Detection of glucose concentration using ion-exchange channel waveguide

Optik 124 (2013) 2318–2323

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Detection of glucose concentration using ion-exchange channel waveguide Jin Liu a,b,c , Baoxue Chen a,c,∗ , Haima Yang a , Mamoru Iso d a

School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China College of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620 China c Shanghai Key Laboratory of Modern Optical System, Shanghai 200093, China d Department of Chemical Engineering, Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan b

a r t i c l e

i n f o

Article history: Received 16 February 2012 Accepted 27 June 2012

Keywords: Integrated optics Optical waveguide technology Solution concentration sensing Ion exchange

a b s t r a c t An integrated sensor structure based on channel waveguide is constructed. The single-mode channel waveguide is prepared using 0.1% AgNO3 –99.9% NaNO3 mixed molten salts under the condition that the diffusion coefficient can be assumed as constant. An experimental method is proposed and implemented to determine the equivalent diffusion coefficient and surface refractive index increment. The refractive index distribution of the channel waveguide is fitted and inferred. Ten glucose samples with different concentrations are tested at different wavelengths. The imaginary part of the propagation is determined by the Kramers–Kronig diversification. The correlation coefficient is designated as R2, and it is within the range of 0.9850–0.9961. The lowest detection limit of 0.1 ␮M is realized in the trace test. Crown Copyright © 2012 Published by Elsevier GmbH. All rights reserved.

1. Introduction Glucose is an important material utilized by organisms to maintain normal operations; detection of its concentration plays an important role in biomedical research. Optical sensors provide numerous advantages, such as being non-destructive, fast signal-generating capacity, and rapid signal reading; thus, they are the most commonly used sensing technologies. Ample literature about integrated optical biochemical sensors is available, which use guided wave or surface wave as signal carrier, such as the early moisture waveguide sensors [1], the recent surface plasmon resonance biosensors [2–6], and sensors based on the mode spectra of waveguide [7,8]. All these biosensors are planar waveguide structures, so aligning them with optic fibers for online measurement is difficult, and prisms must be used for both input and output coupling. The operational difficulty presents an obstacle in application, which can be solved by using the structure of a channel waveguide to align the optic fiber. There are many techniques in preparing channel waveguide, including the ion-exchange method, which are low cost and can be easily aligned with optic fiber. The evanescent field of the guided mode interacts with the dielectric medium for detection, and channel waveguide has broad application potential in the field of optical waveguide sensing [9–11]. As the distribution of evanescent field is different under different modes, the single-mode waveguide is usually used for accurate detection, and the transmission loss is used for sensing [13,14]. To detect the change in transmission loss, the refractive index distribution of a single-mode waveguide is necessary. The distribution of the refractive index in a single-mode ion-exchange waveguide is difficult to test compared with that of a planar waveguide. Currently, no effective and practical methods are available. An experimental method is proposed to address the problem. The key is to find the ion-exchange condition where the diffusion coefficient can be assumed constant. The equivalent diffusion coefficient of the ion exchange and the increment of surface refractive index are experimentally determined. The general solution of the two-dimensional diffusion equation is derived in the preparation process of the ion-exchange channel waveguide. The distribution of the refractive index is fitted and inferred. The refractive index dispersion in multiwavelength test is solved by the introduction of the dispersion relation of glass, and the imaginary part of the propagation constant, which represents the absorption loss of the guided mode in the sample test, is determined by the Kramers–Kronig (KK) diversification [12]. An integrated sensor structure based on channel waveguide is constructed, and the glucose concentration is measured. The lowest detection limit of 0.1 ␮M is realized in a trace test. The validity of this method has been verified.

