Spectroscopy Chromatography PhysChem Naming Drawing and Databasing Enterprise Solutions Software for...

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Software for Interactive Curve Resolution

using SIMPLISMA

Andrey Bogomolov, Michel Hachey, and Antony Williams


SIMPLISMA is…

SIMPLe-to-Use• Intuitive

Interactive• Operator is involved in the process

Self-modeling• No prior information is required

Mixture Analysis


Willem Windig

SIMPLISMA Reference:

[1] W. Windig and J. Guilment, Anal. Chem. 65 (1991), 1425.


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


General Curve Resolution Problem

assumptions


Curve Resolution and PCA

rRaw Data

Reproduced Data

Errors

+

c n C-Profiles

Spe

ctraCR

rRaw Data

Reproduced Data

Errors

+

c n Loadings

Sco

resPCA


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)


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…


Self-Modeling Basic Steps (Factor-Based Methods)

Deducing the number of components (PCA)

Obtaining initial curve estimates

Iterative improvement using system-specific constraints


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?


Purity Function

Purity Function

Mean

Standard Deviation

c

ijijcj d

1

21

j c iji

c

d11

j

jjp 1


Purity-Corrected Standard Deviation


Overestimated Purity Problem


Overestimated Purity Problem

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

j

jjp


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


SIMPLISMA Result


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!


Live Data Example


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


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


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!


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

Spectroscopy Chromatography PhysChem Naming Drawing and Databasing Enterprise Solutions Software for...

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