Hindawi Publishing Corporation
Journal of Electrical and Computer Engineering
Volume 2011, Article ID 953064, 12 pages
doi:10.1155/2011/953064
Research Article
RegressionMethods for Ophthalmic Glucose Sensing
UsingMetamaterials
Philipp Rapp,1 MartinMesch,2 Harald Giessen,2 and Cristina Tarı´n1
1 Institute for System Dynamics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany
2 4th Physics Institute, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
Correspondence should be addressed to Philipp Rapp, rapp@isys.uni-stuttgart.de
Received 31 May 2011; Accepted 5 August 2011
Academic Editor: David Hamilton
Copyright © 2011 Philipp Rapp et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We present a novel concept for in vivo sensing of glucose using metamaterials in combination with automatic learning systems. In
detail, we use the plasmonic analogue of electromagnetically induced transparency (EIT) as sensor and evaluate the acquired data
with support vector machines. The metamaterial can be integrated into a contact lens. This sensor changes its optical properties
such as reflectivity upon the ambient glucose concentration, which allows for in situ measurements in the eye. We demonstrate
that estimation errors below 2% at physiological concentrations are possible using simulations of the optical properties of the
metamaterial in combination with an appropriate electrical circuitry and signal processing scheme. In the future, functionalization
of our sensor with hydrogel will allow for a glucose-specific detection which is insensitive to other tear liquid substances providing
both excellent selectivity and sensitivity.
1. Introduction
Diabetes is the direct cause of over 1.1 million deaths in
2005, and the diabetes death rate is estimated to double by
2030. The World Health Organization (WHO) indicates in
[1] that nowadays more than 220 million people have to live
with diabetes. In order to allow the patients to maintain a
healthy life avoiding coronary artery, peripheral arterial and
cerebral vascular disease, or heart failure, early diagnosis and
continuous management are crucial. Current practice for di-
abetes management relies on intensive insulin therapy in-
volving frequent blood glucose measurements. Using inva-
sive glucose sensors means that patients have to prick their
finger for a drop of blood multiple times a day, about 1800
times per year, which also involves higher risk of infection.
For these reasons, in the last decades new techniques have
been employed to develop noninvasive devices for blood glu-
cose monitoring.
The technologies under consideration include infrared
(IR) spectroscopy [2], fluorescence spectroscopy, Raman
spectroscopy, optical polarization rotation measurements,
photoacoustic probes, and surface plasmon resonances.
However, none of these devices has been made commercially
available or was approved to substitute direct invasive glucose
measurement. In order to overcome these shortcomings, al-
ternative approaches have been developed to measure glu-
cose concentration in an accessible body fluid, including
urine, saliva, and tear fluid.
The undeniable advantage of estimating blood glucose
levels through tear fluid lies in the facts that tears are more
simply and noninvasively accessible than other body fluids,
more continuously obtainable, and less susceptible to dilu-
tion than urine. Tear fluid provides a unique opportunity to
develop a noninvasive interface between a sensor and the
body that could be used to monitor several physiological and
metabolic indicators, most notably glucose. The noninvasive
feature would be the main advantage of this sensing scheme.
1.1. Ophthalmic Glucose Sensing. Tear fluid is the aqueous
layer on the ocular surface and has many functions as part of
the optical system, that is, lubrication and nourishing. Tear
fluid consists of over 20 components, including salt water,
proteins, lactate, urea, pyruvate, ascorbate, glucose, as well as
2 Journal of Electrical and Computer Engineering
some small metallic ions. Its average rate of production lies in
the range of 0.52–2.2 μL/min; about 0.72–3.2mL of tears are
secreted per day.
The idea of using tear fluid as amedium for glucosemon-
itoring has been discussed since the 1930s involving human
and animal models to estimate correlation between tear glu-
cose and blood glucose. The current technique is to collect
tear fluid samples in capillary tubes and then assay the sam-
ples for glucose ex situ using standard laboratory instrumen-
tation. Using this technique, there are many reports demon-
strating that tear glucose is higher in diabetic subjects than
in healthy ones and that there effectively exists correlation
of tear glucose and blood glucose. It should be noted that
the discrepancy of the correlation coefficient between blood
glucose and tear glucose can be attributed to the different tear
collection methods, for example, filter paper or microcap-
illary methods. In [3] a profound review of several studies
resumes the most important findings.
However even after 70 years of research, there are no clin-
ical studies that have satisfactorily resolved the relationship
between tear and blood glucose concentrations. Disagree-
ments between reports may not invalidate the correlation
between tear and blood glucose because, regardless of the
exact mechanism of glucose transport into tear fluid, the in-
dividual accuracy holds true for each set of experimental
conditions.
An alternative approach developed recently uses an in
vivo glucose sensing method that can be placed in the tear
canal and that therefore reduces variability due to probe ex-
traction technique [4]. It allows measurements to be carried
out in situ. This amperometric sensor is comprised of three
electrodes that are screen-printed on a flexible polyamide
substrate which allows the sensor to be wound into a tight
roll that fits in the tear canal for in situ monitoring.
