Glucose Difference Between a Fingerstick and Dexcom Reading

Biosensors (Basel). 2018 Dec; eight(4): 93.

Differences Between Flash Glucose Monitor and Fingerprick Measurements

Heidi Marie Umbach Hansen

^twoPrediktor Medical, 1630 Gamle Fredrikstad, Norway; on.rotkiderp@idieh

Sverre Christian Christiansen

³Department of Clinical and Molecular Medicine, NTNU, 7491 Trondheim, Norway; on.untn@nesnaitsirhc.errevs (Southward.C.C.); on.untn@neslrac.nevs (S.Grand.C.)

^ivDepartment of Endocrinology, St. Olavs University Hospital, 7491 Trondheim, Norway

Sven Magnus Carlsen

³Section of Clinical and Molecular Medicine, NTNU, 7491 Trondheim, Norway; on.untn@nesnaitsirhc.errevs (Southward.C.C.); on.untn@neslrac.nevs (S.M.C.)

^fourDepartment of Endocrinology, St. Olavs University Hospital, 7491 Trondheim, Norway

Received 2018 Aug 27; Accepted 2018 October 15.

Abstruse

Freestyle Libre (FL) is a factory calibrated Wink Glucose Monitor (FGM). We investigated Mean Absolute Relative Departure (MARD) between Self Monitoring of Blood Glucose (SMBG) and FL measurements in the first day of sensor wear in 39 subjects with Type 1 diabetes. The overall MARD was 12.3%, while the private MARDs ranged from four% to 25%. Five participants had a MARD ≥ xx%. We estimated bias and lag between the FL and SMBG measurements. The estimated biases range from −1.8 mmol/L to 1.4 mmol/L, and lags range from two min to 24 min. Bias is identified equally a main crusade of poor individual MARDs. The biases seem to persist in days ii–7 of sensor usage. All cases of MARD ≥ 20% in the showtime day are eliminated past bias correction, and overall MARD is reduced from 12.3% to 9.2%, indicating that calculation back up for voluntary user-supplied bias correction in the FL could improve its operation.

Keywords: blood glucose, measurement, fault analysis, continuous glucose monitor, flash glucose monitor, self monitoring of blood glucose

1. Introduction

People with diabetes need to command their claret glucose level to exist equally close equally possible to the normal range, in society to avoid acute and chronic consequences of the disease. Continuous glucose monitoring (CGM) is an important tool for people with diabetes, primarily to detect potentially unsafe blood glucose levels and to assist in insulin bolusing. Secondarily, CGMs assistance patients with diabetes to sympathise the dynamics of their blood glucose levels, due east.one thousand. learning which foods give what glucose responses, which activities or situations trigger glucose fluctuation, or how their glucose level varies overnight. CGMs are and so-chosen minimally invasive glucose measurement devices, meaning that they have a small electrochemical sensor inserted under the skin for the duration of the sensor clothing, which at present is between seven and 14 days [i].

Due to the diffusion time of glucose from the capillaries to the subcutaneous interstitial fluid and diffusion across sensor membranes, CGM measurements are delayed compared to glucose measured in blood [ii,iii,iv,5]. Consequently, CGM systems have a disadvantage compared to direct blood glucose measurements, and lag is a known upshot with nowadays CGM systems that users demand to be aware of. Nevertheless, recent CGM systems provide accurate results despite this lag, achieving Mean Accented Relative Divergence (MARD) of below 10% when comparing against blood glucose measurements [vi].

A recent addition to the family unit of glucose monitoring devices is the Flash Glucose Monitor (FGM) [7], of which there is currently only one system on the marketplace—Abbott's Freestyle Libre (FL) [8]. The FL uses the same minimally invasive electrochemical sensing principle as conventional CGMs. A main difference between FGM and conventional CGM is in its usage; FL but provides a reading when the user scans the sensor using a hand held scanner device or a About Field Communication (NFC) enabled smart phone. The current glucose level forth with historic glucose data for the last eight h is displayed on the scanner/smart telephone. A consequence of this user-initiated information transfer betwixt sensor and brandish unit is that the FL cannot provide alarm functionality, like CGMs practise. Although the common usage blueprint of FGM is different from CGM, in parts of this paper nosotros treat the FGM data as if it is from a CGM, since the measurement principle is common betwixt the systems, and our FGM data are oftentimes sampled.

CGMs have until recently required calibration against finger capillary blood measurements provided by Self Monitoring of Blood Glucose (SMBG) meters. Calibration is usually performed twice daily, and is intended to gainsay drift and minimize bias. However, the user supplied calibration values may also impair the overall accuracy of the system, e.m., if the user does non input the SMBG values correctly, the calibration is performed in periods of high glucose variation, or if the SMBG measurements are not correct. Calibration of CGMs is discussed in item by Acciaroli et al. [9].

