Blood glucose control - Rensselaer Polytechnic...
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Artificial Pancreas Improved blood glucose regulation using (i) frequent subcutaneous and (ii) infrequent blood glucose measurements B. Wayne Bequette, Sandra Lynch and Francis Moussy (U. Conn.) Presented at the Diabetes Technology Conference, San Francisco, November 2001
Transcript of Blood glucose control - Rensselaer Polytechnic...
Artificial Pancreas
Improved blood glucoseregulation using
(i) frequent subcutaneous and
(ii) infrequent blood glucosemeasurements
B. Wayne Bequette, Sandra Lynchand Francis Moussy (U. Conn.)
Presented at the Diabetes Technology Conference, San Francisco, November 2001
B. Wayne Bequette
Overview
l Motivationl Sensor/Pump/Control state of the artl Feedback control
Ø State estimation
Ø Model predictive control
l Simulation resultsØ Single-rate (subcutaneous glucose only)
Ø Multi-rate (s.c. & capillary blood glucose)
l Future work
B. Wayne Bequette
Motivation
DCCT (1983-93) Intensive Therapy Regimen- 1400 IDDM volunteers
l Advantages - reduced risk of:Ø Eye disease by 76%
Ø Kidney failure by 50%
Ø Nervous disease by 60%
l DisadvantagesØ Three times risk of hypoglycemic
incidences
B. Wayne Bequette
Feedback Control: Basic Idea
controller
desired glucoseconcentration
pump patient
insulinflowrate
pumpspeed
bloodglucoseconcentration
sensormeasured glucoseconcentration
B. Wayne Bequette
Current Practice
l Patient serves as “feedback controller”
l Several “finger pricks”/day for capillaryblood glucose measurement
l Multiple injections/day, or continuousinfusion
B. Wayne Bequette
Pump & Sensor Technology
l External (worldwide) & internal (Europe)pumps available
l Many sensors under developmentØ Glucose electrodes, microdialysis, non-
invasive
l Minimed - FDA approval for 3-day useØ Glucose electrode
Ø Re-calibrate daily w/blood glucose
Ø Return to physician for analysis
B. Wayne Bequette
Control Background
l Many simulation studiesØ IV and s.c. (sensor and infusion)
l ExperimentsØ Human - s.c. sensor, s.c. & i.v. infusion, PD control
(Shimoda et al., 1997)
Ø Animal - venous blood, adaptive control (Fisher etal., 1987)
l Medical Research Group (Shah et al., 2000)Ø Animal - IV sensor and implantable pump
l Our focus - s.c. infusion, s.c. glucose sensor
B. Wayne Bequette
Motivation for Our Multi-rate MPC Research
l Experience with anesthesia & classicalchemical process control
l New/improved sensors (Moussy)Ø Long-term implantable electrode
l State estimation-based model predictive controlØ Frequent samples - s.c. glucose
Ø Infrequent samples - capillary blood glucose
l Estimate blood glucose and meal disturbances(frequently), and s.c. sensor sensitivity(infrequently)
B. Wayne Bequette
Subcutaneous measurements
l Subcutaneous glucose measurementavailable at frequent intervals
l Use model to:Ø Estimate meal disturbance
Ø Estimate blood glucose
B. Wayne Bequette
Estimation - Basic Idea
Blood glucose
Measured subcutaneous glucose
Sensor
Insulin infusionrate
Meal disturbance
IDDMPatient
+_
PatientModel
ModelFeedback
SensorModel
Predicted subcutaneousglucose
Estimates: Blood glucose Subcutaneous glucose Glucose meal disturbance
Estimator
B. Wayne Bequette
Discrete-time Model
xk +1 = Φxk + Γuk + Γdd k
dk +1 = dk + wk
yk = Cxk + vk
insulin glucose meal
disturbance
subcutaneous
glucose
glucose (blood and s.c.),
insulin states
zero-mean white noise
Form an augmented state description toperform disturbance estimation
B. Wayne Bequette
Estimation: Basic idea of Kalman Filter
l Based on expected measurement andprocess noise, estimate the “maximumlikelihood” values for the state variables
l Original formulation is for perfectlymodeled systems
l Technique extended for parameter ordisturbance estimation (Extended KalmanFilter)
B. Wayne Bequette
Kalman Filter w/Augmented States
xk +1
dk +1
xk +1a
1 2 3 =
Φ Γd
0 1
Φ a
1 2 4 3 4
xk
dk
x ka
{+
Γ0
Γ a{
uk +0
1
Γ a , w{
wk
yk = C 0[ ]Ca
1 2 3 xk
dk
x ka
{+ vk
Predictor-corrector equations:
ˆ x k |k−1a = Φa ˆ x k−1|k−1
a + Γauk −1
ˆ x k |ka = ˆ x k |k −1
a + Lk yk − Ca ˆ x k|k−1a( )
Kalman gain
Augmented state (includes mealdisturbance)
Measured s.c. glucose
Insulin infusion
Aug. state
estimate
B. Wayne Bequette
Model Predictive Control
t kcurrent step
setpoint
y
actual outputs (past)
PPredictionHorizon
past controlmoves
u
max
min
MControl Horizon
past future
model prediction
t k+1current step
setpoint
yactual outputs (past)
PPredictionHorizon
past controlmoves
u
max
min
MControl Horizon
model predictionfrom k
new model prediction
Find current and future insulininfusion rates that best meet adesired future blood glucosetrajectory. Implement first “move.”
