Periodontal ligament influence on the stress distribution in a removable partial denture supported by implant: a finite element analysis
Identifieur interne : 000608 ( Pmc/Corpus ); précédent : 000607; suivant : 000609Periodontal ligament influence on the stress distribution in a removable partial denture supported by implant: a finite element analysis
Auteurs : Carlos Marcelo Archangelo ; Eduardo Passos Rocha ; João Antônio Pereira ; Manoel Martin Junior ; Rodolfo Bruniera Anchieta ; Amilcar Chagas Freitas JúniorSource :
- Journal of Applied Oral Science [ 1678-7757 ] ; 2012.
Abstract
The non-homogenous aspect of periodontal ligament (PDL) has been examined using finite element analysis (FEA) to better simulate PDL behavior. The aim of this study was to assess, by 2-D FEA, the influence of non-homogenous PDL on the stress distribution when the free-end saddle removable partial denture (RPD) is partially supported by an osseointegrated implant.
Six finite element (FE) models of a partially edentulous mandible were created to represent two types of PDL (non-homogenous and homogenous) and two types of RPD (conventional RPD, supported by tooth and fibromucosa; and modified RPD, supported by tooth and implant [10.00x3.75 mm]). Two additional FE models without RPD were used as control models. The non-homogenous PDL was modeled using beam elements to simulate the crest, horizontal, oblique and apical fibers. The load (50 N) was applied in each cusp simultaneously. Regarding boundary conditions the border of alveolar ridge was fixed along the x axis. The FE software (Ansys 10.0) was used to compute the stress fields, and the von Mises stress criterion (σvM) was applied to analyze the results.
The peak of σvM in non-homogenous PDL was higher than that for the homogenous condition. The benefits of implants were enhanced for the non-homogenous PDL condition, with drastic σvM reduction on the posterior half of the alveolar ridge. The implant did not reduce the stress on the support tooth for both PDL conditions.
The PDL modeled in the non-homogeneous form increased the benefits of the osseointegrated implant in comparison with the homogeneous condition. Using the non-homogenous PDL, the presence of osseointegrated implant did not reduce the stress on the supporting tooth.
Url:
DOI: 10.1590/S1678-77572012000300012
PubMed: 22858705
PubMed Central: 3881771
Links to Exploration step
PMC:3881771Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Periodontal ligament influence on the stress distribution in a removable
partial denture supported by implant: a finite element analysis</title>
<author><name sortKey="Archangelo, Carlos Marcelo" sort="Archangelo, Carlos Marcelo" uniqKey="Archangelo C" first="Carlos Marcelo" last="Archangelo">Carlos Marcelo Archangelo</name>
<affiliation><nlm:aff id="aff01"> DDS, PhD, Professor, Federal Institute of Paraná - IFPR, Londrina, PR, Brazil.</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Rocha, Eduardo Passos" sort="Rocha, Eduardo Passos" uniqKey="Rocha E" first="Eduardo Passos" last="Rocha">Eduardo Passos Rocha</name>
<affiliation><nlm:aff id="aff02"> DDS, PhD, Associate Professor, Department of Dental Materials and Prosthodontics, Faculty of Dentistry of Araçatuba, UNESP - Univ. Estadual Paulista, Araçatuba, SP, Brazil.</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Pereira, Joao Antonio" sort="Pereira, Joao Antonio" uniqKey="Pereira J" first="João Antônio" last="Pereira">João Antônio Pereira</name>
<affiliation><nlm:aff id="aff03"> MEng, PhD, Associate Professor, Department of Mechanical Engineering, Faculty of Engineering of Ilha Solteira, UNESP - Univ. Estadual Paulista, Ilha Solteira, SP, Brazil.</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Martin Junior, Manoel" sort="Martin Junior, Manoel" uniqKey="Martin Junior M" first="Manoel" last="Martin Junior">Manoel Martin Junior</name>
<affiliation><nlm:aff id="aff01"> DDS, PhD, Professor, Federal Institute of Paraná - IFPR, Londrina, PR, Brazil.</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Anchieta, Rodolfo Bruniera" sort="Anchieta, Rodolfo Bruniera" uniqKey="Anchieta R" first="Rodolfo Bruniera" last="Anchieta">Rodolfo Bruniera Anchieta</name>
<affiliation><nlm:aff id="aff04"> DDS, MS, PhD student, Department of Dental Materials and Prosthodontics, Faculty of Dentistry of Araçatuba, UNESP - Univ. Estadual Paulista, Araçatuba, SP, Brazil.</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Freitas Junior, Amilcar Chagas" sort="Freitas Junior, Amilcar Chagas" uniqKey="Freitas Junior A" first="Amilcar Chagas" last="Freitas Júnior">Amilcar Chagas Freitas Júnior</name>
<affiliation><nlm:aff id="aff04"> DDS, MS, PhD student, Department of Dental Materials and Prosthodontics, Faculty of Dentistry of Araçatuba, UNESP - Univ. Estadual Paulista, Araçatuba, SP, Brazil.</nlm:aff>
</affiliation>
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<sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Periodontal ligament influence on the stress distribution in a removable
partial denture supported by implant: a finite element analysis</title>
<author><name sortKey="Archangelo, Carlos Marcelo" sort="Archangelo, Carlos Marcelo" uniqKey="Archangelo C" first="Carlos Marcelo" last="Archangelo">Carlos Marcelo Archangelo</name>
<affiliation><nlm:aff id="aff01"> DDS, PhD, Professor, Federal Institute of Paraná - IFPR, Londrina, PR, Brazil.</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Rocha, Eduardo Passos" sort="Rocha, Eduardo Passos" uniqKey="Rocha E" first="Eduardo Passos" last="Rocha">Eduardo Passos Rocha</name>
<affiliation><nlm:aff id="aff02"> DDS, PhD, Associate Professor, Department of Dental Materials and Prosthodontics, Faculty of Dentistry of Araçatuba, UNESP - Univ. Estadual Paulista, Araçatuba, SP, Brazil.</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Pereira, Joao Antonio" sort="Pereira, Joao Antonio" uniqKey="Pereira J" first="João Antônio" last="Pereira">João Antônio Pereira</name>
<affiliation><nlm:aff id="aff03"> MEng, PhD, Associate Professor, Department of Mechanical Engineering, Faculty of Engineering of Ilha Solteira, UNESP - Univ. Estadual Paulista, Ilha Solteira, SP, Brazil.</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Martin Junior, Manoel" sort="Martin Junior, Manoel" uniqKey="Martin Junior M" first="Manoel" last="Martin Junior">Manoel Martin Junior</name>
<affiliation><nlm:aff id="aff01"> DDS, PhD, Professor, Federal Institute of Paraná - IFPR, Londrina, PR, Brazil.</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Anchieta, Rodolfo Bruniera" sort="Anchieta, Rodolfo Bruniera" uniqKey="Anchieta R" first="Rodolfo Bruniera" last="Anchieta">Rodolfo Bruniera Anchieta</name>