∗ Corresponding author at: School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China. Tel.: +86 21 67791127; fax: +86 21 67791128. E-mail addresses: [email protected], fl[email protected] (B. Chen). 0030-4026/$ – see front matter. Crown Copyright © 2012 Published by Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2012.06.092

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2. Basic principle and method 2.1. Sensing principle Testing liquid samples were made and used as cladding of the channel waveguide. A change in glucose concentration leads to a change of the absorption coefficient and refractive index of the cladding. A change in absorption coefficient and field distribution leads to a change in the transmission loss of the guided mode, and a change in the refractive index of the cladding leads to a phase and a field distribution changes. The sensing mechanism consists of two aspects: one is the waveguide dispersion, and the other is the interaction of the evanescent field with the sample media. As the sample cladding has an absorption property, the refractive index of the cladding (nc ) is composed of the real part (ncr ) and the imaginary part (nci ). The refractive index distribution of the single-mode channel waveguide is given by



n(x, y) =

ns + nUA (x, y)

x ≥ 0,

ncr − jnci

x<0

−∞
(1)

where ns is the refractive index of the glass substrate, n is the increment of the surface refractive index, and f(x,y) is the profile function of the refractive index. The transmission in the guided mode is attenuated, and the propagation constant is in a complex form (ˇ = ˇr − jˇi ) with real part (ˇr ) and imaginary part (ˇi ). The eigen equations for the TE (transverse electric) and TM (transverse magnetic) modes of the channel waveguide are derived from the equivalent refractive index and the WKB (Wenzel,Kramers,Brillouin) methods, with equal real and imaginary parts.





xc

0

R1 cos



0

  1

2

dx =



 1 tan−1 + 4 2



1+V>0

1 =

xc

1−V

+ tan−1

 U  1+V

+ (2 − 1 )

 (2a)

1−V>0

0

, 2 = 1 1+V<0



 U 



R1 sin

0

  1

2

1 1−V<0



dx =

1 (1 + V )2 + U 2 ln 4 (1 − V )2 + U 2

(2b)

where

⎧   −   k2 n(0, 0) dn(x, 0)   3  ⎪ R2  2 3 3 ⎪ cos + 0 cos TE mode ⎪  ⎪ 2 2 dx ⎨ R3 x=0 2 R33   U=    −   2 (x, 0) ⎪ k02 n (0, 0) cos(33 /2) /2) cos( R dn(x, 0)  n ⎪ 2 2 3 3 ⎪ − 4 + cos − TM mode   ⎪  ⎩ R4 R3 2 dx x=0 2 R3 n(0, 0) R 3

3

⎧   −   k2 n(0, 0) dn(x, 0)   3  ⎪ R2  2 3 3 ⎪ sin − 0 sin TE mode ⎪  ⎪ 2 2 dx ⎨ R3 x=0 2 R33   V=    −   2 (0, 0) ⎪ k02 n(0, 0) sin(33 /2) R dn(x, 0)  sin( /2) n ⎪ 2 2 3 3 ⎪ − 4 − sin − TM mode   ⎪  ⎩ R4 R3 2 dx x=0 2 R3 n(0, 0) R

R1 = R2 = R3 = R4 =

   

A21 + B12 ,

1 = tan−1

A22 + B22 ,

2 = tan−1

A23

+ B32 ,

A24 + B42 ,

3 =

tan−1

4 = tan−1

B  1

A1

B  2

A2

B  3

A3

B  4

A4

(2d)

3

3

and

(2c)

,

A1 = k02 n2 (x, 0) − ˇr2 + ˇi2 ,

B1 = 2ˇr ˇi

,

A2 = ˇr2 − ˇi2 − k02 n2cr + k02 n2ci ,

B2 = 2(k02 ncr nci − ˇr ˇi ) (2e)

k02 n2 (0, 0) − ˇr2

,

A3 =

,

A4 = n2cr − n2ci ,

+ ˇi2 ,

B3 = B1 B4 = −2ncr nci

where xc denotes the inflection point and ˇr = k0 n(xc ,0). The transmission loss is a directly measured parameter of the single-mode waveguide, and the imaginary part of the propagation constant (ˇi ) can be measured using optical means. The other three parameters: ˇr , ncr , and nci , are unknown. Fortunately, the real and imaginary parts of the refractive index are not independent of each other. Their relationship is given by the KK relation: 2 ncr (ω) = 1 + P.V · 



0

∞

ω nci (ω ) ω 2 − ω2

dω

(3)

where the symbol P.V. denotes the Cauchy integral and ω is the circular frequency of light. The relationship of absorption coefficient (˛c ) with the solution, concentration (C), and imaginary part of the refractive index (nci ) is given by ˛c = ˛0 (ω)C = 2k0 nci

(4)

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where ˛0 (ω) is the intrinsic absorption coefficient of the testing component. The real and imaginary parts of the cladding refractive index are expressed as ˛0 (ω)C 2k0

nci (ω) =

C ncr (ω) = 1 + P.V · k0

 0

∞

ω ˛0 (ω ) ω 2 − ω2

.

