Table of Contents  
Year : 2011  |  Volume : 2  |  Issue : 1  |  Page : 21-25  

Methods for the determination of limit of detection and limit of quantitation of the analytical methods

Department of Pharmaceutical Analysis, B. R. Nahata College of Pharmacy, Mhow Neemuch Road, Mandsaur, Madhya Pradesh - 458 001, India

Date of Web Publication14-Apr-2011

Correspondence Address:
Alankar Shrivastava
Department of Pharmaceutical Analysis, BR Nahata College of Pharmacy, Mhow-Neemuch Road, Mandsaur, Madhya Pradesh 458 001
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/2229-5186.79345

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The quality of an analytical method developed is always appraised in terms of suitability for its intended purpose, recovery, requirement for standardization, sensitivity, analyte stability, ease of analysis, skill subset required, time and cost in that order. It is highly imperative to establish through a systematic process that the analytical method under question is acceptable for its intended purpose. Limit of detection (LOD) and limit of quantification (LOQ) are two important performance characteristics in method validation. LOD and LOQ are terms used to describe the smallest concentration of an analyte that can be reliably measured by an analytical procedure. There has often been a lack of agreement within the clinical laboratory field as to the terminology best suited to describe this parameter. Likewise, there have been various methods for estimating it. The presented review provides information relating to the calculation of the limit of detection and limit of quantitation. Brief information about differences in various regulatory agencies about these parameters is also presented here.

Keywords: Detection limit, limit of detection, limit of quantitation, quantitation limit, methods for determination of LOD and LOQ

How to cite this article:
Shrivastava A, Gupta VB. Methods for the determination of limit of detection and limit of quantitation of the analytical methods. Chron Young Sci 2011;2:21-5

How to cite this URL:
Shrivastava A, Gupta VB. Methods for the determination of limit of detection and limit of quantitation of the analytical methods. Chron Young Sci [serial online] 2011 [cited 2020 Feb 23];2:21-5. Available from:

   Introduction Top

Analytical method development and validation procedures are vital in the discovery and development of drugs and pharmaceuticals. Analytical methods are used to aid in the process of drug synthesis, screen potential drug candidates, support formulation studies, monitor the stability of bulk pharmaceuticals and formulated products, and test final products for release. The quality of analytical data is a key factor in the success of a drug and formulation development program. During the post approval commercial production stage of bulk drugs and pharmaceutical products, the official or in-house test methods that have resulted from the analytical method development and validation process cycle become indispensable for reliable monitoring of the integrity, purity, quality, strength and potency of the manufactured products. There is often a need to transfer methodology from one laboratory to another and/or to include it in official compendia. Such exercises include the use of a method by large numbers of people, in various laboratories across the globe and on instruments manufactured by different manufacturers, thereby causing a greater probability of decreased reproducibility and reliability. These problems can be foreseen and avoided by thorough validation of the analytical method. [1]

Limit of detection (LOD) and limit of quantitation (LOQ) parameters are related but have distinct definitions and should not be confused. The intent is to define the smallest concentration of analyte that can be detected with no guarantee about the bias or imprecision of the result by an assay, the concentration at which quantitation as defined by bias and precision goals is feasible, and finally the concentration at which the analyte can be quantitated with a linear response. [2] Comparison of regulatory authorities such as United States Pharmacopoeia (USP), [3] Foods and Drugs Administration (FDA), [4] International Union of Pure and Applied Chemistry (IUPAC), [5] International Conference on Harmonisation (ICH) [6] and Association of Analytical Communities (AOAC) [7],[8] for limit of detection and limit of quantitation are produced in [Table 1] and [Table 2], respectively.
Table 1: Comparison of different guidelines for ''detection limit'' parameter of analytical method validation[1]

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Table 2: Comparison of different guidelines for 'quantitation limit' parameter of analytical method validation[1]

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   Detection and Quantitation Limits (LOD and LOQ) Top

