Measurement and characterization of glucose in NaCl aqueous solutions by electrochemical impedance spectroscopy

Biomedical Signal Processing and Control 14 (2014) 9–18

Contents lists available at ScienceDirect

Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc

Measurement and characterization of glucose in NaCl aqueous solutions by electrochemical impedance spectroscopy Oscar Olarte a,∗ , Kurt Barbé a , Wendy Van Moer a,b , Yves Van Ingelgem c , Annick Hubin c a b c

Dept. ELEC, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium University of Gävle, Kungsbäcksvägen 47, 801 76 Gävle, Sweden Dept. SURF, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium

a r t i c l e

i n f o

Article history: Received 25 February 2014 Received in revised form 23 May 2014 Accepted 23 June 2014 Keywords: Modeling Electrochemical impedance spectroscopy Odd random phase multisine Glucose sensor Best linear approximation Parametric model Nonparametric model Rational model

a b s t r a c t Electrochemical impedance spectroscopy (EIS) allows measuring the properties of the system as a function of the frequency as well as distinguishing between processes that could be involved: resistance, reactance, relaxation times, amplitudes, etc. Although it is possible to find related literature to in vitro and in vivo experiments to estimate glucose concentration, no clear information regarding the condition and precision of the measurements are easily available. This article first address the problem of the condition and precision of the measurements, as well as the effect of the glucose over the impedance spectra at some physiological (normal and pathological) levels. The significance of the measurements and the glucose effect over the impedance are assessment regarding the noise level of the system, the experimental error and the effect of using different sensors. Once the data measurements are analyzed the problem of the glucose estimation is addressed. A rational parametric model in the Laplace domain is proposed to track the glucose concentration. The electrochemical spectrum is measured employing odd random phase multisine excitation signals. This type of signals provides short acquisition time, broadband measurements and allows identifying the best linear approximation of the impedance as well as estimating the level of noise and non-linearities present in the system. All the experiments were repeated five times employing three different sensors from the same brand in order to estimate the significance of the experimental error, the effects of the sensors and the effect of the glucose over the impedance. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Electrochemical Impedance Spectroscopy (EIS) is a growing technique that generates high interest in biology and pharmaceutical industry. This technique presents several advantages: on-line detection, non-destructive and non-invasive sensing, easy integration and high-throughput screening. Pathologies such as diabetes type I and II require frequent monitoring of glucose levels in the blood. Hence, the development of techniques or new technologies that allow the glucose estimation is a topic of great interest. Electrochemical impedance spectroscopy and dielectric spectroscopy have been employed to study the glucose influence in erythrocytes [1–5], aqueous or phosphate buffer solutions [1,6–11], complete blood or serum [1,12,10,11,13], over the skin [14,15] and, even, in animal and human experiments [10,16]. Some of the reported results present some drawbacks. For one side the

∗ Corresponding author. Tel.: +32 471261963. E-mail addresses: [email protected], [email protected] (O. Olarte). http://dx.doi.org/10.1016/j.bspc.2014.06.007 1746-8094/© 2014 Elsevier Ltd. All rights reserved.

electrode configuration is not always adequate, some articles report very high excitation levels infringing the condition of linearity in the data acquisition [17–19], while others do not mention the excitation level. In our experiments the linear condition is verified for each experiment as will be described in Section 2. In an EIS setup the two, three and four electrodes configuration are available. The two electrodes configuration measures the impedance between the counter and working electrode, including the impedance and polarization of both electrodes. This makes difficult to analyze the data results since the contribution of each electrode is not the same [17–19]. The four electrode configuration excludes the effect of the electrode–electrolyte interfaces but its common use is to measure junction potentials between two nonmiscible phases or across a membrane [17–19]. The experiments developed in the present article are done employing a three electrode configuration system. The use of this configuration is aimed because allows measuring the potential changes of the working electrode, independent of changes that may occur at the counter electrode. This isolation allows that a specific reaction can be studied with confidence and accuracy [18,20].

10

O. Olarte et al. / Biomedical Signal Processing and Control 14 (2014) 9–18

In general the impedance is obtained by imposing multiple frequencies, sweeping frequency by frequency, a sinusoidal excitation signal to the system and recording the resulting response signal. Doing such sweep requires a lot of time (proportional to the sum of periods of the excited frequencies [21]) where any change in the system, during the data acquisition, can affect the impedance estimation. In time domain impedance spectroscopy [22–26], the voltage excitation signal having a time-dependence shape (ramp, triangle, square function, etc.) is applied and the resulting current signal is measured. The conversion into the frequency domain allows calculating the impedance. This method has at least two drawbacks [25]. First, to obtain the equal spectral density and a good signal to noise ratio (SNR) along a wide frequency range, the excitation pulse must be very short, in the time, but with high amplitude. However, in practice, the excitation should be low to preserve the linearity affecting the SNR. And second, for this type of signals, only part of the energy is concentrated into a frequency range (the principal lobe), while another part falls outside. The energy out of the principal band will be “wasted” or lost in the analysis. It is, the impedance analysis is done in the principal lobe, while the signal present out of this lobe is discarded given that do not provide good SNR [25,26]. In this article the employed excitation signal is an odd random phase multisine (ORPM), which allows control of the spectral excitation and reduces the measurement time. The time reduction allows measure the impedance in a stationary state, while the periodicity and control of the excitation frequencies of the multisine, allows identifying the noise level and the level of non-linearities in order to acquire the impedance in a linear or pseudo-linear state, as is described in Section 2. In a first attempt towards the in vivo identification of blood glucose levels, in vitro experiments are required. In this paper a sodium-chloride (NaCl) solution is used as a base solution given its prevalence in blood and its influence in the electrical conductivity process. During the experiments the concentration of the NaCl is constant and its impedance is evaluated over a number of physiological (normal and pathological) glucose levels. The impedance measurements are acquired in the frequency range of 1 Hz to 30 kHz. Range where groups as [1,6,9,10] and [11] have found important influences of the glucose in the impedance. In order to identify if the glucose concentration affects significantly the impedance spectra, the measured data will be analyzed regarding the uncertainty sources as is established by [27]. In our experiments the sources of uncertainty are the level of noise, the experimental repetition errors (ERE) and the sensor effect. Based on this, the effect of the glucose over the impedance (defined as the difference between the impedance at different glucose concentrations) is assessed regarding the different uncertainty sources. Based on our results the glucose effect (for the physiological glucose concentrations employed) are significant over the noise level and the ERE, but not to the sensor effect as will be described in Section 4. The parametric characterization of the impedance measurements allows centralizing all the information present in the data spectrum in a group of parameters that describe the whole system. In [6] the experimental impedance spectrum data is modeled by an equivalent circuit showing a correlation between the glucose and the parameter related to the charge transfer resistance. In [1] the spectrum data is analyzed concluding that the frequency of 1.17 kHz optimizes the reaction of their sensors. In our attempt to estimate the glucose content based on the electrochemical impedance spectrum, a parametric rational model in the Laplace domain is developed employing a frequency domain approach [28]. The identified parametric model is analyzed based on the poles and zeros locations and their standard deviations. The developed model shows a clear relationship between the distance poleszeros and the glucose content with low uncertainty. The results

