Method of multi-dimensional moment analysis for the characterization of signal peaks
View Patent ↗A method of multi-dimensional moment analysis for the characterization of signal peaks can be used to optimize the operation of an analytical system. With a two-dimensional Péclet analysis, the quality and signal fidelity of peaks in a two-dimensional experimental space can be analyzed and scored. This method is particularly useful in determining optimum operational parameters for an analytical system which requires the automated analysis of large numbers of analyte data peaks. For example, the method can be used to optimize analytical systems including an ion mobility spectrometer that uses a temperature stepped desorption technique for the detection of explosive mixtures.
1. A method of multi-dimensional moment analysis for the characterization of signal peaks, comprising:
measuring two or more signal peaks having at least two different dimensions of an analytical system comprising an ion mobility spectrometer with a preconcentrator;
calculating a zero moment for each of the signal peaks;
calculating a first moment in each dimension for each of the signal peaks;
calculating a second moment in each dimension for each of the signal peaks; and
selecting an operating parameter of the analytical system based upon a ratio of the first and second moments of each signal peak wherein each signal peak is a two-dimensional signal peak with the first dimension comprising the drift time in the ion mobility spectrometer and the second dimension comprising the real time desorption from the preconcentrator.
2. The method of claim 1 , wherein the real time desorption comprises temperature stepped desorption from two or more heating steps of the preconcentrator.
3. The method of claim 1 , wherein the ion mobility spectrometer further comprises a gas chromatograph.
4. The method of claim 1 , wherein each signal peak is a two-dimensional signal peak and the zero moment is calculated according to
M
r
0
=
M
d
0
=
∫
t
r
=
-
∞
t
r
=
∞
∫
t
d
=
-
∞
t
d
=
∞
C
(
t
d
,
t
r
)
ⅆ
t
d
ⅆ
t
r
,
where C is the signal as a function of a first dimension t d and a second dimension t r .
5. The method of claim 4 , wherein the first moments are calculated according to
M
r
1
=
t
r
_
=
∫
t
r
=
-
∞
t
r
=
∞
∫
t
d
=
-
∞
t
d
=
∞
t
r
C
(
t
d
,
t
r
)
M
r
0
ⅆ
t
d
ⅆ
t
r
M
d
1
=
t
r
_
=
∫
t
r
=
-
∞
t
r
=
∞
∫
t
d
=
-
∞
t
d
=
∞
t
d
C
(
t
d
,
t
r
)
M
d
0
ⅆ
t
d
ⅆ
t
r
.
6. The method of claim 5 , wherein the second moments are calculated according to
M
r
2
=
σ
r
2
=
∫
t
r
=
-
∞
t
r
=
∞
∫
t
d
=
-
∞
t
d
=
∞
(
t
_
-
t
r
)
2
C
(
t
d
,
t
r
)
M
r
0
ⅆ
t
d
ⅆ
t
r
M
d
2
=
σ
d
2
=
∫
t
r
=
-
∞
t
r
=
∞
∫
t
d
=
-
∞
t
d
=
∞
(
t
_
-
t
d
)
2
C
(
t
d
,
t
r
)
M
d
0
ⅆ
t
d
ⅆ
t
r
.
7. The method of claim 6 , wherein the ratio of the first and second moments comprises a Péclet number that is calculated according to
Pe
=
2
(
t
_
d
2
t
_
r
2
σ
r
2
t
_
d
2
+
σ
d
2
t
_
r
2
)
.
8. The method of claim 7 , wherein the step of selecting comprises selecting the operating parameter of the analytical system corresponding to the signal peak having the highest Péclet number.