Mean Glucose Slope Principal Component Analysis Classification to Detect Insulin Infusion Set Failure

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1 Mean Glucose Slope Principal Component Analysis Classification to Detect Insulin Infusion Set Failure Rubén Rojas*. Winston Garcia-Gabin** B. Wayne Bequette*** * Electrical Engineering Department, Universidad de Los Andes, Mérida 5101, Venezuela (Tel: ; rdrojas@ula.ve). ** Automatic Control Laboratory, KTH Royal Institute of Technology, SE Stockholm, Sweden. ( wgarcia@kth.se). *** Chemical and Biological Engineering Department, Rensselaer Polytechnic Institute. Troy, NY USA, ( bequette@rpi.edu).} Abstract: The bivariate classification technique using the mean glucose slope (MGS) and the first component of the principal component analysis (PCA), is applied to insulin infusion set failure detection (IISF), a challenging problem faced by individuals with type 1 diabetes that are on continuous insulin infusion pump therapy. The objective of this study was to determine if the proposed approach could be used to distinguish between normal patient data and data from patients under IISF online, in a reasonably short period of time. The proposed approach was applied to simulated glucose concentrations for 10 patients, based on a nonlinear physiological model of insulin and glucose dynamics. Although it presents few false alarms, it was capable of detecting most drifting (ramp) infusion set failures before complete failure occurred. Keywords: Artificial pancreas, biomedical systems, fault detection, multivariate analysis, type 1 diabetes, 1. INTRODUCTION Individuals with type 1 diabetes mellitus (T1DM) depend on insulin therapy to maintain blood glucose levels within safe range, since they have little or no endogenous insulin production. Exogenous insulin can enable T1DM patients to achieve tight blood glucose control, avoiding hypoglycemic or hyperglycemic events, significantly reducing the risk of the disease's devastating complications. Insulin treatment is received as multiple daily injections, or by continuous insulin infusion pumps. The development of a closed-loop artificial pancreas, which includes a continuous blood glucose monitor (CGM), a continuous subcutaneous insulin infusion pump, and a closed-loop control algorithm, is an active research endeavor. This technology has been reviewed by Bequette (2005), Doyle et al. (2007), Kumareswaran et al. (2009), Cobelli et al. (2009), and Bequette (2010). An important consideration of any closed-loop artificial pancreas is the possibility of an undetected insulin infusion set failure, which could lead to hyperglycemia and ketoacidosis within several hours. A 10-year Food and Drug Administration (FDA) retrospecttive study of adverse events in adolescents using insulin pump technology is presented by Cope et al. (2008). A total of 1674 reports have been identified from January 1, 1996, through December 31, 2005, involving insulin pumps. Several reports indicated severe hypoglycemic or hyperglycemic events that seemed to be device-related. There were 987 (61.9%) reports with patient problems of hyperglycemia, and 46.6% of these indicated that the patient had ketoacidosis (a serious condition that can lead to diabetic coma or even death). Insulin infusion set failure (IISF) and infection of infusion site are the most frequent events according to a report of pump malfunctions recorded between 2001 and 2004 in 376 pumps used by patients treated with continuous subcutaneous insulin infusion therapy in Brittany (Guilhem et al. (2006)). Common causes of IISF include blocked or dislodged sets, inflammation, or insulin leakage back to the skin surface. All of them produce hyperglycemic and ketoacidosis as consequence of the high level of glucose, because even though the control algorithm has calculated the correct infusion rate, insulin is not properly delivered. Thus, IISF is associated with transient loss of metabolic control, and is a major cause of ketoacidosis and long-term complications in eyes, kidneys, nerves, heart, and blood vessels. Patients should be aware that the simple pump alarm systems usually do not detect leakages. Moreover, in more than 85% of occlusion events, the metabolic deterioration occurs before the activation of high pressure alarms (Guilhem et al. (2006)). For this reason an artificial pancreas for ambulatory use should include an effective system for fault detection. The aim of fault detection algorithm is to detect the malfunction and accordingly take corrective actions to avoid Copyright by the International Federation of Automatic Control (IFAC) 14127

