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A Wavelet-Based Method for Multifractal Analysis of Medical Signals: Application to Dynamic Infrared Thermograms of Breast Cancer

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Nonlinear Dynamics of Electronic Systems (NDES 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 438))

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Abstract

We use the wavelet transform modulus maxima (WTMM) method to perform multifractal analysis of the temporal fluctuations of breast skin temperature recorded using infrared (IR) thermography. When investigating thermograms collected from a panel of patients with breast cancer and some female volunteers with healthy breasts, we show that the multifractal complexity of temperature fluctuations observed on intact breast is lost in mammary glands with malignant tumors. These results highlight dynamics IR imaging as a very valuable non-invasive technique for preliminary screening in asymptomatic women to identify those with risk of breast cancer. Besides potential clinical impact, they also shed a new light on physiological changes that may precede anatomical alterations in breast cancer development.

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References

  1. Schlesinger, M., West, B.: Random Fluctuations and Pattern Growth: Experiments and Models. Kluwer, Boston (1988)

    Google Scholar 

  2. Bassingthwaighte, J., Liebovitch, L., West, B.: Fractal Physiology. Oxford University Press, New York (1994)

    Google Scholar 

  3. Goldberger, A.L., Amaral, L.A.N., Hausdorff, J.M., Ivanov, P.C., Peng, C.K., Stanley, H.E.: Fractal dynamics in physiology: alterations with disease and aging. Proc. Natl. Acad. Sci. USA 99, 2466–2472 (2002)

    Article  Google Scholar 

  4. Bunde, A., Kropp, J., Schellnhuber, H.: The Science of Disasters: Climate Disruptions, Heart Attacks, and Market Crashes. Springer, Berlin (2002)

    Google Scholar 

  5. Arneodo, A., Vaillant, C., Audit, B., Argoul, F., d’Aubenton-Carafa, Y., Thermes, C.: Multi-scale coding of genomic information: From DNA sequence to genome structure and function. Phys. Rep. 498, 45–188 (2011)

    Article  Google Scholar 

  6. Muzy, J.F., Bacry, E., Arneodo, A.: The multifractal formalism revisited with wavelets. International Journal of Bifurcation and Chaos 4, 245–302 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  7. Arneodo, A., Bacry, E., Muzy, J.F.: The thermodynamics of fractals revisited with wavelets. Physica A 213(1-2), 232–275 (1995)

    Article  Google Scholar 

  8. Kantelhardt, J.W., Zschiegner, S.A., Koscielny-Bunde, E., Havlin, S., Bunde, A., Stanley, H.E.: Multifractal detrended fluctuation analysis of nonstationary time series. Physica A 316, 87–114 (2002)

    Article  MATH  Google Scholar 

  9. Ihlen, E.A.F.: Introduction to multifractal detrended fluctuation analysis in Matlab. Front. Physiol. 3(141), 1–18 (2012)

    Google Scholar 

  10. Muzy, J.F., Bacry, E., Arneodo, A.: Wavelets and multifractal formalism for singular signals: Application to turbulence data. Phys. Rev. Lett. 67(25), 3515–3518 (1991)

    Article  Google Scholar 

  11. Muzy, J.F., Bacry, E., Arneodo, A.: Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima methods. Phys. Rev. E 47(2), 875–884 (1993)

    Article  Google Scholar 

  12. Bacry, E., Muzy, J.F., Arneodo, A.: Singularity spectrum of fractal signals from wavelet analysis: Exact results. Journal of Statistical Physics 70(3-4), 635–674 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  13. Jaffard, S., Lashermes, B., Abry, P.: Wavelet leaders in multifractal analysis. In: Wavelet Analysis and Applications, pp. 219–264. Birkhuser (2006)

    Google Scholar 

  14. Wendt, H., Abry, P., Jaffard, S.: Bootstrap for empirical multifractal analysis. IEEE Signal Proc. Mag. 24, 38–48 (2007)