There are several terms that have been used to define LOD and LOQ. In general, the LOD is taken as the lowest concentration of an analyte in a sample that can be detected, but not necessarily quantified, under the stated conditions of the test. The LOQ is the lowest concentration of an analyte in a sample that can be determined with acceptable precision and accuracy under the stated conditions of test. [9]

Although reagent package inserts may state that an assay has a dynamic range that extends from zero concentration to some upper limit, typically an assay is simply not capable of accurately measuring analyte concentrations down to zero. Sufficient analyte concentration must be present to produce an analytical signal that can reliably be distinguished from "analytical noise," the signal produced in the absence of analyte. [10]

However, some common methods [11] for the estimation of detection and quantitation limit are

  • Visual definition
  • Calculation from the signal-to-noise ratio (DL and QL correspond to 3 or 2 and 10 times the noise level, respectively)
  • Calculation from the standard deviation of the blank
  • Calculation from the calibration line at low concentrations


F: Factor of 3.3 and 10 for DL and QL, respectively

SD: Standard deviation of the blank, standard deviation of the ordinate intercept, or residual standard deviation of the linear regression

b: Slope of the regression line

The estimated limits should be verified by analyzing a suitable number of samples containing the analyte at the corresponding concentrations. The DL or QL and the procedure used for determination, as well as relevant chromatograms, should be reported.

Signal- to-noise

By using the signal-to-noise method, the peak-to-peak noise around the analyte retention time is measured, and subsequently, the concentration of the analyte that would yield a signal equal to certain value of noise to signal ratio is estimated. The noise magnitude can be measured either manually on the chromatogram printout or by auto-integrator of the instrument. A signal-to-noise ratio (S/N) of three is generally accepted for estimating LOD and signal-to-noise ratio of ten is used for estimating LOQ. This method is commonly applied to analytical methods that exhibit baseline noise. [11]

For chromatography a test sample with the analyte at the level at which detection is required or determined is chromatographed over a period of time equivalent to 20 times the peak width at half-height [Figure 1]. The signal-to-noise ratio is calculated from Equation (1).
Figure 1: Signal-to-noise examples of 10:1 (top) and 3:1 (bottom), using the method of the EP

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where H is the height of the peak, corresponding to the component concerned, in the chromatogram obtained with the prescribed reference solution, and measured from the maximum of the peak to the extrapolated baseline of the signal observed over a distance equal to 20 times the width at half-height h is the peak-to-peak background noise in a chromatogram obtained after injection or application of a blank, observed over a distance equal to 20 times the width at half-height of the peak in the chromatogram obtained.

This approach is specified in the European Pharmacopoeia. [5] It is important that the system is free from significant baseline drift and/or shifts during this determination.

[Figure 1] shows examples of S/N ratios of 10:1 and 3:1 which approximate the requirements for the QL and DL, respectively. This approach works only for peak height measurements.

Blank determination

It is assumed that they both have the same variance and are normally distributed. As the curves overlap there is a probability that we could conclude that we have detected the analyte when this is in fact due to the blank signal (false positive, α error or type 1 error). Alternatively, we can conclude that the analyte is not detected when it is in fact present (false negative, β error or type 2 error). When addressing the issue about when an analyte has been detected it is always a matter of risk. [11]

The blank determination is applied when the blank analysis gives results with a nonzero standard deviation. LOD is expressed as the analyte concentration corresponding to the sample blank value plus three standard deviation and LOQ is the analyte concentration corresponding to the sample blank value plus ten standard deviations as shown in the following equations:

LOD=Xb1 +3Sb1 ,

LOQ=Xb1 +10Sb1 ,

where Xb1 is the mean concentration of the blank and Sb1 is the standard deviation of the blank. This is a simple and quick method. The weakness is that there is no objective evidence to prove that a low concentration of analyte will indeed produce a signal distinguishable from a blank (zero concentration) sample. [9]

Linear regression

For a linear calibration curve, it is assumed that the instrument response y is linearly related to the standard concentration x for a limited range of concentration. [9] It can be expressed in a model such as


This model is used to compute the sensitivity b and the LOD and LOQ. Therefore, the LOD and LOQ can be expressed as

LOD=3S a/b,

LOQ=10S a/b,

where S a is the standard deviation of the response and b is the slope of the calibration curve. The standard deviation of the response can be estimated by the standard deviation of either y-residuals, or y-intercepts, of regression lines. This method can be applied in all cases, and it is most applicable when the analysis method does not involve background noise. It uses a range of low values close to zero for calibration curve, and with a more homogeneous distribution will result in a more relevant assessment.