The FL is manufactory calibrated, meaning that the user does non need to calibrate information technology with SMBG measurements during the sensor wearable. This is marketed as a profound comeback in the world of CGMs, and is probable responsible for a great deal of the popularity of the FL system, since the twice-daily SMBG calibration of near of its current CGM competitors is a brunt to the users. However, the FL does not provide a means to bias-correct the measurements fifty-fifty if the user wants to. The FL has a congenital-in SMBG meter in the scanning device that would easily enable bias correction, but according to Bailey et al. [vii], the built-in SMBG reader of the FL has no influence on the FGM readings. DexCom G6 is another calibration-free organization that has recently been launched.

The introduction of calibration-free systems like FL eliminates the hazard of failed calibration due to user error, but it comes with a price: it eliminates a machinery that can reduce or ideally remove an inherent sensor bias due to either inaccurate factory scale or some sensor-person interaction effect.

CGM/FGM data are useful for research purposes. For some uses information technology is of import to place the a model of the fault in the datax. This has been done for conventional CGM systems by Facchinetti et al. [x]. The introduction of factory calibration means that a different model needs to be applied for systems similar the FL. Label experiments like the one reported in this paper are needed to accomplish this. Beingness familiar with the characteristics of FGM signals and whatever limitations or challenges related to factory calibration is also important to patients and health care professionals.

In this paper we investigate the accurateness of FL measurements compared to SMBG measurements, and we investigate in detail the characteristics of the errors in the FL information, focusing on biases and lags in the FL glucose estimates. This has previously been requested by other researchers [eleven].

The current paper expands upon piece of work presented orally at the Advanced Technologies & Treatments for Diabetes (ATTD) conference in Vienna, Feb 2018.

2. Method

ii.1. Data Drove

In a written report of 39 individuals with Blazon ane diabetes, simultaneous SMBG (Freestyle Liberty Low-cal, Abbott) and FGM (Freestyle Libre, Abbott) measurements were taken every 10 min. These sessions lasted from 2.5–6 h and were performed in a research ward within 24 h of FL sensor insertion and activation.

In these sessions the participants were non-fasting and used their regular insulin regime and sugary drinks or meals to manipulate their glucose level. The nerveless glucose responses typically had iii flanks (i.e., upwards/down/up, or downwardly/upward/downward) with approx. five mmol/L every bit the lower turning indicate and approx. ten mmol/L as the upper turning point, respectively. The overall range of glucose in our dataset as measured by SMBG was three mmol/Fifty to 26 mmol/L. Four representative examples of the SMBG and FGM data resulting from these sessions are shown in Figure ane.

Examples of Flash Glucose Monitor (FGM) and Self Monitoring of Claret Glucose (SMBG) recordings in our study. Top left: Depression Mean Accented Relative Difference (MARD). Top right: Large positive bias. Lesser left: Large negative bias. Bottom right: Big lag. Points are measurements, and the line betwixt points is the result of smoothing, as described by Staal et al. [12].

Afterward the frequent-sampling session, the participants went on to utilize the sensor in their everyday surround for days 2–7 after insertion, performing sporadic SMBG measurements and scanning the FL at least every eight hours. Of the 39 sensors, 11 were dislodged before the seven days had passed. Data from these sensors were included in the assay, implying that for these participants, the data from days 2–7 are incomplete.

All participants signed consent forms prior to the report. The study was approved past the Regional Ideals Committee (REK Midt 2016/1172). The participant demographics is given in Table 1.

Tabular array 1

Participant demographics, mean (range).

Sexual activity	14 female, 25 male person
Age	42 (18–72) years
Elapsing of diabetes	23 (3–45) years
Trunk Mass Index (BMI)	27 (21–38) k g/m 2

The paired FL and SMBG measurements are included in the supplementary information. The demographics data are non made publicly available, since they may enable identification of the study participants.

ii.ii. Information Analysis

Looking at the initial session (solar day 1) data, the MARD betwixt corresponding FL scanned values (y F Thou M) and SMBG data points (y S K B G) was computed, both on an overall level and on a per individual level (M A R D p).

M A R D = 1 North a l l ∑ i = 1 Due north a l l | y i F Thousand M − y i S M B G | y i S M B G

(one)

One thousand A R D p = one N p ∑ i = i p i p + N p | y i F G Thou − y i Southward Thousand B G | y i S M B Chiliad

(2)

here N a 50 l is the overall number of paired points in our report. i p is the get-go measurement from participant p and Northward p are the number of paired points for participant p.

A Parkes/Consensus error grid (PEG) analysis [xiii] was performed on an overall level, using all paired points.