<affiliation><nlm:aff id="aff04"> DDS, MS, PhD student, Department of Dental Materials and Prosthodontics, Faculty of Dentistry of Araçatuba, UNESP - Univ. Estadual Paulista, Araçatuba, SP, Brazil.</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Freitas Junior, Amilcar Chagas" sort="Freitas Junior, Amilcar Chagas" uniqKey="Freitas Junior A" first="Amilcar Chagas" last="Freitas Júnior">Amilcar Chagas Freitas Júnior</name>
<affiliation><nlm:aff id="aff04"> DDS, MS, PhD student, Department of Dental Materials and Prosthodontics, Faculty of Dentistry of Araçatuba, UNESP - Univ. Estadual Paulista, Araçatuba, SP, Brazil.</nlm:aff>
</affiliation>
</author>
</analytic>
<series><title level="j">Journal of Applied Oral Science</title>
<idno type="ISSN">1678-7757</idno>
<idno type="eISSN">1678-7765</idno>
<imprint><date when="2012">2012</date>
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<front><div type="abstract" xml:lang="en"><sec><title>ABSTRACT</title>
</sec>
<sec><title>Objective</title>
<p>The non-homogenous aspect of periodontal ligament (PDL) has been examined using
finite element analysis (FEA) to better simulate PDL behavior. The aim of this
study was to assess, by 2-D FEA, the influence of non-homogenous PDL on the stress
distribution when the free-end saddle removable partial denture (RPD) is partially
supported by an osseointegrated implant. </p>
</sec>
<sec><title>Material and Methods</title>
<p>Six finite element (FE) models of a partially edentulous mandible were created to
represent two types of PDL (non-homogenous and homogenous) and two types of RPD
(conventional RPD, supported by tooth and fibromucosa; and modified RPD, supported
by tooth and implant [10.00x3.75 mm]). Two additional FE models without RPD were
used as control models. The non-homogenous PDL was modeled using beam elements to
simulate the crest, horizontal, oblique and apical fibers. The load (50 N) was
applied in each cusp simultaneously. Regarding boundary conditions the border of
alveolar ridge was fixed along the x axis. The FE software (Ansys 10.0) was used
to compute the stress fields, and the von Mises stress criterion (σvM) was
applied to analyze the results. </p>
</sec>
<sec><title>Results</title>
<p>The peak of σvM in non-homogenous PDL was higher than that for the
homogenous condition. The benefits of implants were enhanced for the
non-homogenous PDL condition, with drastic σvM reduction on the posterior
half of the alveolar ridge. The implant did not reduce the stress on the support
tooth for both PDL conditions. </p>
</sec>
<sec><title>Conclusion</title>
<p>The PDL modeled in the non-homogeneous form increased the benefits of the
osseointegrated implant in comparison with the homogeneous condition. Using the
non-homogenous PDL, the presence of osseointegrated implant did not reduce the
stress on the supporting tooth.</p>
</sec>
</div>
</front>
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<pmc article-type="research-article"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">J Appl Oral Sci</journal-id>
<journal-id journal-id-type="iso-abbrev">J Appl Oral Sci</journal-id>
<journal-id journal-id-type="publisher-id">J. Appl. Oral. Sci.</journal-id>
<journal-title-group><journal-title>Journal of Applied Oral Science</journal-title>
</journal-title-group>
<issn pub-type="ppub">1678-7757</issn>
<issn pub-type="epub">1678-7765</issn>
<publisher><publisher-name>Faculdade de Odontologia de Bauru da Universidade de São
Paulo</publisher-name>
</publisher>
</journal-meta>
<article-meta><article-id pub-id-type="pmid">22858705</article-id>
<article-id pub-id-type="pmc">3881771</article-id>
<article-id pub-id-type="doi">10.1590/S1678-77572012000300012</article-id>
<article-categories><subj-group subj-group-type="heading"><subject>Original Articles</subject>
</subj-group>
</article-categories>
<title-group><article-title>Periodontal ligament influence on the stress distribution in a removable
partial denture supported by implant: a finite element analysis</article-title>
</title-group>
<contrib-group><contrib contrib-type="author"><name><surname>ARCHANGELO</surname>
<given-names>Carlos Marcelo</given-names>
</name>
<xref ref-type="aff" rid="aff01">1</xref>
<xref ref-type="corresp" rid="c01"></xref>
</contrib>
<contrib contrib-type="author"><name><surname>ROCHA</surname>
<given-names>Eduardo Passos</given-names>
</name>
<xref ref-type="aff" rid="aff02">2</xref>
</contrib>
<contrib contrib-type="author"><name><surname>PEREIRA</surname>
<given-names>João Antônio</given-names>
</name>
<xref ref-type="aff" rid="aff03">3</xref>
</contrib>
<contrib contrib-type="author"><name><surname>MARTIN JUNIOR</surname>
<given-names>Manoel</given-names>
</name>
<xref ref-type="aff" rid="aff01">1</xref>
</contrib>
<contrib contrib-type="author"><name><surname>ANCHIETA</surname>
<given-names>Rodolfo Bruniera</given-names>
</name>
<xref ref-type="aff" rid="aff04">4</xref>
</contrib>
<contrib contrib-type="author"><name><surname>FREITAS JÚNIOR</surname>
<given-names>Amilcar Chagas</given-names>
</name>
<xref ref-type="aff" rid="aff04">4</xref>
</contrib>
</contrib-group>
<aff id="aff01"><label>1</label>
DDS, PhD, Professor, Federal Institute of Paraná - IFPR, Londrina, PR, Brazil.</aff>
<aff id="aff02"><label>2</label>
DDS, PhD, Associate Professor, Department of Dental Materials and Prosthodontics, Faculty of Dentistry of Araçatuba, UNESP - Univ. Estadual Paulista, Araçatuba, SP, Brazil.</aff>
<aff id="aff03"><label>3</label>
MEng, PhD, Associate Professor, Department of Mechanical Engineering, Faculty of Engineering of Ilha Solteira, UNESP - Univ. Estadual Paulista, Ilha Solteira, SP, Brazil.</aff>
<aff id="aff04"><label>4</label>
DDS, MS, PhD student, Department of Dental Materials and Prosthodontics, Faculty of Dentistry of Araçatuba, UNESP - Univ. Estadual Paulista, Araçatuba, SP, Brazil.</aff>
<author-notes><corresp id="c01"><bold>Corresponding address: </bold>
Prof. Adj. Dr. Carlos Marcelo Archangelo - Rua
José Bonifacio, 1193, Vila Mendonça - Araçatuba - SP - Brasil - 16010-050 - Phone:
55-18-36363290 - e-mail: <email>carlosarchangelo@uol.com.br</email>
</corresp>
</author-notes>
<pub-date pub-type="ppub"><season>May-Jun</season>
<year>2012</year>
</pub-date>
<volume>20</volume>
<issue>3</issue>
<fpage>362</fpage>
<lpage>368</lpage>
<history><date date-type="received"><day>18</day>
<month>10</month>
<year>2010</year>
</date>
<date date-type="rev-recd"><day>07</day>
<month>8</month>
<year>2011</year>
</date>
<date date-type="accepted"><day>01</day>
<month>9</month>
<year>2011</year>
</date>
</history>
<permissions><license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by-nc/3.0/"><license-p>This is an open-access article distributed under the terms of 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><sec><title>ABSTRACT</title>
</sec>
<sec><title>Objective</title>
<p>The non-homogenous aspect of periodontal ligament (PDL) has been examined using