(5)

dω

As ˛0 (ω) is determinate, ncr and nci are functions of concentration (C). The unknown parameters are thus reduced. If the refractive index distribution (n(x,y)) of the channel waveguide is determined, ˇr and C can be derived from eigen Eqs. (2a) and (2b). The mixed modes, excited by the channel waveguide, are quasi TE and quasi TM. After ˇi is experimentally measured, ˇr and C can be derived from the quasi TE and TM mode eigen equations, respectively. Then, the resulting average value is used. Obviously, the problem of how to determine the refractive index distribution of single-mode channel waveguide is resolved. 2.2. Design of single-mode channel waveguide and derivation of the refractive index distribution If the diffusion coefficient (Deff ) of the ion exchange in the Ag+ –Na+ exchange method is assumed constant in the preparation of the channel waveguide, the corresponding two-dimensional diffusion equation can be written as ∂UA (x, y; t) = Deff ∂t







∂2 UA (x, y; t) ∂2 UA (x, y; t) + , 2 ∂x ∂y2

x ≥ 0,

− ∞ < y < ∞,

t≥0

1 |y| < w

(6)

UA (x = 0, t) = 0 UA (x, y; t = 0) = 0

|y| > w

where UA (x,y;t) denotes the normalized concentration of Ag+ and 2w is the window width of the metal on the surface of the glass. The Green function method is used to solve Eq. (6), and the analytical solution is shown as follows: 1 UA (x, y; t) =  x ≥ 0,



x deff

 



exp −

− ∞ < y < ∞,

x deff

2  

(w/deff )((y/w)+1)

(w/deff )((y/w)−1)

exp(−2 ) 2

(x/deff ) + 2

d

(7)

t≥0



where deff = 2 Deff t denotes the equivalent diffusion depth and t is the time of ion exchange. The validity of Eq. (7) can be verified by the boundary and the initial conditions. When the window width tends to infinity, Eq. (7) becomes the complementary error function of the one-dimensional diffusion. Once the ion exchange is completed, the exchange time is a constant; then, the two-dimensional refractive index distribution of the channel waveguide can be written as Eq. (1). The remaining questions now are how to determine n and how to find the ion-exchange condition where the diffusion coefficient can be assumed constant. 2.3. Experimental determination of Deff and n One-dimensional ion-exchange is used in the experiments to determine Deff and n. Ion-exchange experiments are performed in molten salts rich in Ag+ . The amount of Ag+ in the ion exchange is small, and the diffusion process adopted is the constant surface concentration diffusion. ∂UA (x, t) ∂ = ∂t ∂x

UA =



⎧ 1 x=0 ⎪ ⎨



∂UA (x, t) DA , · ∂x 1 − UA (x, t)

x ≥ 0,

t≥0 (8)

⎪ ⎩0 x → ∞ 0

t=0

where UA (x,t) is the normalized concentration of Ag+ and shows the degree of nonlinearity value, i.e., =



1−

DA DB



CA0

(9)

where DA and DB are the self-diffusion coefficients of Ag+ and Na+ , respectively, and CA0 is the ion concentration ratio of Ag+ on the surface to Na+ in the glass. is a constant proportional to the concentration of Ag+ in molten salts. If the concentration of Ag+ in the molten salts is very low, will be a small value. The nonlinear factor ( UA (x,t)) in Eq. (8) is very small. Thus, the solution of Eq. (8) can be approximated as the complementary error function. DA /[1 − UA (x,t)] can be approximated as a constant (Deff ), and it is the equivalent diffusion coefficient related only to the concentration of Ag+ and the ion-exchange temperature. If the molar ratio of Ag+ is less than 0.05% in the Ag+ –Na+ ion-exchange process, is less than 0.26, and the numerical solution of Eq. (1) is very close to the complementary error function [15]. The Ag+ –Na+ exchange is used in our experiments, and optical glass Schott B270 is used as the substrate. Mixed molten salts consisting of 0.1% AgNO3 –99.9% NaNO3 are used whose Ag+ molar ratio is less than 0.0498%, and

