Page 83 - Control Theory in Biomedical Engineering

70 Control theory in biomedical engineering

during the meal consumption periods are presented. Subsequently, the
PMM-AP control formulation is presented.

3.1 Adaptive glycemic and plasma insulin risk indexes

An adaptive glycemic risk index (GRI) is used to determine the weighting
matrix for penalizing the deviations of the controlled variables (outputs)
from their nominal set-point values (Hajizadeh et al., 2019b, c). The
GRI asymmetrically increases the set-point tracking weight when outputs
diverge from the target range. Since hypoglycemic events have serious
short-term implications, the set-point penalty increases rapidly in response
to hypoglycemic excursions and more gradually in hyperglycemic excur-
sions. A plasma insulin risk index (PIRI) is defined to manipulate the
weighting matrix for penalizing the amount of input actuation (aggressive-
ness of insulin dosing) depending on the estimated PIC, thus suppressing the
infusion rate if sufficient insulin is present in the bloodstream (Hajizadeh
et al., 2019b, c). As it is impractical to directly consider the estimates of
the PIC to define parameters of the AL-MPC due to the variability among
subjects, the normalized value of the PIC is employed, which eliminates the
dependency of the PIC estimates to a particular subject by standardizing with
the known patient-specific basal PIC value.

3.2 Plasma insulin concentration bounds

In the proposed AL-MPC, the estimated future PIC is dynamically bounded
depending on the value of the CGM measurements. For instance, if the
CGM values are elevated, the bounds on the PIC are increased to ensure
sufficient insulin is administered to regulate the glucose concentration. Fur-
thermore, the PIC bounds also constrain the search space in the optimization
problem, thus improving the computational tractability of the proposed
AL-MPC. The PIC bounds are determined based on the CGM measure-
ments as X PIC :¼ðP fasting + P meal ÞX yðÞ, where X PIC defines the lower
k
and upper bounds and a desired target for the normalized PIC through
the predicted CGM. P meal is a parameter that modifies the PIC bounds
when there is a rapid increase in CGM values. P fasting is a patient-specific
parameter that defines the controller aggressiveness/conservativeness during
the fasting period. These bounds and the reference target for the normalized
PIC are defined as a function of the CGM value, and the AL-MPC solution
should satisfy the PIC constraints while maintaining the PIC close to the
desired value. The nominal PIC bounds can be determined by multiplying