Net Analyte Signal Based

Multivariate Calibration Methods

By:

Bahram HemmateenejadMedicinal & 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

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15Concentration

Ab

sorb

ance

Optimization of conditions

• Effect of pH

• Effect of Temperature

• Effect of Ionic Strength

• Effect of Concentration

• …

Optimum number of factors

0

20

40

60

80

100

120

1 6Number of Factors

PR

ES

S

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)

x

y M1

2x 3x

M2 M3

y

2y

3y

x

M1

M2

M3

• 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 = F Rk + F R-k, F R-k = 0

• F R = F Rk R* = F sk ck = sk* ck

• 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

• Rk = sk ck

• R-k = R – Rk

• ILS approach

• R-k = R - r ck

• r is a linear combination of the rows of R

• ck = R R-1 ck

= 1/ rT R+ ck

• Another approach

• R-k = [ I – ck(ckT ck)-1 ck

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 (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

Effect of added noise

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* = 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 ||ri*|| / ci or ||s*||

• Selectivity ||ri*|| / ||ri|| or ||s*|| / ||s||

• LOD 3Sc / m, 3 |||| ||bk|| / m

• LOQ 10Sc / m, 10 |||| ||bk|| / m

Applications• Wavelength region selection

Net Analyte Signal Regression Plot

(NASRP)

• 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 ck

T]R

• Thanks for you attention