Method for determining atomic isotope masses
A method for determining atomic isotope masses in mass spectrometry, atomic isotope ratios being determined from molecular isotope ratios measured by means of an isotope mass spectrometer—ion correction, the determination of the atomic ratios being carried out by setting up and solving a system of equations which describes relationships between the atomic and the molecular ratios, and the system of equations having to have at least as many independent equations as there are atomic ratios. The entire system of equations is linearized by means of suitable numerical methods in a first step, in particular by means of a Taylor expansion or similar method, and in which the linearized system of equations is subsequently solved as a whole without transforming the individual equations.
1. A method for determining atomic isotope masses in mass spectrometry, in which atomic isotope ratios are determined from molecular isotope ratios measured by means of an isotope mass spectrometer—ion correction, the determination of the atomic isotope ratios being carried out by the steps of:
a) setting up and solving a system of equations which describes relationships between the atomic isotope ratios and the molecular isotope ratios, wherein the system of equations have at least as many independent equations as there are atomic isotope ratios
b) linearizing the entire system of equations by means of suitable numerical methods in a first step; and
c) subsequently solving the linearized system of equations as a whole without transforming the individual equations.
2. The method as claimed in claim 1 , wherein, in order to standardize the measurements, molecular ratios are determined from standard values of atomic ratios—inverse ion correction, the same linearized system of equations being used both for the inverse ion correction and for the ion correction.
3. The method as claimed in claim 1 , wherein the system of equations before the linearization is of the form F({right arrow over (R mol, R at, )})=0.
4. The method as claimed in claim 1 , wherein, for the determination of the iron correction, the linearization of the system of equations is carried out with the effect of a Taylor expansion with respect to an initial vector {right arrow over (R at 0 )}.
5. The method as claimed in claim 1 , wherein, for the purpose of fast convergence of the method, the known atomic ratios of the standard are used as the initial vector {right arrow over (R at 0 )}.
6. The method as claimed in claim 2 , wherein, for the purpose of fast convergence of the method, the known atomic ratios of the standard are used as the initial vector {right arrow over (R at 0 )}.
7. The method as claimed in claim 3 , wherein, for the purpose of fast convergence of the method, the known atomic ratios of the standard are used as the initial vector {right arrow over (R at 0 )}.
8. The method as claimed in claim 4 , wherein, for the purpose of fast convergence of the method, the known atomic ratios of the standard are used as the initial vector {right arrow over (R at 0 )}.
9. The method as claimed in claim 4 , wherein the expansion with respect to the initial vector {right arrow over (R at 0 )} is of the form:
F
(
R
moi
,
⟶
R
at
,
⟶
)
≈
ⅆ
F
ⅆ
R
at
,
⟶
*
(
R
at
,
⟶
-
R
at
0
⟶
)
F
(
R
moi
,
⟶
R
at
0
⟶
)
.
10. The method as claimed in claim 9 , wherein, the slope vector
ⅆ
F
ⅆ
R
at
,
→
is determined from
δ
F
δ
R
at
,
j
→
=
F
(
R
mol
,
→
R
at
,
i
=
j
,
→
,
[
R
at
,
j
(
1
+
δ
]
)
)
-
F
(
R
mol
,
→
R
at
,
i
=
j
,
→
,
[
R
at
,
j
(
1
-
δ
)
]
)
2
δ
R
at
,
j
,
j
=
1
,
2
,
3
…
11. The method as claimed in claim 1 , wherein the linearized form of the equation in matrix notation is solved in accordance with the Gauss algorithm.
12. The method as claimed in claim 4 , wherein the linearized form of the equation in matrix notation is solved in accordance with the Gauss algorithm.
13. The method as claimed in claim 9 , wherein the linearized form of the equation in matrix notation is solved in accordance with the Gauss algorithm.
14. The method as claimed in claim 10 , wherein the solution of the slope vector is used as initial vector for a further iteration step.
