Photoelastic and Finite Element Analyses of Occlusal Loads in Mandibular Body
Identifieur interne : 002815 ( Pmc/Curation ); précédent : 002814; suivant : 002816Photoelastic and Finite Element Analyses of Occlusal Loads in Mandibular Body
Auteurs : Ana Cláudia Rossi [Brésil] ; Alexandre Rodrigues Freire [Brésil] ; Felippe Bevilacqua Prado [Brésil] ; Luciana Asprino [Brésil] ; Lourenço Correr-Sobrinho [Brésil] ; Paulo Henrique Ferreira Caria [Brésil]Source :
- Anatomy Research International [ 2090-2743 ] ; 2014.
Abstract
This study proposed to evaluate the mandibular biomechanics in the posterior dentition based on experimental and computational analyses. The analyses were performed on a model of human mandible, which was modeled by epoxy resin for photoelastic analysis and by computer-aided design for finite element analysis. To standardize the evaluation, specific areas were determined at the lateral surface of mandibular body. The photoelastic analysis was configured through a vertical load on the first upper molar and fixed support at the ramus of mandible. The same configuration was used in the computer simulation. Force magnitudes of 50, 100, 150, and 200 N were applied to evaluate the bone stress. The stress results presented similar distribution in both analyses, with the more intense stress being at retromolar area and oblique line and alveolar process at molar level. This study presented the similarity of results in the experimental and computational analyses and, thus, showed the high importance of morphology biomechanical characterization at posterior dentition.
Url:
DOI: 10.1155/2014/174028
PubMed: 25374695
PubMed Central: 4206929
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Box 52, 13414903 Piracicaba, SP, Brazil</nlm:aff><country xml:lang="fr">Brésil</country><wicri:regionArea>Department of Morphology, Anatomy Area, Piracicaba Dental School, UNICAMP, Limeira Avenue 901, P.O. Box 52, 13414903 Piracicaba, SP</wicri:regionArea></affiliation></author><author><name sortKey="Freire, Alexandre Rodrigues" sort="Freire, Alexandre Rodrigues" uniqKey="Freire A" first="Alexandre Rodrigues" last="Freire">Alexandre Rodrigues Freire</name><affiliation wicri:level="1"><nlm:aff id="I1">Piracicaba Dental School, State University of Campinas, UNICAMP, Piracicaba, SP, Brazil</nlm:aff><country xml:lang="fr">Brésil</country><wicri:regionArea>Piracicaba Dental School, State University of Campinas, UNICAMP, Piracicaba, SP</wicri:regionArea></affiliation></author><author><name sortKey="Prado, Felippe Bevilacqua" sort="Prado, Felippe Bevilacqua" uniqKey="Prado F" first="Felippe Bevilacqua" last="Prado">Felippe Bevilacqua Prado</name><affiliation wicri:level="1"><nlm:aff id="I1">Piracicaba Dental School, State University of Campinas, UNICAMP, Piracicaba, SP, Brazil</nlm:aff><country xml:lang="fr">Brésil</country><wicri:regionArea>Piracicaba Dental School, State University of Campinas, UNICAMP, Piracicaba, SP</wicri:regionArea></affiliation></author><author><name sortKey="Asprino, Luciana" sort="Asprino, Luciana" uniqKey="Asprino L" first="Luciana" last="Asprino">Luciana Asprino</name><affiliation wicri:level="1"><nlm:aff id="I1">Piracicaba Dental School, State University of Campinas, UNICAMP, Piracicaba, SP, Brazil</nlm:aff><country xml:lang="fr">Brésil</country><wicri:regionArea>Piracicaba Dental School, State University of Campinas, UNICAMP, Piracicaba, SP</wicri:regionArea></affiliation></author><author><name sortKey="Correr Sobrinho, Lourenco" sort="Correr Sobrinho, Lourenco" uniqKey="Correr Sobrinho L" first="Lourenço" last="Correr-Sobrinho">Lourenço Correr-Sobrinho</name><affiliation wicri:level="1"><nlm:aff id="I1">Piracicaba Dental School, State University of Campinas, UNICAMP, Piracicaba, SP, Brazil</nlm:aff><country