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. 2012 Nov 1;6(6):1401-12.
doi: 10.1177/193229681200600621.

Use of a Food and Drug Administration-Approved Type 1 Diabetes Mellitus Simulator to Evaluate and Optimize a Proportional-Integral-Derivative Controller

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Use of a Food and Drug Administration-Approved Type 1 Diabetes Mellitus Simulator to Evaluate and Optimize a Proportional-Integral-Derivative Controller

Srinivas Laxminarayan et al. J Diabetes Sci Technol. .
Free PMC article

Abstract

Background: Clinical studies have shown that the Medtronic proportional-integral-derivative (PID) control with insulin feedback (IFB) provides stable 24 h glucose control, but with high postprandial glucose. We coupled this algorithm to a Food and Drug Administration-approved type 1 diabetes mellitus simulator to determine whether a proportional-derivative controller with preprogrammed basal rates (PDBASAL) would have better performance.

Methods: We performed simulation studies on 10 adult subjects to (1) obtain the basal profiles for the PDBASAL controller; (2) define the pharmacokinetic/pharmacodynamic profile used to effect IFB, (3) optimize the PID and PDBASAL control parameters, (4) evaluate improvements obtained with IFB, and (5) develop a method to simulate changes in insulin sensitivity and assess the ability of each algorithm to respond to such changes.

Results: PDBASAL control significantly reduced peak postprandial glucose [252 (standard error = 11) versus 279 (14) mg/dl; p < .001] and increased nadir glucose [102 (3) versus 92 (3) mg/dl; p < .001] compared with PID control (both implemented with IFB). However, with PDBASAL control, fasting glucose remained elevated following a 30% decrease in insulin sensitivity [156 (6) mg/dl; different from the target of 110 mg/dl; p < .001] and remained below target following a 30% increase in insulin sensitivity [84 (2) mg/dl; p < .001]. In both cases, PID control returned glucose levels to target.

Conclusions: PDBASAL provides better postprandial glucose control than PID but is not appropriate for subjects whose basal requirements change with insulin sensitivity. Simulations used to compare different control strategies should assess this variability.

Figures

Figure 1
Figure 1
Simulated meal response with (green curve, open squares) and without (blue curve, asterisks) an optimal meal bolus. Plot shows means (standard errors) of the glucose response of the 10 subjects. Meal simulations were performed with basal rates calculated to maintain glucose at target in the absence of a meal (black line, open circles). The optimal meal bolus was calculated to yield nadir BG ≥ 70 mg/dl for each subject
Figure 2
Figure 2
PK/PD responses of the 10 simulated subjects after 0.2 U/kg insulin bolus. The left axis represents means (standard errors) of plasma insulin PKs (asterisks) and the corresponding PK model fit (solid curve). The peak response time was 50 (3) min. The right axis represents means (standard errors) of glucose infusion rates (circles) and the corresponding PD model fit (dashed curve). The peak response time was 130 (10) min
Figure 3
Figure 3
Postprandial glucose control with gain (KP; U/h per mg/dl) set in proportion to each subject’s daily insulin requirement, via a GF. For (A) PID control and (B) PDBASAL control, blue thin solid curves show response obtained at optimal settings (optimal GF) and red dashed curves show worst case subject at the upper region of safe control (maximum GF). For PDBASAL control, the green thick solid curve shows the response at the lower region of safe control (minimum GF). For PID control, no GF prevented BG from remaining above 180 mg/dl for longer than 4 h and nadir BG from falling below 70 mg/dl
Figure 4
Figure 4
Glucose response to a 100 g meal given at 07:00 h: (A) comparison of PID and PDBASAL control without IFB and (B) comparison of PID and PDBASAL control with IFB
Figure 5
Figure 5
Hyperglycemic rebound with existing integrator windup protection rules (blue solid curve, worst case subject 7) compared with rebound obtained with modified rules (see text). Hypoglycemia was avoided with the modified rules (nadir BG 57 versus 61 mg/dl, unmodified versus modified). Responses included a meal (100 g at 07:00 h) and a 30% increase in insulin sensitivity during night (starting at 22:00 h)
Figure 6
Figure 6
Controller responses to ±30% changes in subjects’ insulin sensitivity at 22:00 h on the first night: (A) PID control and (B) PDBASAL control. Simulation time > 4 days (114 h)
Figure 7
Figure 7
University of Virginia simulator coupled with the Medtronic PID controller. The UVA simulator generates plasma glucose, referred to as BG in the present report, and interstitial glucose (ISFG) as outputs. ISFG is sampled every minute and filtered with an order-7 finite impulse response filter to obtain sensor glucose (SG). The derivative of SG is obtained by filtering ISFG with an order-15 Savitzky–Golay filter. Calculations are shown as a function of the discrete variable z. Integrator windup protection (IWP) limits the integral component to be between 0 and IMAX. PID output is modified by feedback of model-predicted plasma (Îp) and subcutaneous (ÎSC) insulin concentrations

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