Physiology-Invariant Meal Detection for Type 1 Diabetes

James Weimer; Sanjian Chen; Amy Peleckis; Michael R Rickels; Insup Lee

doi:10.1089/dia.2015.0266

. 2016 Oct 1;18(10):616–624. doi: 10.1089/dia.2015.0266

Physiology-Invariant Meal Detection for Type 1 Diabetes

James Weimer ^1,,^*, Sanjian Chen ^1,,^*,^✉, Amy Peleckis ², Michael R Rickels ^2,^✉, Insup Lee ¹

PMCID: PMC6528748 PMID: 27704875

Abstract

Background: Fully automated artificial pancreas systems require meal detectors to supplement blood glucose level regulation, where false meal detections can cause unnecessary insulin delivery with potentially fatal consequences, and missed detections may cause the patient to experience extreme hyperglycemia. Most existing meal detectors monitor various measures of glucose rate-of-change to detect meals where varying physiology and meal content complicate balancing detector sensitivity versus specificity.

Methods: We developed a novel meal detector based on a minimal glucose–insulin metabolism model and show that the detector is, by design, invariant to patient-specific physiological parameters in the minimal model. Our physiological parameter-invariant (PAIN) detector achieves a near-constant false alarm rate across all individuals and is evaluated against three other major existing meal detectors on a clinical type 1 diabetes data set.

Results: In the clinical evaluation, the PAIN-based detector achieves an 86.9% sensitivity for an average false alarm rate of two alarms per day. In addition, for all false alarm rates, the PAIN-based detector performance is significantly better than three other existing meal detectors. In addition, the evaluation results show that the PAIN-based detector uniquely (as compared with the other meal detectors) has low variance in detection and false alarm rates across all patients, without patient-specific personalization.

Conclusions: The PAIN-based meal detector has demonstrated better detection performance than existing meal detectors, and it has the unique strength of achieving a consistent performance across a population with varying physiology without any individual-level parameter tuning or training.

Background

Type 1 diabetes (T1D) affects ∼1.25 million people in the United States and 5 million Americans are expected to have T1D by 2050.¹ T1D patients depend on daily insulin therapy to control glucose levels to avoid numerous long-term complications associated with hyperglycemia.² Meal carbohydrates cause significant disturbance to one's glucose level in T1D, making it critical to cautiously plan insulin injections around meal times to avoid postprandial hyperglycemia and subsequent postcorrection hypoglycemia. Artificial pancreas (AP) systems^3–5 aim to regulate the glucose level by automatically delivering insulin and free T1D patients from the cognitive burden of frequent glucose monitoring, carb counting, and insulin dosing decision making.

A key challenge of meal-time glycemic control is the sensing and action delays: the glucose level starts to rise a certain time after the onset of a meal and there is a delay between the injection of insulin and the action of insulin to dispose of glucose. To cope with this challenge, the AP systems need meal information either by announcement⁶ or by meal detection.^7–13 This work concerns accurate and timely meal detection—that is, detecting whether carbohydrates have been ingested in the recent past. Accurate meal detection not only serves as the first step toward meal estimation (i.e., estimating the amount of carbohydrates ingested) but can also be employed by meal estimation algorithms as a safety backup, especially in situations where user input is erroneous.¹⁰ The problems of carbohydrate estimation and insulin bolus calculation¹³ are not considered herein and left as future work.

A meal detector aims to identify, in real-time, carbohydrate ingestion based on continuous glucose monitor (CGM) readings. Several meal-detection strategies already exist in the literature. Dassau et al. propose a voting-based meal detector that tracks the glucose rate-of-changes (RoCs) estimated by different methods including Kalman Filtering and announces a meal when three out of the four RoC estimates cross prespecified thresholds.¹⁰ Using similar Kalman Filtering techniques, Lee and Bequette develop a meal detector that announces a meal based on RoCs crossing thresholds and estimates the meal size by feeding the filtered glucose RoCs into a finite response filter.¹⁴ Harvey et al. recently proposed a meal-detection algorithm that announces meals based on a two-stage CGM filtering process and an RoC criteria.¹¹ Cameron et al. developed a meal-detection algorithm that uses a simple glucose model to match the RoC of the CGM readings to temporal trajectories assuming both no-meal and meal scenarios.⁷

