Intelligent peak deconvolution through in-depth study of the data matrix from liquid chromatography coupled with a photo-diode array detector applied to pharmaceutical analysis
Introduction
Pharmaceutical components and the mixtures of related impurities exhibit huge diversity and complexity, and highly efficient separation methods are required to accomplish precise and accurate quantification of their components for pharmaceutical development. Recent advances in high-speed and efficient separations, such as the use of ultra-high pressure liquid chromatography (UHPLC) [1], have considerably increased the peak capacities per unit-time of HPLC separations as compared to more conventional HPLC methods. However, the use of high-end UHPLC systems introduce several trade-offs that should be considered, especially in that the desired separation condition is often obtained at the cost of decreased instrument robustness, which impacts maintenance intervals and may negate the financial benefit of using UHPLC. As an alternative, monolithic silica columns [2] have been employed in pharmaceutical development [3] and other related research areas [4] and are known to provide highly-efficient separations in a long column format, primarily due to their high permeability, allowing them to compensate for some of the disadvantages of UHPLC by achieving incredibly high-resolution separations with shallow gradients. [5] However, separations of this nature require long-analysis times, on the order of 10 h or more, to maximize the efficiency of monolithic silica materials. The time-consuming nature has led to general rejection of monolithic silica separations for routine application in pharmaceutical development applications.
To further address the issue of obtaining fast separations that efficiently resolve components from one another, several researchers have developed approaches that combine actual chromatographic separations by (U)HPLC, chemometrics, and a mathematical understanding of the three dimensional data matrix of photodiode array (PDA) detectors that are conventionally used in pharmaceutical research. [6], [7], [8], [9], [10], [11], [12] In these approaches, the use of multivariate curve resolution-alternating least squares (MCR-ALS) methods has significantly increased. [13] MCR-ALS has been applied to measure drug concentrations in human serum with acceptable resolution and quantification results in the presence of overlapped profiles, while keeping experimental time and extraction steps to a minimum. [14] In another example, it has been successfully applied to the determination of estrogens in water samples without the need for sample extraction and clean up steps to remove potential matrix interferences that could co-elute with the compounds of interest. [15] Additionally, it is still of great interest to apply chemometric approaches to chromatographic separations in the pharmaceutical development field. In this publication, we discuss the feasibility of applying a newly developed algorithm that uses expectation maximization (EM) estimates to achieve mathematical resolution of overlapped chromatographic peaks and makes it possible to obtain good separation results due to a Bidirectional Exponentially Modified Gaussian (BEMG) model function that constrains the chromatographic profile. Several pharmaceutical applications that simulate the performance of the deconvolution algorithm are shown, and the optimal usage is discussed.
Section snippets
Peak deconvolution using spectra in HPLC-PDA data
HPLC-PDA measurement signal D can be modeled as a direct product (outer product) of vector S, from a substance's characteristic absorption spectrum, and vector C, from its chromatogram. For example, if the measurement signal comprises m elements, D can be expressed by the following equation.
Determining C and S vectors that satisfy this relationship has served as the basis for peak deconvolution using spectra, with MCR-ALS and other techniques having been proposed for doing
Quantitation of a two-component model mixture
The spectra obtained from analysis of data acquired for DFBP and VP standard samples with relative concentration 100 are shown in Fig. 2. A similarity of 0.8286 (DFBP/VP) was obtained between spectra for the wavelength range from 200 to 340 nm and a resolution Rs of 0.8 was obtained between peaks.
Fig. 3 shows the chromatograms at a wavelength of 210 nm (dashed curves) in data acquired for five samples containing both DFBP and VP in the relative concentration ratios 100/1, 100/10, 100/50, 100/100,
Conclusion
An algorithm was developed for using differences in chromatogram and spectra shape to separate co-eluting peaks in data obtained from an HPLC-PDA system. The algorithm uses a BEMG model function to estimate the chromatogram for respective components and then separates the data by MCR-ALS based on a maximum likelihood criterion that minimizes the squared errors between the direct product of the chromatogram and spectrum vectors and the measurement signal using an EM algorithm.
The algorithm
Acknowledgements
We thank Naoki Asakawa for kind suggestions during this study.
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