A SOFTWARE PLATFORM TO ANALYZE MR IMAGES

BASED ON 3D FRACTAL DIMENSION

Application in Neurodegenerative Diseases

J. Jiménez

, A. M. López

, F. J. Esteban

, P. Villoslada

, J. Navas

and J. Ruiz de Miras

Department of Computer Science, University of Jaén, Campus Las Lagunillas s/n, 23071 Jaén, Spain

Department of Experimental Biology, University of Jaén, Jaén, Spain

Department of Neurology, Hospital Clinic-IDIBAPS, Barcelona, Spain

Department of Mathematics, University of Jaén, Jaén, Spain

Keywords: Medical Imaging, Image-based Diagnosis, 3D Fractal Dimension, Multiple Sclerosis, Alzheimer.

Abstract: Previous studies carried out by our group have demonstrated that 3D fractal dimension algorithms detect

changes in apparently normal magnetic resonance (MR) images of the brain in patients suffering early

stages of Multiple Sclerosis. In addition, 3D fractal dimension has also been demonstrated to be useful for

detecting brain abnormalities in other cerebral diseases, as in Alzheimer’s disease and in children born after

intrauterine growth restriction. Thus, 3D fractal dimension detection has been proposed as a valuable and

powerful diagnostic tool. To our knowledge, no user-friendly software is available to obtain the 3D fractal

dimension of volumetric MR images. In this paper, we present an optimized Web platform that allows

computing the 3D fractal dimension value for uploaded MR images in an interactive user-friendly way.

Moreover, and because the computational cost of the involved algorithms is very high for interactive use,

we have focused our efforts on the optimization of the appropriate algorithms using the parallel computing

power of current GPUs and multi-core CPUs.

1 FRACTAL DIMENSION

A geometry object self-similar at different scales is a

fractal. Fractals are described by fractal geometry,

which was first proposed by Benoit Mandelbrot

(Mandelbrot, 1983). In contrast to Euclidean

geometry, where the dimension value is 1 for a line,

2 for a plane and 3 for a volume, fractal dimension

(FD) is a non-integer number that characterizes an

irregular shape. Thus, FD is 1 for a straight line, but

it has a value between 1 and 2 for an irregular line;

however, the Euclidean dimension is 1 for both a

straight line and an irregular one. With this simple

example, we may figure out how the FD describes a

natural object in a better way than Euclidean

dimension does. Fractal theory has also been

proposed as an unifying theory for different results

in biomedical research that previously were

apparently not related among them (West et al.,

1987).

One accepted procedure to obtain the FD of an

object, in a metric space, is the box-counting

method. It is based on cover the object with grids of

boxes with different sizes, and, for each size, to

estimate how many boxes are filled by the object.

(Hou et al., 1990).

2 FRACTAL DIMENSION IN

NEUROLOGICAL DISEASES

The characterization and quantification of the brain

morphology using FD analyses, in health and

disease, is getting increased attention and interest

from the biomedical community. Most recent studies

focus on 2D analyses from individual MR or SPECT

images (Zhang et al., 2008), where the two-

dimensional FD (2DFD) no longer fulfils the

complexity of the structure. To obtain the 2DFD,

general and wide-use image analysis programs are

available, such as ImageJ (http://rsb.info.nih.gov/ij/),

and even others more specific for FD calculation

such as HarFA – Harmonic and Fractal Image

Analysis

(http://www.fch.vutbr.cz/lectures/imagesci/).

554

Jiménez J., M. López A., J. Esteban F., Villoslada P., Navas J. and Ruiz de Miras J..

A SOFTWARE PLATFORM TO ANALYZE MR IMAGES BASED ON 3D FRACTAL DIMENSION - Application in Neurodegenerative Diseases.

DOI: 10.5220/0003892505540559

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (MIAD-2012), pages 554-559

ISBN: 978-989-8425-89-8

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

The cortex of the human brain is highly

convoluted, and structural changes in this complex

region has been related to developmental disorders

(for example, epilepsy or cerebral palsy), and also

associated with neurodegenerative diseases such as

Multiple Sclerosis or Alzheimer’s disease. Even

thought some of these alterations are easily detected

in MR and computerized tomography (CT) images,

many of them consists of subtle structural changes

difficult to detect and quantify. As previously

suggested (Fernández and Jelinek, 2001), FD is a

good quantitative descriptor of not only the

convolutions of the cerebral cortex but also the

white matter. Thus, the structural brain

abnormalities taking place in several diseases can be

revealed by changes in its FD (Thompson et al.,

1996; Kiselev et al., 2003; Liu et al., 2003).

Moreover, and as stated before, FD approaches are

particularly useful to detect those subtle changes that

cannot be conventionally identified in MR images

(Free et al., 1996), and to characterize disorders

without an apparent structural abnormality of the

brain matter, such as schizophrenia and obsessive-

compulsive disorders (Ha et al., 2005). Until now,

most studies has been focused to obtain the 2DFD of

MR images of specific coronal sections, and some

authors even did a step ahead developing pseudo-3D

extrapolations. Thus, no so much efforts have been

made in the three-dimensional FD (3DFD) structural

characterization, an approach that may include

relevant information otherwise lost in the study. In

this sense, FD changes of the aged white matter have

been detected both in MR images both at the

pseudo-3D level and in 3D (Zhang et al., 2006;

2007).