All the aforementioned meal detectors require identifying patient-specific parameters (e.g., insulin sensitivity and insulin diffusion rate), most of which vary with time. Due to the inherent physiological dependency, the RoC-based detectors may suffer from high false positives, considering that nonmeal disturbance factors may also cause significant glucose fluctuations (e.g., exercising,¹⁵ stress,¹⁶ and depletion of insulin-on-board¹⁷). In addition, the trajectory-matching meal detector has a long average detection delay.¹⁸ As an alternative, recent work by Turksoy et al. simultaneously aims to estimate physiological variables and model parameters to provide accurate meal detection and estimation; however, no guarantees are provided that the physiological parameter estimates converge to their true value.¹³ Quick and reliable meal detection is critical for the AP systems: false detections can lead to unnecessary insulin delivery that may trigger life-threatening hypoglycemia; missed detections or significant detection delays can leave the patient with marked postprandial hyperglycemia.

This article presents a novel meal-detection algorithm that is based on a commonly accepted minimal glucose physiological model and is “invariant” to individual physiological parameters—that is, it achieves a near-constant false alarm rate (CFAR) across the population without needing individual tuning. We compare our meal detector with three published meal-detection techniques.^10,11,14 Evaluations on a real T1D clinical data set collected through the Rodebaugh Diabetes Center of the University of Pennsylvania Health System (UPHS) show that our detector outperforms (often significantly) other detectors in terms of detection rate and false-positive rate, while also having significantly less performance variation between patients.

Methods

In this section, we present our meal detector based on a parameter-invariant (PAIN) design approach²⁵ used to achieve a CFAR. In many medical monitoring applications, including meal detection, unknown or uncertain physiology presents a fundamental challenge in generating mathematical models useful for detector design. The PAIN approach uses physiological models and trends to capture the effects of the unknown nuisance parameters, then establishes invariance to the nuisance parameters by projecting the measurements onto a space that is unaffected by the unknown parameters, mathematically known as a null space projection. The benefit of the PAIN approach is that the projected measurements will be the same, regardless of the patient's unknown physiology, allowing the design of powerful detectors that leverage this population-level consistency. The PAIN design approach has been successfully applied to various engineering applications with unknown parameters^19–21 and has recently been extended to medical monitor design.^22–25

To present the meal detector, this section uses Figure 1 as a visual aid and references the Appendix for useful mathematics related to its formulation. In this work, we perform meal detection in two steps. First, at time k shown in Figure 1, we use a time window of measurements (denoted by w in Fig. 1) and comparatively test, using PAIN techniques,²⁵ two consecutive subwindows of time ending δ time steps before k (represented by d₀ and d₁ in Fig. 1) for the presence of a meal. The time steps correspond to a CGM sampling period of 1 min. Second, we sequentially filter the test decisions generated at each time step k to generate a threshold-based test for meal detection. The remainder of this section describes, in detail, the key components of the meal detector, namely, modeling glucose–insulin physiological trends, designing physiology-invariant tests, and filtering test decisions.

FIG. 1. — A meal detection example of the PAIN-based detector. PAIN, parameter invariant.

Modeling glucose–insulin physiological trends

Many models exist for describing glucose–insulin physiology, ranging from high-fidelity maximal models^26,27 to an assortment of low-fidelity minimal models.²⁸ For the PAIN technique to be useful, the chosen model must capture the general physiological trends that discriminate meal occurrence or absence. Thus, to capture the real-life scenario where the glucose level is measured at a subcutaneous site and carbohydrates enter plasma through a digestion pathway, we use a modified 5th-order linear Bergman model²⁸ augmented with minimal compartmental models that describe the subcutaneous insulin pathway^29,30 and meal carbohydrate digestion pathway.³¹

The complete augmented physiological model is a five-state linear system (provided in the Appendix, Equation 1) and contains several specific physiological parameters, for example, the insulin sensitivity,²⁸ the insulin diffusion rate,³⁰ and the time of maximum glucose appearance.³¹ Identifying these parameters for each individual requires time-consuming tests in strictly controlled clinical settings, which may be inaccurate outside the controlled setting. Thus, a core element of our meal detector is the design of tests invariant to the unknown time-varying physiological parameters.

