Improved self-referenced biosensing with emphasis on...

Improved self-referenced biosensing withemphasis on multiple-resonance nanorodsensorsAHMED ABUMAZWED,1,* WAKANA KUBO,2 TAKUO TANAKA,3 ANDANDREW G. KIRK1

1ECE Department, McGill University, 3480 University Street, Montreal H3A 2A9, Canada2Department of Electrical and Electronic Engineering, Tokyo University of Agriculture and Technology,2-24-16 Naka-cho, Koganei-shi, Tokyo, 184-8588, Japan3Metamaterials Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama, 351-0198, Japan*[email protected]

Abstract: We present a novel approach to improve self-referenced sensing based on multiple-resonance nanorod structures. The method employs the maximum likelihood estimation (MLE)alongside a linear response model (LM), relating the sensor response (shifts in resonancewavelengths) to the changes due to surface binding and bulk refractive index. We also providea solution to avoid repetitive simulations, that have been previously needed to determine theadlayer thickness sensitivity when measuring biological samples of different refractive indices.The finite element method (FEM) was used to model the nanorod structure, and the nanoimprintlithography was employed to fabricate them. The standard deviation of the results based on theMLE method is lower than that associated with the LM results. The method can be applied to anextended number of resonances to achieve a higher accuracy and precision.© 2017 Optical Society of America

OCIS codes: (120.3890) Medical optics instrumentation;(130.6010) Sensors; (170.4520) Optical confinement andmanipulation; (280.1415) Biological sensing and sensors; (280.4788) Optical sensing and sensors; (240.6680) Surfaceplasmons; (350.4238) Nanophotonics and photonic crystals.

References and links1. G. G. Nenninger, J. B. Clendenning, C. E. Furlong, and S. S. Yee, “Reference-compensated biosensing using a

dual-channel surface plasmon resonance sensor system based on a planar lightpipe configuration,” Sens. Actuators BChem. 51(1/3), 38–45 (1998).

2. P. Schuck, and H. Zhao, “The Role of Mass Transport Limitation and Surface Heterogeneity in the BiophysicalCharacterization of Macromolecular Binding Processes by SPR Biosensing,” Methods in Molecular Biology 627, 15(2010).

3. D. G. Drescher, N. A. Ramakrishnan, and M. J. Drescher, “Surface Plasmon Resonance (SPR) Analysis of BindingInteractions of Proteins in Inner-Ear Sensory Epithelia,” Methods in Molecular Biology 493, 323 (2009).

4. S. Nizamov and V. M. Mirsky, “Self-referencing SPR-biosensors based on penetration difference of evanescentwaves,” Biosens. Bioelectron. 28(1), 263–269 (2011).

5. J. Homola, H.B. Lu, and S.S. Yee, “Dual-channel surface plasmon resonance sensor with spectral discrimination ofsensing channels using dielectric overlayer,” Electron. Lett. 35(13), 1105 (1999).

6. R. Slavik, J. Homola, and H. Vaisocherová, “Advanced biosensing using simultaneous excitation of short and longrange surface plasmons,” Meas. Sci. Technol. 17(4), 932–939 (2006).

7. J.T. Hastings,J. Guo, P. D. Keathley, P. B. Kumaresh, Y. Wei, S. Law, and L. G. Bachas, “Optimal self-referencedsensing using long- andshort- range surface plasmons,” Opt. Express,15(26), 17661 (2007).

8. N. Nehru, E. U. Donev, G. M. Huda, L. Yu, Y. Wei, and J. T. Hastings, “Differentiating surface and bulk interactionsusing localized surface plasmon resonances of gold nanorods,” Opt. Express 20, 6905 (2012).

9. N. Nehru, Y. Linliang, W. Yinan, J. T. Hastings, “Using U-Shaped Localized Surface Plasmon Resonance Sensors toCompensate for Nonspecific Interactions,” IEEE Trans. Nanotech. 13(1), 55–61 (2014).

10. F. Bahrami, M. Maisonneuve, M. Meunier, J. S. Aitchison, and M. Mojahedi, “Self-referenced spectroscopy usingplasmon waveguide resonance biosensor,” Biomed. Opt. Express 5, 2481 (2014).

11. L. L. Scharf, Statistical Signal Processing: Detection, Estimation, and Time Series Analysis (Addison-Wesley, 1991).12. L. S. Jung , C. T. Campbell , T. M. Chinowsky , M. N. Mar , and S. S. Yee, “Quantitative Interpretation of the

Response of Surface Plasmon Resonance Sensors to Adsorbed Films,” Langmuir 14(19), 5636 (1998).