Multiple Sclerosis is a neurodegenerative disease

mainly characterized by the appearance of white

matter lesions. The different manifestations of the

disease can be associated with its progression and,

because the onset of symptoms and the development

of visible damages in the MR images are related, an

early detection of the structural alterations of the

brain are crucial for clinical making decision

including an appropriate treatment. The most critical

to detect are the early stages of Multiple Sclerosis, in

which the white matter appears as apparently normal

in the MR images, even thought some of the

underlying cellular and molecular processes are

taking place (inflammatory cellular infiltration,

axonal degeneration and even gliosis).

Magnetization transfer imaging has been proposed

as a promising method for detecting changes in

apparently normal white matter in Multiple

Sclerosis. However, this method not only shows

some contradictory results in terms of their

sensitivity, but it is also expensive and difficult to be

included in the daily clinical diagnostic procedures

in most hospitals (Filippi et al., 1999). Our research

group has recently demonstrated that changes in

both the white matter (Esteban et al., 2007) and grey

matter (Esteban et al., 2009) are well-characterized

by the FD (2D and 3D respectively) using MR

images which are apparently normal in early stages

of Multiple Sclerosis. This approach has been

proposed as an useful tool for an early diagnostic of

the disease and, therefore, clinical decision making.

In addition, we have also detected changes in the

3DFD of the brain in one year-old children who had

intrauterine growth restriction (IUGR), when

compared with premature infants without IUGR and

full-term controls (Esteban et al., 2010).

3 COMPUTER GRAPHICS,

VOLUME MODELLING AND

ALGORITHM OPTIMIZATION

WITH GPU

Volume modelling is an important area of Computer

Graphics. Volume modelling gives solutions based

on the description of the volume occupied by the

represented objects, instead of the traditional

representation based on the surface. An important

effort to provide biomedical applications is being

developed in this area, mainly in 3D modelling and

visualization of scientific data obtained from

techniques such as CT, MR imaging or microscopy

(Muraki and Kita, 2006).

Just as the pixel is the basic element in a 2D

image, the voxel is the basic unit for representing 3D

volumes. Thus, volume modelling focuses on

providing techniques related to the construction,

processing and display of real structures by using

voxels. As commented above, the most generally

accepted approach for calculating the 2DFD is the

so-called box-counting method. Following the same

principles, calculating the 3DFD implies the

construction of the volumetric representation (using

voxels) of the objects that are being studied.

The typical way to obtain volumetric

representations from a set of medical MR or CT

images is to construct a 3D matrix by stacking Z

images of X x Y pixels each. From this 3D matrix,

there are a wide variety of algorithms to display,

processing or reconstruction of the region of interest

in each case study (Muraki and Kita, 2006; Lorensen

and Cline, 1987).

A SOFTWARE PLATFORM TO ANALYZE MR IMAGES BASED ON 3D FRACTAL DIMENSION - Application in

Neurodegenerative Diseases

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Figure 1: 3DFD web application. Brain data uploaded to the server.

There are alternative representations for a 3D

volume that maintain their topologic essence and are

more compact, such as the so-called skeletons. This

representation may allows an accurate classification

of the represented volume (Cornea et al., 2007).

The computational cost of the algorithms that

process 3D volumes is usually very high, especially

when acceptable levels of precision are required.

Thus, the searching for efficient solutions is crucial

to provide interactivity to user-friendly applications.

The ability to program the Graphics Processing

Units (GPUs) of any current mid-range PC has

revolutionized many fields where high

computational cost algorithms are required (Owens

et al., 2007). The evolution of these GPUs and their

low cost, especially compared with traditional

parallel computers, place them as one of the most

interesting solutions when the programmer wants to

optimize data-parallel algorithms.

Many volume modelling algorithms are based on

performing independent operations on each voxel.

For these cases, applying GPU-based optimizations

is very suitable. Iso-surface extraction algorithms,

segmentation of medical images, or interactive

visualization of volumes are examples of such

algorithms (Stone et al., 2008; Fan et al., 2008).

GPU programming is based on the classic

graphic display pipeline. However, using the GPU to

code algorithms that are not related with graphics

may be quite complicated, since it requires

knowledge of the architecture and the operation of

the graphic processor. For this reason, several GPU

programming paradigms, that do not require any

knowledge of graphics, have recently emerged.

NVIDIA CUDA (Luebke, 2008) and OpenCL

(Khronos group, 2010) stand out among these new

paradigms. These programming models exploit the

inherent GPU parallelism by writing simple

programs (threads) running into hundreds of

thousands of parallel invocations on the GPU. There

are many examples of successful use of GPU

optimization in the biomedical area (with

improvements in time between x10 and x100), such

as CT reconstruction or interactive MR imaging

visualization (Xu and Mueller, 2007; Zhao et al.,

2009).

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Figure 2: 3DFD web application. Box-counting and 3DFD calculation.