xml:lang="fr">Brésil</country><wicri:regionArea>Piracicaba Dental School, State University of Campinas, UNICAMP, Piracicaba, SP</wicri:regionArea></affiliation></author><author><name sortKey="Caria, Paulo Henrique Ferreira" sort="Caria, Paulo Henrique Ferreira" uniqKey="Caria P" first="Paulo Henrique Ferreira" last="Caria">Paulo Henrique Ferreira Caria</name><affiliation wicri:level="1"><nlm:aff id="I1">Piracicaba Dental School, State University of Campinas, UNICAMP, Piracicaba, SP, Brazil</nlm:aff><country xml:lang="fr">Brésil</country><wicri:regionArea>Piracicaba Dental School, State University of Campinas, UNICAMP, Piracicaba, SP</wicri:regionArea></affiliation></author></analytic><series><title level="j">Anatomy Research International</title><idno type="ISSN">2090-2743</idno><idno type="eISSN">2090-2751</idno><imprint><date when="2014">2014</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>This study proposed to evaluate the mandibular biomechanics in the posterior dentition based on experimental and computational analyses. The analyses were performed on a model of human mandible, which was modeled by epoxy resin for photoelastic analysis and by computer-aided design for finite element analysis. To standardize the evaluation, specific areas were determined at the lateral surface of mandibular body. The photoelastic analysis was configured through a vertical load on the first upper molar and fixed support at the ramus of mandible. The same configuration was used in the computer simulation. Force magnitudes of 50, 100, 150, and 200 N were applied to evaluate the bone stress. The stress results presented similar distribution in both analyses, with the more intense stress being at retromolar area and oblique line and alveolar process at molar level. This study presented the similarity of results in the experimental and computational analyses and, thus, showed the high importance of morphology biomechanical characterization at posterior dentition.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Korioth, Twp" uniqKey="Korioth T">TWP Korioth</name></author><author><name sortKey="Romilly, Dp" uniqKey="Romilly D">DP Romilly</name></author><author><name sortKey="Hannam, Ag" uniqKey="Hannam A">AG Hannam</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Schwartz, Gt" uniqKey="Schwartz G">GT Schwartz</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Mavropoulos, A" uniqKey="Mavropoulos A">A Mavropoulos</name></author><author><name sortKey="Kiliaridis, S" uniqKey="Kiliaridis S">S Kiliaridis</name></author><author><name sortKey="Bresin, A" uniqKey="Bresin A">A Bresin</name></author><author><name sortKey="Ammann, P" 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<front><journal-meta><journal-id journal-id-type="nlm-ta">Anat Res Int</journal-id><journal-id journal-id-type="iso-abbrev">Anat Res Int</journal-id><journal-id journal-id-type="publisher-id">ARI</journal-id><journal-title-group><journal-title>Anatomy Research International</journal-title></journal-title-group><issn pub-type="ppub">2090-2743</issn><issn pub-type="epub">2090-2751</issn><publisher><publisher-name>Hindawi Publishing Corporation</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">25374695</article-id><article-id pub-id-type="pmc">4206929</article-id><article-id pub-id-type="doi">10.1155/2014/174028</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title>Photoelastic and Finite Element Analyses of Occlusal Loads in Mandibular Body</article-title></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="false">http://orcid.org/0000-0002-8718-4898</contrib-id><name><surname>Rossi</surname><given-names>Ana Cláudia</given-names></name><xref ref-type="aff" rid="I1"><sup>1</sup></xref><xref ref-type="aff" rid="I2"><sup>2</sup></xref><xref ref-type="corresp" rid="cor1">*</xref></contrib><contrib