finite element analysis (FEA) to better simulate PDL behavior. The aim of this
study was to assess, by 2-D FEA, the influence of non-homogenous PDL on the stress
distribution when the free-end saddle removable partial denture (RPD) is partially
supported by an osseointegrated implant. </p>
</sec>
<sec><title>Material and Methods</title>
<p>Six finite element (FE) models of a partially edentulous mandible were created to
represent two types of PDL (non-homogenous and homogenous) and two types of RPD
(conventional RPD, supported by tooth and fibromucosa; and modified RPD, supported
by tooth and implant [10.00x3.75 mm]). Two additional FE models without RPD were
used as control models. The non-homogenous PDL was modeled using beam elements to
simulate the crest, horizontal, oblique and apical fibers. The load (50 N) was
applied in each cusp simultaneously. Regarding boundary conditions the border of
alveolar ridge was fixed along the x axis. The FE software (Ansys 10.0) was used
to compute the stress fields, and the von Mises stress criterion (σvM) was
applied to analyze the results. </p>
</sec>
<sec><title>Results</title>
<p>The peak of σvM in non-homogenous PDL was higher than that for the
homogenous condition. The benefits of implants were enhanced for the
non-homogenous PDL condition, with drastic σvM reduction on the posterior
half of the alveolar ridge. The implant did not reduce the stress on the support
tooth for both PDL conditions. </p>
</sec>
<sec><title>Conclusion</title>
<p>The PDL modeled in the non-homogeneous form increased the benefits of the
osseointegrated implant in comparison with the homogeneous condition. Using the
non-homogenous PDL, the presence of osseointegrated implant did not reduce the
stress on the supporting tooth.</p>
</sec>
</abstract>
<kwd-group><kwd>Removable partial denture</kwd>
<kwd>Dental implant</kwd>
<kwd>Finite element analysis</kwd>
<kwd>Periodontal ligament</kwd>
</kwd-group>
</article-meta>
</front>
<body><sec><title>INTRODUCTION</title>
<p>Conventional removable partial dentures (RPD) show a complex biomechanical behavior,
mainly when the RPD is supported by teeth and fibromucosa, such as in Kennedy Class
I<sup><xref ref-type="bibr" rid="r25">25</xref>
</sup>
. This behavior has been
better controlled when an osseointegrated implant is placed and acts as an additional
support, retainer, or both, improving the stability and retention of the RPD, which
reduces the demand on the support structures<sup><xref ref-type="bibr" rid="r14">14</xref>
</sup>
.</p>
<p>In this context, the use of RPD and implants has been presented in a series of clinical
possibilities that reflect individual experiences with some singularities according to
the number and position of the remaining teeth in the arch, as well as the size of the
prosthetic space and degree of bone loss<sup><xref ref-type="bibr" rid="r02">2</xref>
-<xref ref-type="bibr" rid="r04">4</xref>
,<xref ref-type="bibr" rid="r09">9</xref>
-<xref ref-type="bibr" rid="r11">11</xref>
,<xref ref-type="bibr" rid="r13">13</xref>
,<xref ref-type="bibr" rid="r14">14</xref>
,<xref ref-type="bibr" rid="r16">16</xref>
,<xref ref-type="bibr" rid="r17">17</xref>
,<xref ref-type="bibr" rid="r20">20</xref>
,<xref ref-type="bibr" rid="r26">26</xref>
,<xref ref-type="bibr" rid="r28">28</xref>
</sup>
. The usual
clinical responses from patients are represented by better RPD stability, retention and
comfort when this association is done<sup><xref ref-type="bibr" rid="r14">14</xref>
</sup>
.</p>
<p>Mitrani, et al.<sup><xref ref-type="bibr" rid="r18">18</xref>
</sup>
(1993) investigated
the free-end saddle RPD combined with an implant on the distal extension wearers for a
mean period of 2.5 years. Those authors showed that the implant placed on the distal
extension of RPD increases patient satisfaction, reduces the marginal bone loss, and
establishes the peri-implant tissues<sup><xref ref-type="bibr" rid="r18">18</xref>
</sup>
. Nonetheless, data about the abutment tooth behavior over time are
still not reported and remain inconclusive.</p>
<p>Finite element (FE) studies can provide valuable information about the stress reduction
on the support structures promoted by implants. However this information is
controversial because the benefits of the osseointegrated implant are more evident on
the alveolar ridge and hardly conclusive for the RPD abutment tooth<sup><xref ref-type="bibr" rid="r23">23</xref>
</sup>
.</p>
<p>There are some concerns about the tooth behavior in a RPD supported by implant and tooth
through finite element analysis (FEA), mainly because the periodontal ligament (PDL) has
not been properly modeled as a non-homogenous structure. The homogenous aspect of the
PDL in FEA might negatively change the results. Atmaram and Mohammed<sup><xref ref-type="bibr" rid="r01">1</xref>
</sup>
(1981) reported that the homogeneous
condition of the PDL is closer to more uniform stress distribution and unable to direct
the forces applied in accordance with the set of fibers <italic>in vivo</italic>
. In
addition, the magnitude of stresses is shown to be less pronounced than under the
non-homogeneous condition. This is particularly important in face of forces with
non-axial incidence, producing terminal torqueing forces against the abutment teeth and
the soft tissue<sup><xref ref-type="bibr" rid="r19">19</xref>
</sup>
.</p>
<p>Other authors have pointed out that the non-homogeneous PDL was necessary in order to
understand how occlusal loads are absorbed by the PDL<sup><xref ref-type="bibr" rid="r22">22</xref>
</sup>
. Therefore, this condition is decisive to analyze the
results of RPD associated with an osseointegrated implant by FEA. Nevertheless, the
benefits of the combination between RPD and osseointegrated implant may be analyzed from
this perspective. The analysis of the stress distribution in the studies by Atmaram and
Mohammed<sup><xref ref-type="bibr" rid="r01">1</xref>
</sup>
(1981) and Rees and
Jacobsen<sup><xref ref-type="bibr" rid="r22">22</xref>
</sup>
(1997) did not show
the behavior of the abutment tooth.</p>
<p>The objective of this study was to evaluate the influence of PDL condition (homogenous
and non-homogenous) on the stress distribution of a free-end saddle RPD associated with
an osseointegrated implant through 2-D FEA. The hypothesis tested was that
non-homogeneous PDL increases the benefits of implant, reducing the stress on the
supporting tooth of the RPD supported by tooth and implant.</p>
</sec>
<sec sec-type="materials|methods"><title>MATERIAL AND METHODS</title>
<p>Six mandibular models (A, B, C, D, E, and F) were modeled using graphic software
(AutoCAD, Autodesk Inc., San Rafael, CA, USA). In a sagittal view, all models simulated
partially edentulous hemi-arches without posterior dental support (Kennedy Class I). In
addition, all models had the remaining tooth 33 and a distal extension ridge.</p>
