1. INTEGRAL-BASED IDENTIFICATION OF A PHYSIOLOGICAL INSULIN AND GLUCOSE MODEL ON EUGLYCAEMIC CLAMP AND IVGTT TRIALS T Lotz 1, J G Chase 1, K A McAuley 2, J Lin 1, J Wong 1, C E Hann 1 and S Andreassen 3 1 Centre for Bioengineering, University of Canterbury, Christchurch, New Zealand 2 Edgar National Centre for Diabetes Research, University of Otago, Dunedin, New Zealand 3 Centre for Model-based Medical Decision Support, Aalborg University, Denmark

2. Why model glucose and insulin kinetics? Glycaemic control from critically ill to diabetic individuals –Tight glycaemic control in ICU reduces mortality by up to 45% –Type 1 and insulin dependent Type 2 diabetes growing rapidly Diagnosis of insulin resistance –Requires knowledge of glucose and insulin kinetics –Currently, diagnosis occurs ~7 years after initial occurrence Current models not physiological, difficult to identify, or do not provide high resolution in clinical validation!

3. ID - Goals 1.Physiologically accurate model identification Higher predictive power and resolution 2.Simple application in a clinical setting Simple identification without the need of complicated tests (minimal data required) Use population parameters where possible, fit critical parameters Computationally efficient

4. 2-compartment insulin kinetics model + glucose pharmacodynamics PLASMA INTERSTITIAL FLUID KIDNEYS LIVER diffusion CELLS PANCREAS nCnC nKnK nLnL nInI x·u en u ex GLUCOSE IQ

5. ID - problems 2-exponential insulin model but 8 parameters Physiological solution required Try to identify a priori as many parameters as possible Fit only the most critical parameters! Critical parameters: –Hepatic clearance n L –First pass extraction of endogenous insulin x (if enough resolution in data) –Insulin sensitivity S I –Insulin independent glucose clearance p G –Distribution volumes (if enough resolution in data)

6. A priori ID - Similarities with C-peptide PLASMA V P INTERSTITIAL FLUID V Q KIDNEYS PANCREAS nKnK nInI u en PLASMA V P INTERSTITIAL FLUID V Q KIDNEYS LIVER CELLS PANCREAS nCnC nKnK nLnL nInI x·u en Additional losses C-peptide (Van Cauter et al 1992) Insulin Equimolar secretion

7. A priori ID – insulin model Distribution volumes (V P, V Q ), transcapillary diffusion (n I ), kidney clearance (n K ) assumed to match values for C-peptide (similar molecular size, equimolar secretion) Parameters taken from well validated population model for C-peptide kinetics (Van Cauter et al. 1992) Saturation of hepatic clearance (α I ) fixed from published literature Clearance by the cells (n C ) fixed to achieve ss-concentration gradient between the compartments (I ss /Q ss =5/3) (Sjostrand et al 2005) 1 (2) key insulin parameters to be estimated, liver clearance n L (+ first pass hepatic extraction x if data available)

8. A priori ID – glucose model Glucose clearance saturation α G = 1/65 (from literature mean, validated in glycemic control trials) Equilibrium glucose concentration G E = fasting glucose level Glucose distribution volume V G = 0.19 x body weight (can be estimated if data allows) Estimate p G, S I, (V G )

9. Integral-based fitting method Convex, not starting point dependent Reduces ID to solving a set of very well known linear equations 2 steps, first insulin, then glucose Integrate insulin model between [t 0,t 1 ]: I(t) estimated by interpolating between discrete data Q(t) known from analytical solution: Inputs u(t) known (endogenous insulin estimated from C-Peptide)

10. Integral-based fitting method Repeat for different time-steps [t 0,t 1 ]... [t n-1,t n ]: known identify solve identify known

11. Integral-based fitting method ID glucose model – same approach as shown on insulin solve

12. Example of result accuracy Estimation of two parameters in insulin model, n L and x 2D error grid Identified values in 1 iteration! n L = 0.21 x= 0.3 0.3 0.21

13. Validation on clamps Euglycaemic clamp trials (N=146) V G =0.19xbw u en (t) assumed suppressed Fitting errors within measurement noise: e G =5.9±6.6% SD; e I =6.2±6.4% SD nLnL 0.1 ± 0.024 min -1 pGpG 0.01 ± 0.002 min -1 SISI 12 ± 3.8 x 10 -4 l/mU/min VPVP 4.49 ± 0.37 l VQVQ 5.6 ± 0.56 l VGVG 12.1 ± 1.07 l nKnK 0.021 ± 0.003 min -1 nInI 0.272 ± 0.028 l/min nCnC 0.032 ± 0.0004 min -1 GEGE 4.85 ± 0.59 mmol/l G(t) I(t) Q(t)

14. Validation on IVGTT Data taken from Mari (Diabetologia 1998) N=5 normal subjects 22g glucose, 2.2U insulin (5min IV infusion) Errors in area under curve: e AG =1.6%; e AI =6.7% nLnL 0.13 min -1 x0.39 pGpG 0.023 min -1 SISI 8.4 x 10 -4 l/mU/min VGVG 10.7 l VPVP 4.22 l VQVQ 4.37 l nKnK 0.06 min -1 nInI 0.22 l/min nCnC 0.033 min -1 GEGE 5.2 mmol/l I(t) Q(t) G(t)

15. Clinical validation: Dose response test at low and high dosing I(t) Q(t) G(t) 10g glucose/ 1U insulin20g glucose/ 2U insulin I(t) Q(t) G(t) nLnL 0.23 min -1 x0.34 pGpG 0.011 min -1 0.01 min -1 SISI 12.3 x 10 -4 l/mU/min16.2 x 10 -4 l/mU/min VGVG 13.6 l15.4 l VPVP 4.54 l VQVQ 5.69 l nKnK 0.06 min -1 nInI 0.28 l/min nCnC 0.033 min -1 GEGE 4.1 mmol/l4.7 mmol/l Same subject on 2 different visits

16. Conclusions Physiological insulin kinetics model Easy a-priori identification with C-peptide population model Additional fitting of key parameters (1(2) for insulin, 2(3) for glucose) Integral-based fitting method convex, accurate and not starting point dependent Great potential for use in clinical applications

17. Acknowledgements – Questions? Geoff ChaseGeoff Shaw Dominic Lee Steen Andreassen Jim Mann Kirsten McAuley Jessica LinChris HannJason Wong