Ketone-Based Alert System for Insulin Pump Failures

Abstract

Background:

An increasing number of individuals with type 1 diabetes (T1D) manage glycemia with insulin pumps containing short-acting insulin. If insulin delivery is interrupted for even a few hours due to pump or infusion site malfunction, the resulting insulin deficiency can rapidly initiate ketogenesis and diabetic ketoacidosis (DKA).

Methods:

To detect an event of accidental cessation of insulin delivery, we propose the design of ketone-based alert system (K-AS). This system relies on an extended Kalman filter based on plasma 3-beta-hydroxybutyrate (BOHB) measurements to estimate the disturbance acting on the insulin infusion/injection input. The alert system is based on a novel physiological model capable of simulating the ketone body turnover in response to a change in plasma insulin levels. Simulated plasma BOHB levels were compared with plasma BOHB levels available in the literature. We evaluated the performance of the K-AS on 10 in silico subjects using the S2014 UVA/Padova simulator for two different scenarios.

Results:

The K-AS achieves an average detection time of 84 and 55.5 minutes in fasting and postprandial conditions, respectively, which compares favorably and improves against a detection time of 193 and 120 minutes, respectively, based on the current guidelines.

Conclusions:

The K-AS leverages the rapid rate of increase of plasma BOHB to achieve short detection time in order to prevent BOHB levels from rising to dangerous levels, without any false-positive alarms. Moreover, the proposed novel insulin-BOHB model will allow us to understand the efficacy of treatment without compromising patient safety.

Introduction

Rapid advances in the development and implementation of automated insulin delivery (AID) systems for people with type 1 diabetes (T1D) have yielded marked improvements in glycemic outcomes. ¹ Despite these advances, interruption of insulin delivery for even a few hours due to pump or infusion site malfunction can rapidly initiate ketogenesis, hyperketonemia, and diabetic ketoacidosis (DKA). An event of DKA can be dangerous or even fatal, thus continuing to be a challenge to the health and safety of those living with T1D.^2-5

A common cause of unintentionally missed insulin in patients with T1D using an AID system is pump or infusion site malfunction, ⁶ which can be caused by mechanical defects ⁷ or kinking, occlusion, and displacement.^8,9 This occurs frequently; for example, data from the T1D Exchange clinic registry demonstrated 17 device-related adverse events out of 124 subjects, including severe hyperglycemia with plasma 3-beta-hydroxybutyrate (BOHB) levels greater than 0.6 mmol/L or accompanied by symptoms of nausea, vomiting, or abdominal pain in only one year.^10,11 Eleven of these events were attributable to infusion set issues. After such unintentional cessation of insulin delivery, ketosis can occur rapidly; for example, experimental cessation of delivery of lispro insulin resulted in ketosis as early as 180 minutes later, with BOHB levels rising above 0.4 mmol/L and to greater than 0.6 mmol/L at 240 minutes. ¹²

A continuous ketone monitor (CKM) can be integrated into an AID system with the aim of detecting an event of accidental cessation of insulin delivery during continuous subcutaneous insulin infusion (CSII) therapy. We propose the design of alert system relying on an extended Kalman filter (EKF) that uses noisy plasma BOHB measurements to estimate the disturbance acting on the insulin injection input. The EKF was chosen as the observer because it supports a real-time model for making estimates of the current plasma ketone state. The EKF design is based on a novel pharmacokinetic (PK) model capable of simulating the ketone dynamics in response to a change in the insulin state.

Although several compartmental models have been developed to account for ketone body kinetics in healthy humans based on clinical data,^13,14 glucose and ketone body turnover in individuals with T1D remains open research questions.

Previous work to develop a simulation tool for a sample of people with diabetes involved creating a pediatric diabetes simulation incorporating both blood glucose (BG) and urine ketones as outputs. ¹⁵ We now use blood BOHB measurements as they change more rapidly in response to insulin deficiency and well as insulin repletion than urine ketone measurements, which detect acetoacetate that reflects an average of urine ketone concentration over hours since the last void. ¹⁶

Automatic methods for the detection of insulin pump malfunction have been reported in the literature using model-based fault detection techniques relying on BG values, meal announcements, and injected insulin information.^17-23 To the best of our knowledge, no prior work has used blood ketone measurements directly in a strategy to detect insulin pump malfunction.