contribute to the use of EIS methods for potential development of glucose sensors. The paper is organized starting in Section 2 with an explanation of the measured methodology for electrochemical impedance spectroscopy in the presence of non-linear distortions. In Section 3 the experimental setup is described together with the methodology. Section 4 shows the impedance results and the analysis of the non-parametric model. In Section 5 the parametric model in the frequency domain is presented together the pole-zero behavior for the analyzed samples. Section 6 discusses the results and, finally, Section 7 gives the conclusions of the present work. 2. Impedance measurements in the presence of non-linear distortions The impedance (Z) of a system can be determined by applying a voltage signal (V) to the system and measuring the current (I) response. The word spectroscopy refers to the fact that the impedance is determined at different frequencies. The impedance (Z) is a complex value, since the response of the system can differ not only in terms of the amplitude but it can also show a phase shift between the excitation voltage and measured current signal. 2.1. Odd random phase multisine (ORPM) From the vast amount of existing broadband signals, in this work an optimized multisine will be used as excitation. This type of signal is flexible, since the user can control the number of excited frequencies and the amplitude of each frequency. This kind of signals allows short measurement time, proportional to the lower excited frequency and good quality of the measurements [21,29]. An example of such a signal is presented in equation (1) u(t) =

N 

Ak sin(ωk t + k )

(1)

k=1

in which Ak are the deterministic amplitudes of the different sine waves. k are the random phases that are uniformly distributed in the interval [0, 2[, and ωk are the excited frequencies of the multisine. This signal is periodic and consists of a sum of N sine waves that are harmonically related. From the different family signals that can be developed by (1) we use the odd random phase multisine signal. For this type of signals, only the odd harmonics are excited: Ak = 0 for k = 2n with n ∈ N and per group of 3 consecutive odd harmonics, one is randomly omitted. This creates an odd random phase multisine with a random harmonic grid that allows estimating the levels of the non-linear contributions as will be extended in the next section. The lowest frequency in the signal is the fundamental frequency. The maximum frequency is limited by the Nyquist theorem, and the minimum frequency will determine the measurement time. Proportional to the minimum excited frequency [21]. 2.2. Best linear approximation (BLA) Although it is well known that, in practice, systems are seldom perfectly linear, a linear model is very useful. It gives an intuitive comprehension of the general behavior of the system. A pure linear system satisfies the equation: Y (jωk ) = Go (jωk )U(jωk )

(2)

where Y(jωk ) and U(jωk ) represent the output and the input signals respectively, Go (jωk ) is the linear time-invariant transfer function of the system, and ωk represents the angular frequencies where the system is defined. For a nonlinear system, it is no longer possible to employ this relation exactly. However, if the system is

O. Olarte et al. / Biomedical Signal Processing and Control 14 (2014) 9–18

mainly linear, the relationship between Y(jωk ) and U(jωk ) can be approximated by a linear-time invariant relation. In [28] it has been proven that if a nonlinear system is excited with a spectrally rich signal (as the ORPM), the frequency response function (FRF) of the nonlinear system can be approximated by the following equation: G(jωk ) = GBLA (jωk ) + GS (jωk ) + NG (jωk )

(3)

where G(jωk ) is the FRF of the system under test, GS (jωk ) is the stochastic non-linear contributions of the FRF, NG (jωk ) is the disturbing noise of environment and measurement equipment and GBLA (jωk ) is the BLA of the system under test. The BLA consists of two parts: GBLA (jωk ) = Go (jωk ) + GB (jωk )

(4)

where Go (jωk ), as in (2), is the underlying linear system and GB (jωk ) is the bias or systematic non-linear contributions to the FRF. These last contributions do not depend on the actual phases of the random multisine, but they do depend on the applied power spectrum [28]. GB (jωk ) is related to nonlinearities of the system and need to be low in order to develop measurements in a linear or pseudolinear state. ˆ BLA (jωk ) is estimated as: The average G ˆ ˆ BLA (jωk ) = Y (jωk ) G ˆ U(jω k)

(5)

ˆ where Yˆ (jωk ) and U(jω k ) are the output and input average spectra respectively, obtained along multiple periods of the excitation signal with the same phase realization. Due that the linear and non-linear distortions are periodic at periodic excitations [28] the variance of the excited frequencies (jωk ) along the acquired periods provides an estimation of the noise contributions. It is: 1  [p] 2 ˆ |G (jωk ) − G(jω k )| P−1 P

ˆ G2

BLA

,n (jωk ) =

(6)

p=1

where G[p] (jωk ) = Y[p] (jωk )/U[p] (jωk ) is the FRF by period. Since both, the linear and non-linear response are periodic, the discrimination between them are not possible. However, at the output of the system, the total variance (noise plus non-linear distortions) can be estimated at the non excited frequencies (jωl ) as: ˆ 2ˆ (jωl ) = |Yˆ (jωl )|2

(7)

Y

Since the non-linear distortions are periodic, the noise can be quantified by the sample variance 1  [p] |Y (jωl ) − Yˆ (jωl )|2 P−1 P

2 ˆ Y,n (jωl ) =

(8)

p=1

Finally, the nonlinear distortions at the non excited frequencies are: 2 ˆ Y,S (jωl ) = ˆ 2ˆ (jωl ) − Y