    Article  Google Scholar 

  15. Lashermes, B., Roux, S.G., Abry, P., Jaffard, S.: Comprehensive multifractal analysis of turbulent velocity using wavelet leaders. Eur. Phys. J. B 61, 201–215 (2008)

    Article  Google Scholar 

  16. Delour, J., Muzy, J.F., Arneodo, A.: Intermittency of 1D velocity spatial profiles in turbulence: A magnitude cumulant analysis. Eur. Phys. J. B 23(2), 243–248 (2001)

    Article  Google Scholar 

  17. Audit, B., Bacry, E., Muzy, J.F., Arneodo, A.: Wavelet-based estimators of scaling behavior. IEEE Trans. Info. Theory 48, 2938–2954 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  18. Arneodo, A., Decoster, N., Kestener, P., Roux, S.G.: A wavelet-based method for multifractal image analysis: From theoretical concepts to experimental applications. Adv. Imaging Electr. Phys. 126, 1–92 (2003)

    Article  Google Scholar 

  19. Kestener, P., Arneodo, A.: Three-dimensional wavelet-based multifractal method: The need for revisiting the multifractal description of turbulence dissipation data. Phys. Rev. Lett. 91(19), 194501 (2003)

    Article  Google Scholar 

  20. Kestener, P., Arneodo, A.: Generalizing the wavelet-based multifractal formalism to random vector fields: Application to three-dimensional turbulence velocity and vorticity data. Phys. Rev. Lett. 93(4), 044501 (2004)

    Google Scholar 

  21. Arneodo, A., Audit, B., Kestener, P., Roux, S.G.: Wavelet-based multifractal analysis. Scholarpedia 3, 4103 (2008)

    Article  Google Scholar 

  22. Arneodo, A., Manneville, S., Muzy, J.F.: Towards log-normal statistics in high Reynolds number turbulence. Eur. Phys. J. B 1(1), 129–140 (1998)

    Article  Google Scholar 

  23. Arneodo, A., Muzy, J.F., Sornette, D.: “Direct” causal cascade in the stock market. Eur. Phys. J. B 2(2), 277–282 (1998)

    Article  Google Scholar 

  24. Muzy, J.F., Sornette, D., Delour, J., Arneodo, A.: Multifractal returns and hierarchical portfolio theory. Quant. Finance 1, 131–148 (2001)

    Article  MathSciNet  Google Scholar 

  25. Khalil, A., Joncas, G., Nekka, F., Kestener, P., Arneodo, A.: Morphological analysis of H I features. II. Wavelet-based multifractal formalism. Astrophys. J. Suppl. Ser. 165(2), 512–550 (2006)

    Article  Google Scholar 

  26. Venugopal, V., Roux, S.G., Foufoula-Georgiou, E., Arneodo, A.: Revisiting multifractality of high-resolution temporal rainfall using a wavelet-based formalism. Water Resour. Res. 42(6), W06D14 (2006)

    Google Scholar 

  27. Arneodo, A., Audit, B., Decoster, N., Muzy, J.F., Vaillant, C.: The Science of Disasters: Climate Disruptions, Heart Attacks, and Market Crashes, pp. 26–102. Springer, Berlin (2002)

    Book  Google Scholar 

  28. Roland, T., Khalil, A., Tanenbaum, A., Berguiga, L., Delichère, P., Bonneviot, L., Elezgaray, J., Arneodo, A., Argoul, F.: Revisiting the physical processes of vapodeposited thin gold films on chemically modified glass by atomic force and surface plasmon microscopies. Surf. Sci. 603(22), 3307–3320 (2009)

    Article  Google Scholar 

  29. Khalil, A., Grant, J.L., Caddle, L.B., Atzema, E., Mills, K.D., Arneodo, A.: Chromosome territories have a highly nonspherical morphology and nonrandom positioning. Chromosome Res. 15(7), 899–916 (2007)