Designing physiology-invariant tests

Applying standard time-series analysis techniques,³² we can write the CGM measurement model at time step k (as shown in Fig. 1), assuming meal window d_i for Inline graphic as , where y_k is a vector of the w CGM measurements, and is a known matrix (defined in the Appendix, Equation 2) that relates how the CGM measurements are affected by the lumped-physiological parameters, . The value of is a function of the unknown physiological variables.^a In addition, Inline graphic represents an unknown uncertainty associated with a zero-mean noise, n. Using the CGM measurement model, we can generate two invariant statistics, and , as defined in Equation 3 in the Appendix.

In other words, for Inline graphic , we project the CGM measurements onto the null space of ,³³ then generate using the ratio of the remaining measurement energy in the space of to the measurement energy not remaining in . The form of is commonly referred to as an F-ratio in the signal processing and statistics literature,³² and has the useful feature that its value is invariant to the noise level Inline graphic as well as the lumped-physiological parameters . In the context of this work, represents the ratio of measurement energy aligned with (and only with) the meal effects of d₁ to the measurement energy that cannot be explained exclusively by meals within d₁. Comparing to a threshold Inline graphic , selected to achieve a specified probability of false alarm, generates a decision. Similarly, is generated by first projecting the measurements onto the null space of , then generating an F-statistic using and comparing with a threshold .

The selection of the PAIN-based detector parameters, d₀, d₁, Inline graphic , and w, can significantly affect its performance. In this work, we select d₀ and d₁ to be 10 time steps, to be 20 time steps, and w to be 120 time steps. These values are chosen because they provided the best detection rates among the range of values evaluated. A discussion of the PAIN-based detector parameter effects is provided in the Appendix along with a detailed presentation of the test statistics.

Figure 1 illustrates how the PAIN-based detector^b works on simulated scenarios generated by the FDA-accepted simulator.²⁷ In this figure, we use simulated data (as opposed to the real population data used for evaluation) to clearly illustrate our approach to meal detection; thus, the CGM measurements correspond to a 1-min sampling rate of the interstitial glucose level shown in Figure 1. The true meal happens around 22 min (the pink upper triangle in the top plot of Fig. 1). The PAIN-based detector works in a sliding-window manner: at time k, the detector run tests on the d₀ and d₁ windows using the past w CGM measurements; the relevant time windows at time k are scoped by the green box in Figure 1; the detector generates a decision at each time and the time windows (as highlighted in the green box) shift forward in time with the detector to generate sequential statistics (whose values are shown in the second and third subfigures in Fig. 1).

In Figure 1, as the d₀ window approaches the true meal event (the detector never knows when a meal actually happens and tests every time step), the statistic Inline graphic (the red dashed line in the figure's middle graph) starts rising and becomes separated from (the solid green line), indicating a meal is more likely to have occurred in d₀ than in d₁. Then as the detector moves further ahead, the true meal enters the d₁ window, and increases while Inline graphic decreases, indicating that a meal is more likely in d₁ than in d₀. This sequential rise and fall of the statistics and are leveraged to design a sequential test.

Filtering sequential test decisions

To leverage the structured sequential rise and fall of the statistics, we design an algorithm that generates a cumulative decision score based on the statistics Inline graphic and and corresponding thresholds and . The statistics have the useful property that an increasingly positive implies an increasing likelihood that a meal has occurred in the window d₁ (and vice versa). Thus, the algorithm generates an S-score, , for each time step j (assuming is initialized to zero) and accumulates S-scores according to the rules in Table 1, where a larger S-score indicates a higher confidence in the occurrence of a meal.

Table 1.