Definitely, integrating a glucose sensor into a contact lens
would provide a way to continuously and reliably sense met-
abolites and especially glucose in tear fluid. Different ideas
to implement such a sensor have been proposed and are at
present in different stages of development. They rely on plac-
ing a photonic sensor in a contact lens and envision a hand-
held readout unit for measuring the signal. Thus far, holo-
graphic hydrogels and fluorescent indicators have been ex-
plored as glucose-responsive elements. In [5] a polarimetric
glucose sensor for monitoring ocular glucose is developed.
There it is indicated that the time lag between blood glucose
and anterior aqueous humor glucose concentrations was on
average about five minutes. Another approach is based on a
contact-lens-based sensor [6, 7].
It is likely that contact-lens-based glucose sensors have
great potential to realize continuous and noninvasive diabe-
tes control, that is, contact lenses have applications beyond
vision correction. Luminescent/fluorescent contact-lens-bas-
ed sensors represent a feasible technique because they require
no electrodes or electric circuits. Further efforts are needed
to improve the resolution and sensitivity of the new device
and to determine a physiologically relevant and baseline tear
glucose concentration [8, 9].
Existing methods of fluorescent glucose sensing apply
Fluorescence Resonance Energy Transfer (FRET) [10]. This
method is based on the dual measure, that is, the FRET and
fluorescence intensity measurements. FRET is an inexpensive
and very sensitive method to apply to molecule imaging.
However, barriers to secure a feasible contact lens sensor in-
clude the photobleaching of fluorescencemolecules, low con-
centration of tear samples, low fluorescence intensity, and
vision influence. In addition, one safety concern is that some
harming substances may be released from the lens into the
body.
1.2. Our Concept: Metamaterial-Based Biosensing. In the
present contribution a revolutionary concept for tear glucose
measurement is developed. This sensing is based on the use
of metamaterials, that is, artificial materials with special ele-
ctromagnetic properties that do not occur naturally. In [11]
a method how to manufacture such metamaterials is report-
ed for the first time: a periodic structure design with unit cells
much smaller than the wavelength of the incident radiation
leads to a specific electromagnetic response on a wide spectr-
al range. Also based on this work, the concepts of perfect lens
as well as cloaking are developed in [12, 13]. Tailoring of op-
tical properties using the plasmonic analogue of EIT offers
the possibility to obtain sharp resonances in the transmit-
tance profile of a material leading to enhanced spectral fea-
tures that can eventually be pushed to the limit of detecting
single molecules [14]. Other designs such as plasmonic oli-
gomers are also possible [15, 16]. They rely on the formation
of suitable sharp spectral Fano resonances [17].
Metamaterials are able to detect even minute changes in
the dielectric properties of their environment, hence selec-
tivity to a particular type of molecule has to be added. This
is achieved by covering the metamaterial with a glucose-sen-
sitive hydrogel [18]. When using inverse opal photonic crys-
tals, the optical diffraction changes upon glucose exposure
[19]. In Figure 1 a schematic of our proposed design is
shown: a contact lens material supports a few nanometers
of a gold-based metamaterial which is functionalized with
glucose-sensitive hydrogel. This design is transparent in the
visible and near-infrared range and thus can be designed as
contact lens to be inserted into the patient’s eye. The readout
is carried out by an external light-emitting diode (LED)
in the infrared (eye-safe range at wavelengths longer than
1.4 μm) which is used as light source, and the reflected light
is captured by a photodiode whose intensity response is
evaluated. Signal postprocessing stages based on regression
methods allow the reliable estimation of the tear glucose
content.
This new method has the potential to be extremely suc-
cessful for noninvasive glucose sensing for several reasons.
(1) Glucose selectivity: this sensor does not take advan-
tage of the rather poor optical differences between the
glucose molecule and other substances contained in
the surrounding fluid (blood stream, tear fluid, etc.),
but rather on the ability of the glucose to change se-
lectively the refractive index of a specific material,
that is, the hydrogel in the vicinity of the metama-
terial.
Journal of Electrical and Computer Engineering 3
y
u uS
Laser/LED Amplifier
Reflected light
Glucose-sensitive hydrogel
Metamaterial layer
Nonsensitive hydrogel
Eye
Figure 1: Schematic of the proposed design.
(2) Sensitivity: due to the fact that the metamaterial is
sensitive to even minute changes in the refraction
index (molecular changes in the hydrogel) the meas-
urement can be performed in the range of physiolog-
ical glucose concentration in the tear fluid.
(3) Biocompatibility: the metamaterial is made of a sev-
eral nanometers thick gold structure, transparent for
the human eye, and absolutely biocompatible due to
the properties of noble metals. The hydrogel is com-
monly used for contact lenses and therefore well char-
acterized. The optical readout is based on an eye-safe
LED.
