Fractal dimension of trabecular bone: comparison of three histomorphometric computed techniques for measuring the architectural two-dimensional complexity
Trabecular bone has been reported as having two‐dimensional (2‐D) fractal characteristics at the histological level, a finding correlated with biomechanical properties. However, several fractal dimensions (D) are known and computational ways to obtain them vary considerably. This study compared thre...
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| Veröffentlicht in: | The Journal of pathology 2001-11, Vol.195 (4), p.515-521 |
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| creator | Chappard, Daniel Legrand, Erick Haettich, Bénédicte Chalès, Gérard Auvinet, Bernard Eschard, Jean-Paul Hamelin, Jean-Pierre Baslé, Michel-Félix Audran, Maurice |
| description | Trabecular bone has been reported as having two‐dimensional (2‐D) fractal characteristics at the histological level, a finding correlated with biomechanical properties. However, several fractal dimensions (D) are known and computational ways to obtain them vary considerably. This study compared three algorithms on the same series of bone biopsies, to obtain the Kolmogorov, Minkowski–Bouligand, and mass‐radius fractal dimensions. The relationships with histomorphometric descriptors of the 2‐D trabecular architecture were investigated. Bone biopsies were obtained from 148 osteoporotic male patients. Bone volume (BV/TV), trabecular characteristics (Tb.N, Tb.Sp, Tb.Th), strut analysis, star volumes (marrow spaces and trabeculae), inter‐connectivity index, and Euler–Poincaré number were computed. The box‐counting method was used to obtain the Kolmogorov dimension (Dk), the dilatation method for the Minkowski–Bouligand dimension (DMB), and the sandbox for the mass‐radius dimension (DMR) and lacunarity (L). Logarithmic relationships were observed between BV/TV and the fractal dimensions. The best correlation was obtained with DMR and the lowest with DMB. Lacunarity was correlated with descriptors of the marrow cavities (ICI, star volume, Tb.Sp). Linear relationships were observed among the three fractal techniques which appeared highly correlated. A cluster analysis of all histomorphometric parameters provided a tree with three groups of descriptors: for trabeculae (Tb.Th, strut); for marrow cavities (Euler, ICI, Tb.Sp, star volume, L); and for the complexity of the network (Tb.N and the three D's). A sole fractal dimension cannot be used instead of the classic 2‐D descriptors of architecture; D rather reflects the complexity of branching trabeculae. Computation time is also an important determinant when choosing one of these methods. Copyright © 2001 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/path.970 |
| format | Article |
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However, several fractal dimensions (D) are known and computational ways to obtain them vary considerably. This study compared three algorithms on the same series of bone biopsies, to obtain the Kolmogorov, Minkowski–Bouligand, and mass‐radius fractal dimensions. The relationships with histomorphometric descriptors of the 2‐D trabecular architecture were investigated. Bone biopsies were obtained from 148 osteoporotic male patients. Bone volume (BV/TV), trabecular characteristics (Tb.N, Tb.Sp, Tb.Th), strut analysis, star volumes (marrow spaces and trabeculae), inter‐connectivity index, and Euler–Poincaré number were computed. The box‐counting method was used to obtain the Kolmogorov dimension (Dk), the dilatation method for the Minkowski–Bouligand dimension (DMB), and the sandbox for the mass‐radius dimension (DMR) and lacunarity (L). Logarithmic relationships were observed between BV/TV and the fractal dimensions. The best correlation was obtained with DMR and the lowest with DMB. Lacunarity was correlated with descriptors of the marrow cavities (ICI, star volume, Tb.Sp). Linear relationships were observed among the three fractal techniques which appeared highly correlated. A cluster analysis of all histomorphometric parameters provided a tree with three groups of descriptors: for trabeculae (Tb.Th, strut); for marrow cavities (Euler, ICI, Tb.Sp, star volume, L); and for the complexity of the network (Tb.N and the three D's). A sole fractal dimension cannot be used instead of the classic 2‐D descriptors of architecture; D rather reflects the complexity of branching trabeculae. Computation time is also an important determinant when choosing one of these methods. Copyright © 2001 John Wiley & Sons, Ltd.