Prediction of precision from signal and noise measurement in liquid chromatography: Limit of detection

Determination of the Signal-To-Noise Ratio Enhancement in Comprehensive Three-Dimensional Gas Chromatography

We investigate the extent to which comprehensive three-dimensional gas chromatography (GC³) provides a signal enhancement (SE) and a signal-to-noise ratio enhancement (S/N_Rel) relative to one-dimensional (1D)-GC. Specifically, the SE is defined as the ratio of the tallest ³D peak height from the GC³ separation to the 1D peak height from the unmodulated 1D-GC separation. A model is proposed which allows the analyst to predict the theoretically attainable SE (SE_T) based upon the peak width and sampling density inputs. The model is validated via comparison of the SE_T to the experimentally measured SE (SE_M) obtained using total-transfer GC³ (100% duty cycle for both modulators) with time-of-flight mass spectrometry detection. Two experimental conditions were studied using the same GC³ column set, differing principally in the modulation period from the ¹D to ²D columns: 4 s versus 8 s. Under the first set of conditions, the average SE_M was 97 (±22), in excellent agreement with the SE_T of 97 (±18). The second set of conditions improved the average SE_M to 181 (±27), also in agreement with the average SE_T of 176 (±26). The average S/N_Rel following correction for the mass spectrum acquisition frequency was 38.8 (±11.2) and 59.0 (±27.2) for the two sets of conditions. The enhancement in S/N is largely attributed to moving the signal to a higher frequency domain where the impact of "low frequency" noise is less detrimental. The findings here provide strong evidence that GC³ separations can provide enhanced detectability relative to 1D-GC and comprehensive two-dimensional gas chromatography (GC×GC) separations.

An automated system for predicting detection limit and precision profile from a chromatogram

This paper presents a basic model of an automated system for predicting the detection limit and precision profile (plot of relative standard deviation (RSD) of measurements against concentration) in chromatography. The fundamental assumption is that the major source of response errors at low sample concentrations is background noise and at high concentrations, it is the volumes injected into an HPLC system by a sample injector. The noise is approximated by the mixed random processes of the first order autoregressive process AR(1) and white noise. The research procedures are: (1) the description of the standard deviation (SD) of measurements in terms of the parameters of the mixed random processes; (2) the algorithm for the parameter estimation of the mixed processes from actual background noise; (3) the mathematical distinction between noise and signal in a chromatogram. When compounds are chromatographically separated, each obtained signal is given the detection limit and precision profile on laboratory-made software. A file of a chromatogram is the only requirement for the theoretical prediction of measurement uncertainty and therefore the repeated measurements of real samples can be dispensed with. The theoretically predicted RSDs are verified by comparing them with the statistical RSDs obtained by repeated measurements. Signal shapes on noise are illustrated at the detection limit and quantitation limit, the signal-to-noise ratios of which are close to the widely adopted values, 3 and 10, respectively.

Theoretical analysis of a magnetophoresis-diffusion T-sensor immunoassay

We present the analytical investigation of a microfluidic homogeneous competitive immunoassay that incorporates antibody-conjugated superparamagnetic nanoparticles and magnetophoretic transport to enhance the limits of detection and dynamic range. The analytical model considers the advective, diffusive, and magnetophoretic transport of the antibody-coated nanoparticles relative to the labeled and sample antigens of interest in a T-sensor configuration. The magnetophoresis-diffusion immunoassay identified clear improvements to the assay response and reductions to the limit of detection for increased magnetophoretic velocities and larger nanoparticles. The externally applied magnetophoretic transport enriched the antibody-antigen accumulation region, while larger nanoparticles led to decreased diffusive peak broadening. The integration of nanoparticles to the diffusion immunoassay (NP-DIA) demonstrated an approximately 3-fold improvement to the limit of detection of the basic antibody/antigen system, while the integration of superparamagnetic nanoparticles and magnetophoretic transport (MIA) established an order of magnitude improvement in sensitivity as well as means to greatly reduce response time. The implementation of an external magnetic force enabled the detectable antigen size spectrum to extend from small molecules i.e., 10's Da to 100's Da, up to large proteins and macromolecules, i.e., 50 kDa to 150 kDa, for a single class of binding species, i.e., superparamagnetic nanoparticle. This investigation provides guidelines for the design and development of a magnetophoresis-diffusion T-sensor immunoassay, and clearly identifies the regimes for optimal operation.

Uncertainty estimates of purity measurements based on current information: toward a "live validation" of purity methods

Purpose

To predict precision and other performance characteristics of chromatographic purity methods, which represent the most widely used form of analysis in the biopharmaceutical industry.

Methods

We have conducted a comprehensive survey of purity methods, and show that all performance characteristics fall within narrow measurement ranges. This observation was used to develop a model called Uncertainty Based on Current Information (UBCI), which expresses these performance characteristics as a function of the signal and noise levels, hardware specifications, and software settings.