1 2 ˆ (jωl ) P Y,n

Y

estimating the non-linear distortion on the measured FRF as BLA ,S

(jωk ) =

2 (jω ) ˆ Y,S k

(10)

|U0 (jωk )|2

and the total variance as the sum of the level of the non-linear distortions and the noise level: ˆ G2

BLA ,total

(jωk ) = ˆ G2

BLA ,S

This equation summarize the contributions of the noise and the non-linear behavior of the system over the BLA. In the case that the system be linear or mainly-linear, the first term of the right in the equation should be zero and the total standard deviation will be given for the noise contributions. 3. Experimental setup and methodology 3.1. Solutions One liter of saline solution (NaCL solution) at a concentration of 700 mg/dL is used as a base solution. This solution was made using demineralized water from a Millipore MilliQ Element system and Sodium-chloride at 99% from VWR-laboratory. This base solution was divided in five sub-groups and glucose was added to obtain five different NaCl–glucose solutions at 0, 70, 120, 180 and 240 mg/dL. The glucose was acquired from Sigma–Aldrich Laboratories with 99% of purity. The sample solution were stored into a refrigerator at 4 ◦ C. The glucose levels were chosen based on the physiological range, normal values and common Postprandial or random blood glucose tests. In [30] the glucose measurements taken in 74 normal people aged between 9 and 65 years old over a period of 3–7 days shows that glucose concentrations were between 70 and 120 mg/dL for 91% of the day. In [31] the preprandial goal is set between 70 and 130 mg/dl while the postprandial one is set <180 mg/dL. Finally, patients with hyperglycemia present random blood glucose >200 mg/dL [31]. 3.2. Instrumentation The electrodes used to contact the solutions were screenprinted electrodes from DropSens [32]. These electrodes consist of a working electrode of Platinum (4 mm diameter), a counter electrode of Platinum and a reference electrode of Silver (Dropsens). The use of three electrodes configuration is aimed because allows measuring the potential changes of the working electrode, independent of changes that may occur at the counter electrode. This isolation allows that a specific reaction can be studied with confidence and accuracy [18,20]. The dimensions of the screen-printed electrodes are 3.4 cm × 1.0 cm × 0.05 cm (Length × Width × Height). These sensors were chosen since they exhibit a high electrochemical activity and good repeatability [33]. The cell for screen-printed electrodes is a cylindric cell designed to perform batch analysis with large volumes of solution (5–8 mL). The cell allows temperature control by mean of a thermostatic jacket. The dimensions of the cell are 5.8 cm (height) × 4.5 cm (diameter). A detailed description of the sensors and cell can be found in [32]. The Potentiostat Bank POS2 configured for three electrodes experimentation was employed, the signals were generated and recorded by a NI 4461 PCI DAQ card. The temperature was controlled by the pump Lauda Master Proline RP845.

(9)

if the Eq. (9) is approximately zero the system is mainly linear. The interpolation of the levels of non-linear distortions (9) and the total variance (7), at the output, from the non-excited frequen2 (jω ) and  cies to the excited ones gives the ˆ Y,S ˆ 2ˆ (jωk ). This allows k

ˆ G2

11

(jωk ) + ˆ G2

BLA ,n

(jωk )

(11)

3.3. Methodology Each sample is introduced in the cell and warmed until reach the temperature of 37 ◦ C. Once the temperature is reached the impedance of the solution is measured. In any case the, electrical stimulation only is applied approximately after 15 min the sample is put in the cell. After each measurement the sensor and the cell are cleaned with demineralized water and dried carefully before measure a new sample. All the experiments are done for three different sensors and repeated M =5 times. The impedance measurements are performed with respect to the open-circuit potential (OCP). The excitation signal is an ORMP, as was described in Section 2.1. The frequency range employed for the impedance evaluation is

12

O. Olarte et al. / Biomedical Signal Processing and Control 14 (2014) 9–18

between 1 Hz to 30 kHz. The amplitude of the excitation signal is 20 mV r.m.s. At this amplitude the total standard deviation (ˆ Z2 ,total (jωk )) and the noise level (ˆ Z2 ,n (jωk )) are approximately BLA

BLA

at the same level indicating that the system is excited at a linear or pseudo-linear state, as is described by the equation (11) and will be show in the results of the non-parametric model analysis in the next section. For P = 6 periods in steady state the impedance (Zˆ BLA (jωk )), the standard deviation of the noise (ˆ Z2 ,n (jωk )) and the total standard deviation (ˆ Z2

BLA ,total

BLA

(jωk )) are calculated for the different glucose

concentrations (0, 70, 120, 180 and 240 mg/dL). Based on the measurements and the employed methodology, the significance of the glucose changes in the impedance spectrum can be evaluated based on the level of the total standard deviation ˆ Z2 ,total (jωk ), the noise BLA

level ˆ Z2 ,n (jωk ), the effect of error repetitions (calculated based on BLA M =5 different repetitions), and the effect of using different sensors (calculated based on three different sensors). A parametric model is identified in order to estimate the glucose level based on the spectral information obtained from a sample of glucose-saline solution. The model verification is done based on the residual analysis. The model order selection is addressed using the AIC (Akaike information criterion) and MDL (minimum description length) which penalize the complexity of the model (see [34,35]). The identification of the glucose effect over the identified parametric model is done based on the pole/zero configuration. 4. Non-parametric model analysis In this section the estimated BLA of the impedance at the different glucose concentrations is presented and analyzed. The significance of the changes in the impedance spectrum, given changes in glucose concentration, are analyzed based on the level of noise and the total standard deviation, the effect the error repetitions and the effect of the employed sensors. 4.1. Impedance spectral response and the glucose effect Fig. 1 presents the magnitude of the BLA of the impedance (|Zˆ BLA (jωk )|) for the different NaCl–glucose solutions. In this

