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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
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