# Adaptive Method for Quantitative Estimation of Glucose and Fructose Concentrations in Aqueous Solutions Based on Infrared Nanoantenna Optics

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Pre-Processing the SEIRA Measurement

^{−1}and 1078 cm

^{−1}, whereas we obtain 1063 cm

^{−1}and 1080 cm

^{−1}for fructose. Since the second characteristic wavenumber of glucose and fructose are spectrally close together, we choose to only evaluate the peaks at $\mathit{\nu}={\left[1034,1063,1078\right]}^{T}{\mathrm{cm}}^{-1}$ in the following.

#### 3.2. Basis Function Approximation

^{−1}in panel (a) and at 1063 cm

^{−1}in panel (b). At this point we are not sure about the origin of these deviations. In order to include this influence, we decided to design the analysis routine adapted to the sensor data. This means that for each measurement cycle a calibration is carried out to identify the constants ${k}_{i}$ of Equations (1) and (2), characterizing the influence of pure water.

#### 3.3. Validation of Algorithm for Quantitative Concentration Estimate

## 4. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

^{−1}the mean value of the variance (panel (d)) and the standard deviation (panel (f)) are below 10

^{−5}and 4 × 10

^{−3}respectively. Only for wavenumbers below 1000 cm

^{−1}or above 6000 cm

^{−1}the variance and standard deviation increase which is shown in panels (c) and (e). These inaccuracies in the border regions can be explained with the sensor design. It is tuned to provide best measurement results for the fingerprint region.

**Figure A1.**Statistical analysis of exemplary measurement data. The shown reflectance (

**a**,

**b**) results from a mixed solution with 50 g/l glucose and 50 g/l fructose. The measurement data consist of thirty individual spectra. The variance and the standard deviation between those spectra are calculated for each wavenumber and depicted in panels (

**c**,

**d**) and (

**e**,

**f**) respectively. The chosen measurement set reveals one of the largest variances because the reflectance of one spectra exhibits an almost constant offset. However, the qualitative features are preserved.

**Figure A2.**Statistical analysis of the measurement sets for each of the three cycles. The glucose/fructose concentration for each set is depicted in panels (

**a**–

**c**). The corresponding mean value of the variance within the fingerprint region ranging from 1000–1100 cm

^{−1}(compare to panel (d) of Figure A1) is visualized in panels (

**d**–

**f**). The corresponding mean value of the standard deviation is depicted in panels (

**g**–

**i**).

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**Figure 1.**Measurement principle and sensor design. Aqueous pure glucose and fructose solutions as well as mixed solutions are flushed over plasmonic nanoatennas resonant with the characteristic mid-infrared vibrational modes of these monosaccharaides. The tailored flow cell allows to simultaneously acquire reflectance spectra, as sketched on the right hand side. The reflectance peaks of the antennas are modified by the vibrational signatures of the molecular species present in the analyte. From their spectral position the molecular species can be determined, from their modulation depth, in principle, the concentration, given appropriate evaluation and calibration, which is the key result reported here.

**Figure 2.**Schematic description of the developed adaptive process for evaluation of surface enhanced infrared absorption (SEIRA) measurement data to quantitatively estimate glucose and fructose concentrations in aqueous solutions.

**Figure 3.**Employed measurement cycles with different concentrations of glucose (

**a**), fructose (

**b**), or both (

**c**). Panels (

**d**) to (

**f**) show the corresponding relative reflectance of each of the eleven SEIRA measurement sets with the expected fingerprint region for molecular vibrations of glucose and fructose highlighted in light green or light blue, respectively.

**Figure 4.**(

**a**) Relative reflectance measured for 50 g/l aqueous glucose together with a set of baselines for varying parameters $\lambda $; (

**b**) Zoom in on the relevant range of wavenumbers at which vibrational resonances are expected to appear for glucose and fructose; (

**c**,

**d**) Baseline corrected signals and the influence of $\lambda $ on the vibrational features.

**Figure 5.**Relative reflectance of baseline corrected signals with $\lambda =500$ and $p=0.99$ for glucose cycle (

**a**), fructose cycle (

**b**), and mixed cycle (

**c**).

**Figure 6.**Signal peaks $\mathsf{\Delta}s$ evaluated at the three characteristic wavenumbers ${\nu}_{1}=1034{\mathrm{cm}}^{-1}$ (

**a**), ${\nu}_{2}=1063{\mathrm{cm}}^{-1}$ (

**b**), and ${\nu}_{3}=1078{\mathrm{cm}}^{-1}$ (

**c**) originating from pure water for each of the three measurement cycles (gc = glucose cycle, fc = fructose cycle, and mc = mixed cycle).