The data from all runs were plotted to investigate the characteristics and reason for high MARDs, and information technology was seen that bias and lag effects were present in the data. Therefore, an estimator based on a Rauch-Tung-Striebel Kalman smoother [12,fourteen,15] was implemented to approximate the bias and lag from the data, using the following dynamic model of the FGM measurements:

Hither, G p is plasma glucose, M i is interstitial fluid glucose, and τ i is a time constant governing the diffusion between these compartments. This time abiding also models any diffusion dynamics across the FGM sensor membranes. The procedure noise is modeled by v ( t ). Furthermore, y F G 1000 , k is the FGM measurement at time step k, b F One thousand M is a bias abiding, and w thou is the measurement noise process. The parameters b F Yard M and τ i were estimated per individual data set using the Kalman smoother and the higher up model, using the same noise modeling as Staal et al. [12]. The give-and-take "lag" is sometimes interpreted as a pure time delay, or a combination of a pure time delay and a time constant [16], but in this paper we utilize lag as a synonym for the time constant.

Nosotros investigated the issue on MARD of correcting the 24-hour interval 1 information for only bias, only lag, and both. The bias correction was done simply by subtracting the estimated bias b F G M per participant from all measurements y i F G Thousand from that participant, producing y F G M , B c o r r. The lag correction is more complicated, and tin be done in different ways [17,18]. We used Equations (3) and (four) in a Kalman smoother that use the participant lag, bias and FGM data to produce lag- and bias-corrected FGM measurements, y F G Chiliad , B L c o r r. By not providing the bias to the smoother we tin produce an but lag-corrected signal, y F G Thou , L c o r r, to investigate the result on MARD of merely correcting for lag. By providing neither bias nor lag information, we can produce an uncorrected signal y F G 1000 , south chiliad o o t h eastward d that has been subjected to all the processing of our method simply has not really corrected for anything. This latter signal was used to get an idea of how much MARD is influenced by the smoothing introduced past our method. Both Kalman smoothers described above for parameter estimation and state estimation are working in fixed interval mode, i.eastward., they use all data in the information gear up, thus this is an offline method. A detailed clarification of the state estimation Kalman filter is provided in Appendix A.

The bias and lag estimates computed by the Kalman smoother are accurate considering of the many points used. Basing a real-fourth dimension bias estimation on this method is non practical due to the many SMBG measurements required. In a practical bias calibration, just one or two information points per day should be used, as in normal CGM calibration regimes. Nosotros therefore likewise computed a ane-indicate bias correction, finding a bias b F G M , i p based on the error in the first paired data betoken from each twenty-four hour period 1 session. Correcting for this bias produces a betoken y F G K , B c o r r 1 p. Nosotros as well computed a ii-indicate bias b F 1000 M , 2 p based on the mean of the errors in the kickoff and final paired signal from each session, producing the point y F Grand Thousand , B c o r r 2 p. The dissimilar biases were used to correct data from 24-hour interval i and days ii–7. A block diagram providing an overview of the method we employed is shown in Figure 2.

An overview of the point processing. Items in blue are individual parameters estimated from day i data, and used to right both mean solar day 1 and days 2–vii information for that private. The parameters and signals shown are described in the main text, Section 2.two.

To investigate whether the biases seen in the first day of use persisted throughout the use of the sensor, we performed an assay of the data from days ii–vii. Participants were grouped based on the bias they had in the first day. Individuals experiencing more than one mmol/L bias in day 1 were assigned to the positive bias grouping. Those that had less than −1 mmol/Fifty bias were assigned to the negative bias group. The remaining participants were assigned to the unbiased group. The data were plotted based on this grouping, and the hateful and standard deviation was computed in each group, for both day 1 and day 2–7 data. A t-test was performed to determine if the grouped means in days 2–7 were significantly different from the unbiased group. We besides used a t-test to determine if the group ways changed from twenty-four hours one to days 2–7. A like analysis for the lag was not possible, due to the sparsity of data in days 2–7.

Finally, we checked if participant characteristics were associated with the observed biases and lags. We investigated BMI, height, weight, age, sexual activity, duration of diabetes, use of blood pressure medication, utilise of any other medication and whether or non the sensor fell off during days two–7. For binary variables (sex, medication use, sensor fall-off) we used a t-exam at p = 0.05 to test if there was a divergence in the hateful between groups. For continuous variables we performed a linear fit and estimated the 95% conviction interval (CI) of the correlation coefficient. If this CI spanned 0, the correlation was considered insignificant.

