The Effect of a Global,Subject,and Device-Specific Model on a Noninvasive Glucose Monitoring Multisensor System

Abstract

Background:

We study here the influence of different patients and the influence of different devices with the same patients on the signals and modeling of data from measurements from a noninvasive Multisensor glucose monitoring system in patients with type 1 diabetes. The Multisensor includes several sensors for biophysical monitoring of skin and underlying tissue integrated on a single substrate.

Method:

Two Multisensors were worn simultaneously, 1 on the upper left and 1 on the upper right arm by 4 patients during 16 study visits. Glucose was administered orally to induce 2 consecutive hyperglycemic excursions. For the analysis, global (valid for a population of patients), personal (tailored to a specific patient), and device-specific multiple linear regression models were derived.

Results:

We find that adjustments of the model to the patients improves the performance of the glucose estimation with an MARD of 17.8% for personalized model versus a MARD of 21.1% for the global model. At the same time the effect of the measurement side is negligible. The device can equally well measure on the left or right arm. We also see that devices are equal in the linear modeling. Thus hardware calibration of the sensors is seen to be sufficient to eliminate interdevice differences in the measured signals.

Conclusions:

We demonstrate that the hardware of the 2 devices worn on the left and right arms are consistent yielding similar measured signals and thus glucose estimation results with a global model. The 2 devices also return similar values of glucose errors. These errors are mainly due to nonstationarities in the measured signals that are not solved by the linear model, thus suggesting for more sophisticated modeling approaches.

Keywords

diabetes optical algorithm electromagnetic perturbations wearable device

Various noninvasive glucose monitoring (NIGM) technologies have demonstrated their ability to monitor changes in glucose levels in the human body under highly restricted conditions typical of hospital or laboratory environments.^1-3 As soon as these conditions become less favorable, NIGM fails to demonstrate the same level of functionality. An example of NIGM based on a single sensor under controlled and “uncontrolled” conditions was shown by Caduff et al.³ The data showed that a change from a controlled to an uncontrolled environment lead to a significant reduction in signal quality of NIGM. It was argued that environmental (temperature changes) and physiological (blood perfusion, sweat events, etc) perturbations lead to such deteriorations in the signal quality. In the last few years much attention has been given to identify, describe, and characterize such perturbations. It has been highlighted that amongst other perturbations, the migration of water in skin, sweat on skin, relocation, and changes in blood volume fraction or effects of temperature variations are additional parameters that can significantly affect the biophysical characteristics of the skin and underlying tissue^4-8 and thus adversely affect NIGM.

Consequently, to help address these perturbations, a sensor concept based on multiple sensors (the Multisensor) has been developed with the intention to iso-chronically measure perturbing effects together with the glucose related effects to allow for compensation.⁹ Similar Multisensor concepts but with different data combination logics have been proposed in Harman-Boehm et al and Amaral et al.^10,11 In all these situations, the working hypothesis was that this would provide a more reliable glucose tracking compared to the single sensor approach.

At the same time an improved understanding of the basic link between the impact of glucose variations in the tissue and the underlying biophysical processes and phenomena that drive these variations is required. The link between the measurable impact of glucose variations in the tissue and underlying biophysical processes and phenomena has been discussed in a series of publications of the Feldman group and others.^12-17

Considering in vivo evidence, it has been argued that additional sensors allow to independently characterize biophysical processes contributing to the main signal and allows for the compensation of disturbing effects. The contribution of disturbance to the major dielectric signal would depend on the individual skin characteristics, such as thickness of layers, hydration, and micro-vascularization. It can be assumed that the mathematical model, accounting for the contribution of disturbances has coefficients specific to the individual. These coefficients can be obtained by investigating the skin with appropriate techniques and assessment of coefficients based on a complete analytical model. Alternatively, if a mechanistic model is not available, the relation of the involved sensor signals can be derived based on the data acquired with the Multisensor with a black-box approach.¹⁸ Similar statistical approaches are used also with other noninvasive technologies based on spectral analysis such as principal component analysis and partial least squares regression.^19,20

On the other hand, variations in the parameters of devices should be minimized to be able to guarantee the consistency in the performance of different devices. This can be achieved by calibration of the sensors at the production stage (so-called hardware calibration). After hardware calibration, the devices can be considered as being equal in the sense that they are interchangeable in the analytical models.