2 damages in the system. The different methods to detect and isolate failures can be classified according to Venkatasubramanian et al. (2003a, b, c) as follows: (i) quantitative model-based, (ii) qualitative model-based, and (iii) process data history-based methods. Much of the focus is on complex, large-scale chemical process systems. Frank (1990) and Isermann (2005) provide reviews, with selected applications, of quantitative model-based fault detection and diagnosis techniques. Both reviews distinguish between abrupt (or sudden) faults, and slowly developing (drifting) faults. IISF must be detected in as short a time as possible by the fault detection algorithm then it activates an alarm to warn the patient to take action. The major challenge of fault detection in insulin infusion, particularly compared to most manufacturing systems, is the limited number of measurements that are available: (i) continuous glucose signals from the CGM, (ii) infrequent reference glucose (finger-stick) measurements, and (iii) insulin infusion rates. Multivariate statistical analysis has been used as a process data history method that could help in such a situation (Varmuza et al. (2009)). Principal component analysis (PCA) is a mathematical procedure that allows transformation of a number of possibly correlated variables into a smaller number of uncorrelated variables called linear latent variables. It has been successfully employed in numerous areas including data compression, feature extraction, image processing, pattern recognition, signal analysis, and process monitoring (Jolliffe (1986)). Because of its simplicity and efficiency in processing different amounts of process data, PCA is recognized as a powerful statistical process monitoring tool and widely used in the process industry for fault detection and diagnosis (Venkatasubramanian et al. (2003c)). Recent developments in the PCA technique include adaptive process monitoring using, for instance, recursive implementation of PCA (Li et al. (2000)), fast moving window PCA (Wang et al. (2005)) or kernel PCA (Liu et al (2009)). In the artificial pancreas framework, PCA has been applied to both simulated and experimental T1DM data: to determine its capability to distinguish between normal patient data and data for abnormal conditions including a variety of faults (Finan et al. (2010)) a posteriori on a daily base; and also as a multivariate analysis approach to detect insulin set failures online (Rojas et al. (2011)). A combined approach for dynamic IISF detection in an artificial pancreas framework is investigated in this article using bivariate classification based on the last two hour mean glucose slope and the first principal component of the PCA decomposition. The proposed algorithm has been evaluated in silico, using a simulation environment with virtual diabetic subjects. The FDA approved University of Virginia/Padova T1DM Simulator (Dalla Man et al. (2007); Kovachev et al. (2009)) has been used to develop and test the algorithms. The paper is structured as follows: Methodology as section 2 briefly describes the initial settings, the retrospective and the MGS-PCA detection algorithms development. Results as section 3 summarize the in silico results obtained for the different scenarios; and finally section 4 presents the Conclusions. 2.1 Initial Settings 2. METHODOLOGY The UVa/Padova T1DM simulator (Dalla Man et al. (2007); Kovachev et al. (2009)), was modified to simulate infusion set failures during the second day of a three day scenario, with three regular meals each day. The IISF were simulated as ramp insulin infusion delivery degradations from 100% to 0% in a six hour period, for all the children simulator patients (one classified as the average child (see Fig. 1) and 10 other simulated child patients) without bolus delivery after the failure. This is the worst-case scenario for the basal rate because the failure happens gradually and can easily go unnoticed. As can be seen in Fig. 2, for further complication the failure was applied at different times of insulin therapy the ramp infusion degradation was introduced at midnight (12:00 a.m.) when no meals are present, at noon (12:00 p.m.) simultaneous with the lunch meal and at 4:00 p.m., two hours before the dinner meal, causing changes in the glucose time courses. The CGM signal was sampled every five minutes. Fig. 1. Simulated insulin set failures as a ramp delivery degradation starting at midnight, at noon and at 4:00 p.m. for the simulated average child. 2.2 Retrospective Detection Algorithm As a gold standard for comparison of the proposed algorithm a retrospective mathematical interpretation of the IISF was defined. In such a sense, IISF can be considered when the mean plasma glucose slope over a four-hour period (4H MGS) is high (about 1 mg/dl/min) while it is assumed that the normal insulin infusion is delivered (total insulin on board, IOB black line in Fig. 1), but no apparent correction is observed. This four-hour observation window is a typical standard in clinical applications. To apply the retrospective algorithm, two classes are assumed: Normal and Faulty classes. The idea is to find a way to separate the two classes using both variables 4H MGS and IOB (bivariate classification, Varmuza et al. (2009); Rojas et al. (2011)). For simulation purposes the 4H MGSj, at any point j, was 14128