Vol. 25, No. 20 | 2 Oct 2017 | OPTICS EXPRESS 24803

#294480 https://doi.org/10.1364/OE.25.024803 Journal © 2017 Received 26 Apr 2017; revised 25 Sep 2017; accepted 25 Sep 2017; published 29 Sep 2017

https://crossmark.crossref.org/dialog/?doi=10.1364/OE.25.024803&domain=pdf&date_stamp=2017-10-03

13. A. J. Haes and R. P. Van Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based onthe localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc. 124(35),10596–10604 (2002).

14. P.B. Johnson, and R.W. Christy, “Optical Constants of the Noble Metals,” Physical Review B 6(12), 4370 (1972).15. CAD/Art Services, Inc, http://www.outputcity.com16. D. Qin, Y. Xia and G. M. Whitesides, “Soft lithography for micro- and nanoscale patterning,” Nature Protocols 5,

491 (2010).17. Thermo Fisher Scientific, T., EZ-Link HPDP-Biotin Instructions.18. ProteoChem, http://www.proteochem.com19. G. G. Nenninger, M. Piliarik and J. Homola, “Data analysis for optical sensors based on spectroscopy of surface

plasmons,” Meas. Sci. Technol. 13, 2038 (2002).20. L. Tian, E. Chen, N. Gandra, A. Abbas, and S. Singamaneni, “Gold Nanorods as Plasmonic Nanotransducers:

Distance-Dependent Refractive Index Sensitivity,” Langmuir 28(50), 17435 (2012).21. H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold

nanoparticles,” Langmuir 24(10), 5233–5237 (2008).22. D.R. Lide, 86th Handbook of Chemistry and Physics (CRC, 2006) Chap. 8.

1. Introduction

In propagating surface plasmon resonance (SPR) sensors, a reference channel is required tocompensate for artifacts due to temperature drift and bulk RI changes [1]. However, the referenceand sensing channels are not identical (for example: different metal thickness) due to fabricationimperfections, the difference in analyte transport in both channels [2], and the uncorrelated effectsin each channel during the binding events (presence of air bubbles and changes in speed of fluidflow in either channel) [3]. These artifacts have motivated many researchers to seek alternativemethods where the reference channel could be abandoned to avoid any external or intrinsic effectsin the two-channel sensing platforms. A self-referenced SPR sensor has previously employed theexcitation of a dual-mode SPR (with different penetration depths) using two laser sources [4],which increases the instrumental complexity. Alternative approaches included the excitation ofdual-mode SPR and use it as reference/sensing channels based on a linear response model. Thiswas achieved by either exciting two modes at different locations on the metal surface [5], orexciting the long range and short range SPR modes on the same location of the SPR surface [6,7].The linear response model assumes that each resonance wavelength shift (∆λ) is a linear functionof both adlayer thickness (d) and bulk RI change (∆n) as follows

∆λi = SBi ∆n + Sdi d (1)

where SBi = ∂λi/∂n is the bulk RI sensitivity, and Sdi = ∂λi/∂d is the adlayer sensitivity at theith resonance. The same approach (i.e. a linear response model) has been applied to gold nanorodstructures, U-shaped structures and propagating plasmon waveguide resonance biosensor [8–10].Although various approaches have been introduced for self-referencing SPR platforms, lesseffort has been previously paid to self-referencing based on localized surface plasmon resonance(LSPR) sensors. This paper presents the MLE approach to improve the precision and accuracy ofthe results based on the linear response model. The paper also provides a method to overcomethe repetitive simulation to determine the sensitivity to adlayer thickness for various analytes andcorrect it based on the measured bulk RI sensitivity.

2. Concept of self referencing based on multiple resonances

As described above, estimating the unknown quantities (adlayer thickness and bulk RI change)requires at least two resonances. The multiple resonance characteristic of nanorod structures canbe employed to generate multiple systems each of which provides solutions for the estimates.Herein, a three-resonance nanorod structures is considered as the first resonance is used withthe second and third resonances to generate three systems of linear equations based on a linear


response model [Eq. (1)], and the adlayer and bulk RI change can be estimated accordingly asfollows∆n12

d12

=SB1 Sd1

SB2 Sd2

−1 ∆λ1

∆λ2

︸︷︷︸LM1: f romλ1, λ2

,

∆n13

d13

=SB1 Sd1

SB3 Sd3

−1 ∆λ1

∆λ3


,

∆n23

d23

=SB2 Sd2

SB3 Sd3

−1 ∆λ2

∆λ3


For a system based on more resonances, the linear model can be employed to obtain i numberof estimates (di and ∆ni) that are related to the true values (d̂ and ∆̂n) by

di = Cdi d̂ ± εdi (2)

∆ni = Cni∆̂n ± εni (3)

where Cdi and Cni are weighting factors, relating these estimates to the true values (d̂ and ∆̂n),and the errors (due to the effect of noise) in the measured LM results are represented by εdi andεni , for the adlayer thickness and bulk RI change, respectively.The estimated adlayer thickness and bulk RI change based on the application of the LM to a

multiple systems of linear equations can be be represented by the following vectors

ddd =

d1...

di

, ∆n∆n∆n =

∆n1...