contrib-type="author"><name><surname>Freire</surname><given-names>Alexandre Rodrigues</given-names></name><xref ref-type="aff" rid="I1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Prado</surname><given-names>Felippe Bevilacqua</given-names></name><xref ref-type="aff" rid="I1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Asprino</surname><given-names>Luciana</given-names></name><xref ref-type="aff" rid="I1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Correr-Sobrinho</surname><given-names>Lourenço</given-names></name><xref ref-type="aff" rid="I1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Caria</surname><given-names>Paulo Henrique Ferreira</given-names></name><xref ref-type="aff" rid="I1"><sup>1</sup></xref></contrib></contrib-group><aff id="I1"><sup>1</sup>Piracicaba Dental School, State University of Campinas, UNICAMP, Piracicaba, SP, Brazil</aff><aff id="I2"><sup>2</sup>Department of Morphology, Anatomy Area, Piracicaba Dental School, UNICAMP, Limeira Avenue 901, P.O. Box 52, 13414903 Piracicaba, SP, Brazil</aff><author-notes><corresp id="cor1">*Ana Cláudia Rossi: <email>anaanatomia@gmail.com</email></corresp><fn fn-type="other"><p>Academic Editor: Friedrich Paulsen</p></fn></author-notes><pub-date pub-type="ppub"><year>2014</year></pub-date><pub-date pub-type="epub"><day>8</day><month>10</month><year>2014</year></pub-date><volume>2014</volume><elocation-id>174028</elocation-id><history><date date-type="received"><day>16</day><month>6</month><year>2014</year></date><date date-type="rev-recd"><day>22</day><month>8</month><year>2014</year></date><date date-type="accepted"><day>3</day><month>9</month><year>2014</year></date></history><permissions><copyright-statement>Copyright © 2014 Ana Cláudia Rossi et al.</copyright-statement><copyright-year>2014</copyright-year><license xlink:href="https://creativecommons.org/licenses/by/3.0/"><license-p>This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p></license></permissions><abstract><p>This study proposed to evaluate the mandibular biomechanics in the posterior dentition based on experimental and computational analyses. The analyses were performed on a model of human mandible, which was modeled by epoxy resin for photoelastic analysis and by computer-aided design for finite element analysis. To standardize the evaluation, specific areas were determined at the lateral surface of mandibular body. The photoelastic analysis was configured through a vertical load on the first upper molar and fixed support at the ramus of mandible. The same configuration was used in the computer simulation. Force magnitudes of 50, 100, 150, and 200 N were applied to evaluate the bone stress. The stress results presented similar distribution in both analyses, with the more intense stress being at retromolar area and oblique line and alveolar process at molar level. This study presented the similarity of results in the experimental and computational analyses and, thus, showed the high importance of morphology biomechanical characterization at posterior dentition.</p></abstract></article-meta></front><floats-group><fig id="fig1" orientation="portrait" position="float"><label>Figure 1</label><caption><p>Schematic representation of the division and numbering of the areas evaluated in the mandibular body.</p></caption><graphic xlink:href="ARI2014-174028.001"></graphic></fig><fig id="fig2" orientation="portrait" position="float"><label>Figure 2</label><caption><p>Application of the load in the photoelastic analysis. WLS: white light source; P: polarizing filter; S: support.</p></caption><graphic xlink:href="ARI2014-174028.002"></graphic></fig><fig id="fig3" orientation="portrait" position="float"><label>Figure 3</label><caption><p>Schematic representation of the division and numbering of the 14 areas evaluated in the mandibular body on the epoxy resin model.