Chemometric Studies On Multiway Calibration Algorithm And Figures Of Merit

With the emergence of new high-order analytical instruments and the automatization of data collection,it is easy to obtain multiway data arrays consisting of hundreds and thousands data points(such as three-way data array,four-way data array,five-way data array).With these multiway data arrays,multiway calibration methods based on multilinear models can provide one with some advantages,such as(1)quantifing analyte(s)of interest even in the presence of unknown interference,that is the so-called "second-order advantage",(2)improved sensitivity devrived from the redundant data,and(3)increased selectivity due to an additional degree of partial selectivity by a new data mode.A series of multiway calibration methodologies have been developed to solve some difficulties which can't be tacked by traditional methods.Based on the trend of multiway calibration in chemometrics,the research works in this thesis focus on algorithms in multiway calibration,figures of merits and the application of multiway calibration in complex biological matrix,mainly including the following aspects:Part ?:Study on quadrilinear decomposition algorithm to the four-way calibration method(Chapter 2)Four-way calibration methods based on the quadrilinear component model are gaining more and more attentions after three-way calibration methods.In Chapter 2,the slicing matrix in three-way data arrays is extended to the four-way scenario and a novel quadrilinear decomposition algorithm of the quadrilinear component model is proposed,i.e.,slicing alternating quadrilinear decomposition(SAQLD).The algorithm deals with the four-way data array in slicing boxes not in fully or pseudo fully stretched matrices.Operation of extracting diagonal elements is adopted,which makes SAQLD focus on extracting the quadrilinear parts in data,leading to a significant decrease in the loss function and finally a high-performance computing strategy for SAQLD,i.e.,fast convergence.Besides,SAQLD has the capability of tolerating the excessive components,since it utilizes the Moore-Penrose generalized inverse based on the thin SVD algorithm.It means that SAQLD can provide a accurate quadrilinear decomposition only if the selected number of underlying factors is no less than the actual one.Actually,the proposed algorithm SAQLD can be considered as a generalization of the alternating trilinear decomposition(ATLD)to four-way case.Experimental measurements involving the excitation-emission-solvent-sample four-way data array demonstrate that third-order calibration method based on the SAQLD algorithm allows one to obtain quantitative information regarding known constituents present in samples without worrying about other interferents.Additionally,a theoretical extension of the proposed algorithm to the multilinear component model,i.e.,slicing alterntating multilinear decomposition(SAMLD),is developed for multiway calibration.Part ?:Studies on multiway figures of merit(Chapter 3,Chapter 4 and Chapter 5)The Sensitivity occupies one of the prominent places among figures of merit.The situation regarding the definition of sensitivity in multiway cases becomes more complex than in univariate and multivariate cases.In Chapter 3,three-way calibration based on ATLD algorithm and four-way calibrations based on AQLD and SAQLD algorithms are investigated carefully by the uncertainty propagation.Assumed that calibration concentratin and signals are precise,the main source of uncertainty in the predicted concentration is the one stemming from the test sample signals,and the ratio of these uncertainties is a good measure of the sensitivity.In the uncertainty strategy,ATLD,AQLD and SAQLD sensitivities are shown to be accounted by the computation of the Jacobian matrix associated to the fitted parameters.It is found by simulation data that sensitivities regarding ATLD,AQLD and SAQLD algorithms in multiway calibrations are independed on wherther other components in the system being studied are calibrated.Besides,the comparision among different algorithms in multway calibrations show that sensitivity is heavily related to the algorithm being exploited in the identical calibration situation,and unfolding in data processing(such as vectorization,fully stretched matrix and pseudo-fully stretched matrix)can obtain a higher sensitivity.Standard error of prediction concentration is a parameter to describe the disperse degree of predicted concentration.In Chapter 4,standard error of prediction concentration in multiway calibration is estimated by an uncertainty propagation equation,which takes proper account of errors in calibration concentrations and also in measured analytical signals from both calibration and unknown samples.Assumed that calibration signals and prediction signals are errorless,the uncertainty of predicted concentration stemming from the uncertainty of calibration concentration can be derived.Similarly,the uncertainty of predicted concentration stemming from the uncertainties of calibration signals and prediction signals can be obtained.By the derived uncertainty progation equations,standard error of prediction concentration in multiway calibrations based on ATLD,AQLD and SAQLD algorithms can be estimated.Full Monte Carlo simulations performed by adding random noise to both concentrations and signals(calibration and unknown)in several theoretical binary and ternary mixtures are in good aggrement with the proposed approach.Besides,it is found that concentrations of other components in the unknown sample have no effect on the standard error of prediction concentration in multiway calibrations,which is contrary to multivariate calibration.In multivariate calibration,the standard error of prediction concentration is heavily depended on concentrations of other components.Hence,an additional advantage is founded in multiway calibration,i.e.,the standard error of prediction concentration is little influenced by contents of other components in the unknown sample.In practical application,ATLD can provide the proper trilinear decomposition with an overestimated number of components,and the excess component is decomposed as a random noise component.According to the uncertainty principle,more fitting parameters in the process of fitting will lead to a higher uncertainty.Then,the excess components may give rise to a higher standard error of prediction concentration due to a higher uncertainty when an overestimated number of components is choosed for ATLD.In Chapter 5,the influence of the excess components on the standard error of prediction concentration is investigated carefully by extensive Monte Carlo noise addition simulations.The homoscedastic and heteroscedastic errors in sample signals are considered since the heteroscedastic error in instrumental data is common in chemical measurements.An experimental example involving the determination of Pefloxacin(PEF)and Ofloxacin(OFL)in human urine using excitation-emission matrix(EEM)fluorescence in combination with second-order calibration method is described in detail.The results show that the excess components have no significant effect on the standard error of prediction concentration in the experimental case as well as the simulation case.In multiway calibration,there are two strategies to achieve "second-order advantage" in the case of multiple unknown samples,i.e.,calibration samples are simultaneously modeled with multiple unknown samples,and calibration samples are individually modeled with one unknown sample.The comparision between these two strategies shows no significant difference regarding the standard error of prediction concentration in experimental example.It can provide some theoretical basis for multiple unknown samples being simultaneously modeled in multiway calibration.Part III:Simultaneous quantitative analysis of tyrosine and levodopa in human plasma using four-way calibration method(Chapter 6)Parkinson's disease is a progressive motor disease marked by selective degeneration of dopaminergic neurons of the substantia nigra and formation of fibrillary cytoplasmic inclusions.Tyrosine(Tyr)and levodopa(Lev)are served as key substances in the dopamine biosynthetic pathway,and simultaneous determination of Tyr and Lev in human plasma is of great importance for the treatment and study of the mechanism of Parkinson's disease.In chapter 6,an enzyme-induced excitation-emission-kinetic third-order calibration method for the simultaneous determination of two target analytes Tyr and Lev in human plasma is presented.Polyphenol oxidase is used as a catalyst for the oxidation reactions of Tyr and Lev,and the enzyme-induced kinetic processes are monitered spectrofluorimetrically as the function of time.The significant difference of kinetic behaviors between Tyr and Lev can provide an opportunity to introduce an additional dimension to multiway data array and enhance the ability of resolving the spectra overlapping among Tyr,Lev and the interference from human plasma.The results demonstrate that the strategy of combining excitation-emission-kinetics-sample four-way fluorescence data array with four-way calibration method based on the quadrilinear decomposition algorithm SAQLD can successfully quantify Tyr and Lev in human plasma even in the presence of uncalibrated spectral interference.