To be able to evaluate the feasibility of Multisensor self-calibration as well as to assess the consistence of signals from different devices after hardware calibration, we have developed linear models specific to an individual (personal model), to a Multisensor device (device model), and a universal model, which uses the same coefficients for all individuals and all devices (global model).

The contribution of this work is not to show new modeling approaches applied to this kind of Multisensor data,^20-22 but rather to use previously considered tools in a variety of analyses tasks, for assessing performance with global, personal, and device specific models.

Methods

Four patients with type 1 diabetes mellitus (T1DM, age 43.5 ± 9.5 years; BMI 24.5 ± 3.8 kg m⁻², duration of diabetes 22.0 ± 11.3 years; HbA1c 7.7 ± 0.5%) participated in this study. The study was performed in accordance with Good Clinical Practice and the Declaration of Helsinki. All patients signed an informed consent agreement, performed the screening visit and were then enrolled in the study.

Study Performance

Four Multisensor devices were used in total in this study and 2 devices were worn simultaneously during each study visit by the patient. One on the left and the other on the right upper arm as illustrated in Figure 1b. Each patient performed a total of 4 study visits undergoing 4 different glycemic profiles that were designed for spanning different glucose range and different glucose rate of change. The devices were rotated according to a Greco-Latin square. This means that each of the 4 devices was applied once on each arm in the 4 patients. In each study visit different glycemic profiles were induced by oral carbohydrate and intravenous insulin administration respectively. A total of 16 testing visits were thus performed collecting data from 2 devices simultaneously. The data of 1 device of 1 study visit are referred to as run.

Figure 1.

(a) Schematic illustration of combination of the optical diffuse reflectance sensors and electrodes of the dielectric sensor on the substrate of the Multisensor system. (b) Attachment of the Multisensor to the upper arm with a flexible band.

The patients arrived in the clinical study unit in the morning. After measurement of blood glucose, an intravenous insulin infusion was established and a Multisensor was attached each to the left and to the right upper arm by an expandable band as illustrated by Figure 1b (proximal/distal location). After a run-in period of 75 minutes during which the glucose level was stabilized at an euglycemic level, glucose was administered orally and insulin intravenously to induce the different hyper- and hypoglycemic excursions (typical hyperglycemic target level of 12-15 mmol L⁻¹ or 215-270 mg dL⁻¹) within approximately 8 hours. During all study visits, patients were lying in a bed. Reference blood glucose (RBG) was routinely measured every 10 to 20 min using a HemoCue Glucose Analyzer (HemoCue AG, Switzerland). The first 75 minutes after the attachment of the Multisensor at the beginning of each study visit have been removed for the analyses since parts of these data are dominated by an equilibration processes related to occlusion effects on the skin. As reference values, the measured BG values of the reference method (HemoCue) were used.

Multisensor System

To effectively perform NIGM, a Multisensor approach has been taken. Different sensors are employed for monitoring the perturbations caused by various exogenous and endogenous factors, such as temperature and humidity variations, skin perfusion, sweating, movement, and others. It is suggested that combining these sensor signals allows a more reliable noninvasive monitoring of glucose variations.

Dielectric properties are studied in 3 frequency regions: 1-200 kHz, 0.1-100 MHz, and 1-3 GHz. The frequency regions overlap, but they refer to electrodes with different geometrical shapes and thus able to measure at different tissue depth. This results in the measurements of the same bio-physical process parameters occurring in different skin layers.