figure is possible to identify the slight effect of the glucose over the impedance. At employed low frequencies there is a inverse relation glucose-impedance. The changes are small and slightly detectable in the figure. Around 10 kHz there is an inflection point and after this frequency the impedance become practically flat and the relation glucose impedance become proportional. A less perceptible behavior is present around the inflection point, where the impedance of the solution at different glucose concentrations crosses over the base solution. The exact frequency of the crossing point depends on the glucose concentration. Previous works have reported similar results. In [10], where the objective is to identify the complex dielectric of glucose in aqueous solutions, is possible to observe different inflections and crossing points along the analyzed frequencies (10 mHz to 10 MHz). In [6] is presented the complex plane plot showing the effect of the glucose over the impedance principally at low frequencies (the employed frequencies were between 100 mHz to 10 kHz). In [11] a similar behavior is present but no crossing between the impedance spectrum at different glucose concentrations were reported, while the is a proportional relation glucose-impedance along all the frequency axes (0.1 Hz to 10 MHz). The differences in the results between the different works can be explained by the employed sensors and sensor configuration. In [10], where the goal is to measure the dielectric properties of the glucose the configuration of two electrodes is employed. This configuration has the disadvantage that both electrodes contribute to the impedance making difficult the interpretation of the measurements, as is described briefly in the introduction. In [11] was employed the four electrodes configuration but this configuration is developed to avoid the polarization in the interphase electrode–electrolyte, its most common use is to measure the impedance across some solution phase–interphase such as a membrane [17,18]. Finally in [6] and [1] the three electrodes configuration was employed but the sensors were covered by glucose oxidase in order to develop enzymatic sensors. Other important observation in Fig. 1 is that at the employed excitation level (20 mV r.m.s.) the level of noise ˆ Z2 ,n (jωk ) and the total variance ˆ Z2

BLA ,total

BLA

(jωk ) are similar. This means that the system

is excited at the linear or pseudo-linear state, as was described in Section 2.2, and the impedance response can be accurately modeled by the BLA.

Fig. 1. Magnitude of the Zˆ BLA (jωk ) for the NaCl solution at five different glucose concentrations (colors). The zoom represents the |Zˆ BLA (jωk )| around 10 kHz. Around this frequency the spectral impedance response, at different glucose concentrations, presents crosses over the base solution (0 mg/dL) that depend on the glucose concentration. The level of noise (.) and the level of total standard deviation (+) are approximately to the same level indicating that the data were taken at semilinear state. The data set correspond to one experiment realization by glucose concentration employing the sensor two. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

O. Olarte et al. / Biomedical Signal Processing and Control 14 (2014) 9–18

13

Fig. 2. The differences between the impedances at different glucose concentrations, defined in the Eq. (12), are mayor than the noise level (|cnt Zˆ BLAp,q (jωk )| > ˆ Z2

BLA ,n

(jωk ))

along all the frequencies, which mean that changes in glucose concentration generates significant changes in the impedances measured. The plotted data set correspond to one experiment repetition employing the sensor two and five different glucose concentration solutions (0, 70, 120, 180 and 240 mg/dL). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

In order to evaluate if the changes in the impedance are significant, the differences between the Zˆ BLA (jωk ) at each glucose concentration should be calculated and compared with the level of noise of the system. The differences between the impedances at different glucose concentration are defined as:

The level of the ERE is defined as the standard deviation of the mean impedance along M different repetitions for a specific concentration. It is:

 cnt ˆ

|

ZBLAp,q (jωk )| = |Zˆ BLAp (jωk ) − Zˆ BLAq (jωk )|

(12)

where the sub-indexes p and q refer to different glucose concentrations with p = / q. The differences between the |Zˆ BLA (jωk )| at the different glucose concentrations are significant if they are larger than the level of noise. This is, |cnt Zˆ BLAp,q (jωk )| > ˆ Z2 ,n (jωk ). BLA Fig. 2 shows the significance of the impedance measurements at different glucose concentrations. In this figure the magnitude of the impedance (|Zˆ BLA (jωk )|),for the different glucose concentrations, is plotted by continuous dotted lines. The level of noise (ˆ Z2 ,n (jωk )) and the total standard deviation (ˆ Z2

BLA ,total

BLA

(jωk )) are presented with

dots and crosses respectively. Finally, the differences between the impedance at different glucose concentrations (|cnt Zˆ BLAp,q (jωk )|) in Eq. (12) are the orange lines. In the figure, the biggest impedance difference (upper orange line) corresponds to the differences between the impedance response for the solutions with glucose concentration zero and 240 mg/dL, while the lower impedance difference (button orange line) is obtained between the glucose concentration of 180 and 240 mg/dL. This result was present for all sensors and experimental repetitions. From the figure, it is possible to note that all the impedance differences are greater than the noise level along all the frequencies(|cnt Zˆ BLAp,q (jωk )| > ˆ Z2 ,n (jωk )). BLA It is means that the effect of the glucose, at the employed concentrations, generates significant changes in the measured impedances.

4.2. Effect of the experimental repetitions over glucose discrimination In order to analyze the effect of experimental repetition errors (ERE), M =5 repetitions were performed for each NaCl–glucose concentration.

[•] BLAp

G

  M [m] [•]  |GBLAp (jωk ) − GBLA (jωk )|2 p (jωk ) = 

(13)

M−1

m=1

where the index p mean a specific glucose concentration, and [•] GBLA (jωk ) is the mean value of the impedance over M repetitions p

at the glucose concentration P. In order to analyze the effects of the ERE represented by  [•] (jωk ) they should be compared to the level of noise G

ˆ Z

BLAp

BLA ,n

(jωk ) and the differences between the impedances at dif-

ferent glucose concentration |cnt Zˆ BLAp,q (jωk )|. It is, if the ERE are higher than the level of noise ( [•] (jωk ) > ˆ Z ,n (jωk )) the ERE G

BLAp

BLA

are significant they will affect the resolution of the system. On the other hand, if the ERE are lower than the differences between the impedances at different glucose concentration ( [•] (jωk ) < G

BLAp

|cnt Zˆ BLAp,q (jωk )|)

the impedance changes due to the glucose concentration are significant even over the ERE. In general, the ERE ( [•] (jωk )) are higher than the level of G

BLAp

noise (ˆ Z ,n (jωk )) suggesting that the experiments are not 100% BLA reproducible. However, the differences between the impedance at different concentrations (|cnt Zˆ BLAp,q (jωk )|), for the employed concentrations, are higher than the level of ERE ( [•] (jωk )). Thus, G

BLAp

even in the presence of ERE, the effect of the glucose over the impedance spectral response is significant at the employed glucose levels. The Fig. 3 shows an example of the here described. The figure shows the behavior of the level of ERE specifically for the case where the difference between the impedances are the lowest (the impedance difference for the concentration 180 and 240 mg/dL). In the figure is clear that the level of ERE are between the noise floor of the system and the differences between the impedance concentrations.