(4) Nondegrading: during the lifetime of the sensor (up
to 24 hours) both the metamaterial and the hydrogel
maintain its optical properties even when immersed
in body fluid.
2. Methods
2.1. Metamaterials. The metamaterial structures are fabri-
cated by electron beam lithography. For laboratory experi-
ments, a 30–40 nm layer of gold is deposited on a 10 ×
10mm2 quartz substrate using electron-beam evaporation.
Next, a negative photo resist is spin-coated on top of the sub-
strate, allowing the desired structures to be defined by elec-
tron-beam lithography. After development of the resist, di–
rected argon ion beam etching is carried out to transfer the
structure into the gold layer.
Multilayer designs can be achieved by combining this
process with a stacking technique [20]. In this case, one
starts with the evaporation of several gold alignment marks
with a thickness of about 250 nm using positive resist with
subsequent gold evaporation and lift-off. The first layer can
then be manufactured following exactly the procedure given
for a single layer. Afterwards, a spacer layer is applied by spin
coating. The spacer currently consists of a hardenable photo-
polymer and can vary in height from ten to several hundreds
Substrate Substrate Substrate
Au Au PEG-biotin Streptavidin
Figure 2: The principle of biological sensing with metamaterial
gold structures.
of nanometers. Additional layers may be added by repetition
of those steps while accurate alignment between the layers is
assured using the gold marks during the electron beam ex-
posure.
2.2. Biosensing. In general, broadband electromagnetic radi-
ation in the optical domain is used to investigate the re-
spective properties of nanostructures in sensing applica-
tions. One possibility is the recording of transmittance or
reflectance spectra which exhibit characteristic dips and
peaks. Due to the localized electric field in and around the
metallic pattern, the resonance positions are highly sensitive
to changes of the electric permittivity or the refractive index,
respectively, in the nearest vicinity of the plasmonic nanos-
tructures. Exploiting this fact allows to monitor, for example,
the concentration of pure solutions on top of the structure by
evaluating the shift of a distinct spectral feature [19].
However, such gold structures are not able to detect spe-
cific substances in an unfunctionalized fashion. To realize a
chemically selective sensor, we have to assure that the changes
in the refractive index are exclusively caused by the desired
analyte. For biological sensing, the existence of molecule
pairs with strong affinity can be beneficial. Ranking among
the strongest noncovalent interactions known in nature, the
biotin-streptavidin complex, for example, is a commonly
used system for proof of concept experiments (see Figure 2).
The vitamin biotin can be functionalized with a thiol group
by utilising polyethylene glycol as a spacer. This allows the
whole molecule to bind to the gold nanostructures. If the
structure is now rinsed with an analyte containing streptavi-
din, the molecules will attach to the biotin and due to their
presence affect the dielectric environment of the gold struc-
ture. This effect, and therefore the detectable change in the
optical spectrum, will remain even after washing away other
substances that may have an impact on the measurement
[21].
From a conceptual point of view, the method of embed-
ding the functionalization into a hydrogel is similar. Hydro-
gels are polymer networks that, due to their hydrophilic
properties, absorb a considerable amount of water which
causes substantial swelling. Lee et al. have shown that replac-
ing several sites in the polymer chains with a molecule which
will form a charged complex with a glucose molecule estab-
lishes a relation between the swelling of the hydrogel and the
glucose concentration in the surrounding water [18]. As
those changes in volume also imply a varying refractive in-
dex, they again are subject to detection by the metamaterial
structure.
4 Journal of Electrical and Computer Engineering
The resulting spectra in both cases can be analyzed in dif-
ferent ways. An important value is the so-called sensitivity
sλ = Δλ
Δn
or sE = ΔE
Δn
(1)
which describes the shift in nm or eV of the resonance per
refractive index unit (RIU). According to Sherry et al. the
linewidth of the resonance also plays an important role [22].
Therefore one can define a figure of merit
FOMλ,E = sλ,EFWHM, (2)
where FWHM denotes the full width at half maximum.
These values have in common that a spectrometer is
needed to determine both. This rather complex and cost-ex-
tensive method is only applicable in scientific research. In
commercial products it is more likely that intensity changes
at a specific wavelength are evaluated. This leads to the inten-
sity dependent sensitivity
sI = ΔI
Δn
(3)
and the related figure of merit
FOMI = sI
I
(4)
describing the relative intensity change per refractive index
unit.
2.3. Simulation Model. Scattering matrix theory was used to
simulate the spectra of the metamaterial structures. This
method which uses a Fourier modal decomposition of the
electric and magnetic fields has been introduced by Whit-
taker and Culshaw [23] and has later been extended and im-
proved by Tikhodeev et al. [24] as well as recently by Weiss
et al. [25].
The dielectric functions for the materials used to define
the periodically repeated unit cell can be retrieved from a da-
tabase or entered as parameters for the Drude model.
