Fractal correlation structure in fMRI data of rat brain

Abstract

The raw fMRI data are normally analyzed by statistical methods (Student's t or non-parametric tests) to yield measures of physiological responses. This analysis assumes that successive events in the raw signal are independent (white noise) 1 and hence have a Gaussian distribution. Colored noise if present in the dynamic fMRI data can cause high rate of false positives 2. Such positive correlations have been reported in human fMRI data 1, 2 which are characterized by a spectrum with increasing power toward the low frequencies (1/f pattern). This 1/f pattern can be numerically characterized by a fractal parameter, the Hurst exponent, H. The fMRI experiments of the a-chloralose (40 mg/kg/hr) anesthetized rats (n=12) were conducted on a 4.0 T or 9.4 T spectrometer using a 1 H resonator/surface-coil radio-frequency probe 3 and echo-planar imaging (EPI). Gradient-echo EPI data were acquired with repetition time of 200 ms in matrices of 3232 (4.0 T) and 6464 (9.4 T). Data were collected in vivo and post mortem. Scaled windowed variance (SWV) method 4 was used to calculate the fractal parameter, H and the nearest neighbor correlation coefficient, r1 5 from the fMRI time series. The length of the time series, 4096 scans (4.0 T) and 8192 scans (9.4 T), were adequate for a reliable estimation of H 6. The fMRI data from the 4.0T magnet was dominated by white noise with H=0.530.014. All 9.4 T fMRI time series showed fractional Gaussian noise (fGn) with H>0.5, different from white noise. The H of fGn within its lower and upper bounds of 0 and 1 characterizes the correlation structure itself: with H=0.5 the signal is random, H 0.5 indicates correlation with positive r1 6. Representative Hurst exponent maps obtained in vivo and post mortem were obtained for both 4.0 T and 9.4 T. In vivo cortical and subcortical gray matter regions exhibited much higher values of H (0.730.05) with r1=0.38 than white matter regions (H=0.570.01, r1=0.10). The post mortem results showed a significant (p<0.05) decrease in fractal structure obtained in both gray and white matter regions (H=0.610.03 and H=0.560.03, respectively) and the fractal or colored noise correlation structures were mainly broken in the gray matter regions (r1=0.17). High magnetic field fMRI data reveal fractal patterns across different brain regions. These findings should have implications in fMRI data processing: successive events of the fMRI signal are correlated hence statistical mapping should be used with prior treatment of data, such as creating surrogate time series, which destroys the correlation structure in a time series without the modification of actual values 7.