Results

We applied the UCBI model to assess the uncertainty of purity measurements, and compared the results to those from conventional qualification. We demonstrated that the UBCI model is suitable to dynamically assess method performance characteristics, based on information extracted from individual chromatograms.

Conclusions

The model provides an opportunity for streamlining qualification and validation studies by implementing a “live validation” of test results utilizing UBCI as a concurrent assessment of measurement uncertainty. Therefore, UBCI can potentially mitigate the challenges associated with laborious conventional method validation and facilitates the introduction of more advanced analytical technologies during the method lifecycle.

Electronic supplementary material

The online version of this article (doi:10.1007/s11095-012-0836-z) contains supplementary material, which is available to authorized users.

Biogenic amines and their metabolites in mouse brain tissue: development, optimization and validation of an analytical HPLC method

A simple and fast HPLC method based on an isocratic, reversed-phased ion-pair with amperometric end-point detection for simultaneous measurement of noradrenergic (MHPG/NA and A), dopaminergic (DOPAC, HVA/DA) and serotonergic (5-HIAA/5-HT) compounds in mouse brain tissue was developed. In order to improve the chromatographic resolution (Rs) with an acceptable total analysis time, experimental designs for multivariate optimization of the experimental conditions were applied. The optimal conditions for the separation of the eight neurotransmitters and metabolites, as well as two internal standards, i.e., DHBA and 5-HMT, were obtained using a mixture of methanol-phosphate-citric buffer (pH 3.2, 50 mM) (9:91, v/v) containing 2 mM OSA as mobile phase at 32°C on a microbore ALF-115 column (150 mm × 1.0 mm, 3 μm particle size) filled with porous C(18) silica stationary phase. In this study, a two-level fractional factorial experimental design (½ 2(K)) was employed to optimize the separation and capacity factor (k') of each molecule, leading to a good separation of all biogenic amines and their metabolites in brain tissue. A simple method for the preparation of different bio-analytical samples in phosphate-citric buffer was also developed. Results show that all molecules of interest were stabilized for at least 24 h in the matrix conditions without any antioxidants. The method was fully validated according to the requirements of SFSTP (Société Française des Sciences et Techniques Pharmaceutiques). The acceptance limits were set at ±15% of the nominal concentration. The method was found accurate over a concentration range of 4-2000 ng/ml for MHPG, 1-450 ng/ml for NA, 1-700 ng/ml for A, 1-300 ng/ml for DOPAC, 1-300 ng/ml for 5-HIAA, 1-700 ng/ml for DA, 4-2800 ng/ml for HVA and 1-350 ng/ml for 5-HT. The assay limits of detection for MHPG, NA, A, DOPAC, 5-HIAA, DA, HVA and 5-HT were 2.6, 2.8, 4.1, 0.7, 0.6, 0.8, 4.2 and 1.4 pg, respectively. It was found that the mean inter- and intra-assay relative standard deviations (RSDs) over the range of standard curve were less than 3%, the absolute and the relative recoveries were around 100%, demonstrating the high precision and accuracy, and reliability of the analytical method described to apply in routine analysis of biogenic amines and their metabolites in brain tissue.

Detection limit of measurement of pharmaceuticals labeled with short-lived isotopes in HPLC with flow-through gamma-counter

This paper proposes a method for estimating the detection limit, which is defined as 3.3 times the standard deviation (S.D.) of blank measurements under the situations where the repetition of measurement is difficult or impossible because of a short half-life of radioactivity. The FUMI theory, which can estimate an S.D. value without repetition in various instrumental analyses, is adopted and proved here to be available in a radio-HPLC system as well. (99m)Tc-ECD (T(1/2)=360.6 min) that is a lipophilic compound for the diagnosis of regional brain perfusion is taken as an example.

Measurement of uncertainty and discrimination limit in purity tests of drug quality

Because of baseline fluctuation in an instrumental analysis, a purity test can overlook an illegitimate drug which contains an undesirable substance in more amount than a prescribed reference value. This paper proposes a probability theory to predict the lowest (average) signal, E[Y2], of the substance which can be discriminated from the (average) reference signal, E[Y1], with a high probability (here, 95%) in liquid chromatography (LC). The difference between the lowest signal and reference signal, E[Y2]-E[Y1] (> 0), is referred to here as a discrimination limit. The repetition of experiments to estimate the standard deviation of measurements is unnecessary for the probability theory, but a mathematical treatment of instrumental baselines (Fourier transform, etc.) is essential. The Monte Carlo simulation is carried out in which the reference signal and predicted signal for the discrimination limit are overlaid randomly 5000 times on real LC baselines. The result is satisfactory: the observed probability for the right answer is 94.3 or 94.8%; the theoretical one is 95%. The normality of the measurement distribution is examined for LC and capillary electrophoresis to verify the fundamental assumption of the proposed theory.