14

O. Olarte et al. / Biomedical Signal Processing and Control 14 (2014) 9–18

Fig. 3. The ERE defined in the equation (13) are mayor than the level of noise indicating that the experiments are not 100% reproducible. However, The level of the ERE are lower than the differences between the impedances at different glucose concentrations. This means that even in the presence of ERE it is possible to differentiate the glucose concentration at the employed levels. The data correspond to the sensor two, two glucose concentrations and M =5 experimental repetitions. The figure shows the data for the worst case, the lowest difference between impedance spectra, that are obtained employing the glucose concentrations 180 and 240 mg/dL. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

At this point, it is clear the existence of a relationship between the ERE ( [•] (jωk )), the difference between concentraG

BLAp

tions (|cnt Zˆ BLAp,q (jωk )|) and the resolution of the system. However,

this is out of the scope of the present article and current experimentation. The system resolution need to be calculated employing a more specific experimental design and considering smaller changes of glucose, specially at the borders of hypo-normo glycemia and normo-hyper glycemia. However, our results show that the glucose, at physiological concentrations, affects the impedance significantly. The significance has been assessed based on the level of noise and the presence of experimental errors. 4.3. Effect of the sensor

All the experiments were repeated employing three different sensors from the same brand. The effect of the sensor over the measurements is calculated as the difference between the impedance measurements obtained using different sensors at the same glucose concentration. It is: a,b a b |Sn Zˆ BLA (jωk )| = |Zˆ BLA (jωk ) − Zˆ BLA (jωk )| p p

(14)

p

/ b, and p refers the glucose where a and b refer the sensors with a = a,b concentrations. The effect of the sensor |Sn Zˆ BLA (jωk )| should be p

analyzed regarding the impedance differences between concentrations (|cnt Zˆ BLAp,q (jωk )|). It is, if the difference between sensors for a specific concentrations are higher than the difference between cona,b centration (|Sn Zˆ BLA (jωk )| > |cnt Zˆ BLAp,q (jωk )|) the sensor change p

has an important effect over the impedance measurements avoiding differentiate the glucose concentrations. In order to illustrate the effect of the sensors fig. 4 presents a significant case. This figure shows that the total variance (ˆ Z2 ,total (jωk )) and the level of noise (ˆ Z2 ,n (jωk )) are similar for BLA

BLA

the different sensors and around 40 and 50 dB under the measured a,b impedance (|Sn Zˆ BLA (jωk )|). This behavior is present along all the p

measurements (sensors, repetitions and glucose concentrations). On the other hand, the effect of employing different sensors a,b (red lines in the figure given by |Sn ZBLA (ωk )| in equation (14)) p

are located above the differences between the impedances at

different glucose concentrations (orange lines in the figure given by |cnt Zˆ BLAp,q (jωk )| in equation (12)). Such behavior is presents throughout all measurements (sensors, repetitions and glucose concentrations) indicating that, even when the employed sensors belong to the same brand their effects are significantly higher than the effects of the glucose, at physiological concentrations, in the impedance. This results reveal the need to develop calibration procedures and/or calibration algorithms in order to obtain reliable measurements using different sensors. This could be achieved by, for example, employing a well know substance and calculating the differences along the frequency axis. However, this is beyond the scope of the current experimentation. In this point, given that the effect of the employed sensors is higher than the effect of the glucose, it is not possible to combine the experimental data from different sensors and should be analyzed independently. 5. Parametric model in the frequency domain The analysis of the non-parametric models described in the previous section, shows that there are significant differences between the impedance at the physiological glucose concentrations employed. In the non-parametric model the information is tabulated and involves several groups of data: the impedance Zˆ BLA (jωk ), the excited frequencies (jωk ), the level of noise ˆ Z2 ,n (jωk ), the total variance ˆ Z2 ,total (jωk ), the difference among BLA

BLA

concentrations |cnt Zˆ BLAi,j (jωk )|, etc. On the other hand, a parametric model reduces all the information in a group of parameters that describes the system. An option to generate parametric models is based on rational functions. A rational function is the ratio of two polynomials, typically identified by the degree of the numerator and denominator. The rational function is defined as: nb 

B(jω, ) = Z mod (jω, ) = A(jω, )

br (jω)

r

r=0

na 

(15) aq (jω)

q

q=0

Where B(jω, ) and A(jω, ) are the polynomials in the numerator and denominator respectively. The order of the rational form is

O. Olarte et al. / Biomedical Signal Processing and Control 14 (2014) 9–18

15

Fig. 4. The effect of the sensor over the impedance. The effect of the sensor are higher than the difference between impedance at different glucose concentrations a,b (jωk )| > |cnt Zˆ BLAp,q (jωk )|). This means that the change of sensor has an important effect over the impedance measurements avoiding differentiate the glucose (|Sn Zˆ BLA p

concentrations. The plotted data corresponds to the impedance of the solution at 180 and 240 mg/dL, two repetitions by glucose concentrations and two sensors from the same brand. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

s−plane Zeros Location

imag(ω)

1 0.5 0 −0.5 −1 −15000

−10000

−5000

0

As a convention, for the description of the results, the pole/zero furthest from the origin will be called the pole/zero number one (No.1). The previous one, will be called the pole/Zero No.2, etc. So, the dominant pole/zero, the closest to the origin, will be called the pole/zero No.7. As a example of the behavior of the poles/zeros positions regarding the glucose content, the Fig. 6 presents the mean position of the zero No. 3 (top) and the pole No. 5 (bottom) plus +/− one standard deviation. From this figure it is possible to identify

4

Zero No. 3

x 10

Zero position (rad/sec)

nb /na . Details about the identification in the frequency domain are available in [28]. The modeling procedure of the experimental data leads to a group of models of order 7/7 where the poles and zeros are located along the negative real axis in the Laplace-plane. Fig. 5 shows the mean location of the poles and zeros for the analyzed glucose concentrations. The mean zeros/poles are represented with a o/x. The colors refer the related glucose concentration. From this figure can be concluded that the poles/zeros are located in groups and inside each group the differences in location refer a different glucose concentration.

