Net analyte signal based multivariate calibration methods
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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)


  • M1

    M2

    M3

    y

    x

    2x

    3x

    3y

    M3

    2y

    M2

    y

    M1

    x


    • 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
    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
    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




    • 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)


  • 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

    • 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) 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



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