AveLI: A robust lateralization index in functional magnetic resonance imaging using unbiased threshold-free computation

Abstract

The laterality index (LI) is often applied in functional magnetic resonance imaging (fMRI) studies to determine functional hemispheric lateralization. A difficulty in using conventional LI methods lies in ensuring a legitimate computing procedure with a clear rationale. Another problem with LI is dealing with outliers and noise. We propose a method called AveLI that follows a simple and unbiased computational principle using all voxel t-values within regions of interest (ROIs). This method first computes subordinate LIs (sub-LIs) using each of the task-related positive voxel t-values in the ROIs as the threshold as follows: sub-LI = (Lt − Rt)/(Lt + Rt), where Lt and Rt are the sums of the t-values at and above the threshold in the left and right ROIs, respectively. The AveLI is the average of those sub-LIs and indicates how consistently lateralized the performance of the subject is across the full range of voxel t-value thresholds. Its intrinsic weighting of higher t-value voxels in a data-driven manner helps to reduce noise effects. The resistance against outliers is demonstrated using a simulation. We applied the AveLI as well as other “non-thresholding” and “thresholding” LI methods to two language tasks using participants with right- and left-hand preferences. The AveLI showed a moderate index value among 10 examined indices. The rank orders of the participants did not vary between indices. AveLI provides an index that is not only comprehensible but also highly resistant to outliers and to noise, and it has a high reproducibility between tasks and the ability to categorize functional lateralization.

Introduction

One prominent contribution of functional magnetic resonance imaging (fMRI) is the ability to quantitatively measure hemispheric lateralization in a noninvasive manner (Desmond et al., 1995, Binder et al., 1995, Cuenod et al., 1995, Gaillard et al., 1997). Such measurement is usually referred to as a laterality index (LI) or lateralization/asymmetry index. LIs have been used frequently as a substitute for the Wada test (Wada and Rasmussen, 1960, Wada, 2009), which classifies patients as left or right lateralized for language and memory (but see Meador, 2004). The asymmetry degree indicated by LI can be utilized in correlation studies such as predicting rates of recovery of limb movement (Naccarato et al., 2006, Calautti et al., 2007, Calautti et al., 2010), verbal memory decline after epilepsy surgery (Binder et al., 2008), and postoperative naming deficits (Powell et al., 2008). Another advantage of the LI is increased spatial resolution to the voxel level (Liegeois et al., 2002), which can be helpful in pre-surgical planning (Powell and Duncan, 2005, Sunaert, 2006, Tieleman et al., 2009, Giussani et al., 2010, Mehta and Klein, 2010, Binder, 2011). However, the introduction of the LI has also yielded a series of computational problems (Wilke and Lidzba, 2007, Seghier, 2008). One of the intrinsic problems is the lack of a full rationale for deriving the LI. We propose an intuitively comprehensible LI that indicates how consistent lateralized activation is across all voxel t-value thresholds.

Three primary issues are to be considered in the computation of an LI: the computational unit, activation thresholding, and the computing procedure. First, two measures are conventionally applied to define the computational unit: activated voxel number and t-value summation (Jansen et al., 2006, Wilke and Lidzba, 2007). A frequently used LI counts the number of “activated” voxels that reach a certain statistical threshold, such as p < 0.001, across the statistical parametric map (SPM) of the regions of interest (ROIs) for the left and right hemispheres. These voxel numbers are entered as the terms “Left” and “Right” into the formula (Left − Right)/(Left + Right) (Desmond et al., 1995). However, if we consider a case with equal numbers of activated voxels in each hemisphere but with higher t-values in the left, a measure of t-values instead of activated voxel numbers appears to be more reasonable because it would reflect the greater task-related activation in the left hemisphere. Second, the thresholding of activation is a problem because we often observe a failure of activation in a number of patients at predefined SPM thresholds. To address this problem, researchers often individually customize the threshold. For example, some researchers use half of the mean value of the t-values of the top 5% of activated voxels (Fernández et al., 2001, Calautti et al., 2007), or the mean intensity (Wilke and Lidzba, 2007). A challenge of these procedures is finding a legitimate algorithm using these specific parameters. The definition of the t-value threshold is crucial because the LI varies considerably with the threshold (Fig. 1) (Wilke and Lidzba, 2007, Jones et al., 2010). This difficulty can be addressed by developing a method that does not set a threshold for the t-values.

The last difficulty with the LI is the rationale for the formula used in its computation. The non-thresholding methods proposed so far have included empirical and/or arbitrary techniques without fully supported justifications. Nagata et al. (2001) used the coefficients of an empirically derived approximate equation for the voxel z-score distribution. Others created voxel distributions based on weighted statistical values (Branco et al., 2006, Suarez et al., 2009). The main aim of the weighting is to reduce noise products at lower t-values, but it is important to note that this weighting is arbitrarily defined. A “bootstrap” method that uses resampling and iterated computations from ROIs was also proposed (Wilke and Schmithorst, 2006). The authors actually used only the central 50% of the generated LI histogram in their paper, but it is possible to use the entire range. Jones et al. (2010) examined histograms of t-values from whole hemispheres and analyzed deviations from a normal distribution to provide a faster and more practical method for use prior to surgeries. Another idea was to examine the deviation of voxel number distributions from a normative subject group (Abbott et al., 2010); estimations of the normative data are necessary in advance. Another interesting method uses the spatial coherence of fMRI signals and assumes that the side with more coherent signal changes in the ROI reflects greater lateralization (Wang et al., 2009). This method proposed by Wang et al. touches upon a new aspect of brain activation and needs to be compared further with other LIs.

Here, we propose a comprehensible and rational LI called AveLI that uses the sum of t-values as the computational unit and employs t-values in all voxels for the thresholding.