Net Analyte Signal Based Multivariate Calibration Methods By: Bahram Hemmateenejad Medicinal & Natural Products Chemistry Research Center, Shiraz University of Medical Science

Multivariate Calibration CLS A = C S ILS c = A S PCR A = T P, c = T s PLS A = T P, C = Q U Q = T b

Main Problems Definition of figures of merit Optimization of conditions Optimum number of factors

Figure of merit Sensitivity Selectivity Detection Limit Univariate Calibration

Optimization of conditions Effect of pH Effect of Temperature Effect of Ionic Strength Effect of Concentration …

Optimum number of factors Cross Validation External Validation Minimum PRESS F-Ratio Over-fitting Under-Fitting

Net Analyte Signal (NAS) A. Lorber, Anal. Chem. 58 (1986) 1167 The part of mixture spectrum that is useful for model building NAS is unique for the analyte of interest NAS is a part of mixture spectrum which is orthogonal to the spectrum of all existing components except analyte A part of mixture spectra which is directly related to the concentration of analyte

Net analyte signal, references 1986 Proposed by Lorber. Spectra of pure compounds available (CLS model) Extensions. Inverse calibration (Lorber,Faber,Kowalski) Figures of merit (sensitivity, selectivity, limit of detection) (Faber) Applications, Software. Outlier detection.(Faber, Xu, Ferre) Biomedical & Pharmaceutical.(Goicoechea, Skibsted) Spectral preprocessing.(Faber, Brown, Wentzell) Wavelength selection.(Goicoechea, Xu) Preprocessing and wavelength selection (Skibsted, Boelens)

x y M1 2x3x M2M3 y 2y 3y x M1 M2 M3

R (ixj) matrix of mixture spectra R k (ixj) matrix of analyte k spectra R -k (ixj) matrix of background (other analytes + interferences R = C S R k = s k c k R = R k + R -k F R = F R k + F R -k, F R -k = 0 F R = F R k R* = F s k c k = s k * c k

F = I – R -k + R -k R* = (I – R -k + R -k )R = R - R -k + R -k R (I – R -k + R -k )R -k = 0 Key Step R -k Rank Annihilation Factor Analysis (RAFA)

CLS approach R k = s k c k R -k = R – R k ILS approach R -k = R -  r c k r is a linear combination of the rows of R c k = R R -1 c k  = 1/ r T R + c k

Another approach R -k = [ I – c k (c k T c k ) -1 c k T ]R Other approaches Xu & Schechter Anal. Chem. 69 (1997) 3722 Faber Anal. Chem. 70(1998) 5108

Review of NAS calculation Determining No. of analytes (p) Preparing mixture standard solutions (j) Recording absorbance spectra of solutions at (i) sensors (R matrix) Recording absorbance spectrum of unknown (r un vector) Calculation of R -k

Calculation of calibration NAS R* = (I – R -k + R -k )R Calculation of the NAS for unknown r* un = (I – R -k + R -k )r un Calculation of the pure NAS s* k = (I – R -k + R -k )s k

Effect of added noise

NAS-Multivariate calibration In some case, –N–Nonlinearity –I–Interaction between components –O–Other source of variables The rank of NAS will become greater than 1 Simple NAS method dose not give perfect results MLR, PCR, PLS and … help to enhance the results of NAS calculation

R* is used as input for multivariate models R* = c s* MLR R* = T* P* c = T* b* PCR R* = T* P* c= u q u = T* b* PLS R* can be used as input for ANN In Progress

Figure of merits

Sensitivity ||r i *|| / c i or ||s*|| Selectivity ||r i *|| / ||r i || or ||s*|| / ||s|| LOD 3S c / m, 3 ||  || ||b k || / m LOQ 10S c / m, 10 ||  || ||b k || / m

Applications Wavelength region selection Net Analyte Signal Regression Plot (NASRP)

Error Indicator (EI) Goicoechea and Olivieri, Analyst 124 (1999) 725 EI = {s 2 [1+(N 2 s 2 ) / 4 ||r*|| )]}0.5 / ||r*|| s: standard deviation of the best fitted line N: Number of point in the best fitted line

Temperature insensitive determination of proteins in electrolyte solutions Anal. Chem. 72 (2000) 4985 Determination of Tetracycline in blood serum Anal. Chem. 71 (1999) Determination of drugs in pharmaceutics Determination of drugs in serum Determination of sorbic and benzoic acids in fruit juices

Multivariate Standard Addition Method (MSAM) c k = c u + c s R = R -k + R k R -k = R -  r c k = R -  r (c u + c s ) R -k = [ I – c k (c k T c k ) -1 c k T ]R

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