A coordinate system for the brain: Applications to white matter clustering

The human brain may be considered as a genus-0 shape, topologically equivalent to a sphere. Various methods have been used in the past to transform the brain surface to that of a sphere using harmonic energy minimization methods used for cortical surface matching. How- ever, very few methods have studied volumetric parameterization of the brain using a spherical embedding. Volumetric parameterization is typically used for complicated geometric problems like shape matching, morphing and iso-geometric analysis. Using conformal mapping techniques, we can establish a bijective mapping between the brain and the topologically equivalent sphere. Our hypothesis is that shape analysis problems are simplified when the shape is defined in an intrinsic coordinate system. Our goal is to establish such a coordinate system for the brain. The efficacy of the method is demonstrated with a white matter clustering problem. Initial results show promise for future investigation in these pa- rameterization technique and its application to other problems related to computational anatomy like registration and segmentation. 

Population Specific Brain Atlases and probabilistic region of interests (ROIs)

Spatial normalization is one of the most important steps in population based statistical analysis of brain images. This involves normalizing all the brain images to a pre-defined template or a population specific template. With multiple emerging imaging modalities, it is quintessential to develop a method for building a joint template that is a statistical representation of the given population across different modalities. It is possible to create different population specific templates in different modalities using existing methods. However, they do not give an opportunity for voxelwise comparison of different modalities. A multimodal brain template with probabilistic region of interest (ROI) definitions will give opportunity for multivariate statistical frameworks for better understanding of brain diseases. In this paper, we propose a methodology for developing such a multimodal brain atlas us- ing the anatomical T1 images and the diffusion tensor images (DTI), along with an automated workflow to probabilistically define the different white matter regions on the population specific multimodal template. The method will be useful to carry out ROI based statistics across different modalities even in the absence of expert segmentation. 

A 3D rendering of probabilistic definition of Corpus callosum

The figure shows a 3D rendering of probabilistic definition of corpus callosum created from 123 subjects.

The figure shows the multimodal template. The DTI template is overlayed on the T1 template

Super-resolution of clinical diffusion tensor images using a spatial prior

Diffusion Tensor Imaging (DTI) provides us with valuable information about the white matter fibers and their arrangement in the brain. However, clinical DTI acquisitions are often low resolution, causing partial volume effects. In this paper, we propose a new high resolution tensor estimation method. This method makes use of the spatial correlation between neighboring voxels. Unlike some super-resolution algorithms, the proposed method does not require multiple acquisitions, thus it is better suited for clinical situations. The method relies on a maximum likelihood strategy for tensor estimation to optimally account for the noise and an anisotropic regularization prior to promote smoothness in homogeneous areas while respecting the edges. To the best of our knowledge, this is the first method to produce high resolution tensor images from a single low resolution acquisition. We demonstrate the efficiency of the method on synthetic low-resolution data and real clinical data. The results show statistically significant improvements in fiber tractography. 

Source Code in C++

The HR tensor estimation method shows increase in the number of white matter tracts and also the length of the tracts.

Volumetric parameterization of 3D non-convex domains

Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the boundary of a 3D model (which is a surface). Volumetric parameterization is typically helpful in solving complicated geometric problems pertaining to shape matching, morphing, path planning of robots, and isogeometric analysis etc. A novel method is proposed in which a volume parameterization is developed by mapping a general nonconvex (genus-0) domain to its topologically equivalent convex domain. In order to achieve a continuous and bijective mapping of a domain, first we use the harmonic function to establish a potential field over the domain. The gradients of the potential values are used to track the streamlines which originate from the boundary and converge to a single point, referred to as the shape center. Each streamline approaches the shape center at a unique polar angle () and an azimuthal angle ( ) . Once all the three parameters (potential value , polar angle , azimuthal angle ) necessary to represent any point in the given domain are available, the domain is said to be parameterized. Using our method, given a 3D non-convex domain, we can parameterize the surface as well as the interior of the domain. The proposed method is implemented and the algorithm is tested on many standard cases to demonstrate the effectiveness.

Converting a non-convex domain (head) in this case to a flat atlas.

More details on the projects are coming soon !!!!