Score Accumulation Rules for S(j) at k

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At every step, when the detector claims a meal occurs in window d₀, we add Inline graphic to for each time step j in the d₀ window; similarly, if the detector claims a meal occurs in d₁, we add to for each time step in the d₁ window. If it is likely that a meal was in both windows, then we add to for each time step in d₀ and similarly we add to of each time step in d₁. Note that we drop the factor of 2 in the increments when both residual statistics, Inline graphic and , are positive, thus weakening the confidence of a meal happening in any individual window. If both residual statistics are negative, then neither d₀ nor d₁ is likely to contain a meal; thus, no score accumulation occurs.

The score accumulation rules are highlighted in Figure 1: each colored region corresponds to the rule in Table 1 that applies in that region. In a typical positive meal-detection scenario, one should first see the green region (corresponding to the d₀ window) approaches the meal event, followed by the yellow region as the meal event transitions from d₀ to d₁, and finally see the red region, after which a peak in the Inline graphic curve emerges, indicating that the detector makes a series of decisions at sequential time steps that all point to the same meal time region where the peak emerges.

The magnitude of Inline graphic corresponds to our confidence in a meal occurring at time t. To trigger an alarm (indicating a meal has occurred), we use two design parameters, a threshold S₀ and a minimum width S_w; a peak is characterized by at least S_w consecutive 's that are above S₀. At each time step, the detector raises a meal alarm if a new Inline graphic peak emerges. Parameters S₀ and S_w can be tuned to achieve different detection performance: smaller S₀ and S_w result in higher sensitivity but more false alarms. We note that there are a few steps delay between the actual meal time and the peak, as shown in Figure 1. This delay phenomenon is related to the physiological fact that there is a delay from the onset of eating to when the CGM reading starts changing: in the maximal model,^26,27 meal carbohydrates have to pass several digestion compartments before affecting the plasma glucose.

Experimental Results

This section presents the evaluation results of the PAIN-based detector against three existing meal-detection algorithms: the Dassau (et al.) detector,¹⁰ Harvey (et al.) detector,¹¹ and Lee (and Bequette) detector.¹⁴ We evaluate the detectors using a clinical data set collected by the Rodebaugh Diabetes Center of the UPHS. The clinical data set includes 5-min CGM readings from 61 T1D patients (mean ± standard deviation of age: 45.7 ± 15.3 years; mean ± standard deviation of body weight: 79.2 ± 21.9 kg; average duration of monitoring 17 days).

Each patient counts the carbohydrates in the meal and then inputs that information into his or her insulin pump. The insulin pump will then provide a suggested meal bolus that the patient can accept or override. Since patient reporting of meal time (i.e., the time when the patient inputs the information into the pump) is error prone, we consider any meal alarm within 2 h of the reported meal event to be a correct detection (and a false alarm otherwise). In the event that a meal detector alarms within 30 min of a correction bolus (i.e., nonmeal bolus), we omit this alarm from our false alarm (specificity) analysis since the alarm corresponds to a situation (e.g., unreported meal, “meal-like” critical event, worsening of long-lasting hyperglycemia) requiring an insulin bolus.

We ran the PAIN-based detector, the Dassau detector, Harvey detector, and Lee detector on the same glucose measurements from the 61 patients. Each of the four meal detectors has a set of configurable parameters, for example, the threshold S₀ of the PAIN-based detector and RoC thresholds of the RoC-based detectors. We systematically explore the combinations of each detector's parameters and get their best detection performance.

A receiver operating characteristic (ROC) curve represents the detection rate and false alarm rate of a detector under different configurations. Figure 2 shows the ROC curves of the four detectors. Table 2 lists the operating point of each detector closest to two false alarms per day. This operating point was chosen to compare the relative detection performance (sensitivity) of each detector for a chosen specificity. For all false alarm rates (specificities), the PAIN-based detector has superior performance, where for the operating point reported in Table 2 has an 86.9% sensitivity (meaning that the detector correctly detects 86.9% of meal events within 2 h of the reported meal time) and 2.01 false alarms per day. We note that the evaluation results of the Harvey detector are comparable with those reported in the original publication.¹¹,^c

FIG. 2. — The receiver operating characteristic curves of the four meal detectors on the clinical data set used for analysis.

Table 2.

Operating Points of the Four Detectors on the Clinical Data set Used for Analysis

Detector	Detection rate (%)	False alarms per day
PAIN	86.9	2.01
Dassau¹⁰	74.1	1.99
Lee¹⁴	73.4	1.99
Harvey¹¹	79.4	1.97

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PAIN, parameter invariant.

