(322d) Multi-Parametric Model Predictive Control Algorithm for Insulin Delivery Using Clinical Factors

Type 1 diabetes mellitus (T1DM)
affects two million people in the United States [1]. The Diabetes Control and
Complications Trial concluded that intensive insulin therapy was the best way
to reduce diabetic complications such as blindness and amputations [2].
Effective therapy requires more than ten manual glucose measurements each day;
such vigilance is burdensome to people with T1DM, and thus even if diabetic
complications are reduced, this therapy does not constitute normal, healthy
life, by definition [3].

Closed-loop insulin delivery
could result in vast improvements in the quality of life of people with T1DM.
With the advent of continuous subcutaneous (SC) glucose sensors and insulin
pumps, closed-loop therapy should be possible, as systems combining hardware
and software are becoming available [4]. An important challenge now is the
development of a safe, reliable control algorithm [5].

The lag times of 1?2 h peak
concentration and action associated with subcutaneous insulin delivery
necessitate predictive control [6]. Additionally, a model-based controller
allows further transparency because the model parameters then relate to
physiological characteristics. Model Predictive Control (MPC) is therefore
considered the ideal framework [7, 8, 9]. Because an ?artificial pancreas?
would have less computational power than a desktop computer, a practical
solution to avoid both excessive online optimization and optimization failure
is required. The reformulation of MPC as a multi-parametric programming problem
allows offline optimization and thus both minimal online optimization and a
guarantee of online stability [10]. Prior work in the field using
multi-parametric MPC (mpMPC) has been limited to intravenous insulin delivery
algorithms [11]. This work extends the application to subcutaneous insulin
delivery algorithms, using a dynamic model to guarantee offset elimination.

Studies have attempted to model
the effects of orally ingested carbohydrate (CHO) and subcutaneously
administered insulin on plasma glucose concentrations [12, 13]. The procedures
required to develop these models are too arduous to be practical on an
individual basis, so less intensive protocols are required in practice. In
order to avoid identifiability problems associated with simultaneous excitation
of two inputs, an open-loop protocol consisting of two impulse response tests
was implemented. Two models, each with three parameters were developed to
identify parameters for second order transfer function models; these models
were converted into state-space models for the mpMPC control algorithm.

Due to the difficulties in
identifying a reliable dynamic model, additional safety constraints should be
considered. Modern clinical therapy considers the effects of previously
delivered insulin, so-called insulin-on-board (IOB) using
pharmacokinetic models [14]. The IOB was included in a safety constraint used
to prevent excess insulin delivery [15]. This safety constraint was included in
the mpMPC algorithm for an optimal formulation.

Ten adult subjects from the
UVa/Padova simulator [16] were the virtual cohort for the simulation study. The
open-loop protocol included impulse response tests using a mixed meal (25 g
CHO) and a subcutaneous insulin bolus (1 U) over 12 hours. The closed-loop
protocol included three unannounced meals of up to 100 g CHO over 24 hours.
Robustness was analyzed in the closed-loop simulations by perturbations in the
control law parameters of up to 25%. The mpMPC formulation included output
additive disturbance which eliminated offset in the case of intra-subject
changes in insulin sensitivity.

The models developed accurately
characterized the input-output data (coefficient of variation, R²>90%)
and the impulse response tests and the form of the models were suitable for
uniquely identifying parameters. These models provided adequate information for
mpMPC algorithm to be effective, with the Average Daily Risk Rating [17]
qualified as ?low'. The mpMPC formulation allowed an optimal, constrained
formulation to be implemented at minimal online computational cost. This
algorithm will be implemented clinically in the future studies.

This work was supported by the
Juvenile Diabetes Research Foundation (JDRF) grant 22-2007-1115, and the
Institute for Collaborative Biotechnologies ICB.

Correspondence to:

Department of Chemical
Engineering, University of California, Santa Barbara, Santa Barbara, CA
93106-5080

frank.doyle@icb.ucsb.edu

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