Reduced Periodontal Support for Lower Central Incisor – A 3D Finite Element Analysis of Compressive Stress in the Periodontium

Abstract

Background: The aim of this study was to assess the stress concentration in simulated
periodontal alveolar bone containing healthy teeth with and without attachment loss.
Methods: Six 3-D models of a lower central incisor were created simulating the teeth structure, cancellous and cortical bone and periodontal ligament. Each model presented a 1mm
increasing distance between cement-enamel junction (CEJ) and alveolar bone crest (ABC) (1
to 6mm). A 100N, 45-degree load was applied to the buccal face of the lower central incisor.
The effects of Minimum Principal Stress (MPS) on lamina dura (LD) and ABC were analyzed.
Results: The results showed an increase of MPS in the surrounding bone (ABC and LD)
due to periodontal attachment loss. The 6mm attachment loss model showed the highest
(p<0.001) magnitude in MPS. Each millimeter increase in CEJ-ABC distance generated a
12% pattern of attachment loss and an increase at least of 65.7% for ABC and 33.6% for LD.
Conclusion: Under simulated conditions, attachment loss increases stress concentration
in the surrounding bone suggesting a partly

Full text

© International Academy of Periodontology
Journal of the International Academy of Periodontology 2021 23/1: 65–71
Correspondence to: João Paulo Mendes Tribst, Department of
Dental Materials and Prosthodontics, São Paulo State University
(Unesp), Institute of Science and Technology, Av. Eng. Francisco
José Longo, n° 777, Jardim São Dimas, 12245-000 São José dos
Campos, SP, Brazil. Email: joao.tribst@gmail.com
Introduction
The primary function of the human dentition is food
preparation and processing through a biomechanical
masticatory process. This process is involves transferring
masticatory forces to the periodontium and this is medi-
ated through the teeth (Versluis and Versluis-Tantbirojn,
2011). The periodontal apparatus (cementum, periodontal
ligament and alveolar bone) plays an important role in sta-
bilizing teeth. The forces produced during mastication are
distributed and absorbed by the alveolar process through
the alveolar bone. In health, the tooth-periodontium
complex, maintains tissue homeostasis when subjected
to physiological forces (Cattaneo et al., 2009).
Reduced Periodontal Support for Lower
Central Incisor – A 3D Finite Element
Analysis of Compressive Stress in the
Periodontium
Milena Cerqueira da Rocha,1 Daniel Maranha da Rocha,1
João Paulo Mendes Tribst,2 Alexandre Luiz Souto Borges2 and
Fabiano Alvim-Pereira1
Abstract
Background: The aim of this study was to assess the stress concentration in simulated
periodontal alveolar bone containing healthy teeth with and without attachment loss.
Methods: Six 3-D models of a lower central incisor were created simulating the teeth struc-
ture, cancellous and cortical bone and periodontal ligament. Each model presented a 1mm
increasing distance between cement-enamel junction (CEJ) and alveolar bone crest (ABC) (1
to 6mm). A 100N, 45-degree load was applied to the buccal face of the lower central incisor.
The effects of Minimum Principal Stress (MPS) on lamina dura (LD) and ABC were analyzed.
Results: The results showed an increase of MPS in the surrounding bone (ABC and LD)
due to periodontal attachment loss. The 6mm attachment loss model showed the highest
(p<0.001) magnitude in MPS. Each millimeter increase in CEJ-ABC distance generated a
12% pattern of attachment loss and an increase at least of 65.7% for ABC and 33.6% for LD.
Conclusion: Under simulated conditions, attachment loss increases stress concentration
in the surrounding bone suggesting a partly explanation regarding bone resorption risk
for teeth with periodontal attachment loss.
Keywords: Periodontium, nite element analysis, bone, incisor
1Departament of Dentistry, Universidade Federal de Sergipe,
SE, Brazil; 2Department of Dental Materials and Prosthodontics,
São Paulo State University (Unesp), Institute of Science and
Technology, Brazil.
Chronic periodontal disease is a major public
health condition that affects more than one third of
the population, 10-15% in its most severe form (Eke
et al., 2012). Chronic periodontitis is the primary cause
of tooth loss in people over age 35 (Deng et al., 2010).
Diminished periodontal support results from the sur-
rounding chronic inammation arising in respons to the
presence of a periodontal pathogenic biolm (Cattaneo
et al., 2009). Even after effective chronic periodontal
disease treatment, a subsequent optimal maintenance
phase, and the advances in bone regeneration therapies,
vertical bone regeneration around tooth is an unsolved
challenge for clinicians (Van Dyke et al., 2015).
Evidence in the literature indicates that previous at-
tachment loss is classied as a risk indicator for recurrent
disease (Takeuchi et al., 2010; Martin et al., 2010; Hirata et
al., 2019). This risk may be explained by the diminished
periodontal support removing the capability of teeth to
withstand physiological chewing forces (Takeuchi et al.,
2010; Martin et al., 2010).