Limit of blank

LoB as the highest apparent analyte concentration expected to be found when replicates of a sample containing no analyte are tested. Note that although the samples tested to define LoB are devoid of analyte, a blank (zero) sample can produce an analytical signal that might otherwise be consistent with a low concentration of analyte. LoB is estimated by measuring replicates of a blank sample and calculating the mean result and the standard deviation (SD). [2]

LoB=mean blank +1.645(SD blank )

After calculating this value LOD can be calculated according to LOD=LOB+1.645(SD low concentration sample ).

Precision-based approaches

The quantitation limit can also be obtained from precision studies. [10],[11] For this approach, decreasing analyte concentrations are analyzed repeatedly and the relative standard deviation is plotted against the corresponding concentration (precision function). If a predefined limit is exceeded (such as 10% or 20%), the corresponding concentration is established as the quantitation limit However, in practice, due to the high variability of standard deviations the true precision function is much more difficult to draw unless a large number of concentrations is included.

The QL can be specifically calculated [11] using the actual precision of the analytical procedure at this concentration. The calculation is based on the compatibility between analytical variability and specification acceptance limits. QL can be regarded as the maximum true impurity content of the manufactured batch, i.e., as the basic limit

AL Acceptance limit of the specification for the impurity.

s Precision standard deviation at QL, preferably under intermediate or reproducibility conditions. AL and s must have the same unit (e.g., percentage with respect to active, mg, mg/ml, etc.).

Nassay Number of repeated, independent determinations in routine analyses, as far as the mean is the reportable result, i.e., is compared with the acceptance limits. If each individual determination is defined as the reportable result, n=1 has to be used.

tdf Student t-factor for the degrees of freedom during determination of the precision, usually at 95% level of statistical confidence.

   Conclusion Top

In this review, the authors have tried to give information to the researchers engaged in establishing analytical profiles of the drug substances or products. Data are adequate and sufficient to meet the laboratory's method requirements. The laboratory must be able to match the performance data as described in the standard and to establish these parameters a manufacturer would test a large number of sample replicates to increase the robustness and the statistical confidence of the estimate. Comparison of all of the validation parameters in different regulatory agencies is summarized by Chandran and Singh [1] and is a better option for curious readers.

   References Top

1.Chandran S, Singh RS. Comparison of various international guidelines for analytical method validation. Pharmazie 2007;62:4-14.   Back to cited text no. 1
2.David A, Armbruster TP. Limit of Blank, Limit of Detection and Limit of Quantitation. Clin Biochem Rev 2008;29:S49-52.   Back to cited text no. 2
3.Sanagi MM, Ling SL, Nasir Z, Hermawan D, Ibrahim WA, Abu Naim A. Comparison of Signal-to-noise, Blank Determination, and Linear Regression Methods for the Estimation of Detection and Quantification Limits for Volatile Organic Compounds by Gas Chromatography. J AOAC Int 2009;92:1833-8.  Back to cited text no. 3
4.Putheti RR, Okigbo RN, Patil SC, Advanapu MS, Leburu R. Method Development and Validations: Characterization of Critical Elements in the Development of Pharmaceuticals. Int J Health Res 2008;1:5-14.   Back to cited text no. 4
5.European Pharmacopoeia. European Directorate for the Quality of Medicines. Strasbourg; 2007.  Back to cited text no. 5
6.Ermer J, Miller JH, McB. Method Validation in Pharmaceutical Analysis. KGaA, Weinheim: Wiley-Vch Verlag GmbH and Co.; 2005.   Back to cited text no. 6
7.United States Pharmacopeia. Validation of compendial methods, Twenty-Sixth Revision, National Formulary, 21 st ed. Rockville, MD: The United States Pharmacopeial Convention Inc.; 2003.  Back to cited text no. 7
8.AOAC International. Method Validation Programs. Peer Verified Programs. Gaithersburg, Maryland, USA; 2002  Back to cited text no. 8
9.Analytical Procedures and Methods Validation: Chemistry, Manufacturing, and Controls, Federal Register (Notices). 2000;65:776-7.   Back to cited text no. 9
10.Thompson M, Ellison SL, Wood R. Harmonized guidelines for single laboratory Validation of methods of Analysis. Pure Appl Chem 2002;74:835-55.  Back to cited text no. 10
11.International Conference on Harmonization (ICH) of Technical Requirements for the Registration of Pharmaceuticals for Human Use, Validation of analytical procedures: Text and Methodology. ICH-Q2B, Geneva; 1996.  Back to cited text no. 11