The MHz sensor includes 3 electrodes with different characteristic geometries as illustrated in Figure 1a that have different penetration depths of the electromagnetic field into the various tissue layers.^23-25 The kHz sensor (indicated as “sweat sensor” in Figure 1a) employs interdigitated contact electrodes. GHz measurements are performed at 2 frequencies using 2 grounded coplanar waveguides with different ground-to-signal distances to measure at different depths.⁹ Variation of the blood content in the skin are monitored with 2 identical diffuse reflectance sensors embedded within the long MHz electrode as shown in Figure 1a. Each optical sensor features 3 LEDs located closely to each other with the following nominal optical wavelengths: green (568 nm), red (660 nm), and infrared (798 nm). The acceleration and position are monitored using an integrated accelerometer. In addition, the temperatures of the skin surface and inside the device housing, as well as the ambient humidity are monitored with temperature/humidity sensors. Accelerometer, temperature, and humidity sensors are not visible in Figure 1a since they are located inside the sensor housing.

The various sensors and their arrangement on the Multisensor have been described in more details in Caduff et al.²¹

Model

An algorithm, which is based on a statistically derived model and parameterization, is used to map the measured parameters into glucose related information. Since there is not yet a fully developed quantitative theory to be used linking signals measured by the Multisensor with glucose levels, a multivariate regression model has to be developed based on the measured data:

y = X β + v

In (1), the $(n x p)$ matrix $X$ collects the $n$ samples of the $p$ measured channels by the Multisensor system, the $(n x 1)$ vector $y$ collects the reference BG samples, $β$ is the $(p x 1)$ vector containing the coefficients of the linear model and $v$ is the $(n x 1)$ vector accounting for the unexplained portion of the data by the model.

One option to estimate the coefficients collected in $β$ is to find a multiple linear least-squares regression model through dimension reduction and Akaike’s information criterion (AIC) variable selection techniques as described in Mueller et al.²⁰ Similar evaluation routines based on model estimation through regularization on Multisensor data are described in Zanon et al.²²

The model includes an additive constant per study visit. For practical applications and prospective use of the model (1), an initial baseline adjustment (BLA) considering the first reference BG measurement available at the beginning of each study visit should be used as discussed in Zanon et al, Mueller et al, and Caduff et al.^18,20,21 However, in this work, we provide results with a nonprospective full-run baseline that uses all reference BG measurements of a study visit to simplify the comparison of results. Furthermore, this avoids variations originating from an inadequately chosen initial baseline adjustment points that would affect the whole length of the glucose profile estimated by the model.

Data Analysis

When developing the model on the basis of an experimental data set, it is important to avoid overfitting. Overfitting implies that the coefficients of certain variables are over-adjusted to the data and partly reflect peculiarities that are not useful for the prediction in new data. All results are therefore leave-one-run-out cross-validated. Briefly, N-1 runs, consisting of Multisensor data and reference BG collected in parallel, are used to estimate the linear model coefficients $β$ in (1) and the obtained model tested on the remaining run not considered for the model estimation stage. This procedure is then repeated for all runs.

As discussed above 3 different families of models were derived. The first family includes only variables and corresponding coefficients that are globally valid, hence for all patients and devices (global model). The coefficients of the second family of models were optimized for each of the 4 patients (personal model), hence the coefficients are different for each patient. The third family yields different coefficients for each of the 4 devices (device model). All models are based on the AIC criterion that determined in which order the variables enter the model and whether they are global, personal, or device specific. The model sizes were chosen based on the best performance on cross-validation.

The global model application has also been used to compare the glucose estimations of the Multisensor system attached to the left arm to the glucose estimations of another device attached to the right arm during the same study visit. The identical modeling coefficients have been used for the left and right arm estimation.

Performance Indicators

The errors between the estimated glucose profiles by the model and the reference BG samples are measured in terms of widely used indexes in the diabetes community. In particular, point accuracy is given by the Person’s correlation coefficient, the mean absolute difference (MAD),

M A D = \frac{1}{n} {\sum^{​}}_{i = 1}^{n} | y_{i} - \hat{y_{i}} |

and the mean absolute relative difference (MARD) indicator, which characterizes the relative errors (in %) of the estimated glucose,

M A R D = \frac{1}{n} {\sum^{​}}_{i = 1}^{n} \frac{| y_{i} - \hat{y_{i}} |}{y_{i}}

Clinical accuracy is instead measured with the Clarke error grid.²⁶ The area where estimated glucose by the model and RBG values are displayed as a scatter-plot is broken down into 5 regions (labeled from A to E). Zone A represents those glucose values within 20% of the RBG values and so on. The most dangerous situations are those where estimated glucose values fall into zones C/D/E because, from a clinical point of view, they will lead to unnecessary or even wrong and potentially dangerous treatments.

