Stochastic Insulin Sensitivity Models For Tight Glycaemic Control 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, SI. However, this parameter varies significantly as illness evolves. A 3-D stochastic model of hourly SI 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. STOCHASTIC INSULIN SENSITIVITY (SI) MODEL INTRODUCTION A targeted control algorithm that accounts for interpatient 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. x 10 P[SI n+1 | SI n] SI at hourn+1 (SI n+1) (mU/L/min) nI uex (t ) 1 I I V 6000 5000 8 4000 6 3000 4 2000 2 1000 4 6 8 SI at hour n (SI n) (mU/L/min) 10 12 -4 x 10 0 Figure 2. Fitted hourly SI variation and probability distribution function Blood Glucose Forecast Most likely blood glucose forecast Range of 90% likelihood Desirable blood glucose level Hypoglycemic region 1 ml insulin injection P [SI n+1=y | SI n=x] 3000 7000 • Hourly indentified SI 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 SI given current identified SI. • Figure 2 shows the contour of the 3-D model and the raw identified SI data. Probability distribution of coming hour’s SI 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. raw fitted SI most probable SI forecast inter-quartile probability interval 0.90 probability interval 0.95 probability interval 4000 fitted SI 10 Figure 1. Three-dimensional stochastic model of SI variability Q kQ kI I 12 2 Q Glucose G pG G S I G Ge P (t ) 1 GQ compartment Plasma insulin compartment 8000 potential SI probability distribution function GLUCOSE-INSULIN PHYSIOLOGY MODEL Interstitial insulin compartment -4 2000 1000 0 1 x 10 BEST CONTROL 2 ml insulin injection -3 0.5 SI at hour n+1 (SI n+1) (mU/L/min) 0.4 0 SI n = x 0.8 0.6 0.2 SI at hour n (SI n) (mU/L/min) 0 1 x 10 Too much insulin Hypoglycemia (blood glucose levels too low) can lead to complications and be potentially fetal!!! -3 4 ml insulin injection Figure 3. Stochstic model assist glycaemic control Time RESULTS CLINICAL VALIDATION CONCLUSIONS Table 1. Retrospective probabilistic assessment on clinical control trials Clinical control patients Measurement error Number of within inter-quartile interventions confidence interval Measurement error within 0.90 confidence interval 1 9 2 (22%) 7 (78%) 2 9 5 (56%) 7 (78%) 3 9 1 (11%) 7 (78%) 4 9 1 (11%) 6 (67%) 5 9 7 (78%) 9 (100%) 6 9 8 (89%) 8 (89%) 7 9 5 (56%) 9 (100%) 8 23 10 (43%) 19 (83%) total 86 39 (45%) 72 (84%) VIRTUAL TRIAL SIMULATIONS Clinical Trial 10 9 A 8 7 6 5 4 30 100 200 300 400 500 600 6 5C 4 3 2 1 00 100 200 300 400 500 600 Time (min) Control Inputs Blood Glucose (mmol/L) II. Simulated control trials delivers improved performance Tighter control Less hypoglycaemia occurance and better recovery Control Inputs Blood Glucose (mmol/L) I. Model is validated against retrospective data from 8 idependent clinical control trails Data match probability Intervals Max* Mean* Min* 10 measurement 9 B probabilistic fitted blood 8 prediction glucose 7 6 5 4 30 100 200 300 400 500 600 6 Insulin Input (U) 5 D Dextrose Intake (mmol) 4 3 2 1 00 100 200 300 400 500 600 Time (min) Figure 4. Clinical trial vs. simulated new control results on Patient 4 “Virtual patients” with SI defined by Table 2. Virtual trial results (per 24 hour trial) the stochastic model reflect typical Hourly BG within Hourly BG < 3 Hourly BG < 4 4-6 mmol/L (%**) mmol/L (%***) mmol/L (%***) behaviour Statistics match real clinical data Stochastic control minimise hypos Provides a platform for protocol development and future research Simulated New Control 23 (4.76%) 1 (4.35%) 10.32 (69.62%) 0.01 (0.04%) 0 (100.00%) 0 (0.00%) 5 (21.74%) 0.56 (2.41%) 0 (0.00%) • The 3-D stochastic model defines the variation of SI 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. REFERENCES Hourly BG within inter-quartile probability intervals (%***) 19 (82.61%) 10.59 (46.04%) 4 (17.39%) Hourly BG within 0.90 probability intervals (%***) 23 (100.00%) 20.21 (87.85%) 13 (56.52%) * 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 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.