∆ni

Herein, we use the MLE method to estimate the true values based on the multiple LM estimates,Considering that the noise in the system follows a normal distribution, the error terms can berepresented by a Gaussian distribution with zero mean as εdεdεd ∼ N(0,Rd), and εnεnεn ∼ N(0,Rn) foradlayer thickness and bulk RI change, respectively. Rd and Rn denote the variance associatedwith the adlayer thickness and bulk RI change, respectively, determined by the LM method.Therefore, it is evident that the calculations consider the noise associated with the measuredresonance wavelength shifts in real time, and the errors include covariances that account for asystem of correlated noise sources. In matrix notation, this can be represented by the followingsymmetric matrices

Rd =

Rd11 . . . Rd1i

.... . .

...

Rdi1 . . . Rdii

; Rn =

Rn11 . . . Rn1i

.... . .

...

Rni1 . . . Rnii

Where the main diagonals of these matrices represent the variances of the LM estimates, and thecovariances among them are symmetrically distributed above and below the main diagonal, i.e.Rdi j = Rd j i and Rni j = Rn j i . These matrices are directly based on the real time experiments.Now, we apply the MLE method, employing the LM estimates and including the effect of noise

as given in Eq. (2) and Eq. (3). For simplicity, we apply the method on the adlayer thickness results,and the same steps can be followed in estimat the bulk RI change. Since we have considereda normal distribution for the noise, the likelihood of obtaining the estimated adlayer thicknessbased on the linear model (di), given the true value (d̂) can be obtained by multiplying the normaldistributions for these estimates as follows∏

iN(d1, ...di |Cd1 d̂, ...Cdi d̂,RdRdRd) ≡1

(2π)i/2 |RdRdRd |1/2exp

(− 1

2 RdRdRd

∑i(di − Cdi d̂)2

)


In matrix notation, this multivariate normal distribution can be represented by

P(ddd |d̂ CdCdCd,RdRdRd) =1

(2π)i/2 |RdRdRd |1/2exp

(− 1

2(ddd − d̂ CdCdCd)TR−1

dR−1dR−1d (ddd − d̂ CdCdCd)

)According to the MLE technique, the estimate that maximizes this likelihood is obtained whenits derivative with respect to the true value approaches zero [11]. For simplicity, we obtain thelog of the above likelihood as follows

ln(

P(ddd |d̂ CdCdCd,RdRdRd))= − i

2ln(2π) − 1

2ln|RdRdRd | −

12(ddd − d̂ CdCdCd)T RdRdRd

−1(ddd − d̂ CdCdCd)

Now, the true value (d̂) can be estimated such that the derivative of the log likelihood with respectto this true value approaches zero [11].

∂

∂ d̂ln

(P(ddd |d̂ CdCdCd,RdRdRd)

)≡ ∂

∂ d̂

((ddd − d̂ CdCdCd)T RdRdRd

−1(ddd − d̂ CdCdCd))= 0

This can be solved to obtain the true value (d̂) as follows

d̂ =CTd

CTdCTd

R−1d

R−1dR−1d

ddd

CTd

CTdCTd

R−1d

R−1dR−1d

CdCdCd

, R−1dR−1dR−1d =

R−1d11

. . . R−1d1i

.... . .

...

R−1di1

. . . R−1dii

(4)

The bulk RI change can be estimated in a similar manner as the above based on∆n∆n∆n,CnCnCn and RnRnRn.Herein, the adlayer thickness and bulk RI change, determined by the LM (ddd and ∆n∆n∆n) are giventhe same weight; therefore,CT

dCTdCTd= CT

nCTnCTn = [1 1... 1] and the following formulas can be extracted for

the estimated adlayer thickness and bulk RI change

d̂ =

∑im=1

∑ik=1 dm R−1

dmk∑im=1

∑ik=1 R−1

dmk

, ∆̂ n =

∑im=1

∑ik=1 ∆nmR−1

nmk∑im=1

∑ik=1 R−1

nmk

(5)

In the case of the three-resonance nanorod structures, proposed here, substituting for i=3 in Eq.(5), the adlayer thickness and bulk RI change can be estimated as

d̂ =(R−1

d11 + R−1d12 + R−1

d13) d1 + (R−1d12 + R−1

d22 + R−1d23) d2 + (R−1

d13 + R−1d23 + R−1

d33) d3

R−1d11 + R−1

d22 + R−1d33 + 2 (R−1

d12 + R−1d13 + R−1

d23)(6)

∆̂n =(R−1

n11 + R−1n12 + R−1

n13)∆n1 + (R−1n12 + R−1

n22 + R−1n23)∆n2 + (R−1

n13 + R−1n23 + R−1

n33)∆n3

R−1n11 + R−1

n22 + R−1n33 + 2 (R−1

d12 + R−1d13 + R−1

d23)(7)