Results

Variations of the signals measured with different devices and different individuals can be demonstrated with the absolute levels of the impedance signals. Figure 2 shows statistics of dielectric signals at 25 MHz for each subject (right-hand side) and for each device (left-hand side). In contrast to the differences between the subjects, the measurements across devices are consistent. The data show subject-specific characteristics, but no device-specific characteristics. Therefore, we can expect that the glucose estimation models would not benefit from adjustments to the device, but potentially to the subject. Based on this, glucose estimations from simultaneous measurements on the left and the right arm with 2 different, but consistent devices should be in good agreement because they originate from the same subject.

Figure 2.

Boxplots (including mean and standard deviation in orange) of 25 MHz data. Values are given per device on the left-hand side (green), per subject on the right-hand side (blue), and over all data (16 study visits) in the middle (gray).

Device and Subject Cross-Comparison

The personal and device-specific models were forced to have the same variables for all subjects and devices, but were allowed to have different coefficients. Different coefficients per subject or device increases the degree of freedom of the models. The models are therefore smaller because the size was controlled by cross-validation to avoid overfitting.

The Clarke error grid and the time series estimated with the most general (global) model are shown in Figure 3 and Figure 4, respectively. It can be seen that model is able to achieve a good agreement with the reference measurement. A comparison of the performance between device-specific, personal, and global models is presented in Table 1. We can observe that personal model performs better than the global model. This confirms the observation drawn from Figure 2 showing different characteristics of the signals measured from different subjects. It can therefore be concluded that accounting for the personal differences can improve noninvasive continuous glucose monitoring with the Multisensor system. Moreover, the global model also achieves a good agreement with the reference measurement. In contrast, the device model performs worse than all other models. The forced additional degrees of freedom (coefficients must be device-specific) lead merely to overfitting, indicating that a device specific model estimated on data from a specific device will not generalize well when used on a different device. Based on this result we can conclude that hardware calibration undertaken at a production stage sufficiently eliminates differences between Multisensor devices.

Figure 3.

Clarke error grid for the global model. Different colors refer to data from different subjects.

Figure 4.

Time series of the cross-validated global model. Estimations of the Multisensor attached to the left arm (red solid line) and to the right arm (green solid line) are compared against reference glucose values (black dotted line).

Table 1.

Key Indicators of the Cross-Validated Global, Personal, and Device Models.

Key indicators	Correlation (average over runs)	MAD (mg dL⁻¹)	MARD (%)	Clarke (%) A+B (A)
Global model	.86	29.8	21.1	96.8 (60.8)
Personal model	.91	24.7	17.8	98.4 (70.9)
Device model	.82	34.7	25.0	95.8 (57.1)

Left and Right Arm Comparison

Figure 4 shows the glucose estimations of the global model of the devices attached to the left and right arm on the same axis for each study visit.

Differences between the left and right estimations are mostly present at the beginning of a run whereas deviations to the reference readings (often the same for left and right) occur evenly distributed during the study visits.

Key indicators from the comparison of the reference measurements to the estimations of the devices attached to the left and right arm are given in Table 2. They show that very similar errors are obtained for left and right devices indicating the independence of the models to the measurement site.

Table 2.

Key Indicators of the Cross-Validated Global Model.

Key indicators global model	Correlation (average over runs)	MAD (mg dL⁻¹)	MARD (%)	Clarke (%) A+B (A)
Left vs RBG	.86	29.6	21.1	96.6 (61.2)
Right vs RBG	.86	30.0	21.1	97.0 (60.5)

Estimations of the Multisensor attached to the left arm and to the right arm are compared to the reference readings.

Discussion

Results in the previous section showed that the Multisensor devices can be considered identical with respect to modeling with linear multiple regression. Adjusting the models to the devices merely led to overfitting. We can conclude that the applied hardware calibration procedure can compensate the differences from the manufacturing process and thus once hardware calibrated, the devices can be considered equal for linear glucose estimation.