3 calculated as the average of the plasma glucose slope from two-hour before the actual instant of time to two-hour after. Fig. 3. Bivariate Classification using IOB and 4H MGS, the faulty region is considered for all objects above L1 and L2. Fig. 2. Plasma Glucose responses for three simulated ramp set failures. This means that a two-hour-ahead predictor is needed or the estimated time should be considered two hours after the actual instant of time (that is why this approach is called retrospective). The four-hour period mean plasma glucose slope is calculated as follows: S i = (x i x i ) T (x i x i ) /[(x i x i ) T (T i T i )] (2) Where m is the number of sampled data points in a two-hour period (24 points), S i is the estimated slope at the i-point, x i and T i are vectors containing the last 45 min data (10 points) for plasma glucose and daily time, respectively. Finally and stand for the vectors mean values. Assuming that the simulated average child represents the mean response of the diabetic children population, a scatter plot using these two variables allows a discrimination of both classes. The boundary region for the faulty class (defined as the region where only faulty elements are present), is defined as a threshold to detect when any patient glucose time course enters the faulty region (see, L1 and L2 in Fig. 3). For any child patient simulation, if three consecutive calculated pairs < IOB i, 4H MGS i > are over L1 and L2, a IISF is assumed. 2.3 MGS-PCA Detection Algorithm Rojas et al. (2011) show that the Bivariate Classification algorithm is very sensitive to changes in plasma glucose slope, causing a high rate of false positives. The PCA algorithm showed the smallest rate of false positives without significant degradation in the actual time of IISF detection. Better times of IISF detection were obtained when the PCA with IOB was used, but the rate of false positives was higher. (1) In this case, the proposed IISF detection algorithm is a combined approach that includes bivariate classification and PCA by using the first component score, PC1, obtained by PCA and the two- hour period mean plasma glucose slope, 2H MGS j, calculated as follows: as variables for the bivariate classification. Note that only previous known data is used. For the principal component analysis, once again the simulated average child given by the simulator represents the mean response of the diabetic children population and its data set was arranged in a feature matrix X where each row (object) corresponds to the actual analyzed element x i, used to calculate the slope (10 plasma glucose measurements over the last 45 min window). Because x i only contains plasma glucose measurements, each column (feature) is highly correlated with the others so a PCA reduction to extract the main information of the plasma glucose was carried out. Then, the mean-centered feature matrix Xc was calculated as follows: where k corresponds to the feature matrix columns (in our case n = 10). Principal components of Xc, were calculated to find that the first component, represents 97.7% of the data variation and 99.96% can be represented by the first three principal components. In the MGS-PCA algorithm, the boundary region for the faulty class (L3) defines the threshold for the <PC1 i, 2H MGS i > pairs, detecting the IISF if the patient glucose time course enters the faulty region (see, Fig. 4). For any child patient simulation, if three consecutive calculated pairs <PC1 i, 2H MGS i > are to the right of L3, an IISF is assumed. This three consecutive pairs cause a fifteen minutes delay in the actual detection that is a good trade- off between (3) (4) 14129

