Chemometrics and Multivariate Resolution and its Application in analysis of TCM

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Chemometrics and Multivariate Resolution and its
Application in analysis of TCM

• ????????????? ???

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Chemometrics

• Chemometrics is a new chemical discipline
  that uses the theory and methods from
  mathematics, statistics, computer science and
  other related disciplines to optimize the
  procedure of chemical measurement, and to extract
  chemical information as much as possible from
  chemical data. Chemometrics could be defined as a
  discipline of fundamental theory and methodology
  of chemical measuring.
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  ????,???????????????????????,????????????????????

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Brief History of Chemometrics

• Svante Wold used it firstly for applying
  scientific project in 1970 in Sweden
• Wold and Kowalski founded the International
  Chemometric Society in 1974
• Analytical Chemistry published special review on
  Chemometrics every two year since 1978
• Two special chemometric international journals
  named J.Chemom. and ChemLab appeared in 1987
  from both American and Europe.

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Contents in chemometrics
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Chemometrics consists of fundamental and
methodology of chemical measurements.
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Necessary fundamental knowledge of statistics and
linear algebra

• Vector and Matrix

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Is Mathematics really useful for chemists?

• Data exploding
• Extract chemical information from the data
• Revolution of Information technique
• Progress in Computer ability

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Vector in analytical chemistry

• All the spectra, chromatograms and etc. can be
  numerated into a group of numbers, which is
  called a vector in mathematics.

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Hyphenated Instruments, such as HPLC-DAD, GC-MS,
GC-IR, HPLC-MS

• Two-way data containing both chromatography and
  spectra
• Data matrix with more than 10 Megabytes
• Data base of lots of chemical standards

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The mixture spectrum of two different chemical
compounds a and b according to the Lambert-Beer
law
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Geometric sense of vector addition
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Geometric sense of vector subtraction
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Direction and length of vector

• The direction of a vector is decided by all its
  elements, since the different ratios between them
  can defines different directions in linear
  subspace
• The length of a vector is also decided by
  magnitudes of its elements, since we have,
• a(a12.an2)1/2

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different ratios between them can defines
different directions in linear subspace
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Subtraction of two vectors defines the distance
between the two points in n dimensional space
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Numerical multiplication of vectors
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The spectra of different concentrations
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Inner product and outer product between the
vectors
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Inner or dot product between two vectors
producing a number
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Geometric sense of inner product between two
vectors
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Inner product and projection between vectors
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Outer product between two vectors producing a
bilinear matrix, which is of special importance
in multivariate resolution
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What is the chemical meaning of rank of a matrix?

• Linearly independent?
• Rank of a matrix the number of the chemical
  components in the mixture?
• Mixture number and compound number?

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A part of a real two-way data measured for Cortex
Cinnamomi (??)
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Lambert-Beer Law
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The problem here for chemists to solve is that,
with the measurement matrix at hand, one needs to
find out

• The number of absorbing chemical components A
• The spectrum of each chemical component si (i1,
  2, , A) (first step of qualifications)
• The concentration profile of each chemical
  component ci (i1, 2, , A) (first step for
  quantification)
• Is it possible?
• Yes, if we have the two-way data!!

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Mixture spectra and compound spectra

• This is a two compound system
• Two red vectors are the compound spectra
• Seven blue vectors are mixture spectra

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Linearly independent

• The two spectra are from two different chemical
  compounds, so they are independent with each
  other
• Seven spectra are all from the spectra of the two
  chemical compounds, so they are dependent upon
  the concentrations of the two compounds in the
  mixture

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Mixture number and compound number
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Rank of a matrix the number of the chemical
components in the mixture?

• Unchanged are chemical compounds
• Rank of a matrix is also certain, which is not
  changed
• Thus, if we collect all the spectra to form a
  matrix, the rank of which should be 2.

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How can we find the rank of a matrix with
measurement noise?

• What are noises and how do they influence the
  data analysis?
• Thus, we need statistics and also algebra
• Useful technique Principal component analysis!!

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This is really a difficult problem!

• Now, lets go through this problem step by step.

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Single value decomposition
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Question 2

• We have a data matrix at hand, we need to know
  there are how many chemical components in it.
  What technique do you want to use?
• Principal component analysis? Can we use singular
  value decomposition to solve the problem?

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Multivariate calibration and multivariate
resolution

• This is the major topic in analytical
  chemometrics, we will discuss it in some detail.

