Table 1. Maximum von Mises stress values (MPa) on teeth for each model
Models
Maximum Von Mises Stress Values (MPa)
Osse
ou
s S
uppo
rt
Teeth
Ce
ntral incis
or
Lat
eral
inciso
r
Ca
nin
e
First p
rem
olar
Seco
nd prem
ol
ar
Models
50%
NC
3.10
3.20
3.40
14.50
13.10
1UC3
5.10
5.03
5.75
9.78
35.22
2UC3
5.74
7.42
7.38
10.48
63.32
1UC4
5.04
5.05
5.68
10.40
32.7
2UC4
5.80
7.67
7.45
10.63
56.42
1UC5
4.99
5.01
5.62
11.30
31.8
2UC5
4.18
9.70
16.11
23.22
135.62
Table 2. Maximum von Mises stress values (MPa) on teeth for each model
Models
Maximum Von Mises Stress Values (MPa)
Osse
ou
s S
uppo
rt
Periodontal ligaments
Ce
ntral
incis
or
Lat
eral i
nciso
r
Ca
nin
e
First p
rem
olar
Seco
nd prem
ol
ar
Models
50%
NC
0.912
0.468
0.576
1.740
4.900
1UC3
0.955
0.642
0.489
1.730
8.220
2UC3
0.957
0.781
0.498
1.680
9.580
1UC4
0.947
0.634
0.488
1.760
8.220
2UC4
0.948
0.766
0.486
1.720
9.650
1UC5
0.941
0.624
0.475
1.770
8.220
2UC5
0.823
0.656
0.451
1.970
10.160
All parametric models were subsequently imported into the FEA program, where a linear
static analysis was performed (Algor; Algor Inc, Pittsburg, Pa). The adjustment analysis‘
parameters (boundary conditions, loading case and materials properties) for the FEA analysis
Petros Koidis and Manda Marianthi
80
was defined. [108, 133]Stress distribution patterns of the connectors, the periodontal
ligaments and the teeth were obtained by calculating von Mises equivalent stresses and
described in Figures 6-8. The relative stress values for the connectors are described
elsewhere, [133] while the stress values for the periodontal ligaments and teeth are shown in
Tables 1 and 2.
Figure 6. Stress distribution of the connectors: NC3: No-cantilever FPD, 1UC3: 1-unit cantilever FPD,
3mm-connector, 2UC3: 2-unit cantilever FPD, 3mm-connector, 1UC4: 1-unit-cantilever FPD, 4mm-
connector, 2UC4: 2-unit cantilever FPD, 4mm-connector, 1UC5: 1-unit cantilever FPD, 5mm-
connector, 2UC5: 2-unit cantilever FPD, 5mm-connector, colored measurement bar (MPa).
Biomechanics of Rehabilitating the Perioprosthetic Patient
81
Figure 7. Stress distribution of the teeth of the models: NC3: No-cantilever FPD, 1UC3: 1-unit
cantilever FPD, 3mm-connector, 2UC3: 2-unit cantilever FPD, 3mm-connector, 1UC4: 1-unit-
cantilever FPD, 4mm-connector, 2UC4: 2-unit cantilever FPD, 4mm-connector, 1UC5: 1-unit
cantilever FPD, 5mm-connector, 2UC5: 2-unit cantilever FPD, 5mm-connector, colored measurement
bar (MPa).
The present study suggests that the higher stress concentration is located within the
connectors and the areas of splinted crowns around the connectors,while both 1- and 2- unit
cantilever restorations presented the highest stress values proximal to the retaining abutment,
independently of connectors VD. More specific, the higher stress values were reported for the
connectors distal to the retaining abutment, while the stress values calculated for the
connector distal to the retaining abutment of the 2-unit cantilever restoration were almost
doubled compared to the connector of the 1-unit cantilever restoration. These outcomes are in
accordance with the results derived from the FEA studies of Awadalla (1992), Yang (1996)
and Wang (1998) as well as the photoelastic study of Wylie and Caputo (1991), who
investigated theoretical models of FPDs with conventional connectors. [81, 118-121]
However, to authors‘ knowledge, there are no relevant studies investigating the
biomechanical effect of varying the connectors VD of cross-arch FPDs in the perioprosthetic
patient, in order to allow for a comparative assessment of this study's results.
