Neda Sepasian

CUDA-accelerated geodesic ray-tracing for fiber tracking

Diffusion Tensor Imaging (DTI) allows to noninvasively measure the diffusion of water in fibrous tissue. By reconstructing the fibers from DTI data using a fiber-tracking algorithm, we can deduce the structure of the tissue. In this paper, we outline an approach to accelerating such a fiber-tracking algorithm using a Graphics Processing Unit (GPU). This algorithm, which is based on the calculation of geodesics, has shown promising results for both synthetic and real data, but is limited in its applicability by its high computational requirements. We present a solution which uses the parallelism offered by modern GPUs, in combination with the CUDA platform by NVIDIA, to significantly reduce the execution time of the fiber-tracking algorithm. Compared to a multithreaded CPU implementation of the same algorithm, our GPU mapping achieves a speedup factor of up to 40 times.

Multivalued geodesic ray-tracing for computing brain connections using diffusion tensor imaging

Diffusion tensor imaging (DTI) is a magnetic resonance technique used to explore anatomical fibrous structures, like brain white matter. Fiber-tracking methods use the diffusion tensor (DT) field to reconstruct the corresponding fibrous structure. A group of fiber-tracking methods trace geodesics on a Riemannian manifold whose metric is defined as a function of the DT. These methods are more robust to noise than more commonly used methods where just the main eigenvector of the DT is considered. Until now, geodesic-based methods were not able to resolve all geodesics, since they solved the Eikonal equation, and therefore were not able to deal with multivalued solutions. Our algorithm computes multivalued solutions using an Euler–Lagrange form of the geodesic equations. The multivalued solutions become relevant in regions with sharp anisotropy and complex geometries, or when the first arrival time does not describe the geodesic close to the anatomical fibrous structure. In this paper, we compare our algorit...

A ray tracing method for geodesic based tractography in diffusion tensor images

We present multi-valued solution algorithm for geodesic-based fiber tracking in a tensor-warped space given by diffusion tensor imaging data. This technique is based on solving ordinary differential equations describing geodesics by a ray tracing algorithm. The algorithm can capture all possible geodesics connecting two given points instead of a single geodesic captured by Hamilton-Jacobi based algorithms. Once the geodesics have been computed, using suitable connectivity measures, we can choose among all solutions the most likely connection pathways which correspond best to the underlying real fibrous structures. In comparison with other approaches, our algorithm gives the possibility of applying different cost functions in a fast post-processing. Moreover, the algorithm can be used for capturing possible multi-path connections between two points that can happen when, e.g., pathologies are presented. Synthetic second order diffusion tensor data in a two dimensional space are employed to illustrate the potential applications of the algorithm to fiber tracking.

Employing visual analytics to aid the design of white matter hyperintensity classifiers

Accurate segmentation of brain white matter hyperintensities (WMHs) is important for prognosis and disease monitoring. To this end, classifiers are often trained – usually, using T1 and FLAIR weighted MR images. Incorporating additional features, derived from diffusion weighted MRI, could improve classification. However, the multitude of diffusion-derived features requires selecting the most adequate. For this, automated feature selection is commonly employed, which can often be sub-optimal. In this work, we propose a different approach, introducing a semi-automated pipeline to select interactively features for WMH classification. The advantage of this solution is the integration of the knowledge and skills of experts in the process. In our pipeline, a Visual Analytics (VA) system is employed, to enable user-driven feature selection. The resulting features are T1, FLAIR, Mean Diffusivity (MD), and Radial Diffusivity (RD) – and secondarily, \(C_S\) and Fractional Anisotropy (FA). The next step in the pipeline is to train a classifier with these features, and compare its results to a similar classifier, used in previous work with automated feature selection. Finally, VA is employed again, to analyze and understand the classifier performance and results.

Adaptive Enhancement in Diffusion MRI Through Propagator Sharpening

In this short note we consider a method of enhancing diffusion MRI data based on analytically deblurring the ensemble average propagator. Because of the Fourier relationship between the normalized signal and the propagator, this technique can be applied in a straightforward manner to a large class of models. In the case of diffusion tensor imaging, a commonly used ‘ad hoc’ \(\min\)-normalization sharpening method is shown to be closely related to this deblurring approach. The main goal of this manuscript is to give a formal description of the method for (generalized) diffusion tensor imaging and higher order apparent diffusion coefficient-based models. We also show how the method can be made adaptive to the data, and present the effect of our proposed enhancement on scalar maps and tractography output.

