Evaluation of a plasma Insulin Model for Glycaemic Control in Intensive Care Jennifer Dickson, Felicity Thomas, Chris Pretty, Kent Stewart, Geoffrey Shaw, J. Geoffrey Chase jennifer.dickson@canterbury.ac.nz

Motivation Hyperglycaemia is prevalent in critical care Impaired insulin production and increased insulin resistance lead to high blood glucose (BG) Average blood glucose values > 10mmol/L are not uncommon All due to the stress of the patient’s condition Exacerbated by natural positive feedback mechanisms Glycaemic control may save both lives and money Some studies suggest maintaining normo-glycaemia has a number of significant benefits Reduced mortality (up to 45% [van den Berghe, Krinsley]) and morbidity Shorter ICU stays and reduced overall costs (Savings of $1500-3000 per patient treated [van den Berghe, Krinsley]) Costly treatments & tests (mech. ventilation, transfusions, … ) are also reduced

Insulin can be used to reduce blood glucose levels Motivation Insulin can be used to reduce blood glucose levels But hypoglycaemia (very low blood glucose) is dangerous Tight Glucose Control Hypoglycaemia

Insulin can be used to reduce blood glucose levels Motivation Insulin can be used to reduce blood glucose levels But hypoglycaemia (very low blood glucose) is dangerous However: Required treatment dose is highly patient specific Current methods for dosing insulin use cohort wide sliding scales or are ad hoc, often resulting in poor control and hypoglycaemia Tight Glucose Control Hypoglycaemia Tight Glucose Control Hypoglycaemia

Motivation Model based glycaemic control for intensive care patients Model based: use mathematics to describe and predict glucose and insulin response to therapy Use statistics to predict future blood glucose outcomes Quantify and manage the risk of hypoglycaemia Blood Glucose Too high = bad Target range 95th BG 5th BG LIKELY BG OUTCOME RANGE Too low = bad Time Time now Time next

Motivation Model based glycaemic control for intensive care patients Model based: use mathematics to describe and predict glucose and insulin response to therapy Use statistics to predict future blood glucose outcomes Quantify and manage the risk of hypoglycaemia Aim: Balance the risks and benefits of tight glycaemic control Tight Glucose Control Hypoglycaemia

Model-Based Glycaemic Control Effective Model-Based Glycaemic Control must: Have a good model Sufficiently describing key physiology, mechanisms, and pathways Mathematically identifiable using common clinical measures Clinically identifiable and useful Physiologically accurate Approximations and assumptions Requires dense and detailed measurements

Objectives Aim: evaluate performance of a glucose-insulin model Model based off the minimal model (Bergman et al) Required measurements: blood glucose concentrations Methods: Using plasma Insulin measurements from another study Evaluate dynamic and steady state performance of insulin kinetic model

ICING model Equations Endogenous and Exogenous Insulin Liver Production Parenteral Nutrition Enteral Nutrition Cellular degradation Liver and kidney clearance Kidney clearance Central Nervous System

Sepsis Study Patient Cohort 19 patients enrolled in a prospective clinical trial studying sepsis Age≥ 16 years Expected Survival ≥ 72 hours & expected ICU stay ≥ 48 hours Suspected Sepsis or SIRS score ≥ 3 Entry to SPRINT glycaemic control protocol Patients received insulin under the SPRINT protocol Insulin boluses and nutrition modulation to target 4 – 7 mmol/L N 19 Age (years) 68 [57-75] Gender (M/F) 10/9 APACHE II score 22.0 [18.3-26.8] Confirmed Sepsis 79% Hospital mortality (L/D) (13/6) Diagnosed T2DM 3

Study Protocol Two sets of samples (4 blood samples each): Sample Set 1: At commencement of SPRINT Protocol Sample Set 2: when patient consistently met <2 of SIRS criteria t = 0 Insulin Bolus Blood Samples t = -1 t = 10 t = 40 t = 60min

Analysis of Model Accuracy Two errors analysed Vertical Error: Direct difference with model solution Perpendicular Error: Takes into consideration timing errors

Liver and kidney clearance ICING model Equations Cellular degradation Liver and kidney clearance To test sensitivity of insulin dynamics to clearance parameter values: nL, nK, nI and nC were multiplied by a constant, ξ ξ allowed to range between 0.1 and 3.0 to find minimum perpendicular and vertical error