Figure 3 compares the performance variability, in terms of false alarm and detection rates, of each meal detector on different patients in the data set. These results provide a measure of the consistency of detection performance at the individual level, that is, whether a detector can perform particularly bad on any patient. The duration of glucose monitoring varies across patients in the data set. Eight patients are excluded from the individual-level analysis because their data contains fewer than 10 reported meals. Over the remaining 53 patients, the PAIN-based detector detects at least 55% of all reported meals and never has a false alarm rate greater than 3.7 false alarms per day. In sharp contrast to the PAIN-based detector, all other three detectors miss significantly more meals (both on average and worst case), and have false alarm rates with higher variances and higher worst-case values.

FIG. 3. — Distributions of the four detectors' false alarm and detection rates on different patients in the clinical data set used for analysis. The ‘+’ marks corresponds to outliers in patient performance for each detector.

Discussion

The experimental evaluation shows that the PAIN-based detector significantly improves the detection performance when compared with the other three detectors. For example, compared with the Harvey detector, the PAIN-based detector reduces the number of missed detections by 36% without increasing the false alarm rate in the experimental evaluation. The performance distribution over the patients validates the unique strength of the PAIN-based detector: it is designed to be “invariant” to differences in patients' physiological parameters and thereby achieves low variance detection performance across a real population. This unique feature of the PAIN-based detector is critical to the AP: A meal detector that frequently misses true meal events on some patients could result in postprandial hyperglycemia and possibly subsequent postcorrection hypoglycemia.

In theory, the performance of the RoC-based detectors may be further improved by carefully tuning the detector parameters for each individual. However, such tuning process may require frequent clinic visits because patients' physiological characteristics change over time. Moreover, even with parameter tuning, the RoC-based meal detectors have their fundamental limitation because the postmeal glucose rise rate depends on many other factors such as the nutrition composition of meals³⁴ and insulin-on-board,³⁵ which cannot be mitigated by simply tuning the threshold parameters. In contrast, the experimental evaluation demonstrates that the PAIN-based detector is able to achieve low-variance performance without any individual-level parameter tuning.

Conclusion

This article proposes a PAIN-based meal detector that is based on a physiological model. The clinical data set evaluation demonstrates that the PAIN-based meal detector has better detection performance than three existing meal detectors. In addition, the evaluation results validate that the PAIN-based detector has the unique strength of achieving highly consistent performance across a real population, with varying physiology, without any individual-level parameter tuning. Although accurate and timely meal detection remains an open problem, the performance improvement provided by the PAIN approach suggests it is better suited, compared with other approaches, to provide meal alerts to a closed-loop controller and/or to act as a safety backup for meal information provided by a user or other meal detectors.

Acknowledgments

This research was supported, in part, by NSF grant CNS-1035715 (to I.L.), in part, by NIH grant R01- DK091331 (to M.R.R.), and, in part, by the DGIST Research and Development Program of the Ministry of Science, ICT, and Future Planning of Korea (CPS Global Center). The authors would like to acknowledge support from the Human Metabolism Resource of the Institute for Diabetes, Obesity & Metabolism at the University of Pennsylvania.

Appendix

This appendix provides the mathematical details and supporting discussion for implementation of the parameter-invariant detector. Deriving the detector test statistics requires null space transformations, where the null space of an arbitrary matrix X is³³

and has an orthonormal basis transposed, Inline graphic , satisfying³³

graphic file with name inl-2.jpg

where V^T denotes the transpose of matrix V.³³ The following employs the mentioned notation to present, mathematically, the meal-detector test statistics implemented in this work.

For completeness, we begin by stating the augmented 5th-order linear Bergman model employed in this work,

graphic file with name inl-3.jpg

where Inline graphic denote the physiological state for plasma glucose, plasma glucose appearance rate, digestive compartment glucose, plasma insulin, and subcutaneous insulin, respectively. The insulin bolus and meals are represented by u and D_G, respectively. All other variables represent unknown physiological parameters. For a complete discussion of the model in Equation 1, see our previous publication [8], section 4.2. Applying standard time-series discretization techniques, the model in Equation 1 can be written as a 5th-order discrete time system, assuming piecewise constant insulin and meal inputs.

