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  • Replies bone structure and fractals

    Hello everybody,

    On Wed, 29 Nov 1995 I wrote :

    > Dear subscribers,
    >
    > recently, we have been following a short course about fractals in our group.
    > Now, we wondered whether trabecular bone could be considered to have a
    > fractal structure. And if so, whether one could use these fractal
    > characteristics to model the trabecular structure or to find some
    > relationship between e.g. fractal dimension and mechanical (and other)
    > properties.
    >
    > Does any one of you know anything about research that has been carried out
    > on this subject ? Please send some references.
    >
    > Thank you for your courtesy.
    >
    > Luc Labey
    >

    I was very happy with all replies I got for this question. Thanks to all
    those who responded.
    Here is a summary of the replies :

    People who responded :
    From: Ed Wachtel
    From: "Beth Todd"
    From: grabiner@bme.ri.ccf.org
    From: hou@bjc.hfh.edu (Fu Hou)
    From: BAIER@ubvms.cc.buffalo.edu
    From: Francesco
    From: lk1boq76@icineca.cineca.it (Luca Cristofolini)
    From: bfinlay@julian.uwo.ca (Bryan Finlay)
    From: lk1boq72@icineca.cineca.it (LTM-IOR) (Fabio Baruffaldi)
    From: "Paul Steven Weinhold"
    From: Gabriel Landini
    From: LEONARD ELBAUM
    From: Paul Treffner
    From: dmichels@slate.Mines.EDU (Diana L. Michels)
    From: mlb@bihobl2.bih.harvard.edu (Mary L. Bouxsein)
    From: Arthur Brandwood
    From: G0KUSTER@sgcl1.unisg.ch
    From: Rane Curl

    Some people who did work on the subject or are still working on it :

    1. Dr. J. Malcolm Carter
    Director, Graduate Program in Biomaterials
    State University at Buffalo
    New York, 14214
    USA
    supervised a Master's thesis on the subject.
    2. Dr. Joe Natiella
    Department of Oral Diagnostic Sciences
    SUNY Buffalo Dental School
    Buffalo, NY
    USA
    3. Prof. Raj Acharya
    Department of Computer Science
    State University of New York at Buffalo
    226 Bell Hall
    Buffalo, NY 14260-2000
    USA
    4. Prof. Sharmilla Majumdar(cfr. reference list below)
    Department of Radiology
    University of California
    San Francisco
    USA
    5. Dr E.R. Bogoch, MD, FRCS(C)
    Room 429, E.K. Jones Building
    The Wellesley Hospital
    160 Wellesley Street East
    Toronto ON M4Y 1J3
    he presented a paper on this topic at the Annual meeting of the
    Canadian Orthopaedic Research Society two or three years ago.
    6. Dr. Richard Voss (voss@walt.ccs.fau.edu)
    Center for Complex Systems
    Florida Atlantic University
    777 Glades Rd.
    PO Box 3091
    Boca Raton FL 33431-099
    USA


    This is a list of references about fractals and bone structure :

    1. RS Weinstein and S Majumdar, 'Fractal Geometry and Vertebral
    Compression Fractures', Journal of Bone and Mineral Research,
    Vol.9, No.11, 1994, pp. 1797-1802.
    2. Berry J.L., Towers J.D., Webber R.L., Jerome C., Pope T.L.,
    Zimmerman M., "Changes in trabecular architecture as measured by
    fractal dimension"; abstracts 2nd WCB, Blankervoort & Koolos
    eds., vol.2: p. 238
    3. Fortin C.;Kumaresan R.;Ohley W. and Hoefer S.,Fractal dimension
    in the analysis of medical images,IEEE Eng.Med.Biol.,June,
    pp 65-71,1992
    4. Webber R.;Underhill T.E.;Horton R.A.;Dixon R.L. and Pope Jr.T.L.,
    Predicting osseous changes in ankle fractures. A fractal based
    radiographic analysis,IEEE Eng.Med.Biol.,March, pp 103-110,1993
    5. Vannier M.W.;Hildebot C.F.;Gilula L.A.;Pilgram T.K.;
    Mann F.;Monsess B.S.;Murphy W.A.;Totty W.G. and Offut C.J.,
    Calcaneal and pelvic fractures: diagnostic evaluation by three-
    dimensional computer tomography scans, J.Digit.Imaging,4,
    pp 143-152,1991,
    6. Matthews S.;Pearcy M.J.;Fazzalari N.L.;Parkinson I.H.;
    Manthey B.A.;Schultz C.G.and Howie D.W.,Correlations between the
    mechanical properties, radiology and histomorphometry of human
    femoral bone,Clin.Biomech.,7,153-160,1992,
    7. Tsatsanis M.K. and Giannakis G.B.,Object and texture
    classification using higher order statistics,IEEE
    Trans.Patt.Anal.Machine Intell.,14,733-750,1992,
    8. Buckland-Wright, et al (1994) Fractal signature analysis of
    macroradiographs measures trabecular organization in lumbar
    vertebrae of postmenopausal women. Calcif Tissue Int 54:106-112.
    9. Chen J, et al (1994) Fractal analysis of trabecular patterns in
    projection radiographs. An assessment. Invest. Radiol 29:
    pp 624-629.
    10. Cross et al (1993) Trabecular bone does not have a fractal
    structure on light microscopic examination. J Pathology 170:
    pp 311-3.
    11. Chung HW et al (1994) On the fractal nature of trabecular
    structure., Med Phys 21:1535-1540.
    12. Caligury PC, Giger ML, Favus M: Multifractal radiographic
    analysis of osteoporosis. Med Phy 21(4): 503 - 508 (1994)
    13. Majumdar S, Weinstein RS, Prasad R. Application of fractal
    geometry techniques to the study of trabeculat bone. Med Phys
    20(6): 1611 - 1619 (1993)
    14. Curl, R.L.(1986) _Fractal Dimensions and Geometries of Caves_,
    Math. Geol., Vol. 18, No. 8, pp 765-783.


    )( Address :
    () Luc Labey
    )( Division of Biomechanics and Engineering Design
    () Celestijnenlaan 200A
    )( B-3001 HEVERLEE
    )( Belgium
    () tel. : 32 16 32 7535
    )( fax : 32 16 32 7994
    () e-mail : Luc.Labey@mech.kuleuven.ac.be
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