66 Journal of the International Academy of Periodontology (2021) 23/1
Among the methods for stress analysis of complex
structures, nite element method (FEM) is a widely ap-
plied tool for bioengineering studies in dentistry (Dal
Piva et al., 2019; Tribst et al., 2020). Different mechanical
stimuli can impact the balance of bone homeostasis
(Mercuri et al., 2016). The relationship between bone and
mechanical stimuli has been evaluated by FEM analysis
and PET/CT scanning (in vivo) with good correlation
between these two methods (Suenaga et al., 2015).
Three-dimensional nite element analysis has been
used in periodontology to estimate the potential effects
of mechanical stimuli and stress on the periodontal
apparatus (Poiate et al., 2008; Ona and Wakabayashi,
2006; Kondo and Wakabayashi, 2009; Tajima et al., 2009;
Papadopoulou et al., 2013; Wakabayashi et al., 2008).
Therefore, the aim of this study was to use nite ele-
ment analysis to measure and map the stress distribution
of simulated normal and reduced periodontal support.
Materials and Methods
A computational-laboratorial study was conducted using
a three-dimensional human lower central incisor model,
constructed into the BioCAD protocol that consists of
creating virtual geometric models of biological struc-
tures based on anatomical references (Papadopoulou
et al., 2013). A three-dimensional scanned image of a
lower central incisor with 19 mm length (9 mm crown;
10 mm root) was used as the reference for modeling the
structures (Poiate et al., 2009). The complete model was
constituted of cancellous bone, 1.0 mm cortical bone,
0.2 mm periodontal ligament (Wakabayashi et al., 2010)
space and tooth (enamel, dentin and pulp) (Figure 1).
Computer-aided design (CAD) software Rhinoceros
4.0 (McNeel North America) was used to achieve the
3-D model. Six different geometries of periodontal at-
tachment were performed, in order to simulate different
levels of periodontal attachment loss. In each situation
different distances (1 mm; 2 mm; 3 mm; 4 mm; 5 mm
and 6 mm) between the enamel-cement junction (CEJ)
and alveolar bone crest (ABC) were simulated.
The geometric data were imported into Ansys soft-
ware (version 16.0; Ansys, Canonsburg, PA) for static
structural analysis. The mechanical properties of the
tissues mechanical considered were: elastic, homoge-
neous, linear and isotropic. Biomechanical proprieties
of the tissues was based on previously published data
(Table 1) for bone (Moroi et al., 1993), enamel, dentin
and periodontal ligament (Monteiro et al., 2018) and
pulp (Toparli et al., 1999).
Figure 1. Geometric modeling of structures
Material/tissue Young’s Moduli
(GPa) Poisson Ratio
Enamel 84,1 0,30
Dentin 14,7 0,31
Pulp 0,000003 0,45
Periodontal ligament 0,0118 0,45
Cortical bone
(Moroi, 1993) 14,7 0,30
Cancellous bone
(Moroi, 1993) 0,49 0,30
Table 1. Mechanical properties of materials/tissues
simulated
Mesh generation used tetrahedral elements. The
overall mean number of units was 197,908 elements
and 347,271 nodes. The elements had 0.2 mm mean size
and mesh surface convergence applied was 5%. It was
ensured that all contacts were considered fully bonded,
which means that the model was considered solid, with
no gaps between structures.
A simulated 100N and 45-degree angled load applied
at the buccal incisal edge of the lower central incisor.
Nodal restriction was applied at the cortical bone base in
all directions. The Consistency of the results was veried
by total displacement analysis and von Mises criteria.
The stress concentration was analyzed using the
Minimum Principal Stress (MPS) criteria, where positive
values were related to tensile stresses and negative values
to compressive stresses. Data processing performed
was arranged in stress color maps and numeric values.
Mechanical stress was analyzed in the cortical bone
and focused in two critical structures: alveolar bone crest
and lamina dura. Stress variations are presented as a scale
color map, where different colors mean different stress