15. An apparatus for determining atomic isotope masses in a mass spectrometer, having an input interface, a computing unit and an output interface, wherein:
data about molecular isotope ratios which can be measured by means of an isotope mass spectrometer is transmitted to the computing unit via the input interface,
atomic isotope ratios are determined from the data about molecular isotope ratios in accordance with a method for determining atomic isotope masses in mass spectrometry, atomic isotope ratios are determined from molecular isotope ratios measured by means of an isotope mass spectrometer—ion correction, the determination of the atomic isotope ratios being carried out by setting up and solving a system of equations which describes relationships between the atomic isotope ratios and the molecular isotope ratios, and the system of equations having to have at least as many independent equations as there are atomic isotope ratios, wherein the entire system of equations is linearized by means of suitable numerical methods in a first step and in which the linearized system of equations is subsequently solved as a whole without transforming the individual equations, and
the atomic isotope ratios are output via the output interface.
16. The apparatus as claimed in claim 15 , wherein, for the determination of the iron correction, the linearization of the system of equations is carried out with the effect of a Taylor expansion with respect to an initial vector {right arrow over (R at 0 )}.
17. The apparatus as claimed in claim 16 , wherein the expansion with respect to the initial vector {right arrow over (R at 0 )} is of the form:
F
(
R
moi
,
⟶
R
at
,
⟶
)
≈
ⅆ
F
ⅆ
R
at
,
⟶
*
(
R
at
,
⟶
-
R
at
0
⟶
)
F
(
R
moi
,
⟶
R
at
0
⟶
)
.
18. A computer program embodied on one or more computer readable media for controlling a computer to determine atomic isotope masses in mass spectrometry the computer program comprising:
program code for selling up and solving a system of equations which describes relationships between atomic isotopes ratios and molecular isotope ratios, and the system of equations has to have at least as many independent equations as there are atomic ratios;
program code for linearizing the entire system of equations by means of suitable numerical methods in a first step
program code for solving the linearized system of equations as a whole without transforming the individual equations; thereby producing a result determining atomic isotope masses in mass spectrometry,
wherein atomic isotope ratios are determined from molecular isotope ratios measured by means of an isotope mass spectrometer.
19. The computer program as claimed in claim 18 , wherein, for the determination of the iron correction, the linearization of the system of equations is carried out with the effect of a Taylor expansion with respect to an initial vector {right arrow over (R at 0 )}.
20. The computer program as claimed in claim 19 , wherein the expansion with respect to the initial vector {right arrow over (R at 0 )} is of the form:
F
(
R
moi
,
⟶
R
at
,
⟶
)
≈
ⅆ
F
ⅆ
R
at
,
⟶
*
(
R
at
,
⟶
-
R
at
0
⟶
)
F
(
R
moi
,
⟶
R
at
0
⟶
)
.
21. The method as claimed in claim 3 , wherein the system of equations before the linearization is of the form:
0
=
∑
i
=
1
i
max
n
i
R
(
m
i
+
1
)
-
R
(
1
+
∑
i
=
1
i
max
n
i
m
i
)
0
=
∑
i
=
1
i
max
n
i
R
(
m
i
+
2
)
+
∑
i
=
1
i
max
n
i
R
(
m
i
+
1
)
∑
j
=
i
i
max
njR
(
m
j
+
1
)
+
∑
i
=
1
i
max
Pos
(
n
i
-
1
)
R
(
m
i
+
1
)
2
-
R
(
2
+
∑
i
=
1
i
max
n
i
m
i
)
0
=
∑
i
=
1
i
max
n
i
R
(
m
i
+
3
)
+
∑
i
=
1
i
max
n
i
R
(
m
i
+
2
)
∑
j
=
i
i
max
njR
(
m
j
+
1
)
+
∑
i
=
1
i
max
n
i
R
(
m
i
+
1
)
(
∑
j
=
i
i
max
njR
(
m
j
+
1
)
∑
k
=
j
i
max
njR
(
m
j
+
1
)
)
+
∑
i
=
1
i
max
Pos
(
n
i
-
1
)
R
(
m
i
+
1
)
2
∑
j
=
1
i
max
n
j
R
(
m
j
+
1
)
+
∑
i
=
1
i
max
Pos
(
n
i
-
2
)
R
(
m
i
+
1
)
3
-
R
(
3
+
∑
i
=
1
i
max
n
i
m
i
)
0
=
.
.
.
22. The method as claimed in claim 1 , wherein the entire system of equations is linearized by means of a Taylor expansion or similar method.
23. The apparatus as claimed in claim 15 , wherein the entire system of equations is linearized by means of a Taylor expansion or similar method.