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Table 1 Experimental fitted values of Deff and n. Exchange time (h)

Modulus

n

Deff (10−4 ␮m2 /s)

1 2 3 4 Average value

2 3 3 4

0.02632 0.02679 0.02742 0.02776 0.0273

5.15243 5.14875 5.13911 5.12616 5.1416

Fig. 1. Fitting results of the refractive index distribution.

Fig. 2. Single-mode design results.

Fig. 3. Test result of the mode field distribution.

Fig. 4. Experimental structure of the solution concentration sensing.





the equivalent diffusion coefficient is approximately constant. The solution of Eq. (8) is UA (x, t) = erfc 0.5x/ of the refractive index is proportional to the normalized concentration of Ag+ , it can be expressed as

 n(x) = ns + n · erfc



Deff t . As the distribution

 x



2

,

Deff t

x ≥ 0,

t≥0

(10)

where ns is the refractive index of the glass substrate B270. The eigen equation of the TE modes is obtained by the WKB method.



xm

 k02 n2 (x) − ˇ2 dx =

0



m+

 1 4

⎡ ⎢



 + tan−1 ⎣ 

ˇ2

⎤ − k02 n2c

k02 n2 (0) − ˇ2

+

⎥  ⎦ , m = 0, 1, 2, . . .

k02 n(0)dn(x)/dx|x=0 3 2 k02 n2 (0) − ˇ2



(11)

where xm is the inflection point of the mth TE mode and ˇ = k0 n(xm ) is the propagation constant of the mth TE mode. Four multi-mode gradient waveguides with different exchange times of 4, 3, 2, and 1 h were prepared in the mixed molten salts on the glass substrates at a constant temperature of 350 ◦ C. The propagation constant of the TE guided mode was detected using a prism coupling device (Model 2010 by Metricon Company) at 1550 nm. By considering the measured propagation as constant and introducing Eq. (10) into Eq. (11), Deff and n can be derived using the iterative fitting method [16,17]; the result is listed in Table 1. The experimental values of both Deff and n under different exchange times are approximately equal. This result shows that both Deff and n are constants. The constant feature of Deff indicates that the approximation of the equivalent diffusion coefficient is reasonable under low ion source concentration condition. The constant feature of n fits the diffusion result of the ion source. The refractive index distribution can be derived from Deff , n (as given in Table 1), and Eq. (10). Fig. 1 shows the fitted values of the refractive index distribution of the 2 and 4 h samples. The “+” point is the measured value of the mode refractive index (ˇ/k0 ), the transfer point is calculated from ˇ = k0 n(xm ), and the data correspond with theoretical results.

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Fig. 5. Intrinsic absorption coefficient of glucose.

Fig. 6. Correlation between ˇi and sample concentration.

Fig. 7. Responses of the glucose solution with concentration of 10 ␮M at 1450 nm.

3. Experiment and results As Deff and n are determined by experiments, w and t can be obtained using the effective index method under the single-mode condition using Eq. (8). For the mixed modes, the quasi TE and quasi TM modes are used to calculate and average the values of w, and the t values are obtained. The single-mode design results at 1550 nm are shown in Fig. 2. The mask window width and exchange time of the single-mode waveguide can be selected under the curve. Glass B270, whose two surface sides are optically polished, was selected to prepare the single-mode channel waveguide. A 0.2-␮m thick Al film was prepared on the glass surface using vacuum coating technique. Lithography was used to pattern a window whose width was 2w = 4 ␮m. Ion exchange was conducted in the 0.1% AgNO3 –99.9% NaNO3 mixed molten salts. The exchange temperature was 350 ◦ C with an exchange time of 50 min. Automatic alignment between waveguide and optic fiber was used to excite the guided mode [18,19] at 1550 nm. The single-mode characteristic was detected by C5840 mode distribution tester of Hamamatsu. Fig. 3 shows the test result of the mode field distribution, showing a good single-mode characteristic. Fig. 4 shows the schematic of the detection system. Automatic alignment between the waveguide and the fiber array is realized. Ultraviolet adhesive B300 is used for curing. Two sample boxes whose length is L =4 mm are prepared on the surface of the waveguide. Spherical silica particles with a diameter of 30 ␮m are put between the surface of the waveguide and the glass cover. The four corners are stuck. The test solution is injected through capillary effect. Light source and detector are provided by the spectrometer Agilent-86140B. This structure has the advantage of eliminating self-loss, coupling loss, and other system losses. Measurement is done two steps: the first step is the measurement of the output power Pout1 when the liquid sample is poured into one sample box; the second step is the measurement of the output power Pout2 when the liquid sample is poured into the two boxes. ˇi is derived from the following equation: 2ˇi =