<p>The characteristics of the abutment - the length of the distal extension ridge, the
dimensions and characteristics of the support and protective periodontium, the
mandibular bone height, the thickness of the CoCr metal structure, and the number of
artificial teeth - were kept constant. The difference was the PDL in models D, E, and F,
which was reproduced in accordance with the <italic>in vivo</italic>
characteristic,
with representation of the following 4 groups of fibers: crest, horizontal, oblique and
apical (<xref ref-type="fig" rid="f01">Figure 1</xref>
).</p>
<fig id="f01" orientation="portrait" position="float"><label>Figure 1</label>
<caption><p>Description of finite element models, finite element mesh and boundary condition.
A: Models A, B, and C. B - Model B with the removable partial denture (RPD). C:
Model C with RPD and implant. Areas (1 to 6) selected to perform the analysis in
all models. D:- The beam elements used to build the non-homogeneous periodontal
ligament (PDL). E and F: Mesh refinements for tooth apex and implant,
respectively. L shows the distributed loading scheme. The entire right and left
sides were fixed on the x axis. The bone at the bottom of the model was fixed on
the x and y axes</p>
</caption>
<graphic xlink:href="jaos-20-03-0362-g01"></graphic>
</fig>
<p>After the models had been created, the files were exported to ANSYS 8.0 (Swanson
Analysis Systems, Houston, PA, USA) to discriminate the regions and generate the FE
mesh. Models A, B, and C, (<xref ref-type="fig" rid="f01">Figure 1</xref>
) were
considered homogeneous, isotropic, and linearly elastic. The mechanical properties
adopted for all materials (elastic modulus and Poisson's ratio) were established
according to the literature (<xref ref-type="table" rid="t01">Table 1</xref>
)<sup><xref ref-type="bibr" rid="r01">1</xref>
,<xref ref-type="bibr" rid="r08">8</xref>
,<xref ref-type="bibr" rid="r15">15</xref>
,<xref ref-type="bibr" rid="r23">23</xref>
,<xref ref-type="bibr" rid="r24">24</xref>
,<xref ref-type="bibr" rid="r29">29</xref>
</sup>
.</p>
<table-wrap id="t01" orientation="portrait" position="float"><label>Table 1</label>
<caption><p>Mechanical properties of the materials. E - Elastic modulus. v - Poisson's ratio.
PDL - Periodontal ligament. Ti - Titanium</p>
</caption>
<table frame="hsides" rules="groups"><thead><tr align="center"><td style="background-color:#CCCCCC" rowspan="1" colspan="1"><bold>Structures</bold>
</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1"><bold>E (GPa)</bold>
</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1"><bold>References</bold>
</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1"><bold>v</bold>
</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1"><bold>References</bold>
</td>
</tr>
</thead>
<tbody><tr align="center"><td rowspan="1" colspan="1">Enamel</td>
<td rowspan="1" colspan="1">41</td>
<td rowspan="1" colspan="1">17</td>
<td rowspan="1" colspan="1">0.3</td>
<td rowspan="1" colspan="1">17</td>
</tr>
<tr align="center"><td style="background-color:#CCCCCC" rowspan="1" colspan="1">Dentin</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">18.6</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">18</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">0.31</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">18</td>
</tr>
<tr align="center"><td rowspan="1" colspan="1">Homogenous PDL</td>
<td rowspan="1" colspan="1">0.175</td>
<td rowspan="1" colspan="1">15</td>
<td rowspan="1" colspan="1">0.45</td>
<td rowspan="1" colspan="1">15</td>
</tr>
<tr align="center"><td style="background-color:#CCCCCC" rowspan="1" colspan="1">Non-homogenou PDL</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">0.35</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">15</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">0.45</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">15</td>
</tr>
<tr align="center"><td rowspan="1" colspan="1">Fibromucosa</td>
<td rowspan="1" colspan="1">0.68</td>
<td rowspan="1" colspan="1">17</td>
<td rowspan="1" colspan="1">0.45</td>
<td rowspan="1" colspan="1">17</td>
</tr>
<tr align="center"><td style="background-color:#CCCCCC" rowspan="1" colspan="1">Cortical bone</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">13.7</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">18</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">0.3</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">18</td>
</tr>
<tr align="center"><td rowspan="1" colspan="1">Medullar bone</td>
<td rowspan="1" colspan="1">1.37</td>
<td rowspan="1" colspan="1">18</td>
<td rowspan="1" colspan="1">0.3</td>
<td rowspan="1" colspan="1">18</td>
</tr>
<tr align="center"><td style="background-color:#CCCCCC" rowspan="1" colspan="1">Implant (Ti)</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">103.4</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">20</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">0.35</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">20</td>
</tr>
<tr align="center"><td rowspan="1" colspan="1">Healing abutment (Ti)</td>
<td rowspan="1" colspan="1">103.4</td>
<td rowspan="1" colspan="1">20</td>
<td rowspan="1" colspan="1">0.35</td>
<td rowspan="1" colspan="1">20</td>
</tr>
<tr align="center"><td style="background-color:#CCCCCC" rowspan="1" colspan="1">CoCr cast alloy</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">185</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">21</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">0.35</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">21</td>
</tr>
<tr align="center"><td rowspan="1" colspan="1">Acrylic resin</td>
<td rowspan="1" colspan="1">8.3</td>
<td rowspan="1" colspan="1">14</td>
<td rowspan="1" colspan="1">0.28</td>
<td rowspan="1" colspan="1">14</td>
</tr>
<tr align="center"><td style="background-color:#CCCCCC" rowspan="1" colspan="1">Artificial teeth</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">8.3</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">14</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">0.28</td>
<td style="background-color:#CCCCCC" rowspan="1" colspan="1">14</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Models D, E, and MF, similar to models A, B, and C, respectively, were considered
homogeneous, isotropic, and linearly elastic, except for the PDL, which was considered a
non-homogeneous structure. Thus, models D, E, and F differed from models A, B and C only
by their structural characteristic of the PDL, being similar in all other factors.</p>
<p>The element used to generate the mesh was the plane 2 element, a triangular element
defined by 6 nodes, with 2 degrees of freedom <italic>per</italic>
node, and quadratic
displacement behavior. The FE mesh showed up to 80,000 nodes and up to 40,000 elements.