  [Figure 1]

  [Table 1], [Table 2]

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56 Analysis of Ni, Cr, Cu, Pb and Cd in marine bioindicators using mixed-micelles with microwave assisted micellar extraction and GF-AAS
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58 Aggregation-Induced Emission and Sensing Characteristics of Triarylborane-Oligothiophene-Dicyanovinyl Triads
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59 Cloud point extraction and diffuse reflectance-Fourier transform infrared spectroscopic determination of chromium(VI): a probe to adulteration in food stuffs
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60 Electrochemical impedance spectroscopy study of Concanavalin A binding to self-assembled monolayers of mannosides on gold wire electrodes
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61 Label-free quantitative detection of nucleic acids based on surface-immobilized DNA intercalators
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62 Electrochemical biosensors for rapid detection of Escherichia coli O157:H7
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63 Invalidation of the Intracavity Optogalvanic Method for Radiocarbon Detection
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64 Multiple biomarkers biosensor with just-in-time functionalization: Application to prostate cancer detection
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65 Optimization of a QuEChERS based method by means of central composite design for pesticide multiresidue determination in orange juice by UHPLC–MS/MS
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66 Occurrence and factors associated with the presence of aflatoxin M1 in breast milk samples of nursing mothers in central Mexico
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67 A screening method of oil-soluble synthetic dyes in chilli products based on multi-wavelength chromatographic fingerprints comparison
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68 Biomimetic potentiometric sensor for chlorogenic acid based on electrosynthesized polypyrrole
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69 A simple and accurate protocol for absolute polar metabolite quantification in cell cultures using q-NMR
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70 Development and Application of a Next Generation Air Sensor Network for the Hong Kong Marathon 2015 Air Quality Monitoring
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71 Pharmacokinetics of meloxicam in adult goats: a comparative study of subcutaneous, oral and intravenous administration
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72 Ionic liquid-based zinc oxide nanofluid for vortex assisted liquid liquid microextraction of inorganic mercury in environmental waters prior to cold vapor atomic fluorescence spectroscopic detection
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73 Attomole quantification and global profile of RNA modifications: Epitranscriptome of human neural stem cells
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74 Development of new UV–vis spectroscopic microwave-assisted method for determination of glucose in pharmaceutical samples
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75 An experimental design approach to optimize an amperometric immunoassay on a screen printed electrode for Clostridium tetani antibody determination
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76 Evaluation of extraction methods for ochratoxin A detection in cocoa beans employing HPLC
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77 Benchtop NMR spectrometers in academic teaching
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78 Comparison of a triple-quadrupole and a quadrupole time-of-flight mass analyzer to quantify 16 opioids in human plasma
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79 High-throughput determination of dissolved free amino acids in unconcentrated freshwater by ion-pairing liquid chromatography and mass spectrometry
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80 Development of a rotary disc voltammetric sensor system for semi-continuous and on-site measurements of Pb(II)
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81 Meat species identification using DNA-redox electrostatic interactions and non-specific adsorption on graphene biochips
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82 Determination of major sodium iodide symporter (NIS) inhibitors in drinking waters using ion chromatography with conductivity detector
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83 Capillary-driven microfluidic paper-based analytical devices for lab on a chip screening of explosive residues in soil
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84 Digestion Procedures for the Elemental Analysis of Wood by Inductively Coupled Plasma–Optical Emission Spectrometry
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85 A highly selective, sensitive and reversible fluorescence chemosensor for Zn2+and its cell viability
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86 Comparative phenolic compound profiles and antioxidative activity of the fruit, leaves, and roots of Korean ginseng (Panax ginseng Meyer) according to cultivation years
