enhance the *brakes* algorithm. This work utilizes historical information to assess hypoglycemic risk allowing us to *anticipate* routine behavioral events, like exercise or consistent overdelivery of insulin, that affect glycemic fluctuation in a temporal and patient-specific way.

The *real-time* data sources that we consider are:

- blood glucose estimates obtained through the use of a continuous glucose monitor (CGM) and
- insulin delivery data obtained from the insulin pump

Using glucose sensor measurements and insulin information at time *t*, we assume a time-invariant, linear model of glucose insulin kinetics and employ a Kalman filtering methodology to estimate the BG concentration of the patient (state space model parameters are described in [8]). Real-time data to estimate the BG level of the patient is employed in conjunction with historical glucose measurement information to better predict impending hypoglycemia risk.

The collection and retrospective analysis of CGM data to modify open loop insulin therapy parameters is considered an important clinical application for CGM devices [10]. Various effective algorithms exist for predicting the BG concentration in real-time using CGM data, including methods based on statistical linear prediction [11], time series [12], and Kalman filter state estimation [13]. Predictive algorithms are typically used to generate hypoglycemia alarms [14], or to inform control algorithms (see [15] for a review). The novelty of the algorithm introduced here is that it employs *insulin information* as a critical component in estimating the BG level with the primary goal being to inform safety algorithms that take automatic action to prevent or mitigate the severity of a hypoglycemic event. In addition, the algorithm anticipates the potential for hypoglycemic risk based on patient’s routine behavioral events, targeting the historical impact that these events have on glycemic fluctuation.

Collected CGM data serves as our historical data source. The choice to collect historical output data (subcutaneous glucose measurements) rather than historical input data (meals, insulin, exercise) is motivated by the fact that output data allows us to focus on modeling a patient’s reaction to a behavior rather than modeling the behavior itself. Let us assume that we collect a set of CGM measurements every cycle-minutes *k* of the day for *k* = {1, 2, …, floor(1440/cycle)}, where the value of “cycle” is chosen to optimize the ability of the algorithm to detect routine fluctuations in the glucose profile that are not attributed to CGM noise. Our goal is to determine the glucose trajectory from stage *k* to stage (*k* + floor(30/cycle)) based on the historical CGM data. We define the time-varying linear model:

$${BG}_{\mathit{hist}}^{(k+\text{floor}(30/\text{cycle}))}={\beta}_{0,k}+{\beta}_{1,k}\xb7{X}^{k}+{\epsilon}_{k}$$

(1)

for *k* = {1, 2, …, floor(1440/cycle)}, where *X ^{k}* represents the CGM value at stage

Additionally, we incorporate as part of our historical model the probability of hypoglycemia based on collected data. Let *p _{hypo}*(

$${p}_{\mathit{hypo}}(k)=\frac{\mid \mathit{CGM}(k)<70\mid}{\mid \mathit{CGM}(k)\mid}$$

(2)

where *CGM*(*k*) represents a historical CGM measurement collected at stage *k* (in accordance with ADA guidelines, any sensor value less than 70 mg/dl is considered a hypoglycemia [16]). *p _{hypo}*(

Let *BG _{risk}*(

$$R({BG}_{\mathit{risk}}(t))=\{\begin{array}{ll}10{[{\gamma}_{\theta}(ln{({BG}_{\mathit{risk}}(t))}^{{\alpha}_{\theta}}-{\beta}_{\theta})]}^{2}\hfill & \text{if}\phantom{\rule{0.16667em}{0ex}}20<{BG}_{\mathit{risk}}(t)<\theta \phantom{\rule{0.16667em}{0ex}}\text{and}{\scriptstyle \frac{{\mathit{dBG}}_{\mathit{risk}}(t)}{dt}}<0\hfill \\ 100\hfill & \text{if}\phantom{\rule{0.16667em}{0ex}}{BG}_{\mathit{risk}}(t)\le 20\hfill \\ 0\hfill & \text{otherwise}\hfill \end{array}$$

(3)

where the assessment of hypoglycemic *risk* is based on the BG symmetrization function and the low blood glucose index (LBGI) introduced by Kovatchev and colleagues [9]. The input to the function is the estimate of BG (mg/dl), the output is a measure of hypoglycemic risk between 0 (no risk) and 100 (high risk). Parameters *γ _{θ}*,

$$\phi (R({BG}_{\mathit{risk}}(t)))=\frac{1}{1+\mathrm{\Gamma}\xb7R({BG}_{\mathit{risk}}(t))}$$

