Wavelet-Based 3D Reconstruction of Microcalcification Clusters from Two Mammographic Views: New Evidence That Fractal Tumors Are Malignant and Euclidean Tumors Are Benign

The 2D Wavelet-Transform Modulus Maxima (WTMM) method was used to detect microcalcifications (MC) in human breast tissue seen in mammograms and to characterize the fractal geometry of benign and malignant MC clusters. This was done in the context of a preliminary analysis of a small dataset, via a novel way to partition the wavelet-transform space-scale skeleton. For the first time, the estimated 3D fractal structure of a breast lesion was inferred by pairing the information from two separate 2D projected mammographic views of the same breast, i.e. the cranial-caudal (CC) and mediolateral-oblique (MLO) views. As a novelty, we define the “CC-MLO fractal dimension plot”, where a “fractal zone” and “Euclidean zones” (non-fractal) are defined. 118 images (59 cases, 25 malignant and 34 benign) obtained from a digital databank of mammograms with known radiologist diagnostics were analyzed to determine which cases would be plotted in the fractal zone and which cases would fall in the Euclidean zones. 92% of malignant breast lesions studied (23 out of 25 cases) were in the fractal zone while 88% of the benign lesions were in the Euclidean zones (30 out of 34 cases). Furthermore, a Bayesian statistical analysis shows that, with 95% credibility, the probability that fractal breast lesions are malignant is between 74% and 98%. Alternatively, with 95% credibility, the probability that Euclidean breast lesions are benign is between 76% and 96%. These results support the notion that the fractal structure of malignant tumors is more likely to be associated with an invasive behavior into the surrounding tissue compared to the less invasive, Euclidean structure of benign tumors. Finally, based on indirect 3D reconstructions from the 2D views, we conjecture that all breast tumors considered in this study, benign and malignant, fractal or Euclidean, restrict their growth to 2-dimensional manifolds within the breast tissue.

[1]  S S Cross,et al.  FRACTALS IN PATHOLOGY , 1997, The Journal of pathology.

[2]  Argoul,et al.  Structural analysis of electroless deposits in the diffusion-limited regime. , 1994, Physical review letters.

[3]  Emmanuel Bacry,et al.  THE THERMODYNAMICS OF FRACTALS REVISITED WITH WAVELETS , 1995 .

[4]  P. Taylor,et al.  A systematic review of computer-assisted diagnosis in diagnostic cancer imaging. , 2012, European journal of radiology.

[5]  Armin Bunde,et al.  The Science of Disasters , 2002 .

[6]  Françoise Argoul,et al.  Wavelet-based multifractal analysis of dynamic infrared thermograms to assist in early breast cancer diagnosis , 2014, Front. Physiol..

[7]  E. Bacry,et al.  Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  M. Eberl,et al.  BI-RADS classification for management of abnormal mammograms. , 2006, Journal of the American Board of Family Medicine : JABFM.

[9]  Dianne Georgian-Smith,et al.  Blinded comparison of computer-aided detection with human second reading in screening mammography. , 2007, AJR. American journal of roentgenology.

[10]  Rainer Stotzka,et al.  Three-dimensional reconstruction of clustered microcalcifications from two digitized mammograms , 1998, Medical Imaging.

[12]  A. Arneodo,et al.  A wavelet-based method for multifractal image analysis. III. Applications to high-resolution satellite images of cloud structure , 2000 .

[13]  Nan-Chyuan Tsai,et al.  Computer-aided diagnosis for early-stage breast cancer by using Wavelet Transform , 2011, Comput. Medical Imaging Graph..

[14]  Peter C Gøtzsche,et al.  Overdiagnosis in publicly organised mammography screening programmes: systematic review of incidence trends , 2009, BMJ : British Medical Journal.

[15]  Lena Costaridou,et al.  Breast Cancer Diagnosis: Analyzing Texture of Tissue Surrounding Microcalcifications , 2008, IEEE Transactions on Information Technology in Biomedicine.

[16]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[17]  Samir Brahim Belhaouari,et al.  A statistical based feature extraction method for breast cancer diagnosis in digital mammogram using multiresolution representation , 2012, Comput. Biol. Medicine.