3. Corrected sensitivity matrices for the linear response model

The sensitivity to adlayer thickness depends on the refractive index of the analyte (na) and thebulk RI sensitivity of the nanorods. Therefore, it needs to be recalculated if other biologicalsamples are considered. Established methods based on the linear response model have previouslyconsidered specific analytes, and employed sensitivity factors based on simulating that specificanalyte (using reported values for size and RI) [9, 10]. However, this requires tedious numericalmodeling to obtain new values. Here, we present a method to avoid the repeated numericalcalculations, by calculating the adlayer thickness sensitivity based on the measured data.The maximum sensor response, ∆λmax , at each resonance is achieved when the adlayer

thickness reaches the saturation, d � ld, where ld is the electromagnetic (EM) decay length


associated with these resonances. The sensor response is related to the adlayer thickness by thefollowing equation [12, 13]

∆λ(d) = ∆λmax[1 − exp(−2 d/ld)] (8)

The linear response model is valid for a thin adlayer thickness, d ≤ ld/10, and the sensor responseis related to the adlayer thickness based on the sensitivity to adlayer thickness Sd as follows

∆λ(d) = Sd d (9)

Substituting ld/10 for d in Eq. (8) and Eq. (9), we obtain

∆λ(ld/10) = Sd ld/10 ≡ 0.18∆λmax

from which the adlayer sensitivity can be evaluated as follows

Sd = 1.8∆λmax/ld (10)

This can be related to the bulk RI sensitivity and the refractive indices for the buffer and analyteas follows

Sd = 1.8 SB (na − nB)/ld (11)where na and nB are the refractive indices for the adlayer and the buffer solution.

4. Methods

We used the FEM to model the gold nanorods and obtain the sensitivity and EM decay lengthfor each resonance. The dielectric properties for gold were obtained from Johnson and Christyexperimental data [14]. The longitudinal mode was excited by a vertical incident plane wavepolarized along the long axis of the gold nanorods. The rods were modeled based on bothperfectly matched layer and periodic boundary conditions. An adlayer of a thickness (d) wasintroduced to calculate the EM decay length as the resonance wavelength shift was tracked withchanging the thickness until the shift is saturated. The simulation domain was discretized usingtriangular mesh and the nanorods and the adlayer were discretized using hexagonal mesh of 1 nmelement size.

The gold nanorods were fabricated using the nanoimprint lithography method: a glass substratewas coated by 50 nm thick cyclic olefin copolymer (COC) by spin coating, and the coatedsubstrate was imprinted by a silicon (Si) mould under 8 MPa pressure and 150 ◦C for 300seconds. The imprinted substrate was then coated with 5 nm and 30 nm thick chromium (Cr) andgold, respectively. The nanorods were formed after a lift-off process. Figure 1 shows a ScanningElectron Microscopy (SEM) image for the fabricated noanord structure.

Replica moulding method was used to fabricate the fluidic channels based on polydimethylsilox-ane (PDMS). A silicon wafer was spin coated with SU-8 negative resist and UV photolithographywas used to pattern the channels using a transparent photomask obtained from [15]. The unexposedSU-8 resist was developed in SU-8 developer and the wafer was blown dry with nitrogen andpost-baked, forming the master for the soft lithography method [16]. The master was then coatedwith a monolayer formed by perfluorooctyltriethoxysilane (Sigma-Aldrich, Oakville, ON, Canada)by siloxane bonding in a desiccator connected to a vacuum line in a fume hood (for 30 minutes).This prevents the PDMS from sticking to the master as the surface becomes hydrophobic. A70 g of Sylgard 184 base was mixed with 7 g of curing agent (10:1 ratio), and the mixture waspoured on the master in a petri-dish. The air bubbles were removed by placing the mater in adesiccator and connecting it to the vacuum line in a fume hood. After removing the air bubbles,the petri-dish (containing the master and PDMS) was placed in an oven at 70 ◦C overnight. Thereplicated PDMS was then peeled off the master, and placed in an oxygen plasma for 60 secondsto transform its surface from hydrophobic to hydrophilic, increasing the bond with the nanorodglass substrate.


Fig. 1. SEM images for the fabricated nanorod structures of a width 70 nm and variouslengths as (a) 120 nm, (b) 150 nm, and (d) 210 nm.

5. Numerical validation

COMSOL Multi-physics was used to calculate the shifts in the resonance wavelengths withdifferent bulk refractive indices to calculate the sensitivity at each resonance. Figure 2(a) shows thesimulation layout based on the periodic boundary condition and ports to calculate the scatteringparameters ∼ S21, which are translated into transmission efficiency as 10S21/20. The simulationwas validated by simulating only the glass substrate of a refractive index of 1.5, and calculatingthe transmission efficiency. Another verification was performed by comparing the results basedon nanorods without a substrate to those obtained based on nanorods in an integrating spherewith perfectly matched layer shown in Fig. 2(b).