Correct for model mismatch(estimate states), thenperform new optimization.
B. Wayne Bequette
Model Predictive Control
l SimulationØ Neural model - Trajonoski et al.
Ø Linear model (various) - Parker et al.n I.V. sensor and infusion
l ExperimentØ Linear (GPC) - Kan et al.
n Insulin & glucose infusion, venous blood sampling
B. Wayne Bequette
Simulation Study Using S.C. Sensor
l Simulated Type I DiabeticØ 19 State (Sorenson, 1985)
Ø Also studied by Parker et al. (1999),among others
l Model for Estimator/ControllerØ Modified Bergman “minimal model”
Ø Parameters fit to Sorenson step response
Ø Augmented state for meal disturbance
B. Wayne Bequette
Simulation Results: S.C. Sensor
0 50 100 150 200 250 300 350 40065
70
75
80
85
90
95
100
Blood Glucose concn, mg/
time, min
SetpointActualEstimated
0 50 100 150 200 250 300 350 40065
70
75
80
85
90
Sc Glucose concn, mg/dL
time, min
ActualEstimated
0 50 100 150 200 250 300 350 4000
10
20
30
40
50
60
insulin infusion rate, mU/min
time,min
50 g glucose mealdisturbance
5% measurementnoise (s.d. = 3.8 mg/dl)
Estimator modelassumes first-order lagbetween blood and s.c.glucose
B. Wayne Bequette
Simulation Results - S.C. Sensor Degradation
50
60
70
80
90
100
110
0 10 20 30 40 50 60 70Time (hours)
Actual Blood glucoseSetpointEstimated blood glucose
50
60
70
80
90
100
0 10 20 30 40 50 60 70
Time (hours)
Sc bloodglucose(actual)
Sc blood glucose(est.)
0
10
20
30
40
50
60
0 10 20 30 40 50 60 70Time (hours)
Insu
lin in
fusi
on
rat
e (m
U/m
in)
00.05
0.10.15
0.20.25
0.3
0 10 20 30 40 50 60 70
Time (hours)
Va
ria
tio
n o
f S
en
so
r g
ain
A
50% sensorsensitivity decreaseover 3 days
Motivates additionalblood capillarymeasurement for s.c.sensor calibration
B. Wayne Bequette
Estimation: Improved (Multi-Rate)
l Problem with s.c. glucose measurementØ Sensor sensitivity changes
l Solution: Incorporate infrequent bloodcapillary measurements
l Use model to:Ø Estimate meal disturbance (5 min)
Ø Estimate blood glucose (5 min)
Ø Update s.c. sensor sensitivity atinfrequent intervals (~4 times/day)
B. Wayne Bequette
Simulation results:Multirate
0 10 20 30 40 50 60 7060
70
80
90
100
Blood Glucose concn, m
time,hours
SetpointActualEstimated
0 10 20 30 40 50 60 7060
70
80
90
Sc Glucose concn, mg/dL
time, hrs
ActualEstimated
0 10 20 30 40 50 60 700
20
40
60
insulin infusion rate, mU/min
time,hrs
0 10 20 30 40 50 60 700.245
0.25
0.255
Parameter A
estimateactual
5% s.c. noise
(s.d. = 3.8 mg/dl)
2% capillary blood noise
(s.d. =1.6 mg/dl)
B. Wayne Bequette
Simulation results:Multirate
0 10 20 30 40 50 60 70 8060
70
80
90
100
Blood Glucose concn, m
time,hours
SetpointActualEstimated
0 10 20 30 40 50 60 70 8060
70
80
90
100
Sc Glucose concn, mg/dL
time, hrs
ActualEstimated
0 10 20 30 40 50 60 70 800
20
40
60
insulin infusion rate, mU/min
time,hrs
0 10 20 30 40 50 60 70 800.1
0.15
0.2
0.25
A
time,hrs
estimateactual
•Sensor degradation (50% over 3 days)
•Sensitivity estimate
5% s.c. noise
(s.d. = 3.8 mg/dl)
2% capillary blood noise
(s.d. =1.6 mg/dl)
B. Wayne Bequette
Proposed Work
l Additional simulation-based studiesl Develop sensor/computer/pump
interconnectionsØ Glucose sensor
Ø Estimation/control algorithms
Ø External insulin infusion pump
l Experimental studiesØ Dogs
B. Wayne Bequette
Implantable Sensor
WC- -
ORKING ELECTRODE:oiled Pt wire coated with:poly(o-phenylenediamine) filmGO/albumin/glutaraldehyde
REFERENCE ELECTRODE:Coiled Ag/AgCl wire
0.5 mm
glucose
oxygen
Platinum electrode PPD Nafion
Glucose oxidase/albumin/glut.
