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Net Analyte Signal Based Multivariate Calibration MethodsPowerPoint Presentation

Net Analyte Signal Based Multivariate Calibration Methods

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### Net Analyte Signal BasedMultivariate Calibration Methods

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

Determination of Tetracycline in blood serum Determination of drugs in pharmaceutics Determination of drugs in serum Determination of sorbic and benzoic acids in fruit juices

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 1997-2000 Extensions. 1998-2002 Applications, Software.

- 1986 Proposed by Lorber.
- Spectra of pure compounds available (CLS model).

- Inverse calibration (Lorber,Faber,Kowalski)
- Figures of merit (sensitivity, selectivity, limit of detection) (Faber)

- 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 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

- In some case,
- Nonlinearity
- Interaction between components
- Other source of variables

- 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

- Temperature insensitive determination of proteins in electrolyte solutions
- Anal. Chem. 72 (2000) 4985

- Anal. Chem. 71 (1999) 4361.

Multivariate Standard Addition Method (MSAM) electrolyte solutions

- 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

- Thanks for you attention electrolyte solutions

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