In the definition of the structure as well as in the calcu-
lations, the design is separated into single layers, beginning
at the superstrate, down to the substrate, each homogeneous
along the z-axis. The first step is to solve Maxwell’s equations
for every layer.
The structured slab couples the incident light with fre-
quency ω and wave vector k to all Bragg-orders retrieved
from Maxwell’s equations with the same frequency and wave
vector
kx,G = kx +Gx, ky,G = ky +Gy , (5)
with the reciprocal lattice vector
G =
(
Gx,Gy , 0
)
= 2π
dx
(
gx, gy , 0
)
,
gx,y = 0,±1,±2, . . . ,±∞
(6)
and the lattice constant dx.
Hence, the S-matrix method is able to calculate the out-
bound 4Ng harmonics from the system (Ng = 2g + 1). The
method is exact forG → ∞. In reality, only a limited number
of lattice vectors are used for the calculation. Because of the
fact that the calculation time increases with N3g , computing
power is the limiting factor. A typical number for Ng is 25×
25.
Themethod can be accelerated and improved in accuracy
by using adaptive spatial resolution and the customisation
of the coordinate system, depending on the individual struc-
ture.
In the next step, the amplitudes of the waves in the single
layers have to be concatenated. Therefore, the respective solu-
tions of Maxwell’s equations have to be separated into a set
of eigenvectors parallel to the z-axis. The amplitudes of the
plane waves can now be written as vectors
A(z) =
⎛
⎝
A+(z)
A−(z)
⎞
⎠. (7)
All components heading to the positive (negative) z-direc-
tion are labelled with + (−). With the aid of a so-called trans-
fer matrix, those vectors are linked at different positions (z-
values) in the layer:
A(z + L) = TL A(z). (8)
The transition from one layer (a) to another (b) can be de-
scribed similarly:
A
∣∣∣
z=zb,a+0
= Tb,a A
∣∣∣
z=zb,a−0
. (9)
In general, it would be possible to calculate the propagation
of light in layered structures using the transfer matrix for-
malism. However in case of evolving evanescent waves, this
method may fail. This is the reason for using the scattering
matrix algorithm. All amplitudes of waves incident on the
sample, as well as the outbound waves, are combined into
one vector:
Bin =
⎛
⎝
A+v (z)
A−s (z)
⎞
⎠, Bout =
⎛
⎝
A+s (z)
A−v (z)
⎞
⎠. (10)
Here, v means “vacuum” (above the sample), and s means
“substrate” (below the sample). The scattering matrix con-
catenates both vectors:
Bout = Sv,sBin. (11)
The whole S-matrix can be obtained by iteration, beginning
with the unit matrix for N = 0 layers and subsequently
calculating the matrix for N + 1 layers with the aid of the
inverse transfer matrix.
Using scattering matrix theory, it is possible to calculate
reflectance, transmittance, extinction, and absorption spec-
tra of metallic structures. Additionally, information about
the electric and magnetic field distribution can be obtained.
Journal of Electrical and Computer Engineering 5
2.4. Regression Methods. The aim in regression is to find a
functional connection between some input x (for example,
x ∈ Rn) in input space and some output y ∈ R, that is,
y = f (x). Once this connection is established using some
training data, it is validated by applying the regression model
on data that was not used during the training process. The
validatedmodel is then employed on unknown input data for
the task of output prediction. In this paper, the method of
support vector machine regression (SVR) [26] is used.
Support vectormachines emerged from the field of learn-
ing theory. They are constructed using training data. Com-
pared to other learning methods, overfitting is avoided by
implementing the paradigm of structural risk minimization
(SRM) [27].
The first step consists of defining Vapnik’s -insensitive
loss function
e
(
xi, yi, f
) = max{0,∣∣yi − f (xi)
∣∣− }, (12)
where (xi, yi) is the ith pair of training data. This can be
thought of as a punishment for the deviation of the estimated
value f (xi) from the given value yi. The affine ansatz
f (x) = 〈w, x〉 + b (13)
is made, where 〈·, ·〉 denotes the scalar product. Implement-
ing the SRM requires minimization of the weighted sum of
the capacity (1/2)〈w,w〉 of the machine and the training
error
∑N
i=1 e(xi, yi, f ), thus leading to
min
1
2
〈w,w〉 + C
N∑
i=1
e
(
xi, yi, f
)
. (14)
Slack variables ξ(∗)i (ξi and ξ
∗
i ) are introduced to account for
outliers [26]. This leads to the Lagrangian function
LP
(
w, b,α(∗),β(∗)
)
= 1
2
〈w,w〉 + C
N∑
i=1
(
ξi + ξ∗i
)−
N∑
i=1
(
βiξi + β∗i ξ
∗
i
)
−
N∑
i=1
αi
(〈w, xi〉 + b − yi +  + ξi
)
−
N∑
i=1
α∗i
(
yi − 〈w, xi〉 − b +  + ξ∗i
)
(15)
in primal space, which has to be minimized with respect to
the primal variables w and b and maximized with respect
to the dual variables α(∗) and β(∗), which are the Lagrange
multipliers.