</p></caption><graphic xlink:href="ARI2014-174028.003"></graphic></fig><fig id="fig4" orientation="portrait" position="float"><label>Figure 4</label><caption><p>(a) Selection of bone and teeth in software InVesalius 3.0b on CT. (b) CAD model. (c) Finite element model (FE mesh).</p></caption><graphic xlink:href="ARI2014-174028.004"></graphic></fig><fig id="fig5" orientation="portrait" position="float"><label>Figure 5</label><caption><p>Representation of the restriction system (insertion of the masseter, medial pterygoid, and lateral pterygoid muscles) and load (L) applied to the computational model in Ansys v14 software.</p></caption><graphic xlink:href="ARI2014-174028.005"></graphic></fig><fig id="fig6" orientation="portrait" position="float"><label>Figure 6</label><caption><p>Schematic representation of the division and numbering of the 14 areas evaluated in the mandibular body on the computational model.</p></caption><graphic xlink:href="ARI2014-174028.006"></graphic></fig><fig id="fig7" orientation="portrait" position="float"><label>Figure 7</label><caption><p>Distribution of isochromatic fringes in photoelastic analysis. Right, scale of the orders of isochromatic fringes. (a) 50 N, (b) 100 N (c) 150 N, and (d) 200 N.</p></caption><graphic xlink:href="ARI2014-174028.007"></graphic></fig><fig id="fig8" orientation="portrait" position="float"><label>Figure 8</label><caption><p>Von Mises stresses of model characterized as epoxy resin. (a) 50 N; (b) 100 N; (c) 150 N; (d) 200 N.</p></caption><graphic xlink:href="ARI2014-174028.008"></graphic></fig><fig id="fig9" orientation="portrait" position="float"><label>Figure 9</label><caption><p>Von Mises stresses of model characterized as bone. (a) 50 N; (b) 100 N; (c) 150 N; (d) 200 N.</p></caption><graphic xlink:href="ARI2014-174028.009"></graphic></fig><table-wrap id="tab1" orientation="portrait" position="float"><label>Table 1</label><caption><p>Mechanical properties of the anatomical structures.</p></caption><table frame="hsides" rules="groups"><thead><tr><th align="left" rowspan="1" colspan="1">Material</th><th align="center" rowspan="1" colspan="1">Young's modulus (MPa)</th><th align="center" rowspan="1" colspan="1">Poisson's ratio</th></tr></thead><tbody><tr><td align="left" rowspan="1" colspan="1">Resin*</td><td align="center" rowspan="1" colspan="1">3102,6</td><td align="center" rowspan="1" colspan="1">0,30</td></tr><tr><td align="left" rowspan="1" colspan="1">Bone [<xref rid="B15" ref-type="bibr">8</xref>]</td><td align="center" rowspan="1" colspan="1">14000 </td><td align="center" rowspan="1" colspan="1">0,30</td></tr></tbody></table><table-wrap-foot><fn><p>*Araltec Chemicals Products Ltda, Hunstman, MPa = megapascal.</p></fn></table-wrap-foot></table-wrap><table-wrap id="tab2" orientation="portrait" position="float"><label>Table 2</label><caption><p>Isochromatic fringes order values and von Mises stress (in MPa) to computational model characterized as resin and as bone.</p></caption><table frame="hsides" rules="groups"><thead><tr><th align="left" rowspan="2" colspan="1">Area</th><th align="center" colspan="4" rowspan="1">Isochromatic fringes order</th><th align="center" colspan="4" rowspan="1">Von Mises stresses (epoxy resin)</th><th align="center" colspan="4" rowspan="1">Von Mises stresses (bone)</th></tr><tr><th align="center" rowspan="1" colspan="1">50 N</th><th align="center" rowspan="1" colspan="1">100 N</th><th align="center" rowspan="1" colspan="1">150 N</th><th align="center" rowspan="1" colspan="1">200 N</th><th align="center" rowspan="1" colspan="1">50 N</th><th align="center" rowspan="1" colspan="1">100 N</th><th align="center" rowspan="1" colspan="1">150 N</th><th align="center" rowspan="1" colspan="1">200 