ln (Pout1 ) − ln (Pout2 ) L

(12)

Once ˇi is measured, the concentration of the liquid samples can be calculated from eigen Eqs. (2a) and (2b). Glucose solutions are selected as samples. Fig. 5 shows the intrinsic absorption coefficient of glucose, detected by colorimeter. It shows a large intrinsic absorption in the 1300–1600 nm range. Ten samples with different concentrations between 5 and 50 ␮M are prepared. Each sample is measured at five different wavelengths between 1350 and 1500 nm at an interval of 50 nm. The dispersion of glass B270 in the different wavelengths is n2 = A0 + A1 2 + A2 −2 + A3 −4 + A4 −6 + A5 −8 where the six constant coefficients A0–A5 are 2.2877828, −9.3148723 × 10−3 , 1.0986443 × 10−2 , 4.8465203 × 10−4 , −3.3944738 × 10−5 , and 1.6958554 × 10−6 , respectively. Fig. 6 shows the relationship of ˇi and the concentration of the sample at different wavelengths. The correlation coefficient is in the range of 0.9850–0.9961, showing a highly significant linear correlation. Fig. 6 also shows that the absorption of the glucose solution is sensitive at 1450 nm. The concentration of the glucose solution sample (C) and the imaginary part of the propagation constant have a linear relationship ˇi = bC + a = 1.8103C − 1.0376 ␮M, where b denotes sensitivity. Fig. 7 shows the real-time measurement at 1450 nm. The sample is a glucose solution with concentration of 10 ␮M, and the vertical axis is ˇi . ˇ0 is the average value of the imaginary part of the propagation constant ˇi when the sample is not injected. ˇf is the average value of ˇi when the sample is injected. When the sample is not injected, 60 points are sampled in 60 s, and the standard deviation is n−1 = 0.059 ␮M. The resultant detection limit is 3 n−1 /b ∼ = 0.1 ␮M, smaller than the detection limit of 0.5 ␮M of the electrochemical method [20]. The trace test is realized and has an important clinical significance. 4. Conclusion An integrated sensor structure based on channel waveguide has been constructed. Single-mode channel waveguide is prepared in the 0.1% AgNO3 –99.9% NaNO3 mixed molten salts under the condition that the diffusion coefficient can be assumed as constant. A new experimental method is proposed and implemented to determine the equivalent diffusion coefficient and surface refractive index increment. The general solution of the two-dimensional diffusion equation is derived in the preparation process of ion-exchange channel waveguide. The distribution of the refractive index is fitted and inferred. The dispersion of the refractive index in the multi-wavelength test is solved with the introduction of the dispersion relationship of glass, and the imaginary part of the propagation constant, which represents the absorption loss of the guided mode in the sample test, is determined by KK diversification. Ten glucose samples with different concentrations are tested at different wavelengths. The correlation coefficient R2 is in the range of 0.9850–0.9961 and shows a significant linear correlation. The lowest detection limit of 0.1 ␮M is realized in the trace test. This structure can be used to detect other materials using corresponding light source and detector and has a common significance.

