Page 245 - Glucose Monitoring Devices
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Results    249




                     Table 12.1 Johnson parameters of the recalibrated and synchronized
                     sensor error distribution.
                      Parameters                 Sensor error value
                      Family type                Unbounded system
                      l                          15.96
                      x                           5.471
                      d                           1.6898
                      g                           0.5444




















                  FIGURE 12.5
                  (A) Autocorrelation function of the sensor error with lag interval of 15 min. (B) Partial
                  autocorrelation function of the sensor error with lag interval of 15 min.

                  Modeling of subcutaneous sensors

                  We found that the discrepancy between sensor and reference glucose differ from
                  random noise by having substantial time-lag dependence and other nonindependent
                  identically distributed (iid) characteristics (i.e., the error is independent of previous
                  errors and drawn from the same time-independent probability distribution). The
                  components of the discrepancy are therefore modeled as follows:
                  (i) Blood-to-interstitium glucose transport described by Eq. (12.6):

                                         8
                                         > vIG     1
                                               ¼  ðIG   BGÞ
                                         >
                                            vt
                                         >
                                         <         s
                                                                                (12.6)
                                         > vG      1
                                         >
                                               ¼     ðG   IGÞ
                                         >
                                            vt    s N
                                         :
                     Here IG is the interstitial and BG is the plasma glucose concentration; s repre-
                  sents the time lag between the two fluids.
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