Document Detail

Fractal analysis of elastographic images for automatic detection of diffuse diseases of salivary glands: preliminary results.
Jump to Full Text
MedLine Citation:
PMID:  23762183     Owner:  NLM     Status:  In-Data-Review    
The geometry of some medical images of tissues, obtained by elastography and ultrasonography, is characterized in terms of complexity parameters such as the fractal dimension (FD). It is well known that in any image there are very subtle details that are not easily detectable by the human eye. However, in many cases like medical imaging diagnosis, these details are very important since they might contain some hidden information about the possible existence of certain pathological lesions like tissue degeneration, inflammation, or tumors. Therefore, an automatic method of analysis could be an expedient tool for physicians to give a faultless diagnosis. The fractal analysis is of great importance in relation to a quantitative evaluation of "real-time" elastography, a procedure considered to be operator dependent in the current clinical practice. Mathematical analysis reveals significant discrepancies among normal and pathological image patterns. The main objective of our work is to demonstrate the clinical utility of this procedure on an ultrasound image corresponding to a submandibular diffuse pathology.
Alexandru Florin Badea; Monica Lupsor Platon; Maria Crisan; Carlo Cattani; Iulia Badea; Gaetano Pierro; Gianpaolo Sannino; Grigore Baciut
Related Documents :
18003293 - Live-wire-based 3d segmentation method.
8402523 - 3d reconstruction of biological objects from sequential image planes--applied on cerebr...
17679063 - Spect versus planar gated blood pool imaging for left ventricular evaluation.
Publication Detail:
Type:  Journal Article     Date:  2013-05-16
Journal Detail:
Title:  Computational and mathematical methods in medicine     Volume:  2013     ISSN:  1748-6718     ISO Abbreviation:  Comput Math Methods Med     Publication Date:  2013  
Date Detail:
Created Date:  2013-06-13     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101277751     Medline TA:  Comput Math Methods Med     Country:  United States    
Other Details:
Languages:  eng     Pagination:  347238     Citation Subset:  IM    
Department of Cranio-Maxillo-Facial Surgery, University of Medicine and Pharmacy "Iuliu Haţieganu", Cardinal Hossu Street 37, 400 029 Cluj-Napoca, Romania.
Export Citation:
APA/MLA Format     Download EndNote     Download BibTex
MeSH Terms

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine

Full Text
Journal Information
Journal ID (nlm-ta): Comput Math Methods Med
Journal ID (iso-abbrev): Comput Math Methods Med
Journal ID (publisher-id): CMMM
ISSN: 1748-670X
ISSN: 1748-6718
Publisher: Hindawi Publishing Corporation
Article Information
Download PDF
Copyright © 2013 Alexandru Florin Badea et al.
Received Day: 10 Month: 3 Year: 2013
Accepted Day: 12 Month: 4 Year: 2013
Print publication date: Year: 2013
Electronic publication date: Day: 16 Month: 5 Year: 2013
Volume: 2013E-location ID: 347238
PubMed Id: 23762183
ID: 3671291
DOI: 10.1155/2013/347238

Fractal Analysis of Elastographic Images for Automatic Detection of Diffuse Diseases of Salivary Glands: Preliminary Results
Alexandru Florin Badea1
Monica Lupsor Platon2
Maria Crisan3*
Carlo Cattani4
Iulia Badea5
Gaetano Pierro6
Gianpaolo Sannino7
Grigore Baciut1
1Department of Cranio-Maxillo-Facial Surgery, University of Medicine and Pharmacy “Iuliu Haţieganu”, Cardinal Hossu Street 37, 400 029 Cluj-Napoca, Romania
2Department of Clinical Imaging, University of Medicine and Pharmacy “Iuliu Haţieganu”, Croitorilor Street 19-21, 400 162 Cluj-Napoca, Romania
3Department of Histology, Pasteur 5-6 University of Medicine and Pharmacy “Iuliu Haţieganu”, 400 349 Cluj-Napoca, Romania
4Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy
5Department of Dental Prevention, University of Medicine Pharmacy “Iuliu Haţieganu”, Victor Babes Street, 400 012 Cluj-Napoca, Romania
6Department of System Biology, Phd School, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy
7Department of Oral Health, University of Rome Tor Vergata, Viale Oxford, 00100 Rome, Italy
Correspondence: *Maria Crisan:
[other] Academic Editor: Shengyong Chen

1. Introduction

In some recent papers [14], the fractal nature of nucleotide distribution in DNA has been investigated in order to classify and compare DNA sequences and to single out some particularities in the nucleotide distribution, sometimes in order to be used as markers for the existence of certain pathologies [59]. Almost all these papers are motivated by the hypothesis that changes in the fractal dimension might be taken as markers for the existence of pathologies since it is universally accepted nowadays that bioactivity and the biological systems are based on some fractal nature organization [3, 4, 1013]. From a mathematical point of view, this could be explained by the fact that the larger the number of interacting individuals, the more complex the corresponding system of interactions is. These hidden rules that lead to this complex fractal topology could be some simple recursive rules, typical of any fractal-like structure, which usually requires a large number of recursions in order to fill the space.