da Rocha et al.: Periodontal support nite element analysis 67
concentrations. Qualitatively the proximity colors with
red in the scale, indicates higher stress concentration. For
quantitative analyses the numerical values of minimum
principal stress distributed in each structure (alveolar bone
crest and lamina dura) were assessed. The colorimetric
scales were adjustable for a visual comparison between
the groups.
Results
The qualitative analysis (Figure 2) shows a color map
illustrating the MPS distribution among the models.
In the analyses of alveolar bone crest, an increase of
compressive zones could be veried when the cement-
enamel junction (CEJ) to the alveolar crest (ABC) dis-
tances were increased. In the 1 mm model compressive
stress concentration peaks were observed on the lingual
bone crest. With an increase in the CEJ-ABC distance,
an increase in the minimum principal stress was located
mainly on lingual face and in the 5 to 6 mm models some
peaks were noted on the buccal face. For the lamina
dura color map, an increasing CEJ-ABC distance lead
to wider compressive stress concentration areas. In the
1 to 3 mm models, compressive areas were primarily
located to proximal regions (near to fulcrum area). For
4 mm, the location peaks of compressive stress started
to spread to buccal and lingual areas. It is noteworthy
that in all models, the 6 mm situation presented the
broadest areas of compressive stress.
Quantitative analyses were also performed and re-
vealed the same pattern of qualitative data, augmented
values of MPS showed an increased distance for CEJ-
ABC. For each millimeter increase in CEJ-ABC distance,
about 11% of the linear attachment was lost up to a 12%
total attachment area loss (Table 2).
Minimum principal stress distributions, as assessed
by scatter plots for 2D distribution, showed statistical
signicant differences (SSD) among groups for changes
in alveolar bone crest and lamina dura. The compres-
sive stress values were also compared in pairs (1 vs. 2,
2 vs. 3, 3 vs. 4, 4 vs. 5 e 5 vs. 6). Statistical signicant
differences were found for both the alveolar bone crest
and lamina dura (Figure 3). Moreover, it was noted that
with a decrease in periodontal support the intra model
variance of MPS display amplication (Figure 3).
Pearson’s correlation coefcient analyses between
attachment loss and peak of MPS were performed for
ABC and LD. Statistical signicant difference and high
Figure 2 - Color mapping of compression stress in the alveolar bone (a) ABC view, (b) LD occlusal view, (c) LD
proximal view

68 Journal of the International Academy of Periodontology (2021) 23/1
positive correlation (p=0.020; r=0.882) were found for
LD. SSD had a very high positive correlation (p=0.001;
r=0.975) for ABC.
The MPS peak increase in the no attachment loss
model, showed that the peak of compression stress
increased by 65.7% (ABC) and 33.6% (LD) with 11%
of attachment loss (2 mm model), and up to 252.6%
(ABC), 464.6% (LD) and 55.6% of attachment loss (6
mm model) (Figure 4).
Discussion
Horizontal attachment loss is a consequence of peri-
odontitis that remains even with the reestablishment of
periodontal health. Reduced periodontal support does
not seem to limit bite force (Kleinfelder and Ludwigt
2002). Subjects with attachment loss can exert up to
three times higher forces on the teeth. These func-
tions may related to affected sensory function of the
periodontal ligament (Johansson et al., 2006). Different
mechanical stimuli can modulate bone-remodeling
processes (Burger et al., 1999), and alter molecular path-
ways in bone metabolism (Rubin et al., 2006). Excessive
mechanical stress during hyper-occlusion may lead to
alveolar bone destruction during occlusal traumatism
(Tsutsumi et al., 2013). An important gap in knowledge
still remains unanswered whether the masticatory loads
in severe attachment loss can exceed bone adaptive load
bearing capability leading to periodontal tissue damage.
In the present study an overall increase in the mini-
mum principal stress (mainly compressive stress) was
Distance of
CEJ-ACB
Alveolar Crestal Bone Lamina Dura
Number of
nodes
% of linear
attachment lost
Minimum
Principal Stress
(MPa) Number of
nodes
% of
attachment
area lost
Minimum
Principal Stress
(MPa)
Peak Peak
1 mm 178 0,0% -14,76 6176 0,0% -21,64
2 mm 183 11,1% -24,46 5463 12,4% -28,91
3 mm 181 22,2% -25,37 4290 24,7% -33,07
4 mm 175 33,3% -33,86 3601 36,9% -45,99
5 mm 170 44,4% -48,96 3080 48,4% -60,51
6 mm 160 55,6% -52,04 2333 59,3% -122,18
CEJ - Cementum Enamel Junction
ABC - Alveolar Bone Crest
MPS - Minimum Principal Stress
Table 2. Descriptive statistics of compressive stress in ABC and LD in each simulated CEJ-ABC distance
Figure 3. Chart of distribution of Minimal Principal Stress values among groups