[18]  S. Astley,et al.  Single reading with computer-aided detection for screening mammography. , 2008, The New England journal of medicine.

[19]  A. Giuliani,et al.  Fractal analysis in a systems biology approach to cancer. , 2011, Seminars in cancer biology.

[20]  M. Lux,et al.  Characterizing mammographic images by using generic texture features , 2012, Breast Cancer Research.

[21]  E. Bacry,et al.  The Multifractal Formalism Revisited with Wavelets , 1994 .

[22]  Berkman Sahiner,et al.  Computer-aided detection of masses in digital tomosynthesis mammography: comparison of three approaches. , 2008, Medical physics.

[23]  Rangaraj M. Rangayyan,et al.  Fractal analysis of contours of breast masses in mammograms via the power spectra of their signatures , 2010, 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology.

[24]  C. D'Orsi,et al.  Influence of computer-aided detection on performance of screening mammography. , 2007, The New England journal of medicine.

[25]  Fahima Nekka,et al.  Morphological Analysis of H I Features. II. Wavelet-based Multifractal Formalism , 2006 .

[26]  Ma Li,et al.  Detections of Microcalcification Clusters Using Multiple Mammographic Views , 2008, 2008 2nd International Conference on Bioinformatics and Biomedical Engineering.

[27]  Wenjun Chris Zhang,et al.  An Expert Support System for Breast Cancer Diagnosis using Color Wavelet Features , 2012, Journal of Medical Systems.

[28]  A. Gavin,et al.  Advanced breast cancer incidence following population-based mammographic screening , 2011, Annals of oncology : official journal of the European Society for Medical Oncology.

[29]  P. Tracqui,et al.  Biophysical models of tumour growth , 2009 .

[30]  J. Kruschke.  Doing Bayesian Data Analysis: A Tutorial with R and BUGS , 2010 .

[31]  D. Miglioretti,et al.  Establishing a gold standard for test sets: variation in interpretive agreement of expert mammographers. , 2013, Academic radiology.

[32]  Michael J. Carston,et al.  Texture Features from Mammographic Images and Risk of Breast Cancer , 2009, Cancer Epidemiology Biomarkers & Prevention.

[33]  S. Mallat.  VI – Wavelet zoom , 1999 .

[34]  Alexander Horsch,et al.  Needs assessment for next generation computer-aided mammography reference image databases and evaluation studies , 2011, International Journal of Computer Assisted Radiology and Surgery.

[35]  Alain Arneodo,et al.  Three-dimensional wavelet-based multifractal method: the need for revisiting the multifractal description of turbulence dissipation data. , 2003, Physical review letters.

[36]  Joann G Elmore,et al.  Short-Term Outcomes of Screening Mammography Using Computer-Aided Detection , 2013, Annals of Internal Medicine.

[37]  L. Sander.  Diffusion-limited aggregation: A kinetic critical phenomenon? , 2000 .

[38]  N. Day.  The NHS breast cancer screening programme , 2003, British Journal of Cancer.

[39]  Richard H. Moore,et al.  THE DIGITAL DATABASE FOR SCREENING MAMMOGRAPHY , 2007 .

[40]  R A Schmidt,et al.  Automated detection of microcalcification clusters for digital breast tomosynthesis using projection data only: a preliminary study. , 2008, Medical physics.

[41]  John K Kruschke,et al.  Bayesian data analysis. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[42]  K. Thangavel,et al.  Unsupervised feature selection in digital mammogram image using rough set theory , 2012, Int. J. Bioinform. Res. Appl..

[43]  M. Giger,et al.  Computerized mass detection for digital breast tomosynthesis directly from the projection images. , 2006, Medical physics.

[44]  Ina,et al.  WAVELET-BASED MULTIFRACTAL FORMALISM TO ASSIST IN DIAGNOSIS IN DIGITIZED MAMMOGRAMS , 2001 .

[45]  H. Stanley,et al.  Behavioral-independent features of complex heartbeat dynamics. , 2001, Physical review letters.

[46]  Computer-aided detection in digital mammography: false-positive marks and their reproducibility in negative mammograms , 2009, Acta radiologica.

[47]  Alain Arneodo,et al.  Automated Detection of Coronal Loops Using a Wavelet Transform Modulus Maxima Method , 2010, 1002.3107.