In recent years, many papers [36, 9, 14, 15] have investigated the multi-fractality of biological signals such as DNA and the possible influence of the fractal geometry on the functionality of DNA from a biological-chemical point of view. Almost all these papers concerning the multifractality of biological signals are based on the hypothesis that the functionality and the evolution of tissues/cells/DNA are related to and measured by the evolving fractal geometry (complexity), so that malfunctions and pathologies can be linked with the degeneracy of the geometry during its evolution time [57, 1618].

From a mathematical point of view, a fractal is a geometric object mainly characterized by the noninteger dimension and self-similarity so that a typical pattern repeats itself cyclically at different scales. A more complex definition of a fractal is based on the four properties: self-similarity, fine structure, irregularities, and noninteger dimension [19]. The fractal dimension is a parameter which measures the relationship between the geometric un-smoothness of the object and its underlying metric space. Since it is a noninteger value, it is usually taken as a measure of the unsmoothness, thus being improperly related to the level of complexity or disorder. Fractality has been observed and measured in several fields of specialization in biology, similar to those in pathology and cancer models [20, 21]. However, only recently have been made some attempts to investigate the structural importance of the “fractal nature” of the DNA. It has been observed in some recent papers that the higher FD corresponds to the higher information complexity and thus to the evolution towards a pathological state [3, 4].

In the following, we will analyse the particularities of the fractal dimension focused on the pathological aspects of some tissues, more specific those belonging to a submandibular gland. For the first time, the FD is computed on images obtained by the new technology of elastographic imaging focused on this salivary gland.

2. Materials and Methods
2.1. Material

A 55-year-old woman presented herself in the emergency room of the Maxilo-Facial Surgery Department for acute pain and enlargement of the left submandibular gland and was selected for ultrasound evaluation. The ultrasound examination was performed using the ACUSON S2000 (Siemens) ultrasound equipment, where the ARFI (acoustic radiation force impulse) and real-time elastography technique were implemented. The ACUSON S2000 is a powerful, non-invasive, ultrasound based device, which gives very accurate B mode and Doppler images of tissues. It has been profitably used for the analysis of abdominal, breast, cardiac, obstetrical, and gynaecological imaging and also for small parts such as thyroid and vascular imaging.

The patient was placed laying down and facing up, while the transducer was placed in contact with skin on the area of the right and then the left submandibular gland successively. The shear wave velocity within the right and the left submandibular gland parenchyma was determined for each submandibular gland (in meters/second); colour elastographic images were also acquired. A colour map was used where stiff tissues were coded in blue and soft tissues in red. These images were studied afterwards for fractal analysis.

Figure 1 represents a 2D ultrasound evaluation in a “grey scale” mode, and Figure 2 represents a combination between 2D ultrasonography and “colour flow map” (CFM, or “duplex sonography”). From the first viewing, we can easily detect, by its enlargement, the gland swelling (Figure 1) and the hyper vascular pattern (Figure 2), both of these pieces of information being highly suggestive for the inflammation diagnosis. The combined clinical and ultrasound evaluation is conclusive for an acute inflammation of the submandibular gland. Figures 3 and 5 (obtained on the right salivary swollen gland) and Figures 4 and 6 (obtained on the left side, normal gland) represent elastography in quantitative mode (Figures 3 and 4), color mode (Figures 5 and 6) (ARFI tissue imaging mapping color).

2.2. Methods

Concerning the fractal analysis in this section, we will summarize some definitions already given in [3].

2.3. Parameters for the Analysis of Complexity and Fractal Geometry

As a measure of the complexity and fractal geometry, we will consider only the fractal dimension and regression analysis (Shannon information entropy, lacunarity, and succolarity will be considered in a forthcoming paper).

