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Development of an optical microfiber immunosensor for prostate specific antigen analysis using a high-order-diffraction long period grating

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Abstract

Fiber-optic biosensors are of great interest to many bio/chemical sensing applications. In this study, we demonstrate a high-order-diffraction long period grating (HOD-LPG) for the detection of prostate specific antigen (PSA). A HOD-LPG with a period number of less than ten and an elongated grating pitch could realize a temperature-insensitive and bending-independent biosensor. The bio-functionalized HOD-LPG was capable of detecting PSA in phosphate buffered saline with concentrations ranging from 5 to 500 ng/ml and exhibited excellent specificity. A limit of detection of 9.9 ng/ml was achieved, which is promising for analysis of the prostate specific antigen.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Prostate cancer is the second most common cancer among men globally [1]. Currently, the most frequently used indicator for early diagnosis of prostate cancer is the level of prostate specific antigen (PSA), which is an intracellular glycoprotein (34 kDa, kallikrein-like protease) serving as a serum biomarker in the blood [2,3]. The PSA cut-off between prostate hyperplasia and cancer is 4 ng/ml, since the PSA level of cancer patients typically ranges from 4–10 ng/mL [4]. As no effective cures are available for prostate cancer at the metastatic stage [5,6], early detection of disease biomarkers is crucial. Thus, there is an urgent need for the development of sensitive and high-speed diagnostic devices for the early screening and monitoring of disease biomarkers.

Using the advantages of optical fibers, including small size, low cost, and simple operation, fiber-optic biosensors have become a fast-developing tool for cancer diagnosis and early screening [7,8]. To date, a number of fiber-optic biosensors have been proposed, including fiber Bragg gratings [9,10], long period gratings (LPGs) [8], tilted fiber gratings [1113], optical fiber interferometers [14,15], lossy mode resonances [7,16], excessively tilted fiber gratings [17], unclad fibers [18,19], and tapered fibers [18,20]. Among these, LPG biosensors possess many useful inherent properties, such as high sensitivity, smart transduction instrumentation, and high reliability. The earliest demonstration of an LPG biosensor was reported by DeLisa, et al., who linked goat anti-human Immunoglobulin G (IgG) antibodies to an etched fiber surface [21]. A change in the refractive index was caused by the antibody-antigen binding and the human IgG binding was observed over a range of 2–100 µg/ml. Since then, LPGs have been exploited to detect antigens [22], DNA [23], viruses [2426], bacteria [27,28], and other medically relevant parameters. However, most reported devices lacked sufficient sensitivity for the lower detection limits, which involves detection of small biomolecules or low concentrations. Consequently, many novel schemes have been developed to enhance device performance; among them, the deposition of thin overlays and fabrication of novel grating structures are two fascinating methods.

For the thin overlay deposition, many studies utilized special material with high refractive indexes (RI), such as gold-doped macroporous silica [29], titania-silica [30], poly(allylamine hydrochloride)/gold coated silica nanoparticles [31], gold nanoparticles [32], and graphene oxide [3335], to increase the effective RI of the selected cladding mode. This improves the sensitivity and boosts the performance of the LPG sensors for bio-sensing. It has been reported that a dual-peak LPG, operating near the turn-around-point, can improve the sensitivity and the use of high RI coatings can further increase the RI sensitivity to 5602 nm/RIU in a glycerol solution [36]. The high RI coating has been used to detect the kinetic binding interaction between IgG and anti-IgG [37] as well. Additionally, the layer thickness of high RI coatings can be optimized for satisfying a specific working environment. Many studies have focused on these aspects, with particular focus on the potential use for LPGs working in transition mode, and the reported results have demonstrated higher sensitivities for biological sample measurements [3840]; however, these LPGs suffered from low mechanical and thermal stability in the measurement setup [41].