4 performance and delay to detect the failure, because it is large enough to avoid excessive FPs and small enough to avoid a large delay in detecting the failures. detection signals were activated for the respective algorithm during the simulated 24h experimental period. These signals are considered false positives, FP (the detection signal is activated when no IISF has occurred). Fig. 4. Bivariate Classification using PC1 and 2H MGS, the faulty region is considered for all elements to the right of L3. 3. RESULTS After applying the initial preprocessing the retrospective detection algorithm was applied to the 10 simulated child data files with: i) no IISF, ii) ramp IISF starting at Midnight, iii) ramp IISF starting at Noon and iv) ramp IISF stating at 4:00 p.m., the overall results were kept as a reference for the MGS-PCA detection algorithm evaluation. Fig. 6. Plasma glucose time course for the simulated child #2 in normal regulated conditions. Three detection signals were activated (false positives) when the MGS-PCA algorithm was used. Table 1 presents the rates of false positives for the retrospective and the MGS-PCA algorithms calculated for each experimental setting where a period without IISF was simulated. Midnight IISF was not included because the experimental simulation window starts with the insulin infusion set failure then there is not time before the simulated IISF. So, for the 24 hour experimental window there are 24, 12 and 16 simulated hours without IISF for the NO IISF, Noon IISF and 4:00 p.m. IISF settings, respectively. This table shows no significant difference between the retrospective and the proposed MGS-PCA algorithms (on average 0.05 FP/hour). Table 1. Rate of False Positives (#FP/hour; Mean [SD]) Experimental Case Retrospective MGS-PCA Algorithm No IISF (24h) 0.04 [0.08] 0.07 [0.08] Noon IISF (12H) 0.07 [0.10] 0.03 [0.06] 4:00 p.m. IISF (16H) 0.04 [0.08] 0.06 [0.07] AVERAGE 0.05 [0.09] 0.05 [0.07] Fig. 5. Plasma glucose time course for the simulated child #2 in normal regulated conditions. Two detection signals were activated (false positives) when the retrospective detection algorithm was used. Fig. 5 and Fig. 6 show the plasma glucose time courses for simulated child #2 for normal condition without IISF when the retrospective and the MGS-PCA detection algorithms were applied, respectively. As can be observed, two and three Fig. 7 and Fig. 8 show the normal and the simulated midnight IISF ramp plasma glucose time courses, for child #4. The IISF detection occurs at 4:15 a.m. and 8:25 a.m. for the retrospective and MGS-PCA detection algorithms, respectively. Although the retrospective detection is just four hours and fifteen minutes after the simulated ramp IISF starts and the MGS-PCA detection is four hours and twenty five minutes later, it must be considered that the retrospective detection used two-hour-ahead information that is unrealistic for an online algorithm but a fear estimated can be considered two-hours later. However on average the MGS-PCA 14130

5 algorithm presents a thirty minutes delay with respect to the retrospective detection (see Table 2). correction is considered (see Table 2). Fig. 9 and Fig. 10 show the normal and the simulated 4:00 p.m. IISF ramp plasma glucose time courses, for child #9. The IISF detection occurs at 6:10 p.m. and 7:20 p.m. with one and three FPs for the retrospective and MGS-PCA detection algorithms, respectively. In this case the retrospective detection is two hours and ten minutes and the MGS-PCA detection is three hours and twenty minutes after the simulated ramp IISF starts, giving a better performance for the MGS-PCA algorithm when the two-hour delay for the retrospective is considered. On average the MGS-PCA algorithm present a detection time of three hours and thirtyseven minutes, which is thirty-four minutes before the retrospective detection when the two-hour correction is considered (see Table 2). Fig. 7. Plasma glucose time course for the simulated child #4 when a ramp IISF starting at Midnight was simulated. IISF was detected at 4:15 a.m. by the retrospective algorithm without FPs. Fig. 9. Plasma glucose time course for the simulated child #9 when a ramp IISF starting at 4:00 p.m. was simulated. IISF was detected at 6:10 p.m. by the retrospective algorithm with one FP. Fig. 8. Plasma glucose time course for the simulated child #4 when a ramp IISF starting at Midnight was simulated. IISF was detected at 8:25 a.m. by the MGS-PCA algorithm without FPs. The same approach was applied for child #5. The IISF detection occurs at 12:15 p.m. and 1:35 p.m. for the retrospective and MGS-PCA detection algorithms, respectively. In this case the retrospective detection is just fifteen minutes and the MGS-PCA detection is one hour and thirty-five minutes after the simulated ramp IISF starts, giving a better performance for the MGS-PCA algorithm when the two-hour delay for the retrospective is considered. On average the MGS-PCA algorithm present a detection time of one hour and fifty-five minutes, which is forty-three minutes before the retrospective detection when the two-hour Fig. 10. Plasma glucose time course for the simulated child #9 when a ramp IISF starting at 4:00 p.m. was simulated. IISF was detected at 7:20 p.m. by the MGS-PCA algorithm with two FP

