Juan Ruiz de Miras

Fractal dimension and white matter changes in multiple sclerosis

The brain white matter (WM) in multiple sclerosis (MS) suffers visible and non-visible (normal-appearing WM (NAWM)) changes in conventional magnetic resonance (MR) images. The fractal dimension (FD) is a quantitative parameter that characterizes the morphometric variability of a complex object. Our aim was to assess the usefulness of FD analysis in the measurement of WM abnormalities in conventional MR images in patients with MS, particularly to detect NAWM changes. First, we took on a voxel-based morphometry approach optimized for MS to obtain the segmented brain. Then, the FD of the whole grey-white matter interface (WM border) and skeletonized WM was calculated in patients with MS and healthy controls. To assess the FD of the NAWM, we focused our analysis on single sections without lesions at the centrum semiovale level. We found that patients with MS had a significant decrease in the FD of the entire brain WM compared with healthy controls. Such a decrease of the FD was detected not only on MR image sections with MS lesions but also on single sections with NAWM. Taken together, the results showed that FD identifies changes in the brain of patients with MS, including in NAWM, even at an early phase of the disease. Thus, FD might become a useful marker of diffuse damage of the central nervous system in MS.

Fractal-dimension analysis detects cerebral changes in preterm infants with and without intrauterine growth restriction

In the search for a useful parameter to detect and quantify subtle brain abnormalities in infants with intrauterine growth restriction (IUGR), we hypothesised that the analysis of the structural complexity of grey matter (GM) and white matter (WM) using the fractal dimension (FD), a measurement of the topological complexity of an object, could be established as a useful tool for quantitative studies of infant brain morphology. We studied a sample of 18 singleton IUGR premature infants, (12.72 months corrected age (CA), range: 12 months-14 months), 15 preterm infants matched one-to-one for gestational age (GA) at delivery (12.6 months; range: 12 months-14 months), and 15 neonates born at term (12.4 months; range: 11 months-14 months). The neurodevelopmental outcome was assessed in all subjects at 18 months CA according to the Bayley Scale for Infant and Toddler Development - Third edition (BSID-III). For MRI acquisition and processing, the infants were scanned at 12 months CA, in a TIM TRIO 3T scanner, sleeping naturally. Images were pre-processed using the SPM5 toolbox, the GM and WM segmented under the VBM5 toolbox, and the box-counting method was applied for FD calculation of normal and skeletonized segmented images. The results showed a significant decrease of the FD of the brain GM and WM in the IUGR group when compared to the preterm or at-term controls. We also identified a significant linear tendency of both GM and WM FD from IUGR to preterm and term groups. Finally, multiple linear analyses between the FD of the GM or WM and the neurodevelopmental scales showed a significant regression of the language and motor scales with the FD of the GM. In conclusion, a decreased FD of the GM and WM in IUGR infants could be a sensitive indicator for the investigation of structural brain abnormalities in the IUGR population at 12 months of age, which can also be related to functional disorders.

Fractal dimension analysis of grey matter in multiple sclerosis

The fractal dimension (FD) is a quantitative parameter that characterizes the morphometric variability of a complex object. Among other applications, FD has been used to identify abnormalities of the human brain in conventional magnetic resonance imaging (MRI), including white matter abnormalities in patients with Multiple Sclerosis (MS). Extensive grey matter (GM) pathology has been recently identified in MS and it appears to be a key factor in long-term disability. The aim of the present work was to assess whether FD measurement of GM in T1 MRI sequences can identify GM abnormalities in patients with MS in the early phase of the disease. A voxel-based morphometry approach optimized for MS was used to obtain the segmented brain, where we later calculated the three-dimensional FD of the GM in MS patients and healthy controls. We found that patients with MS had a significant increase in the FD of the GM compared to controls. Such differences were present even in patients with short disease durations, including patients with first attacks of MS. In addition, the FD of the GM correlated with T1 and T2 lesion load, but not with GM atrophy or disability. The FD abnormalities of the GM here detected differed from the previously published FD of the white matter in MS, suggesting that different pathological processes were taking place in each structure. These results indicate that GM morphology is abnormal in patients with MS and that this alteration appears early in the course of the disease.

Box-counting algorithm on GPU and multi-core CPU: an OpenCL cross-platform study

In this paper, we present the analysis and development of a cross-platform OpenCL implementation of the box-counting algorithm, which is one of the most widely-used methods for estimating the Fractal Dimension. The Fractal Dimension is a relevant image analysis method used in several disciplines, but computing it is in general a time consuming process, especially when working with 3D images. Unlike parallel programming models that strictly depend on the hardware type and manufacturer, like CUDA, OpenCL allows us to provide an implementation suitable for execution on both GPUs and multi-core CPUs, whatever the hardware manufacturer. Sorting is a key part of the fast box-counting algorithm and the final speedup is highly conditioned by the efficiency of the sorting algorithm used. Our study reveals that current OpenCL implementations of sorting algorithms are clearly slower when compared with both CUDA for GPU and specific multi-core CPU implementations. Our OpenCL algorithm has been specifically optimized according the type of the target device and the results show an average speedup of up to 7.46× and 4×, when executed on the GPU and the multi-core CPU respectively, both compared with the single-threaded (sequential) CPU implementation.

