Page 187 - Glucose Monitoring Devices

The Bayesian approach applied to the calibration problem 189

Step 4: parameter update
At each iteration k, the parameter vector p is updated to a new set of values, p kþ1 ,
k
using the NeldereMead simplex algorithm, as described in Ref. [51].
Steps 1e4 are reiterated until one of the following stopping criteria occurs:
6
(i) the step size in parameters update is smaller than a fixed tolerance (e.g., 10 );
(ii) the relative change in the value of the objective function is lower than a fixed
6
tolerance (e.g., 10 ); (iii) the algorithm reaches the maximum number of iterations
4
(e.g., 10 ).
Calibration of the current signal
For each of the M SMBG samples used for calibration, the parameter vector b p,
estimated from Eq. (9.21) by following the five-step procedure described earlier,
is used to calibrate in real time the electrical current signal y I ðtÞ, by inverting the
model of Eq. (9.15):

y I ðtÞ
zðt; b pÞ¼ b b (9.28)
sðt; b s 2 ; b s 3 Þ
In particular, as the SMBG samples are acquired at times ti; i ¼ 1; 2; :::; M,
the parameter estimated at the ith calibration is used to calibrate the current signal
from ti þ 5to ti þ 1 þ 5 min. Indeed, the deconvolution window L is defined to
end 5 min after the reference time of the BG measurement (to avoid edge effects),
thus introducing the need to wait 5 min from any ti before starting a new calibration.

Example of implementation
The algorithm presented in Section Description of a Bayesian calibration algorithm
is here applied to a set of data acquired by the Dexcom G4 Platinum (DG4P) CGM
sensor (Dexcom Inc., San Diego, CA).
Dataset description
Data were collected during a multicenter pivotal study involving 72 diabetic patients
(60 subjects with T1D, 12 subjects with T2D) wearing the DG4P sensor for a 7-day
period [52]. In total, a pool of 108 datasets was available (36 subjects wore two
sensors), each one including the raw electrical current signal and the CGM profile
(mg/dL) originally calibrated by the manufacturer using SMBG measurements
(mg/dL)dalso available in the datasets. In addition, on days 1, 4 and 7, subjects
underwent 12-h clinical sessions during which their BG concentration was moni-
tored, every 15 min, by a reliable laboratory method, the Yellow Springs Instruments
Glucose Analyzer (YSI, Yellow Spring, OH).
An example of the dataset is reported in Fig. 9.8, where the top panel shows the
current signal and the SMBG samples used by the manufacturer for calibration,
whereas the bottom panel represents the correspondent CGM profile and YSI refer-
ences used for accuracy assessment.