Closed-loop insulin control

A closed-loop artificial pancreas reads blood glucose from a continuous glucose monitor and doses insulin to keep the patient in range. Two things can go wrong: glucose climbs too high after a meal, or it drops too low. This study checks a controller against both concerns, on the true glucose signal and probabilistically under sensor noise.

The plant is the FDA-accepted UVA/Padova model of a type-1 patient over a simulated 24-hour day of three meals, with insulin absorbed subcutaneously and a continuous glucose monitor reporting readings at a noise standard deviation of 7 mg/dL. It is the Dalla Man 2007 meal-simulation model with the S2013 risk-based utilization and the average-adult parameters. Two controllers run on the same patient. One skips the lunch bolus and the other doses every meal.

The specifications

We consider 5 specifications and the two that matter for the finding are the euglycemia band, which asks glucose to stay between 70 and 180 mg/dL, and the hypoglycemia-safety check under sensor noise, which asks for at least 95% probability that glucose never drops below 70.

G (glucose > 70 & glucose < 180)              # euglycemia band
G (glucose > 54)                              # no severe hypoglycemia
G (glucose < 250)                             # bounded hyperglycemia
G ((glucose < 70) -> F[0,30] (glucose > 70))  # recovery within 30 min
P>=0.95(G (glucose > 70))                     # hypoglycemia safety under CGM noise

The euglycemia robustness is the tightest margin to either edge of the 70-to-180 band, so a positive value means the whole day stayed in range and a negative value is the worst dip, in mg/dL.

The two controllers

The missed-bolus controller lets glucose run away after the unbolused lunch, and the euglycemia band is violated at robustness -105.02 mg/dL: glucose peaks near 285. The excursion opens at minute 809 and glucose does not re-enter the band until minute 1424, nearly the end of the simulated day. The climb is high enough to break the 250 hyperglycemia ceiling too, at -35.02. The tuned controller doses every meal and holds the band at robustness +7.95, about eight milligrams of margin to the nearer edge across the whole day.

Neither controller goes low. Both clear the severe-hypoglycemia and recovery specs outright, and the probabilistic hypoglycemia-safety check holds for both under the CGM noise at probability 1.0, since neither day ever approaches 70.

Results

Run it

The study runs on CPU and writes results/glucose.json.

python experiments/glucose_control/glucose_control.py

The claims document at docs/CLAIMS.md expects the euglycemia robustness near -105 for the missed-bolus controller and near +8 for the tuned one, the excursion near [809, 1424] minutes, and both hypoglycemia probabilities near 1.0, with tolerances of 6 and 2.5 mg/dL, identical verdicts, and the probability within 0.01.