Groupwise spatial normalization of fMRI data based on multi-range functional connectivity patterns

Highlights

• fMRI data are registered by matching their local functional connectivity patterns.

• Groupwise image registration is achieved by warping images to an implicit template.

• Matching functional connectivity patterns of multiple ranges improves performance.

• The method improves functional consistency across subjects.

Abstract

Spatial alignment of functional magnetic resonance images (fMRI) of different subjects is a necessary precursor to improve functional consistency across subjects for group analysis in fMRI studies. Traditional structural MRI (sMRI) based registration methods cannot achieve accurate inter-subject functional consistency in that functional units are not necessarily located relative to anatomical structures consistently due to functional variability across subjects. Although spatial smoothing commonly used in fMRI data preprocessing can reduce the inter-subject functional variability, it may blur the functional signals and thus lose the fine-grained information. To overcome the limitations of exiting techniques, in this paper, we propose a novel method for spatial normalization of fMRI data by matching their multi-range functional connectivity patterns progressively. In particular, the image registration of different subjects is achieved by maximizing inter-subject similarity of their functional images' local functional connectivity patterns that characterize functional connectivity information for each voxel of the images to its spatial neighbors. The neighborhood size for computing the local functional connectivity patterns is gradually increased with the progression of image registration to capture the functional connectivity information in larger ranges. We also adopt the congealing groupwise image registration strategy to simultaneously warp a group of subjects to an unbiased template. Experimental comparisons between the proposed method and other fMRI image registration methods have demonstrated that the proposed method could achieve superior registration performance for resting state fMRI data. Experiment results based on real resting-state fMRI data have further demonstrated that the proposed fMRI registration method can achieve a statistically significant improvement in functional consistency across subjects.

Introduction

Functional magnetic resonance imaging (fMRI) has been an important tool for understanding the human brain in vivo, enabling researchers to study the human brain's functional architecture (Davatzikos et al., 2005, Kahnt et al., 2012, Latinus et al., 2011, Shen et al., 2010, Wagner et al., 2011) and functional brain difference between different groups of subjects (Fan et al., 2011, Zeng et al., 2012). For such fMRI studies, inter-subject spatial alignment of fMRI data is a necessary precursor and a better inter-subject spatial correspondence often leads to improved statistical analysis results with enhanced statistical significance, although methods have been proposed for group analysis to relieve the requirement for stringent one-to-one voxel correspondence across subjects (Ng et al., 2012).

Inter-subject spatial alignment of fMRI data is typically achieved through registering their co-registered structural MRI (sMRI) images due to their relatively high spatial resolution and good image texture information. Many image registration algorithms for sMRI images have been proposed, including linear spatial transformation based algorithms (Fischer and Modersitzki, 2003, Talairach and Tournoux, 1988) and nonlinear spatial transformation based algorithms (Ashburner, 2007, Beg et al., 2005, Joshi et al., 2004, Rueckert et al., 1999, Shen and Davatzikos, 2002, Vercauteren et al., 2009). In general, the brain image registration algorithms based on nonlinear spatial transformations can achieve better alignment of brain anatomical structures across different subjects. However, a good alignment of brain anatomical structures across different subjects does not necessarily lead to good inter-subject functional consistency in that functional units are not necessarily located relative to anatomical structures consistently due to functional variability across subjects (Ng et al., 2012, Sabuncu et al., 2010). The term functional unit herein denotes a brain region performing specific functions. In order to improve the functional consistency across subjects, spatial smoothing of the functional image of each subject is commonly applied in practice after the structural MRI image based registration. However, the adverse effects of image smoothing, including functional signal blurring and loss of fine-grained information, will be brought into the subsequent group analysis (Sacchet and Knutson, 2013). Hence, it is desired to develop an image registration method capable of achieving better functional consistency across subjects in fMRI studies.