Plugging in the necessary conditions for a saddle point
yields the Lagrangian function
LD
(
α(∗)
)
=− 1
2
N∑
i, j=1
(
αi − α∗i
)(
αj − α∗j
)
〈xi, xj〉
−
N∑
i=1
(
 − yi
)
αi −
N∑
i=1
(
 + yi
)
α∗i
(16)
in dual space, which has to be maximized with respect to α =
(α,α∗) subject to the constraints
N∑
i=1
(
αi − α∗i
) = 0,
0 ≤ αi ≤ C,
0 ≤ α∗i ≤ C.
(17)
In order to achieve nonlinear regression, a mapping
x ∈ Rn 	−→ Φ(x) ∈ R f (18)
from input space to feature space is introduced. Usually
f 
 n holds true. The nonlinear regression in input space
corresponds to a linear regression in some feature space. In-
stead of actually performing the mapping, which might be
computationally expensive, the so-called kernel trick is ap-
plied. It depends on the fact that the training data only occurs
in the form of scalar products and that scalar products in
feature space can be calculated in input space using the kernel
k(·, ·) according to
k
(
xi, xj
)
=
〈
Φ(xi),Φ
(
xj
)〉
. (19)
3. Results
3.1. Simulated Reflectance Spectra. For a first overview, we
simulated spectra for a broad concentration range of aqueous
glucose solutions on top of different metamaterials, namely,
a simple plasmonic dipole and a stacked EIT-type metama-
terial. Starting with pure water, we added
20 · 0.5 (10−n), n = 1, 2, 3, . . . , 10, (20)
weight percent of glucose, corresponding to values from
about 40mg/dL up to 22 g/dL.
Our EIT metamaterial uses a 60 nm displacement of the
dipole bar from the central symmetry axis. The length of the
dipole bar is 340 nm, whereas the quadrupole bar is 345 nm
long. Their width is 80 nm, the gold thickness is 40 nm, and
the spacer thickness is 70 nm.
The simple dipole structure shows one distinct peak,
whereas the coupled dipole and quadrupole antenna devel-
ops an additional reflectance dip in the center of the broad
peak (Figures 3(a)–3(d)). Highly confined electric fields are
responsible for sensitivity and the possibility of extremely
small sensing volumes (Figure 3(e)). The resulting sensitiv-
ities are sI = 4.5/RIU and sλ = 625nm/RIU. The FOMλ is
6.0, and the FOMI is 9.5.
3.2. Sensitivity Analysis. This section deals with the identifi-
cation of those parameters and noise contributions that may
have influence on the expected measurement results. To this
end, the metamaterial simulation tool is extended by a model
of the signal processing units containing noise sources and
nonstationary parameter sets. The block diagram used for
the simulation is depicted in Figure 4. The source consists of
a modulated steering signal u˜(t) that drives the laser diode,
6 Journal of Electrical and Computer Engineering
1400 1600 1800 2000 2200 2400
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Water
R
efl
ec
ta
n
ce
Wavelength (nm)
Glucose solution (20%)
E
(a)
Water
Glucose solution
R
efl
ec
ta
n
ce
Wavelength (nm)
1629.5 1630 1630.5 1631 1631.5
0.538
0.539
0.54
Decreasing
oncc entration
(b)
1400 1600 1800 2000 2200 2400
0
0.1
0.2
0.3
0.4
0.5
Water
R
efl
ec
ta
n
ce
Wavelength (nm)
Glucose solution (20%)
E
(c)
Water
Glucose solution
R
efl
ec
ta
n
ce
Wavelength (nm)
1629.5 1630 1630.5 1631 1631.5
Decreasing
oncc entration
0.24
0.241
0.242
(d)
z
xzx
y y
0
1.00e8
9.34e7
8.72e7
8.11e7
7.5e7
6.89e7
6.28e7
5.66e7
5.05e7
4.44e7
3.83e7
3.21e7
2.6e7
1.99e7
1.38e7
7.65e6
(V/m)
(e)
Figure 3: S-matrix simulations of a simple dipole structure (a) and a coupled dipole and quadrupole antenna (c) with water and 20%
glucose solution on top. A detailed view for smaller concentrations ranging from 1.25% down to 0.04% is given in (b) and (d), respectively.
Figure (e) depicts the time averaged absolute values of the electric field in and around the structure at the resonance position.
fromwhich both the output power P˜0(t) and the actual wave-
length λ(t) are measured. Laser diodes show some deviation
Δλ from their nominal wavelength due to the manufacturing
processes, and their wavelength also varies significantly with
temperature.
The contact lens block contains the embedded metama-
terial spectra which functionally attenuates the power output
P˜0(t) to the received reflected power P˜(t), depending on the
actual wavelength λ(t).