Let px(n) be the probability to find the value x at the position n, the fractal dimension is given by [3, 4, 22]

[Formula ID: EEq1]
D=1N∑n=2Nlog⁡ px(n)log⁡ n.
In order to compute the FD, we will make use of the gliding box method on a converted black and white image. Let SN be a given black and white image (BW) with 1 and 0 in correspondence with respectively, black and white pixels, we can consider a gliding box of r-length, so that
[Formula ID: EEq2]
is the frequency of “1” within the box. The corresponding probability is
[Formula ID: EEq3]
Then the box moves to the next position k + 1 so that we obtain the probability distribution
[Formula ID: eq4]
so that we can compute the frequency of “1” within the box. The FD is computed on such gliding boxes through (1).

3. Results
3.1. Fractal Dimension for 2D Ultrasound and Elastographic Images

Concerning the fractal dimension of the elastographic images, as given by (1), we can see (Table 1) that the highest FD is shown by Figure 7 and lowest by the Figure 8.

The images were analyzed in 8-bit using the Image J software (tools box counting).

The figures are referred to a patient with an acute inflammation of the submandibular gland.

Figure 1 shows a 2D ultrasound evaluation in grey scale. Figure 2 shows a 2D colour flow map evaluation (duplex sonography). Figures 3 and 4 were obtained by using the method elastography ARFI-Siemens, and they display quantitative information. The values of fractal dimension (FD) of Figures 3 and 4 are similar, and it is not possible to distinguish between pathological (Figure 3) and normal (Figure 4) states. The Figures 5 and 6 are obtained through elastography ARFI with qualitative information. From the fractal analysis by the box counting method, we have noticed that the value of Fd is lower (1.650) in Figure 5 (pathological condition) than Figure 6 (normal state). Figures 7 (pathological state) and 8 (normal state) were obtained through real time elastography.

From the computations, we can note that the higher value of Fd belongs to the pathological state (1.907), thus suggesting that the Fd increases during the evolution of the pathology (increasing degeneracy). Therefore, from Fd, analysis is possible to distinguish between pathological state and normal state of tissues by real time elastography because it is the better method to discriminate Fd values in a clear, sharp way.

4. Discussion

Elastography is an ultrasonographic technique which appreciates tissue stiffness either by evaluating a colour map [23, 24] or by quantifying the shear wave velocity generated by the transmission of an acoustic pressure into the parenchyma (ARFI technique) [2527]. In the first situation, the visualization of the tissue stiffness implies a “real-time” representation of the colour mode elastographic images overlapped on the conventional gray-scale images, each value (from 1 to 255) being attached to a color. The system uses a color map (red-green-blue) in which stiff tissues are coded in dark blue, intermediate ones in shades of green, softer tissues in yellow and the softest in red, but the color scale may be reversed in relation to how the equipment is calibrated. Depending on the color and with the help of a special software, several elasticity scores that correlate with the degree of tissue stiffness can be calculated [23]. Numerous clinical applications using these procedures were introduced into routine practice, many of them being focused on the detection of tumoral tissue in breast, thyroid, and prostate.

In the last years, a new elastographic method, based on the ARFI technique (acoustic radiation force impulse imaging), is available on modern ultrasound equipment. The ARFI technique consists in a mechanical stimulation of the tissue on which it is applied by the transmission of a short time acoustic wave (<1 ms) in a region of interest, determined by the examiner, perpendicular on the direction of the pressure waves, and leading to a micronic scale “dislocation” of the tissues. Therefore, in contrast with the usual ultrasonographic examination, where the sound waves have an axial orientation, the shear waves do not interact directly with the transducer. Furthermore, the shear waves are attenuated 10.000 faster than the conventional ultrasound waves and therefore need a higher sensitivity in order to be measured [2529]. Detection waves, which are simultaneously generated, have a much lower intensity than the pressure acoustic wave (1 : 1000). The moment when the detection waves interact with the shear waves represents the time passed from the moment the shear waves were generated until they crossed the region of interest. The shear waves are registered in different locations at various moments and thus the shear wave velocity is automatically calculated, the stiffer the organ the higher the velocity of the shear waves. Therefore, the shear wave velocity is actually considered to be an intrinsic feature of the tissue [2529]. In current clinical practice, the same transducer is used both to generate the pressure acoustic wave and to register the tissue dislocation. Since the technique is implemented in the ultrasound equipment through software changes, B mode ultrasound examination, color Doppler interrogation and ARFI images are all possible on the same machine [30].

Currently, elastography is widely studied in relation to different clinical applications: breast, thyroid, liver, colon and prostate [29, 3136]. The application in salivary gland pathology has been singularly considered at least in our literature database. Some reports present the utility of elastography in a better delineation of tumors of these glands. Applications on diffuse disease are few although the importance of this kind of pathology is important! Inflammations of salivary glands occur in many conditions and the incidence is significant. There is a need for accurate diagnosis, staging, and prognosis. The occurrence of complications is also very important! Elastography represents a “virtual” way of palpation reproductive and with possibility of quantification.

