Introduction
Resting-state fMRI (rs-fMRI) has been widely used to explore the functional coupling between distinct brain regions by calculating low-frequency spontaneous fluctuations in the time series, i.e., functional connectivity (Biswal et al.
1995; Fox and Raichle
2007; Buckner et al.
2013; Song and Jiang
2012). Functional connectivity has been a powerful tool to identify the resting-state networks (Greicius et al.
2003; Tomasi and Volkow
2012; Damoiseaux et al.
2006). Recently, rs-fMRI has also been exploited to delineate distinct subregions within a larger brain region based on differential patterns of functional connectivity (Craddock et al.
2012; Kim et al.
2010; Nelson et al.
2010; Yeo et al.
2011; Shen et al.
2010; Deen et al.
2011). As we know, the functional connectivity could be influenced by various artifacts in rs-fMRI data including physiological artifacts (Birn et al.
2008), transient head motion (Van Dijk et al.
2012), different scanning conditions (Patriat et al.
2013) and preprocessing procedures (Van Dijk et al.
2010; Satterthwaite et al.
2013). Hereby, these artifacts might also have impacts on the parcellation results. Generally, there are three approaches proposed to reduce the impact of noise during the parcellation procedures. The first is to average the connectivity profiles (Deen et al.
2011; Yeo et al.
2011) or similarity matrices across subjects (Craddock et al.
2012), which, however, eliminates inter-individual variability, which has been widely reported in both structure and function of the human brain (Mueller et al.
2013; Rademacher et al.
2001; Zilles and Amunts
2013). The second is to employ spatial constraints to improve the stability of parcellation (Craddock et al.
2012), which might bias the results towards spherical-shaped clusters. Another approach is to remove the noisy edges lying between clusters by constructing a sparse similarity matrix, for instance the KNN graph (Shen et al.
2010; von Luxburg
2007). But the KNN graph method requires a global sparsity parameter, which is often difficult to determinate (Nadler and Galun
2006) and could significantly affect the performance of parcellation (Shen et al.
2010). Thus, a more efficient sparse technique is required, which could generate robust brain parcellation by guaranteeing the stability of parcellation and retaining the individual variability at the same time.
The sparse representation theory (Elad
2010) has been widely employed in the classification of face, natural and medical images (Wright et al.
2009,
2010; Su et al.
2012; Wee et al.
2014; Mairal et al.
2008). Recently, it also has been proposed for data clustering and achieved robustness on high-dimensional data (Elhamifar and Vidal
2013), which construct a sparse similarity graph based on the sparse representation coefficients and employ the spectral clustering to cluster local subspaces (Elhamifar and Vidal
2009). Instead of identifying the linear dependence relations between each pair of variables, sparse representation employs the multivariate regression model to characterize the unique contribution of each point to the objective point. In addition to the self-representation model, an extra sparsity constraint on the representation coefficients is emphasized to identify the most relevant variables. Consequently, noise effects can be reduced (Elad and Aharon
2006; Elhamifar and Vidal
2013) and the signals may be recovered (Elad
2010). More importantly, the sparse representation coefficients may identify the nearest subspaces for each point with minimum embedding dimensions (Elhamifar and Vidal
2013; Wang and Xu
2013), which gives hints to the local organization of data. Thus, the similarity matrix constructed based on these representation coefficients could be used for data clustering (Elhamifar and Vidal
2013; Vidal
2011). Additionally, with the approximately block diagonal form (Elhamifar and Vidal
2013), the similarity matrix could maintain a hierarchical consistency when different clusterings were performed. All these properties could be very helpful for rs-fMRI-based brain parcellation.
Here, we propose a brain parcellation method based on the sparse representation, which is robust to noise and preserves individual variability during brain parcellation. We tested the method on simulated, multi-site and different spatially smoothed rs-fMRI datasets. The robustness of the method was first tested on the simulated rs-fMRI data. To further assess the stability of the method, two different brain areas, i.e., the medial frontal cortex (MFC, including SMA and pre-SMA) and parietal operculum (OP), were parcellated on multi-site rs-fMRI datasets. The parcellation of MFC with a clear segregation between SMA and pre-SMA has been widely used as a validation for parcellation methods (Johansen-Berg et al.
2004; Klein et al.
2007), especially on rs-fMRI data (Kim et al.
2010; Ryali et al.
2013; Crippa et al.
2011; Nanetti et al.
2009). Area OP, on the other hand, has been widely accepted as a heterogeneous region (Keysers et al.
2010; Zu Eulenburg et al.
2013; Burton et al.
2008), with cytoarchitectonic mapping of this region (Eickhoff et al.
2006a) available as a representation of its microstructure and a clear somatotopic organization (Eickhoff et al.
2007) among its subdivisions. Thus, we first subdivided MFC on multi-site datasets to evaluate the consistency across different datasets and on differently smoothed datasets to study the influence of smoothing conditions. Then, we parcellated OP using rs-fMRI data and compared its functional parcellation with the cytoarchitectonic subdivisions (Eickhoff et al.
2006a).
Conclusion
In the current study, we presented a robust brain parcellation method using rs-fMRI data, which could achieve stable individual parcellation results with high robustness to noise. It provided an efficient approach to construct a sparse similarity matrix through solving sparse representation equations and generated stable individual parcellation with the aid of spectral clustering. Using the proposed method, similar results were generated using local time-varying BOLD signals and whole-brain connectivity patterns. Moreover, the method outperformed commonly used methods with higher robustness to noise on all simulated rs-fMRI datasets. Highly consistent parcellations were achieved on multi-site real rs-fMRI datasets, along with little influence from different smoothing conditions. Therefore, this parcellation framework using sparse representation presented an efficient approach to robust brain parcellation using resting-state fMRI.