The reflected laser ray is detected by the photodiode.
Figure 5 shows a scheme of the circuitry which is used to
amplify the current of the photodiode [28]. A characteristic
feature for this kind of feedback amplifier is the virtual
ground at the node of the inverting input terminal which
Journal of Electrical and Computer Engineering 7
Modulated signal source
Laserdiode
Contact lens
Photodiode
Demodulation and filtering
Physiological glucose
concentration cglucose
u˜(t)
λ(t)
λ(t)
˜P0(t)
˜P(t)
y˜(t)∼ ˜i(t)
y ∼ i
Figure 4: Block diagram used for simulation including signal proc-
essing scheme and embedded metamaterial model.
enables a higher bandwidth [29]. The bias resistor RB reduces
the effect of the bias current, which is nonzero for any real
operational amplifier. In the simulation model, the current
i˜(t) of the photodiode is converted to an output voltage y˜(t)
using unit amplification.
Finally, demodulation and filtering are performed. In or-
der to avoid higher frequency noise contributions and to de-
tect the steady state value, low-pass filtering is performed and
its output signal y is then evaluated.
The selected wavelengths represent the spectra at their
steepest slope. In fact, for the dipole metamaterials, λdipole =
1823nm is used, and for the EIT metamaterials, λEIT =
1631nm.
3.2.1. Noise Sources. Considering this simulation model the
noise sources are analyzed qualitatively in order to find out
which of them are relevant.
According to [28, 30], the total noise in a photodiode is
the sum of its thermal noise (Johnson-Nyquist noise), shot
noise, 1/f noise, and generation-recombination noise.
The thermal noise I2th and the shot noise I
2
sh are calculated
according to
I2th =
4kTΔ f
R
,
I2sh = 2qIDΔ f ,
(21)
with the real part R of the impedance, Boltzmann’s constant
k = 1.38 × 10−23 J/K, the temperature T in Kelvin, the elec-
tron charge q = 1.602 × 10−19 C, the diode current ID, and
uS
RF
y
RB
+
−
Figure 5: Circuitry used for the amplification of the photodiode
current.
101 102 103
−25
−20
−15
−10
−5
0
5
10
f (Hz)
N
(f
)
(d
B
)
Figure 6: Noise filter used to shape white thermal and shot noise.
the noise bandwidth Δ f . Both thermal and shot noise are
modelled as white noise. They form the 0 dB line of the noise
filter (Figure 6), which takes into account 1/f-noise and gen-
eration-recombination noise. In the presented simulations,
the sampling frequency fS = 2000Hz is used. The Nyquist
frequency is therefore fN = fS/2 = 1000Hz.
According to the modeled noise sources the noise power
of the photodiode noise decreases as the frequency increases.
Exactly for this reason, the laser signal is modulated with
f mod, which is chosen to be f mod = fN /2 = 500Hz for the
presented simulations, thus taking advantage of the noise
reduction at higher frequencies. This fact becomes apparent
when analyzing the power spectral density (PSD) of the pho-
todiode current: almost the entire signal power is contained
within the band around f mod (see Figure 7), where the noise
can be disregarded. Thus we conclude that the influence of
the photodiode noise can be neglected with regard to the
glucose measurement results.
3.2.2. Parameter Variation. Significant parameter variation is
expected with regard to temperature and laser wavelength.
8 Journal of Electrical and Computer Engineering
0 100 200 300 400 500 600 700 800 900 1000
−160
−140
−120
−100
−80
−60
−40
−20
f (Hz)
fmod
P
di
od
e,
id
ea
l
(d
B
)
(a)
f (Hz)
460 470 480 490 500 510 520 530 540
−140
−130
−120
−110
−100
−90
−80
−70
−60
−50
−40
−30
P
di
od
e,
id
ea
l
(d
B
)
(b)
Figure 7: PSD of the ideal photodiode current signal. (a) depicts
the entire spectrum, whereas (b) shows a detailed view of the power
spectral density around the modulation frequency f mod.
(i) Temperature. A change in temperature modifies the
wavelength of the laser and thus is considered to be a crucial
parameter.
The influence of the temperature is investigated for a
constant concentration cglucose = 10% and for both metama-
terial structures (dipole and EIT). The results are depicted in
Figure 8, where we observe that the normalized photodiode
current sensitivity to temperature deviations is of ST =
ΔI/ΔT = 0.017mA/K for dipole metamaterial and of ST =
0.03mA/K for the EIT metamaterial. Therefore, the tem-
perature drift must be taken into account when evaluating
measurements.