</description><identifier>ISSN: 0022-3417</identifier><identifier>EISSN: 1096-9896</identifier><identifier>DOI: 10.1002/path.970</identifier><identifier>PMID: 11745685</identifier><identifier>CODEN: JPTLAS</identifier><language>eng</language><publisher>Chichester, UK: John Wiley & Sons, Ltd</publisher><subject>Biological and medical sciences ; bone architecture ; bone histomorphometry ; bone structure ; Cluster Analysis ; fractal dimension ; fractal geometry ; Fractals ; Humans ; Image Processing, Computer-Assisted ; Investigative techniques, diagnostic techniques (general aspects) ; Least-Squares Analysis ; Linear Models ; Male ; male osteoporosis ; Medical sciences ; Middle Aged ; Miscellaneous. Technology ; Osteoporosis - pathology ; Pathology. Cytology. Biochemistry. Spectrometry. Miscellaneous investigative techniques</subject><ispartof>The Journal of pathology, 2001-11, Vol.195 (4), p.515-521</ispartof><rights>Copyright © 2001 John Wiley & Sons, Ltd.</rights><rights>2002 INIST-CNRS</rights><rights>Copyright 2001 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3850-a4e02fce86afb5f937abadb277c4c4de4325787e08eb1272522c36360a02dffc3</citedby><cites>FETCH-LOGICAL-c3850-a4e02fce86afb5f937abadb277c4c4de4325787e08eb1272522c36360a02dffc3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fpath.970$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fpath.970$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27901,27902,45550,45551</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=14108909$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/11745685$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Chappard, Daniel</creatorcontrib><creatorcontrib>Legrand, Erick</creatorcontrib><creatorcontrib>Haettich, Bénédicte</creatorcontrib><creatorcontrib>Chalès, Gérard</creatorcontrib><creatorcontrib>Auvinet, Bernard</creatorcontrib><creatorcontrib>Eschard, Jean-Paul</creatorcontrib><creatorcontrib>Hamelin, Jean-Pierre</creatorcontrib><creatorcontrib>Baslé, Michel-Félix</creatorcontrib><creatorcontrib>Audran, Maurice</creatorcontrib><title>Fractal dimension of trabecular bone: comparison of three histomorphometric computed techniques for measuring the architectural two-dimensional complexity</title><title>The Journal of pathology</title><addtitle>J. Pathol</addtitle><description>Trabecular bone has been reported as having two‐dimensional (2‐D) fractal characteristics at the histological level, a finding correlated with biomechanical properties. However, several fractal dimensions (D) are known and computational ways to obtain them vary considerably. This study compared three algorithms on the same series of bone biopsies, to obtain the Kolmogorov, Minkowski–Bouligand, and mass‐radius fractal dimensions. The relationships with histomorphometric descriptors of the 2‐D trabecular architecture were investigated. Bone biopsies were obtained from 148 osteoporotic male patients. Bone volume (BV/TV), trabecular characteristics (Tb.N, Tb.Sp, Tb.Th), strut analysis, star volumes (marrow spaces and trabeculae), inter‐connectivity index, and Euler–Poincaré number were computed. The box‐counting method was used to obtain the Kolmogorov dimension (Dk), the dilatation method for the Minkowski–Bouligand dimension (DMB), and the sandbox for the mass‐radius dimension (DMR) and lacunarity (L). Logarithmic relationships were observed between BV/TV and the fractal dimensions. The best correlation was obtained with DMR and the lowest with DMB. Lacunarity was correlated with descriptors of the marrow cavities (ICI, star volume, Tb.Sp). Linear