[48]  Alessandro Giuliani,et al.  Metabolism and cell shape in cancer: a fractal analysis. , 2011, The international journal of biochemistry & cell biology.

[49]  Chelsi J. Snow,et al.  Muscle development is disrupted in zebrafish embryos deficient for fibronectin , 2008, Developmental dynamics : an official publication of the American Association of Anatomists.

[50]  Wendy Bruening,et al.  Computer-aided detection mammography for breast cancer screening: systematic review and meta-analysis , 2009, Archives of Gynecology and Obstetrics.

[51]  David B. Dunson,et al.  Bayesian data analysis, third edition , 2013 .

[52]  Luís A. Nunes Amaral,et al.  From 1/f noise to multifractal cascades in heartbeat dynamics. , 2001, Chaos.

[53]  Rangaraj M. Rangayyan,et al.  Fractal Analysis of Contours of Breast Masses in Mammograms , 2007, Journal of Digital Imaging.

[54]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[55]  Hilde Bosmans,et al.  Evaluation of clinical image processing algorithms used in digital mammography. , 2009, Medical physics.

[56]  G Landini,et al.  HOW IMPORTANT IS TUMOUR SHAPE? QUANTIFICATION OF THE EPITHELIAL–CONNECTIVE TISSUE INTERFACE IN ORAL LESIONS USING LOCAL CONNECTED FRACTAL DIMENSION ANALYSIS , 1996, The Journal of pathology.

[57]  Berkman Sahiner,et al.  Computer-aided detection system for breast masses on digital tomosynthesis mammograms: preliminary experience. , 2005, Radiology.

[58]  Shadi AlZu'bi,et al.  Multiresolution Analysis Using Wavelet, Ridgelet, and Curvelet Transforms for Medical Image Segmentation , 2011, Int. J. Biomed. Imaging.

[59]  A. Arneodo,et al.  A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and anisotropic random rough surfaces , 2000 .

[60]  S S Cross,et al.  Fractal and Integer‐Dimensional Geometric Analysis of Pigmented Skin Lesions , 1995, The American Journal of dermatopathology.

[61]  Samir Brahim Belhaouari,et al.  A comparison of wavelet and curvelet for breast cancer diagnosis in digital mammogram , 2010, Comput. Biol. Medicine.

[62]  Li Ke,et al.  Mass auto-detection in mammogram based on wavelet transform modulus maximum , 2009, 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[63]  Tessamma Thomas,et al.  A New Fast Fractal Modeling Approach for the Detection of Microcalcifications in Mammograms , 2010, Journal of Digital Imaging.

[64]  E. Bacry,et al.  Wavelets and multifractal formalism for singular signals: Application to turbulence data. , 1991, Physical review letters.

[65]  C. D'Orsi,et al.  Effectiveness of computer-aided detection in community mammography practice. , 2011, Journal of the National Cancer Institute.

[66]  F. Jamitzky,et al.  Local scaling properties for diagnostic purposes , 2002 .

[67]  Ehsan Samei,et al.  Automated breast mass detection in 3D reconstructed tomosynthesis volumes: a featureless approach. , 2008, Medical physics.

[68]  D. Engelman,et al.  Image analysis of soft-tissue in-growth and attachment into highly porous alumina ceramic foam metals. , 2009, Medical engineering & physics.

[69]  Alain Arneodo,et al.  CHARACTERIZING COMPLEXITY IN SOLAR MAGNETOGRAM DATA USING A WAVELET-BASED SEGMENTATION METHOD , 2010, 1005.1536.

[70]  Chelsi J. Snow,et al.  Time-Lapse Analysis and Mathematical Characterization Elucidate Novel Mechanisms Underlying Muscle Morphogenesis , 2008, PLoS genetics.

[71]  Brian R Huntyx,et al.  How projections affect the dimension spectrum of fractal measures , 1997 .

[72]  M. Goody,et al.  NAD+ Biosynthesis Ameliorates a Zebrafish Model of Muscular Dystrophy , 2012, PLoS biology.

[73]  R M Nishikawa,et al.  On the orientation of mammographic structure. , 2011, Medical physics.

[74]  Argoul,et al.  Self-similarity of diffusion-limited aggregates and electrodeposition clusters. , 1988, Physical review letters.