(ii) Wavelength. The deviation Δλ of the laser wavelength
from its nominal value is investigated in relation to the
photodiode current. Figure 9 shows the photodiode current
over Δλ for Δλmax = ±3nm for both the dipole and the EIT
14.2
14.25
14.3
14.35
14.4
14.45
14.5
14.55
P
h
ot
od
io
de
cu
rr
en
t(
m
A
)
24 26 28 30 32 34 36 38 40
T (◦C)
(a)
24 26 28 30 32 34 36 38 40
P
h
ot
od
io
de
cu
rr
en
t(
m
A
)
7.15
7.2
7.25
7.3
7.35
7.4
7.45
7.5
7.55
7.6
7.65
T (◦C)
(b)
Figure 8: Photodiode current over temperature T for the dipole
metamaterial (a) and for the EIT metamaterial (b).
metamaterial for a constant concentration of cglucose = 10%.
The resulting wavelength deviations sensitivity is Sλ =
ΔI/Δλ = 0.05mA/nm for dipole metamaterial and Sλ =
0.1mA/nm for EIT metamaterial.
Thus, the laser diode wavelength drift is an even more
significant parameter than temperature.
3.2.3. Glucose Concentration Sensitivity. Finally an evalua-
tion of the measurement sensitivity is performed. In Figure
10, the photodiode current is shown as a function of the
glucose concentration for both dipole metamaterial and
EIT metamaterial. One can observe that the dynamic range
of the current is larger for the EIT metamaterial due to
the steeper slope. The measurement sensitivity results in
S = ΔI/Δcglucose = 6 × 10−5 mA/[mg/dL] for the dipole
metamaterial and in S = 10 × 10−5 mA/[mg/dL] for EIT
metamaterial.
Journal of Electrical and Computer Engineering 9
−3 −2 −1 0 1 2 3
14.25
14.3
14.35
14.4
14.45
14.5
14.55
14.6
14.65
14.7
P
h
ot
od
io
de
cu
rr
en
t(
m
A
)
Δλ (nm)
(a)
−3 −2 −1 0 1 2 3
P
h
ot
od
io
de
cu
rr
en
t(
m
A
)
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
Δλ (nm)
(b)
Figure 9: Photodiode current over wavelength deviation Δλ for the
dipole metamaterial (a) and for the EIT metamaterial (b).
3.3. Estimation Using Support Vector Regression. The anal-
ysis of measurement errors in glucose monitoring systems
presents a particularly troublesome problem, because the
importance (that is, the clinical consequence) of any particu-
lar error depends on the absolute value of both the reference
and measured values and not just on the percentage of
deviation. Moreover, this dependence is not easily described
by any simple mathematical relationship. Although Error
Grid Analysis (EGA) was introduced in the mid-1980s [31],
an evaluation based on standardized signal processing and
statistical tools is more meaningful for a preclinical analysis,
which suits our purpose.
In the presented systems the glucose level concentration
corresponds to the concentration used in the spectrum
simulation. In order to obtain a predicted concentration,
support vector regression is employed. The training data is
the simulated photodiode current as independent variable
and the associated glucose concentration as dependent vari-
able. The results are validated using k-fold cross-validation.
10−2 10−1 100 101
13.8
13.9
14
14.1
14.2
14.3
14.4
14.5
cglucose (%)
P
h
ot
od
io
de
cu
rr
en
t(
m
A
)
(a)
10−2 10−1 100 101
cglucose (%)
P
h
ot
od
io
de
cu
rr
en
t(
m
A
)
6.7
6.8
6.9
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
(b)
Figure 10: Photodiode current over glucose concentration for the
dipole metamaterial (a) and for the EIT metamaterial (b).
Support vector regression will also be employed in the ac-
tual measurement device. In that case, the training data con-
sists of themeasured photodiode current as independent var-
iable as well as the associated glucose concentration as de-
pendent variable. Given a measured photodiode current, the
SVR is used to predict the corresponding glucose level.
Two different kernels are employed for the SVR [26].
(1) Gaussian radial basis function kernel
k
(
xi, xj
)
= exp
⎛
⎝−
∥∥∥xi − xj
∥∥∥
2σ2
⎞
⎠. (22)
(2) Complete polynomial of degree d
k
(
xi, xj
)
=
(〈
xi, xj
〉
+ 1
)d
. (23)
10 Journal of Electrical and Computer Engineering
10−2
102
10−1 100
100
101
101
10−2
10−1
cglucose (%)
c e
rr
(%
)
rbf σ = 0.1
rbf σ = 1
rbf σ = 10
Polynomial deg 1
Polynomial deg 2
2% error level
Figure 11: Statistical evaluation using k-fold cross-validation for
nominal temperature T = 25◦C and nominal wavelength (Δλ =
0nm). The grey line denotes the 2% error level.
The first simulations are carried out for T = 25◦C and
the nominal wavelength of the respective laser; see Figure 11.
The relative error
cerr = |c − cest||c| · 100 (24)
as function of the estimated glucose concentration cest given
in percent is depicted over the respective glucose concentra-
tion. The polynomial kernel of degree d = 1 corresponds to
linear regression. It turns out that the error is very large in
this case. That motivates the use of nonlinear support vector
regression. The Gaussian radial basis function kernel with
σ = 1 yields estimation errors below 2% for physiological
concentrations.