4 A SOFTWARE PLATFORM TO

CALCULATE THE 3DFD OF

MR IMAGES

A general software to compute the 3DFD of MR

images has been developed by our research group in

previous studies, which has become a very useful

and high social-interest tool (Ruiz de Miras et al.,

2011). The different exiting hardware and software

platforms to obtain the MR images, the wide profile

of potential users of the software, and the need for

constant maintaining and updating in this kind of

programs, imply that the software has to be made

available to the scientific community in the most

flexible and user-friendly way. Thus, we have

decided to integrate our software into a Web

platform, a project with the aim of providing a

universal access through a simple Web browser. A

Web platform instantly gives the user the latest

version of the software and, when correctly related

to a database, a large number of medical images,

uploaded by different users, can be collected,

classified and analyzed, which otherwise cannot be

accessed to and managed.

Figure 1 and Figure 2 shows sample snapshots of

our developed web platform. In the first one, the

main data of an uploaded 3D image, including the

set of slices, is showed. The interactive computation

of the 3DFD for the uploaded 3D image is showed

in Figure 2. The obtained results are represented in

the scattered graphic for slope analysis, allowing us

to discard the initial and final points out of linearity.

The final value of 3DFD is the slope of the resulting

regression line, which can be directly stored by

pushing the "Save Results" button. The value of the

box-counting and image segmentation input

parameters (maximum voxel size and threshold,

respectively) can also be tuned, thus obtaining

different 3DFD values which can also be also stored

A SOFTWARE PLATFORM TO ANALYZE MR IMAGES BASED ON 3D FRACTAL DIMENSION - Application in

Neurodegenerative Diseases

557

in the database.

The computational cost of the different

algorithms needed to calculate the 3DFD is very

high, which is a handicap when interactivity and

fast feedback to the user are essential, as in data

analysis Web platforms. The algorithms required in

the engine are those related to volume visualization,

box-counting calculation for different voxel

resolutions and the computation of the curve-

skeleton of the represented 3D image. Because all

these algorithms can be reduced to individual

operations on each voxel of the volume, and taking

into account that these operations can be run in

parallel using the recent hardware and software

platforms based on GPU programming, we have

adapted and improved them to be run on these

massively parallel platforms. Thus, the degree of

interactivity needed to integrate the 3DFD

calculation, in a really useful and user friendly Web

platform, has been achieved.

The most time-consuming algorithm is the

curve-skeleton calculation; in our case we selected

and implemented the thinning approach as the most

appropriate (Palágyi and Kuba, 1999). A 3D curve-

skeleton is a very compact representation of a three

dimensional object, and its 3DFD provides very

good and reliable results.

Figure 3: Curve-skeleton generation time and speedup for

executions over 512 x 512 x 512 voxelized models. GPU

executions on the NVIDIA GTX 580. CPU execution on

Intel i7-920, an eight-threaded CPU.

A standard calculation of a 3D skeleton takes

around 8 minutes to be obtained, which is a very

time-consuming process. After the 3D thinning

algorithm multi-threaded implementation, for GPU

and multi-core CPUs, we obtained a substantial

execution-time improvement, when compared to the

traditional mono-threaded version. We used two

parallel programming models: CUDA and OpenCL.

Figure 3 shows the running time of each parallel

version, where the speedup achievement using the

optimized parallel algorithms for the GPU is showed

to be improved 97,9x against the CPU single-

process version, and more than 19x over the CPU

multithreaded version, being this two interesting

results.

Figure 4: Box-Counting optimization. C-CPU algorithm

(mono-threaded) vs. CUDA-GPU algorithm (multi-

threaded). Execution time and speedup.

We have also designed and implemented a

parallel optimized version of the box-counting

algorithm. This algorithm run faster in CPU than the

curve-skeleton calculation, taking just a few

seconds, which may be considered a good execution

time. However, the execution time may be tediously

longer when performing the box-counting

calculation on a set of n case studies. In addition, the

segmentation threshold (which is an input parameter,

as seen in Figure 2) may need to be tuned and, thus,

several runs have to be executed using different m

threshold values. Thus, the execution time has to be

multiplied by n and m in the simplest case. Figure 4

shows the CUDA implementation runtime of the

box-counting algorithm. The obtained results

detected an average 27-fold improvement for the

best case, thus decreasing the execution time from

around 28 seconds to only one second when using

the highest model of resolution (512 x 512 x 512

pixels).

5 CONCLUSIONS

We have developed effective and efficient

algorithms to obtain the FD from 3D images,

obtaining a complete brain characterization. These

algorithms have been drastically optimized and

implemented in a user-friendly Web platform that

currently is in the last stage of testing by our

research group and selected medical staff. This

advanced platform will be available soon to the

scientific community and we hope it may be a useful

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558

tool for early diagnosis of several neurodegenerative

diseases.

ACKNOWLEDGEMENTS

This work has been partially supported by the

University of Jaén, the Caja Rural de Jaén, the

Andalusian Government and the European Union

(via ERDF funds) through the research projects

UJA2009/13/04 and PI10-TIC-5807.

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Neurodegenerative Diseases

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