[75]  Karsten Juhl Jørgensen.  Is the tide turning against breast screening? , 2012, Breast Cancer Research.

[76]  E. Weibel,et al.  Fractals in Biology and Medicine , 1994 .

[77]  L. Amaral,et al.  Multifractality in human heartbeat dynamics , 1998, Nature.

[78]  E. Burnside,et al.  Computer-aided diagnostic models in breast cancer screening. , 2010, Imaging in medicine.

[79]  Ahmet Sertbas,et al.  Mammographic Mass Detection using Wavelets as Input to Neural Networks , 2010, Journal of Medical Systems.

[80]  Gabriel Landini,et al.  Quantification of the global and local complexity of the epithelial-connective tissue interface of normal, dysplastic, and neoplastic oral mucosae using digital imaging. , 2003, Pathology, research and practice.

[81]  Berk,et al.  Scale-invariant behavior and vascular network formation in normal and tumor tissue. , 1995, Physical review letters.

[82]  C Velayutham,et al.  Entropy based unsupervised Feature Selection in digital mammogram image using rough set theory , 2012, Int. J. Comput. Biol. Drug Des..

[83]  D. Sgroi,et al.  Spread of human cancer cells occurs with probabilities indicative of a nongenetic mechanism , 2005, British Journal of Cancer.

[84]  E Claridge,et al.  Shape analysis for classification of malignant melanoma. , 1992, Journal of biomedical engineering.

[85]  R. Rangayyan,et al.  Application of fractal analysis to mammography , 2010, 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology.

[86]  A. Arneodo,et al.  Revisiting the physical processes of vapodeposited thin gold films on chemically modified glass by atomic force and surface plasmon microscopies , 2009 .

[87]  A. Arneodo,et al.  Chromosome neighborhood composition determines translocation outcomes after exposure to high-dose radiation in primary cells , 2007, Chromosome Research.

[88]  M. Goody,et al.  Nrk2b-mediated NAD+ production regulates cell adhesion and is required for muscle morphogenesis in vivo: Nrk2b and NAD+ in muscle morphogenesis. , 2010, Developmental biology.

[89]  M L Giger,et al.  Computerized Detection of Mass Lesions in Digital Breast Tomosynthesis Images Using Two- and Three Dimensional Radial Gradient Index Segmentation , 2004, Technology in cancer research & treatment.

[90]  M. Lacquement,et al.  Positive predictive value of the Breast Imaging Reporting and Data System. , 1999, Journal of the American College of Surgeons.

[91]  S. Orel,et al.  BI-RADS categorization as a predictor of malignancy. , 1999, Radiology.

[92]  Françoise Argoul,et al.  Multifractal analysis of dynamic infrared imaging of breast cancer , 2013 .

[93]  K. J. Ray Liu,et al.  Fractal modeling and segmentation for the enhancement of microcalcifications in digital mammograms , 1997, IEEE Transactions on Medical Imaging.

[94]  N. Decoster,et al.  A wavelet-based method for multifractal image analysis. II. Applications to synthetic multifractal rough surfaces , 2000 .

[95]  A. Arneodo,et al.  Chromosome territories have a highly nonspherical morphology and nonrandom positioning , 2007, Chromosome Research.

[96]  Alain Arneodo,et al.  A wavelet-based method for multifractal image analysis: From theoretical concepts to experimental applications , 2003 .

[97]  R Di Paola,et al.  A fractal approach to the segmentation of microcalcifications in digital mammograms. , 1995, Medical physics.

[98]  P. Gøtzsche,et al.  Thirteen years of breast screening had no measurable effect on breast cancer mortality in Norway , 2013, International journal of cancer.

[99]  A. Arneodo,et al.  Perinuclear distribution of heterochromatin in developing C. elegans embryos , 2010, Chromosome Research.

[100]  Richard H. Moore,et al.  Current Status of the Digital Database for Screening Mammography , 1998, Digital Mammography / IWDM.

[101]  F. Pansera.  Fractals and cancer. , 1994, Medical hypotheses.

[102]  G Coppini,et al.  Detection of single and clustered microcalcifications in mammograms using fractals models and neural networks. , 2004, Medical engineering & physics.