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87 High-performance liquid chromatography as a technique to determine protein adsorption onto hydrophilic/hydrophobic surfaces
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88 An improved HPLC method for single-run analysis of the spectrum of hop bittering compounds usually encountered in beers
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89 Determination of 3,4-methylenedioxypyrovalerone (MDPV) in oral and nasal fluids by ion mobility spectrometry
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90 New1H NMR-Based Technique To Determine Epoxide Concentrations in Oxidized Oil
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91 Comparative pharmacokinetics of enrofloxacin, danofloxacin and marbofloxacin following intramuscular administration in sheep
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92 Azo dye functionalized graphene nanoplatelets for selective detection of bisphenol A and hydrogen peroxide
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93 Improved quantitative analysis of molecular constituents of wastewater sludge pellets using double-shot thermochemolysis-GCMS
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94 A New Approach for Quantitative Determination of ?-Cyclodextrin in Aqueous Solutions: Application in Aggregate Determinations and Solubility in Hydrocortisone/?-Cyclodextrin Inclusion Complex
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95 Biological imaging without autofluorescence in the second near-infrared region
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96 A candidate reference method using ICP-MS for sweat chloride quantification
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97 Advances in liquid chromatography–high-resolution mass spectrometry for quantitative and qualitative environmental analysis
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98 Comparison between Folin-Ciocalteu and Prussian Blue Assays to Estimate The Total Phenolic Content of Juices and Teas Using 96-Well Microplates
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99 Volatile organic compounds generated by cultures of bacteria and viruses associated with respiratory infections
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100 2-Acetyl-1-Pyrroline Augmentation in Scented indica Rice (Oryza sativa L.) Varieties Through ?1-Pyrroline-5-Carboxylate Synthetase (P5CS) Gene Transformation
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101 Simultaneous quantification of labeled 2H5-glycerol, 13C6-glucose, and endogenous D-glucose in mouse plasma using liquid chromatography tandem mass spectrometry
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102 A novel method for quantification of human hemoglobin from dried blood spots by use of tandem mass spectrometry
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103 Reduced Graphene Oxide-Poly(3,4-ethylenedioxythiophene) Polystyrenesulfonate Based Dual-Selective Sensor for Iron in Different Oxidation States
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104 Discrimination of geographical origin of rice (Oryza sativa L.) by multielement analysis using inductively coupled plasma atomic emission spectroscopy and multivariate analysis
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105 Enhancement of performance in porous bead-based microchip sensors: effects of chip geometry on bio-agent capture
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106 HPLC method for urinary theobromine determination: Effect of consumption of cocoa products on theobromine urinary excretion in children
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107 Extraction-spectrophotometric and theoretical (Hartree-Fock) investigations of a ternary complex of iron(II) with 4-nitrocatechol and 2,3,5-triphenyl-2H-tetrazolium
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108 Extractive spectrophotometric determination of five selected drugs by ion-pair complex formation with bromothymol blue in pure form and pharmaceutical preparations
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109 Carboxylated, Fe-Filled Multiwalled Carbon Nanotubes as Versatile Catalysts for O2Reduction and H2Evolution Reactions at Physiological pH
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110 The simultaneous detection and quantification of p-aminobenzoic acid and its phase 2 biotransformation metabolites in human urine using LC–MS/MS
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111 Reduced graphene oxide decorated with tin nanoparticles through electrodeposition for simultaneous determination of trace heavy metals
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112 Sol-Gel Deposition of Iridium Oxide for Biomedical Micro-Devices
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114 Development of a Method for the Quantitation of Three Thiols in Beer, Hop, and Wort Samples by Stir Bar Sorptive Extraction within SituDerivatization and Thermal Desorption–Gas Chromatography–Tandem Mass Spectrometry