The parameters of the proposed PK model are obtained and validated by leveraging previous published works in which the time course of ketosis development has been assessed using sequential measurements of plasma ketones after discontinuation of insulin pump therapy,^24,25 by computing root mean square error (RMSE) to determine the prediction errors.

The performance of the ketone-based alert system (K-AS) is demonstrated on 10 in silico subjects from the United States Food and Drug Administration-accepted University of Virginia (UVA)/Padova T1D Metabolic Simulator ²⁶ using two real-life use-case scenarios, simulating the condition when the insulin is delivered by the pump but not received by the user.

Methods

We propose a physiological-based model to describe the ketone-insulin system. The model connects the ketone concentration in the plasma $(K_p)$ with ketone fluxes, specifically: endogenous ketone production $(EKP(t)),$ ketone utilization $(U(t)),$ and ketone elimination $(E(t)).$ Ketone kinetics is described with a one-compartment linear model, as follows:

$$\stackrel{.}{K_p}(t)=EKP(t)-U(t)-E(t).$$ (1)

with $K_p(0)=K_{pb}$ , where $K_{pb}$ is the basal plasma ketone concentration.

Ketone production, utilization, and elimination terms are a sum of two components: a basal term, representing the constant rates when the plasma insulin concentration is at its basal value, and the alteration in the rates of change in the insulin signal.

The utilization rate $U(t)$ increases progressively, while the elimination rate E(t) is markedly decreased after acute withdrawal of insulin. The utilization rate is assumed to be linearly dependent on plasma ketones, while the elimination rate is depending on ketones in the plasma by a Michaelis-Menten relationship, as follows:

$$U(t)=U_b+k_u{K}_p(t)$$

$$E(t)=E_b-\frac{V_{max}{K}_p(t)}{k_m-K_p(t)}*\frac{1}{V_k}$$

with $U_b$ [mM/kg/min] and $E_b$ [mM/kg/min] representing the basal utilization and elimination rates, respectively; $k_u$ $[mi{n}^{-1}]$ is the utilization rate constant; $V_{max}$ $[mi{n}^{-1}]$ is the constant representing the maximum ketone elimination rate; $k_m$ [mM] is the half-saturation value; and $V_k$ [L/kg] is the volume of distribution of the plasma ketones.

Endogenous ketone production $EKP(t)$ is assumed to be linearly dependent on a delayed insulin signal and increases when plasma insulin decreases under the basal insulin delivery, as described below:

$$EKP(t)=EK{P}_b+k_p(I_b-X^L(t))V_i$$

$EK{P}_b$ [mM/kg/min] represents the basal production rates; $k_p$ $[mi{n}^{-1}]$ is the production rate constant; $I_b$ [mM/L] and $X^L$ [mM/L] are the basal and delayed insulin action in the liver; and $V_i$ [L/kg] is the volume of distribution of the plasma insulin. The model of the delayed insulin action proposed in Man et al ²⁶ was used where the delayed insulin action in the liver was defined as:

$$\stackrel{.}{X^L(t)}=k_i\left[X^L(t)-I^{\prime (t)}\right]$$

$$\stackrel{.}{I^{\prime }}(t)=k_i\left[I^{\prime }(t)-I_p(t)\right]$$ (2)

with $X^L(0)=I_b,$ and $I^{\prime }(0)=I_b;$ $I_p$ [mM/L] is the plasma insulin concentration; and $k_i[mi{n}^{-1}]$ is a rate parameter. ²⁶

The inflow to the insulin plasma compartment is determined by the injected insulin $(u(t)),$ which is absorbed from subcutaneous compartments as follows^27,28:

$$\stackrel{.}{I_{sc1}}(t)=-k_{a1}{I}_{sc1}(t)+k_d{I}_{sc1}(t)+u(t)+d(t)$$

$$\stackrel{.}{I_{sc2}}(t)=k_d{I}_{sc1}(t)-k_{a2}{I}_{sc2}(t)$$

$$\stackrel{.}{I_p}(t)=k_{a1}{I}_{sc1}(t)+k_{a2}{I}_{sc2}(t)-\frac{k_1\cdot I_p(t)}{k_2+I_p(t)}$$ (3)

where $I_{sc1}$ [pmol/kg] is the first SC compartment representing insulin in a non-monomeric state; $I_{sc2}$ [pmol/kg] represents insulin in the monomeric and active state; $k_d,$ $k_{a1},$ and $k_{a2}[mi{n}^{-1}]$ are the transfer rates between the compartments ²⁷ ; and $k_1[mi{n}^{-1}]$ and $k_2[\mathrm{pmol}/\mathrm{kg}]$ are the constants representing the maximum plasma insulin clearance rate and the half-saturation value, respectively. ²⁸ A non-measurable, integrated input disturbance $d(t)$ is included in the model to account for any insulin delivery issues.

