Transcript Slide 1

Software for
Interactive Curve Resolution
using SIMPLISMA
Andrey Bogomolov, Michel Hachey, and
Antony Williams
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SIMPLISMA is…
 SIMPLe-to-Use
• Intuitive
 Interactive
• Operator is involved in the process
 Self-modeling
• No prior information is required
 Mixture
 Analysis
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Willem Windig
SIMPLISMA Reference:
[1] W. Windig and J. Guilment, Anal. Chem.
65 (1991), 1425.
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SIMPLISMA is a Multivariate
Curve Resolution Algorithm
 Extract pure component spectra from a
series of spectroscopic observations of a
mixture while the component concentrations
vary
 Obtain component concentration profiles
for processes evolving in time
 Detect the number of mixture components
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General Curve Resolution
Problem
assumptions
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c
r
Raw Data
CR
PCA
n
Loadings
C-Profiles
Spectra
Scores
Curve Resolution and PCA
Reproduced
Data
+
Errors
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Practical Applications
 Qualitative characterization of
unknown mixtures
 Interactive process monitoring
 Studying chemical reactions’ kinetics
and mechanisms
 Obtaining equilibrium constants
 Resolving co-eluting signals in
hyphenated chromatography
(HPLC/DAD)
 Quantitative analysis (calibration is
required)
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Self-Modeling Curve Resolution
Algorithms
 Evolving Factor Analysis (EFA)
 Window/Subwindow Factor Analysis
(WFA/SFA)
 Iterative Target Transformation Factor
Analysis (ITTFA)
 Rank Annihilation Factor Analysis
(RAFA)
 Direct Exponential Curve Resolution
Algorithm (DECRA) by W. Windig
 and more…
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Self-Modeling Basic Steps
(Factor-Based Methods)
 Deducing the number of components
(PCA)
 Obtaining initial curve estimates
 Iterative improvement using systemspecific constraints
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SIMPLISMA is a Purity-Based
Approach
 A pure variable represents the
component concentration profile
 Find a pure variable for each
component
 Solve for the component spectra by
means of regression
 How to find pure variables?
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Purity Function
p j1 
 Purity Function
 Mean
j 
c
1
c
d
j
 j 
ij
i 1
 Standard Deviation
j 
 d
c
1
c
i 1
j
2
ij
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Purity-Corrected Standard
Deviation
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Overestimated Purity Problem
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Overestimated Purity Problem
pj 
j
 j 
 Purity tends to the infinity when the
mean approaches zero
 Offset  serves to compensate for this
effect
 Offset is usually defined as % of the
mean
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Deducing the Number of
Components
 Shape of Residuals
 Shape of the Resolved Curves
 Shape of Purity and Purity-Corrected
Standard Deviation Spectra
 TSI vs LSQ plot
 Cumulative %Variance
 IND Function
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SIMPLISMA Result
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SIMPLISMA with 2nd Derivative
 The algorithm assumes that each
component has pure variable
 Often, in real-world mixtures this
requirement is not met
 Inverted 2nd derivative may help!
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Live Data Example
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Advantages of SIMPLISMA
 Interactive: unlike black-box
algorithms, lets a human interfere
 Intuitive: spectrum-like curves are
easily interpreted by spectroscopists
 Fast: does not perform timeconsuming iterative improvements
 Flexible: does not use prior
assumptions about spectral and curve
shapes
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Limitations and Workarounds
 Real purity is unknown
=> assess purity by other algorithms
 No variance—no component
=> more experiments to make it vary
 Too complex data
=> try to split
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CONCLUSION
 SIMPLISMA is a curve resolution
program designed for use by
spectroscopic experts
 Commercial implementation has been
transformed into a chemical software
interface
 Therefore, the hurdles to widespread
usage have been overcome!
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Acknowledgments
 Willem Windig for the invention
 Eastman Kodak for licensing the
SIMPLISMA algorithm
 Yuri Zhukov and Alexey Pastutsan,
the ACD/Labs programmers
 Antony Williams and Michel Hachey,
colleagues and co-authors
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