−1.5

−2

−2.5

real(ω)

−3

s−plane Poles Location

Sensor 1

1

Pole No. 5

0 −0.5 −1 −15000

Sensor 3

−600

−10000

−5000

0

real(ω) zero/pole model for 0 mg/dL 1 0 zero/pole model for 70−1 mg/dL −1. 2−1 1 zero/pole model for 120−1. mg/dL 4

zero/pole model for 180xmg/dL 10 zero/pole model for 240 mg/dL

Pole position (rad/sec)

imag(ω)

0.5

Sensor 2

−700 −800 −900 −1000 −1100 Sensor 1

Fig. 5. Mean Zero (Top) and mean Pole (bottom) position from the model at different glucose concentration employing the data from the sensor one. The colors refer the different glucose concentrations. Note that the poles and zeros are located close each other, and for this reason the figure presents them in two different sub-figures (top: zeros, bottom: poles). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Sensor 2

Sensor 3

Fig. 6. Zero/pole mean position and +/− one standard deviation for the zero No. 3 and the pole No. 5 for the identified model. The colors represent the correspondent glucose concentration: 0 mg/dL (blue), 70 mg/dL (green), 120 mg/dL (magenta), 180 mg/dL (cian) and 240 mg/dL (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

16

O. Olarte et al. / Biomedical Signal Processing and Control 14 (2014) 9–18

Distance Between Pole−Zero 2

6. Discussion

−4000

The analysis of the non-parametric models shows that the effect of the glucose over the impedance is significant since the difference between the glucose concentrations |cnt ZBLAi,j (jωk )| is greater than the experimental repetition errors  [•] (jωk ) and

(rad/sec)

−6000

G

BLAp

−8000

those ones greater than the noise level ˆ Z2 variance ˆ Z2

−12000

Sensor 1 4

−0.4

x 10

Sensor 2

Sensor 3

Distance Between Pole−Zero 3

(rad/sec)

−0.6 −0.8 −1 −1.2 −1.4 −1.6

BLA

BLA ,total

−10000

Sensor 1

Sensor 2

Sensor 3

Fig. 7. Mean difference between the poles and zeros two and three for the identified model +/− one standard deviation. The colors represent the correspondent glucose concentration: 0 mg/dL (blue), 70 mg/dL (green), 120 mg/dL (magenta), 180 mg/dL (cian) and 240 mg/dL (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

a relation between the glucose concentration and the zero position. However, that relation is not always clear and the standard deviation covers zero position related to different glucose concentrations. Regarding the behavior of the poles, it is more difficult to identify a clear tendency for the different glucose concentrations. All the other poles and zeros (not shown) present similar behavior. From the previous description it is possible to say that the mean position of the zeros of the system give certain degree of correlation regarding the glucose concentration but that correlation is not easily identifiable in the poles. On the other hand, the standard deviation, either in the poles or zeros of the system, is quite large that covering the pole/zero positions for the different glucose concentrations avoiding to identify the glucose content. In conclusion the poles and zeros by apart do not reveal the glucose effect over the impedance spectrum. In order to relate the poles and zeros position of the identified model, the distance between the poles and zeros of the system is calculated. The Fig. 7 presents the result for the mean difference poles-zeros No. 2 and No. 3 and +/− one standard deviation for the different glucose concentrations and employed sensors. In this figure is possible to see that the difference between the poles and zeros shows a clear correlation regarding the glucose content present in the solution. Based in these results, we can affirm that the employed methodology, identification of the BLA of the impedance employing ORPM and identification of a rational parametric model in the Laplace domain, is a promised technique to estimate the glucose changes at physiological concentrations. The technique can be easily implemented. However, it is necessary to delve in a variety of related aspects such as the resolution of the system, as well as the behavior of the system in more complex solution-matrices (plasma, complete blood, etc.)

(jωk ) and the total ,n

(jωk ).

The results show that the employed sensors affect significantly the impedance measurement. This performance may be due to small changes in the sensor given the manufacturing process, handling or transport. Therefore, a calibration procedure need to be studied to reduce these effects in a practical application. There are different ways to characterize the impedance of a group of solutions. The most desirable is a mathematical expression that fully explains the physical processes present in the system. However, most of the time, such a mathematical expression is not known. Instead of that, a well-known technique in electrochemistry is to model the measurement data with a plausible electrical circuit that represents the spectral behavior of the impedance. The equivalent circuit model should be made up of circuit’s elements interconnected such that, represents the physical processes which are believed likely to be present. Nevertheless, there are several difficulties to reach the correct equivalent circuit’s model. The principal difficulties can be summarized as: (1) it is always possible to find more than one equivalent circuit to simulate the spectrum impedance for a particular system. (2) There is no way to say what of the different circuit’s configuration is correct. (3) It is always possible to improve the fitting by adding more electrical components but losing the physical meaning of the model. Given these difficulties, the present work, models the impedance employing a rational model. This model is a black box type model where the correspondence with the physical phenomena is not direct. It is, the information present in the system should be analyzed based on the experimental conditions. In the current experimentation, the system reveals the glucose content as a function of the poles and zeros behavior. It is clear that the present technique requires deeper experimentation in order to obtain a fully usable system. However, the goals of our article have been reached: The effect and significance of the glucose changes over the impedance have been assessed, and a parametric model that allows tracking those changes has been proposed. The identified rational parametric model is able to discriminate the glucose concentration based on the position of the poles and zeros. In general, the impedance spectrum of high conductive solutions, as the physiological, presents fractional behavior given the electrode electrolyte interphase. Such behavior has been modeled in equivalent circuits models by distributed elements [17,18]. An example of one distributed elements is the constant phase element represented by the equation (16). Zv (jω) = A(v)(jω)

−v

(16)

where A(v) is a parameter that represent the capacitance of the interphase electrode-electrolyte. ω is the angular frequency, and v defined between 0 < v < 1 refers the fractional characteristic of this element. In this context, it is not surprising that our model presents a relative high order (7/7) since the modeling of a fractional behavior in the Laplace domain (v = 1) requires a high number of poles and zeros [36,37]. Here, probably a modeling of the impedance spectrum in the fractional domain could be more adequate.