Next, the influence of temperature variation is inves-
tigated; see Figure 12. The Gaussian radial basis function
kernel with σ = 1 is used in each simulation run. The tem-
perature T is varied from 25◦C to 40◦C.
Finally, simulations are carried out varying the wave-
length deviation Δλ = −1nm . . . 1nm (Figure 13). Once
again, the Gaussian radial basis function kernel with σ = 1 is
employed.
4. Discussion
4.1. Metamaterial Shape. The metamaterial shape (dipole or
EIT) plays a key role for the available maximum slope in the
spectrum. A steeper slope in turn leads to a broader dynamic
range of the photodiode current. Therefore, the use of the
EIT shape is preferable.
When comparing simple dipole plasmonic structures
with plasmonic EIT sensors, we find that in terms of con-
centration sensitivity, the EIT concept is superior by at least a
factor of two over the simple dipole. However, as a drawback,
10−2 10−1 100 101
10−2
10−1
100
101
102
103
104
105
T = 25◦C
T = 26◦C
T = 30◦C
T = 40◦C
cglucose (%)
c e
rr
(%
)
Figure 12: Statistical evaluation using k-fold cross validation for
nominal wavelength (Δλ = 0nm), showing the effect of temper-
ature variation.
10−3
10−4
10−2 10−1 100 101
10−2
10−1
100
101
102
103
104
cglucose (%)
c e
rr
(%
)
Δλ = −1nm
Δλ = −0.5nm
Δλ = −0.1nm
Δλ = 0nm
Δλ = 0.1nm
Δλ = 0.5nm
Δλ = 1nm
Figure 13: Statistical evaluation using k-fold cross validation for
nominal temperature T = 25◦C, showing the effect of wavelength
deviation.
the EIT concept due to its steeper resonances is also more
prone to wavelength shifts due to temperature variations.
However, this problem can be circumvented by using a tem-
perature stabilization scheme for the laser diode.
On top of that, the EIT shape offers four specific wave-
lengths with a large slope, compared to the dipole shape with
only two points. This increases the flexibility for choosing a
specific wavelength, as not every wavelength is available in
commercial lasers.
Journal of Electrical and Computer Engineering 11
4.2. Statistical Evaluation. Special care has to be taken when
the temperature or the wavelength differ from their nominal
values. As the SVR does not contain those parameters, the
prediction deteriorates. The relative errors for the deter-
mination of the glucose concentration are presented in
Section 3.3. They become very large even for small variations
of those parameters.
In order to overcome this issue, temperature will be in-
cluded as independent variable in the SVR in future work. On
top of that, the system will be calibrated in order to correct
the wavelength deviation of a specific laser.
5. Conclusion and FurtherWork
5.1. Proof of Concept. The present paper demonstrates a
novel concept for in vivo sensing of glucose using metamate-
rials in combination with automatic learning systems.
The novelty of the approach lies in the fact that this sen-
sor does not take advantage of the rather poor optical differ-
ences between the glucose molecule and other substances
contained in the surrounding fluid (blood stream, tear fluid,
etc.), but rather on the ability of the glucose to change select-
ively the refractive index of a specific metamaterial.
High sensitivity of our detection scheme is warranted be-
cause metamaterials are able to detect even minute changes
in the dielectric properties of their environment. The basic
concept relies on a contact lens material that supports a few
nanometers of a gold-based metamaterial which is function-
alized with glucose-sensitive hydrogel. This design is trans-
parent in the visible and near-infrared range and thus can
be designed as contact lens to be inserted into the patient’s
eye. The readout is carried out by an external LED, and the
reflected light is captured by a photodiode whose intensity
response is evaluated. Signal postprocessing stages based on
regression methods allow the reliable estimation of the tear
glucose content.
A complex simulation environment is built to evaluate
the main signal contributions together with the most impor-
tant noise sources as well as the most relevant parameter un-
certainties. The simulation results have shown that estima-
tion errors below 2% at physiological concentrations are
possible.
5.2. Functionalization with Glucose-Sensitive Hydrogel for
Contact Lens Implementation. The plasmonic sensor concept
has proven to be suitable for glucose detection at physiologi-
cal concentrations.
In the future, we are going to implement a glucose select-
ive layer on the plasmonic structure. This includes a func-
tionalization layer with a glucose-specific hydrogel [18, 32].
The hydrogel allows only glucose to penetrate the func-
tionalization layer and not other chemical agents that are
present in the tear fluid.
Furthermore, the hydrogel is quite biocompatible, in par-
ticular for the human eye environment. In fact, soft contact
lenses already use those kinds of hydrogels as surface layers.
Acknowledgments
The authors would like to thank the Ministerium fu¨r Wis-
senschaft, Forschung und Kunst Baden-Wu¨rttemberg as well
as BMBF and DFG (Open Access Publishing Fonds) for
granting financial support.
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