Page 294 - Glucose Monitoring Devices

Closed-loop glycemic control algorithms 301

Therefore the glycemic excursions in the undesirable high predicted glycemic
values (within the hyperglycemia and severe hyperglycemia range) and the undesir-
able low predicted glycemic values (within the hypoglycemic or severe hypoglyce-
mic range) are minimized as the zone MPC manipulates the insulin delivery to
maximize the time spent in the desired euglycemic zone. The zone MPC algorithm
reduces variations in the control input moves and can attenuate abrupt variations in
the pump activity in response to noisy glucose measurements.

Adaptive control

The glucose-insulin dynamics vary substantially over time (intrasubject variability),
which renders a single time-invariant model of the glycemic dynamics inaccurate for
controlled insulin delivery. This realization has motivated adaptive control tech-
niques that accommodate the intrasubject variability by adapting aspects of the con-
trol law computation such as the dynamic model or the controller parameters.
Recursive modeling
Adapting the glucose-insulin models employed in the design of model-based predic-
tive controllers to track the time-varying glycemic dynamics is a common feature in
adaptive MPC algorithms. The models may be adapted with each new glucose mea-
surement sample or be adapted after a predefined elapsed time period to ensure the
validity of the models. Adapting models after a specified time period may require
less computation time and can be readily implemented through the reidentification
of the model parameters. Updating the model parameters at each sampling instance
can better capture the transient dynamics and unknown disturbance effects, thus bet-
ter tracking the evolving glycemic dynamics.
A number of techniques ranging from recursive subspace-based system identifi-
cation to nonlinear recursive filtering algorithms are employed to model the glucose
measurement and infused insulin data. A commonly employed algorithm for its nu-
merical simplicity and computational tractability is developing autoregressive exog-
enous input (ARX) models or autoregressive moving average with exogenous input
(ARMAX) models with the parameters identified online through recursive least
squares [39,59]. The ARX models are linear difference equation models that char-
acterize the relationship between the current output variable and previous values
of the output and input variables. The ARX model has the form

y u
y k ¼ a 1 y k 1 a 2 y k 2 . a n y k n y þ b 1 u k 1 þ b 2 u k 2 þ . þ b n u k n u
þ g þ ε k
where the output glucose concentration y k is a linear combination of past output
, g is
measurements y k 1 . y k n y and past exogenous input variables u k 1 . u k n y
a constant disturbance, and ε is white Gaussian noise. The input variables typically
include the insulin infusion rate and the amount of carbohydrates consumed in meals
and snacks. The parameters of the ARX model to be identified include the