As reported by Pleus et al. [19], the FL generates ii fourth dimension series of glucose estimates that are bachelor in its export file. Scanned glucose is the instantaneous glucose the sensor estimates at the time when the sensor is scanned. Historic glucose is generated past the sensor every 15 min independently of the scanning. Up to eight h of historic data are stored in the sensor and transferred to the display unit as function of a browse. We used the scanned glucose values in the analysis of the high-frequency sampling session (solar day 1), since SMBG measurements and FGM scans were performed simultaneously in this session. In the analysis of days 2–vii, we used historic glucose values since there were too few occurrences of concurrent FL scans and SMBG measurements during the normal use in an everyday environment. The historic glucose values were interpolated equally described by Staal et al. [12] to enable matching with the SMBG measurements.

3. Results

3.1. Overall MARD Analysis in Twenty-four hours 1 Data

At that place were 1053 paired measurements from the frequent-sampling sessions in day i, having an overall MARD of 12.iii%. A Parkes/Consensus error grid (PEG) analysis found all measurements to be within zones A+B, with 81.7% in zone A. The PEG plot is shown in Effigy iii.

Parkes/Consensus Error Grid plots. Left: Uncorrected Correct: Bias corrected Bias correction per private makes 91.2% of the paired points lie in zone A.

3.two. Day 1 Individual Participant MARD, Bias and Lag Analysis

There were on average 27 paired measurements per individual. Individual participant MARDs varied between 4.0% and 25.5%. A total of 18 participants had MARD <10%, however five had MARD ≥ 20%. Biases varied between −i.eight mmol/L, and +1.4 mmol/L, with a mean of −0.4 mmol/50. Time constants ranged from ii min to 24 min, with a mean of 9 min. Histograms of individual MARDs, biases and lags on twenty-four hours ane are shown in Figure 4. The most extreme cases of bias and lag are shown as fourth dimension series in Effigy one. Other effects likewise bias and lag are seen in some sets, e.g., overestimation in periods of loftier glucose (data non shown).

Histograms from day 1. Upper left: Estimated individual biases, b F K One thousand. Upper right: Estimated individual time constants, τ i. 2nd row: private MARDs, uncorrected. Third row: individual MARDs, bias corrected. Bottom row: individual MARDs, bias and lag corrected.

If the data are corrected for the biases found, the overall MARD on 24-hour interval 1 falls significantly (p < 10 − 6) from 12.3% to nine.2%. The participant with the largest MARD (25.5%) got a MARD of half dozen.4% with bias correction. The maximal individual MARD later on bias correction is 17%. Of the 39 participants, 27 got a MARD below 10% after bias correction. For ix participants, the bias correction led to an increase in MARD, with one participant getting an increase of more than 3 percent points. The MARD subsequently bias correction is well correlated with the estimated lag; see Figure 5.

Effect of bias and lag correction. Left: Uncorrected MARD plotted confronting absolute bias. Middle left: MARD changes as a result of bias correction with individual participant tracing. Points belonging to the 12 participants whose MARD changed past more than than 3 per centum points are continued by a dotted line (blue when MARD is reduced; red when MARD is increased). Middle correct: Bias corrected MARD plotted against lag. Right: MARD changes as a result of lag correction. Regression lines are plotted in dashed black and 95% CIs in dotted black.

Compensating only for lag gave an overall MARD of xi.7%, while compensating for both bias and lag resulted in an overall MARD of 6.6%. The overall MARD, MAD and PEG zone A and A+B of uncorrected and corrected FGM data are listed in Tabular array ii. Like analyses for days 2–seven are given in Table A1 in Appendix B.

Table 2

Influence on overall MARD of different indicate processing of solar day 1 data to right for bias and lag.

Bespeak Processing	Symbol	MARD (%)	MAD (mmol/L)	PEG zone A/A+B (%)
None (raw FGM scans vs SMBG)	y F Yard M	12.3	i.0	81.7/100
Bias corrected, multipoint	y F G Yard , B c o r r	9.2	0.8	91.two/100
Bias corrected, one-point	y F Grand Yard , B c o r r 1 p	eleven.4	0.9	83.0/100
Bias corrected, 2-betoken	y F G M , B c o r r 2 p	nine.seven	0.seven	87.seven/100
Bias and lag corrected, multipoint	y F G G , B Fifty c o r r	6.6	0.5	97/100
Just lag corrected, multipoint	y F G M , L c o r r	eleven.7	0.9	81.v/100
But smoothed, multipoint	y F G Grand , s m o o t h e d	xi.nine	1.0	82.2/100

3.iii. Persistence of Biases through Days two–7

There were 356 data indicate pairs from days 2–seven, these were plotted using the negative, positive and unbiased grouping based on twenty-four hour period 1 biases, every bit described in Department 2.two. The plot is shown in Figure 6. The results of the grouped analysis of these data are given in Tabular array iii. The difference of the hateful between paired points from days two–7 from each biased group compared to the paired points from the unbiased group is meaning, judging past a t-test (p < 10 − 6). Inside each group, the difference of the mean between paired points in solar day 1 and day 2–7 changes insignificantly, except for the negative bias grouping, which has a significant change (p < 10 − 6) moving towards zip.