When comparing the glucose estimations of 2 Multisensors from the same subject, 1 attached to the left and the other attached to the right upper arm, we found good agreement. This result supports the conclusion of equality of the devices. The remaining small differences might originate from the local attachment of the Multisensor to the skin.

However, systematic differences were found when measuring with the same devices in different subjects. Our data show subject-specific characteristics that are also reflected in the modeling properties. This result supports the general understanding that skin characteristics, such as morphology, hydration or microvascularization, are different between subjects. For example, Arnold et al have studied the micro local differences in skin and underlying tissue,^2,7 mapping the differences of water, type I collagen protein, keratin protein, and fat content on an area significantly smaller than the Multisensor surface. It was shown that skin is essentially heterogeneous both in depth as well as locally. Various other authors have looked at the same questions, highlighting intra- and interpersonal differences.^27-32

We can therefore conclude that either more sophisticated global models or a (partial) adjustment of the model to the subject can improve the further performance of the glucose estimations with the current sensor design.

Finally, key indicators in Table 1 and Table 2 show that glucose point accuracy estimated with the Multisensor system is not yet at the same level of finger prick based devices due to nonstationarities in the measured signals that are not solved by the linear model with fixed parameters. In these particular conditions future work is required for developing more sophisticated modeling approaches able to adapt the model parameters in time to follow changes of the underlying system. However, glucose rate of change has an acceptable accuracy and a potential immediate application as provider of adjunctive trend information to the so-called self-monitoring (finger-prick-based) glucose monitors that can be used to help the diabetic patient in judging the danger of hypo- and hyperglycemic events. Results are not showed here because outside the scope of the present work, but extensive information can be found in Zanon et al and Guerra et al^18,33 and are applicable since the models are derived using the same techniques from the same devices in previous trials.

Conclusions

Diabetes is a disease affecting millions of people worldwide and noninvasive devices for glucose monitoring are useful for avoiding long- and short-term complications and particularly appealing for reasons related to patient’s comfort. In particular, Multisensor approaches gained considerable attention in the last years allowing a broader characterization of the skin and underlying tissues.

In this work, we used several Multisensor devices and subjects to illustrate the effects of different devices and subjects on the signals and modeling with the purpose of noninvasive glucose monitoring. The device- and subject-specificity has been systematically analyzed. Furthermore, simultaneous measurements with 2 devices in the same patient have been compared and characterized.

Results showed that differences among devices are negligible, that is, once hardware calibrated, a model obtained from data of a device is successfully applied to different devices. On the other side, differences among subjects are not negligible since it is expected that each subject presents peculiar skin characteristics calling for more sophisticated modeling techniques. In this sense, directions for further improvement can be focused on black-box statistical models, similar to those presented in this work, but more complicated, like nonlinear or adaptive in the parameters models.³⁴ A different approach would instead combine knowledge of the system into the modeling phase as investigated in the past for minimally invasive glucose monitoring devices.^35,36 Finally, we showed that comparable results are obtained when measuring either on the left and right arms.

With the results of this study it can be concluded that it is safe to use a larger number of devices in future studies and the resulting raw data are truly reflecting various biophysical characteristics of the individual skin and underlying tissue of the subject in a reliable way. This will not only help continue algorithm development in a focused manner but also to expand the basic understanding of fundamental in vivo phenomena over a wide frequency range and different underlying mechanisms. To achieve this, the use of the same Multisensor device with the respective data evaluation routine within a regular home use study under daily life conditions with T1DM patients can be applied. Moreover, the findings here further support a step by step type of NIGM realization of a trend indicator first, since it cannot yet be considered a substitute but rather a companion to invasive devices, followed by a trend and level combination scenario on the way toward a fully integrated solution with trend, level, and number details.

Footnotes

Acknowledgements

Thanks goes to various people from former Solianis Monitoring AG and to dedicated international partners for their solid contributions, which allowed expanding on the understanding of underlying mechanisms and characterization of phenomena related to noninvasive glucose monitoring.

Abbreviations

BG, blood glucose; BLA, baseline adjustment; MAD, mean absolute difference; MARD, mean absolute relative difference; NIGM, noninvasive glucose monitoring; T1DM, type 1 diabetes mellitus.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Solianis Monitoring AG.