Petros Koidis and Manda Marianthi
82
Figure 8. Stress distribution of the periodontal ligaments: NC3: No-cantilever FPD, 1UC3: 1-unit
cantilever FPD, 3mm-connector, 2UC3: 2-unit cantilever FPD, 3mm-connector, 1UC4: 1-unit-
cantilever FPD, 4mm-connector, 2UC4: 2-unit cantilever FPD, 4mm-connector, 1UC5: 1-unit
cantilever FPD, 5mm-connector, 2UC5: 2-unit cantilever FPD, 5mm-connector, colored measurement
bar (MPa).
The conventional connectors (3mm) proximal to the retaining abutments in the models
1UC-3 and 2UC-3 present the higher stress values compared to the same connectors of all the
models investigated, while the stress in the 3mm-connector distal to the retaining abutment of
the 2-unit cantilever restoration approaches the yield strength of the material used. These
observations are also justified by the results published on clinical studies, reporting on the
success rate of extensive restorations on severely reduced periodontal tissues, made by
general practitioners, not previewing the special dimensioning of the connectors. A
considerable increase of technical failure rate is reported, [134, 34, 36, 91] rising up to 41% in
a 2-year period. [134]
On the contrary, clinical investigations, which were carried on by experts and emphasized
on the designing of the restorations, demonstrated considerably less technical failures
compared to published studies, which did not incorporate special design demands. [103,
110]More specific, Nyman and Lindhe (1979) and Lundgren (1987), investigating the long–
Biomechanics of Rehabilitating the Perioprosthetic Patient
83
term prognosis of cantilever cross-arch FPDs on minimal periodontal tissues, including
special modifications of the prosthesis design, reported 0-8% technical complications within a
5- to 8- year period. [103, 110] These design modifications were referring to the
dimensioning of connectors, which involved the increase of the VD and HD of the connectors
proximal to the retaining abutment up to 6mm and 5mm, respectively. [105, 107] In the
present study, the variable investigation involved the increase of the connectors VD up to
5mm, while the HD remained at 2,5mm. This was selected due to the limitation of the teeth
size existing in the specific human population group and the use of the restorative materials.
The VD increase of the connector distal to the retaining abutment proved to be quite
beneficial for the stress field developed within. Particularly, the gradual increase from 3mm
to 5mm resulted in a stress decrease of about 50%. This is particularly significant for the 2-
unit cantilever restorations, where their conventional connector distal to the retaining
abutment presented stress values that were close to the critical yield strength value of its
material. This determined the VD at the connection of the cantilever segment distal to the
retaining abutment as a serious prognostic factor for the longevity of the 1- and 2- unit
cantilever FPDs, even if it is not accompanied by simultaneous increase of the HD.
The fact, that the increase of the VD causes a decrease of the maximum von Mises stress
appearing on the connector distal to the retaining abutment, is explained from the technical
theory of bending. In particular and without loss of generality, the dominating mechanical
behaviour of the retaining abutment under the application of occlusal forces is bending as
shown in Figure 7, A and B.In more details, the retaining abutment and the cantilever unit are
shown in Figure 7, A and B, where in Figure 7, A the connector VD for a section AA‘ located
at x
A
is h1 and in Figure 7, B the connector VD in the corresponding section AA‘ is h2>h1.