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Single value decomposition and number of chemical
component in the system
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Local factor analysis and Zero component regions

• Evolving factor analysis (EFA)
• Fix-sized moving window evolving factor
  analysis(FSMWEFA)
• Eigenstructure tracking analysis (ETA)
• Evolving latent projections

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Evolving Factor Analysis
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Evolving factor analysis
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Fix-sized Moving Window Evolving Factor
Analysis(FSMWEFA)
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Fix-sized Moving Window Evolving Factor
Analysis(FSMWEFA)
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Some problems with local factor analysis

• Local rank
• Zero component regions,
• Window size
• Eigenstructure tracking analysis
• Rank map and local data structure
• Evolving latent projections

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Principal Component analysis and Latent
projections
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Evolving latent projections
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Selective information and Evolving latent
projections
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Zero component region and noise level
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A simple example
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Resolution into pure chromatograms and spectra

• Because ACSt
• If we have pure spectra S, then we can use the
  following equation
• CAS(StS)-1

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Resolution into pure chromatograms and spectra
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?????16??PAH?????(Sulpeco)???9???a???,?14??????
??????????
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Peaks 5 and 6 in the plot
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?5??6?????????5??5???????16382,2436,1294,22,11
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J.C Giddings in Statistical theory of component
overlap in multicomponent chromatograms claimed
that

• It is shown that, relative to the maximum peak
  content or peak capacity for closely spaced
  peaks, a random chromatogram will never contain
  more than about 37 of its potential peaks and,
  worst of all from an analytical point of view,
  18 of its potential single-component peaks.
• The number of observed peaks is not, then, the
  same as the number of distinct chemical
  components. The loss of analytical information
  resulting from this overlap is by itself serious,
  but the severity of the problem is greatly
  magnified if we do not have a good estimate of
  the magnitude of the loss.
• Anal. Chem. 1983, 55, 418-424

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Application to environmental chemistry

• PAHs represent a class of organic pollutants that
  are widely found in the environment. They have
  been shown to exert a very strong carcinogenic
  action on animals.
• This is an example for qualitative and
  quantitative analysis of PAHs in air-borne
  particulates in Hong Kong city by the chemometric
  resolution method.

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1.8.2 HELP ??

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  ??????? ?

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• ??Xi,???????Xi????????,?
• ??????

2)??????????????????????? ?????????????????????

3)?????????????????????? ????????
4)??????????????????????? ??????,??? ???????
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Figure 2.6 The amplified total ion current
chromatogram of fraction N6 obtained from GC-MS.
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1.9 ????

• ??????????,?????????????????

???B??????????,?????
6-methoxy-2-methyl-beta-carboline(C13H12N2O)? 3,3
-dimethyl-1,1-biphenyl-4,4-
diamine(C14H16N2)? 2,5-dimethyl-4-3-amino-4-methy
lphenylpyridine(C14H16N2) 5-acetyl-4-amino-2-meth
ylthio-thiophene(C8H8N2OS2)? 4,9-dimethyl-naphtho-
2,3-b-thiophene(C14H12S)? 1,2,5,6-tetramethylace
naphthylene(C16H16)
????,????????????,?????????????1200???????130?????
??
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?????????????????????

• ???30?60??,??????????(Interest in medical plants
  progressing significantly diminished in the 1930s
  and botancals fell into almost complete disuse
  until 1960s, Roy Upton, Herbalist Executive
  Director, American Herbal Pharmacopoeia),???(2000)
  Global Herbal Market US 19.6 billion
  !!(196????)

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???????????????EG6761,??????????????,?????????????
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Health Products (Western Countries)
Ginggo Biloba (??)
St. Jones Wort(????)
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Health Products (Western Countries)
Green tea(??)
Echinacea(???)
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Traditional Chinese Medicine (TCM) Health
Products
Dong Quai(??)
Ginseng(??)
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Traditional Chinese Medicine (TCM) Health
Products
Cordyceps(????)
Galic(??)
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Natural Product Market

• Global Herbal Market 2000 US 19.6 billion !!
  

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Natural Product Market
 
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????????????????????

• Despite its existence and continued use over many
  centuries, and its popularity and extensive use
  during the last decade, traditional medicine has
  not been officially recognized in most countries.
  The quantity and quality of the safety and
  efficacy data on traditional medicine are far
  from sufficient to meet the criteria needed to
  support its use worldwide. The reasons for the
  lack of research data are due not only to health
  care policies, but also to a lack of adequate or
  accepted research methodology for evaluating
  traditional medicine.

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????????????????????

• ????????(?????????)
• ??????(????,????)
• ?????????????????(GAP ?GEP),???????(GMP),????????
  ???????
• ????????(????,????)
• ???????????????
• ???(??????)?(????)????
• ?????????????

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Essential Constituents of Ramulus Cinnamomi(??)
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???????????

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• ?????????????????
• ????(?????),????????????????
• ???????????????????!

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?????????????

• ?????????????,?????????