References

Larin

Eledrisi

Motamedi

Esenaliev

. Noninvasive blood glucose monitoring with optical coherence tomography: a pilot study in human subjects. Diabetes Care. 2002;25(12):2263-2267.

Arnold

Small

. Perspectives in analytical chemistry: noninvasive glucose sensing. Anal Chem. 2005;77(17):5429-5439.

Caduff

Dewarrat

Talary

Stalder

Heinemann

Feldman

. Non-invasive glucose monitoring in patients with diabetes: a novel system based on impedance spectroscopy. Biosens Bioelectron. 2006;22(5):598-604.

Caduff

Talary

Zakharov

. Cutaneous blood perfusion as a perturbing factor for noninvasive glucose monitoring. Diabetes Technol Ther. 2010;12(1):1-9.

Zakharov

Dewarrat

Caduff

Talary

. The effect of blood content on the optical and dielectric skin properties. Physiol Meas. 2011;32(1):131-149.

Zakharov

Talary

Kolm

Caduff

. Full-field optical coherence tomography for the rapid estimation of epidermal thickness: study of patients with diabetes mellitus type 1. Physiol Meas. 2010;31(2):193-205.

Alexeeva

Arnold

. Impact of tissue heterogeneity on noninvasive near infrared glucose measurements in interstitial fluid of rat skin. J Diabetes Sci Technol. 2010;4:1041-1054.

Pleitez

Lieblein

Bauer

Hertzberg

von Lilienfeld-Toal

Mäntele

. In vivo noninvasive monitoring of glucose concentration in human epidermis by mid-infrared pulsed photoacoustic spectroscopy. Anal Chem. 2013;85(2):1013-1020.

Caduff

Talary

Mueller

. Non-invasive glucose monitoring in patients with type 1 diabetes: repeatability in the same subjects using a multisensor system. Biosens Bioelectron. 2009;24(9):2778-2784.

10.

Harman-Boehm

Gal

Raykhman

Naidis

Mayzel

. Noninvasive glucose monitoring: increasing accuracy by combination of multi-technology and multi-sensors. J Diabetes Sci Technol. 2010;4(3):583-595.

11.

Amaral

Brischwein

Wolf

. Multiparameter techniques for non-invasive measurement of blood glucose. Sensors Actuators B-Chem. 2009;140(1):12-16.

12.

Hayashi

Livshits

Caduff

Feldman

. Dielectric spectroscopy study of specific glucose influence on human erythrocyte membranes. J Phys D Appl Phys. 2003;36(4):369-374.

13.

Caduff

Livshits

Hayashi

Feldman

. Cell membrane response on d-glucose studied by dielectric spectroscopy. erythrocyte and ghost suspensions. J Phys Chem B. 2004;108:13827-13830.

14.

Lev

Puzenko

Manevitch

. D-glucose-induced second harmonic generation response in human erythrocytes. J Phys Chem B. 2009;113(8):2513-2518.

15.

Livshits

Caduff

Talary

. The role of GLUT1 in the sugar induced dielectric response of human erythrocyte membranes. J Phys Chem B. 2009;113(7):2212-2220.

16.

Di Biasio

Cametti

. D-glucose-induced alterations in the electrical parameters of human erythrocyte cell membrane. Bioelectrochemistry. 2010;77(2):151-157.

17.

Caduff

Heinemann

Talary

Lutz

di Benedetto

Theander

. Dynamics of blood electrolytes in repeated hyper- and/or hypoglycaemic events in patients with type 1 diabetes. Diabetologia. 2011;54(10):2678-2689.

18.

Zanon

Sparacino

Facchinetti

. Non-invasive continuous glucose monitoring: improved accuracy of point and trend estimates of the Multisensor system. Med Biol Eng Comput. 2012;50(10):1047-1057.

19.

Pleitez

Lieblein

Bauer

Hertzberg

von Lilienfeld-Toal

Mäntele

. Windowless ultrasound photoacoustic cell for in vivo mid-IR spectroscopy of human epidermis: low interference by changes of air pressure, temperature, and humidity caused by skin contact opens the possibility for a non-invasive monitoring of glucose in the interstitial fluid. Rev Sci Instrum. 2013;84(8):084901.