This configuration allowed the appropriate refinement of the mesh in thin structures,
such as the cortical bone and the PDL, reaching the convergence norm.</p>
<p>As far as the creation of the non-homogeneous PDL is concern, using the methodology
established by Atmaram and Mohammed<sup><xref ref-type="bibr" rid="r01">1</xref>
</sup>
(1981) with some modifications, the composition of the PDL in the FE model was
established under the <italic>in vivo</italic>
condition<sup><xref ref-type="bibr" rid="r05">5</xref>
</sup>
. For this, beam elements were used to represent 4 groups
of PDL fibers in a sagittal cut (crest, horizontal, oblique and apical fibers) and their
directions. To support the bending movements, as well as tensile and compression loads,
the cross-sectional area and the moment of inertia for the beam elements were used to
describe the PDL. Thus, the following equations were used:</p>
<p>Cross sectional area: A=πx(r)<sup>2</sup>
</p>
<p>Moment of inertia: I=πx(d)<sup>4</sup>
/64</p>
<p>where:</p>
<p>A=cross sectional area; I=moment of inertia; π=3.14; d=4 µm or 4x10<sup>-6</sup>
m;
r=2x10<sup>-6</sup>
m.</p>
<p>Grant, et al.<sup><xref ref-type="bibr" rid="r12">12</xref>
</sup>
(1988) determined a
value of 4 µm for the PDL fibers of an RPD abutment tooth. Thus, the values found for
the cross-sectional area and the moments of inertia of each element were
1,256x10<sup>-5</sup>
mm<sup>2</sup>
and 0.785x10<sup>-12</sup>
mm<sup>4</sup>
,
respectively.</p>
<p>In accordance with that established by Atmaram and Mohammed<sup><xref ref-type="bibr" rid="r01">1</xref>
</sup>
(1981), the number of periodontal fibers adopted under
the non-homogeneous condition was half the number of elements present in the PDL under
the homogeneous condition. Thus, all models with a homogeneous PDL (A, B, and C)
contained 824 elements in the PDL region, and the models with a non-homogeneous PDL (D,
E, and F) contained 412 fibers for composition of the PDL.</p>
<p>As the boundary condition, the left and right sides of the models were fixed only in the
x direction, in order to prevent lateral movement of the structures. This allowed the
vertical movement of the RPD base over the fibromucosa and, consequently, the
deformation of the cortical and medullar bone beneath it, as well as simulation of the
bilateral mandibular condition. Only the cortical bone at the base of the models was
fixed in the x and y directions (<xref ref-type="fig" rid="f01">Figure 1</xref>
).</p>
<p>The models were loaded with vertical forces (50 N) distributed at each cusp,
fractionated into 5 point loads of 10 N each to prevent the occlusal contact
characterized by only one point load (<xref ref-type="fig" rid="f01">Figure
1</xref>
).</p>
<p>The von Mises equivalent stress criterion (σ<sub>vM</sub>
) was adopted to analyze
the stress distribution. Each structure was individually analyzed following specific
areas (<xref ref-type="fig" rid="f01">Figure 1</xref>
), as well as to allow the data to
be refined into regions of interest, as follows:</p>
<p>Area 1: Root apex; Area 2: Mesial side of the abutment tooth and adjacent structures;
Area 3: Distal side of the abutment tooth and adjacent structures; Area 4: Distal bone
crest of the abutment tooth; Area 5: Anterior half of the alveolar ridge; Area 6:
Posterior half of the alveolar ridge; Area 7: Osseointegrated implant.</p>
<p>For more details and to allow the comparison with the study of Atmaram and
Mohamed<sup><xref ref-type="bibr" rid="r01">1</xref>
</sup>
(1981), the previously
determined areas 2 and 3 were sub-divided into 10 parts.</p>
</sec>
<sec sec-type="results"><title>RESULTS</title>
<sec><title>Cortical bone</title>
<p>For the homogeneous PDL, the stress concentration on the cortical bone around tooth
33 gradually increased in the bone crest (tooth apex direction) in areas 2 and 3 of
models A, B, and C. The presence of the conventional RPD (model B) drastically
increased the stress on areas 5 and 6 in comparison with MA, and the presence of the
osseointegrated implant (model C) reduced the σ<sub>vM</sub>
on the posterior
half of the ridge, mainly in area 6 (<xref ref-type="table" rid="t02">Table
2</xref>
).</p>
<table-wrap id="t02" orientation="portrait" position="float"><label>Table 2</label>
<caption><p>von Mises stress (σ<sub>vM</sub>
), in MPa, for the cortical bone
according to specific areas in models A to F. Note the subdivision of regions 2
and 3 into 10 segments (1 to 10) around the abutment tooth</p>
</caption>
<table frame="hsides" rules="groups"><thead><tr><td colspan="12" align="center" style="background-color:#CCCCCC" rowspan="1"><bold>Subdivision of the regions 2 and 3 around the abutment
tooth</bold>
</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"><bold>Models</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>Areas</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>1</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>2</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>3</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>4</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>5</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>6</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>7</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>8</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>9</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>10</bold>
</td>
</tr>
</thead>
<tbody><tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">A</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">1</td>
<td colspan="10" align="center" style="background-color:#CCCCCC" rowspan="1">10.5</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">2</td>
<td align="center" rowspan="1" colspan="1">10.5</td>
<td align="center" rowspan="1" colspan="1">10.5</td>
<td align="center" rowspan="1" colspan="1">12.2</td>
<td align="center" rowspan="1" colspan="1">12.2</td>
<td align="center" rowspan="1" colspan="1">14</td>
<td align="center" rowspan="1" colspan="1">15.7</td>
<td align="center" rowspan="1" colspan="1">17.5</td>
<td align="center" rowspan="1" colspan="1">19.2</td>
<td align="center" rowspan="1" colspan="1">21</td>
<td align="center" rowspan="1" colspan="1">19.2</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> </td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">3</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">8.7</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">5.2</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">5.2</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">7</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">7</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">8.7</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">8.7</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">10.5</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">12.2</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">19.2</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">4</td>
<td colspan="10" align="center" rowspan="1">8.7</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> </td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">5</td>
<td colspan="10" align="center" style="background-color:#CCCCCC" rowspan="1">3.5</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">6</td>
<td colspan="10" align="center" rowspan="1">1.7</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">B</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">1</td>
<td colspan="10" align="center" style="background-color:#CCCCCC" rowspan="1">33.4</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">2</td>
<td align="center" rowspan="1" colspan="1">14.3</td>
<td align="center" rowspan="1" colspan="1">14.3</td>
<td align="center" rowspan="1" colspan="1">20.7</td>
<td align="center" rowspan="1" colspan="1">20.7</td>
<td align="center" rowspan="1" colspan="1">20.7</td>
