Biomedical Engineering Reference
In-Depth Information
25.3.2
Limitations of the FFT in radiation oncology
of the prostate
There are also a number of problems with the current reliance upon ratios of Cho to
citrate for prostate cancer assessment. On the one hand, as mentioned, low citrate is
seen in normal stromal prostate, and in metabolic atrophy. Moreover, high citrate is
usually observed in BPH, even with coexistent malignancy [
14
]. Other limitations
of current applications of MRS and MRSI in prostate cancer diagnostics include
poor resolution and lack of consistent added diagnostic value when used with
MRI [
2
]. Notwithstanding progress in coil design and other technological advances,
resolution remains an important drawback to wider application of MRSI for prostate
cancer diagnostics and management. Attempts to improve resolution and SNR by
increasing the static magnetic field strength are noted to affect the spectral shape of
citrate and its ratio to choline, and thus are considered of questionable benefit [
15
].
Another drawback of Fourier-based MRSI is low sensitivity for detecting smaller
prostate cancers [
2
].
25.4
Optimal solutions via advanced signal processing
by the fast Pade transform
The FPT is an advanced signal processor, particularly appropriate for
in vivo
MRS
and MRSI [
1
,
2
,
4
,
16
]. The FPT is a high-resolution, parametric estimator, which
unequivocally determines the true number
of metabolites. It exactly reconstructs
the spectral parameters from which metabolite concentrations, including those
from very tightly overlapping resonances, can be reliably computed [
2
,
16
]. Once
the spectral parameters, such as the fundamental frequencies and the associated
amplitudes
K
f!
k
;d
k
g .1 k
K/
of the given time signal
fc
n
g .0
n
N 1/
have been retrieved, the
corresponding complex-valued total shape spectrum is automatically generated via
P
kD1
d
k
=.
of length
N
and sampling time
D
T=N
z
1
z
k
/ W
X
X
z
1
/
d
k
z
1
P
K1
.
d
k
z
k
c
n
D
H)
D
:
(25.1)
z
1
k
z
1
/
Q
K
.
kD1
kD1
e
i!
;
e
i!
k
;
Here,
z
D
z
k
D
Im
.!
k
/>0;!D 2; !
k
D 2
k
where
!
and
are angular and linear frequency. In (
25.1
), the spectrum
P
kD1
d
k
=.
z
1
z
k
/
is explicitly summed up to give the polynomial quotient
P
K1
=Q
K
which is the
para-diagonal Pade approximant. Also frequently employed is the diagonal Pade
approximant,
P
K
=Q
K
:
The Pade approximant, or the fast Pade transform, as alternatively called in
signal processing, is long known as the work-horse of theoretical physics, including
quantum mechanics. Therefore, the FPT is the method of choice for spectral analysis