    Article  Google Scholar 

  30. Grant, J., Verrill, C., Coustham, V., Arneodo, A., Palladino, F., Monier, K., Khalil, A.: Perinuclear distribution of heterochromatin in developing C. elegans embryos. Chromosome Res. 18(8), 873–885 (2010)

    Article  Google Scholar 

  31. Snow, C.J., Goody, M., Kelly, M.W., Oster, E.C., Jones, R., Khalil, A., Henry, C.A.: Time-lapse analysis and mathematical characterization elucidate novel mechanisms underlying muscle morphogenesis. PLoS Genet. 4(10), e1000219 (2008)

    Google Scholar 

  32. Khalil, A., Aponte, C., Zhang, R., Davisson, T., Dickey, I., Engelman, D., Hawkins, M., Mason, M.: Image analysis of soft-tissue in-growth and attachment into highly porous alumina ceramic foam metals. Med. Eng. Phys. 31(7), 775–783 (2009)

    Article  Google Scholar 

  33. Ivanov, P.C., Rosenblum, M.G., Peng, C.K., Mietus, J., Havlin, S., Stanley, H.E., Goldberger, A.L.: Scaling behaviour of heartbeat intervals obtained by wavelet-based time-series analysis. Nature 383(6598), 323–327 (1996)

    Article  Google Scholar 

  34. Ivanov, P.C., Amaral, L.A., Goldberger, A.L., Havlin, S., Rosenblum, M.G., Struzik, Z.R., Stanley, H.E.: Multifractality in Human Heartbeat Dynamics. Nature 399(6735), 461–465 (1999)

    Article  Google Scholar 

  35. Ivanov, P., Goldberger, A., Stanley, H.: Fractal and multifractal approaches in physiology. In: Bunde, A., Kropp, J., Schellnhuber, H. (eds.) The Science of Disasters: Climate Disruptions, Heart Attacks, and Market Crashes, pp. 219–258. Springer (2002)

    Google Scholar 

  36. Kestener, P., Lina, J.M., Saint-Jean, P., Arneodo, A.: Wavelet-based multifractal formalism to assist in diagnosis in digitized mammograms. Image Anal. Stereol. 20, 169–174 (2001)

    Article  MATH  Google Scholar 

  37. Batchelder, K.A., Tanenbaum, A.B., Albert, J., Guimond, L., Arneodo, A., Kestener, P., Khalil, A.: Wavelet-based 3D reconstruction of microcalcification clusters from two mammographic views: Fractal tumors are malignant and Euclidean tumors are benign. PLoS ONE (submitted, 2014)

    Google Scholar 

  38. Gerasimova, E., Audit, B., Roux, S.G., Khalil, A., Argoul, F., Naimark, O., Arneodo, A.: Multifractal analysis of dynamic infrared imaging of breast cancer. Europhys. Lett. 104, 68001 (2013)

    Article  Google Scholar 

  39. Gerasimova, E., Audit, B., Roux, S.G., Khalil, A., Gileva, O., Argoul, F., Naimark, O., Arneodo, A.: Wavelet-based multifractal analysis of dynamic infrared thermograms to assist in early breast cancer diagnosis. Front. Physiol. 5, Article 176, 1–11 (2014)

    Google Scholar 

  40. Nass, S.J., Henderson, I.C., Lashof, J.C.: Mammography and Beyond: Developing Technologies for the Early Detection of Breast Cancer. National Academy Press, Washington (2000)

    Google Scholar 

  41. Bronzino, J.D.: Biomedical Engeneering Handbook. CRC Press, Boca Raton (2006)

    Google Scholar 

  42. Tamini, R.M., Colditz, G.A., Hankinson, S.E.: Circulating carotenoids, mammographic density, and subsequent risk of breast cancer. Cancer Res. 69, 9323–9329 (2009)

    Article  Google Scholar 

  43. Vinitha Sree, S., Ng, E.Y.K., Kaw, G., Acharya, U.R., Chong, B.K.: The use of skin surface electropotentials for breast cancer detection–preliminary clinical trial results obtained using the biofield diagnostic system. J. Med. Syst. 35, 79–86 (2009)