Persistence of bias in days two–7. The individual sensor errors (SMBG–FGM) are plotted against time and colored co-ordinate to what bias grouping the participant was in at solar day 1. If the bias observed in day 1 is not persistent, one would expect the blue and scarlet data points to kickoff mixing every bit time progresses. The solar day 1 session is included in this plot, but the analysis of bias persistence considered information from days 2–seven separately from day 1 data.

Tabular array three

Group summaries from bias persistence analysis. Hateful: Hateful of the errors [mmol/L]. SD: Standard difference of the errors [mmol/Fifty]. N: number of paired points. †: Group mean in days 2–seven is significantly different from the group mean in day 1. *: Group mean is significantly different from the unbiased group mean (days ii–7).

Group	Number of Participants	Mean ± SD (Northward) Day 1	Mean ± SD (North) Days two–7
Positive bias	iii	i.28 ± 1.03 (96)	i.35 ± 1.44 (35) *
Unbiased	28	0.09 ± 1.06 (755)	0.14 ± 1.00 (270)
Negative bias	8	− ane.45 ± 0.87 (202)	− 0.74 ± 0.73 (51) † *

3.4. Participant Factors vs. Bias and Llag

In the xviii comparisons we did to investigate correlation betwixt bias, lag and the factors listed in Section 2.2, we constitute only one correlation with p < 0.05. This was between lag and age (p = 0.046). Applying a Bonferroni correction, the p-level needed to achieve significance is 0.0027, thus this lag-historic period correlation is too considered insignificant.

4. Word

Several studies have reported an overall functioning of the FL comparable to that of other state-of-the-art CGM systems [vii,20,21,22,23,24,25,26,27,28,29]. Our main results are in line with previous observations every bit we find an overall MARD of 12.3% and one-half of the participants having a MARD at or below 10%. All the same, five of our 39 participants experienced a MARD at or above 20%. Several of the previous FL performance studies too study individual MARDs, where some are as large as nosotros observed in our report [7,22,27]. The studies past Ólafsdóttir et al. [21] and Alsaffar et al. [24] report a bias in the measurements, but on an overall level but. To the best of our knowledge, the present study is the first to written report on individual bias and lag issues equally reasons for the high variation in individual MARDs in FL.

We observe that a bias is present in several of the the worst-performing sensors, and that bias correction significantly improves MARDs, both overall and on the individual level for about participants, come across Effigy 5. We tin can speculate that either the factory scale is not authentic for these sensors, or that these biases ascend from person-sensor interaction furnishings that are non anticipated from whatever of the participant factors we investigated.

For some participants, bias correction increased MARD slightly, east.g., the participant shown in red in Figure five. There are several reasons why this may happen. Firstly, since we merely correct the bias, and not the lag, the MARD may go upwardly. Secondly, the bias is found in a way that does non try to optimize MARD. Thirdly, since only bias and lag are modeled in our method, the bias estimate may be inaccurate if other errors are present in the data. We do see effects in some of the data sets that are not explainable by only bias and lag. For example, we saw some cases of overestimation of high glucose values that looks like a gain effect. The data from participant iii shown in the upper right of Figure 1 shows this tendency. An increase in MARD after bias correction can happen in datasets where furnishings other than bias and lag are nowadays, or in datasets where the lag is large. The former could lead to inaccurate bias/lag estimation by the Kalman smoother, because the model it uses (Equations (3) and (4)) accounts for no other effects than bias and lag. The latter, large lag, may exist a cause of increased MARDs afterwards bias correction, since the MARD computation penalizes deviations from low reference values more than the same difference from high reference values. The bias correction may well pb to less alignment of the low glucose values to give better alignment of the loftier glucose values, which will increment MARD. In our investigation of participant factors we found only one barely pregnant correlation (p = 0.046) between historic period and lag, shown in Figure 5. We presume that this is a spurious correlation, firstly considering we did enough comparisons to brand it probable that one of them shows significance at p = 0.05 fifty-fifty if the underlying data are truly uncorrelated. Secondly, the negative correlation goes confronting our intuition about how tissue develops with historic period; if anything, we would await higher age to give more than delay between blood and interstitial fluid, non less.

