Long Term Verification of Glucose-Insulin Regulatory System Model Dynamics THE 26th ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY J. Lin, J. G. Chase, G. M. Shaw, T. F. Lotz, C. E. Hann, C. V. Doran, D. S. Lee Department of Mechanical Engineering University of Canterbury Christchurch, New Zealand

Hyperglycemia in the ICU Stress-induced hyperglycemia Insulin resistance or deficiency enhanced High dextrose feeds don’t suppress glucagon release or gluconeogenesis Drug therapy Source: There is a need for validated Models to aid treatment

Physiological Model Blood Plasma The utilisation of insulin and the removal of glucose over time Liver Produces endogenous glucose (G E ) Exogenous Glucose Food intake etc. (P(t)) Exogenous Insulin Insulin injection etc. (u ex (t)) Pancreas Produces endogenous insulin I(t)I(t) GEGE P(t) G

Glucose Dynamics The ability to regulate blood glucose level Tissue sensitivity to insulin Blood Plasma The utilisation of insulin and the removal of glucose over time Saturated effect of insulin over time Q(t) time

Parameter Fitting Requirements Very low computation time required if fitting over long periods of several days or using for control High accuracy for tracking changes in time varying patient specific parameters p G and S I Physiologically realistic values of optimised parameters Convex and not starting point dependent, like the commonly used non-linear recursive least squares (NRLS) method

Parameter Values ParameterControlsValue VIVI Insulin Volume of Distribution 12 L n 1 st Order Plasma Insulin Decay 0.16 min -1 k Delay in Interstitial Transfer min -1 αGαG Insulin Receptor Saturation L∙min∙mU -1 αIαI Insulin Transport Saturation 1.7 × L∙min∙mU -1 Generic Parameters found from an extensive literature review

Integration-Based Optimization Use different values of t and t 0 to develop a number of linear equations, where p G and S I at different times are the only unknowns Approximate glucose curve between data points as linear

Error Analysis Approximate glucose curve does not compromise the fitting quality

Advantages Least squares problem (constrained) Integration based approach to fitting reduces noise Effectively low-pass filter noise with numerical integration Not starting point dependent like typical methods Convex, easily solved, single global minima

Patient Data and Methods Patients selected from retrospective study were those with glucose measurement intervals < 3 hours – 17 out of 201 patients – Good general cross-section of ICU population Details from patient charts used in the fitting process – Glucose Measurements – Insulin Infusions – Feed Details 1.4 – 12.3 days were fit to the model (average is 3.1 days) – Not always entire length of stay Resulting patient specific parameters, p G and S I, were smoothed to reduce noise, and the overall fit was compared to measured glucose data

Results – Patient 1090 Mean Error = 0.87 % Standard Deviation = 0.80 %

Results – Patient 87 Mean Error = 2.35 % Standard Deviation = 2.69 %

Absolute Error Metric Mean Absolute Error → 4.39 % – Mean Error Range across 17 patients → 1.03 – 7.62 % – Measurement Error is 3.5 – 7 % (Arkray Inc, 2001) Standard Deviation → 4.45 % – SD Range across 17 patients → % Fitting Error

“Chi-square” quantity – Value used in non-linear, recursive, least-squares fitting Expected value – (Number of Measurements – Number of Variables)  i = 4.79 % matches model across all patients – Within measurement Error of % (Arkray Inc, 2001) Fitting Error

Predictive Ability Verification Using previous 8 hours of measured data Hold p G and S I constant over the next hours Compare with measured data 1 hour predictions have an average absolute error of 2- 11% 8 hour window of modelling e G time Patient No. of predictions Average prediction error e [%] Error standard deviation [%] One hour predictions

Conclusions Minimal computation and rapid identification of time-varying parameters p G and S I using the integral-based fitting method presented Long term validation of the physiological model Accurate results and significant computational speed compared to traditional NRLS method Forward prediction error ranging 2-11% as further validation

Acknowledgements Engineers and Docs Dr Geoff Chase Dr Geoff Shaw Students Maxim Bloomfield AIC2, Kate, Carmen and Nick AIC3, Pat, Jess, and MikeThomas Lotz Maths and Stats Gurus Dr Dom Lee Dr Bob Broughton Dr Chris Hann Prof Graeme Wake Questions ? The Danes Steen Andreassen