K-AS for Pump Failure

An EKF insulin observer was developed by combining Equation 1 with Equations 2 to 3. To obtain an estimate of $d(t)$ at each time instant, a fictitious parameter dynamic is introduced with the assumption that $d(t)$ is a constant value:

$$\left[\begin{array}{c}{\stackrel{.}{I}}_{sc1}\\ {\stackrel{.}{I}}_{sc2}\\ {\stackrel{.}{I}}_p\\ {\stackrel{.}{I}}^{\prime }\\ {\stackrel{.}{X}}^L\\ {\stackrel{.}{K}}_p\\ \stackrel{.}{d}\end{array}\right]=\left[\begin{array}{c}-k_{a1}{I}_{sc1}+k_d{I}_{sc1}\\ k_d{I}_{sc1}-k_{a2}{I}_{sc2}\\ k_{a1}{I}_{sc1}+k_{a2}{I}_{sc2}-k_1\cdot I_p/\left(k_2+I_p\right)\\ k_i{I}^{\prime }-k_i{I}_p\\ k_i{X}^L-k_i{I}^{\prime }\\ EK{P}_b+k_p\left(I_b-X^L\right)V_i-U_b-k_u{K}_p-E_b-V_{max}{K}_p/\left(k_m-K_p\right)V_k\\ 0\end{array}\right]$$ (4)

The continuous-time model was discretized using forward Euler integration, obtaining the associated discrete-time state-space equations. The model sampling time $Dt$ was set to five minutes ²⁹ :

$$x_{k+1}=f\left(x_{k,}{u}_k\right)+w_k^{EKF}$$

$$y_k=g\left(x_k,u_k\right)+v_k^{EKF}$$

where $x$ is the state vector of the insulin concentration in each compartment, the ketone concentration in the plasma compartment, and the disturbance acting on the input; $u$ is the administered insulin dose, $y$ is the measured state (ie, the ketone concentration), and $f(\cdot ),g(\cdot )$ are the state and output equations of the EKF, respectively. The process and measurement noises are normally distributed as follows:

$$w_k^{EKF}~N\left(0,Q^{EKF}\right)$$

$$v_k^{EKF}~N\left(0,R^{EKF}\right)$$

where $Q^{EKF}$ is the process noise covariance and $R^{EKF}$ is the measurement noise covariance. With the same approach proposed in Aiello et al, ²⁸ the authors considered the work from Alva et al ³⁰ to characterize the measurement noise covariance $R^{EKF}.$ An error of 0.129 mM for the ketone sensor was used to characterize the uncertainties in the ketone measurements.

Additional information comes from Rawlings and Risbeck ²⁹ on the propagation and update of the state vectors at each time instant.

Since continuous plasma ketones cannot yet be measured in real time, the EKF design assumes that the unknown ketone measurements of the system are provided by a hypothetical ketone sensor that can perform continuous monitoring of ketone levels. The estimated disturbance $(\hat{d})$ is used to trigger an advisory alert based on the detection of inflection points on $\hat{d}.$ Given $\hat{d},$ the curve $\hat{d}(k)$ has a point of inflection at $k=c$ if and only if $\hat{d}″(c)=0$ and $d″(c)$ changes its sign on either side at $k=c.$ The detection of an inflection point in $\hat{d}$ generates a square wave signal that transitions from a low state (eg, 0) to a high state (eg, 1), or vice versa, and holds the value until the next trigger event when the input signal transitions from a high state to a low state, or vice versa. Signal edge detection is then performed to generate an alert. The edge detection is represented by an output Boolean signal, which has the value 1, when a rising edge is detected, representing the start of an event of “pump occlusion,” that is, insulin is delivered by the pump but not received by the user, or has the value 0, when a falling edge is detected, corresponding to the end of the occlusion event. Figure 1 shows the proposed advisory scheme for a pump failure detection event.