Recently, significant attention has also been given to novel gratings with cladding etched, side polished and fiber tapered structures. Similar to a high RI overlays strategy, the dispersion property of LPGs during the etching process can also be controlled to produce dual peaks close to the dispersion turn-around-point. Reported results showed an ultrahigh sensitivity of near 1500 nm/RIU and the capacity of detecting the IgG/anti-IgG interaction with a limit of detection (LOD) of 50 µg/L (330 pM) [41]. Reported LPGs formed on the side-polished fiber surface of a DNA biosensor showed a sensitivity improvement of ∼2.5 times, compared with previous results based on a dual-peak LPG as well [42]. A cladding tapered LPG-based in-fiber Michelson interferometer has shown an 8.5-fold sensitivity enhancement for the detection of the rabbit IgG compared with those without the cladding tapering. Additionally, with the development of new grating structures, photonic-crystal-fiber long-period gratings (PCF-LPGs) were also demonstrated to measure the thicknesses of a monolayer of poly-L-lysine and double-stranded DNA [43]. The maximum sensitivity of PCF-LPGs was 1500 nm/RIU at a RI of 1.33 [44]. Furthermore, a PCF-LPG immunoassay was developed with a wavelength shift of 1.6 nm, for the specific binding of goat anti-mouse IgG to anti-rat bone sialoprotein with a thickness of 2.4 nm [45]. With a mixed range of special sensor designs being investigated, the sensitivity of LPG biosensors has been significantly improved, as compared with LPGs in conventional single mode fiber (SMF) devices.

As the requirements for trace ultra-low concentration biosensors include high sensitivity and compactness, significant efforts have been devoted to produce optical fiber LPG biosensors with better performance. However, the lengths of these gratings are typically more than 2–3 cm for strong resonant coupling. Furthermore, micro-bending and other uncertain factors may significantly disrupt the optical spectrum and deteriorate the detection performance of such LPG sensors, which introduces further technical burdens to the modification, packaging and operation. Therefore, there is great interest and practical significance in the study of new long-period grating devices with higher sensitivity, compactness and stability.

Herein, a HOD-LPG is proposed as an effective and elegant tool to detect PSA concentration. The sensor fabrication and the working principle are discussed in detail. Then, to understand the inherent distinctive properties, we compared the RI sensing, temperature, and bending characteristics of the HOD-LPG with the conventional LPG. As shown in Fig. 1, the HOD-LPG was then biofunctionalized through a series of biochemical treatment processes, thus, the variation caused by the specific capture of a tiny amount of PSA antigens in buffer conditions could be detected. Finally, the specificity was examined. With the demonstrated high reproducibility, stability, and flexibility, the proposed sensor provides a new approach to improve early detection of prostate cancer.

 figure: Fig. 1.

Fig. 1. Schematic for the biosensing process when the HOD-LPG was biofunctionalized to detect PSA. (BBS represents Broad Band Source and OSA represents Optical Spectrum Analyzer)

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2. Methods

2.1 Materials

Sulfuric acid (98%), hydrogen peroxide, hydrochloric acid, ethanol, phosphate buffered saline (PBS), and alpha-fetoprotein (AFP) antigen were purchased from Sangon Biotech Co. Ltd. (China). 3-aminopropyl-triethoxysilane (APTES) was purchased from Aladdin (Shanghai, China). Prostate specific antigen (PSA) was obtained from Cholun Medical (Shenzhen, China). Mouse Anti-PSA Monoclonal antibody was purchased from Bioss Biotechnology Co. Ltd. (Beijing, China).

A piranha solution was prepared by mixing the 98% sulfuric acid and hydrogen peroxide in a volume ratio of 3:1. The 5% APTES solution was prepared by dissolving the purchased 99% APTES in absolute ethanol. The anti-p53 antibody solution, with a concentration of 1 µg/mL, was prepared using PBS. For adaption to the log linear axis and convenience of dilution, the PSA protein solutions concentrations were intentionally chosen and prepared, utilizing PBS at 500, 100, 50, 10, 5, 1, and 0.5 ng/mL.

2.2 Sensor fabrication and characterization

Figure 2 shows the schematic of the HOD-LPG, characterized using the electric arc discharge method. The HOD-LPG fabrication is divided into two steps: the tapering step and the point-to-point grating writing step. A conventional SMF was tapered to a microfiber, using the Fujikura FSM-100P+ machine. In the machine tapering process, we set the transition length, the uniform diameter region length, and the microfiber diameter d as ∼7 mm, ∼4 mm, and ∼12.5 µm, respectively. The system employed three motors to drive the corresponding transmission stages in the Z direction, namely, the ZL, ZR, and SWEEP motors. The optical fiber, which was fixed by the fiber holders, could move along the fiber axis with a movement speed driven by the SWEEP motor. As shown in Fig. 2(a), when the arc discharge was applied, the electric current was set at approximately 12.0 mA and the two ends of the microfiber were simultaneously stretched by the movement of the ZL and ZR motors. By controlling the movement velocity, a specific microfiber configuration, which we had previously determined, can be obtained. As seen in Fig. 2(e), the insertion loss of the device was −2.5 dB. In the second fabrication step, as shown in Fig. 2(b), periodical tapering was applied to a portion of the microfiber by arc discharging from point to point, with the grating pitch Λ set to 400 µm. When a point of the microfiber was tapered, the electric current, the arc duration, and the number of discharges are set as ∼9.8 mA, ∼0.8 s, and ∼8 times, respectively. The grating period number N was increased and the corresponding transmission spectra are shown in Fig. 2(e). The figure illustrates the measured evolution of the transmission spectra, with respect to the period number N of the HOD-LPG, for N equal to 3, 6, and 8. When the period number varies, the strength of the resonance peak gradually decreases. Finally, as shown in Figs. 2(c) and 2(e), the HOD-LPG was realized, and the resonance notch increased to −25 dB when the period number N = 10. Additionally, the grating length was only 4 mm.