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Instruments Commonly used for Chemical Analysis
of Chinese Medicine

• Thin Layer Chromatography (TLC)(????)
• ? qualitative analysis semi-quantitative
  analysis
• High Performance Liquid Chromatography
  (HPLC)(??????)
• ? Both qualitative analysis quantitative
  analysis
• Gas Chromatography (GC)(????)
• ? Both qualitative analysis quantitative
  analysis
• DNA Analysis( DNA??)
• Capillary Electrophoresis (CE) (?????)

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????????????

• ??????

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Hyphenated Instrument (????)

• Most modern and advanced analytical
  instrument.e.g. HPLC-DAD, GC-MS, CE-DAD, etc.
• Combination of two or more instruments

e.g. HPLC DAD (diode-array detector)GC
MS (Mass-spectrometer)
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Hyphenated Instrument (????)

• Get more data/information

• HPLC -DAD

3D chromatogram
HPLC chromatogram of nuclueside of Cordyceps
Sinensis (???) at one wavelength
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Hyphenated Instrument (????)
GC chromatogram of peptic powder (???)
GC instrument

• Mass spectrum taken at retention time 10.2
  minutes

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Hyphenated Instrument (????)

• Advantages
• More data is obtained at a retention time.
• More spectral information acquired to give three
  dimensional (3D) data.
• Much more information available to analyze
  complicated system like TCM.

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Hyphenated Instrument (????)

• Disadvantages
• Huge amount of 3D data is obtained.
• Need data processing methods for information
  extraction, pattern recognition, etc.
• Computer power was poor before.
• Usual practice Use a few data obtained from
  HPLC-DAD/GC-MS to find marker components or
  active ingredients.
• Now, everything becomes possible with high
  tech.!

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????????????????????????????????????????

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  ??????????,...?????????????,?????????????????????
  ???,??????????,????????????????????????????????,?
  ????????????????????????,???????????????????,?????
  ??????????????????????????????????????????????????
  ???,???????????????????????????????,???????????,??
  ??????????????,??????????????????????,??????,???
  ??????,????????.????????,????????????????.

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?????????????

• ??????????

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Traditional Chinese medicines

• ??????????????????HPLC-DAD?GC-MS??
• ????????????????????????,??????mono-graphs
• ???????????????????????????????????????

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Chemometrics Cordyceps sinensis
Chromatograms of the fungal part of Cordyceps
sinensis at wavelength (a) 234 nm, (b) 260nm and
the larva part of Cordyceps sinensis
at wavelength (c) 234 nm, (d) 260 nm.
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A simple example
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Chemometrics Cordyceps sinensis
(a) The selective chromatograms of the fungus
part from 11.0 to 14.0 minutes with an interval
of 5 nm and (b) shows the spectra of the fungus
part in the range of 195 to 312 nm with an
interval of 0.1 minute. (c) and (d) show the
corresponding eigenvalues plot and the latent
project graph of .(e) and (f) show
the resolved chromatograms and spectra for
components f1 and f2 in the fungal part.
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Chemometrics Cordyceps sinensis
The overall resolved chromatogram of the fungal
part
The overall resolved chromatogram of the larval
part
The HELP method was used for resolving these
chromatograms.
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• Fan Gong, Yizeng liang, F.t. Chau, Anal. Lett.,
  33(2000)2105-2128
• Gan Feng and Yizeng Liang , Analytical Science,
  16 (2000) 603-607
• Chengjian Xu, Yizeng Liang and Jianhui Jiang,
  Analytical Letters, 33 (2000) 2105-2128
• Hailin Shen, Yizeng Liang, O.K. Kvalheim and R.
  Manne, Chemometrics and Intelligent Laboratory
  Systems, 51 (2000) 49-59 (in English)
• Hailin Shen, L. Stordrange, R. Manne, O.M.
  Kvalheim and Yizeng Liang, Chemometrics and
  Intelligent Laboratory Systems, 51 (2000) 37-47
  (in English)
• Hailin Shen, Xiaoning Li, Yizeng Liang, Chinese
  Science Bulltin(????), 45 (2000) 587-592
• Hailin Shen, Youqun song, Hui Cui, Yizeng Liang,
  Acta Chimica Sinica (????), 58 (2000) 438-442
• Qingsong Xu, Yizeng Liang and Kaitai Fang,
  Chemometrics and Intelligent Laboratory Systems,
  52 (2000) 155-166.

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Peptic powder

• Peptic powder is an ancient concentrated
  preparation in China. It can clear away
  pathogenic dampness, moisturize spleen, promote
  the circulation of qi and regulate the stomach.
  The formulation is composed of four single herbs.
  They are Rhizoma Atractylodis (atractylodes
  rhizome), Pericarpium Citri Reticulatae
  (tangerine peel), Cortex Magnoliae Officinalis
  (magnolia bark) and Radix Glycyrrhizae (licorice
  root). The volatile constituents of peptic powder
  are pharmacological active.