Figure 1.

Advisory scheme for “pump occlusion” event detection (ie, insulin is delivered by the pump but not received by the user). An extended Kalman filter uses noise plasma ketone measurements to estimate the disturbance acting on the insulin injection input (d). The estimated disturbance $(\hat{d})$ is used to trigger an advisory alert based on the detection of inflection points on $\hat{d}.$ Given $\hat{d},$ the curve $\hat{d}\left(k\right)$ has a point of inflection at $k=c$ if and only if $\hat{d}″\left(c\right)=0$ and $\hat{d}″(c)$ changes its sign on either side at $k=c$ . The detection of an inflection point in $\hat{d}$ generates a square wave signal that transitions from a low state (eg, 0) to a high state (eg, 1), or vice versa, and holds the value until the next trigger event when the input signal transitions from a high state to a low state, or vice versa. Signal edge detection is then performed to generate an alert. The edge detection is represented by an output Boolean signal, which has the value 1, when a rising edge is detected, representing to the start of an event of “pump occlusion,” or has the value 0, when a falling edge is detected, corresponding to the end of the occlusion event.

Performance Metrics

We evaluated the performance of the proposed K-AS through in silico studies using 10 in silico adult subjects in the UVA/Padova simulator. ²⁶ Simulations were 24 hours in duration, starting at midnight with a 30-g carbohydrate meal at 8 am, 50-g meal at 1 pm, and 80-g meal at 8 pm. All meals were announced, with meal boluses delivered at the start of meal ingestion.

Two different scenarios were designed to assess the performance of the proposed K-AS during overnight fasting and post-prandial conditions:

• Scenario A: the insulin delivery is suspended starting from 3 am.

• Scenario B: the insulin delivery is suspended starting from 8 am, that is, the insulin bolus for breakfast is not received.

Scenario A represents a critical condition because individuals do not usually check glucose or ketone levels during the night; moreover, the overnight period is characterized by a natural increase in BOHB levels ³ during the fasted state, and generally reductions in insulin levels. Furthermore, with interruption of insulin delivery, due to fasting, BG levels may not rise sufficiently to generate an alarm and detection of the CSII malfunction may be delayed. Furthermore, the rate of rise in BOHB in response to an interruption in insulin delivery is faster than the rate of rise in glucose levels. ³¹ Scenario B aims to simulate a CSII interruption, which causes non-delivery of a meal bolus; in this setting, the occlusion can be hidden by the expected increase in BG in response to the meal intake.

When the occlusion is detected, an alert is raised and the nominal insulin correction bolus is administered at the time of the detection, with the assumption that CSII is resumed at the time of the detection. The nominal insulin correction bolus is computed as:

$${\mathrm{I}}_{\mathrm{cb}}=(G(t_r)-120)/\mathrm{CF}$$

where G [mg/dL] is the BG concentration; $t_r$ is the time when the occlusion is detected; and CF is the patient-specific correction factor.

We proceeded to compare the results achieved by the proposed K-AS against the likely delayed responses obtained from an alert action based on the current guidelines^32,33 (G-AS). According to general practice recommendations, individuals with T1D are advised to check their postprandial BG (or continuous glucose monitoring [CGM]) two to three hours after the start of a meal and then administer a correction insulin dosage aimed at reducing postprandial BG levels to <180 mg/dL.^32,34 In fasting conditions, individuals with T1D are recommended to maintain their BG (CGM) levels below either 140 or 180 mg/dL, depending on the intensity of their management. ³³ The higher threshold can be chosen to reduce the risk of hypoglycemic event in the overnight period.

Performance metrics include the time to detection $(D{t}_D),$ peak values of plasma BOHB levels $(K_{peak}),$ and the time required to lower the plasma BOHB levels to the recommended threshold of 0.2 mM/L after peak $(D{t}_{0.2})$ . Non-parametric Wilcoxon rank-sum test was performed to compare the K-AS results against G-AS results.

Results

We identified the parameters for the kinetic model of ketone production, utilization, and elimination using the data reported in Miles et al ²⁴ and validated our model by comparing the model predictions with the available plasma BOHB levels reported in Orsini-Federici et al. ²⁵ To validate our model, we replicated the protocols using the 10 adults from the UVA/Padova simulator. ²⁶ The simulated protocols included a preliminary fasting period, followed by a period of insulin deprivation with the administration of a subcutaneous bolus at the end, followed by resumption of the usual basal insulin infusion.

