On the Determination of Uncertainty and Limit of Detection in Label-Free Biosensors
Abstract
:1. Introduction and Review of Basic Concepts
2. Determination of Uncertainty in a Measuring Interval and the Limit of Detection through the Calibration Function Data
3. Analysis of Standard Immunoassay Situations
3.1. Simulated Immunoassay
3.2. Experimental Immunoassay
- ○
- The biosensor response is non-linear, with a noticeable lack of repeatability at the end of its scale (over 20 μg/mL).
- ○
- Variability increases with concentration probably due to differences in sensing cells or biofuntionalization performance among other possible factors (standard deviations do not pass the Hartley’s test [29]).
- ○
- The degrees of freedom of the problem , where is the number of the parameters to be determined during the fitting: five for the 5PL, for the polynomials.
- ○
- The weighted sum of squares , where is . is the fitted calibration curve.
- ○
- The critical value of a Chi-square distribution with degrees of freedom corresponding to a confidence level of .
- ○
- .
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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C (μg/mL) | 0 | 1 | 10 | 20 | 25 | 30 | 40 | 50 | 60 | 100 | 200 | 300 | 400 | 500 |
Signal (A.U.) | 0 | 1.9 | 17.7 | 32.3 | 38.5 | 44.2 | 54.1 | 62.2 | 68.9 | 85.7 | 97.9 | 99.0 | 99.1 | 99.2 |
S (A.U.) | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
a([A.U.]/[μg/mL] | b([A.U.]) | ua([A.U.]/[μg/mL] | ub([A.U.]) | r |
1.17 | 4.88 | 0.05 | 1.66 | −0.79 |
LoD (μg/mL) | LoQ (μg/mL) | Umin (μg/mL) | Umax (μg/mL) | CMax(μg/mL) |
5.7 | 16.8 | 4.5 | 6.3 | 60 |
N = 9 | N = 8 | N = 7 | N = 6 | |
---|---|---|---|---|
a([A.U.]/[μg/mL] | 1.17 | 1.27 | 1.38 | 1.49 |
b([A.U.]) | 4.88 | 3.37 | 2.03 | 1.04 |
LoD (μg/mL) | 5.7 | 5.4 | 5.1 | 4.9 |
LoQ (μg/mL) | 17.1 | 16.2 | 15.3 | 14.7 |
Cmax(μg/mL) | 60 | 50 | 40 | 30 |
Umin (μg/mL) | 4.5 | 4.3 | 4 | 3.8 |
Umax (μg/mL) | 6.3 | 5.9 | 5.6 | 5.1 |
Concentration (μg/mL) | Transduction Signal (nm) | Mean (nm) | Si (nm) | |||||
---|---|---|---|---|---|---|---|---|
j = 1 | j = 2 | j = 3 | j = 4 | j = 5 | j = 6 | |||
1 | 0.13 | 0.15 | 0.00 | 0.09 | 0.11 | 0.07 | 0.09 | 0.05 |
2.5 | 0.52 | 0.43 | 0.03 | 0.28 | 0.26 | 0.45 | 0.33 | 0.18 |
5 | 0.61 | 0.72 | 0.44 | 0.35 | 0.59 | 0.45 | 0.53 | 0.14 |
7.5 | 0.87 | 0.90 | 0.67 | 0.87 | 0.67 | 0.51 | 0.75 | 0.16 |
10 | 1.43 | 1.39 | 1.17 | 1.39 | 1.08 | 0.85 | 1.22 | 0.23 |
15 | 2.22 | 2.10 | 2.00 | 2.10 | 1.92 | 1.71 | 2.01 | 0.18 |
20 | 3.40 | 3.28 | 3.31 | 3.40 | 2.97 | 2.60 | 3.16 | 0.32 |
30 | 3.92 | 3.80 | 3.96 | 4.18 | 3.37 | 3.14 | 3.73 | 0.40 |
50 | 4.55 | 4.82 | 4.68 | 4.30 | 4.26 | 3.73 | 4.39 | 0.39 |
70 | 5.38 | 5.07 | 5.24 | 4.94 | 4.77 | 4.91 | 5.05 | 0.22 |
100 | 6.14 | 5.69 | 5.76 | 5.66 | 5.37 | 5.05 | 5.61 | 0.37 |
Type of Curve | Deegres of Freedom | Weighted Sum of Squares | Chi-Square Critical Value | Akaike Information Criterion AICc |
---|---|---|---|---|
Polynomial g = 1 | 5 | 37.1 | 11.1 | 18.7 |
Polynomial g = 2 | 4 | 8.66 | 9.49 | 15.5 |
Polynomial g = 3 | 3 | 6.31 | 7.81 | 27.3 |
Polynomial g = 1 | 2 | 4.16 | 5.99 | 66.4 |
5PL | 2 | 2.01 | 5.99 | 61.3 |
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Lavín, Á.; Vicente, J.D.; Holgado, M.; Laguna, M.F.; Casquel, R.; Santamaría, B.; Maigler, M.V.; Hernández, A.L.; Ramírez, Y. On the Determination of Uncertainty and Limit of Detection in Label-Free Biosensors. Sensors 2018, 18, 2038. https://doi.org/10.3390/s18072038
Lavín Á, Vicente JD, Holgado M, Laguna MF, Casquel R, Santamaría B, Maigler MV, Hernández AL, Ramírez Y. On the Determination of Uncertainty and Limit of Detection in Label-Free Biosensors. Sensors. 2018; 18(7):2038. https://doi.org/10.3390/s18072038
Chicago/Turabian StyleLavín, Álvaro, Jesús De Vicente, Miguel Holgado, María F. Laguna, Rafael Casquel, Beatriz Santamaría, María Victoria Maigler, Ana L. Hernández, and Yolanda Ramírez. 2018. "On the Determination of Uncertainty and Limit of Detection in Label-Free Biosensors" Sensors 18, no. 7: 2038. https://doi.org/10.3390/s18072038