    Article  Google Scholar 

  44. Sterns, E.E., Zee, B., SenGupta, S., Saunders, F.W.: Thermography: Its relation to pathologic characteristics, vascularity, proliferation rate, and survival of patients with invasive ductal carcinoma of the breast. Cancer 77, 1324–1328 (1996)

    Article  Google Scholar 

  45. Yahara, T., Koga, T., Yoshida, S., Nakagawa, S., Deguchi, H., Shirouzou, K.: Relationship between micro vessel density and thermographic hot areas in breast cancer. Surg. Today 33, 243–248 (2003)

    Article  Google Scholar 

  46. Keyserlingk, J.R., Ahlgren, P.D., Yu, E., Belliveau, N., Yassa, M.: Biomedical Engineering Handbook, pp. 97–158. CRC Press, Boca Raton (2006)

    Google Scholar 

  47. Head, J.F., Wang, F., Lipari, C., Elliott, R.L.: The important role of infrared imaging in breast cancer. IEEE Eng. Med. Biol. Mag. 19(3), 52–57 (2000)

    Article  Google Scholar 

  48. Amalu, W.C., Hobbins, W.B., Head, J.F., Elliott, R.L.: Biomedical Engineering Handbook, pp. 1–21. CRC Press, Boca Raton (2006)

    Google Scholar 

  49. Itoh, T., Kato, T., Igarashi, Y., Ishihara, S., Sasamon, H., Sekiya, T.: Contact-thermography in breast cancer mass screening (in Japanese with English abstract). Biomed. Thermol. 10, 49–51 (1990)

    Google Scholar 

  50. Iwase, T., Yoshimoto, M., Watanabe, S., Fujio, K., Nishi, M., Ohashi, Y.: Relation between hot spot and tumor location in the thermogram of breast cancer (in Japanese with English abstract). Biomed. Thermol. 10, 60 (1990)

    Google Scholar 

  51. Yokoe, T.: The relationship between thermographic positive pattern and pathological factors of breast cancer (in Japanese with English abstract). Biomed. Thermol. 12, 60 (1990)

    Google Scholar 

  52. Ng, E.Y.K.: A review of thermography as promising non-invasive detection modality for breast tumor. Int. J. Therm. Sci. 49, 849–859 (2009)

    Article  Google Scholar 

  53. Joro, R., Lääperi, A.L., Dastidar, P., Soimakallio, S., Kuukasjäri, T., Toivonen, T., Saaristo, R., Järvenpää, R.: Imaging of breast cancer with mid- and long-wave infrared camera. J. Med. Eng. Technol. 32, 189–197 (2008)

    Article  Google Scholar 

  54. Thomsen, L.L., Miles, D.W.: Role of nitric oxide in tumour progression: Lessons from human tumours. Cancer Metast. Rev. 17(1), 107–118 (1998)

    Article  Google Scholar 

  55. Anbar, M., Milescu, L., Naumov, A., Brown, C., Button, T., Carty, C., Dulaimy, K.: Detection of cancerous breasts by dynamic area telethermometry. IEEE Eng. Med. Biol. Mag. 20(5), 80–91 (2001)

    Article  Google Scholar 

  56. Button, T.M., Li, H., Fisher, P., Rosenblatt, R., Dulaimy, K., Li, S., O’Hea, B., Salvitti, M., Geronimo, V., Jambawalikar, S., Weiss, R.: Dynamic infrared imaging for the detection of malignancy. Phys. Med. Biol. 49(14), 3105–3116 (2004)

    Article  Google Scholar 

  57. Joro, R., Lääperi, A.L., Soimakallio, S., Järvenpää, R., Kuukasjäri, T., Toivonen, T., Saaristo, R., Dastida, P.: Dynamic infrared imaging in identification of breast cancer tissue with combined image processing and frequency analysis. J. Med. Eng. Technol. 32, 325–335 (2008)

    Article  Google Scholar 

  58. Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, New York (1998)