Our study was not designed to resolve the affair of whether the biases are linked to the sensor or the individual. This is an obvious follow upwards question to the present report. Answering this question would crave a study with at least two FL sensors per person, for instance as in the study performed past Freckmann et al. [29], where each of the xx participants wore two FL sensors and two DexCom G5 sensors (DG5), and SMBG was measured every hr during 3 clinic visits. A larger betwixt-sensor discrepancy was seen in FL than in DG5, every bit measured by Precision Accented Relative Departure (PARD), and it was seen that iv of 20 participants had a PARD ≥ xv. This is supported by the biases we observed in our written report, and suggests that the biases might follow the sensor rather than the individual. Farther, we tin speculate that since DG5 is a conventional CGM which requires calibration SMBG measurements twice daily, the increased PARD of DG5 over FL could exist caused by factory calibration issues in the FL. In a written report performed by other researchers in our group [xxx], it was seen that the in vitro responses of iv different sensors had a trend to be start from each other. This consequence likewise points at the sensor as the source of the bias rather than some sensor/participant interaction event.

Insights into the factory scale procedure of FL is provided past Hoss and Budiman [31]. The FL manufactory scale is accomplished through low sensor-to-sensor variability within a sensor lot, and performing in vitro tests of a sample of sensors inside a lot to produce a factory calibration valid for all sensors of that lot. The authors country that "The manufacturing plant calibration process is based on the assumption that the in vitro sensor sensitivity predicts the in vivo sensor response". While this supposition may be truthful on an overall level where information from 10 or more sensors and individuals are pooled and averaged, it allows having significant errors on the individual level. This may exist what nosotros are observing.

A limitation of our study is that our data set did not include blood glucose measurements using lab glucose analyzers, east.1000., YSI 2300 Stat Plus. Had such data been recorded we would have been able to eliminate SMBG measurement bias as a possible cause of the FGM vs SMBG biases. Since SMBG measurement errors have been reported to not exist correlated in time [32], and SMBG measurements are not reported to exhibit biases of the magnitudes nosotros observed [33,34], we are inclined to believe that the bias is a problem with the FL measurements, not the SMBG measurements.

Effigy half dozen and Tabular array three indicate that the private biases persist in days ii–seven, notwithstanding, the negative bias group seems to exist moving towards zip. More frequent data sampling in days 2–7 from more than participants would exist needed to ostend that this is the case. To confidently answer the question of how the bias develops throughout a sensor session, bias must be accurately adamant per twenty-four hour period, requiring simultaneous interpretation of the lag, similar we did for twenty-four hours i. To reach this we would take needed several frequent sampling sessions throughout the 14-day sensor lifetime. An alternative is to minimize the influence of lag by making sure that SMBG measurements used for calibration are taken in periods of low glycemic variation, as is the recommended practise in calibration of CGMs. Our information fix contains too few such periods.

The performance of the bias correction on day 2–vii data signal no significant improvement from whatsoever of the bias correction methods we applied, see Table A1 in Appendix B. The data from day 1 in our study is unsuitable for finding an accurate bias using merely 1- or 2-point calibration, due to the lack of periods of low glycemic variation. This could be part of the reason why these corrections failed to improve MARD. However, the "best possible" multipoint bias estimated using a Kalman smoother also failed to improve MARD in days 2–vii. This could exist an indication that the bias changes over time, which seems to be the case for the negative bias grouping of participants (see Table 3). If so, a bias correction based on twenty-four hours one data would lead to over-correction in days 2–7, which seems to be the case at least for the negative bias group, encounter Figure A2 in Appendix B. The non-improving MARDs could likewise exist caused by lag in the data. Nonetheless, when nosotros tried to also right for the lag observed in day one, this did not improve MARDs in days two–7 (see Table A1), indicating that what is measured in day 1 is insufficient to right the situation in days ii–7. Another explanation could lie in the difference between "scanned" and "celebrated" glucose values in the Freestyle Libre, every bit we based the bias estimate on scanned values from 24-hour interval 1 only correct historic values in days two–7. Further research is needed to reply these questions, using more frequent SMBG sampling of data in days two–7.

Assuming that the bias and lag observed in day ane stays constant throughout the sensor lifetime seems like an invalid supposition to make. There are several physiological and technical reasons why both lag and bias may vary during the sensor lifetime, some of which are:

1. The insertion of the sensor into the interstitial fluid introduces local trauma to and/or modest bleeds in the tissue around the sensor, altering the glucose flow, thus making the sensor less accurate in the time immediately later insertion [1].

2. Biofouling of the sensor contributes to making sensor feature changes over the habiliment fourth dimension probable.

3. On the technical side, the electrochemical sensor may suffer from non-physiological drift in the initial period of sensor wear [9].

4. Effects like Pressure Induced Sensitivity Attenuation (PISA) [35] may be present in the FGM data.

In addition, SMBG measurement outliers tin can occur, which volition be difficult to detect and recoup for when there are but a few SMBG data points per person per day. Increasing the number of participants would also exist advantageous in guild to get sufficient statistical power to make a determination virtually the bias evolution with time.

