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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

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net analyte signal based multivariate calibration methods

Net Analyte Signal BasedMultivariate Calibration Methods

By:

Bahram Hemmateenejad

Medicinal & Natural Products Chemistry Research Center, Shiraz University of Medical Science

multivariate calibration
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
Main Problems
  • Definition of figures of merit
  • Optimization of conditions
  • Optimum number of factors
figure of merit
Figure of merit
  • Sensitivity
  • Selectivity
  • Detection Limit

Univariate Calibration

optimization of conditions
Optimization of conditions
  • Effect of pH
  • Effect of Temperature
  • Effect of Ionic Strength
  • Effect of Concentration
optimum number of factors
Optimum number of factors

Cross Validation

External Validation

Minimum PRESS

F-Ratio

Over-fitting

Under-Fitting

net analyte signal nas
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
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)
slide9
M1

M2

M3

y

x

2x

3x

3y

M3

2y

M2

y

M1

x

slide10
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
slide11
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)

slide12
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
slide13
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
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
slide15
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
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
slide66
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

slide68
Sensitivity ||ri*|| / ci or ||s*||
  • Selectivity ||ri*|| / ||ri|| or ||s*|| / ||s||
  • LOD 3Sc / m, 3 |||| ||bk|| / m
  • LOQ 10Sc / m, 10 |||| ||bk|| / m
applications
Applications
  • Wavelength region selection

Net Analyte Signal Regression Plot

(NASRP)

slide70
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
slide71
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
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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