Figure 3. Log-log plot of simulated oscillating phantom, assuming a Gaussian-shaped field. Field constants a1=a2=0.1. The data initially plateau,

then at larger n curve back toward the theoretical best.

Study of Scanner Stability in Functional Magnetic Resonance ImagingDepartment of Physics, CWRU, 10900 Euclid Ave.,

Cleveland, Ohio 44106

Lisa BauerAdvisor: Robert Brown

Abstract

While traditional Magnetic Resonance Imaging is used to visualize the structure of the body, Functional Magnetic Resonance Imaging (fMRI) measures neural activity in the brain and spinal cord, providing a mechanism to study brain function. In order to detect brain activations (intensity changes as small as a few percent), fMRI requires that the scanner be sensitive and consistent. However, scanner drift and hardware imperfections introduce systematic error, which, if large enough, may significantly degrade the contrast-to-noise ratio and define a lower limit of detection. This project seeks to gain a better understanding of MR scanner instability as it pertains to fMRI experiments, and the main objective is to understand and model potential sources of instability. Using MatLab, I have written a program that models motion in the system, and have examined its effect on simulated fMRI data. We were then able to compare results of the simulation to data from stability experiments.

Introduction Magnetic Resonance Imaging (MRI) is realized by the properties of a spinning proton (a small magnetic moment, or “spin”). MRI correlates signal measurements with spatially encoded frequency components by applying a gradient magnetic field Gx. Signals with spatially varying frequencies are produced according to x=Gx, where is the gyromagnetic ratio. Fourier transforms are used to “invert” information from signal space to position space, after which an image can be reconstructed. Functional MRI (fMRI) is a relatively new technique used to study neural activity in the brain and spinal cord. When a region of the brain is activated, it causes small signal intensity changes (~0.5-3%). An fMRI experiment requires consistency in the scanner; trials may last for days or weeks. In reality, scanners drift over time (even between image acquisitions), and hardware imperfections may vary site-to-site. Even when usual performance indicators (such as the signal-to-noise ratio) are consistent, there may be significant image intensity fluctuations across a series. These fluctuations have the potential to degrade the contrast-to-noise ratio, which is a measure of the “usefulness” of an experiment.

Acknowledgements This project would not have been possible without the guidance, advice, and generosity of Prof. Robert Brown. In addition, I owe many thanks to Minhua Zhu for her insight and assistance with finding and analyzing data. I am incredibly grateful for the time both have shared with me. Thanks also goes to Michael Steckner and Toshiba Medical Research Institute of Cleveland, Ohio, who allowed me the use of data from stability experiments. I enjoyed having the opportunity to visit and observe experiments.

Figure 1. Log-log plot of data from actual stability experiment. Deviation from the theoretical best is

observed, as well as a plateau in the relative fluctuation.

Methods

The goal of this project is to compare data from stability experiments that (supposedly) induced correlated noise to simulations that model potential sources of instability. Two potential sources (that are easy to model) are translational and oscillatory motion. A simulation program was written (in MatLab), that generates a phantom and assumes it is moving. The Weisskoff analysis was then performed for both types of motion. Next, a spatially varying magnetic field was added for each type of motion.

Conclusions

We have been able to model translational and oscillatory motion, as well as varying magnetic fields. We have studied their effects on simulated phantom data and compared that to actual data from stability experiments. It is evident that motion in the phantom plays a role in experiment stability, but it is more likely that the shape of the magnetic field plays a greater role. This is supported by experimental data.

Figures 2a and 2b. As a simple example (and to try the Weisskoff analysis), I tracked 100 students leaving Nord and recorded their

gender. I divided the list into groups of 10 students and calculated the fluctuation function for n students in each group (n=1, first student; n=2,

first two students, etc.).

Figure 2a. 100 successive students. The deviation of Fn suggests student are correlated, which is in fact what the record shows. (Groups

of 3 males/females were common.)

Figure 2b. 100 students, waiting 10 seconds in between each, so that students are independent of each other.

Fluctuation Measurement

Define a relative fluctuation

Fn=n/mn

where mn is the average mean signal of an nn region of interest (ROI) across a time series of images (length j=1:N)

mj=(1/n2)sigj

mn=(1/N)mj

and n is the standard deviation

n=(1/N)(mn-mn)2

If there were only random noise in the system, Fn should fall as 1/n. In reality, it deviates from theory, suggesting there is correlation between pixels. From this we can conclude that the scanner is introducing correlated noise.

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Weisskoff Simulation

Translational and oscillatory motions are a possibility; they add the same noise to all pixels. For a boxcar phantom moving in one direction, motion is reflected as an additional phase in the Fourier transform to signal space:

S(k) = (x')exp(-2ikx')exp(2ick2)dx’The same is true for an oscillating phantom, although the phase is different:

S(k) = (x')exp(-2ikx')exp[2iAcos(Ck)]dx'where c, A, and C are constants. These phases were treated as sources of correlation in the Weisskoff simulation program.

The shape of the magnetic field was also taken into consideration. If the field is not constant across all space, as spins move they will be subjected to a varying magnetic field. This was implemented in simulations by using a Gaussian-shaped field, multiplying the original signal by:

exp(-a1kx2)*exp(-a2ky

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