1. ABSTRACT Hyperglycaemia is prevalent in critical care, and tight control reduces mortality. Targeted glycaemic control can be achieved by frequent fitting and prediction of a modelled insulin sensitivity index, S I. However, this parameter varies significantly as illness evolves. A 3-D stochastic model of hourly S I variability is constructed using retrospective data from 18 critical care patients. The model provides a blood glucose probability distribution one hour following an intervention, enabling accurate prediction and more optimal glycaemic control. INTRODUCTION A targeted control algorithm that accounts for inter- patient variability and evolving physiological condition was previously verified clinically (Chase et al., 2005). The adaptive control approach identifies patient dynamics, particularly insulin sensitivity, to determine the best control input. Hence better understanding and modelling of patient variability in the ICU can lead to better glycaemic management. The goal of this study is to produce model-base blood glucose confidence bands to optimise glycaemic control. These bands are based on stochastic models developed from clinically observed model-based variations, and allow targeted control with user specified confidence on the glycaemic outcome. Figure 2. Fitted hourly S I variation and probability distribution function Figure 1. Three-dimensional stochastic model of S I variability Stochastic Insulin Sensitivity Models For Tight Glycaemic Control Glucose compartment Interstitial insulin compartment Plasma insulin compartment GLUCOSE-INSULIN PHYSIOLOGY MODEL STOCHASTIC INSULIN SENSITIVITY (S I ) MODEL Hourly indentified S I variation from 18 ICU patients was studied (Hann et al., 2005). The developed stochastic model shown in Figure 1 defines the conditional probability for a coming hour’s S I given current identified S I. Figure 2 shows the contour of the 3-D model and the raw identified S I data. Probability distribution of coming hour’s S I can be derived. Probabistic forcase and probability intervals for the change in blood glucose levels can be calculated, and therefore assist clinical control interventions, as demonstrated in Figure 3. RESULTS CLINICAL VALIDATION VIRTUAL TRIAL SIMULATIONS inter-quartile probability interval 0.90 probability interval 0.95 probability interval raw fitted S I most probable S I forecast Figure 3. Stochstic model assist glycaemic control Blood Glucose Forecast Time 1 ml insulin injection 2 ml insulin injection 4 ml insulin injection BEST CONTROL Too much insulin Hypoglycemia (blood glucose levels too low) can lead to complications and be potentially fetal!!! Most likely blood glucose forecast Range of 90% likelihood Desirable blood glucose level Hypoglycemic region Clinical control patients Number of interventions Measurement error within inter-quartile confidence interval Measurement error within 0.90 confidence interval 192(22%)7(78%) 295(56%)7(78%) 391(11%)7(78%) 491(11%)6(67%) 597(78%)9(100%) 698(89%)8 795(56%)9(100%) 82310(43%)19(83%) total8639(45%)72(84%) Hourly BG within 4-6 mmol/L (%**) Hourly BG < 3 mmol/L (%***) Hourly BG < 4 mmol/L (%***) Hourly BG within inter-quartile probability intervals (%***) Hourly BG within 0.90 probability intervals (%***) Max*23(4.76%)1(4.35%)5(21.74%)19(82.61%)23(100.00%) Mean*10.32(69.62%)0.01(0.04%)0.56(2.41%)10.59(46.04%)20.21(87.85%) Min*0(100.00%)0(0.00%)0 4(17.39%)13(56.52%) 0100200300400500 600 3 4 5 6 7 8 9 10 Blood Glucose (mmol/L) Clinical Trial 0100200300400500 600 3 4 5 6 7 8 9 10 Blood Glucose (mmol/L) Simulated New Control 0100200300400500 600 0 1 2 3 4 5 6 6 AB Time (min) Control Inputs 0100200300400500600 0 1 2 3 4 5 Time (min) Control Inputs Insulin Input (U) Dextrose Intake (mmol) C D measurement probabilistic prediction fitted blood glucose I.Model is validated against retrospective data from 8 idependent clinical control trails Data match probability Intervals Table 1. Retrospective probabilistic assessment on clinical control trials Table 2. Virtual trial results (per 24 hour trial) II.Simulated control trials delivers improved performance Tighter control Less hypoglycaemia occurance and better recovery Figure 4. Clinical trial vs. simulated new control results on Patient 4 CONCLUSIONS The 3-D stochastic model defines the variation of S I for critical care patients. The probability distribution of BG one hour following a known insulin and/or nutrition intervention can be determined. The probabilistic knowledge can enhance control: assists clinical control decisions. maximises the probability of achieving the desired tight control. mintaining patient safety. Realistic, validated virtual patients created from the stochastic model provide a plateform for developing new protocols. * Virtual cohort size n = 200 ** Percentage of time blood glucose levels stayed within 4-6 mmol/L once blood glucose levels had reduced to ≤6 mmol/L *** Total number of hourly blood glucose levels excluding the starting blood glucose level = 23 “Virtual patients” with S I defined by the stochastic model reflect typical behaviour Statistics match real clinical data Stochastic control minimise hypos Provides a platform for protocol development and future research REFERENCES Chase, J. G., Shaw, G. M., Lin, J., Doran, C. V., Hann, C., Lotz, T., Wake, G. C. and Broughton, B. (2005). "Targeted glycemic reduction in critical care using closed-loop control." Diabetes Technol Ther 7(2): 274-82. Hann, C. E., Chase, J. G., Lin, J., Lotz, T., Doran, C. V. and Shaw, G. M. (2005). "Integral-based parameter identification for long-term dynamic verification of a glucose-insulin system model." Comput Methods Programs Biomed 77(3): 259-70.