Optimizations with CUDA: A Case Study on 3D Curve-Skeleton Extraction from Voxelized Models

In this paper, we show how we have coded and optimized a complex and not trivially parallelizable case study: a 3D curve-skeleton calculation algorithm. For this we use NVIDIA CUDA, which allows the programmer to easily code algorithms for executing in a parallel way on NVIDIA GPU devices. However, when working with algorithms that have high data-sharing or data-dependence requirements, like the curve-skeleton calculation, it is not always a trivial task to achieve acceptable acceleration rates. So we detail step by step a comprehensive collection of optimizations to be considered in this class of algorithms, and in general in any CUDA implementation. Two different GPU architectures have been used to test the implications of each optimization, the NVIDIA GT200 architecture and the Fermi GF100. As a result, although the first direct CUDA implementation of our algorithm ran even slower than its CPU version, overall speedups of 19x (GT200) and 68x (Fermi GF100) were finally achieved.

Adaptive trimming of cubic triangular Bézier patches

We present a method to handle cubic trimmed triangular Bézier patches. This scheme makes use of levels of detail and surface subdivision to achieve a fast and flexible hierarchical data structure that is specially useful to compute surface intersections in a robust and efficient way. The accuracy of the results can be adjusted by adding or subtracting elements to the levels of detail hierarchy, and it is also easy to obtain a decomposition of a trimmed patch into single triangular Bézier patches.

Fractal Analysis in MATLAB: A Tutorial for Neuroscientists

MATLAB is one of the software platforms most widely used for scientific computation. MATLAB includes a large set of functions, packages, and toolboxes that make it simple and fast to obtain complex mathematical and statistical computations for many applications. In this chapter, we review some tools available in MATLAB for performing fractal analyses on typical neuroscientific data in a practical way. We provide detailed examples of how to calculate the fractal dimension of 1D, 2D, and 3D data in MATLAB. Furthermore, we review other software packages and several online tools available for fractal analysis.

GPU inclusion test for triangular meshes

Abstract Querying the relative position of a point regarding a solid defined by a triangular mesh is a fundamental algorithm in geometric modelling. This algorithm has many applications in fields like Computer Graphics or Computer Aided Design and is the basis of many other basic algorithms in these areas. In this paper we present an efficient implementation of one of the classic algorithms for solving this problem, the point-in-solid test of Feito and Torres based on simplicial coverings. This algorithm is simple, robust and valid for non-manifold solids. Our implementation resolves the test, including all the special cases, needing no conditional branches. This fact allows us to obtain a parallel and very efficient GPU implementation of the algorithm. We have coded the algorithm in CUDA and the results showed that this GPU implementation achieved a speedup of up to 142 × with respect to a CPU single-thread implementation of the same optimized algorithm. Against a multi-thread implementation in CPU, our CUDA algorithm obtains a speedup of up to 38 × . We have also compared our algorithm to a previous GPU implementation in CUDA of the inclusion test of Feito and Torres. Against this GPU implementation, our algorithm achieved a speedup of up to 11.8 × .

Methodology to Increase the Computational Speed to Obtain the Fractal Dimension Using GPU Programming

Computing the fractal dimension (FD) can be a very time-consuming process. Nowadays, the data precision or resolution of many sensors is increasingly high (magnetic resonance, ultrasounds, microcomputed tomography, etc.) and, furthermore, some applications require 3D data post-processing. The processing of large data sets is also very common in several analyses and applications. Therefore, fast algorithms for computing the FD are required, above all for interactive applications. Graphics processing unit (GPU) programming has become a standard tool for optimizing certain sorts of time-consuming algorithms. If the problem fits the GPU programming model well, high speedups can be achieved. CUDA and OpenCL are two of the most popular GPU technologies since they do not require special knowledge of computer graphics programming. In this chapter, we present our experience optimizing the processing time of the classic box-counting algorithm to compute the FD by means of CUDA and OpenCL GPU programming. Speedups of up to 28× (CUDA) and 6.3× (OpenCL) against the single-thread CPU version of the algorithm have been obtained. CUDA results are better because the box-counting algorithm has a strong dependency on sorting, and the OpenCL implementations of the best sorting algorithms are not as efficient as the CUDA ones.