<td align="center" rowspan="1" colspan="1">27</td>
<td align="center" rowspan="1" colspan="1">27</td>
<td align="center" rowspan="1" colspan="1">27</td>
<td align="center" rowspan="1" colspan="1">27</td>
<td align="center" rowspan="1" colspan="1">20.7</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> </td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">3</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">20.7</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">20.7</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">27</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">27</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">27</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">33.4</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">33.4</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">39.7</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">77.8</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">77.8</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">4</td>
<td colspan="10" align="center" rowspan="1">27</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> </td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">5</td>
<td colspan="10" align="center" style="background-color:#CCCCCC" rowspan="1">20.7</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">6</td>
<td colspan="10" align="center" rowspan="1">14.3</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">C</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">1</td>
<td colspan="10" align="center" style="background-color:#CCCCCC" rowspan="1">25.1</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">2</td>
<td align="center" rowspan="1" colspan="1">25.1</td>
<td align="center" rowspan="1" colspan="1">12.9</td>
<td align="center" rowspan="1" colspan="1">19</td>
<td align="center" rowspan="1" colspan="1">19</td>
<td align="center" rowspan="1" colspan="1">25.1</td>
<td align="center" rowspan="1" colspan="1">25.1</td>
<td align="center" rowspan="1" colspan="1">31.2</td>
<td align="center" rowspan="1" colspan="1">31.2</td>
<td align="center" rowspan="1" colspan="1">31.2</td>
<td align="center" rowspan="1" colspan="1">19</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> </td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">3</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">25.1</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">19</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">25.1</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">25.1</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">25.1</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">31.2</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">37.4</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">43.5</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">74</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">74</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">4</td>
<td colspan="10" align="center" rowspan="1">25.1</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> </td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">5</td>
<td colspan="10" align="center" style="background-color:#CCCCCC" rowspan="1">19</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">6</td>
<td colspan="10" align="center" rowspan="1">12.9</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">D</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">1</td>
<td colspan="10" align="center" style="background-color:#CCCCCC" rowspan="1">8.6</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">2</td>
<td align="center" rowspan="1" colspan="1">103</td>
<td align="center" rowspan="1" colspan="1">42.9</td>
<td align="center" rowspan="1" colspan="1">42.9</td>
<td align="center" rowspan="1" colspan="1">42.9</td>
<td align="center" rowspan="1" colspan="1">42.9</td>
<td align="center" rowspan="1" colspan="1">42.9</td>
<td align="center" rowspan="1" colspan="1">42.9</td>
<td align="center" rowspan="1" colspan="1">42.9</td>
<td align="center" rowspan="1" colspan="1">51.2</td>
<td align="center" rowspan="1" colspan="1">51.2</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> </td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">3</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">77.2</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">17.2</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">8.6</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">8.6</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">8.6</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">8.6</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">8.6</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">8.6</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">17.2</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">25.7</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">4</td>
<td colspan="10" align="center" rowspan="1">77.2</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> </td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">5</td>
<td colspan="10" align="center" style="background-color:#CCCCCC" rowspan="1">17.2</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">6</td>
<td colspan="10" align="center" rowspan="1">8.6</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">E</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">1</td>
<td colspan="10" align="center" style="background-color:#CCCCCC" rowspan="1">34.8</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">2</td>
<td align="center" rowspan="1" colspan="1">86.3</td>
<td align="center" rowspan="1" colspan="1">43.4</td>
<td align="center" rowspan="1" colspan="1">34.8</td>
<td align="center" rowspan="1" colspan="1">34.8</td>
<td align="center" rowspan="1" colspan="1">34.8</td>
<td align="center" rowspan="1" colspan="1">34.8</td>
<td align="center" rowspan="1" colspan="1">34.8</td>
<td align="center" rowspan="1" colspan="1">34.8</td>
<td align="center" rowspan="1" colspan="1">34.8</td>
<td align="center" rowspan="1" colspan="1">34.8</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> </td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">3</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">86.3</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">52</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">43.4</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">52</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">52</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">52</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">52</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">60.6</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">103.5</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">103.5</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">4</td>
<td colspan="10" align="center" rowspan="1">86.3</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> </td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">5</td>
<td colspan="10" align="center" style="background-color:#CCCCCC" rowspan="1">26.3</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">6</td>
<td colspan="10" align="center" rowspan="1">17.7</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">F</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">1</td>
<td colspan="10" align="center" style="background-color:#CCCCCC" rowspan="1">33.5</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">2</td>
<td align="center" rowspan="1" colspan="1">91.6</td>
<td align="center" rowspan="1" colspan="1">41.8</td>
<td align="center" rowspan="1" colspan="1">41.8</td>
<td align="center" rowspan="1" colspan="1">41.8</td>
<td align="center" rowspan="1" colspan="1">41.8</td>
<td align="center" rowspan="1" colspan="1">41.8</td>
<td align="center" rowspan="1" colspan="1">41.8</td>
<td align="center" rowspan="1" colspan="1">33.5</td>
<td align="center" rowspan="1" colspan="1">33.5</td>
