Breast cancer and non-malignant breast data: Quantification by FPT - Signal Processing in MRS with Biomedical Applications - page 311

proton MR visible compounds, namely: choline (3.21 ppm), PCho (3.22 ppm)
and GPC (3.23 ppm), thereby emphasizing the clinicobiological importance
of analyzing the relationship among these closely overlapping resonances. On
the other hand, by summing these three metabolites as “total choline”, as is
currently done with in vivo MRS, substantial information for breast cancer
diagnostics is missed.

10.4 Performance of the FPT for MRS data from breast

tissue

In the present analysis [32] the FPT is applied to time signals that are rem
iniscent of in vitro MRS data as encoded from extracted breast specimens
[395]. We generated three FIDs of the type c n =

K

k=1 d k e inτ ω k from (3.1),
where Im(ω k ) > 0. This was via a sum of K = 9 damped complex exponentials
exp (inτω k ) (1≤k≤9) with stationary amplitudes{d k }. We then quantified

time signals using the FPT, as described in [10].
For the normal noninfiltrated breast, we derived the input data for the
|d k |'s using median concentrations{C k } k=1 (expressed in M/g ww) of metabo
lites from the data of Gribbestad et al. [395], based upon tissue samples from
twelve patients. The input|d k |'s for benign breast tissue were derived from
the concentrations of the nine metabolites for a fibroadenoma from Ref. [395].
For breast cancer, we derived the input data for the|d k |'s from median con
centrations from the data of Ref. [395] for fourteen samples taken from twelve
patients. Two samples each were taken from two of the patients. In Ref. [395]
metabolite concentrations were computed in only six and nine malignant sam
ples respectively for the metabolites β−glucose and myoinositol.
The time signals from Ref. [395] were recorded with a static magnetic field
strength B 0 ≈14.1T (Larmor frequency of 600 MHz). We used a bandwidth

of 6 kHz (the inverse of this bandwidth is the sampling time τ) and set the
total signal length N = 2048.
We grouped the resonances into two bands, the first from 1.3 ppm to 1.5
ppm and the second from 3.2 ppm to 3.3 ppm. There were seven resonances
within the latter band, including two nearly degenerate resonances at 3.22
ppm. These were phosphocholine (k = 4) and phosphoethanolamine (k = 5)
separated by only 2.03×10 −4 ppm.
The input peak amplitudes{|d k |}were computed from the reported concen
trations{C k }using (3.15) via|d k |= 2C k /C ref where C ref = 0.05 M/g ww.
Also, TSP (3(trimethylsilyl) 3,3,2,2tetradeuteropropionic acid) was used as
the internal reference by Gribbestad et al. [395], such that|d k |= C k /(25M/g
ww). The T 2 relaxation times were not reported in Ref. [395].
The line widths, or more precisely, the full widths at half maximum, were