rac 4 hplc_dad

8/8/2019 Rac 4 Hplc_dad

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By: Parvaneh Ebrahimi


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Introduction1

Rank Annihilation Correction (RAC)2

Correction Function3

Optimization Routines4

Experiments & Results5


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Introduction1






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Chromatography columnaging

Temperature fluctuation

Pressure fluctuation

Shifts inShifts in

retention timeretention time

dimensiondimension


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According to BeerLamberts law, each matrix can

bedecomposed into the product of the matrices CA

andCB of concentration profiles and the matrix A of molarabsorption spectra.

YA = CA * A and YB = CB * A

CA & CB have dimensions: (nt m)

A has the dimension: (m nl)

YA & YB have dimensions: (nt nl)


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The inconsistency which was explained must

be corrected and the goal is to rectify the

inconsistency of the retention times

The idea of the method to solve this is

reducing the rank of [YA,YB] from 2m to m.


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First:

Correction function is foundand

correction I done

the time vector t at which the

spectraof YB were measured is

corrected by anappropriate

function, defined by a set of

parameters:

t new = f (t original, parameters)

Then:

Interpolation is done so that time

vectors in YA* & YB*are matched


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Introduction1






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Often thereareno theoretically defined functions for the

appropriatecorrectionand therefore polynomials ofany

degreeareobvious choices. Logarithmicorexponential

distortion

sare

othe

r po

ssibilities:

Thecorrection functiondiscussed in this

paper is a polynomial ofdegreeone:

t new = p0 +p1t original


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Grid search is done to find theoptimum parameters.

[Y*A,Y*B]

All P0 interval is scanned

For first value in P1 scan interval

reconstructed [YA,YB]:

With fixed P1, for every P0:

For every P1 value:

P1 scan interval

t new = p0 +p1t original


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Theconcatenated matrix is decomposedaccording to the

singular valuedecomposition:

is calculated fordifferent numbers of retained vectors in

U, S, and V , and its percent residual variance is

calculated forall numbers ofeigenvectors and

eigenvalues retained

[Y*A,Y*B]=USV + R

R = [Y*A,Y*B] [U(:, i) * S(1:i,1:i) * V(:, i)]


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The logarithm of the percent residual varianceagainst P0

retaining oneup to six eigenvectors .There is adistinct

minimum for the inclusionof fourand moreeigenvectors

at the parameter valueof 0.149


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Correlation between parameters can be very high. Generally, mean

centering of retention time vector will reduce this correlation, dramatically.


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Introduction1






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Insteadof inspectionof graphical results suchas those

displayed in previous slides, any non-linearoptimization

routinecan beused to localize theoptimum. This is

particu

larly imp

ortan

t forca

ses wit

hmo

re

than

two

parameters, as thesecannot be represented graphically.

Algorithms:

Algorithms range from the simpleSimplex algorithm tomore sophisticated gradient techniques. Weused the

MATLAB fminsearch function, which is anadvanced

simplex algorithm.


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Initial guesses and/or boundaries for the parameters should be made sensibly.

If initial guesses are too farout, most algorithms will fail toconverge.

therealways is the possibility

ofoneor several local minima.


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Introduction1






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Mixtures of anthracene, pyrene, fluorene, and fluoranthene in acetonitrilewere analyzed by an HPLC DAD system.

chromatograms were measured at 25 and 27.5 C before and after

application of RAC, are plotted:


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the temperature was varied between 25 and40 C and the flowrate was either 1 or 1.25 ml min1 and temperature, P1 and P0

were plotted against each other.

There is a good linear relationship

betweenP1 and the temperature

and this is independently thecase

for both flow rates.

There is a strong negative

relationship between the shift

parameter p0 and temperature

and, interestingly, it is independent

of the flow rate.

theneat relationship shown

in Fig. is aclear indication for the

reliability and robustness of the

procedure


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A generally applicable method for the correction

of instrumental inconsistencies in retention time

dimension has been introduced. Experimentalexamples discussed in this paper comprise the

successful correction of non-uniform retention

time drifts in chromatography due to

temperature or pressure changes.


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