<td align="center" rowspan="1" colspan="1">25.2</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> </td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">3</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">83.3</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">50.1</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">50.1</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">50.1</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">50.1</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">50.1</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">50.1</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">58.4</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">100</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">100</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">4</td>
<td colspan="10" align="center" rowspan="1">83.3</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> </td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">5</td>
<td colspan="10" align="center" style="background-color:#CCCCCC" rowspan="1">25.2</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"> </td>
<td align="center" rowspan="1" colspan="1">6</td>
<td colspan="10" align="center" rowspan="1">8.6</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>For the non-homogeneous PDL (models D, E, and F), the svM in areas 2 and 3 of model D
diminished in the bone crest (root apex direction). The presence of the conventional
RPD (model E) increased the σ<sub>vM</sub>
in areas 1, 4, 5, and 6 compared
with model D, and the presence of the osseointegrated implant (model F) drastically
reduced the stresses in area 6 of the alveolar ridge (<xref ref-type="table" rid="t02">Table 2</xref>
).</p>
</sec>
<sec><title>Medullar bone</title>
<p>The incorporation of the RPD (model B) drastically increased the
σ<sub>vM</sub>
on the trabecular bone for areas 5 and 6 by approximately
1235% and 834%, respectively, when compared with the respective areas of model A
(<xref ref-type="table" rid="t03">Table 3</xref>
). The presence of the
osseointegrated implant (model C) reduced the σ<sub>vM</sub>
in those areas,
similar to what occurred in the cortical bone.</p>
<table-wrap id="t03" orientation="portrait" position="float"><label>Table 3</label>
<caption><p>von Mises stress (σ<sub>vM</sub>
), in MPa, for the medullar bone
according to specific areas (1 to 6) in the models (A to F)</p>
</caption>
<table frame="hsides" rules="groups"><thead><tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> </td>
<td colspan="6" align="center" style="background-color:#CCCCCC" rowspan="1"><bold>Areas</bold>
</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"><bold>Models</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>1</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>2</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>3</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>4</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>5</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>6</bold>
</td>
</tr>
</thead>
<tbody><tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">A</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">8.3</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">2.8</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">2.8</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">1.4</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">0.7</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">0.7</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1">B</td>
<td align="center" rowspan="1" colspan="1">17.8</td>
<td align="center" rowspan="1" colspan="1">5.1</td>
<td align="center" rowspan="1" colspan="1">5.1</td>
<td align="center" rowspan="1" colspan="1">3.7</td>
<td align="center" rowspan="1" colspan="1">9.3</td>
<td align="center" rowspan="1" colspan="1">6.5</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">C</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">18.1</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">4.4</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">6.4</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">4.4</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">8.3</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> 4.4</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1">D</td>
<td align="center" rowspan="1" colspan="1">11.4</td>
<td align="center" rowspan="1" colspan="1">5.7</td>
<td align="center" rowspan="1" colspan="1">1.9</td>
<td align="center" rowspan="1" colspan="1">3.8</td>
<td align="center" rowspan="1" colspan="1">1.9</td>
<td align="center" rowspan="1" colspan="1">1.9</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">E</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">17.4</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">4.4</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">5.8</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">11.6</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">10.2</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">7.3</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1">F</td>
<td align="center" rowspan="1" colspan="1">17.6</td>
<td align="center" rowspan="1" colspan="1">4.9</td>
<td align="center" rowspan="1" colspan="1">6.1</td>
<td align="center" rowspan="1" colspan="1">11.8</td>
<td align="center" rowspan="1" colspan="1">11.9</td>
<td align="center" rowspan="1" colspan="1"> 4.3</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>For the non-homogeneous PDL, model E increased the σ<sub>vM</sub>
in areas 5
and 6 (<xref ref-type="table" rid="t03">Table 3</xref>
) compared with areas 5 and 6
of model B for the homogeneous PDL. The osseointegrated implant (model F) also
reduced the stress levels in area 6 of the ridge (<xref ref-type="table" rid="t03">Table 3</xref>
).</p>
</sec>
<sec><title>Fibromucosa</title>
<p>The high σ<sub>vM</sub>
in areas 5 and 6 of the fibromucosa in model B,
corroborate those found for the same cortical and trabecular bone areas in relation
to the homogeneous PDL. The osseointegrated implant (model C) also provided the
fibromucosa with stress relief in areas 5 and 6 of the ridge, when compared with the
σ<sub>vM</sub>
of model B (<xref ref-type="table" rid="t04">Table
4</xref>
).</p>
<table-wrap id="t04" orientation="portrait" position="float"><label>Table 4</label>
<caption><p>von Mises stress (σ<sub>vM</sub>
), in MPa, for the fibromucosa according
to specific areas (4 to 6) in the models (A to F)</p>
</caption>
<table frame="hsides" rules="groups"><thead><tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> </td>
<td colspan="3" align="center" style="background-color:#CCCCCC" rowspan="1"><bold>Areas</bold>
</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1"><bold>Models</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>4</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>5</bold>
</td>
<td align="center" rowspan="1" colspan="1"><bold>6</bold>
</td>
</tr>
</thead>
<tbody><tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">A</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">5.7</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">0.9</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">0.9</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1">B</td>
<td align="center" rowspan="1" colspan="1">7</td>
<td align="center" rowspan="1" colspan="1">8.6</td>
<td align="center" rowspan="1" colspan="1">7.8</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">C</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">7.1</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">8</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1"> 3.7</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1">D</td>
<td align="center" rowspan="1" colspan="1">95</td>
<td align="center" rowspan="1" colspan="1">8.3</td>
<td align="center" rowspan="1" colspan="1">8.3</td>