da Rocha et al.: Periodontal support nite element analysis 69
demonstrated in the target bone structures (alveolar bone
crest and lamina dura). This result shows that even with
the same force (that simulated bite forces), the tooth
surrounding bone structures were subjected to higher
compressive stress. Cyclic stress may generate cumulative
damage to the bone (Hambli et al., 2016). Therefore, if
a tooth has reduced periodontal support, the cyclic oc-
clusal forces can intensify bone damage. In periodontal
maintenance therapy, reinforcement of oral hygiene and
biolm removal is indicated (Armitage et al., 2016). Also
in this phase, occlusal adjustment has been reported to
improve periodontal health in terms of bacterial prole
and clinical appearance (Meynardi et al., 2016).
The distribution of stress values presented a non-
parametric distribution in the investigated bone struc-
tures, this is expected due to anatomic characteristics of
the designed structures, the vector force incidence, and
the axis of tooth rotation. Other studies have shown
a similar distribution conguration (Ona and Waka-
bayashi, 2006; Geramy et al., 2004).
Stress values exceeding the critical threshold of
between 50 and 60 MPa have been reported to cause
detrimental effects on human cortical bone (Sugiura et
al., 2000). In our study, peaks of MPS were reached in
the 5 and 6 mm model in lamina dura. These ndings
are not in agreement with a previous study that found
the height bone reduction potentially did not cause
mechanical damage (Ona and Wakabayashi, 2006). It is
noteworthy that literal interpretation of the stress values
is not a straightforward matter and characteristics such
as position of the teeth (Gerami et al., 2016), oclusal
dynamic and cyclic loading conditions should all be
taken into account (Benazzi et al., 2013). Caution also
is necessary since the effects of forces are dependent
on the accuracy of the elastic properties that are being
fed into the program and the accurate biomechanical
proprieties of tissues (McGuinness et al., 1991). Alveolar
bone was chosen for analysis because it is one of the
rst tissues affected by the inammatory response to
bacterial stimuli (Nakamura et al., 2010). Biochemical
mediators regulate inammation and bone resorption
and some in vitro studies have shown that these sites can
also be be modulated by mechanical stimuli (Hienz et
al., 2015). The lamina dura area was chosen for analysis
because it has an intimate anatomical relationship with
the root surface and during injury, adaptive remodeling
occurs during the repair phase aiming to better cope
with excessive loads (Gerami et al., 2016).
An increase in the intensity of the MPS peak was
clearly seen in the LD when 40% of the attachment
area was lost, this increase also showed a peak increase
in the ABC, but without any change in pattern. The
correlation coefficient between the MPS peak and
percentage of attachment loss reveled the high degree
dependence between these parameters. When the force
of occlusion was constant, and the attachment area of
the tooth became smaller, the compressive/area stress
tended to increase.
Even considering the inherent limitations of
finite element analysis, and the restrictions in the
created computational mathematical model, such as
simplification of structures mechanical properties
(Cook and Mongeau 2007), the specic dental element
designed and its anatomical morphology are reasonable
Figure 4. Chart of Minimal Principal Stress peak increase in relation to no attachment loss model

70 Journal of the International Academy of Periodontology (2021) 23/1
if their impact on the conclusions is carefully taken
into account. It has been shown, for example, that the
assumption properties for periodontal ligament could
interfere with the stress values, but this did not change
the biomechanical behavior of tooth-periodontal
structure (Wood et al., 2011). Moreover, force application
is a difcult task to mimic because of the nature of
masticatory function and natural loading scenario.
However, the patterns of compressive stress distribution
values found in the simulated models, clearly indicated
a trend towards increase stress concentration when
periodontal attachment was reduced.
The results of this study provide some knowledge to
understanding the relationahip between occlusal trauma
in teeth with reduced attachment apparatus and normal
periodontal ligament space. Clinically, this suggests that
in vivo, similar clinical situations, submitted to chewing
forces can generate stresses that exceed physiological
limits and cause periodontal bone damage. Questions
about the threshold capability should be explored. These
ndings may potentially assist in the development of
treatment strategies and prevention to avoid alveolar
bone injury during periodontal treatment maintenance
phase. Thus, teeth with attachment loss and normal peri-
odontal ligament space, should receive special attention
in relation to occlusal relations and masticatory loads.
Limitations of this study are that the present models
do not represent all the oral variations such as changes
in pH, temperature, sliding occlusal loading, pres-
ence of bacteria, different antagonistic materials, and
parafunctional habit. The simulated condition used for
this study were considered isotropic and homogeneous
with a simplied behavior.
Conclusion
The results of this study demonstrate that attachment
loss around teeth increases stress concentration in the
surrounding bone. Despite inherent limitations of the
model used the results dene a biomechanical chang-
ing in stress pattern, which help to partly explain bone
resorption risk for teeth with periodontal attachment
loss and normal ligament space.
Acknowledgment
CAPES/FAPITEC/SE supported this research.
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