Radiation Physics and Chemistry 95 (2014) 258–260

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Radiation Physics and Chemistry

0969-80

http://d

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christia

journal homepage: www.elsevier.com/locate/radphyschem

Proposal of an algorithm for analysis of bone demineralizationusing synchrotron radiation X-ray mCT images

Christiano Jorge Gomes Pinheiro n, Anderson Alvarenga de Moura Meneses, Delson Braz,Luıs Fernando de Oliveira, Regina Cely Rodrigues Barroso

UFES, Departamento de Quımica e Fısica, Alto Universitario, s/no.—Guararema, 16 Alegre, ES, Brazil

H I G H L I G H T S

c The characterization of complex 3D structures is a challenge to researchers.c High-resolution X-ray Computed Tomography systems are employed in a wide range of areas.c The Synchrotron Radiation beams enables innovative imaging techniques.c The connectivity is seen as an alternative to analysis surfaces.

a r t i c l e i n f o

Article history:

Received 30 September 2012

Accepted 1 January 2013Available online 11 January 2013

Keywords:

Synchrotron radiation

X-Ray

Micro-computed tomography

Topology

Connectivity

6X/$ - see front matter & 2013 Elsevier Ltd.

x.doi.org/10.1016/j.radphyschem.2013.01.001

esponding author. Tel.: þ55 28 35528717.

ail addresses: christrieste@yahoo.it,

no.pinheiro@ufes.br (C.J.G. Pinheiro).

a b s t r a c t

Research on radiation effects on bony tissue, osteoporosis and other diseases demands the assessment

of bone structures. Synchrotron Radiation (SR) X-ray micro-Computed Tomography (mCT) is an imaging

technique that allows the investigation of such structures in the micrometer level. With the high

coherence as well as the monochromaticity of the SR beam, it is possible to assess pathological

conditions in those structures accurately, providing quantitative information for decision making.

Topology and Histomorphometry provide parameters which describe the relationships between pores,

canals and the connectivity in structures. Thus, with periodical assessment of the bone structure by SR-

mCT imaging, it is possible to verify the evolution of a disease or the impact of a treatment. In the

present summary we describe the application of Topology concepts for quantitative assessment of bone

structures in the analysis of SR-mCT images acquired at the Elettra Laboratory (Trieste, Italy).

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The characterization of complex 3D structures such as pumice-stone, cancellous bone or porous material is a challenge to physi-cians, physicists, chemists and engineers. Therefore, how to quantifythese structures and which parameters should be used are funda-mental questions to be answered. The quantitative Stereology, usedin medical and biological investigations, provides a set of morpho-logical parameters which relates areas and volumes. In the case ofspecific problems, when the Stereology is applied to bones, theresult is the histomorphometry. However, morphological aspects arenot sufficient to characterize complex 3D structures since informa-tion about voids, porous, connections and orientations are notcollected. In order to overcome this limitation, some topologicalquantification can be added to the methodology, specially theconcepts of connectivity and anisotropy.

All rights reserved.

The connectivity is based on notions of topology, mainly on theconcept of homeomorphism, and reflects the degree of intercon-nections present on the sample (Odgaard, 1999; de Oliveira et al.,2003). The connectivity has relationship is related to histomor-phometric parameter BS/BV (surface to volume ratio), bothindicating changes in the sample structures. Due to the greatdifficulty in quantifying structures with complex surfaces, thecalculation of connectivity is seen as an alternative to analysis ofthose surfaces (Feldkamp et al., 1989).

In mathematics, and more specifically in algebraictopology and polyhedral combinatorics, the Euler characteristicis a topological invariant, that is, a number that describes atopological space’s shape or structure regardless of the way itis bent.

The Euler characteristic was originally defined for surfaces ofpolyhedra and used to prove various theorems about them and itis commonly denoted by w. Any polyhedron’s surface has theEuler characteristic according to

V�AþF ¼ w¼ 2 ð1Þ

C.J.G. Pinheiro et al. / Radiation Physics and Chemistry 95 (2014) 258–260 259

where V, E and F are respectively the numbers of vertices(corners), edges and faces in the given polyhedron (Hoffman,1989).

From a topological viewpoint, the simplest solids are thosethat have a closed orientable surface and no holes or interiorvoids. We assume that each face is bounded by a single loop ofadjacent vertices; that is, the face is homeomorphic to a closeddisk (Feldkamp et al., 1989; Odgaard and Gundersen, 1993; Kimet al., 2004).

Assume the fact that such solids are topologically equivalent(homeomorphic), to a sphere with zero or more handles. Thenumber of handles of the surface is called the genus (G). TheEuler–Poincare formula can be generalized adding the possibilityof internal voids. These voids are bounded by separate closedmanifold surfaces, called shells, denoted by S.

Generalizing, G is equal to the number of paths (connections)less a unit and the assessment of the genus value indicates howmuch connected the structure is, i.e., the connectivity. Moreover,the presence of voids within the structure does not interfere withthe genus; it just increases the number of surfaces. The Eq. (1)does not account the genus or the surfaces, but it is noticeablethat the characteristic number becomes more negative as thegenus increases and more positive as the number of surfacesincreases. A change in the formulation of Euler characteristicnumber introduces both quantities genus and surfaces, resultingin a general expression known as Euler–Poincare formula:

w�2 NS�NGð Þ ¼ 0 ð2Þ

where NS is the number of surfaces and NG is the genus of thestructure (Hoffman, 1989). The parameter NS quantifies the totalnumber of internal and external surfaces. So, NS can be replacedby (SEþSI), where SE and SI are the numbers of external andinternal surfaces, respectively (Pinheiro, 2008).