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• Gong Fan, Y.Z. Liang, Hui Cui, F.T. Chau, Benny
  T.P. Chan, Determination of volatile components
  in peptic powder by gas chromatography-mass
  spectrometry and chemometric resolution, J.
  Chromatography A, 905(2001)193-205 (in English)
• Gong Fan, Y.Z. Liang, Qing-Song Xu, F.T. Chau,
  Gas chromatography-mass spectrometry and
  chemometric resolution applied to determination
  of essential oils in Cortex Cinamomi, J.
  Chromatography A, 909(2001)237-247 (in English)
• ??, ???, ???,???, ??, A.K.M. Leung, Foo-tim
  Chau,????????, 2001 (in press).

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• Gan Feng, Jia-hong Yang and Y.Z. Liang, Liberary
  search of mass spectra with a new matching
  algorithm based on substructure similarity,
  Analytical Science, 17 (2001) 635-638 (in
  English)
• Y.Z. Liang and O.M. Kvalheim, Resolution of
  two-way data theoretical background and
  practical problem solving Part 1 theoretical
  background and methodology, Frenenius Anal.
  Chem., 370 (2001) 694-704. (in English)
• Minghao Zhang and Yizeng Liang, Analyst, (2001)
  (in press).
• Gong Fan, Y.Z. Liang, Qing-song Xu,F.T. Chau,
  King-man Ng, Anal. Chim. Acta, 2001 (in press).
  (in English)
• Y.Z. Liang, K.T. Fang, Q. S. Xu, Chemometrics and
  Intelligent Laboratory Systems, 2001 (in press).
• Chengjian Xu, Y.Z. Liang, You-Qun Song and
  Ji-shan Li, Frenenius Anal. Chem., (2001) (in
  press)

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fingerprints for some herbal medicinest Top
part (?????) Lower part (?????)
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Finding Fingerprint HELP
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peptic powder(???)

• There are four herbs in peptic powder say
  Rhizoma Atractylodis (atractylodes rhizome),
  Pericarpium Citri Reticulatae (tangerine peel),
  Cortex Magnoliae Officinalis (magnolia bark), and
  Radix Glycyrrhizae (licorice root).
• The results obtained so far showed that the
  volatile oil in peptic powder are almost the
  mixture of the above four herbs proportional to
  their relative amounts taken in the preparation.

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Finding FingerprintChemical Composition Approach

• A TCM preparation Si-wu decoction (???)
• 100g Radix Angelicae Sinensis ,??
• 80g Rhizoma Chuanxiong, ??
• 120g Radix Paeoniae Alba,??
• 120g Radix Rehmanniae Praeparata,??
• Volatile oil extraction
• According to the standard extraction method in
  Chinese Pharmacopoeia

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Finding FingerprintChemical Composition Approach
Rhizoma Chuanxiong ??
Radix Angelicae Sinensis??
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Finding FingerprintChemical Composition Approach
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  5.27?
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  ?,??5????????????????
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  ???4-?????-??????????????????????,???????????????
  ??
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  ??????????,????????????????????????????????????

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?????????????????????GC/MS??

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  ?,???????????????????????????

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?????????????TIC?
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?????????????????TIC?????????????
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SFA???????
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????????????
The paper entitled Analysis of the volatile
fraction of Schisandra chinensis Turez. Bail.
With GC/MS and chemometric resolution is well
written and technically most competent. I am sure
this technique will find increasing use in the
resolution of complex plant extracts such as is
demonstrated with this plant.
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• 2.1 ????????????,???????????????????????????,???
  ????????????????????????????????,???????????? ?

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2.2
????????????????? ?????????

• 2.3

GC-MS ??
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2.5 ??
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3. ???????????? ???????????

• 3.1 ????????

??????,??????(????????????)???????????????????????
????,???????????????(???)?
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3.2 ???????????

• 1.??????????????

2.????????????2000???,??2004??????????????????????
??????,????????????????????????????,???????,??????
??????????? ?
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3.3 ??????

• ?????????,?????????????????,??????(???)?????????
  ????????????????,?????????????????,???????????.

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3.4 ??
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0.9998
0.9940
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2000
7-a
260 nm
?
Sample 1
Sample 2
1000
Absorbance (AU)
0
-1000
0
5
10
15
20
25
Retention time (min)
2000
7-b
260 nm
?
1000
Absorbance (AU)
0
-1000
0
5
10
15
20
25
Retention time (min)
139

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  ?????????????????????????????,????????????????????
  ?,?????????????????????????????????????