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Acknowledgements This work is supported by the National Natural Science Foundation of China under Grant Nos. 61077042 and 60677032, the Shanghai Key Laboratory Project under Grant No. 08DZ2272800, and the Shanghai Leading Academic Discipline Project under Grant No. S30502, the Science and Technology Commission of Shanghai Municipality Project under Grant No. 10160501700. References [1] K. Tiefenthaler, W. Lukosz, Integrated optical switches and gas sensors, Opt. Lett. 10 (4) (1984) 137–139. [2] C.E. Berger, R.P. Kooyman, J. Greve, Resolution in surface plasmon microscopy, Rev. Sci. Instrum. 65 (1994) 2829–2836. [3] K. Johansen, H. Arwin, I. Lundstrom, B. Liedberg, Imaging surface plasmon resonance sensor based on multiple wavelengths: sensitivity considerations, Rev. Sci. Instrum. 71 (2000) 3530–3538. [4] B.P. Nelson, A.G. Frutos, J.M. Brockman, M. Robert, Corn near-infrared surface plasmon resonance measurements of ultrathin films. 1. Angle shift and SPR imaging experiments, Anal. Chem. 71 (1999) 3928–3934. [5] A.J. Haes, R.P. Van Duyne, Preliminary studies and potential applications of localized surface plasmon resonance spectroscopy in medical diagnostics, Expert Rev. Mol. Diagn. 4 (2004) 527–537. [6] J.W. Chung, S.D. Kim, R. Bernhardt, J.C. Pyun, Application of SPR biosensor for medical diagnostics of human hepatitis B virus 0aI-mv, Sens. Actuators B 111 (2005) 416–422. [7] X. Xie, Q. Liu, Z. Lu, The development of biomedical detection by optical waveguide light mode spectroscopy (OWLS) system, Laser Optoelectron. Prog. 43 (11) (2006) 33–42. [8] J. Ramsden, J. Dreie, Kinetics of the interaction between DNA and the type IC restriction enzyme ECOR124II, Biochemistry 35 (1996) 3746–3753. [9] K. Aki, Integrated Optics (L. Ruilin, Trans.), Science Press, Beijing, 2004, p. 394. [10] I.E. Araci, S.B. Mendes, N. Yurt, et al., Highly sensitive spectroscopic detection of heme-protein submonolayer films by channel integrated optical waveguide, Opt. Express 15 (9) (2007) 5595–5603. [11] R. Zou, B. Chen, H. Wang, The sensing structure optimization of planer optical waveguide with fermi refractive index, J. Lightwave Technol. 28 (23) (2010) 3439–3443. [12] K.-E. Peiponen, E.M. Vartiainen, Kramers–Kronig relations in optical data inversion, Phys. Rev. B 44 (1991) 8301–8303. [13] J. Albert, G.L. Yip, Wide single-mode channels and directional coupler by two-step ion-exchange in glass, J. Lightwave Technol. 6 (4) (1988) 552–563. [14] J. Johansson, G. Djanta, J.-L. Coutas, Optical waveguides fabricated by ion exchange in high-index commercial glasses, Appl. Opt. 31 (15) (1992) 2796–2799. [15] S. Sawa, K. Ono, M. Yamasaki, A study of ion exchanged optical waveguides (II). Memoirs of the Faculty of Eng, Ehime Univ. 11 (3) (1988) 141–150. [16] B.X. Chen, H. Hamanaka, K. Iwamura, Recovery of refractive-index profiles of planar graded-index waveguides from measured mode indices: an iteration method, J. Opt. Soc. Am. A 9 (8) (1992) 1301–1305. [17] L. Dongbo, T. Jie, M. Iso, et al., Recovery of refractive index profiles of proton exchanged waveguides using statistical optimum iteration method, Acta Opt. Sinica 22 (6) (2002) 670–673. [18] G. Sui, B. Chen, X. Zhang, et al., Automatic waveguide-fiber coupling system based on multi-objective evolutionary algorithm, Appl. Opt. 46 (30) (2007) 7452–7459. [19] C. Long, B. Chen, H. Sha, et al., Acta Opt. Sinica 24 (4) (2004) 442–447. [20] L. Jiang, X. Cai, H. Liu, et al., Research on biosensor for low concentration glucose determination, Instrum. Tech. Sens. 2 (2009) 1–4.