Limit of detection and limit of determination are often used as quality criteria for analytical methods. The values are calculated from S/N-ratios or calibration functions and are not obtained in real samples. Therefore they are not useful as criteria in routine analysis. Calculations from standard addition can be a helpful tool.

The limits obtained in real samples by standard addition can serve as testing values for analytical results more than as quality criteria of methods.

Introduction

To evaluate and to describe the quality of an analytical method the limit of detection (LOD) and limit of determination (LOQ) are used frequently.
In literature various possibilities are published on how to estimate the LOD and LOQ [1]. However, these estimations are often carried out in standard samples i.e. not in a real matrix, since a real matrix can hardly be simulated in trace analysis. In literature as well as in regulations of standardization organizations real matrices are recommended. However, some matrices such as cell culture supernatants are easily obtained [2, 3]. The overall questions of the analysts concerning the LOD/LOQ as quality criteria are:
1. Can the LOD/LOQ, which is estimated without matrix, be used as a quality criterion in routine analysis with samples of different matrices?
2. Can e.g. an over-all LOD/LOQ for a given matrix be calculated from standard addition experiments?
3. What are the differences between the LOD/LOQ estimated from the calibration function in matrix-free and real samples (obtained by i. e. standard addition)?

This article tries to show these limitations and the dilemma of the LOD and LOQ in routine and research analysis. The estimation model and the type of matrix used for the different analytes in this article are

• calibration function (Eq. (9) and (19) according to [1]) without matrix for metals, heavy metals and prostaglandins
• calibration function (Eq. (9) and (19) according to [1]) in matrix with and without internal standard for prostaglandins
• signal/noise-ratio (LOD = 3 S/N, LOQ = 10 S/N) in matrix for prostaglandins
• standard addition in real samples (with matrix) for metals, heavy metals [4]

Experimental

The water analysis of elements, in all real (with matrix) and calibration (without matrix) samples, was carried out after digestion in a microwave oven (CEM Mars Express) [5] of the filtered (ground water unfiltered) sample with AAS (PE Analyst 600) and ICP OES (PE Optima 4300), according to the German Standard Methods for Water Analysis [6-9].

For the determination of trace elements in river sediments with AAS and ICP-OES, increasing amounts of a certified river sediment (NIST Buffalo River Sediment 8704) were digested in a microwave oven with 5 mL HCl, 3 mL HNO3, and 0.5 mL HF (all acids suprapur) for 250 mg sediment and were also analyzed with AAS and ICP-OES.
Standard addition experiments were done after spiking the digested real sample (matrices: surface water, ground water, waste water, and sediment) with four increasing concentrations.
The estimation of the LOD and LOQ from the calibration function using spiked matrix was carried out for the determination of prostaglandins in cell culture supernatant (hMSC-TERT + IN), which were spiked with the analytes using capillary liquid chromatography - tandem mass spectrometry (LC-MS/MS), after on-line sample preparation according to [2,3].
Absorbance or peak area and mass concentration were used to calculate the LOD and LOQ with the calibration function model, using the calculation program SQS 2000 (Lerhardt, 1998/2001) with a confidence interval of 95%, which is based on the German standard [10], identical with eq. 9 and 19 in [1]. Matrix-free, standard addition and spiked matrix samples were used.
Also the LOD and LOQ were calculated from the signal/noise ratios in spiked matrix which were multiplied with the factor 3 and 10 respectively [2, 3].

Conclusions

Because of limited space the data from over 600 experiments can not be presented. Interested readers can contact the authors for details. First it should be pointed out that an analytical value is always only statistically certain if it is higher than the LOQ (x > LOQ) [4]. As results of the experiments it could be stated that

• there are by no means unique LODs and LOQs obtained by standard addition for a given analyte even in a single matrix
• the LODs/LOQs obtained by standard addition depend strongly on the concentration of the analyte in the real sample
• in most cases the LODs/LOQs obtained by standard addition are higher than the LODs/LOQs obtained through the calibration function (matrix-free) due to the higher Student-t-factor resulting from lesser than 10 calibration points.
• the standard addition had to be carried out very carefully depending on the concentration of the analyte in the real sample and is therefore not suitable for multi-component-methods such as HPLC, GC, ICP-OES, and ICP-MS
• standard addition is time consuming, if not automated (like it is possible with AAS-measurements) [11]
• no matrix-dependences can be calculated out of the concentration-dependences of the LODs/LOQs obtained by standard addition
• if a blank matrix is available, standard addition can be used as calibration to estimate the LODs/LOQs

This leads to the statement that the answer to the questions 1-2 is no! The LODs/LOQs from standard addition experiments are higher than from calibration functions in matrix-free samples but depend in contrary strongly from the concentration of the analyte (question 3).