 figure: Fig. 2.

Fig. 2. (a) Schematic for the fabrication process of tapering SMF to a microfiber. (b-c) Schematic for the remainder of the fabrication process of HOD-LPGs, including (b) periodic deformation at the discharged section of the microfiber, and (c) formation of the HOD-LPG. (d) Scanning electron microscopy (SEM) image of the HOD-LPG. (e) Evolution of transmission spectra for the period numbers N = 0, 3, 6, 8, and 10. (f) Transmission spectra of the HOD-LPG in air and water. (g) Measured (points) and modeled (curves) peak wavelengths as functions of the grating period, for different diffraction orders.

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The HOD-LPG promotes coupling between the fundamental mode and high order mode. The high attenuation of the high order modes results in distinct resonant loss bands in the transmission spectrum, at a wavelength satisfying the relation described in Eq. (1):

$$\lambda = {{({{n_{eff1}} - {n_{eff2}}} )\cdot \Lambda } \mathord{\left/ {\vphantom {{({{n_{eff1}} - {n_{eff2}}} )\cdot \Lambda } q}} \right.} q}$$
where λ is the wavelength, neff1 and neff2 are the effective RI values for the fundamental and the coupled higher-order modes, respectively, Λ is the grating pitch and q is the diffraction order. Figure 2(f) shows the transmission spectrum of the grating in both air and water, with dips observed at the wavelengths of 1350 and 1450 nm. The HOD-LPG was realized with an almost symmetric geometry and it was shown that the LP02 mode is the most easily excited mode. The phase matching (Λ-λ) curves of the HOD-LPG in air were calculated, and are shown in Fig. 2(g). The simulated results are consistent with the experimental loss at peak wavelengths, for the gratings surrounded by air. The number of grating periods increases as the diffraction order q is increased from 100 to 1000. The proposed HOD-LPGs was produced with a grating pitch equal to 400 µm and a diffraction order equal to 3. Figure 2(d) shows the SEM microscopic image of the periodic tapers in a HOD-LPG, with the period number N, grating pitch Λ, and microfiber diameter d equal to 10, 400 µm, and 12 µm, respectively.

2.3 Refractive index detection of the HOD-LPG

To investigate the HOD-LPG RI sensitivity, compared to the LPG, the responses of the HOD-LPG and conventional LPG in different RI were investigated by tracing the loss dip in the transmission spectra. The conventional LPG (Λ = 350 µm, N = 50) was made from a SMF. The liquid used in the HOD-LPG was a mixture of ethanol and de-ionized (DI) water. By changing the concentration of the ethanol, the RI range was changed from 1.333 to 1.365. The temperature was controlled at 23 °C. According to Fig. 3(a), the linear fitting RI sensitivity of the HOD-LPG is ∼827.4 nm/RIU at a RI of 1.3334 and ∼1733.65 nm/RIU at a RI of 1.3626. For the proposed HOD-LPG, the spectral RI sensitivity can be expressed by Eq. (2):

$$S = {{d\lambda } \mathord{\left/ {\vphantom {{d\lambda } {dRI}}} \right.} {dRI}} = ({{\lambda \mathord{\left/ {\vphantom {\lambda \Gamma }} \right.} \Gamma }} )\times ({{{\partial \Delta n} \mathord{\left/ {\vphantom {{\partial \Delta n} {\partial RI}}} \right.} {\partial RI}}} )$$
The sensitivity is determined by dispersion factor Γ and the RI-induced variation of intermodal index ∂Δn/∂RI [46]. In this investigation, we can calculate Γ < 0 and ∂Δn/∂RI < 0, enforcing that the sensitivity S > 0. Moreover, it is important to note that the HOD-LPG is insensitive to the diffraction order q [47]. Subsequently, as shown in Fig. 3(b), maintaining the HOD-LPG (d = 12 µm, Λ = 430 µm) in DI water, the long-time wavelength movement of the dip was investigated and the standard deviation σ of wavelength drift was estimated as 0.024 nm which showed excellent stability.

 figure: Fig. 3.