Recently, several functional information based image registration methods have been proposed for achieving better consistency of brain functions across subjects (Conroy et al., 2009, Jiang et al., 2012a, Khullar et al., 2011, Langs et al., 2010, Sabuncu et al., 2010). A cortical surface alignment method was proposed to maximize similarity of functional signals between subjects in Sabuncu et al. (2010). The method proposed by Sabuncu et al. is suitable for the registration of fMRI data driven by synchronized tasks across different subjects. In this method, the Pearson correlations between inter-subject functional signals were maximized to register different subjects' cortex surface meshes based upon an assumption that functional signals are synchronic across different subjects. However, such an assumption is not necessarily true in most cases. In resting-state fMRI (rs-fMRI) images, for instance, even at a subject's same location, no significant correlations exist between the functional signals scanned at different times. Thus, such a method is not suitable for rs-fMRI images. To overcome this problem, methods have been proposed to achieve functional image registration by maximizing similarity of functional connectivity patterns at the same spatial locations between different subjects, i.e., using functional connectivity measures as features to drive the image registration (Conroy et al., 2009, Jiang et al., 2012a, Langs et al., 2010). The functional connectivity between two voxels in fMRI data is typically measured by correlation coefficient between their functional signals. In the cortical surface registration method proposed in Conroy et al. (2009), the whole-brain functional connectivity matrix was used as a descriptor of functional information on the cortical surface and cortical surface meshes of different subjects were registered by minimizing Frobenius norm of difference between their functional connectivity matrices. However, the global functional connectivity matrix based functional image registration is not robust since the global functional connectivity matrices are sensitive to local perturbations. A small spatial rotation or shift of functional units may alter the global functional connectivity matrices, thus leads to unstable image registration. In Langs et al. (2010), features were first extracted from the whole-brain functional connectivity matrix using a spectral embedding technique (von Luxburg, 2007), functional images were then aligned by a point set registration method (Myronenko et al., 2007) in the feature space, i.e., the so called functional geometry (Langs et al., 2010), and finally the transformation information was mapped back to the original fMRI image space for achieving image registration. A problem of the spectral embedding based feature extraction is that ad hoc techniques have to be utilized to make the extracted features of different subjects comparable since the spectral embedding is defined up to rotation, order, and sign of individual coordinate axes (Langs et al., 2010). In (Jiang et al., 2012a), a local functional connectivity pattern based functional information description was proposed for fMRI image registration, which could overcome the limitations of global functional connectivity pattern based image registration. However, this method might not be able to achieve the optimal functional consistency across subjects since the spatial range of functional connectivity patterns is fixed in the image registration. In Khullar et al. (2011), an ICA decomposition was first performed and the registration of fMRI data was driven by matching their specific components (e.g., Temporal Lobe component, or Default Mode Network component). However, it remains unclear that among all the components which one or what combination is the best choice for the fMRI registration.

To overcome the limitations in the existing registration methods for fMRI data, we propose a multi-range functional connectivity pattern based functional image registration method. Instead of maximizing the correlation of inter-subject functional signals or similarity of the global functional connectivity patterns of different subjects, we use local functional connectivity patterns (Jiang et al., 2012a) to guide the image registration in a hierarchical way. At the early stage of functional image registration, a local functional connectivity pattern is computed in a small spatial local neighborhood of each voxel to describe its functional information. With the progression of image registration, the local functional connectivity patterns become more consistent across subjects. Therefore, the size of spatial neighborhood for computing local functional patterns can be gradually increased to capture functional connectivity patterns in larger spatial ranges. In this way, the optimal consistency can be achieved gradually with the progression of image registration. Compared with the functional connectivity matrix based global functional connectivity pattern representation that could be altered by small local perturbations, it is much more robust to use the local functional connectivity pattern at the early stage of image registration, especially when a small spatial neighborhood is used for computing the functional connectivity pattern. To make the functional connectivity patterns invariant to the order of voxels in the spatial neighborhood of the voxel considered, a kernel density estimation technique is utilized to transfer the functional connectivity pattern into a probability distribution representation (Bishop, 2006). We also adopt the congealing strategy (Balci et al., 2007, Huang et al., 2007, Learned-Miller, 2006, Zollei et al., 2005) to simultaneously register a group of images by minimizing the sum of entropy along each voxel stack without utilizing any intermediate template, which is different from those pairwise registration strategies adopted in (Conroy et al. (2009) and Sabuncu et al. (2010).

We have compared the proposed method with other fMRI data registration methods, and the results have demonstrated that our method could achieve superior registration performance for resting state fMRI data. The experiment results on real resting-state fMRI data have illustrated that the proposed method can achieve a statistically significant improvement in functional consistency across subjects. The preliminary results of this study have been reported in Jiang et al. (2012b).