    Google Scholar 

  59. Roux, S., Muzy, J.F., Arneodo, A.: Detecting vorticity filaments using wavelet analysis: About the statistical contribution of vorticity filaments to intermittency in swirling turbulent flows. Eur. Phys. J. B 8(2), 301–322 (1999)

    Article  Google Scholar 

  60. Gileva, O.S., Freynd, G.G., Orlov, O.A., Libik, T.V., Gerasimova, E.I., Plekhov, O.A., Bayandin, Y.V., Panteleev, I.A.: Interdisciplinary approaches to early diagnosis and screening of tumors and precancerous diseases (for example, breast cancer). Vestnik RFFI (2-3), 93–99 (2012)

    Google Scholar 

  61. Ng, E.Y.K., Sudharsan, N.M.: Computer simulation in conjunction with medical thermography as an adjunct tool for early detection of breast cancer. BMC Cancer 4, 17 (2004)

    Article  Google Scholar 

  62. Panteleev, I.A., Plekhov, O.A., Naimark, O.: Mechanibiology study of structural homeostasis in tumor using infrared thermography data. Phys. Mesomech. 15(3), 105–113 (2007)

    Google Scholar 

  63. Xu, F., Lu, T.J., Steffen, K.A.: Biothermomechanical behavior of skin tissue. Acta Mech. Sin. 24, 1–23 (2008)

    Article  MathSciNet  Google Scholar 

  64. Lin, Q.Y., Yang, H.Q., Xie, S.S., Wang, Y.H., Ye, Z., Chen, S.Q.: Detecting early breast tumour by finite element thermal analysis. J. Med. Eng. Technol. 33, 274–280 (2009)

    Article  Google Scholar 

  65. Bissel, M.G., Hines, W.C.: Why don’t we get more cancer? a proposed role of the microenvironment in restraining cancer progression. Nat. Med. 17(3), 320–329 (2011)

    Article  Google Scholar 

  66. Quail, D.F., Joyce, J.A.: Microenvironmental regulation of tumor progression and metastasis. Nat. Med. 19(11), 1423–1437 (2013)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratory of Physical Foundation of Strength, Institute of Continuous Media Mechanics UB RAS, Perm, Russia

    Evgeniya Gerasimova & Oleg Naimark

  2. Université de Lyon and Laboratoire de Physique, ENS de Lyon, CNRS, UMR 5672, Lyon, France

    Benjamin Audit, Stephane-G. Roux, Françoise Argoul & Alain Arneodo

  3. Department of Mathematics and Statistics, University of Maine, Orono, Maine, USA

    André Khalil

  4. Department of Therapeutic and Propedeutic Dentistry, Perm State Academy of Medicine, Perm, Russia

    Olga Gileva

  5. Laboratoire de Physique, CNRS, ENS Lyon, 46 Alle d’Italie, Lyon, F69007, France

    Alain Arneodo

Authors
  1. Evgeniya Gerasimova
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  2. Benjamin Audit
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  3. Stephane-G. Roux
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  4. André Khalil
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  5. Olga Gileva
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  6. Françoise Argoul
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  7. Oleg Naimark
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Editor information

Editors and Affiliations

  1. Technical University of Sofia, 8 St. Kl. Ohridski Blvd., 1000, Sofia, Bulgaria

    Valeri M. Mladenov

  2. Physics Department, Boston University, 590 Commonwealth Avenue, 02215, Boston, MA, USA

    Plamen Ch. Ivanov

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Gerasimova, E. et al. (2014). A Wavelet-Based Method for Multifractal Analysis of Medical Signals: Application to Dynamic Infrared Thermograms of Breast Cancer. In: Mladenov, V.M., Ivanov, P.C. (eds) Nonlinear Dynamics of Electronic Systems. NDES 2014. Communications in Computer and Information Science, vol 438. Springer, Cham. https://doi.org/10.1007/978-3-319-08672-9_34

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  • DOI: https://doi.org/10.1007/978-3-319-08672-9_34

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