6 As can be observed the proposed MGS-PCA algorithm presents a low rate of false positives (Table 1), with no significant difference respect to the retrospective estimation (Table 2). On average the MGS-PCA algorithm present a larger detection time for the ramp IISF starting at midnight while a shorter for the ramp IISFs starting at noon and at 4:00 p.m. when the two hour correction is considered that are reasonable good times for IISF detection algorithms to be implemented online. Table 2. Detection time (HH:MM; Mean [SD]) Experimental Case Retrospective MGS-PCA Algorithm Midnight IISF (24h) 06:56 [1:46] 07:29 [1:12] Noon IISF (12H) 14:38 [1:54] 13:55 [1:13] 4:00 p.m. IISF (16H) 20:11 [0:53] 19:37 [0:47] 4. CONCLUSIONS The proposed algorithm combining MGS and PCA using Bivariate Classification is a promising tool for insulin infusion set failure detection in an artificial pancreas framework. This preliminary study indicates that the proposed algorithm was capable of detecting most drifting (ramp) infusion set failures before complete failure occurred with relative low rate of false alarms. These results suggest expecting good performance in real time applications. It would avoid the hyperglycemia episodes given by the pump failures with a reasonable rate of false positive. 5. ACKNOWLEDGMENTS RR was supported by the Fulbright Visiting Scholars program during his sabbatical stay at Rensselaer Polytechnic Institute, which led to the work presented in this paper. BWB acknowledges support from the Juvenile Diabetes Research Foundation (JDRF) Artificial Pancreas Program. The authors wish to acknowledge many fruitful discussions with Fraser Cameron, Bruce Buckingham and Darrell Wilson. REFERENCES Bequette, B.W. A Critical Assessment of Algorithms and Challenges in the Development of an Artificial Pancreas. Diabetes Technol. and Ther.,7 (1), 28-47, Bequette, B.W. Continuous Glucose Monitoring: Real-Time Algorithms for Calibration, Filtering and Alarms. J. Diabetes Sci. and Technol., 4(2), , Cobelli, C., Dalla Man, C., Sparacino, G., Magni, L., De Nicolao, G., Kovatchev, B. Diabetes: models, signals and control. IEEE Rev. Biomed. Eng., 2, 54-96, Cope, J.U., Morrison, A.E, Samuels-Reid J. Adolescent use of insulin and patient-controlled analgesia pump technology: a 10-year FDA retrospective study of adverse events. Pediatrics, 121 (5), e1133-8, Dalla Man, C., Raimondo, D.M., Rizza, R.A. and Cobelli C. GIM, simulation software of meal glucose insulin model, J. Diabetes Sci. Technol., 1 (3), , Doyle, F.J. III, Jovanovic, L., Seborg, D.E. A tutorial on biomedical process control: glucose control strategies for treating type 1 diabetes mellitus. J. Process. Control., 17 (7), , Frank, P.M. Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy a survey and some new results, Automatica, 26 (3), , Finan, D.A., Zisser, H., Jovanovič, L., Bevier, W.C., Seborg, D.E. Automatic detection of stress states in type 1 diabetes subjects in ambulatory conditions Ind. Eng. Chem. Res. 49, , Guilhem, I., Leguerrier, A.M., Lecordier, F., Poirier, J.Y., Maugendre, D. Technical risks with subcutaneous insulin infusion. Diabetes Metab, 32, , Isermann, R. Model-based fault-detection and diagnosis status and applications, Annual Reviews in Control, 29, 71-85, Jolliffe, I.T. Principal Component Analysis. Springer-Verlag, New York, Kovatchev, B.P., Breton, M., Dalla Man, C. and Cobelli C. In silico preclinical trials: a proof of concept in closed-loop control of type 1 diabetes, J. Diabetes Sci. Technol., 3 (1), 44-55, Kumareswaran, K, Evans, M.L., Hovorka, R. Artificial pancreas: an emerging approach to treat Type 1 diabetes. Expert Rev. Med. Dev., 6 (4), , Li, W., Yue, H., Valle-Cervantes, S. and Joe Qin, S. Recursive PCA for Adaptive Process Monitoring. J. Process. Control, 10 (5), , Liu, X., Kruger, U., Littler, T., Xien, L. and Wang S. Moving window kernel PCA for adaptive monitoring of nonlinear processes. Chemometrics and Intelligent Laboratory Systems, 96, , Rojas, R., Garcia-Gabin, W. and Bequette, B.W. Multivariate Statistical Análisis to Detect Insulin Infusión Set Failure. American Control Conference Varmuza, K., and Filzmoser, P. Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca de Raton Venkatasubramanian, V., Rengaswamy, R., Yin, K. and Kavun S.N. A review of process fault detection and diagnosis. Part I: Quantitative model-based methods, Comp. Chem. Engng., 27, , 2003a. Venkatasubramanian, V., Rengaswamy, R., Yin, K. and Kavun S.N. A review of process fault detection and diagnosis. Part II: Qualitative models and search strategies, Comp. Chem. Engng., 27, , 2003b. Venkatasubramanian, V., Rengaswamy, R., Kavuri, S.N. and Yin K. A review of process fault detection and diagnosis. Part III: Process history based methods, Comp. Chem. Engng., 27, , 2003c. Wang X, Kruger U, Irwin G W. Process monitoring approach using fast moving window PCA. Ind. Eng. Chem. Res. 44: ,