Although there are several improvements, the main limitation of elastography is the dependency of the procedure to the operator's experience. This characteristic makes elastography vulnerable with a quite high amount of variations of elastographic results and interpretation. A more accurate analysis of the elastographic picture based on very precise evaluation as fractal analysis is an obvious step forward. In our preliminary study, the difference between normal and pathologic submandibular tissue using the fractal analysis was demonstrated. Because of the very new technologies accessible in practice as elastography is, and because of the mathematical instruments available as fractal analysis of the pictures, we are encouraged to believe that the ultrasound procedure might become operator independent and more confident for subtle diagnosis. However, a higher number of pictures coming from different patients with diffuse diseases in different stages of evolution are needed.

5. Conclusion

In this work, the multi-fractality of 2D and elastographic images of diffuse pathological states in submandibular glands has been investigated. The corresponding FD has been computed and has shown that images with the highest FD correspond to the existence of pathology. The extension of this study with incrementing the number of ultrasound images and patients is needed to demonstrate the practical utility of this procedure.

Conflict of Interests

The authors declare that there is no conflict of interests concerning the validity of this research with respect to some possible financial gain.

1. Anh V,Zhi-Min G,Shun-Chao L. Fractals in DNA sequence analysisChinese PhysicsYear: 2002111213131318
2. Buldyrev SV,Dokholyan NV,Goldberger AL,et al. Analysis of DNA sequences using methods of statistical physicsPhysica AYear: 19982491–44304382-s2.0-0031996849
3. Cattani C. Fractals and hidden symmetries in DNAMathematical Problems in EngineeringYear: 2010201031 pages2-s2.0-77954525762507056
4. Pierro G. Sequence complexity of Chromosome 3 in Caenorhabditis elegansAdvances in BioinformaticsYear: 2012201212 pages287486
5. Bedin V,Adam RL,de Sá BCS,Landman G,Metze K. Fractal dimension of chromatin is an independent prognostic factor for survival in melanomaBMC CancerYear: 201010, article 2602-s2.0-77953073626
6. Ferro DP,Falconi MA,Adam RL,et al. Fractal characteristics of May-Grünwald-Giemsa stained chromatin are independent prognostic factors for survival in multiple myelomaPLoS ONEYear: 2011662-s2.0-79959279611e20706
7. Metze K,Adam RL,Ferreira RC. Robust variables in texture analysisPathologyYear: 20104266096102-s2.0-7795692100520854091
8. Metze K. Fractal characteristics of May Grunwald Giemsa stained chromatin are independent prognostic factors for survival in multiple myelomaPLoS OneYear: 20116618
9. Dey P,Banik T. Fractal dimension of chromatin texture of squamous intraepithelial lesions of cervixDiagnostic CytopathologyYear: 201240215215422246932
10. Voss RF. Evolution of long-range fractal correlations and 1/f noise in DNA base sequencesPhysical Review LettersYear: 19926825380538082-s2.0-000020487810045801
11. Voss RF. Long-range fractal correlations in DNA introns and exonsFractalsYear: 19922116
12. Chatzidimitriou-Dreismann CA,Larhammar D. Long-range correlations in DNANatureYear: 199336164092122132-s2.0-00274596848423849
13. Fukushima A,Kinouchi M,Kanaya S,Kudo Y,Ikemura T. Statistical analysis of genomic information: long-range correlation in DNA sequencesGenome InformaticsYear: 2000113153316
14. Li M. Fractal time series-a tutorial reviewMathematical Problems in EngineeringYear: 2010201026 pages2-s2.0-77951489276157264
15. Li M,Zhao W. Quantitatively investigating locally weak stationarity of modified multifractional Gaussian noisePhysica AYear: 20123912462686278
16. D’Anselmi F,Valerio M,Cucina A,et al. Metabolism and cell shape in cancer: a fractal analysisInternational Journal of Biochemistry and Cell BiologyYear: 2011437105210582-s2.0-7995810935220460170
17. Pantic I,Harhaji-Trajkovic L,Pantovic A,Milosevic NT,Trajkovic V. Changes in fractal dimension and lacunarity as early markers of UV-induced apoptosisJournal of Theoretical BiologyYear: 201230321879222763132