Fig. 2. (a) Schematic for simulating periodic array of nanorods covered by an adlayer and abulk RI of nB . Periodic boundary conditions were enforced such that the structure is periodicin the xy plane. The structure is excited using port 1 (lower xy plane), and the transmittedlight is calculated using port 2. (b) Simulating a single nanorod, by using a perfectly matchedlayer (PML) over an integrating sphere to calculate the extinction efficiency. The nanorod isexcited by a plane wave polarized along the z axis and propagating in the negative x direction.

After validating the simulation set-up, the sensitivity to bulk RI change (SB) was calculated


700 720 740

Wavelength [nm]

0

0.2

0.4

0.6

0.8

1

1.2

Tra

nsm

issio

n [

a.u

.]

(a)

820 840 860

Wavelength [nm]

(b)

nB

=1.3

nB

=1.35

nB

=1.4

1000 1020 1040 1060

Wavelength [nm]

(c)

1.3 1.35 1.4

Bulk refractive index

0

10

20

30

40

50

∆ λ

[nm

]

(d)

SB1

=340 nm/RIU

SB2

=365 nm/RIU

SB3

=465 nm/RIU

Fig. 3. Simulated transmission curves, demonstrating resonance wavelength shift with bulkRI change at (a) λ1=705 nm, (b) λ2=821 nm, and (c) λ3=1000 nm. (d) Shifts in the resonancewavelengths vs bulk RI change to extract the bulk RI sensitivity for each resonance.

based on the corresponding transmission dip locations for all the resonances as shown in Fig.3. As expected, the third resonance (at 1000 nm) exhibited the highest sensitivity to bulk RIchange which is attributed to the long EM decay length. To estimate the EM decay length, theadlayer thickness was varied from 6 – 25 nm, and the corresponding shift in each resonancewavelength was tracked to plot the resonance shift against adlayer thickness. The EM decaylengths are then estimated by fitting the simulated data using Eq. (8), as shown in Fig. 4. As well,the simulated adlayer sensitivity can be determined as the slope of the curves in the linear regime(0 < d < ld/10). To investigate the effect of the noise on the results, an adlayer of 5 nm thickness

0 50 100

d [nm]

0

10

20

30

40

50

λr [

nm

]

(a)

FEM, ld=47 nm

Linear fit, Sd=1.31

700 7500

0.5

1T

λ (nm)

d=10 nm

→

d=20 nm

0 50 100

d [nm]

0

10

20

30

40

50

λr [

nm

]

(b)

FEM, ld=55 nm

Linear fit, Sd=1.2

820 840 8600

0.5

1T

d=10 nm

d=20 nm

λ (nm)→

0 50 100

d [nm]

0

10

20

30

40

50

λr [

nm

]

(c)

FEM, ld=64 nm

Linear fit, Sd=1.32

1000 10500

0.5

T d=10 nm

d=20 nm

λ (nm)→

Fig. 4. Resonance wavelength shift against adlayer thickness change, based on the simulatedresults shown in the insets, for (a) the first resonance (λ1=705 nm), (b) the second resonance(λ2=821 nm), and (c) the third resonance (λ3=1000 nm). The EM decay length (ld) for eachresonance is extracted such as Eq. (8) provides the best fit to the resonance wavelength shiftvs adlayer thickness, and the sensitivity to adlayer thickness change (Sd) is calculated as theslope of each curve at the linear regime (d ∼ ld/10).

and 1.4 refractive index was introduced to the nanorods in the periodic simulation layout, and the


corresponding shifts in the resonance wavelengths were determined. Last, noise (with differentlevels) was simulated by adding uncertainties (various σλ) to the simulated wavelength shifts.The linear response models and the proposed MLE method were then employed to estimate theinput parameters used in the FEM simulation. The signal to noise ratio (SNR) based on theestimates were calculated as the ratio between their mean and standard deviation, as shown inFigs. 5(a) and 5(b), respectively, revealing that the MLE method can improve the precision ofthe linear response model results. The MLE method is less affected by the fluctuations in theresonance wavelengths as the overall variance becomes lower than any of those associated withthe results based on the linear response model, applied to various linear systems, LM1 (λ1, λ2),LM2 (λ1, λ3) and LM3 (λ2, λ3).The accuracy of the methods can be determined based on the percentage error in the estimates

compared with the true values that were used in the simulation as follows

εx̂ % =x̂ − x

x× 100 (12)

where εx̂ % is the percentage error in the estimates x̂ (d̂ or ∆̂n) with respect to the true values x,representing d or ∆n. The error in the estimates was calculated based on the estimated adlayerthickness and bulk RI change based on various uncertainties in the resonance shifts. The averagederror in the estimated adlayer thickness and bulk RI change is shown in Figs. 5(c) and 5(d),respectively. These results suggest that the MLE method achieves the best accuracy among theresults obtained by the linear response model, based on the simulated data.

