Currently available methods on resting-state fMRI time-series use spatiotemporal information to produce spatial maps of functional brain abnormalities. Some methods rely on the correlation of time-series between different brain regions (functional connectivity), while others analyze the harmonic frequency spectrum of brain fluctuations. However, so far, the temporal characteristics, in particular irregularities, of the time-series, have not been studied yet. For the current study, we present a novel method that yields a “temporal homogeneity” (TeHo) measure, which captures temporal abnormalities of Blood-Oxygen-Level-Dependent (BOLD) time-series as changes in wavelet energy entropy (i.e. order/disorder) as a function of frequency. As an application we have analyzed abnormalities in the resting-state BOLD time-series of children with Rolandic epilepsy. For epilepsy in general it is known that the brain may express abnormal dynamic fluctuations either as epileptiform or direct seizure activity. We used wavelet analysis (i) to determine the frequency structure of the resting-state time-series signal in patients relative to healthy controls and (ii) to find neuronal correlates with the typical decrements in language function¹.

Data Acquisition: We included children with Rolandic epilepsy (n=22, age 8-14years) and age matched healthy controls (n=22). Resting-state fMRI data were acquired with a 3.0-Tesla unit using an echo-planar imaging (EPI) sequence with the following parameters: TR=2s, TE=35ms, Flip Angle 90°, 31 transverse 4-mm thick slices, and 195 dynamic volumes. For anatomical reference and tissue segmentation, a fast spoiled gradient echo T1-weighted image set was acquired.

Image processing: The functional images were slice-time and motion corrected, co-registered to the anatomical template and smoothed with an 8-mm Gaussian kernel (SPM8 software). To correct for non-neurophysiological fluctuations, the time-series from the cerebrospinal fluid and white matter were included as co-variates in the linear regression analysis. Gray matter, white matter, and cerebrospinal fluid voxels were segmented from the T1-weighted images (Freesurfer) to obtain the specific time-series signals. The Rolandic strip (pre and post-central cortex) and known language regions (parsopercularis and supramarginal) were segmented to infer on any abnormalities in these regions.

Temporal homogeneity: Each time-series was decomposed into different wavelet subbands using the Daubechies-4 wavelet full tree decomposition (upto 3 levels)². The wavelet coefficients/subbands (S_j) of the lowest (<31mHz) and highest (>188mHz) subbands were excluded from analysis to avoid contamination of slow signal drifts and aliasing artifacts, respectively. The method to compute TeHo is as follows:

Let S_j(k) represent the time-point k of subband j. Energy E_j in subband j will be given as $$$E_j=\sum_{k=1}^N{S_j(k)}^2$$$, where N is the number of time-points per subband. The total energy over all the subbands is given as $$$E_T=\sum_{j=1}^5{E_j}$$$ and the wavelet energy entropy (WEE)^3,4,5 for a subband j is computed as $$$WEE_j=-({E_j}/{E_T})log({E_j}/{E_T})$$$. The absolute value of average decrease of WEE as a function of wavelet subband(1-5) is defined as the temporal homogeneity (TeHo).

A complete random signal will have wavelet representation with same energy over all subbands, hence WEE will be same in all subbands and TeHo will be zero. On other hand a wavelet representation of a signal with a contribution to only one subband (j), thus shows no distribution, WEE will be zero (as log(E_j/E_T)=log(1)=0). However, a typical BOLD signal reflects a frequency structure in which energy roughly decreases as a function of frequency (subband)³. When the distribution of energies over frequency subbands becomes more equal (i.e. more random), the variation of WEE over subbands decreases and thus TeHo decreases.

Wavelet subbands from patients and controls as a function of time are shown in figure 1. TeHo, in patients is lower than for controls, indicative of altered frequency structure in patients (figure 2). TeHo values are listed in table 1. In patients, both the left and right hemispheres showed significantly decreased TeHo relative to controls(p<0.05). In patients, the right Rolandic strip, left parsopercularis and right supramarginal region had significantly reduced TeHo(p<0.05). Neither in the Rolandic strip nor the language regions did TeHo show any significant (Pearson) correlation with patients’ (core) language scores.

The temporal homogeneity method was found sensitive to detect abnormal cerebral fluctuations in BOLD time-series in children with Rolandic epilepsy. These patients showed reduced temporal homogeneity, which indicates altered, more random, frequency structure due to epilepsy. Temporal homogeneity was reduced in patients in the right Rolandic strip, left Broca and right Wernicke areas, which was also reported in literature using functional connectivity based measures⁶ in the same patients. This study presents a novel technique for quantifying BOLD fluctuations in brain time-series due to epilepsy. Results on Rolandic epilepsy patients are encouraging and in future, the proposed technique could be explored on different epilepsies.