18. Vasilescu C,Giza DE,Petrisor P,Dobrescu R,Popescu I,Herlea V. Morphometrical differences between resectable and non-resectable pancreatic cancer: a fractal analysisHepatogastroentologyYear: 201259113284288
19. Mandelbrot B. The Fractal Geometry of NatureYear: 1982New York, NY, USAW. H. Freeman
20. Baish JW,Jain RK. Fractals and cancerCancer ResearchYear: 20006014368336882-s2.0-003466089010919633
21. Cross SS. Fractals in pathologyJournal of PathologyYear: 199718211189227334
22. Backes AR,Bruno OM. Segmentação de texturas por análise de complexidadeJournal of Computer ScienceYear: 2006518795
23. Friedrich-Rust M,Ong MF,Herrmann E,et al. Real-time elastography for noninvasive assessment of liver fibrosis in chronic viral hepatitisAmerican Journal of RoentgenologyYear: 200718837587642-s2.0-3384720222417312065
24. Sǎftoui A,Gheonea DI,Ciurea T. Hue histogram analysis of real-time elastography images for noninvasive assessment of liver fibrosisAmerican Journal of RoentgenologyYear: 20071894W232W2332-s2.0-3534885317517885039
25. Dumont D,Behler RH,Nichols TC,Merricks EP,Gallippi CM. ARFI imaging for noninvasive material characterization of atherosclerosisUltrasound in Medicine and BiologyYear: 20063211170317112-s2.0-3375091351917112956
26. Zhai L,Palmeri ML,Bouchard RR,Nightingale RW,Nightingale KR. An integrated indenter-ARFI imaging system for tissue stiffness quantificationUltrasonic ImagingYear: 2008302951112-s2.0-5274908457818939611
27. Behler RH,Nichols TC,Zhu H,Merricks EP,Gallippi CM. ARFI imaging for noninvasive material characterization of atherosclerosis part II: toward in vivo characterizationUltrasound in Medicine and BiologyYear: 20093522782952-s2.0-5834909787319026483
28. Nightingale K,Soo MS,Nightingale R,Trahey G. Acoustic radiation force impulse imaging: in vivo demonstration of clinical feasibilityUltrasound in Medicine and BiologyYear: 20022822272352-s2.0-003621869511937286
29. Lupsor M,Badea R,Stefanescu H,et al. Performance of a new elastographic method (ARFI technology) compared to unidimensional transient elastography in the noninvasive assessment of chronic hepatitis C. Preliminary resultsJournal of Gastrointestinal and Liver DiseasesYear: 20091833033102-s2.0-7394912350319795024
30. Fahey BJ,Nightingale KR,Nelson RC,Palmeri ML,Trahey GE. Acoustic radiation force impulse imaging of the abdomen: demonstration of feasibility and utilityUltrasound in Medicine and BiologyYear: 2005319118511982-s2.0-2494448076616176786
31. Goertz RS,Amann K,Heide R,Bernatik T,Neurath MF,Strobel D. An abdominal and thyroid status with acoustic radiation force impulse elastometry—a feasibility study: acoustic radiation force impulse elastometry of human organsEuropean Journal of RadiologyYear: 2011803e226e23020971591
32. Rafaelsen SR,Vagn-Hansen C,Sørensen T,Lindebjerg J,Pløen J,Jakobsen A. Ultrasound elastography in patients with rectal cancer treated with chemoradiationEuropean Journal of RadiologyYear: 2013
33. Taverna G,Magnoni P,Giusti G,et al. Impact of real-time elastography versus systematic prostate biopsy method on cancer detection rate in men with a serum prostate-specific antigen between 2.5 and 10 ng/mLISRN OncologyYear: 201320135 pages584672
34. Rizzo L,Nunnari G,Berretta M,Cacopardo B. Acoustic radial force impulse as an effective tool for a prompt and reliable diagnosis of hepatocellular carcinoma—preliminary dataEuropean Review for Medical and Pharmacological SciencesYear: 201216111596159823111977
35. Zhang YF,Xu HX,He Y,et al. Virtual touch tissue quantification of acoustic radiation force impulse: a new ultrasound elastic imaging in the diagnosis of thyroid nodulesPLoS OneYear: 2012711e49094
36. Dighe M,Luo S,Cuevas C,Kim Y. Efficacy of thyroid ultrasound elastography in differential diagnosis of small thyroid nodulesEuropean Journal of RadiologyYear: 2013

Article Categories:
  • Research Article

Previous Document:  Evaluation of the diagnostic power of thermography in breast cancer using bayesian network classifie...
Next Document:  Classification of Prolapsed Mitral Valve versus Healthy Heart from Phonocardiograms by Multifractal ...