A Web platform for the interactive visualization and analysis of the 3D fractal dimension of MRI data.

This study presents a Web platform (http://3dfd.ujaen.es) for computing and analyzing the 3D fractal dimension (3DFD) from volumetric data in an efficient, visual and interactive way. The Web platform is specially designed for working with magnetic resonance images (MRIs) of the brain. The program estimates the 3DFD by calculating the 3D box-counting of the entire volume of the brain, and also of its 3D skeleton. All of this is done in a graphical, fast and optimized way by using novel technologies like CUDA and WebGL. The usefulness of the Web platform presented is demonstrated by its application in a case study where an analysis and characterization of groups of 3D MR images is performed for three neurodegenerative diseases: Multiple Sclerosis, Intrauterine Growth Restriction and Alzheimer's disease. To the best of our knowledge, this is the first Web platform that allows the users to calculate, visualize, analyze and compare the 3DFD from MRI images in the cloud.

Fractal dimension analysis of states of consciousness and unconsciousness using transcranial magnetic stimulation.

BACKGROUND AND OBJECTIVE: Knowing whether a subject is conscious or not is a current challenge with a deep potential clinical impact. Recent theoretical considerations suggest that consciousness is linked to the complexity of distributed interactions within the corticothalamic system. The fractal dimension (FD) is a quantitative parameter that has been extensively used to analyse the complexity of structural and functional patterns of the human brain. In this study we investigate FD to assess whether it can discriminate between consciousness and different states of unconsciousness in healthy individuals. METHODS: We study 69 high-density electroencephalogram (hd-EEG) measurements after transcranial magnetic stimulation (TMS) in 18 healthy subjects progressing from wakefulness to non-rapid eye movement (NREM) sleep and sedation induced by different anaesthetic agents (xenon and propofol). We quantify the integration of thalamocortical networks by calculating the FD of a spatiotemporal voxelization obtained from the locations of all sources that are significantly activated by the perturbation (4DFD). Moreover, we study the temporal evolution of the evoked spatial distributions and compute a measure of the differentiation of the response by means of the Higuchi FD (HFD). Finally, a Fractal Dimension Index (FDI) of perturbational complexity is computed as the product of both quantities: integration FD (4DFD) and differentiation FD (HFD). RESULTS: We found that FDI is significantly lower in sleep and sedation when compared to wakefulness and provides an almost perfect intra-subject discrimination between conscious and unconscious states. CONCLUSIONS: These results support the combination of FD measures of cortical integration and cortical differentiation as a novel paradigm of tracking complex spatiotemporal dynamics in the brain that could provide further insights into the link between complexity and the brain's capacity to sustain consciousness.

Fast box-counting algorithm on GPU.

The box-counting algorithm is one of the most widely used methods for calculating the fractal dimension (FD). The FD has many image analysis applications in the biomedical field, where it has been used extensively to characterize a wide range of medical signals. However, computing the FD for large images, especially in 3D, is a time consuming process. In this paper we present a fast parallel version of the box-counting algorithm, which has been coded in CUDA for execution on the Graphic Processing Unit (GPU). The optimized GPU implementation achieved an average speedup of 28 times (28×) compared to a mono-threaded CPU implementation, and an average speedup of 7 times (7×) compared to a multi-threaded CPU implementation. The performance of our improved box-counting algorithm has been tested with 3D models with different complexity, features and sizes. The validity and accuracy of the algorithm has been confirmed using models with well-known FD values. As a case study, a 3D FD analysis of several brain tissues has been performed using our GPU box-counting algorithm.

UJA-3DFD: a program to compute the 3D fractal dimension from MRI data.

This work presents a computer program for computing the 3D fractal dimension (3DFD) from magnetic-resonance images of the brain. The program is based on an algorithm that calculates the 3D box counting of the entire volume of the brain, and also of its 3D skeletonization. The validity and accuracy of the software has been confirmed using solids with well-known 3DFD values. The usefulness of the program developed is demonstrated by its successful characterization of several neurodegenerative diseases.