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Long Term Verification of Glucose-Insulin Regulatory System Model Dynamics

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

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Long Term Verification of Glucose-Insulin Regulatory System Model Dynamics

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  1. 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

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

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

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

  5. 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 pG and SI • Physiologically realistic values of optimised parameters • Convex and not starting point dependent, like the commonly used non-linear recursive least squares (NRLS) method

  6. Parameter Values Generic Parameters found from an extensive literature review

  7. Integration-Based Optimization Approximate glucose curve between data points as linear Use different values of t and t0 to develop a number of linear equations, where pG and SI at different times are the only unknowns

  8. Error Analysis Approximate glucose curve does not compromise the fitting quality

  9. 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

  10. 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, pG and SI, were smoothed to reduce noise, and the overall fit was compared to measured glucose data

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

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

  13. Fitting Error • 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 → 0.93 - 9.75 %

  14. Fitting Error • “Chi-square” quantity • Value used in non-linear, recursive, least-squares fitting • Expected value • (Number of Measurements – Number of Variables) • si = 4.79 % matches model across all patients • Within measurement Error of 3.5 - 7 % (Arkray Inc, 2001)

  15. Predictive Ability Verification 8 hour window of modelling G e time • Using previous 8 hours of measured data • Hold pG and SI constant over the next hours • Compare with measured data • 1 hour predictions have an average absolute error of 2-11% One hour predictions

  16. Conclusions • Minimal computation and rapid identification of time-varying parameters pG and SI 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

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

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