For each participant reported in Orsini-Federici et al, ²⁵ the median and interquartile range (IQR) of the estimated plasma ketone levels are presented in Figure 2. It is observed that the estimates of the $K_p$ showed similar temporal trends to the levels reported in Orsini-Federici et al ²⁵ for all the participants; these were characterized by a rapid increase in ketone levels during the interruption of the insulin pump, followed by the reduction in ketones after the insulin restoration, that is, four hours after the start of the scenario. Note that none of the individual data were used to perform a fine-tuning of parameter values. The median (IQR) RMSE across the participants was 0.20 (0.71) mM/L. For each subject, the median RMSE (IQR) values between the reference measurements and the estimated of the $K_p$ were 0.130 (0.465) mM/L, 0.787 (1.643) mM/L, 0.238 (0.650) mM/L, 0.297 (0.815) mM/L, 0.138 (0.782) mM/L, 0.272 (0.860) mM/L, 0.177 (0.139) mM/L, and 0.173 (0.428) mM/L. The RMSE between the estimated $K_p$ levels and the measurements from Orsini-Federici et al ²⁵ were affected by a mismatch in the basal insulin values, since an incorrect basal rate may trigger ketone production. Although the authors reported the plasma insulin levels, they did not report any basal insulin information. ²⁵ We considered the basal insulin from the 10 adults from the UVA/Padova cohort metabolic simulator, ²⁶ which may not be the best assumption for the participants reported by Orsini-Federici et al. ²⁵ In addition, the change from baseline in ketone body concentrations reported in Orsini-Federici et al ²⁵ can also be attributed to inter- and intra-subject variability.

Figure 2.

Median of estimated plasma ketone levels from the model (blue) with the individual plasma ketone levels (orange) from Orsini-Federici et al. ²⁵ Interquartile ranges of the model predictions of plasma ketone levels are reported in light blue.

K-AS for Pump Failure

Individual and population metrics are reported for Scenario A and B in Tables 1 and 2, respectively, as well as the obtained P-values using the non-parametric Wilcoxon rank-sum test. Figures 3 and 4 present the median and the IQR of the plasma BOHB and BG levels for Scenarios A and B, respectively.

Table 1.

Scenario A.

	$D{t}_D^K$	$D{t}_D^{G140}$	$D{t}_D^{G180}$	$K_{peak}^K$	$K_{peak}^{G140}$	$K_{peak}^{G180}$	$D{t}_{0.2}^K$	$D{t}_{0.2}^{G140}$	$D{t}_{0.2}^{G180}$
Subject 1	106	100	158	1.45	1.39	1.74	255	252	273
Subject 2	72	90	140	2.33	2.65	3.37	298	307	318
Subject 3	74	121	183	1.90	2.65	3.46	279	298	307
Subject 4	116	141	314	1.15	1.30	2.45	239	255	390
Subject 5	100	132	326	1.12	1.33	2.75	214	229	362
Subject 6	71	130	204	2.44	3.65	5.08	295	316	321
Subject 7	63	92	131	1.34	1.61	1.95	264	276	267
Subject 8	91	113	335	0.93	1.05	2.37	197	205	310
Subject 9	77	133	219	0.85	1.18	1.70	217	239	248
Subject 10	122	154	154	1.57	1.82	1.82	262	280	280
Median (IQR)	84.00 (32.00)	125.50 (29.50)	193.50 (135.25)	1.40 (0.68)	1.50 (1.13)	2.41 (1.36)	258.50 (52.75)	265.50 (51.25)	308.50 (45.50)
P-values		.01	<.01		.34	<.01		.449	<.01

Individual values, medians, and P-values of performance metrics. Performance metrics include the time to detection for ketone-based alert system, $D{t}_D^K,$ and guideline-based alert systems, $D{t}_D^{G140}$ and $D{t}_D^{G180};$ peak values of plasma BOHB levels for ketone-based alert system, $K_{peak}^K,$ and guideline-based alert systems, $K_{peak}^{G140}$ and $K_{peak}^{G180};$ the time required to lower the plasma BOHB levels to the recommended threshold of 0.2 mM/L after peak for ketone-based alert system, $D{t}_{0.2}^K,$ and guideline-based alert systems, $D{t}_{0.2}^{G140}$ and $D{t}_{0.2}^{G180}.$

Abbreviations: IQR, interquartile range; BOHB, 3-beta-hydroxybutyrate.