0 500 1000

SNR (∆ λ)

0

100

200

300

SN

R (

d)

(a)

LM1

LM2

LM3

LMMLE

0 500 1000

SNR (∆ λ)

0

500

1000

1500

2000

SN

R (∆

n)

(b)

LM1

LM2

LM3

LMMLE

LM1

LM2

LM3

LMMLE

Method

0

1

2

3

4

ǫd %

(c)

LM1

LM2

LM3

LMMLE

Method

0

0.2

0.4

0.6

0.8

ǫn %

(d)

Fig. 5. Top panel: calculated SNR based on (a) the estimated adlayer thickness to its standarddeviation, and (b) the estimated bulk RI change to its standard deviation. The linear responsemodel and the MLE method were applied to the simulated shifts in resonance wavelengths∆λi with added uncertainties σλi such that SNR(∆λi) = ∆λi/σλi . Bottom panel: thepercentage error associated with each method in (c) the estimated adlayer thickness and (d)the bulk RI change using Eq. (12) based on the true values used in the simulation.


6. Measured results

This section presents the measured results based on bulk RI changes and surface bindingexperiments. Figure 6 shows the experimental set-up used for the sensing experiments. Thefabricated gold nanorods substrate was cleaned by DI water and ethanol solution, blown drywith nitrogen, and plasma treated to remove any biological contaminant. The substrate wasthen incubated in 10 mM phosphate buffer solution (pH 7.2) of 200 µM biotin-hpdp for biotinimmobilization as instructed in [9, 17]. A 0.2 mg/mL streptavidin solution was prepared in a 50mM Tris-buffer solution (pH 8.0) according to [9,17]. The Tris buffer was also used as a baselinefor the sensing experiment. Both streptavidin and hpdp reagents were obtained from [18]. Cary5000 spectrometer was used to measure the extinction curves while introducing the solutions intothe nanorod structures via the PDMS fluidic channel and an automatic pump (Harvard Apparatus−PicoPlus) with 200µL/min flow speed. The resonance locations (centroids) were determinedbased on the dynamic-baseline centroid method [19].

Fig. 6. Experimental set-up used to measure the transmission spectra associated with thenanorod structures. The inset is an exploded view for the PDMS fluidic channel integrationwith the gold nanorod substrate for injecting the biological samples.

Figure 7 shows the measured results for the three-resonance nanorod structures based onethanol solution and biotin-streptavidin binding. The shift of each resonance is tracked in realtime to investigate the self-referencing with bulk and surface binding experiments.The sensor was calibrated for the bulk and adlayer sensitivities. The bulk RI sensitivity

was calculated based on the ethanol solutions of known concentrations and refractive indices.The measured sensitivities are lower than the calculated counterparts. This is attributed to thebiotin layer as the distance between the nanorods and the ethanol solutions is increased afterfunctionalizing the nanorods. A similar behaviour was previously observed for the nanorods [20].The sensitivity to adlayer thickness is directly related to the bulk RI sensitivity, and hence itneeds to be corrected accordingly. We propose a method to correct for this discrepancy using Eq.(11). Both simulated and corrected values are shown in Figs. 8(a) – 8(c) and Figs. 8(d) – 8(f).

Now, we obtain sensitivity matrices based on the true values, accounting for the changes dueto fabrication and experimental conditions, in the form

SSS =S′B1 S′

d1

S′B2 S′

d2


0

5

10

∆ λ

1 [nm

]

(a)I← 1 →I← 2 →I← 1 →I← 3 →I← 1 →I← 4 →I← 5 →I← 4 →I

0

5

10

∆ λ

2 [nm

](b)

0 20 40 60 80 100 120 140 160 180 200

t [minutes]

0

5

10

∆ λ

3 [nm

]

(c)

Fig. 7. Real time response to bulk RI changes and biotin-streptavin binding events based onthree-resonance nanorod structures. The numbers on the graph represent the following: [1]DI water, [2] 8% ethanol solution, [3]16% ethanol solution, [4] Buffer, and [5] Streptavidinsolution.