O. Olarte et al. / Biomedical Signal Processing and Control 14 (2014) 9–18

7. Conclusion The present work shows the significant effect of the glucose over the impedance at physiological glucose values. The BLA combined with ORPM generates information related to the linear behavior of the system, as well as the noise level and the non-linearities present. This information allow analyzing the impedance showing significant differences between the impedance measured at physiological glucose concentrations (0, 70, 120, 180 and 240 mg/dL). Based on the experimental design and methodology it is possible to establish: (1) around the excitation level of 20 mV r.m.s. the system behaves linear or pseudolinear. (2) The acquisition data is not 100% reproducible since the standard deviation of the repetitions (level of ERE) are over the noise floor. (3) The glucose at the employed physiological levels affects the impedance spectrum significantly allowing to differentiate the glucose concentrations. (4) The employed sensors affect significantly the impedance measurement. This performance may be due to small changes in the sensor given the manufacturing process, handling or transport. Therefore, a calibration procedure need to be implemented oriented to a practical application. The developed parametric model based on the BLA of the measured impedances allows identifying a correlation between the poles and zeros of the model and the different glucose concentrations. In the future more complex matrix solutions should be analyzed (plasma, complete blood, cells, etc.) in order to identify the behavior of the impedance for different components and glucose concentrations, as well as to study the effects in the poles/zeros positions. Nonetheless, our preliminary results suggest that the proposed approach has possibilities to detect the impedance changes at physiological glucose levels. Acknowledgments This research was funded by a postdoctoral fellowship of the Research Foundation-Flanders (FWO) and the Flemish Government (Methusalem Fund METH-1).

[10]

[11]

[12]

[13]

[14] [15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

References [1] T.L. Adamson, F.A. Eusebio, C.B. Cook, J.T. LaBelle, The promise of electrochemical impedance spectroscopy as novel technology for the management of patients with diabetes mellitus, Analyst 137 (2012) 4179–4187, http://dx.doi.org/10.1039/C2AN35645G. [2] R. Lisin, B.Z. Ginzburg, M. Schlesinger, Y. Feldman, Time domain dielectric spectroscopy study of human cells. I. Erythrocytes and ghosts, Biochim. Biophys. Acta 1280 (1996) 34–40. [3] A. Caduff, L. Livshits, Y. Hayashi, Y. Feldman, Cell membrane response on D-glucose studied by dielectric spectroscopy. erythrocyte and ghost suspensions, J. Phys. Chem. B 108 (2004) 13827–13830, http://dx.doi.org/10.1021/jp049923x. [4] Y. Hayashi, L. Livshits, A. Caduff, Y. Feldman, Dielectric spectroscopy study of specific glucose influence on human erythrocyte membranes, J. Phys. Appl. Phys. 36 (2003) 369–374. [5] L. Livshits, A. Caduff, M.S. Talary, Y. Feldman, Dielectric response of biconcave erythrocyte membranes to D- and L-glucose, J. Phys. D: Appl. Phys. 40 (2007) 15 http://stacks.iop.org/0022-3727/40/i=1/a=S03 [6] R.K. Shervedani, A.H. Mehrjardi, N. Zamiri, A novel method for glucose determination based on electrochemical impedance spectroscopy using glucose oxidase self-assembled biosensor, Bioelectrochemistry 69 (2006) 201–208, http://dx.doi.org/10.1016/j.bioelechem.2006.01.003. [7] S. Sbrignadello, A. Tura, P. Ravazzani, Electroimpedance spectroscopy for the measurement of the dielectric properties of sodium chloride solutions at different glucose concentrations, J. Spectrosc. 2013 (2013) 1–6. [8] O. Olarte, W. Van Moer, K. Barbe, Y. Van Ingelgem, A. Hubin, Using random phase multisines to perform non-invasive glucose measurements, in: 2011 IEEE International Workshop on Medical Measurements and Applications Proceedings (MeMeA), 2011, pp. 300–304, http://dx.doi.org/10.1109/MeMeA.2011.5966695. [9] O. Olarte, W. Van Moer, K. Barbe, S. Verguts, Y. Van Ingelgem, A. Hubin, Using the best linear approximation as a first step to a new non-invasive glucose measurement, in: 2012 IEEE International

[25]

[26]

[27] [28]

[29]

[30]

[31] [32] [33]