**Figure 7.**Signal peaks $\mathsf{\Delta}s$ evaluated at the three characteristic wavenumbers ${\nu}_{1}=1034{\mathrm{cm}}^{-1}$ (

**a**), ${\nu}_{2}=1063{\mathrm{cm}}^{-1}$. (

**b**), and ${\nu}_{3}=1078{\mathrm{cm}}^{-1}$ (

**c**) originating from pure glucose or pure fructose, respectively. The content of pure water is already subtracted using the corresponding average value. The displayed basis functions ${\phi}_{i}$ and ${\psi}_{i}$ are quadratic polynomials.

**Figure 8.**Estimated levels of concentration for the glucose cycle (

**a**), fructose cycle (

**b**), and mixed cycle (

**c**) using cycle-specific constants ${k}_{i}$, quadratic polynomials ${\phi}_{i}$ and linear basis functions ${\psi}_{i}$.

**Table 1.**Comparison of RMS errors, mean errors, and maximum errors for the estimated concentrations resulting from different combinations of polynomial basis functions ${\phi}_{i}$ and ${\psi}_{i}$ with order ${n}_{glucose}$ or ${n}_{fructose}$ respectively.

${\mathit{n}}_{\mathit{g}\mathit{l}\mathit{u}\mathit{c}\mathit{o}\mathit{s}\mathit{e}}$ | ${\mathit{n}}_{\mathit{f}\mathit{r}\mathit{u}\mathit{c}\mathit{t}\mathit{o}\mathit{s}\mathit{e}}$ | ${\mathit{e}}_{\mathit{r}\mathit{m}\mathit{s}}\text{}[\mathbf{g}/\mathbf{l}]$ | ${\mathit{e}}_{\mathit{m}\mathit{e}\mathit{a}\mathit{n}}\text{}[\mathbf{g}/\mathbf{l}]$ | ${\mathit{e}}_{\mathit{m}\mathit{a}\mathit{x}}\text{}[\mathbf{g}/\mathbf{l}]$ |
---|---|---|---|---|

1 | 1 | 1.27 | 0.81 | 3.86 |

1 | 2 | 1.27 | 0.77 | 3.98 |

1 | 3 | 1.89 | 0.95 | 10.02 |

2 | 1 | 1.20 | 0.73 | 4.13 |

2 | 2 | 1.23 | 0.71 | 4.29 |

2 | 3 | 1.67 | 0.88 | 8.36 |

3 | 1 | 1.51 | 0.80 | 8.03 |

3 | 2 | 1.53 | 0.79 | 8.24 |

3 | 3 | 1.69 | 0.90 | 6.50 |

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**MDPI and ACS Style**

Schuler, B.; Kühner, L.; Hentschel, M.; Giessen, H.; Tarín, C.
Adaptive Method for Quantitative Estimation of Glucose and Fructose Concentrations in Aqueous Solutions Based on Infrared Nanoantenna Optics. *Sensors* **2019**, *19*, 3053.
https://doi.org/10.3390/s19143053

**AMA Style**

Schuler B, Kühner L, Hentschel M, Giessen H, Tarín C.
Adaptive Method for Quantitative Estimation of Glucose and Fructose Concentrations in Aqueous Solutions Based on Infrared Nanoantenna Optics. *Sensors*. 2019; 19(14):3053.
https://doi.org/10.3390/s19143053

**Chicago/Turabian Style**

Schuler, Benjamin, Lucca Kühner, Mario Hentschel, Harald Giessen, and Cristina Tarín.
2019. "Adaptive Method for Quantitative Estimation of Glucose and Fructose Concentrations in Aqueous Solutions Based on Infrared Nanoantenna Optics" *Sensors* 19, no. 14: 3053.
https://doi.org/10.3390/s19143053