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115 Microsphere integrated microfluidic disk: synergy of two techniques for rapid and ultrasensitive dengue detection
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116 NORM in the East Midlandsæ oil and gas producing region of the UK
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117 Evaluation of in-vitro degradation rate of hyaluronic acid-based hydrogel cross-linked with 1, 4-butanediol diglycidyl ether (BDDE) using RP-HPLC and UV–Vis spectroscopy
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118 Growth of healthy and sanitizer-injured Salmonella cells on mung bean sprouts in different commercial enrichment broths
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119 Assessment of tandem mass spectrometry and high-resolution mass spectrometry for the analysis of bupivacaine in plasma
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120 Fast, sensitive and selective colorimetric gold bioassay for dopamine detection
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121 Characteristic investigation of scanning surface plasmon microscopy for nucleotide functionalized nanoarray
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122 ZnO oxide films for ultrasensitive, rapid, and label-free detection of neopterin by surface-enhanced Raman spectroscopy
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124 Changes in the contents and profiles of selected phenolics, soyasapogenols, tocopherols, and amino acids during soybean–rice mixture cooking: Electric rice cooker vs electric pressure rice cooker
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125 Development of a mobile tracer correlation method for assessment of air emissions from landfills and other area sources
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126 Determination of total mercury in fish and sea products by direct thermal decomposition atomic absorption spectrometry
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127 Simultaneous determination of some common food dyes in commercial products by digital image analysis
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128 Determination of environmental safety level with laser-induced breakdown spectroscopy technique
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129 Aging effect and antibody immobilization on COOH exposed surfaces designed for dengue virus detection
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130 Development of a novel and efficient H2O2sensor by simple modification of a screen printed Au electrode with Ru nanoparticle loaded functionalized mesoporous SBA15
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131 Label-free detection of small-molecule binding to a GPCR in the membrane environment
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132 Evaluation of Ultrahigh-Performance Supercritical Fluid Chromatography–Mass Spectrometry as an Alternative Approach for the Analysis of Fatty Acid Methyl Esters in Aviation Turbine Fuel
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133 Epicocconone, a sensitive and specific fluorescent dye for in situ quantification of extracellular proteins within bacterial biofilms
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134 Surface enhanced Raman scattering-active worm-like Ag clusters for sensitive and selective detection of dopamine
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135 Long Range and Long Duration Underwater Localization Using Molecular Messaging
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136 Determination of heavy metals in marine sediments using MAME-GFAAS
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137 Analysis and optimization of a hydrogel matrix for the development of a sandwich-type glucose biosensor
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138 Role of the anionic dopant of poly(3,4-ethylenedioxythiophene) for the electroanalytical performance: electrooxidation of acetaminophen
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139 Polymethacrylate coated electrospun PHB Fibers: An exquisite outlook for fabrication of paper-based Biosensors
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140 A novel approach for application of nylon membranes in the biosensing domain
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141 A carbon nanofiber-based label free immunosensor for high sensitive detection of recombinant bovine somatotropin
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142 Solid lipid nanoparticles loaded with lipoyl–memantine codrug: Preparation and characterization
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143 Scavenging properties of neutrophil 4-hydroxyphenylpyruvate dioxygenase are based on a hypothesis that does not stand up to scrutiny
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145 A novel ion-exclusion chromatography–mass spectrometry method to measure concentrations and cycling rates of carbohydrates and amino sugars in freshwaters
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146 Label-free detection of lysozyme in wines using an aptamer based biosensor and SPR detection
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