University of Illinois at Chicago

Correspondence should be addressed to:

Jerry Sychra, Ph.D.

Dept. of Radiology

University of Illinois

1740 W. Taylor St.

Chicago, Illinois 60612

Email *jsychra@uic.edu*

Submitted for publication: October 15, 1998

Keywords: voxels, image noise, Monte Carlo analysis, brain mapping

ABSTRACT

When voxel values of a small tumor or of a brain activation are very low it is difficult to distinguish them from the random image noise. A tumor or an activation is usually represented by a cluster of voxels. Consequently, when the probability of an observed cluster being formed by noise is negligible, the cluster can be interpreted as a result of a deterministic process. The probability of a cluster generated by random noise is associated with the spatial autocorrelation of the noise. Assuming that the image noise is a Gaussian random field, we have used Monte Carlo approach to calculate cluster probabilities for selected autocorrelation values. The obtained results can be used by the reader to detect tumors or activations in actual images.

INTRODUCTION

In many 2-D or 3-D functional images the sought
after event (e.g., brain activation, tumor) is represented by a small cluster
of voxels with elevated intensity. Often, the corresponding intensity threshold
is close or even lower than the intensity of the most noisy voxels. When
the voxel intensity alone can not be used for the detection of the event,
it is the clustering tendency of the event's voxels that may aid the image
analysis. However, random noise may also form clusters of elevated intensity.
Consequently, the mere existence of a cluster can not be used to confirm
an event if there is a significant probability that the cluster is a result
of noise. In this article we present two Monte Carlo based methods for
the estimation of the probability that a cluster is formed by noise.

A significant amount of published work ^{1-3} has
approached this problem in the analytical mathematical direction. We have
chosen a Monte Carlo approach for its (1) flexibility of modeling the noise
process, ROI size and shape, and of the cluster defining voxel connectivity,
and (2) because it does not depend on constraining assumptions that are
needed to simplify mathematical derivations. Admittedly, our approach is
computationally more demanding.

MATERIALS AND METHODS

**where
_{o}^{2}
is the noise variance and
is the Kronecker delta. (In case of 2-D images the relationships above
can be modified by dropping the third dimension).**

We have calculated (see below) estimates of the probabilities P and P' by the Monte Carlo method on circular ROIs of about 10,000 pixels. One can show that if the size of the ROI is moderately changed with only a small change of its shape (for example, by changing the ratio of the ROI area and of the square of its boundary length only slightly

**
RESULTS AND CONCLUSIONS**

Intuitively, when the event probability is very small (say, less than 0.01), doubling or halving both the number of thresholded voxels and the size of the ROI results in approximately doubling or halving the event probability on the new ROI, respectively. Using the approach described above we have calculated (

In the actual data acquisition the autocorrelation values depend on the scanner's parameters. For an illustration, we have scanned calf brains in a plastic jar by GE SIGNA 1.5 T MRI scanner with EPI pulse sequence, TR= 1066 ms, TE= 60 ms, 3 slices (thickness 7 mm, gap 1 mm), image size 64x64 pixels, FOV = 220 mm , total of 170 images of each slice in the sequence. The first four images of each slice were excluded from the analysis. After subtracting the time-average image to remove the "deterministic component", and after we defined relatively large brain ROIs (1100 to 1200 pixels) on each slice, the following average autocorrelation values in brain ROIs were found: c

To make our results easier to use by the reader we have generated a relatively large number of graphs of the cluster probabilities. The actual IDL computer code used in the Monte Carlo simulation is available on request by e-mail from jsychra@uic.edu. It permits the user to enter an arbitrary combination of c

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The authors wish to express their thanks to Drs. M. Mafee and D. Hier for their support, and to Dr. D. Fiat for his advice. This work has been also supported by internal UIC Neuro-science grant and by Cytogen, Inc..

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