17

Instrumentation and Measurement Technology Conference (I2MTC), 2012, pp. 2747–2751, http://dx.doi.org/10.1109/I2MTC.2012.6229674. J.H. Park, C.S. Kim, B.C. Choi, K.Y. Ham, The correlation of the complex dielectric constant and blood glucose at low frequency, Biosens. Bioelectron. 19 (2003) 321–324, http://dx.doi.org/10.1016/S0956-5663(03)00188-X http://www.sciencedirect.com/science/article/B6TFC-497RBMH-1/2/ 92f7fa5b6e43c1b651a3fc7a31d4cfe6 A. Tura, S. Sbrignadello, S. Barison, S. Conti, G. Pacini, Impedance spectroscopy of solutions at physiological glucose concentrations, Biophys. Chem. 129 (2007) 235–241, http://dx.doi.org/10.1016/j.bpc.2007.06.001 http://www.sciencedirect.com/science/article/B6TFB-4NXRMMT-1/2/ 6ed6052636acf3deeaaafbfef3c4679a M.E. Ghica, C.M. Brett, A glucose biosensor using methyl viologen redox mediator on carbon film electrodes, Anal. Chim. Acta 532 (2005) 145–151, http://dx.doi.org/10.1016/j.aca.2004.10.058. G. Yoon, Dielectric properties of glucose in bulk aqueous solutions: influence of electrode polarization and modeling, Biosens. Bioelectron. 26 (2011) 2347–2353, http://dx.doi.org/10.1016/j.bios.2010.10.009. J. Rosell, J. Colominas, P. Riu, R. Pallasareny, J. Webster, Skin impedance from 1 Hz to 1 MHz, IEEE Trans. Biomed. Eng. 35 (1988) 649–651. A. Lackermeier, A. Pirke, E. McAdams, J. Jossinet, Non-linearity of the skins AC impedance, in: Proceedings of the Annual International Conference on IEEE Engineering, Medicine and Biology society, vol. 18, 1997, pp. 1945–1946. A. Caduff, E. Hirt, Y. Feldman, Z. Ali, L. Heinemann, First human experiments with a novel non-invasive non-optical continuous glucose monitoring system, Biosensors Bioelectronics 19 (2003) 209–217, http://dx.doi.org/10.1016/S0956-5663(03)00196-9, 7th World Congress on Biosensors, Kyoto, Japan, May 15–17, 2002. M.E. Orazem, B. Tribollet, Electrochemical Impedance Spectroscopy, John Wiley & Sons, Inc., Hoboken, New Jersey, 2008, http://dx.doi.org/10.1002/9780470381588. V. Lvovich, Impedance Spectroscopy: Applications to Electrochemical and Dielectric Phenomena, John Wiley & Sons, Inc., Hoboken, New Jersey, 2012, http://dx.doi.org/10.1002/9781118164075. E. Barsoukov, J.R. Macdonald, Impedance Spectroscopy: Theory Experiment and Applications, Wiley-Interscience, Hoboken, NJ, 2005 http://isbnplus.org/9780471647492 T.N. Gamry Instruments, Two-, Three-, and Four-electrode Experiments, Technical Report, Gamry Instruments, http://www.gamry.com/applicationnotes/all-notes/ (accessed 08.04.04). Y. Van Ingelgem, E. Tourwé, O. Blajiev, R. Pintelon, A. Hubin, Advantages of odd random phase multisine electrochemical impedance measurements, Electroanalysis 21 (2009) 730–739, http://dx.doi.org/10.1002/elan.200804471. M. Min, U. Pliquett, T. Nacke, A. Barthel, P. Annus, R. Land, Broadband excitation for short-time impedance spectroscopy, Physiol. Meas. 29 (2008) S185, URL: http://stacks.iop.org/0967-3334/29/i=6/a=S16. Y. Feldman, I. Ermolina, Y. Hayashi, Time domain dielectric spectroscopy study of biological systems, IEEE Trans. Dielectr. Electr. Insul. 10 (2003) 728–753. M. Min, U. Pliquett, T. Nacke, A. Barthel, P. Annus, R. Land, Signals in bioimpedance measurement: different waveforms for different tasks, in: H. Scharfetter, R. Merwa (Eds.), 13th International Conference on Electrical Bioimpedance and the 8th Conference on Electrical Impedance Tomography, vol. 17 of IFMBE Proceedings, Springer, Berlin Heidelberg, 2007, pp. 181–184, http://dx.doi.org/10.1007/978-3-540-73841-1 49. U. Pliquett, Time-domain based impedance measurement: strengths and drawbacks, J. Phys. Conf. Ser. 434 (2013) 012092 http://stacks.iop. org/1742-6596/434/i=1/a=012092 R. Land, P. Annus, M. Min, Time-frequency impedance spectroscopy: Excitation considerations, in: M. Cretu, C. Sarmasanu (Eds.), 15th IMEKO TC4 International Symposium on Novelties in Electrical Measurements and Instrumentations, vol. 1 of 15th IMEKO TC4 Internatinal Symposium on Novelties in Electrical Measurements and Instrumentations Proceedings, CERMI Publishing House, 2007, pp. 328–331. Evaluation of Measurement Data – Guide to the Expression of Uncertainty in Measurement, JCGM 100, 2008. R. Pintelon, J. Schoukens, System Identification: A Frequency Domain Approach, John Wiley & Sons, Inc., Hoboken, New Jersey, 2012, http://dx.doi.org/10.1002/9781118287422. Y. Van Ingelgem, E. Tourwe, J. Vereecken, A. Hubin, Application of multisine impedance spectroscopy, FE-AES and FE-SEM to study the early stages of copper corrosion, Electrochim. Acta 53 (2008) 7523–7530, http://dx.doi.org/10.1016/j.electacta.2008.01.052, 7th International Symposium on Electrochemical Impedance Spectroscopy, Argeles sur Mer, France, June 03–08, 2007. Juvenile, Diabetes Research Foundation Continuous Glucose Monitoring Study Group, Variation of interstitial glucose measurements assessed by continuous glucose monitors in healthy, nondiabetic individuals, Diabetes Care 33 (2010) 1297–1299. American Diabetes Association, Standards of medical care in diabetes – 2006, Diabetes Care 29 (2006) S4–S42. DropSens, Screen-printed Platinum Electrodes. Ref. 550, http://www.dropsens.com/, (accessed 08.04.14). R.O. Kadara, N. Jenkinson, C.E. Banks, Characterisation of commercially available electrochemical sensing platforms, Sens. Actuators B:

18

O. Olarte et al. / Biomedical Signal Processing and Control 14 (2014) 9–18

Chem. 138 (2009) 556–562, http://dx.doi.org/10.1016/j.snb.2009.01.044 http://www.sciencedirect.com/science/article/pii/S0925400509000422 [34] H. Akaike, New look at statistical-model identification, IEEE Trans. Automatic Control AC 9 (6) (1974) 716–723. [35] J. Rissanen, Modeling by shortest data description, Automatica 14 (5) (1978) 465–471. [36] K. Barbé, O. Olarte, W.V. Moer, L. Lauwers, Fractional models for modeling complex linear systems under poor frequency resolution measurements,

Digital Signal Process. 23 (2013) 1084–1093, http://dx.doi.org/10.1016/j.dsp. http://www.sciencedirect.com/science/article/pii/ 2013.01.009 S1051200413000171 [37] R. Mansouri, M. Bettayeb, S. Djennoune, Approximation of high order integer systems by fractional order reduced-parameters models, Math. Comput. Model. 51 (2010) 53–62, http://dx.doi.org/10.1016/j.mcm.2009.07.018 http://www.sciencedirect.com/science/article/pii/S0895717709003045