The special characteristics of Synchrotron Radiation micro-Computed Tomography (SR-mCT), allows the investigation ofdetails in bone structure (Hounsfield, 1973; de Oliveira et al.,2003). The present paper describes the application of the Euler–Poincare equation as the basis of the proposal algorithm, devel-oped for calculating Connectivity, applied to SR-mCT scans of rattibiae obtained at the ELETTRA Laboratory.

Fig. 1. Slice no. 24 of a Wistar rat tibia bone scan, obtained with SR-mCT, after

binarization.

2. Materials and methods

2.1. Synchrotron radiation micro-computed tomography (mCT)

images

The mCT is an emerging technique for the non-destructiveassessment and analysis of the 3D cortical bone structure. Thebasis of tomography is X-ray radiography. According to the Beer–Lambert law (Eq. (3)), which governs the image intensity inprojection imaging, an X-ray beam is sent through a sample andthe transmitted beam is recorded on a detector (Meneses et al.,2010).

I¼ I0 e�R‘m ðsÞds

ð3Þ

SR facilities such as the ELETTRA Laboratory (Trieste, Italy)provide important characteristics for the acquisition of medicalimages. The parallel geometry of the laminar shaped beamsimplifies the slices reconstruction and reduces the geometry-related artifacts that classical cone-beam mCT usually introduces.The images were obtained at the SYRMEP (Synchrotron Radiationfor Medical Physics) beamline of the Elettra Laboratory (Trieste,Italy). High quality images can be acquired by two charge coupleddevice (CCD) cameras with 2048�2048 pixels2, 14�14 mm2

pixel size, coupled to an intensifier screen with magnification

(1:1) available at the SYRMEP. The beamline provides a mono-chromatic laminar-section X-ray with a maximum area of about160�5 mm2 at 20 keV, at a distance of about 23 m from thesource. The system consists of a Si (111) crystal working at theBragg configuration. The useful energy range is 8–35 keV. Theintrinsic energy resolution of the monochromator is about 10�3.Typical flux measured at the sample position at 17 keV is about1.6�108 photons/mm2 s with a stored electron beam of 300 mAas Elettra operates at 2 GeV (Elder et al., 1947; Arfelli et al., 2000).A custom-built ionization chamber is placed upstream to thesample to determine the exposure on the sample. A micrometricvertical and horizontal translation stage allows the positioningand the scanning of the sample with respect to the stationarybeam and a rotational stage allows CT acquisition with a resolu-tion of 0.0011.

The SR-mCT is very useful technique when it comes to 3Dimaging of many geometries. The SR properties enable SR-mCT toreconstruct the highly resolved 3D image even with a high signal-to-noise ratio (Pinheiro, 2008; Meneses et al., 2010).

Other possibilities can be exploited by SR-mCT imaging fordiscerning between similar attenuating elements or also to revealpoor attenuating materials when the whole incident radiation istransmitted. Such a methods lie in the phase contrast (PHC)imaging and the phase retrieval imaging resulting in manyapplication fields such as medicine for the investigation of bonesand soft tissues (Momose et al., 1995; Xu et al., 2001).

2.2. The algorithm

The algorithm, based upon the Topology concepts, was appliedin order to quantify the bony mass of a Wistar rat (Rattus

norvegicus) tibia sample scan (120 slices with 380�420 pixels2),which was acquired at the Elettra Laboratory (Trieste, Italy). Theentire scan was binarized, for application of the new algorithm.The result of the slice binarization is depicted in Fig. 1.

3. Results

In order to validate and demonstrate the ability of the method,six Wistar rat tibia sample were scanned for quantification. Thevolume of interest (VOI) was the area with cortical bone. Once theVOI has been selected, the image was partitioned into multiple

Table 1Results for the Wistar rat tibia sample.

Sample Connectivity Porous number

1 200 231

2 211 234

3 156 288

4 185 87

5 161 232

6 202 116

Fig. 2. Significant linear relationship between 3D connectivity and 3D histomor-

phometric parameter BS/BV.

Fig. 3. By scanning the skeleton, it is possible to visualize the Haversian and

Volkmann canals found in compact bone.

C.J.G. Pinheiro et al. / Radiation Physics and Chemistry 95 (2014) 258–260260

regions (sets of voxels) with 100�100�100 voxels. Each set ofregions averages were calculated. The connectivity and porousnumber and their results for the analysis of the samples scan areexhibited in Table 1.

Preliminary data demonstrated a stronger correlation(r¼0.997) between connectivity 3D and the 3D histomorpho-metric parameter BS/BV (Fig. 2). These data provide the firstevidence that an index of structure can be predicted byconnectivity too.

Using the Zhang & Suen parallel thinning algorithm (Zhangand Suen, 1984), it was possible to visualize and check canals andtortuosity of the porous network calculated with the new algo-rithm (Fig. 3).

4. Conclusions

SR X-ray mCT enables magnified images which may be used asa non-invasive and non-destructive technique for diagnosis andtreatment of diseases, for example, the osteoporosis which hasbecome a major public health problem. The preliminary resultsdemonstrated viability and potential of application of the newalgorithm to SR-mCT bone scans, providing also parameters notgiven by commercial software.

Acknowledgment

C.J.G.P. would like to thank FAPES (Fundac- ~ao de Amparo �aPesquisa do Espırito Santo) for financial support.

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