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Cancer detection on a cell-by-cell basis using a fractal dimension analysis

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Acta Physica Hungarica Series A, Heavy Ion Physics

Abstract

We show that the application of imaging and pattern recognition techniques developed for basic heavy ion research has useful applications in medical imaging. In particular, we utilize the fractal dimension of the perimeter surface of cell sections as a new observable to characterize cells of different types. We propose that it is possible to distinguish cancerous from healthy cells with the aid of this new approach. As a first application we show in an exploratory study that it is possible to perform this distinction between patients with hairy-cell lymphocytic leukemia and those with normal blood lymphocytes.

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References

  1. W.A. Aherne and M.S. Dunnill, Morphometry, Edward Arnold Publishers, London, 1982.

    Google Scholar 

  2. H. von Koch, Arkiv för Mathematik 1 (1904) 681.

    Google Scholar 

  3. L.F. Richardson, General Systems Yearbook 6 (1961) 139–187.

    Google Scholar 

  4. B. Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman, New York, 1977.

    Google Scholar 

  5. B.J. West, Fractal Physiology and Chaos in Medicine, World Scientific, Singapore, 1990.

    MATH  Google Scholar 

  6. A. Bunde and S. Havlin, Fractals in Science, Springer, Heidelberg, 1994.

    MATH  Google Scholar 

  7. J.B. Bassingthwaithe, L.S. Liebovitch and B.J. West, Fractal Physiology, Oxford University Press, New York, 1994.

    Google Scholar 

  8. T.G. Smith, W.B. Marks, G.D. Lange, W.H. Sheriff Jr. and E.A. Neale, J. Neuroscience Methods 27 (1989) 173.

    Article  Google Scholar 

  9. C.-K. Peng, J.E. Mietus, J.M. Hausdorff, S. Havlin, H.E. Stanley and A.L. Goldberger, Phys. Rev. Lett. 70 (1993) 1343.

    Article  ADS  Google Scholar 

  10. R.Z. Gan, Y. Tian, R.T. Yen and G.S. Kassah, Journal of Applied Physiology 75 (1993) 432.

    Google Scholar 

  11. C.E. Priebe, J.L. Solka, R.A. Lorey, G.W. Rogers, W.L. Poston, M. Kallergi, W. Qian, L.P. Clarke, R.A. Clark, Cancer Letters 77 (1994) 183.

    Article  Google Scholar 

  12. E. Ahmed, Int. Jour. Theor. Phys. 32 (1993) 353.

    Article  Google Scholar 

  13. J.C. Buckland-Wright, J.A. Lynch, J. Rymer and I. Fogelman, Calcif. Tissue. Int. 54 (1994) 106.

    Article  Google Scholar 

  14. S.S. Cross, J.P. Bury, P.B. Silcocks, T.J. Stephenson and D.W. Cotton, Journal of Pathology 172 (1994) 317.

    Article  Google Scholar 

  15. G. Landini and J.W. Rippin, Anal. Quant. Cytol. Histol. 15 (1993) 144.

    Google Scholar 

  16. R. Thibert, B. Dubuc, M. Dufour and R. Tawashi, Scanning Microscopy 7 (1993) 555.

    Google Scholar 

  17. M. Battaglia-Parodi and D.D. Giusto, Ophthalmic Research 25 (1993) 307.

    Article  Google Scholar 

  18. S. Traverso, R. Morchio and G. Tamone, Riv. Biol. 85 (1992) 405.

    Google Scholar 

  19. T.G. Smith Jr. and T.N. Behar, Brain Research 634 (1994) 181.

    Article  Google Scholar 

  20. H. Holb, E. Fernandez, J. Schouten, P. Ahnelt, K.A. Linberg and S.K. Fisher, J. Comp. Neurol. 343 (1994) 370.

    Article  Google Scholar 

  21. C. MacAulay and B. Palcic, Anal. Quant. Cytol. Histol. 12 (1990) 394.

    Google Scholar 

  22. A. Sadana and A. Madagula, Biosens. Bioelectron. 9 (1994) 45.

    Article  Google Scholar 

  23. M.A. Aon and S. Cortassa, FEBS Letters 344 (1994) 1.

    Article  Google Scholar 

  24. W. Bauer and C.D. Mackenzie, “Method and System For Detection of Biological Materials”, Michigan State University 4.1-128 (ID 94-030), US Patent 5,848,177 (Dec. 1998).

  25. W. Bauer, D.R. Dean, U. Mosel and U. Post, Phys. Lett. 150B (1985) 53; W. Bauer, Phys. Rev. C 38 (1988) 1927.

    ADS  Google Scholar 

  26. T. Le Brun, H.G. Berry, S. Cheng, R.W. Dunford, H. Esbensen, D.S. Gemmell, E.P. Kantor and W. Bauer, Phys. Rev. Lett. 72 (1994) 3965.

    Article  ADS  Google Scholar 

  27. J. Feder, Fractals, Plenum Press, New York, 1988.

    MATH  Google Scholar 

  28. L.L. Liebovitch and T. Toth, Phys. Lett. 141A (1989) 386.

    ADS  MathSciNet  Google Scholar 

  29. A. Block, W. von Bloh and H.J. Schellnhuber, Phys. Rev. A 42 (1990) 1869.

    Article  ADS  MathSciNet  Google Scholar 

  30. X.-J. Hou, R. Gilmore, G.B. Midlin and H.G. Solari, Phys. Lett. 151A (1990), 43.

    ADS  Google Scholar 

  31. P. Grassberger, Phys. Lett. 97A (1983) 224.

    ADS  MathSciNet  Google Scholar 

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Bauer, W., Mackenzie, C.D. Cancer detection on a cell-by-cell basis using a fractal dimension analysis. APH N.S., Heavy Ion Physics 14, 43–50 (2001). https://doi.org/10.1556/APH.14.2001.1-4.6

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  • DOI: https://doi.org/10.1556/APH.14.2001.1-4.6

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