(4)

where Γ is a patient-specific aggressiveness parameter determined based on the patient’s biometric parameters total daily insulin (U) and correction factor (mg/dl/U). The modified insulin delivery rate, *J _{actual}*(

$${J}_{\mathit{actual}}=\phi (R({BG}_{\mathit{risk}}(t))){J}_{\mathit{command}}(t)$$

(5)

where *J _{command}*(

In its original implementation,
${BG}_{\mathit{risk}}(t)=\widehat{BG}(t+\tau \mid t)$ for *τ* = 15 minutes, where
$\widehat{BG}(t\mid t)$ is the BG estimate obtained from the state observer given CGM and insulin delivery information up to time *t* (as described in [8]) and
$\widehat{BG}(t+\tau \mid t)$ is the linear extrapolation obtained using the linear model of glucose-insulin kinetics with model inputs, insulin and CGM, held constant over the *τ*-minute prediction horizon. The brake activation threshold *θ* is fixed at 120 mg/dl, with parameters *γ _{θ}*,

In the proposed implementation, historical data informs the BG input so that *BG _{risk}*(

$${BG}_{\mathit{risk}}(t)={\beta}_{0,{k}^{\ast}}+{\beta}_{1,{k}^{\ast}}\xb7\widehat{BG}(t\mid t)$$

(6)

where
$\widehat{BG}(t\mid t)$ represents our best current estimate of the BG level based on CGM and insulin information and *k*^{*} such that (*k* · cycle – *t*) for *k* {1, 2, …, floor(1440/cycle)} is minimized and nonnegative. The value of *θ* in the historically-informed brakes implementation varies depending on *p _{hypo}* and is given by

$$\theta =\{\begin{array}{ll}140\hfill & \text{if}\phantom{\rule{0.16667em}{0ex}}{p}_{\mathit{hypo}}({k}^{\ast}+{\tau}_{\mathit{hypo}}^{\ast})>{p}_{\mathit{thresh}}\hfill \\ 120\hfill & \text{otherwise}\hfill \end{array}$$

(7)

where
${\tau}_{\mathit{hypo}}^{\ast}$ minutes and *p _{thresh}* are parameters tuned to optimize the use of historical hypoglycemia probability data. Parameters

In this section, we evaluate the use of historical CGM data to improve *brakes* performance through an in silico study. Our historical model is built with the value of “cycle” = 30 minutes; we choose this cycle length to optimize performance and avoid the disruption in the model parameters that may be caused by CGM noise. We assume that insulin pump delivery can be modified on a minute-by-minute basis. The value of
${\tau}_{\mathit{hypo}}^{\ast}$ is chosen through simulation tests to optimize brakes performance and is set to
${\tau}_{\mathit{hypo}}^{\ast}=60\phantom{\rule{0.16667em}{0ex}}\text{minutes}$.

We simulate and collect 30 days of historical CGM data, where the data assumes the original brakes algorithm employed in patient’s insulin pump delivery settings so that historical data reflects the impact of brake action *without* historical information being employed. Table 1 summarizes the random meal behavior assumptions with meal timing and size drawn from a normal distribution with mean (standard deviation) given in Table 1. Meals, particularly snacks, may be “skipped” if the realized amount of carbohydrates associated with the meal is 0 gCHO. We assume that insulin delivery follows a typical open loop therapy approach with boluses delivered at meal times computed based on the patient’s current carbohydrate ratio (gCHO/U) and correction factor (mg/dl/U) with a target BG of 130 mg/dl (with possibility for reverse correction), and the patient’s basal rate delivered otherwise.

In addition to this, we simulate an unmodeled random disturbance that is likely to result in hypoglycemia. This disturbance is an increase in the patient’s basal rate designed to represent an increase in the patient’s sensitivity to insulin, where the *intensity* of the disturbance is represented by the value of the multiplier on the nominal basal rate. The disturbance has probability
${\scriptstyle \frac{5}{7}}$ with random intensity
(2, .25) and random start time
(900, 15) minutes with disturbance length
(60, 15) minutes. The disturbance remains constant intensity over the disturbance length, after which the intensity decreases linearly for a period of 12 hours.