Table 2.

Scenario B.

	$D{t}_D^K$	$D{t}_D^G$	$K_{peak}^K$	$K_{peak}^G$	$D{t}_{0.2}^K$	$D{t}_{0.2}^G$
Subject 1	72	120	0.49	0.91	193	222
Subject 2	46	120	0.53	2.23	164	255
Subject 3	47	120	0.63	1.74	214	252
Subject 4	81	120	0.45	0.72	159	193
Subject 5	67	120	0.36	0.70	135	190
Subject 6	45	120	0.42	2.08	115	241
Subject 7	38	120	0.24	1.30	43	193
Subject 8	60	120	0.25	0.58	67	154
Subject 9	51	120	0.25	0.70	70	173
Subject 10	87	120	0.59	0.93	178	206
Median (IQR)	55.50 (24.50)	120.00 (0.00)	0.44 (0.24)	0.92 (0.81)	147.00 (93.25)	199.5 (50.00)
P-values		<.01		<.01		<.01

Individual values, medians (IQR), and P-values of performance metrics. Performance metrics include the time to detection for ketone-based alert system, $D{t}_D^K,$ and guideline-based alert system, $D{t}_D^G;$ peak values of plasma ketone levels for ketone-based alert system, $K_{peak}^K,$ and guideline-based alert system, $K_{peak}^G;$ the time required to lower the plasma ketone levels to the recommended 0.2 mM/L after peak for ketone-based alert system, $D{t}_{0.2}^K,$ and guideline-based alert system, $D{t}_{0.2}^G$

Abbreviation: IQR, interquartile range.

Figure 3.

Scenario A. Median and interquartile ranges of (upper panel) ketone levels and (lower panel) blood glucose, in case of K-AS in blue, guideline-based alert with blood glucose threshold value of 140 mg/dL (G-AS₁₄₀) in orange, and guideline-based alert with blood glucose threshold value of 180 mg/dL (G-AS₁₈₀) in green.

Abbreviations: K-AS, ketone-based alert system; G-AS, guideline-based alert system; IQR, interquartile range.

Figure 4.

Scenario B. Median and interquartile ranges of (upper panel) plasma ketone levels and (lower panel) blood glucose levels, in case of K-AS in blue, and guideline-based alert with alert two hours after meal intake if blood glucose value is higher than 180 mg/dL (G-AS) in orange.

Abbreviations: K-AS, ketone-based alert system; G-AS, guideline-based alert system; IQR, interquartile range.

As shown in Figure 3, following the basal insulin suspension at 3 am, both blood BOHB and glucose levels increased: BOHB levels increased rapidly after the pump was stopped, while glucose levels increased at a lower rate, consistently with results reported in the literature.^3,31,35 When a malfunction of the CSII is detected, insulin delivery is restarted and a correction insulin bolus is administered. After the resumption of insulin delivery, BG levels plateau for the next two hours and then decrease before the next meal, while the BOHB levels continue to increase for the next hour and then returned to the normal range of 0.2 mM/L before the glucose normalized. As reported in Table 1, the detection times of the K-AS $(D{t}_D^K)$ were statistically significantly shorter than the detection times for rise in glucose of the G-AS, which raises the alert when the BG levels rise above the 140 $(D{t}_D^{G140})$ and 180 mg/dL $(D{t}_D^{G180})$ thresholds, respectively. This is achieved because the time constants associated with the insulin-ketone model are faster than those of the insulin-glucose model. ³⁶ As reported in Table 1, the shorter detection time of the K-AS resulted in lower peak concentrations of plasma BOHB $(K_{peak}^K)$ and shorter time for the plasma BOHB to return to the 0.2 mM/L baseline $(D{t}_{0.2}^K).$ This difference was statistically significant when comparing $K_{peak}^K$ values with the BOHB peak values achieved when using the G-AS, with BG threshold of 180 mg/dL $(K_{peak}^{G180}),$ while it is not statistically significant with BG threshold of 140 mg/dL $(K_{peak}^{G140}).$