However, it is well-known from the technical theory of bending that the maximum bending
stress at any cross-section AA‘ is equal to:
max
max
yy
M
z
I
(eq.1)
where
3
1
12
yy
I
bh
and
max
z
h
(eq.2)
Introducing (eq.2) in (eq.1), and after basic manipulations, it yields:
max
2
12
1
M
b
h
(eq.3)
where M is the bending moment at the cross-section under consideration. For a specific
configuration, the quantities
M
and
b
are constant. Therefore, from eq.3, it yields that as h,
that is the VD, increases,
max
decreases. However, since bending is the predominant
mechanical behaviour in the case under examination, the appearing maximum von Mises
Petros Koidis and Manda Marianthi
84
stress, predominantly affected by
max
, decreases as well. These observations comply with
the aforementioned clinical studies, [103,110] linking the long-term functionality of the cross-
arch FPDs to the connectors' dimensions and proving the high impact of VD. However, it
must be noticed that despite the considerable stress decrease, the measured values were still
the higher compared to the other connectors among the splinted teeth.
As far as the connector mesial to the retaining abutment is concerned, its VD increase had
not a similar intense impact to the peak stress relief. In the case of the 2-unit cantilever
restoration a small gradual relief of the peak stress value was measured, whereas in the 1-unit
case the same value presented a fluctuated pattern. However it is clear (Figure 5, A through F)
that the connector are benefited in terms of a gradually relieved stress distribution across its
geometry. Either way the changes were relatively small, leading to the assumption of a low
impact of VD on the peak stress for this connector, as well as for all the other mesial
connectors. This can be explained from the fact that the application of the occlusal forces, in
combination with the support provided by the PDL to each tooth, makes the teeth/connectors
assembly behave quite like as a cantilever which is fixed along a significant part of its length
(in opposition to a cantilever with a fixed point-end). This part extends in a zone from the
central incisor to the second premolar (retaining abutment). As a result, increasing the VD
does not affect the stress field of the connectors between the teeth of the aforementioned
zone, within which the relative teeth displacements remain the same.
On the abutment level, the stress values obtained for the teeth #41-44 are not significant,
while a considerable stress concentration is observed at the distal aspect of the #45 for all the
models. Increase of the stress values at almost 100% is observed after the addition of the
second cantilever for all the models, independently of the size of the connector proximal to
the retaining abutment. The previous are in accordance with the FEA studies of Yang (1996)
and Wang (1998). [119, 120]The increase of the connectors‘ vertical dimension does not
result in significant changes for the end-abutment tooth in the 1 unit-cantilever restorations.
Though, increase of the connectors‘ vertical dimension at 5mm for the 2-unit cantilever
restoration results in a stress increase of almost 300% compared to the values obtained for the
same connectors in the 2-unit cantilever restorations. On the abutment level, in a meta-
analysis study, the reported incidence of fracture of abutment teeth in cantilever FPDs was 2.9
and 2.6% of the FPDs were lost as a result of the abutment tooth fracture after an observation
period of 10 years. [103]Clinical studies with special biomechanical demands as far as
concern the dimensioning of the metal framework report low incidence of tooth fracture,
though no data concerning the loss of the tooth vitality are available, which may be related
with the high stress concentration. [33, 110, 35]
On the periodontal ligaments level, the differences of the stress magnitude among the
teeth #41-44 are minor. The stress is concentrated on the periodontal ligament of the #45.
These observations are the same as Wylie and Caputo (1991) and Wang (1998). [40,42] In the
present study, there is a 100% stress increase in the periodontal ligament of the terminal
abutment after the addition of the first cantilever unit, which is not changed by the increase of
the connectors‘ vertical dimension. The addition of the second cantilever unit results a stress
increase of approximately 1MPa, compared to the 1-unit cantilever restoration. Though, the
stress increase is getting higher when the connectors‘ vertical dimension reaches the 5mm, for
the 2-unit cantilever restorations. The above observations are not in accordance with the FEA
study o Yang (1996), who reports marked stress increase on the periodontal ligament after the
Biomechanics of Rehabilitating the Perioprosthetic Patient
85
addition of the second cantilever, but justifies that the limitations for the application of cross-
arch FPDs in the perioprosthetic patient are related to the technical and biomechanical
problems involved rather than to the remaining periodontium to support the restoration
successfully. [119]
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