Unless the manufactory scale of FL can be improved to eliminate the bias errors we observe, voluntary user-supplied bias correction would be a desirable functionality in FL for patients and researchers alike. This correction could be done as in normal CGM systems, e.chiliad., using one or ii SMBG measurements per day (but in the case of FL, they could be voluntary). Such measurements should ideally be taken at periods of low glucose variability to minimize the influence of lag on the bias correction. The evolution of the bias over the 14-twenty-four hours life of the sensor is non known, so a bias correction of the whole menses based on only one or two SMBG measurements from solar day one is not necessarily the correct thing to do. Near studies of FL functioning written report that MARDs improve over time, suggesting that biases may be decreasing over time. This seems to be the example also in our information, at least for the group of participants that had a large negative bias in twenty-four hour period 1. If so, a bias correction based merely on data from the first day of use could be detrimental to the performance of the sensor in the subsequent days, as it could give an over-correction. The all-time fashion to include a voluntary bias correction in existent-time use of the device is not clear. The methods that have been used by CGM systems for this purpose [9] are likely applicative, still these require daily scale measurements. Researchers planning to use FL in studies should consider adding mechanisms for mail-study bias correction of FL information in the study designs, for instance by including sufficient reference measurements to evaluate the bias at the outset, centre and end of the study.

Bias is emphasized in this work, since it is potentially hands corrected for in existent time. However, lag is also a significant reason for high MARDs, as seen in Effigy 5. The private MARDs remaining afterwards bias correction are well correlated with the estimated lags. Correction of the lag gives a further comeback in overall MARD, nonetheless the bias contribution to MARD dominates, and lag correction just has an event on MARD when the bias is also removed. Correction of bias has been commonplace in CGMs, through their daily calibration against SMBG measurements. Existent-time correction of lag is possible in theory, but only if the lag is a pure time abiding that does non modify significantly over time. If instead a pure time delay is present, causality prohibits real-time correction of the lag. Practically viable correction of a time constant requires quite dissonance gratuitous FGM information to avoid introducing new error by the lag correction. Lag correction also needs knowledge of the lag per participant and sensor, which requires combining FGM/CGM data with SMBG data with a similar sampling frequency every bit we used in twenty-four hours 1 of our report. This is practically unfeasible and not acceptable to most users, especially if it must be repeated for every new sensor.

Finally, it should be best-selling that most would consider CGMs with MARD values greater than twenty% unsuited for use by patients to guide them on their actual glucose levels, and fifty-fifty less and then in assisting on deciding insulin doses. Consequently, both patients and health care personnel should be informed that some of the FL sensors accept this limitation. Large positive biases as those experienced past 3 of our participants are especially problematic, since they stand for a adventure of failing to discover hypoglycemia or impending hypoglycemia. Since our analysis is based mainly on data from day 1 of the sensor wearable, which is known to be less accurate than information from subsequent days of wear, in a sense information technology represents a worst instance analysis of the Freestyle Libre performance. Information technology is still important for users and caretakers to know in what way the sensor could be inaccurate also in the first day of wear, since the FL presents glucose estimates to the user 60 min subsequently sensor insertion without whatever alarm to the user that the results are more inaccurate in day 1.

five. Conclusions

The observed overall MARD between SMBG and FL in the showtime day of apply was 12.three%. However, MARDs in individual participants ranged from 4% to 25%. Many of the high private MARD cases are caused primarily by bias. Lag and other effects are as well present. The biases seem to persist beyond mean solar day 1 of wearing the FL. The FL is factory calibrated, and manual bias correction by the user is not possible. Our information indicate that the manufacturer and some patients could benefit from introducing a voluntary calibration mechanism in the FL, which could upshot in an improved MARD for some users. This calibration should likely be based on the same kind of principles every bit those in conventional CGM systems, i.e., using SMBG measurements from periods of low glycemic variation. Researchers using the FL may gain from designing their studies to allow for an external bias correction. Patients and wellness care personnel should be informed about the risks of measurement error in FGM devices, and how these errors may manifest themselves on an private level. Further research is needed to determine if the bias follows the sensor or the patient, to investigate in more detail how the biases and lags evolve over the lifetime of the sensor, and possibly to exploit methods for detection and mitigation of biases and lags.

Acknowledgments

This research was office of the Double Intraperitoneal Artificial Pancreas project, which is a Heart for Digital Life Kingdom of norway (digitallifenorway.org) project. The project is led past the Artificial Pancreas Trondheim research grouping (apt-norway.com).

