The objective of the study was to investigate infinite horizon prediction of post prandial blood glucose dynamics after breakfast ingestion using subspace based identification on empirical data

Ståhl, Fredrik

Cescon, Marzia

Johansson, Rolf

Renard, Eric

English

Lund University Publications

LUND UNIVERSITYPO Box 117221 00 Lund+46 46-222 00 00Infinite Horizon Prediction of Post Prandial Breakfast Glucose ExcursionStåhl, Fredrik; Cescon, Marzia; Johansson, Rolf; Renard, Eric2009Link to publicationCitation for published version (APA):Ståhl, F., Cescon, M., Johansson, R., & Renard, E. (2009). Infinite Horizon Prediction of Post Prandial BreakfastGlucose Excursion. Paper presented at Diabetes Technology Meeting 2009, San Francisco, United States.Total number of authors:4General rightsUnless other specific re-use rights are stated the following general rights apply:Copyright and moral rights for the publications made accessible in the public portal are retained by the authorsand/or other copyright owners and it is a condition of accessing publications that users recognise and abide by thelegal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private studyor research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portalRead more about Creative commons licenses: https://creativecommons.org/licenses/Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will removeaccess to the work immediately and investigate your claim.Infinite Horizon Prediction of Post PrandialBreakfast Glucose ExcursionFredrik Stahl† Marzia Cescon Rolf JohanssonDepartment of Automatic Control, Lund UniversityEric RenardDepartment of Endocrinology, Montpellier University HospitalObjectiveThe objective of the study was to investigate infinitehorizon prediction of post prandial blood glucose dy-namics after breakfast ingestion using subspace basedidentification on empirical data.DataFive, three days long, patient records (type I dia-betes, treated by insulin pump (CSII, n=3) or mul-tiple injections (MDI, n=2)), collected at the Mont-pellier Clinical Investigation Center within the Eu-ropean DIAdvisorTM project (www.DIAdvisor.eu),were used. The data records contained frequentfingerprick measurements (average 38 samples/day,HemoCueTM), continuous glucose monitoring (CGMAbbott FreestyleTM) and information on insulin dosesand carbohydrate ingestion. The plasma glucose curvewas reconstructed from the fingerprick measurementsby interpolation. Plasma insulin levels were calculatedfrom the insulin doses using a linear pharmocokineticmodel (Wilinska et al. 2005). Using a meal modelbased upon (Dalla Man et al. 2006) glucose releasefrom the gut following a meal was also assessed.0 500 1000 1500 2000 2500 3000 3500 4000 4500051015Insulin Dose (IU)Time (min)0 500 1000 1500 2000 2500 3000 3500 4000 4500020406080100Carbohydrates (g)0 500 1000 1500 2000 2500 3000 3500 4000 450050100150200250300Glucose Value(mg/dl)Estimation Data Patient 2  Fingerprick MeasurementCGMSFigure 1: Data record for patient nr 2.Model IdentificationFrom these data series an individualized, third orderstate space model of plasma glucose dynamics wasidentified for each patient using the subspace-based al-gorithm N4SID in the Matlab Identification Toolbox.Recent previous attempts on model identification andprediction have been made in (Cescon et al. 2009) and(Stahl & Johansson 2009).The plasma insulin level and gut flux signals, describedabove, were considered as inputs and the reconstructedplasma glucose curve was used as output. Data fromthe first night and the following second day break-fast constituted estimation data. The model was crossvalidated against the first and third breakfasts andcompared against the performance of the CGM usingClarke Grid Analysis (pointwise and rate) and RMSE.ResultsInfinite horizon prediction was evaluated for both val-idation breakfasts for all patients and compared withthe performance of the CGM signal in terms of predic-tion error/measurement error in relation to the recon-structed plasma glucose curve. The infinite horizonpredictor outperformed the CGM for all five patientsin almost all considered evaluation metrics.120 140 160 180 200 220 240 260 280 300 320100150200250300Glucose Value(mg/dl) Validation data I: Breakfast Day 1  HemoCue CGMS Model3000 3050 3100 3150 3200 3250100120140160180200220240260280300Glucose Value(mg/dl)Validation data II: Breakfast Day 3Time [min]Figure 2: HemoCue values, model predictionand CGM in val. data for patient 4.0 50 100 150 200 250 300 350 400050100150200250300350400Reference Concentration [mg/dl]Predicted Concentration [mg/dl]Clarke’s Error Grid AnalysisADE CC EDBBFigure 3: pCGA for model (green) and CGM(blue) for all patients (validation data).−40 −30 −20 −10 0 10 20 30 40−40−30−20−10010203040AEEDCCDBBRate of Change, Capillary Concentration [mg/dl/10min]Rate of Change, Predicted/CGMS Concentration [mg/dl/10min] Clarke’s Rate Grid AnalysisFigure 4: pCGA for model (green) and CGM(blue) for all patients (validation data).pCGA(A) rCGA(A) RMSEPatnr CGM Model CGM Model CGM Model1 74.2 83.9 74.2 81.7 19.2 142 96.8 95.2 86.7 93.4 23.6 15.63 82.2 100 91.0 93.9 15.0 8.54 58.1 98.4 74.8 88.6 45.2 10.15 58.9 82.2 79.4 89.9 34.6 24.9Ave. 74.0 91.9 81.2 89.5 27.5 14.6Table 1: Performance comparison. Amount ofpoints in zone A in pCGA and rCGA in % andRMSE in mg/dl.DiscussionStatistical analyses show that the difference in pCGA,rCGA and RMSE between the model prediction andCGM is significant. The performance is generally verygood, with no points in zone C, D or E for the pCGA.For the rCGA there is one point in zone C. However,this point occurs in the normoglycemic range, and af-ter a short while the model is back on track both interms of glucose value and direction.ConclusionsEven though the study is small the results indicatethat subspace-based models can be used for predic-tion of postprandial plasma glucose excursion follow-ing breakfasts, with the same accuracy as, or betterthan, CGM.OutlookFurther studies will be undertaken on larger data setsto test the methodology in the DIAdvisorTM projectwithin the European FP7-ICT program, IST-216592.ReferencesDalla Man,C., Camilleri, M., Cobelli, C. (2006). A system model of oral glucose ab-sorption: validation on gold standard data. IEEE TBE, 53(12), 2472-2477Wilinska, M.E., Chassin, L.J., C.Schaller, H., Schaupp, L., Pieber, T.R., Hovorka,R. (2005). Insulin kinetics in type-1 diabetes: Continuous and bolus delivery of rapidacting insulin. IEEE TBE, 52(1),3-12Cescon M., Stahl F., Landin-Olsson M., Johansson R. (2009). Subspace-based ModelIdentification of Diabetic Blood Glucose Dynamics. Proceedings of the 15th IFAC Sym-posium on System Identification.Stahl F, Johansson R. (2009). Diabetes Mellitus Modeling and Short-Term PredictionBased On Blood Glucose Measurements. Mathematical Biosciences 217(2), 101-117.† Corresponding author: Fredrik.Stahl@control.lth.se

Infinite Horizon Prediction of Post Prandial Breakfast Glucose Excursion

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Infinite Horizon Prediction of Post Prandial Breakfast Glucose Excursion

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