</tr>
<tr><td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">E</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">59.7</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">14.1</td>
<td align="center" style="background-color:#CCCCCC" rowspan="1" colspan="1">14.1</td>
</tr>
<tr><td align="center" rowspan="1" colspan="1">F</td>
<td align="center" rowspan="1" colspan="1">61.3</td>
<td align="center" rowspan="1" colspan="1">13.7</td>
<td align="center" rowspan="1" colspan="1">6.9</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>For the PDL under the non-homogeneous condition in areas 5 and 6, the RPD (model E)
increased the σ<sub>vM</sub>
, however, in lower ratio than those observed
under the homogeneous condition, approximately 69% in both areas. The osseointegrated
implant also provided model F with a reduction in σ<sub>vM</sub>
in areas 5
and 6 of the fibromucosa (<xref ref-type="table" rid="t04">Table 4</xref>
).</p>
</sec>
<sec><title>Implant</title>
<p>The osseointegrated implant showed a similar behavior for the homogeneous and
non-homogeneous PDL conditions. The pitch of the internal threads of the implants was
responsible for the high σ<sub>vM</sub>
in models C and F.</p>
</sec>
</sec>
<sec sec-type="discussion"><title>DISCUSSION</title>
<p>The conventional RPD applies moment of force or binary forces on the abutment tooth and
alveolar ridge<sup><xref ref-type="bibr" rid="r06">6</xref>
,<xref ref-type="bibr" rid="r07">7</xref>
</sup>
. The associations of the RPD with an osseointegrated
implant aims to increase the retention and stability, as well as provide a reduction of
the stress on the support tooth, fibromucosa and alveolar ridge<sup><xref ref-type="bibr" rid="r14">14</xref>
</sup>
.</p>
<p>In a previous FEA study with the RPD and implant<sup><xref ref-type="bibr" rid="r23">23</xref>
</sup>
, this reduction of stress on the support tooth was not
confirmed<sup><xref ref-type="bibr" rid="r23">23</xref>
</sup>
. It was considered
that the homogeneous PDL condition might reduce the stress in the alveolar ridge, but
was not efficient in reducing the stress on the abutment tooth when an osseointegrated
implant was distally supporting the acrylic resin base of the RPD.</p>
<p>In the present study, when the homogeneous PDL condition was simulated, the stress
concentration on the cortical and medullar bone remained high at the abutment tooth
apex. The σ<sub>vM</sub>
increased gradually in the bone crest - tooth apex
direction in areas 2 and 3 (models A, B, and C). The greatest benefit of the
osseointegrated implant was the reduction of the stresses on the posterior half of the
alveolar ridge. The peak stress in the implant was observed on the neck closer to the
cortical bone.</p>
<p>In agreement with another study<sup><xref ref-type="bibr" rid="r03">3</xref>
</sup>
, the
higher σ<sub>vM</sub>
found in the medullar bone for the homogenous PDL condition
occurred at the apex of the osseointegrated implant. It is pointed out that the stress
found on the cortical bone around the osseointegrated implant remained below the stress
levels found at the abutment tooth apex, showing that RPD associated with an
osseointegrated implant to be a feasible and safe alternative, according Mitrani, et
al.<sup><xref ref-type="bibr" rid="r18">18</xref>
</sup>
(2003).</p>
<p>Another benefit of the implant (model C) was the stress reduction in the fibromucosa in
the posterior half compared with the model B. The implant provided anchorage for the
acrylic resin base of the RPD, limiting its vertical intrusion movement and reducing the
σ<sub>vM</sub>
when it was compared with the model B.</p>
<p>Nevertheless, the use of the non-homogeneous PDL (models D, E, and F) changed the stress
distribution pattern in practically all regions analyzed. The peak of stress was higher
for almost all structures with the non-homogenous condition than with the homogeneous
condition (models A, B, and C). However, the stress variation around the abutment tooth
was lower compared with models D, E, and F, and its distribution was similar to that
established by others authors<sup><xref ref-type="bibr" rid="r01">1</xref>
,<xref ref-type="bibr" rid="r21">21</xref>
,<xref ref-type="bibr" rid="r27">27</xref>
</sup>
.</p>
<p>The modeling type for PDL has a significant effect on the nature and magnitude of the
alveolar stress<sup><xref ref-type="bibr" rid="r01">1</xref>
,<xref ref-type="bibr" rid="r21">21</xref>
,<xref ref-type="bibr" rid="r27">27</xref>
</sup>
. It occurs
because the modeling of homogeneous PDL is like an assumption of a hypothetical soft
interactive medium in which the stress is shared uniformly; hence, it uniformly
distributes the stresses to bone. In contrast, in the heterogeneous PDL assumption with
the main fibers of the PDL incorporated, there is no direct contact between the
individual fibers, and the stresses among the fibers are not shared equally, resulting
in the wide variation of the stresses in the adjoining structure, such as the cortical
bone, reproducing more accurately the events of the PDL in function. </p>
<p>Similarly to Atmaram and Mohammed<sup><xref ref-type="bibr" rid="r01">1</xref>
</sup>
(1981), in the present study there was an inversion in the direction of stress, since
the stresses around tooth 33 gradually diminished in the direction of the bone crest to
the tooth apex when the non-homogeneous PDL was simulated. Furthermore, the increase of
σ<sub>vM</sub>
on the anterior and posterior halves of the alveolar ridge for
areas 5 and 6 (<xref ref-type="table" rid="t04">Table 4</xref>
) were accentuated in
model B. A similar behavior was not verified in models D and E, as the
σ<sub>vM</sub>
increased 69.1% and 69.1% for those areas, respectively.</p>
<p>The results found in models A, B, and C, with the homogeneous PDL condition, might be
not represent the potentially artificial, since the peak of σ<sub>vM</sub>
, as
well the stress variation was not repeated in the equivalent models, D, E, and F,
respectively. In addition, the stress around the abutment tooth, and in the posterior
area of the alveolar ridge in models C and F, should be closer to that observed in
models A and D, with no RPD, respectively. It was observed that the result closest to
this hypothesis was showed by the posterior half of the fibromucosa. Even with the use
of non-homogeneous PDL, the stress variation around the abutment tooth in models E and F
was small, rejecting the hypothesis of the present study. This aspect partially supports
the results pointed by Keltjens, et al.<sup><xref ref-type="bibr" rid="r14">14</xref>
</sup>
(1993) that the osseointegrated implant does not reduce the stress
on the abutment tooth.</p>
<p>The results of the present study keep valid the data from Atmaram and Mohammed<sup><xref ref-type="bibr" rid="r01">1</xref>
</sup>
(1981) because the direction of demand on
the abutment tooth and the behavior of the bone showed correlation with the
experiment<sup><xref ref-type="bibr" rid="r01">1</xref>
</sup>
. This aspect
reinforces the condition that the PDL used in its non-homogeneous form appropriately
reproduces the PDL in function<sup><xref ref-type="bibr" rid="r21">21</xref>
,<xref ref-type="bibr" rid="r27">27</xref>
</sup>
.</p>
<p>The main benefit of the osseointegrated implant placed in the position as performed in
the present study is reducing the stress on the fibromucosa and alveolar ridge. These
benefits are more evident when the PDL is modeled in its non-homogenous form.</p>
</sec>
<sec sec-type="conclusions"><title>CONCLUSION</title>
<p>The PDL modeled in the non-homogeneous form increases the benefits of the
osseointegrated implant in comparison with the homogeneous condition. Using the
non-homogenous PDL, the presence of osseointegrated implant did not reduce the stress on
the supporting tooth.</p>
</sec>
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