relationships were observed among the three fractal techniques which appeared highly correlated. A cluster analysis of all histomorphometric parameters provided a tree with three groups of descriptors: for trabeculae (Tb.Th, strut); for marrow cavities (Euler, ICI, Tb.Sp, star volume, L); and for the complexity of the network (Tb.N and the three D's). A sole fractal dimension cannot be used instead of the classic 2‐D descriptors of architecture; D rather reflects the complexity of branching trabeculae. Computation time is also an important determinant when choosing one of these methods. Copyright © 2001 John Wiley & Sons, Ltd.</description><subject>Biological and medical sciences</subject><subject>bone architecture</subject><subject>bone histomorphometry</subject><subject>bone structure</subject><subject>Cluster Analysis</subject><subject>fractal dimension</subject><subject>fractal geometry</subject><subject>Fractals</subject><subject>Humans</subject><subject>Image Processing, Computer-Assisted</subject><subject>Investigative techniques, diagnostic techniques (general aspects)</subject><subject>Least-Squares Analysis</subject><subject>Linear Models</subject><subject>Male</subject><subject>male osteoporosis</subject><subject>Medical sciences</subject><subject>Middle Aged</subject><subject>Miscellaneous. Technology</subject><subject>Osteoporosis - pathology</subject><subject>Pathology. Cytology. Biochemistry. Spectrometry. Miscellaneous investigative techniques</subject><issn>0022-3417</issn><issn>1096-9896</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNp10c1u1DAUBWALgei0IPEEyBsQmxT_xHHCrhrRFqkqLAaxtBznmhiSONiO2nkVnrYeJmpXrCzLn--xfBB6Q8k5JYR9nHXqzxtJnqENJU1VNHVTPUebfMQKXlJ5gk5j_EUIaRohXqITSmUpqlps0N_LoE3SA-7cCFN0fsLe4hR0C2YZdMCtn-ATNn6cdXBxPe4DAO5dTH70Ye79CCk4808tCTqcwPST-7NAxNYHPIKOS3DTz3wTsA6md1mkJeTcdOeLx-y8P8wY4N6l_Sv0wuohwut1PUPfLz_vttfFzderL9uLm8LwWpBCl0CYNVBX2rbCNlzqVnctk9KUpuyg5EzIWgKpoaVMMsGY4RWviCass9bwM_T-OHcO_vDkpEYXDQyDnsAvUUmWOeM8ww9HaIKPMYBVc3CjDntFiTr0oA49qNxDpm_XmUs7QvcE14_P4N0KdDR6sEFPxsUnV1JSN6TJrji6OzfA_r-B6tvF7voYvPpcDtw_eh1-q0pyKdSP2ytViS2t5a1QO_4AK2WzWw</recordid><startdate>200111</startdate><enddate>200111</enddate><creator>Chappard, Daniel</creator><creator>Legrand, Erick</creator><creator>Haettich, Bénédicte</creator><creator>Chalès, Gérard</creator><creator>Auvinet, Bernard</creator><creator>Eschard, Jean-Paul</creator><creator>Hamelin, Jean-Pierre</creator><creator>Baslé, Michel-Félix</creator><creator>Audran, Maurice</creator><general>John Wiley & Sons, Ltd</general><general>Wiley</general><scope>BSCLL</scope><scope>IQODW</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope></search><sort><creationdate>200111</creationdate><title>Fractal dimension of trabecular bone: comparison of three histomorphometric computed techniques for measuring the architectural two-dimensional complexity</title><author>Chappard, Daniel ; Legrand, Erick ; Haettich, Bénédicte ; Chalès, Gérard ; Auvinet, Bernard ; Eschard, Jean-Paul ; Hamelin, Jean-Pierre ; Baslé, Michel-Félix ; Audran, Maurice</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3850-a4e02fce86afb5f937abadb277c4c4de4325787e08eb1272522c36360a02dffc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Biological and medical sciences</topic><topic>bone architecture</topic><topic>bone histomorphometry</topic><topic>bone structure</topic><topic>Cluster Analysis</topic><topic>fractal dimension</topic><topic>fractal geometry</topic><topic>Fractals</topic><topic>Humans</topic><topic>Image Processing, Computer-Assisted</topic><topic>Investigative techniques, diagnostic techniques (general aspects)</topic><topic>Least-Squares Analysis</topic><topic>Linear Models</topic><topic>Male</topic><topic>male osteoporosis</topic><topic>Medical sciences</topic><topic>Middle Aged</topic><topic>Miscellaneous. Technology</topic><topic>Osteoporosis - pathology</topic><topic>Pathology. Cytology. Biochemistry. Spectrometry. Miscellaneous investigative