Riemann-Finsler Multi-valued Geodesic Tractography for HARDI

We introduce a geodesic based tractography method for High Angular Resolution Diffusion Imaging (HARDI). The concepts used are similar to the ones in geodesic based tractography for Diffusion Tensor Imaging (DTI). In DTI, the inverse of the second-order diffusion tensor is used to define the manifold where the geodesics are traced. HARDI models have been developed to resolve complex fiber populations within a voxel, and higher order tensors (HOT) are possible representations for HARDI data. In our framework, we apply Finsler geometry, which extends Riemannian geometry to a directionally dependent metric. A Finsler metric is defined in terms of HARDI higher order tensors. Furthermore, the Euler-Lagrange geodesic equations are derived based on the Finsler geometry. In contrast to other geodesic based tractography algorithms, the multi-valued numerical solution of the geodesic equations can be obtained. This gives the possibility to capture all geodesics arriving at a single voxel instead of only computing the shortest one. Results are analyzed to show the potential and characteristics of our algorithm.

Assessing the feasibility of estimating axon diameter using diffusion models and machine learning

Axon diameter estimation has been a focus of the diffusion MRI community for the past decade. The main argument has been that while diffusion models always overestimate the true axon diameter, their estimation still correlates with changes in true value. Until now, this remains more as a discussion point. The aim of this paper is to clarify this hypothesis using a recently acquired cat spinal cord data set, where the diffusion MRI signal of both a multi-shell and Ax-Caliber acquisition have been registered with the underlying histology values. We find that the axon diameter as estimated by signal models and AxCaliber does not correlate with their true sizes for axon diameters smaller than 3 µm. On the other hand, we also train a random forest machine learning algorithm to map signal-based features to histology values of axon diameter and volume fraction. The results show that, in this dataset, this approach leads to a more reliable estimation of physically relevant axon diameters than using sophisticated diffusion models.

Modified geodesic ray-tracing for diffusion tensor imaging

In this paper we develop a modified ray-tracing algorithm for geodesic tractography in the context of brain Diffusion Tensor Imaging (DTI). Our technique is based on computing multi-valued geodesics connecting two given points and tracking the evolution of adjacent geodesics. In order to do so we introduce a new Riemannian metric given by the adjugate sharpened diffusion tensor, combined with a constraint on the tracts outcome based on the geodesic deviation. We present tractography results, and compare our method with the existing ray-tracing approach and deterministic streamlining. Our preliminary results show an improved performance of modified ray-tracing regarding false positive fibers. We also show experiments on subcortical short association U-fibers, whose reconstruction is well-known to be hard in a DTI setting.

Bone reposition planning for corrective surgery using statistical shape model : assessment of differential geometrical features

We discuss a new planning method for corrective osteotomy surgery without the need to make a CT scan of the contralateral bone. We use a statistical shape model to estimate the most likely relative position of two bone segments of an osteotomized bone. To investigate the added value of geometrical properties for planning, different geometrical features of the bone surface are being incorporated. The feasibility and accuracy of our proposed method are investigated using 10 virtually deformed radii and a statistical shape model based on 35 healthy radii.

A simplified algorithm for inverting higher order diffusion tensors

In Riemannian geometry, a distance function is determined by an inner product on the tangent space. In Riemann-Finsler geometry, this distance function can be determined by a norm. This gives more freedom on the form of the so-called indicatrix or the set of unit vectors. This has some interesting applications, e.g., in medical image analysis, especially in diffusion weighted imaging (DWI). An important application of DWI is in the inference of the local architecture of the tissue, typically consisting of thin elongated structures, such as axons or muscle fibers, by measuring the constrained diffusion of water within the tissue. From high angular resolution diffusion imaging (HARDI) data, one can estimate the diffusion orientation distribution function (dODF), which indicates the relative diffusivity in all directions and can be represented by a spherical polynomial. We express this dODF as an equivalent spherical monomial (higher order tensor) to directly generalize the (second order) diffusion tensor approach. To enable efficient computation of Riemann-Finslerian quantities on diffusion weighted (DW)-images, such as the metric/norm tensor, we present a simple and efficient algorithm to invert even order spherical monomials, which extends the familiar inversion of diffusion tensors, i.e., symmetric matrices.