Digital Signal Processing Reference
In-Depth Information
Exact Reconstruction of Metabolite Concentrations by FPT
(−)
Using Only 64 FID Points from N = 1024 : Benign (Top) , Malignant (Bottom)
Curve (Absorption Total Shape Spectrum) , Symbols (Metabolite Concentrations : Input Data "x" , Pade−Reconstructed Data "o")
10000
Lac
Input Data:
ν
L
= 600 MHz
B
0
BENIGN
5000
(1.41 ppm,2479
µ
M/L ww)
3000
2000
≈
14.1T
(5.22,1387)
1000
Glc
Gln
Bandwidth = 6667 Hz
N = 1K = 1024
Ala
500
(2.47,275)
(1.51,293)
300
Val
Thr
200
(1.04,113)
Crn
Signal Processor:
FPT
(−)
(1.33,90)
100
(1.72,101)
(3.13,68)
Lys
(3.05,63)
50
Cr
30
N/16 = 64
20
Met
(3.19,15)
Converged
10
Cho
(2.13,7)
Iso
5
3
2
1
0.5
5
4.5
4
3.5
3
2.5
2
1.5
1
(i) Chemical shift (ppm)
Curve (Absorption Total Shape Spectrum) , Symbols (Metabolite Concentrations : Input Data "x" , Pade−Reconstructed Data "o")
10000
(1.41,6536)
Input Data:
ν
L
= 600 MHz
B
0
MALIGNANT
5000
Lac
3000
Gln
2000
≈
14.1T
(2.47 ppm,828
µ
M/L ww)
Ala
1000
Val
(1.51,586)
Bandwidth = 6667 Hz
N = 1K = 1024
(1.04,395)
Thr
500
(1.72,490)
(1.33,248)
300
Lys
(5.22,260)
200
Crn
Met
Glc
Signal Processor:
FPT
(−)
(3.13,79)
100
(2.13,62)
(3.05,66)
50
(3.19,42)
Cr
Iso
30
N/16 = 64
Cho
20
10
Converged
5
3
2
1
0.5
5
4.5
4
3.5
3
2.5
2
1.5
1
(ii) Chemical shift (ppm)
FIGURE 9.9
Absorption spectra at full convergence (N/16 = 64) achieved by the FPT
for the benign (top panel (i)) and malignant (bottom panel (ii)) ovarian cyst
fluid FIDs derived from the corresponding experimentally measured time sig
nals [343], with the retrieved chemical shifts and concentrations of the 12
metabolites indicated above the corresponding peak.
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