Page 210 - Glucose Monitoring Devices

CGM denoising by Kalman filter 213

Assessment on data
The database used for the test consists of 24 time series, taken from a larger study
[10], collected in type-1 diabetic patients using the Glucoday system (Menarini
Diagnostics, Firenze, Italy). Both MA and the new KF have been applied.
Before filtering, the time series were preprocessed through a simple causal
nonlinear procedure, aimed at reducing the amplitudes of occasional nonphysiolog-
ical spikes. In particular, each glucose sample is compared with the previous one,
and, if the absolute difference (relative to the sampling period) is higher than
the physiological limit of 4 mg/dL per minute [33], it is corrected accordingly.
This hard-bounding procedure is similar to that employed within the Minimed
CGMS device [34].
The performance of the two filtering approaches has been assessed by consid-
ering both the delay measured by index T of Eq. (10.13) and the regularity of the
filtered signal (note that the RMSE as done previously in the simulation context),
measured by the smoothness relative gain (SRG) index, defined as

ESODðyÞ ESODðb uÞ
SRG ¼ (10.14)
ESODðyÞ
where ESOD(u) denotes the energy of the second-order differences of a time series
u, a regularity index already proposed in a CGM prediction context in Ref. [14].
SRG is an index that varies between 0 and 1 and measures the relative amount of
signal regularity introduced by (low-pass) filtering.
Fig. 10.5 shows the results of the application of both MA (black dotted line) and
the new methodology (black solid line) on the same two representative real subjects
illustrated in Fig. 10.1. To better highlight the most important features coming out
from the comparison, two 6-h windows have been selected. For subject #10 (top
2
2
2
panel) b s results equal to 17.1 mg /dL , quantitatively confirming the presence of
a rather low SNR, which could be also detected by eye inspection. KF produces a
very good denoising, with T ¼ 4.6 min lower than MA (where T ¼ 7.0 min), and
SRG ¼ 0.91 higher than MA (where SRG ¼ 0.90), meaning that it is able to perform
a similar smoothing introducing less delay. For subject #8 (bottom panel), where the
SNR appears lower than in subject #10 also by eye inspection, a lower value for the
2 2 2
measurement noise variance is estimated (b s ¼ 3.5 mg /dL ). From a quantitative
point of view, KF gives a profile with SRG ¼ 0.86 and T ¼ 1.4 min, while with
MA returns SRG ¼ 0.91 and T ¼ 3.5 min. Results highlight the fact that, in subject
#8, MA clearly produces oversmoothing, while KF, thanks to the individualization
of the parameters, correctly detects a high SNR. Table 10.2 reports mean (10th and
90th percentiles) values of T and SRG calculated on the 24 subjects of the dataset.
On average, we can observe that the SRG has been reduced only by 0.03, while the
delay T introduced by KF is significantly smaller ( 35%) than MA (P <.01,
Wilcoxon rank-sum test). Interestingly, the 10th and 90th percentiles of both T
and SRG correspond to rather wide intervals, suggesting that KF, with parameters
tuned according to the statistically based criterion and according to the individual