Modelbased Algorithms for Diabetic Blood Glucose Control

1
Model-based Algorithms for Diabetic Blood Glucose
Control

• Robert S. Parker
• Francis J. Doyle III
• Department of Chemical Engineering
• University of Delaware

Winter Research Review February 4, 1998
2
Outline

• Overview
• Advanced Control Structure
• diabetic patient modeling
• controller model identification
• linear model predictive control (MPC)
• Patient Variability
• mathematical modeling
• model-based control w/ parameter estimation
• Conclusions

3
Overview

• Diabetes Mellitus affects 14 million people
• insufficient endogenous insulin secretion
• hyperglycemia causes long-term complications
• glucose gt 120 mg/dl
• retinopathy, nephropathy
• hypoglycemia deprives body of fuel (dangerous)
• glucose lt 60 mg/dl
• diabetic coma, death
• Current therapeutic approaches
• examples subcutaneous injection and continuous
  insulin infusion pumps
• open-loop control methodologies (require
  patient intervention)
• yield inadequate control (sub-optimal)

4
Overview

• Automated methods are necessary for long-term
  normoglycemia
• Closed-loop (implantable) insulin infusion pump
• components glucose sensor, insulin pump,
  control algorithm
• requires computationally tractable controller
  (microchip based)
• classical control methods are insufficient
• process nonlinearities
• system constraints (process and hardware)
• Approach Model-based Predictive Control (MPC)
• successfully applied to other biological systems
• blood pressure (Kwok et al., 1992) and anesthesia
  (Linkens et al, 1995)
• Reverse-engineering the pancreas naturalistic
  objective function

5
Model Predictive Control Algorithm
Arterial Plasma Glucose
Desired Glucose Level
Insulin
Controller
Patient
-
Compartmental Model
Model Predictive Algorithm
Model
-
Controller Model
Update Filter
Kalman Filter

• Controller model structures
• empirical (input-output) data-driven
• state-space Jacobian linearization of the
  nonlinear compartmental model

6
Diabetic Patient Model (Detailed Nonlinear
Compartmental Model)
Brain
arterial glucose measurement
venous blood
Heart/Lungs
hepatic artery
insulin infusion
Gut
Liver
portal vein
glucose meal disturbance
Kidney
Periphery
7
Open-loop Response to a Meal Disturbance (cf.
OGTT)
Arterial Glucose
Concentration (mg/dL)
Time (min)
8
Input-Output Model Identification

• Identify linear FIR model using least-squares
• tradeoff computation speed vs. model fidelity
• sample time (Ts 5 min), model memory (M 36)
• validation residuals are lt10 of the measured
  output

Input sequence (for identification)
Model validation simulation
Insulin Infusion (mU/min, deviation)
Output
Sample Number
Time (min)
9
Linear Model Predictive Control(MPC)

• Discrete time controller
• Solves optimization problem at each time step
• Controller Objective Function
• quadratic programming problem
• unconstrained problem analytic solution

10
Model Predictive Control Implementation

• Controller tuning
• adjust move horizon, m, and prediction horizon,
  p, to determine aggressiveness
• tradeoff between the setpoint tracking and
  move suppression weighting matrices
• Criterion for tuning
• minimum arterial glucose concentration 60 mg/dl.
• minimize glucose tracking error
• minimize manipulated input movement in
  simulations w/ measurement noise

11
Algorithm Constraints

• Input constraints are applied by clipping
• magnitude constraint estimated from physiological
  conditions
• rate constraint determined from pump literature
• Output constraint is checked a posteriori
• minimum glucose concentration 60 mg/dl
• Controller Tuning
• controller settings result from a 2-D search of
  m,p
• move horizon 2, prediction horizon 10
• setpoint tracking weighting matrix 1
• move suppression matrix 0 (noise-free)
  or 1 (noise)

12
Linear Model Predictive Control Results
110
100
Arterial Glucose
90
Concentration (mg/dL)
80
70
60
0
80
160
240
320
400
480
60
50
40
Insulin Infusion
30
(mU/min)
20
10
0
80
160
240
320
400
480
Arterial Glucose
Concentration (with noise)
Time (min)
13
Model Predictive Control with State Estimation

• Improved internal controller model
• ?,?m,C - discrete linearized form of nonlinear
  patient model
• indices use standard statistical notation
• represents the feedback signal (noise
  mismatch)
• K is the Kalman filter gain - adjustable
  parameter
• retune p, ,

14
Model Predictive Control Design(Kalman filter
tuned for meal disturbance noise)
90
85
80
75
70
0
80
160
240
320
400
480
70
60
50
40
30
20
10
0
0
80
160
240
320
400
480
Time (min)
15
Controller Comparison(setpoint tracking,
setpoint 81 mg/dl)
Arterial Glucose Concentration (mg/dl)
Time (min)
16
Controller Comparison(disturbance rejection,
setpoint 81 mg/dl)
IMC FOTD Undershoot 17.2
Arterial Glucose
Concentration (mg/dL)
Linear MPC Undershoot 11.1
MPC w/ State Estimation Undershoot 4.4
Insulin Infusion
(mU/min)
Time (min)
17
Patient Variability

• Patient differences dramatically affect
  controller performance
• Explicitly account for interpatient variability
• variables that are easy to measure
• examples sex, weight, age, race, etc.
• Effects of these variables do not map directly to
  detailed compartmental model
• Alternate method identify parameters within the
  detailed model having the greatest effect on
  blood glucose/insulin dynamics
• Perform online parameter estimation to capture
  variability online

18
Patient VariabilityModeling

• Compartmental mass balance equations
  (peripheral)
• Examine metabolic uncertainty
• Receptor (D) and post-receptor (E) defects for 3
  metabolic pathways
• EIPGU - effect of insulin on peripheral glucose
  uptake
• EGHGU - effect of glucose on hepatic glucose
  uptake
• EGHGP - effect of glucose on hepatic glucose
  production

19
Patient VariabilityParameter Estimation

• Recall linear state-space model
• Augment states with parameters to be estimated
• Parameter updated by Kalman filter based on
  deviation,
• Structured effects of parameters on model

20
Patient VariabilityTabulated Results

• EGHGP (E) selected as estimation parameter
• Sum-squared error (SSE) analyzed for 50g oral
  glucose tolerance test (meal)

21
Parameter EstimationResults
50g meal (OGTT) initiated at time 50min. EGHGP
(E) is the estimated parameter
22
Parameter EstimationResults
Week long series of 50g meals (3 daily at 0800,
1200, and 1800), coincident with a slow
parameter drift in EIPGU (E) from 0.5 to 0.75
over the first 5 days
23
Summary

• Linear MPC outperforms classical methods for
  blood glucose concentration control
• MPC with state estimation yields tighter control
  of blood glucose concentration
• more accurate model
• Kalman filter tuned for noise and mismatch
• Patient variability can be addressed
• parameter estimation for uncertainty
• multiple effects captured by a single uncertain
  parameter
• automated updating of the control algorithm over
  time

24
Future Work

• Patient uncertainty characterization from real
  data
• Robust control design (performance guarantee)
• Nonlinear MPC w/ output constrained formulation
• Reverse-engineering of the actual pancreas
  objective function

25
Acknowledgments

• Prof. Nicholas Peppas (co-advisor, Purdue
  University)
• Undergraduate Researchers
• Chad Lubrecht (University of Delaware)
• Jenny Harting (Purdue University)
• Kevin Rabinovitch (Purdue University)
• Margaret Veslocki (Purdue University)
• NSF (CTS 9257059)
• The Showalter Trust