Abbreviations

The post-obit abbreviations are used in this manuscript:

MARD	Hateful Absolute Relative Difference
PARD	Precision Absolute Relative Difference
FGM	Flash Glucose Monitor
CGM	Continuous Glucose Monitor
SMBG	Self Monitoring of Blood Glucose
NFC	Almost Field Communication
FL	Freestyle Libre
DG5	DexCom G5
CI	Conviction Interval

Appendix A. Kalman Smoothing to Correct for Bias and Lag

Given an FGM signal with a known bias b F G M and a lag τ i, we would like to compute a bespeak that is corrected for both effects. We use the model of glucose dynamics given as Model 2 in the paper by Staal et al. [12], and augment it with the plasma-interstitial model given by Equations (3) and (4)), where τ i and b F K M are now fixed quantities. The overall model becomes:

where T d is a parameter describing the menses between the internal compartments C c and C r, set to ten min. v c ( t ) is procedure racket affecting state C c. For more information about the model, and choice of parameters, process and measurement noises, run across [12].

This arrangement is linear, and can be put on the form x ˙ = A ( τ i ) ten, and a discretized version of the system is x one thousand + ane = Φ x k, where Φ = e A ( τ i ) Δ t. We used Δ t = 0.5 min.

The Kalman filter equations are [15]:

Grand k = P ¯ g H T ( H P ¯ thousand H T + R k ) − ane

(A7)

x ^ chiliad = K k ( y k − b F K M − H k ten ¯ 1000 )

(A8)

hither H is a measurement matrix, Q is the process racket covariance matrix, and R is the measurement matrix. P matrices are land covariance matrices propagated past the filter. We used H = [ 0 0 0 1 ], and we subtracted the bias b F G Yard from each measurement every bit role of the Kalman filter measurement update Equation (A8). The Q matrix we used was all zero, except for the diagonal element corresponding to C c, this was gear up to 0.025. R (scalar in our case) is prepare for each measurement based on ISO 15197 limits, as described in [12].

The Rauch-Tung-Striebel (RTS) algorithm [14] makes utilise of stored data from the Kalman filter forward pass, namely the sequences of a priori and a posteriori state estimates x ¯ k, x ^ chiliad and country covariance matrices P ¯ k and P ^ k. These are input to a backward pass that computes the smoothed estimates ten ^ yard southward and P ^ k due south as follows [15]:

x ^ k s = x ^ 1000 + C 1000 ( x ^ chiliad + 1 south − 10 ¯ m + i )

(A11)

P ^ k south = P ^ 1000 + C k ( P ^ k + ane due south − P ¯ k + 1 ) C k T

(A12)

After smoothing is completed, the bias and lag corrected indicate is available as the offset element in the x ^ s signal, respective to the G p state. Examples of the consequence of the state estimation Kalman smoother is given in Effigy A1.

The smoother does not introduce any boosted delay in the smoothed signal, past virtue of its forward-backward nature.

The Matlab lawmaking of the Kalman smoother for utilize in glucose applications is publicly available, run across [12].

Figure A1

Bias and lag correction of the aforementioned data equally shown in Effigy 1. Here, only the FGM (blue) points, a bias and a lag are used as inputs to the smoother, and the black line shows the corrected signal. Red points are SMBG measurements. Nosotros come across that the bias and lag correction brings the corrected FGM point close to the SMBG measurements in all cases seen hither.

Appendix B. MARD Analysis of Day ii–vii Information Using Different Bias Correction Approaches

Table A1

Influence on overall MARD of different point processing for days ii–7, using biases and lags estimated from twenty-four hour period i data.

Signal Processing	Symbol	MARD (%)	MAD (mmol/L)	PEG zone A/A+B (%)
None (FGM historic information vs SMBG)	y F G M	11.3	0.8	87.three/99.two
Bias corrected, multipoint	y F M Grand , B c o r r	12.5	0.8	89.0/97.vii
Bias corrected, 1-point	y F G One thousand , B c o r r 1 p	13.viii	0.9	82.4/99.7
Bias corrected, 2-point	y F G M , B c o r r ii p	12.2	0.8	89.2/99.7
Bias and lag corrected, multipoint	y F M M , B L c o r r	12.7	0.eight	86.7/97.5

Effigy A2

Aforementioned plot as in Figure half dozen, but with individual bias correction (b F G M) practical. Using biases institute from day one to right day ii–seven data seems to give over-correction, at to the lowest degree in the negative bias group.

Author Contributions

Prediktor Medical, S.C.C. and H.M.U.H. collected information; O.M.Due south. analyzed the data and wrote the paper; Ø.S., A.50.F and S.M.C. supervised the enquiry activities; All authors revised the paper.

Funding

This research was funded by Norges Forskningsråd (grant numbers 242167 and 248872) and Prediktor Medical. Norges Teknisk-Naturvitenskapelige Universitet (NTNU) covered the costs of open access publishing.

Conflicts of Interest

The authors declare no disharmonize of involvement. Prediktor Medical funded the REK Midt 2016/1172 study, and had a part in the study pattern and data drove. The funding sponsors had no influence on the study design, consequence interpretation or decision to publish the results of the present sub-written report.

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Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6316667/

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