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.