Topographic Regularity for Tract Filtering in Brain Connectivity

Tracking and validation techniques for topographically organized tractography

Topographic regularity of axonal connections is commonly understood as the preservation of spatial relationships between nearby neurons and is a fundamental structural property of the brain. In particular the retinotopic mapping of the visual pathway can even be quantitatively computed. Inspired from this previously untapped anatomical knowledge, we propose a novel tractography method that preserves both topographic and geometric regularity. We make use of parameterized curves with Frenet-Serret frame and introduce a highly flexible mechanism for controlling geometric regularity. At the same time, we incorporate a novel local data support term in order to account for topographic organization. Unifying geometry with topographic regularity, we develop a Bayesian framework for generating highly organized streamlines that accurately follow neuroanatomy. We additionally propose two novel validation techniques to quantify topographic regularity. In our experiments, we studied the results of our approach with respect to connectivity, reproducibility and topographic regularity aspects. We present both qualitative and quantitative comparisons of our technique against three algorithms from MRtrix3. We show that our method successfully generates highly organized fiber tracks while capturing bundle anatomy that are geometrically challenging for other approaches.

GIFE: Efficient and Robust Group-wise Isometric Fiber Embedding

Tractography is a prevalent technique for in vivo imaging of the white matter fibers (a.k.a. the tractograms), but it is also known to be error-prone. We previously propose the Group-wise Tractogram Analysis (GiTA) framework for identifying anatomically valid fibers across subjects according to cross-subject consistency. However, the original framework is based on computationally expensive brute-force KNN search. In this work, we propose a more general and efficient extension of GiTA. Our main idea is to find the finite dimensional vector-space representation of the fiber tracts of varied lengths across different subjects, and we call it the group-wise isometric fiber embedding (GIFE). This novel GIFE framework enables the application of the powerful and efficient vector space data analysis methods, such as the k-d tree KNN search, to GiTA. However, the conventional isometric embedding frameworks are not suitable for GIFE due to the massive fiber tracts and the registration errors in the original GiTA framework. To address these issues, we propose a novel method called multidimensional extrapolating (MDE) to achieve GIFE. In our experiment, simulation results show quantitatively that our method outperforms the other methods in terms of computational efficiency/tractability and robustness to errors in distance measurements for real fiber embedding. In addition, real experiment for group-wise optic radiation bundle reconstruction also shows clear improvement in anatomical validity of the results from our MDE method for 47 different subjects from the Human Connectome Project, compared to the results of other fiber embedding methods.

Modeling topographic regularity in structural brain connectivity with application to tractogram filtering

Topographic regularity is an important biological principle in brain connections that has been observed in various anatomical studies. However, there has been limited research on mathematically characterizing this property and applying it in the analysis of in vivo connectome imaging data. In this work, we propose a general mathematical model of topographic regularity for white matter fiber bundles based on previous neuroanatomical understanding. Our model is based on a novel group spectral graph analysis (GSGA) framework motivated by spectral graph theory and tensor decomposition. The GSGA provides a common set of eigenvectors for the graphs formed by topographic proximity of nearby tracts, which gives rises to the group graph spectral distance, or G²SD, for measuring the topographic regularity of each fiber tract in a tractogram. Based on this novel model of topographic regularity in fiber tracts, we then develop a tract filtering algorithm that can generally be applied to remove outliers in tractograms generated by any tractography algorithm. In the experimental results, we show that our novel algorithm outperforms existing methods in both simulation data from ISMRM 2015 Tractography Challenge and real data from the Human Connectome Project (HCP). On a large-scale dataset from 215 HCP subjects, we quantitatively show our method can significantly improve the retinotopy in the reconstruction of the optic radiation bundle. The software for the tract filtering algorithm developed in this work has also been publicly released on NITRC (https://www.nitrc.org/projects/connectopytool).

Kernel-Regularized ICA for Computing Functional Topography from Resting-state fMRI

Topographic regularity is a fundamental property in brain connectivity. In this work, we present a novel method for studying topographic regularity of functional connectivity based on resting-state fMRI (rfMRI), which is widely available and easy to acquire in large-scale studies. The main idea in our method is the incorporation of topographically regular structural connectivity for independent component analysis (ICA). This is enabled by the recent development of novel tractography and tract filtering algorithms that can generate highly organized fiber bundles connecting different brain regions. By leveraging these cutting-edge tractography algorithms, here we develop a kernel-regularized ICA method for the extraction of functional topography with rfMRI signals. In our experiments, we use rfMRI scans of 35 unrelated, right-handed subjects from the Human Connectome Project (HCP) to study the functional topography of the motor cortex. We first demonstrate that our method can generate functional connectivity maps with more regular topography than conventional group ICA. We also show that the components extracted by our algorithm are able to capture co-activation patterns that respect the organized topography of the motor cortex across the hemisphere. Finally, we show that our method achieves improved reproducibility as compared to conventional group ICA.