Exploratory Data Analysis Reveals Spatio-temporal
Structure of Null fMRI Data
R. Baumgartner, L. Ryner, R. Somorjai, R. Summers
Institute for Biodiagnostics, National Research Council Canada, Winnipeg, Manitoba, Canada
Introduction:
Exploratory data analysis (EDA)
as developed
in computational statistics (2) provides methods for exploration of
multidimensional data structures. It is conceptually different from
the classical statistical confirmatory methods as it aims to let the
data speak for itself. However, once the structure of the data is
revealed, the question must be asked: do the structures arise only
by chance, or do they actually reflect some real effect? Here we
investigated the application of EDA tools to in vivo fMR1 data
analysis in a systematic study with varying sampling rate. fMR1
data were acquired under the null hypothesis, i.e. no activation.
Materials and Methods Water phantom: Five (2D) data sets were
acquired with the following
parameters: FAITEIMA
=
60/50/128x128, and with TR variation TR = 334/625/1250/2500
ms (note that TR may be considered as the sampling frequency of
the physiological effects).
In vivo fMR1 data acquired under null condition: Three healthy
subjects were investigated. For each subject, five in vivo data sets
were acquired with the same parameters as for the water phantom.
EDA (PreprocessineX3): Our aim was to divide the fMR1 timecourses (TCs) into two groups. The first group consisted of those
TCs that are contaminated by white noise and the second
comprised TCs that were either contaminated by colored
(physiological) noise or contain the signal of interest. To separate
the two types of TCs the l-lag (rl) and 2-lag (r2) Pearson
autocorrelation coefficient was calculated for each TC. Then a rlr2 plot was created (the horizontal and vertical axes correspond to
rl and r2, respectively). For white data this plot is symmetrically
distributed in a disk around the origin of the coordinate system.
Spatial distribution of the non-white TCs was also displayed.
Fuzzv Clustering EDA (4,5) was applied in the time domain only
to those TCs that survived the preprocessing step, in order to
investigate their temporal behaviour across the TR range.
Results and Conclusion: In Fig. 1 the rl maps obtained from the
in vivo data for the TRs: (a) 3500, (b) 2500, (c) 1250, (d) 625, (e)
335 are displayed. Note that for in vivo data, the spatial pattern of
the pixels contaminated by “physiological” noise is similar and
yields overlapping regions across the whole TR range and the area
contaminated comprises mostly grey matter. The rl-map for the
water phantom (f) (TR=2500) is also displayed. There is no spatial
(4
(4
(b)
(cl
(4
0-J
(4
(e)
(f)
Fig. 2 The rl-r2 plots for the in vivo data (a,b,c,d,e) as in Fig. 1 and
the water phantom (f). Arrows point to the regions where the rl-r2
plots are deformed due to colored noise.
In Fig. 2 the rl-r2 plots for in vivo data (a,b,c,d,e as in Fig.1) and
the water phantom (f) are shown. The rl-r2 plot for the water
phantom is symmetrically distributed around the origin of the
coordinates (OC). For in vivo data the rl-r2 plots are deformed
and contain of two parts. One which is symmetrically distributed
around the OC as in the case of water phantom and another one
which appears as a tail in the upper right corner of this plot. These
points correspond to the pixels highly contaminated by
autocorrelated physiological noise. To identify them a threshold
based on statistical significance of the rl was used (p-value=0.05).
The TCs of the survivors were used as an input to FCA. For all
subjects investigated KA was able to dctcct various kinds of
physi&giutl
noise artifacts for each ‘I’R and consistent tendencies
could be identified. For low TR (high sampling fi’cqucncy),
brcatbing and heart beat artifacts wcrc identified, The higher the
TR, the more the ‘KS were contaminntcd by trends. As tbc regions
co~~t~lt~iliate(iacross rhc ‘IX range overlap, this suggests aliasing
from bigher freyttcncics as the sampling rate (TR) approaches the
Nyquist bar&. Systematic inv~sti~~ltior~of Abealiasillg paitefns in
fMR1 time-series is an importtmt challenge for better identification
of “true activations” in f?vlRl (6). WC showed that iii&based
methods that do not require prior knowledge about ‘the temporal
shapes of the ‘KS offer valuable toois for MR time-series (spatiotemporal) artifact detection.
References
1. Tukey J, Exploratory Data Analysis, Addison-Wesley, 1977.
2. Buja A, Tukey P, Computing and graphics in statistics, SpringerVerlag, 1991. http://www.research.att.com/-andreas
3. Somorjai R, JarmaszM, Baumgartner R, ISMRMP9, Philadelphia,
1999.
4. Somorjai R, Jarmasz M, Baumgartner R, NeuroImage, submitted,
1999.
5. JarmaszM, Somorjai R, ISMRMPI, Sydney, 1998, 2068. Evident a
3D analysissoftware package,
http: //www.ibd.urc.ca/informaGcs
6. Mayhew J, Hu D, Zheng Y, et al. NeuroImage, 7,49-71,1998
Fig. 1 The rl-maps for the in vivo data TR= (a) 3500, (b) 2500,
Proc. Intl. Sot. Mag. Reson. Med. 8 (2000)
(c) 1250, (d) 665 (d) and (e) 335 ms. The water phantom rl-map
(f) is also displayed.
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