After collecting 30 days of simulated historical data for 100 in silico adult subjects, we employ the collected CGM data to construct the time-varying linear models for each adult subject as described by Equation 1. In the next step, we conduct a 1680 minute (28 hour) simulated scenario with the same random meal behavior and unmodeled random disturbance characteristics as described in Table 1, where we apply, for comparison, the brakes algorithm in its original and historically-informed implementations.

Each in silico subject has a unique set of pairs (*β*_{0,}* _{k}*,

For some patients, the increase in basal rate around 3pm does not have a dramatic effect on glycemic fluctuation. For other patients, results show that they are more sensitive to deviations from their nominal insulin sensitivity. It is the latter set of patients for which the historical model proves particularly beneficial. Figure 2 presents the 30 days of collected CGM history for a representative subject.

Figure 3 presents the historical model parameters that result for the same representative subject. We observe that the increase in the activation threshold (corresponding to nonzero *p _{hypo}*) occurs at around 1290 minutes after midnight (9:30pm) and continues through the end of the day and into the morning hours, during which the change in insulin sensitivity from our unmodeled disturbance results in additional hypoglycemic risk for this subject. A value of 60 minutes for
${\tau}_{\mathit{hypo}}^{\ast}$ allows us to anticipate the increased sensitivity by increasing the brake activation threshold

Figure 4 presents, in the top plot, 3 traces for the same representative subject: the blue trace is the patient’s CGM, the red trace is the output value obtained from the historically-informed linear model (the input to the historically-informed brakes), and the green trace represents the BG signal output from the Kalman filter state estimation and prediction procedure (the input to the original brakes algorithm). The corresponding attenuation factor (*R*(*BG _{risk}*(

Top: Blue: CGM, Green: *BG*_{risk} from Original Brakes Implementation, Red: *BG*_{risk} from Historically-Informed Model; Bottom: Corresponding Attenuation Factor (*R*(*BG*_{risk}(*t*)))

A comparison of the traces beginning at 900 minutes indicates that the red trace is able to better anticipate the increased sensitivity to insulin and the resulting lowering of BG than the Kalman filter output shown in green because the red trace is encoded with historical information, resulting in a more aggressive and earlier onset attenuation (seen through the comparison of the red and green traces in the bottom plot of Figure 4). As expected, both the red and green traces improve upon the ability of the CGM (shown in blue) to anticipate the lowering in BG and subsequent attenuation of the insulin delivery rate.

Table 3 presents a collection of the population results for no attenuation, original brakes implementation, and the new historically-informed brakes implementation. Because our goal in the attenuation of insulin delivery rate is prevention of hypoglycemia, our results focus on the ability of the historically-informed brakes algorithm to reduce the incidence of hypoglycemia, particularly when the patient’s risk of hypoglycemia is associated with a behavioral disturbance.

For a small increase in the mean BG and % time in the target range, we are able to reduce the incidence of hypoglycemia overall and in particular in our “critical” range from 900 to 1680 minutes by nearly 25% as compared with the original brakes implementation. There is a statistically significant increase in the *minimum* BG over all 100 in silico subjects when the historically informed brakes are employed (*p* < .05). Additionally, we reduce the total number of subjects experiencing hypoglycemia by 10 (from 28 to 18) when the historically-informed brakes are employed.

The incorporation of behavioral and metabolic historical information regarding patient behavior in an effort to improve glycemic control is becoming increasingly important as part of the development of personalized insulin delivery control algorithms and insulin delivery safety supervisory systems. In this work, we introduce a method for incorporating historical glucose measurement data into an assessment of a patient’s risk of hypoglycemia in real-time. This risk assessment informs the gradual and automatic attenuation of the insulin delivery rate designed to prevent or mitigate hypoglycemia. Results indicate that historical CGM data can improve the performance of the hypo-glycemia prevention method over the use of real-time data alone.

Authors would like to acknowledge the insight of Dr. Goufen Yan, University of Virginia Biostatistics Assistant Professor, and the comments provided by UVA Postdoctoral Fellow Sandip Kulkarni.

^{}This work was sponsored in part by the the NIH NIDDK Grant R01 DK 085623, the National Library of Medicine (Award Number T15LM009462), and National Science Foundation grant CNS-0931633. This content is solely the responsibility of the authors and does not necessarily represent the official views of the National Library of Medicine or the National Institutes of Health.

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