Similarly, two sensitivity matrices are obtained based on the bulk and adlayer sensitivities forthe following combinations: (λ1, λ3) and (λ2, λ3). These matrices must be non-singular andwell conditioned to be valid for the LM calculations [11]. The determinant of each sensitivitymatrices is nonzero, hence non-singular. We also calculated the condition number κ(SSS) by firstnormalizing the columns of each sensitivity matrix, obtaining a normalized matrix sss, and thenmultiplying the norms of the normalized matrix and its inverse as follows

κ(SSS) = ‖sss‖ ‖s−1s−1s−1‖

The calculated condition number of the sensitivity matrices are 25.6, 13 and 25.8 for LM1(λ1,λ2), LM2(λ1, λ2) and LM3(λ2, λ3), respectively. These values mean that the matrices are wellconditioned (κ(SSS) < 100 ). These values are about the same as those obtained based on thesimulated sensitivity matrices ∼25.6, 13, 25.7, implying that correcting the sensitivity to theadlayer thickness results in stable condition numbers, and hence stable numerical accuracy.This can be useful in optimizing the nanorod structures as the condition numbers based on themeasured results agree well with those based on the simulated sensitivity matrices, whilst themeasured bulk RI sensitivities deviated from the simulated counterparts.It is also important to investigate the sensor figure of merit (FoM) based on the full width

at half maximum (FWHM) given by ∼ FoM = SB/FWHM, revealing FoMs of 3.1, 2.7 and2.6 for the first, second and third resonances, respectively. These values exceed reported valuesfor gold nanorods fabricated by the electron beam lithography ∼ 1.9 [8], and are comparable tothose associated with chemically synthesized nanorods ∼ 1.7 − 2.6 [21]. This is attributed tothe increased sensitivity of the nanorods presented in this paper 289 − 382.37 nm RIU−1 due tothe increased width of the nanorods as increasing the rods minor axis was previously linked toincreasing the EM decay length and hence the bulk RI sensitivity [20].Another interesting parameter to consider is the figure of merit based on adlayer-bulk

differentiation [6, 8] that can be determined as χ = |SB1/Sd1 − SB2/Sd2 |; the proposed multiple


0 5 10

∆ ×10-3

-2

0

2

4

6

8

∆ λ

1 [

nm

]

(a)

SB

=340

SB

′=268.2

2 4 6 8

d [nm]

5

10

15

20

25

∆ λ

1 [

nm

]

(d)

Sd=2.1

S′

d=1.66

0 5 10

∆ n ×10-3

-2

0

2

4

6

8

∆ λ

2 [

nm

]

(b)

SB

=365

SB

′=331.1

2 4 6 8

d [nm]

5

10

15

20

25

∆ λ

2 [n

m]

(e)

Sd=1.93

S′

d=1.75

0 5 10

∆ n ×10-3

-2

0

2

4

6

8

∆ λ

3 [

nm

]

(c)

SB

=465

SB

′=382.4

2 4 6 8

d [nm]

5

15

25

∆ λ

3 [n

m]

(f)

Sd=2.1

S′

d=1.73

Fig. 8. Top panel: simulated versus measured shift in resonance wavelengths against bulkRI changes. The bulk RI sensitivities, SB and S′B (nm/RIU), were determined as the slopeof each graph. Bottom panel: simulated and measured resonance shifts versus the adlayerthickness based on the simulated (Sd) and corrected (S′d) adlayer sensitivities. Each correctedsensitivity (S′

d) was obtained using Eq. (11) based on the measured bulk RI sensitivity S′B

for each resonance.

resonance rod structures revealed the following values based on the measured sensitivities: 0.18with LM(λ1,λ2), 0.38 with LM(λ1,λ3) and 0.17 with LM(λ2,λ3) compared to 0.18, 0.38 and 0.17based on the simulated sensitivities, exhibiting an improved stability system as compared toestablished dual-resonance nanorod structures whose measured figure of merit differed from thesimulated counterpart ∼ 0.25 vs 1, respectively [8].

The estimated adlayer thickness and bulk RI changes using the linear response model based onthe corrected sensitivity matrices are shown in Figs. 9(a) – 9(c). The estimates based on the MLEmethod were obtained using Eq. (6) and Eq. (7) with the mean and variance of the estimatesbased on the linear response models. The estimates based on the MLE estimation are shown inFig. 9 (d), exhibiting improved accuracy and precision based on both bulk RI and surface bindingexperiments.We used the data retrieved from Fig. 9 to investigate both the accuracy and precision of the

proposed method compared with the linear response model. Since ethanol solutions with knownrefractive indices were used in the first part of the experiment, we used the reported refractiveindices [22] as a reference to calculate the errors in the estimated RI change. Figure 10(a) showsboth the error and standard deviation of the bulk RI change estimated by the linear responsemodel and the MLE method. The MLE method is shown to improve the accuracy in estimatingRI changes of 0, 5.1 × 10−3 and 1.1 × 10−2 with improved precision (improved RI resolution);the averaged error is 6.1 × 10−3, 1.7 × 10−3, 2.2 × 10−3 and 9.1 × 10−4 for LM1, LM2, LM3 andthe MLE method, respectively. This indicates that the accuracy can be increased by one order ofmagnitude employing the MLE method. The averaged standard deviation of the estimated RI


-2

3

8

d [nm

]

(a)

I←1→I←2 →I← 1→I←3 →I← 1 →I← 4 →I← 5 →I← 4 →I

-0.01

0.01

0.03

∆ n

-2

3

8

d [nm

]

