Software for
Interactive Curve Resolution
using SIMPLISMA
Andrey Bogomolov, Michel Hachey, and
Antony Williams
Spectroscopy • Chromatography • PhysChem • Naming • Drawing and Databasing • Enterprise Solutions
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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Curve Resolution and PCA
n Loadings
C-Profiles
c
Spectra
Reproduced
Scores
CR
PCA
Raw Data Data
r
+
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 system-
specific 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
j
Purity Function p j1
j
c
Mean j 1
c d
i 1
ij
Standard Deviation
d j
c
j 1
c ij
2
i 1
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Purity-Corrected Standard
Deviation
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Overestimated Purity Problem
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Overestimated Purity Problem
j
pj
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 time-
consuming 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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