The improvement in the performance is more evident when analyzing the simulation results of Scenario B, which aims to simulate an interruption of insulin delivery at 8 am coincident with a breakfast meal. Figure 4 shows that an earlier detection of the CSII malfunctioning can be achieved by the K-AS. As shown in Table 2, the K-AS achieved an average detection time $(D{t}_D^K)$ of 55.5 minutes, which was statistically significantly shorter than the detection time of G-AS $(D{t}_D^G),$ which was based on the two- to three-hour recommended period to check BG levels in the postprandial time.^32,34 A faster detection prevented plasma BOHB from rising above 0.5 mM/L, while G-AS allowed the blood BOHB to increase above 0.5 mM/L up to 1.8 mM/L, as shown in Figure 4. This difference is shown when comparing the peak values of the plasma BOHB, which are reported in Table 2. Similarly, the average times for the plasma BOHB to return to baseline were statistically shorter on the order of one hour when using the K-AS, as shown in Table 2. It is important to highlight that the K-AS does not cause any false alarms in the two proposed case studies.

Discussion

Since CKM is now a demonstrated technology,^16,30 although not yet clinically available, we aimed to show how CKM can be used in the future in protective systems to prevent episodes of hyperketonemia and DKA in people with T1D using CSII systems. Insulin pump occlusions are not necessarily noted immediately, as it takes time to build up sufficient back pressure until an occlusion is detected by internal checks followed by alerts to the user. ⁶ However, an early detection based on the metabolic consequences of interruption to insulin delivery might prevent subsequent hyperglycemia and potential development of DKA.

With an average basal rate of 1.0 U/h, pump systems detected the occlusion after approximately two to three hours. If a lower basal rate than 1.0 U/h is used, even longer times are to be expected. ³⁷ Currently, the detection of malfunctioning events in CSII therapy has been investigated by leveraging CGM by several groups, such as detecting set failures with a glucose threshold. Rojas et al ³⁸ used bivariate classification based on the last two hours’ mean glucose slope. Cescon et al ³⁹ proposed a combination of both a rising trend in average daily CGM readings along with increasing daily doses of insulin. Facchinetti et al ¹⁹ used a linear observer to generate the residual signals, indicating the presence of faults.

A K-AS for occlusion detection can achieve shorter detection times without any or minimal false alarms, becoming an important feature of the next generation of AID systems. To achieve more accurate detection, it would be important to include the impact of additional external factors, such as counterregulatory hormones, insulin resistance, and medications, including SGLT2 inhibitors, which can alter ketone body kinetics. ⁴⁰ Moreover, the proposed insulin-ketone model represents an opportunity for manual insulin correction bolusing in response to elevated ketone concentrations to achieve the shortest time to lower the BOHB levels while not causing hypoglycemia. Future work is needed to quantify the impact that the lag of the novel CKM technology has on the detection of an event of accidental cessation of insulin delivery. The proposed EKF algorithm is modular and can easily be expanded to include estimates for interstitial BOHB measurement by adding an additional compartment that can be used to represent the ketone diffusion process between the plasma BOHB and the interstitial BOHB concentration.^41,42 Moreover, the EKF scheme can be used for real-time personalization of the population-level estimates of the production, utilization, and elimination rates of the ketone bodies, by using the EKF to estimate deviations from the population-level estimates. ²⁸

Conclusion

We proposed a novel PK model that describes the alterations in the rates of production and utilization of plasma BOHB, the main ketone body predictive of progression to DKA. The simulation capabilities of the proposed model were validated by comparing the simulated traces with clinical data available in the literature. It is important to note that the proposed validation approach aims to verify that the model reproduces observed system behavior evidenced by available input-output experiments. To achieve a rigorous validation of the structure and parameter values, a future clinical protocol, including tracer administration, is needed to accurately estimate the ketone body flux in vivo.

Moreover, we propose a potential integration of a CKM into an AID system by designing an alert system able to detect events of accidental cessation of insulin delivery. Simulation scenarios were designed to mimic realistic and potentially critical situations. The K-AS leverages the faster rate of rise of plasma BOHB to achieve a shorter detection time than waiting for the development of clinically important hyperglycemia in response to insulin attenuation and prevents BOHB levels from rising to dangerous levels, without false-positive alarms.