(b)

-0.01

0.01

0.03

∆ n

-2

3

8

d [nm

]

(c)

-0.01

0.01

0.03

∆ n

0 20 40 60 80 100 120 140 160 180 200

t [minutes]

-2

3

8

d [nm

]

(d)

-0.01

0.01

0.03

∆ n

Fig. 9. Estimated adlayer thickness (left y-axis) and bulk RI change (right y-axis) based onthe measured results after applying (a) LM1(λ1, λ2), (b) LM2(λ1, λ3), (c) LM3(λ2, λ3), and(d) the MLE method. The cycles on the graph represent the following: [1] DI water, [2] 8 %ethanol solution, [3] 16 % ethanol solution, [4] Buffer, and [5] Streptavidin solution.

change by the LM1, LM2, LM3 and the MLE method was 3.6 × 10−3, 1.9 × 10−3, 5.4 × 10−3 and1.2 × 10−3, respectively. We used the measured data for biotin-streptavidin binding experiment toobtain the mean and standard deviation in the estimated adlayer thickness and bulk RI changeas shown in Figs. 10(b) and 10(c). The MLE method exhibits a decreased standard deviationbased on both estimated adlayer thickness and bulk RI change during the baseline phase andboth association and dissociation phases. The estimated adlayer thickness was 6 nm and 4 nmduring the association and dissociation phases, respectively, as shown in Fig. 10(b). This suggeststhat the gold nanorods were not completely functionalized, and there were empty locations thathave not been occupied by biotin. The linear response models with higher condition numberand lower cross sensitivity figure of merit, χ, revealed the worst results in terms of accuracyand precision. This, however, did not impact the overall results based on the MLE method. Theaveraged standard deviation was 1.3 nm, 0.54 nm, 1.22 nm and 0.37 nm for LM1, LM2, LM3 andthe MLE method, respectively. The MLE method improves the precision and accuracy by factorsof 3 and 3.7, respectively.


0 0.0051 0.11

∆ n

-5

0

5

10

15

20

ǫn

×10-3 (a)

LM1

LM2

LM3

MLE

Buffer Strep. Buffer

Sensing event

-5

0

5

10

15

20

∆ n

×10-3 (c)

LM1

LM2

LM3

MLE

Buffer Strep Buffer

Sensing event

0

2

4

6

8

d [nm

]

(b)

LM1

LM2

LM3

MLE

Fig. 10. (a) Error in estimated RI change after applying the linear response model (LM1,LM2, LM3), and the MLE method to the measured results. The error was calculated asthe difference between the estimated RI changes and the reported counterparts based onrefractometer results for ethanol solutions of various concentrations (0%, 8%, and 16 %).The data is obtained from the first five steps in Fig. 9 (steps: 1, 2, 1, 3, 1). (b) Estimatedadlayer thickness and (c) bulk RI change after applying the linear response model (LM1,LM2, LM3) and the MLE method to the surface binding experimental results. The error barsdenote the standard deviation of the estimated values obtained from the last three steps inFig. 9 (steps: 4, 5, 4).

7. Conclusion

This paper presented a method to improve the accuracy of estimating the adlayer thickness andbulk RI change. The method is based on multiple resonance sensors to generate more than asingle system of linear equations, and applies the MLE method to the solutions obtained by thesesystems to maximize the likelihood of the results with lower variance. The paper also introduceda method to generate sensitivity matrices based on the experimental conditions, reducing errorsbased on the mismatch between the calculated and measured sensitivities. Moreover, this canreduce the numerical calculations if different biological samples are measured, or if the numberof resonances is increased. The linear response model is limited to biological adlayers of amaximum thickness of ∼ ld/10. However, LSPR biosensors are aimed to detect such smallbiological samples. Although the sensing experiments yielded noisy results (based on resonanceshift) when compared to some reported measurements, the MLE method improved the resultsbased on the estimated adlayer thickness and bulk RI change. The precision and accuracy wereimproved by factors of 3 and 3.7 when compared to the averaged results obtained by the linearresponse model, proving that the MLE method can leverage improved self-referenced LSPRsensors. Increasing the number of resonances would improve both accuracy and precision of theestimates. The averaged FoM associated with the fabricated nanorods was 2.8 RIU−1 and theaveraged figure of merit based on the adlayer/bulk RI cross sensitivity, was 0.24; increasing theFoM would further improve the precision, and increasing the adlayer/bulk RI cross sensitivityfigure of merit can achieve improved accuracy. Additional improvement in the precision andaccuracy can be achieved by optimizing the nanorods based on these parameters.

Acknowledgements

We would like to thank Professor Bruce Lennox and Professor David Juncker (Chemistry andBiomedical EngineeringDepartments,McGill University) for providing access to the spectroscopyand fabrication facilities. COMSOL Multiphysics package was provided by CMC Microsystems.


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