e-
negat.
+
Schematic diagram of the sensor's membranes with their functions. Not to scale.
H 2O2
Figure 4: Implantable Glucose Sensor
small electrochem.interferences
entire sensor coated with Nafion
mol.large
B. Wayne Bequette
Summary
l State estimation-based model predictivecontrol
l Frequent s.c. glucose measurementsØ Estimate blood glucose and meal
disturbance
l Infrequent blood capillary glucosemeasurementsØ Estimate (update) s.c. sensor sensitivity
l Simulation resultsl Future experimental work
B. Wayne Bequette
Acknowledgments
l Brian AufderheideØ Model development
B. Wayne Bequette
References
The Diabetes Control and Complications Trial Research Group “The Effect of Intensive Treatment of Diabetes on theDevelopment and Progression of Long-Term Complications in Insulin-Dependent Diabetes Mellitus,” N. Eng. J. Med.,329:977-986 (1993).
Fisher, U., W. Schenk, E. Salzsieder, G.Albrecht, P. Abel and E.J. Freyse “Does Physiological Blood Glucose ControlRequire an Adaptive Control Strategy?,” IEEE Trans. Biomed. Eng., 34(8):575-582 (1987).
Gross, T.M., B.W. Bode, D. Einhorn, D.M. Kayne, J.H. Reed, N.H. White and J.J. Mastrototaro “PerformanceEvaluation of the MiniMed Continuous Glucose Monitoring System During Patient Home Use,” Diabetes Technologyand Therapeutics, 2(1), 49-56 (2000).
Jaremko, J. and O. Rorstad “Advances Toward the Implantable Artificial Pancreas for Treatment of Diabetes,” DiabetesCare, 21(3):444-450 (1998).
Kan, S., et al. “Novel Control System for Blood Glucose Using a Model Predictive Method,” ASAIO J. 657-
Mercado, R.C. and F. Moussy “In Vitro and In Vivo Mineralization of Nafion Membrane Used for Implantable GlucoseSensors,” Biosensors and Bioelectronics, 13(2):133-145 (1998).
Parker, R.S., F.J. Doyle, III and N.A. Peppas “A Model-Based Algorithm for Blood Glucose Control in Type I DiabeticPatients,” IEEE Trans. Biomed. Eng., 46(2), 148-157 (1999).
Parker, R.S., F.J. Doyle, III and N.A. Peppas “The Intravenous Route to Blood Glucose Control,” IEEE Engineering inMedicine and Biology Magazine, 20(1), 65-73 (Jan/Feb, 2001).
Shah, R., M. Miller, Y. Zhang, T. Bordeaux, K. Torres, B. Moran and R. Lebel “Glucose Sensor Control of anImplantable Insulin Pump,” presented at the American Diabetes Association Conference (abstract 509), June (2000).
Shichiri, M., M. Sakakida, K. Nishida and S. Shimoda “Enhanced, Simplified Glucose Sensors: Long-Term ClinicalApplication of Wearable Artificial Endocrine Pancreas,” Artificial Organs, 22(1):32-42 (1998).
Sorensen, J.T. A Physiologic Model of Glucose Metabolism in Man and Its Use to Design and Assess Improved InsulinTherapies for Diabetes,” Ph.D. Thesis, Dept. Chem. Eng., MIT, Cambridge, MA (1985).
Trajanoski, Z. and P. Wach “Neural Predictive Controller for Insulin Delivery Using the Subcutaneous Route,” IEEETrans. Biomed. Eng., 45(9):1122-1134 (1997).
Valdes, T.I. and F. Moussy “A Ferric Chloride Pre-treatment to Prevent Calcification of Nafion Membrane Used forImplantable Biosensors,” Biosensors and Bioelectronics, 14:579-585 (1999).
