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Net Analyte Signal Based Multivariate Calibration Methods

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### Net Analyte Signal BasedMultivariate 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

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).
- 1997-2000 Extensions.
- Inverse calibration (Lorber,Faber,Kowalski)
- Figures of merit (sensitivity, selectivity, limit of detection) (Faber)
- 1998-2002 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)

R (ixj) matrix of mixture spectra

- Rk(ixj) matrix of analyte k spectra
- R-k (ixj) matrix of background (other analytes + interferences
- R = C S
- Rk = sk ck
- R = Rk + R-k
- F R = FRk + FR-k, FR-k = 0
- F R = FRk R* = F sk ck= sk* ck

F = I – R-k+ R-k

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

(RAFA)

CLS approach

- Rk = skck
- R-k = R – Rk
- ILS approach
- R-k = R - r ck
- r is a linear combination of the rows of R
- ck = RR-1ck
- = 1/ rTR+ck

Another approach

- R-k = [ I – ck(ckT ck)-1 ckT]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 (run 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)run
- Calculation of the pure NAS
- s*k = (I – R-k+ R-k)sk

NAS-Multivariate calibration

- In some case,
- Nonlinearity
- Interaction between components
- 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* = cs* MLR
- R* = T* P* c = T* b* PCR
- R* = T* P* c= uqu = T* b* PLS
- R* can be used as input for ANN

In Progress

Sensitivity ||ri*|| / ci or ||s*||

- Selectivity ||ri*|| / ||ri|| or ||s*|| / ||s||
- LOD 3Sc / m, 3 |||| ||bk|| / m
- LOQ 10Sc / m, 10 |||| ||bk|| / m

Error Indicator (EI)

- Goicoechea and Olivieri, Analyst 124 (1999) 725
- EI = {s2 [1+(N2s2) / 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) 4361.
- Determination of drugs in pharmaceutics
- Determination of drugs in serum
- Determination of sorbic and benzoic acids in fruit juices

Multivariate Standard Addition Method (MSAM)

- ck = cu + cs
- R = R-k + Rk
- R-k = R - r ck = R - r (cu + cs)
- R-k = [ I – ck(ckT ck)-1 ckT]R

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