N</th><th align="center" rowspan="1" colspan="1">50 N</th><th align="center" rowspan="1" colspan="1">100 N</th><th align="center" rowspan="1" colspan="1">150 N</th><th align="center" rowspan="1" colspan="1">200 N</th></tr></thead><tbody><tr><td align="left" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">2</td><td align="center" rowspan="1" colspan="1">3</td><td align="center" rowspan="1" colspan="1">1,64</td><td align="center" rowspan="1" colspan="1">3,65</td><td align="center" rowspan="1" colspan="1">5,35</td><td align="center" rowspan="1" colspan="1">6,89</td><td align="center" rowspan="1" colspan="1">1,77</td><td align="center" rowspan="1" colspan="1">3,93</td><td align="center" rowspan="1" colspan="1">5,00</td><td align="center" rowspan="1" colspan="1">6,59</td></tr><tr><td align="left" rowspan="1" colspan="1">2</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">2</td><td align="center" rowspan="1" colspan="1">3</td><td align="center" rowspan="1" colspan="1">0,89</td><td align="center" rowspan="1" colspan="1">1,86</td><td align="center" rowspan="1" colspan="1">2,60</td><td align="center" rowspan="1" colspan="1">3,75</td><td align="center" rowspan="1" colspan="1">0,85</td><td align="center" rowspan="1" colspan="1">1,91</td><td align="center" rowspan="1" colspan="1">2,17</td><td align="center" rowspan="1" colspan="1">3,03</td></tr><tr><td align="left" rowspan="1" colspan="1">3</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">2</td><td align="center" rowspan="1" colspan="1">3</td><td align="center" rowspan="1" colspan="1">0,76</td><td align="center" rowspan="1" colspan="1">1,39</td><td align="center" rowspan="1" colspan="1">2,36</td><td align="center" rowspan="1" colspan="1">3,06</td><td align="center" rowspan="1" colspan="1">0,58</td><td align="center" rowspan="1" colspan="1">1,13</td><td align="center" rowspan="1" colspan="1">1,73</td><td align="center" rowspan="1" colspan="1">2,23</td></tr><tr><td align="left" rowspan="1" colspan="1">4</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">2</td><td align="center" rowspan="1" colspan="1">3</td><td align="center" rowspan="1" colspan="1">0,46</td><td align="center" rowspan="1" colspan="1">0,83</td><td align="center" rowspan="1" colspan="1">1,26</td><td align="center" rowspan="1" colspan="1">1,83</td><td align="center" rowspan="1" colspan="1">0,37</td><td align="center" rowspan="1" colspan="1">0,69</td><td align="center" rowspan="1" colspan="1">0,97</td><td align="center" rowspan="1" colspan="1">1,41</td></tr><tr><td align="left" rowspan="1" colspan="1">5</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">2</td><td align="center" rowspan="1" colspan="1">0,20</td><td align="center" rowspan="1" colspan="1">0,48</td><td align="center" rowspan="1" colspan="1">0,71</td><td align="center" rowspan="1" colspan="1">2,03</td><td align="center" rowspan="1" colspan="1">0,11</td><td align="center" rowspan="1" colspan="1">0,28</td><td align="center" rowspan="1" colspan="1">0,40</td><td align="center" rowspan="1" colspan="1">0,54</td></tr><tr><td align="left" rowspan="1" colspan="1">6</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">2</td><td align="center" rowspan="1" colspan="1">0,48</td><td align="center" rowspan="1" colspan="1">1,03</td><td align="center" rowspan="1" colspan="1">1,49</td><td align="center" rowspan="1" colspan="1">2,03</td><td align="center" rowspan="1" colspan="1">0,39</td><td align="center" rowspan="1" colspan="1">0,74</td><td align="center" rowspan="1" colspan="1">1,11</td><td align="center" rowspan="1" colspan="1">1,51</td></tr><tr><td align="left" rowspan="1" colspan="1">7</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">0,29</td><td align="center" rowspan="1" colspan="1">0,71</td><td align="center" rowspan="1" colspan="1">1,06</td><td