Fig. 3. (a) Resonant wavelength shift of the HOD-LPG against varied surrounding RI. (b) wavelength fluctuation versus time. (c) resonant wavelength shift of the HOD-LPG against varied surrounding temperature. (d) transmission spectra of a HOD-LPG with different bending curvatures. Inset indicates the partial enlargement of resonance dips.

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2.4 Temperature and bending sensitivity of the HOD-LPG

The response of the HOD-LPGs to temperature was investigated by placing the sensor in a resistance furnace in air. The temperature of the furnace was artificially controlled by an electric circuit, from 18 to 100 °C, and recorded by a thermometer. Figure 3(c) shows the resonant wavelength response to different temperatures. The temperature coefficient that represents the temperature sensitivity was approximately 13.5 pm/°C at 1350 nm. The reason for this low coefficient is that most of energy (LP01 and LP02 modes) in the microfiber remains in the silica cladding region and mode indexes vary with the external environmental temperature changes. Thus, the thermal-optic effect is expected to be self-compensated and the devices consequently exhibit a low temperature sensitivity.

The bending property of a HOD-LPG was investigated and the spectral response to different bending curvatures are shown in Fig. 3(d). When the HOD-LPG is bent at a 90° angle, a dip occurs at the same wavelength (from 1455.461 to 1455.504 nm) and the transmission loss of the peak changed from −27.421 to −23.744 dB, with a transmission change of 0.24%. When the grating was bent at a 180° angle, the wavelength of the top blue-shifted, by 1.24 nm, to 1454.22 nm, and the transmission loss was −25.851 dB. This bending insensitivity improves the overall stability of the bio-sensing equipment. Furthermore, the device is capable of operating as a U-shaped probe, thus making the measurement process easier and reducing biological sample consumption.

We briefly summarize the RI sensing character, temperature, and bending properties of both conventional LPGs and HOD-LPGs in Table 1. Compared with the conventional LPG, the proposed HOD-LPG is a highly RI sensitive, temperature-insensitive, and bending-independent sensor, making it a competitive candidate for high-performance excellent bio-sensing implementation.

Tables Icon

Table 1. A performance comparison of conventional LPG and HOD-LPG.

2.5 Functionalizing for the HOD-LPG immunosensor

As shown in Fig. 4(a), the functionalization of the HOD-LPG probe was done by the following procedures. First, the piranha solution was used for 30 min to produce silicon hydroxyl groups and regenerate the sensing layer after each bio-sensing experiment. The surface was then silanized with 5% APTES for 1 h to form amidogen(-NH2). The surface was then treated with Crosslink 2.5% glutaraldehyde solution for 30 min; the probe was subsequently immersed in an anti-PSA solution (1 µg/mL) for 1 h. Finally, the concentration of the target antigen solution was detected. DI water was used to rinse the probe at the end of each procedure to ensure molecule conjunction stability.

 figure: Fig. 4.

Fig. 4. (a) Schematic diagram for the surface functionalization procedure. AFM images of the surface of (b) the bare fiber and (c) the functionalized surface anchored with anti-PSA. Fluorescence microscope image of the fiber (d) without immobilized and (e) with immobilized, labeled anti-PSA. (f) Sensorgram for surface activation and PSA detection at bulk concentrations of 1 and 5 ng/ml. (g) Measured dip wavelength drift in DI water, after the device was immersed into 1 µg/ml antibody and 500 ng/ml PSA solutions within the entire immunosensing process.