20.

Mueller

Talary

Falco

Stahel

Caduff

. Data processing for non-invasive continuous glucose monitoring with a multi-sensor device. J Diabetes Sci Technol. 2011;5(3):703-713.

21.

Caduff

Mueller

Megej

. Characteristics of a multisensor system for non invasive glucose monitoring with external validation and prospective evaluation. Biosens Bioelectron. 2011;26(9):3794-3800.

22.

Zanon

Mattia

Sparacino

Giovanni

Facchinetti

Andrea

Talary

Mark S.

Caduff

Andreas

Cobelli

Claudio

. Regularised Model Identification Improves Accuracy of Multisensor Systems for Noninvasive Continuous Glucose Monitoring in Diabetes Management. J Appl Math. 2013. doi:10.1155/2013/793869

23.

Dewarrat

Falco

Caduff

Talary

Feldman

Puzenko

. Measurement and simulation of conductive dielectric two-layer materials with a multiple electrodes sensor. IEEE Trans Dielectr Electr Insul. 2008;15(5):1406-1414.

24.

Talary

Dewarrat

Huber

Caduff

. In vivo life sign application of dielectric spectroscopy and non invasive glucose monitoring. J Non Cryst Solids. 2007;353(47):4515-4517.

25.

Talary

Dewarrat

Caduff

Puzenko

Ryabov

Feldman

. An RCL sensor for measuring dielectrically lossy materials in the MHz frequency range. Part I. Comparison of hydrogel model simulation with actual hydrogel impedance measurements. IEEE Trans Diel Elect Insul. 2006;13(2):247-256.

26.

Clarke

Cox

Gonder-Frederick

Carter

Pohl

. Evaluating clinical accuracy of systems for self-monitoring of blood glucose. Diabetes Care. 1987;10(5):622-628.

27.

Nishimura

Kida

Tamura

. Characterization of optical parameters with a human forearm at the region from 1.15 to 1.52 microm using diffuse reflectance measurements. Phys Med Biol. 2006;51(11):2997-3011.

28.

Diridollou

De Rigal

Querleux

Leroy

Holloway Barbosa

. Comparative study of the hydration of the stratum corneum between four ethnic groups: influence of age. Int J Dermatol. 2007;46(suppl 1):11-14.

29.

Kikuchi

Kobayashi

Le Fur

Tschachler

Tagami

. The winter season affects more severely the facial skin than the forearm skin: comparative biophysical studies conducted in the same Japanese females in later summer and winter. Exogenous Dermatol. 2002;1(1):32-38.

30.

Mehling

Fluhr

. Chronobiology: biological clocks and rhythms of the skin. Skin Pharmacol Physiol. 2006;19(4):182-189.

31.

Le Fur

Reinberg

Lopez

Morizot

Mechkouri

Tschachler

. Analysis of circadian and ultradian rhythms of skin surface properties of face and forearm of healthy women. J Invest Dermatol. 2001;117(3):718-724.

32.

Latreille

Guinot

Robert-Granie

Le Fur

Tenenhaus

Foulley

. Daily variations in skin surface properties using mixed model methodology. Skin Pharmacol Physiol. 2004;17(3):133-140.

33.

Guerra

Sparacino

Facchinetti

Schiavon

Dalla Man

Cobelli

. A dynamic risk measure from continuous glucose monitoring data. Diabetes Technol Ther. 2011;13(8):843-852.

34.

Hastie

Tibshirani

Friedman

. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2nd ed. Berlin, Germany: Springer; 2009.

35.

Facchinetti

Sparacino

Cobelli

. Reconstruction of glucose in plasma from interstitial fluid continuous glucose monitoring data: role of sensor calibration. J Diabetes Sci Technol. 2007;1(5):617-623.

36.

Lunn

Wei

Hovorka

. Fitting dynamic models with forcing function: application to continuous glucose monitoring in insulin therapy. Stat Med. 2011;30(18):2234-2250.