Digital Signal Processing Reference
In-Depth Information
gal concern, and for this reason clinicians have to err on the side of caution.
Substituting one doubtful test with another leads to no greater certainty in
clinical decision making” (p. 467).
We emphasize here that estimates of metabolite concentrations, including
those of Ref. [343], were mainly obtained via integration of the areas under
the peaks in the Fourier absorption spectra. This procedure is subjective since
lower and upper integration limits are not unequivocally defined. Integration
of peak areas is particularly troublesome when the peaks overlap. This has
been termed “spectral crowding”, which is known to create quantification
problems [346]. It should be pointed out that concentrations of adjacent
resonances such as threonine (1.33 ppm), lactate (1.41 ppm) and alanine (1.51
ppm) and the nearly overlapping resonances isoleucine and valine in the region
of 1.02 ppm to 1.04 ppm appear to be of major importance for distinguishing
benign and cancerous ovarian specimens. Thus, with respect to MRS applied
to ovarian cancer diagnostics, exact, unequivocal quantification is needed not
only for spectra whose peaks are completely distinct, but also especially for
spectra with overlapping resonances. We will now examine how the fast Pade
transform can advantageously be used to tackle this clinically urgent task.
9.3
Pade versus Fourier for in vitro MRS data derived
from benign and malignant ovarian cyst fluid
In Refs. [27, 29] we examined the performance of the FPT applied to time
signals as encoded in vitro from benign and malignant ovarian cyst fluid at a
magnetic field strength of B
0
≈14.1T in a 600 MHz NMR spectrometer from
Ref. [343]. We synthesized two FIDs of the type c
n
=
K
k=1
d
k
e
inτ ω
k
via a
sum of K = 12 damped complex exponentials exp (inτω
k
) (1≤k≤12), as
in (3.1), with the timeindependent amplitudes d
k
. These time signals were
subsequently quantified using the FPT, as described in [10].
The input data for the spectral parameters were derived from the median
concentrations{C
k
}
1
k=1
(expressed in M/L) of twelve metabolites charac
teristic of benign ovarian cyst fluid from Ref. [343]. These concentrations
reported in Ref. [343] were based upon twentythree patients with benign
ovarian cysts. On the other hand, the concentrations related to malignant
ovarian cysts correspond to the median values from twelve patients, as given
in Ref. [343]. These latter quantities are used as the input data for the
malignant case.
Table 9.1
displays all the mentioned input data.
In Ref. [343] the time signals were recorded at a bandwidth of 6667 Hz.
The inverse of this bandwidth is used for the sampling time τ in the presently
synthesized FIDs. The total signal length N from Ref. [343] was selected
in accordance with the Fourier resolving power ω
min
= 2π/T. This latter
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