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To ensure that the anti-PSA had been anchored onto the optical surface, the roughness of the fiber surface for both the bare fiber and the functionalized probe, with immobilized with anti-PSA was measured and is shown in the Atomic Force Microscope (AFM) images in Figs. 4(b) and 4(c), respectively. The images were processed by 2th flatten order; the roughness of the fiber surface was changed from 0.231 to 1.14 nm. The surface of the functionalized probe was more wrinkled than the bare one, indicating that biomaterials are covalently linked to the surface. In addition, to further verify this functionalization, PSA antibody conjugated with fluorescein isothiocyanate was applied via the fluorophores. The comparison of the fluorescent images in Fig. 4(d) and Fig. 4(e) shows that the PSA protein specifically bonded to the functionalized surface of the optical fiber. Figure 4(f) recorded the spectral response of the dip throughout the entire functionalization process, after hydroxylating with the piranha solution. This contains the surface functionalization and immune reaction process. The spectral response was recorded for the process steps occurring after the hydroxylation procedure. When moving the probe from the DI water to the APTES solution, an abrupt red-shift of approximately 60 nm was observed, which was followed by a further gradual red-shift that eventually became stable. At the end of the process, the fiber was rinsed in DI water to remove non-covalently adsorbed silane compounds and this step resulted in an obvious blue-shift. All subsequent procedures exhibited a similar signal evolution, which occurs because substances such as the APTES solution possess a higher RI than DI water and the higher RI causes the dip to occur at a longer wavelength. Furthermore, the junction of molecules may slightly increase the surface RI [49]. It is important to note that, as shown in Fig. 4(f), between every DI water rinsing step, the same red-shifting trend was observed, indicating that the corresponding materials were firmly anchored to the fiber surface. We compared the loss peak wavelength in DI water to a variety of other steps to indicate the RI variation of the fiber surface. As shown in Fig. 4(g), after PSA protein was introduced at a bulk concentration of 500 ng/ml incubation, the bind-induced spectral shift was 0.37 nm.

3. Results and discussion

3.1 Protein PSA detection

After being anchored with anti-PSA antibody, we placed the probes into PSA solutions with concentrations of 500, 100, 50, 10, 5, 1, and 0.5 ng/mL. Before each step, in which we changed the solution concentration, the probe was rinsed in DI water and the wavelength was recorded. The wavelength difference in DI water, Δλ, could therefore be calculated and discussed. By investigating the corresponding responses to PSA proteins at different concentrations (C), the calibration curve can be drawn with error bars. Each error bar represents the standard deviation of three independent measurements, taken with the same biosensor. As shown in Fig. 5(a), the curve clearly exhibits an “S” shape, ranging between 0.5–500 ng/ml. The response curve can then be fitted by a Logistic function [50,51], shown in Eq. (3):

$$\Delta \lambda = 0.42454 - \frac{{0.43812}}{{1 + {{({C/37.46152} )}^{0.73402}}}},\,({R^2} = {0.9880} )$$

From the calibration curve, the linear regression equation is expressed as y (nm) = -0.04926 + 0.16084 × log (C (ng/mL)) (R2 = 0.985). With a log-linear response from 5 to 500 ng/ml, the fitted sensitivity is approximately S = 0.16084 nm/(ng/ml). The theoretical LOD can be estimated as xLOD = f−1(${\bar {y}}_{\textrm{black}}$+ 3σmax) [49], where ${\bar {y}}_{\textrm{black}}$ represents the mean value of the blank sample and σmax represents the maximum standard deviation. In our study, we measured${\bar {y}}_{\textrm{black}}$= 0.003 nm and σmax = 0.036 nm; the final LOD value was calculated as 9.9 ng/mL.

 figure: Fig. 5.

Fig. 5. (a) Measured biosensor response as a function of PSA concentration. (b) Measured response to the biomarker of specificity, demonstrated by the PSA response, and non-specificity, demonstrated by the AFP response and the response of the various ionic solutions. Statistically significant differences, with the *** indicating P < 0.01 were determined by the ANOVA method, carried out with the GraphPad Prism (Graphpad Software).

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3.2 Specificity

For the specificity test, we selected AFP, Na+, K+, and Pb+ as control assays. AFP is a protein found in humans that is encoded by the AFP gene, which has been commonly used as a control protein. It was adopted to reasonably evaluate the specificity of the biosensors [6,52]. Additionally, three different ion solutions were used to investigate the specificity of this immunosensor. Figure 5(b) shows the measured response to both control proteins and PBS, compared with the response to PSAs. Samples of AFP, NaCl, KCl, and PbCl2, each with a concentration up to 500 ng/ml in PBS were applied to the immunosensor. As expected, Fig. 5(b) shows that only the spectral signal of the PSA produced obvious enhancements, while the wavelength shifts produced by the other samples were very low. The strong response of the PSA, in terms of wavelength shift, indicates the quality of the assay specificity for PSA recognition in PBS and the responses obtained for each substrate exhibit statistically significant differences (P < 0.01). To further improve the specificity of the biosensor, a blocking solution, such as bovine serum albumin, can be used before specific detection.