Time since TGC onset [hrs] C-peptide concentration [pmol/L] Results Time since TGC onset [hrs] Insulin [mU/L] C-peptide concentration [pmol/L] Sample set 1 - 24.0 [10.4 – 52.7] 2050 [993 – 2770] Sample set 2 84 [77-142] 20.9 [7.9 – 42.9] 758[487 – 1052] All 20.9 [8.6 – 51.4] 1270 [558 – 2345] C-peptide concentration significantly higher in Sample Set 2 (p<<0.001) Either insulin secretion was higher Or kidney C-peptide (but not insulin) clearance was lowered

Results Insulin kinetics of model likely slower than reality Huge variability between patients and sample sets ICING model kinetics fall within what might be clinically observed

Analysis of Model Accuracy Model fit to insulin assay data for different insulin clearance parameters. Data is Median [IQR]. ξ=1.0 Minimum error RMS Vertical error [mU/L] Perpendicular error ξ Vertical error Sample set 1 202 [116.2 – 454.3] 24.8 [18.9 – 71.7] 2.4 [1.1 – 2.7] 158.6 [64.6 –318.9] 16.0 [11.7 – 31.2] Sample set 2 87.4 [101.1 -128.3] 18.6 [13.7 – 33.2] 1.8 [1.3 – 2.3] 62.1 [29.6 – 128.6] 11.3 [ 4.7 – 18.0] All 123.7 [89.2 – 234.7] 22.7 [15.4 – 37.9] 2.1 [1.3 – 2.7] 97.1 [43.5 – 192.5] 13.3 [9.3 – 19.8] ξ > 1 suggests that insulin clearance is higher than modelled Insulin clearance is on average faster in the first sample set (septic) than the second (SIRS score <2) In septic patients (at least) one or more insulin clearance dynamics is significantly faster than currently modelled

Analysis of Model Accuracy Model fit to insulin assay data for different insulin clearance parameters. Data is Median [IQR]. ξ=1.0 Minimum error RMS Vertical error [mU/L] Perpendicular error ξ Vertical error Sample set 1 202 [116.2 – 454.3] 24.8 [18.9 – 71.7] 2.4 [1.1 – 2.7] 158.6 [64.6 –318.9] 16.0 [11.7 – 31.2] Sample set 2 87.4 [101.1 -128.3] 18.6 [13.7 – 33.2] 1.8 [1.3 – 2.3] 62.1 [29.6 – 128.6] 11.3 [ 4.7 – 18.0] All 123.7 [89.2 – 234.7] 22.7 [15.4 – 37.9] 2.1 [1.3 – 2.7] 97.1 [43.5 – 192.5] 13.3 [9.3 – 19.8] Insulin clearance is on average higher in the first sample set (septic) than the second (SIRS score <2) Higher inter-patient variability in Sample Set 1 (septic) Better model fit in Sample set 2 (SIRS score <2) When patients are most ill they are most variable!

Analysis of Model Accuracy Perpendicular error: Scale of X axis makes a difference (here in min) But: much lower perpendicular error means slight changes/mismatches in timing significantly affect model error 62 11

Results Sampling regime did not optimally capture dynamics:  5, 10, 20 and 60 minutes would have more clearly shown insulin clearance dynamics

Discussion Original model formulation: Grid search for clearance parameters over likely physiological range Aim: minimise blood glucose fitting error Blood glucose measurements less frequent (~ every 2 – 3 hours) Thus original model formulation better suited for long term dynamics than short term dynamics Insulin clearance could thus be faster than currently modelled BUT: It seems clearance depends on patient condition

Conclusions Modelled insulin dynamics fall within what is clinically observed High inter-patient variability in clearance dynamics In generally insulin clearances should be faster than currently modelled in this cohort Insulin clearance seems to be higher when a patient is septic Septic cohort only one of several ICU cohorts, the model needs to adequately capture a wide cohort Future work: Analyse model insulin fit in other ICU cohorts Is the faster Insulin clearance dynamics a function of sepsis only?

Acknowledgements Felicity Thomas Kent Stewart Dr Chris Pretty Dr Geoff Shaw Prof. Geoff Chase

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