Transcript Slide 1

Non-linearity and EFA
Single component elution in HPLC-DAD system
20% non-linearity
Non-linear
Ideal
Spectra in two dimensional wavelength space
Non-linear 475-500 nm
Ideal
Spectra in two dimensional wavelength space
Non-linear 495-500 nm
Ideal
Evolving Factor Analysis (EFA)
Non-linear
Ideal
Evolving Factor Analysis (EFA)
Non-linear
Ideal
Embedded elution and EFA
Consecutive elution
tm1= 40, tm2=60
w1= 11, w2=8.5
HPLC-DAD data
Ebedded elution
tm1= 50, tm2=57
w1= 12, w2=6.5
HPLC-DAD data
EFA
Embedded elution
Consecutive elution
EFA
Embedded elution
Consecutive elution
The main assumption of EFA is that the
component, which appears first, will
disappear first. Indeed it is often but
not always the case for sequential
elution.
The main question is ‘which end
belongs to which start?’
Exhaustive Evolving Factor Analysis
E-EFA analyzes all possible sub-matrices of
the measured matrix, which are combined
by the two outsides submatrices of a selected
window, and an apparent difference is found
between the similar results that are obtained
by the traditional EFA.
Exhaustive Evolving Factor Analysis
Rank =2
Rank =2
Exhaustive Evolving Factor Analysis
Rank =2
Rank =2
Exhaustive Evolving Factor Analysis
Rank =2
Rank =2
Exhaustive Evolving Factor Analysis
Rank =2
Rank =2
Exhaustive Evolving Factor Analysis
Rank =2
Rank =2
Exhaustive Evolving Factor Analysis
Rank =1
Rank =1
Exhaustive Evolving Factor Analysis
Rank =0
Rank =0
Exhaustive Evolving Factor Analysis
Rank =2
Rank =2
Exhaustive Evolving Factor Analysis
Rank =2
Rank =2
Exhaustive Evolving Factor Analysis
Rank =2
Rank =2
Exhaustive Evolving Factor Analysis
Rank =1
Rank =2
Exhaustive Evolving Factor Analysis
Rank =1
Rank =2
Exhaustive Evolving Factor Analysis
Rank =1
Rank =1
Sectional Moving Window Factor
Analysis (SMWFA) is a fast, friendly
and useful for automatic resolution of
hyphenated chromatographic data.
Sectional Moving Window Factor Analysis
SMWFA.m file
For sectional moving window
factor analysis of two
component systems
Use the SMWFA.m file and investigate the effects of
noise values on HPLC-DAD data in embedded
elution systems.
?
Rank Deficiency and EFA
Rank deficiency in a system with two
independent chemical processes
HA
HB
[HA]
A- + H+
B- + H+
[A-]
[HB]
[B-]
HA
HB
A-
B-
A- + H+
HA
Ct1 [H+]
[HA] =
[H+] + Ka1
[A-]
Ct1 Ka1
=
[H+] + Ka1
B- + H+
HB
Ct2 [H+]
[HB] =
[H+] + Ka2
[A-]
Ct2 Ka2
=
[H+] + Ka2
[HB] + [B-] = Ct2
Ct1 = a Ct2
[HA] + [A-] = a ([HB] + [B-])
1
1 3 2 6
2 2 4 4
3 1 6 2
3
4
2 + 2 = 4
4
8
3
1
4
4 = (1/2)
8
2
6
8
4
8
4 + 4 = 8
6
1
2
3
+
2
8
3
2
2 + (-1/2)
4
1
6
6
+ (-1/2)
4
2
0
=
0
0
Augmentation
=
1 3 2 6
1 3 2 6
2 2 4 4
2 2 4 4
3 1 6 2
1 3 0 0
2 2 0 0
3 1 0 0
Augmentation
3 1 6 2
1 3 0 0
2 2 0 0
3 1 0 0
1
3
4
2
2
4
3
1
4
1
+
3
=
4
2
2
4
2
6
8
3
1
4
4
4
8
6
2
8
0
+
0
=
0
0
0
0
0
0
0
pKa1=4
pKa2=6
pKa=2.5
Forward and backward eigen analysis
EFA Results
standard
Augmentation
mixture
standard
mixture
Forward
Analysis
standard
mixture
Backward
Analysis
Forward and backward eigen analysis
standard
mixture
EFA Results
standard
mixture
Concentration Profiles
standard
mixture
mixture
Augmentation
standard
mixture
standard
Forward
Analysis
mixture
standard
Backward
Analysis
Forward and backward eigen analysis
mixture
standard
EFA Results
mixture
standard
Concentration Profiles
mixture
standard
standard
mixture
Forward
Analysis
mixture
standard
Backward
Analysis
Forward and backward eigen analysis
Forward and backward eigen analysis
Mixture of H2A
and H2B
H2A
pKa1=2
pKa2=3
pKa1=4.5
pKa2=6.5
H2B
EFARD.m file
EFA on data with rank deficiency
Outputs of EFARD.m
Outputs of EFARD.m