4. Conclusion

In conclusion, we have presented a HOD-LPG, utilized to achieve quantitative detection of PSA proteins. Specifically, the HOD-LPG was produced with a period number of 10 and elongated grating pitch of 400 µm, with −27 dB transmission. The proposed device exhibits high sensitivity to the RI sensing, with a value of approximately 1733.65 nm/RIU at a RI of 1.3626. The results of this study indicate that the device is a promising candidate for a high-performance bio-sensing platform. The microfiber was functionalized to detect PSA concentrations in PBS and the biosensor presents a log-linear response for concentrations ranging from 5 to 500 ng/ml, with excellent specificity. Furthermore, the LOD in this work is relatively low and will dictate the range of applications. Compared with previous LPG biosensors, the characteristics of these HOD-LPG devices make them temperature-insensitive and bending-independent biosensors. Additionally, the high RI sensitivity of the proposed device is expected to further improve by combining it with a high RI overlay and the inherent properties of conventional LPGs. Therefore, the proposed biosensor is cost-effective, compact, and relatively stable, making it a competitive alternative in rapid and early detection of disease biomarkers.

Funding

National Natural Science Foundation of China (61705083, U1701268, 61805106); Natural Science Foundation of Guangdong Province (2019A1515011144, 2018A030313677); Guangdong Province Higher Vocational Colleges and Schools Pearl River Scholar Funded Scheme (2019BT02X105); Fundamental Research Funds for the Central Universities (21617305).

Disclosures

The authors declare no conflicts of interest.

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Figures (5)

Fig. 1.
Fig. 1. Schematic for the biosensing process when the HOD-LPG was biofunctionalized to detect PSA. (BBS represents Broad Band Source and OSA represents Optical Spectrum Analyzer)
Fig. 2.
Fig. 2. (a) Schematic for the fabrication process of tapering SMF to a microfiber. (b-c) Schematic for the remainder of the fabrication process of HOD-LPGs, including (b) periodic deformation at the discharged section of the microfiber, and (c) formation of the HOD-LPG. (d) Scanning electron microscopy (SEM) image of the HOD-LPG. (e) Evolution of transmission spectra for the period numbers N = 0, 3, 6, 8, and 10. (f) Transmission spectra of the HOD-LPG in air and water. (g) Measured (points) and modeled (curves) peak wavelengths as functions of the grating period, for different diffraction orders.
Fig. 3.
Fig. 3. (a) Resonant wavelength shift of the HOD-LPG against varied surrounding RI. (b) wavelength fluctuation versus time. (c) resonant wavelength shift of the HOD-LPG against varied surrounding temperature. (d) transmission spectra of a HOD-LPG with different bending curvatures. Inset indicates the partial enlargement of resonance dips.
Fig. 4.
Fig. 4. (a) Schematic diagram for the surface functionalization procedure. AFM images of the surface of (b) the bare fiber and (c) the functionalized surface anchored with anti-PSA. Fluorescence microscope image of the fiber (d) without immobilized and (e) with immobilized, labeled anti-PSA. (f) Sensorgram for surface activation and PSA detection at bulk concentrations of 1 and 5 ng/ml. (g) Measured dip wavelength drift in DI water, after the device was immersed into 1 µg/ml antibody and 500 ng/ml PSA solutions within the entire immunosensing process.
Fig. 5.
Fig. 5. (a) Measured biosensor response as a function of PSA concentration. (b) Measured response to the biomarker of specificity, demonstrated by the PSA response, and non-specificity, demonstrated by the AFP response and the response of the various ionic solutions. Statistically significant differences, with the *** indicating P < 0.01 were determined by the ANOVA method, carried out with the GraphPad Prism (Graphpad Software).

Tables (1)

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Table 1. A performance comparison of conventional LPG and HOD-LPG.

Equations (3)

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λ = ( n e f f 1 n e f f 2 ) Λ / ( n e f f 1 n e f f 2 ) Λ q q
S = d λ / d λ d R I d R I = ( λ / λ Γ Γ ) × ( Δ n / Δ n R I R I )
Δ λ = 0.42454 0.43812 1 + ( C / 37.46152 ) 0.73402 , ( R 2 = 0.9880 )
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