align="center" rowspan="1" colspan="1">1,45</td><td align="center" rowspan="1" colspan="1">0,25</td><td align="center" rowspan="1" colspan="1">0,46</td><td align="center" rowspan="1" colspan="1">0,74</td><td align="center" rowspan="1" colspan="1">0,92</td></tr><tr><td align="left" rowspan="1" colspan="1">8</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">0,18</td><td align="center" rowspan="1" colspan="1">0,34</td><td align="center" rowspan="1" colspan="1">0,53</td><td align="center" rowspan="1" colspan="1">0,80</td><td align="center" rowspan="1" colspan="1">0,14</td><td align="center" rowspan="1" colspan="1">0,20</td><td align="center" rowspan="1" colspan="1">0,36</td><td align="center" rowspan="1" colspan="1">0,49</td></tr><tr><td align="left" rowspan="1" colspan="1">9</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">0,20</td><td align="center" rowspan="1" colspan="1">0,41</td><td align="center" rowspan="1" colspan="1">0,68</td><td align="center" rowspan="1" colspan="1">0,90</td><td align="center" rowspan="1" colspan="1">0,14</td><td align="center" rowspan="1" colspan="1">0,26</td><td align="center" rowspan="1" colspan="1">0,43</td><td align="center" rowspan="1" colspan="1">0,90</td></tr><tr><td align="left" rowspan="1" colspan="1">10</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">0,15</td><td align="center" rowspan="1" colspan="1">0,31</td><td align="center" rowspan="1" colspan="1">0,72</td><td align="center" rowspan="1" colspan="1">0,93</td><td align="center" rowspan="1" colspan="1">0,12</td><td align="center" rowspan="1" colspan="1">0,20</td><td align="center" rowspan="1" colspan="1">0,36</td><td align="center" rowspan="1" colspan="1">0,45</td></tr><tr><td align="left" rowspan="1" colspan="1">11</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">0,12</td><td align="center" rowspan="1" colspan="1">0,2</td><td align="center" rowspan="1" colspan="1">0,32</td><td align="center" rowspan="1" colspan="1">0,40</td><td align="center" rowspan="1" colspan="1">0,11</td><td align="center" rowspan="1" colspan="1">0,14</td><td align="center" rowspan="1" colspan="1">0,2</td><td align="center" rowspan="1" colspan="1">0,33</td></tr><tr><td align="left" rowspan="1" colspan="1">12</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0,11</td><td align="center" rowspan="1" colspan="1">0,24</td><td align="center" rowspan="1" colspan="1">0,28</td><td align="center" rowspan="1" colspan="1">0,38</td><td align="center" rowspan="1" colspan="1">0,07</td><td align="center" rowspan="1" colspan="1">0,16</td><td align="center" rowspan="1" colspan="1">0,24</td><td align="center" rowspan="1" colspan="1">0,32</td></tr><tr><td align="left" rowspan="1" colspan="1">13</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0,09</td><td align="center" rowspan="1" colspan="1">0,21</td><td align="center" rowspan="1" colspan="1">0,33</td><td align="center" rowspan="1" colspan="1">0,41</td><td align="center" rowspan="1" colspan="1">0,07</td><td align="center" rowspan="1" colspan="1">0,12</td><td align="center" rowspan="1" colspan="1">0,22</td><td align="center" rowspan="1" colspan="1">0,28</td></tr><tr><td align="left" rowspan="1" colspan="1">14</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0</td><td align="center" rowspan="1" colspan="1">0,06</td><td align="center" rowspan="1" colspan="1">0,13</td><td align="center" rowspan="1" colspan="1">0,23</td><td align="center" rowspan="1" colspan="1">0,34</td><td align="center" rowspan="1" colspan="1">0,04</td><td align="center" rowspan="1" colspan="1">0,07</td><td align="center" rowspan="1" colspan="1">0,13</td><td align="center" rowspan="1" colspan="1">0,15</td></tr></tbody></table></table-wrap></floats-group></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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