techniques</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chappard, Daniel</creatorcontrib><creatorcontrib>Legrand, Erick</creatorcontrib><creatorcontrib>Haettich, Bénédicte</creatorcontrib><creatorcontrib>Chalès, Gérard</creatorcontrib><creatorcontrib>Auvinet, Bernard</creatorcontrib><creatorcontrib>Eschard, Jean-Paul</creatorcontrib><creatorcontrib>Hamelin, Jean-Pierre</creatorcontrib><creatorcontrib>Baslé, Michel-Félix</creatorcontrib><creatorcontrib>Audran, Maurice</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><jtitle>The Journal of pathology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chappard, Daniel</au><au>Legrand, Erick</au><au>Haettich, Bénédicte</au><au>Chalès, Gérard</au><au>Auvinet, Bernard</au><au>Eschard, Jean-Paul</au><au>Hamelin, Jean-Pierre</au><au>Baslé, Michel-Félix</au><au>Audran, Maurice</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fractal dimension of trabecular bone: comparison of three histomorphometric computed techniques for measuring the architectural two-dimensional complexity</atitle><jtitle>The Journal of pathology</jtitle><addtitle>J. Pathol</addtitle><date>2001-11</date><risdate>2001</risdate><volume>195</volume><issue>4</issue><spage>515</spage><epage>521</epage><pages>515-521</pages><issn>0022-3417</issn><eissn>1096-9896</eissn><coden>JPTLAS</coden><abstract>Trabecular bone has been reported as having two‐dimensional (2‐D) fractal characteristics at the histological level, a finding correlated with biomechanical properties. However, several fractal dimensions (D) are known and computational ways to obtain them vary considerably. This study compared three algorithms on the same series of bone biopsies, to obtain the Kolmogorov, Minkowski–Bouligand, and mass‐radius fractal dimensions. The relationships with histomorphometric descriptors of the 2‐D trabecular architecture were investigated. Bone biopsies were obtained from 148 osteoporotic male patients. Bone volume (BV/TV), trabecular characteristics (Tb.N, Tb.Sp, Tb.Th), strut analysis, star volumes (marrow spaces and trabeculae), inter‐connectivity index, and Euler–Poincaré number were computed. The box‐counting method was used to obtain the Kolmogorov dimension (Dk), the dilatation method for the Minkowski–Bouligand dimension (DMB), and the sandbox for the mass‐radius dimension (DMR) and lacunarity (L). Logarithmic relationships were observed between BV/TV and the fractal dimensions. The best correlation was obtained with DMR and the lowest with DMB. Lacunarity was correlated with descriptors of the marrow cavities (ICI, star volume, Tb.Sp). Linear relationships were observed among the three fractal techniques which appeared highly correlated. A cluster analysis of all histomorphometric parameters provided a tree with three groups of descriptors: for trabeculae (Tb.Th, strut); for marrow cavities (Euler, ICI, Tb.Sp, star volume, L); and for the complexity of the network (Tb.N and the three D's). A sole fractal dimension cannot be used instead of the classic 2‐D descriptors of architecture; D rather reflects the complexity of branching trabeculae. Computation time is also an important determinant when choosing one of these methods. Copyright © 2001 John Wiley & Sons, Ltd.</abstract><cop>Chichester, UK</cop><pub>John Wiley & Sons, Ltd</pub><pmid>11745685</pmid><doi>10.1002/path.970</doi><tpages>7</tpages></addata></record> |
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| subjects | Biological and medical sciences bone architecture bone histomorphometry bone structure Cluster Analysis fractal dimension fractal geometry Fractals Humans Image Processing, Computer-Assisted Investigative techniques, diagnostic techniques (general aspects) Least-Squares Analysis Linear Models Male male osteoporosis Medical sciences Middle Aged Miscellaneous. Technology Osteoporosis - pathology Pathology. Cytology. Biochemistry. Spectrometry. Miscellaneous investigative techniques |
| title | Fractal dimension of trabecular bone: comparison of three histomorphometric computed techniques for measuring the architectural two-dimensional complexity |
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