For any sampling rate, we denote the k-th sample of the CGM measurement as x_k (as sampled from G) and the injected insulin bolus as u_k. We then write

where we call y_k the measurements (representing a point in the measurement space) and we say F_k spans the measurement space affected by the insulin bolus and physiological dynamics. More importantly, each column of F_k corresponds to the effect, on the measurements, of an unknown lumped-physiological parameter. The mapping of the physiological parameters in Equation 1 to the lumped-physiological parameters is unimportant in implementing the PAIN-based meal detector and consequently omitted from this appendix.

Although F_k spans the measurement space affected by insulin bolus and physiological parameters, it does not (necessarily) span the effect of meals on the measurements. We capture the effect of meals within the hypothesized meal windows, d₀ and d₁ in Figure 1, respectively, as

where 0_{(n) × (m)} denotes an n-by-m matrix of all zeros and I_(m) corresponds to the m-dimensional identity matrix. We note that G_i has Inline graphic columns (as opposed to d_i columns) since the effect of the most recent hypothesized meal (of unknown magnitude) within the d_i window affects measurements up to four time steps later. Thus, we say that G_i spans the measurement subspace affected by meals within d_i (according to the Bergman model).

We write

and say that Inline graphic spans the measurement subspace affected by the combined effect of parameters corresponding to the physiological dynamics, insulin bolus, and the meals within the d_i time window. Assuming a meal occurs exclusively within the time window d_i, then as described in the text.

To present the test statistics, we introduce intermediate variables

where Inline graphic and denote the projection of the measurements and projected meal effects for d₁ onto the nullspace of , respectively (and vice versa for and ). In other words, and denote the measurements and the effects of meals within d₁ that cannot be explained by physiological parameters, insulin bolus, and meals occurring within d₀. Consequently, to quantify whether the projected measurements and projected meal effects are significantly aligned,³⁰ we write test statistics, Inline graphic for , as

For Inline graphic , the numerator denotes the magnitude of the projected measurements aligned with (i.e., in the subspace of) the projected meal effects of d₁, whereas the denominator represents the energy of the projected measurements that cannot be explained exclusively by meals within d₁. Thus, large/small values of Inline graphic imply that a meal within d₁ is likely/unlikely. Similarly, large/small values of indicate that a meal within d₀ is likely/unlikely.

In order for the test statistic in Equation 2 to be nontrivial, necessitates the selection of d₀, d₁, Inline graphic , and w in Figure 1 such that all dimensions within in G₀ and G₁ are non-negative. As stated in the text, this work selects d₀, d₁, and to be five time steps and w to be 300 time steps. In general, the performance of the PAIN-based detector varies with the selected parameters. Qualitatively, increasing w improves the detector performance as long as the Bergman model remains accurate. At the same time, decreasing d₀, d₁, and Inline graphic improves detection accuracy (and time-to-detection) so long as the statistics are nontrivial. Quantifying the detector performance is a subject of future work.

Author Disclosure Statement

No competing financial interests exist.

^{^a}

In this work, we omit the specific mapping of physiological variables to the lumped parameters as it is irrelevant in the design of PAIN detectors,³² that is, designing tests invariant to the lumped parameters is equivalent to designing invariant to the underlying physiological variables.

^{^b}

For aesthetics, the values of d₀, d₁, Inline graphic , and w shown in Figure 1 are not the same as the values used in the evaluation.

^{^c}

Clinical evaluation results of sensitivity versus specificity of the Dassau detector and the Lee detector are not available in their original publications^10,14: the Dassau detector is evaluated in a single-meal test¹⁰ and the Lee detector is evaluated using a simulator.¹⁴

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PERMALINK

Physiology-Invariant Meal Detection for Type 1 Diabetes

James Weimer, PhD

Sanjian Chen, PhD

Amy Peleckis, NP

Michael R Rickels, MD, MS

Insup Lee, PhD

Abstract

Background

Methods

FIG. 1.