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Original Article
Comparison of using different bridge prosthetic
designs for partial defect restoration through
mathematical modeling
Oksana Styranivska1, Nataliia Kliuchkovska1, Nataliya Mykyyevych1

Correspondence: Dr. Oksana Styranivska Department of Prosthetic Dentistry, Lviv National

1

Email: styranivskao@gmail.com Medical University, Lviv Oblast, Ukraine

ABSTRACT
Objective: To analyze the stress–strain states of bone and abutment teeth during the use of different prosthetic designs
of fixed partial dentures with the use of relevant mathematical modeling principles. Materials and Methods: The use of
Comsol Multiphysics 3.5 (Comsol AB, Sweden) software during the mathematical modeling of stress–strain states provided
numerical data for analytical interpretation in three different clinical scenarios with fixed dentures and different abutment
teeth and demountable prosthetic denture with the saddle‑shaped intermediate part. Statistical Analysis Used: Microsoft
Excel Software (Microsoft Office 2017) helped to evaluate absolute mistakes of stress and strain parameters of each
abutment tooth during three modeled scenarios and normal condition and to summarize data into the forms of tables.
Results: In comparison with the fixed prosthetic denture supported by the canine, first premolar, and third molar, stresses
at the same abutment teeth with the use of demountable denture with the saddle‑shaped intermediate part decreased:
at the mesial abutment tooth by 2.8  times, at distal crown by 6.1  times, and at the intermediate part by 11.1  times,
respectively, the deformation level decreased by 3.1, 1.9, and 1.4  times at each area. Conclusions: The methods of
mathematical modeling proved that complications during the use of fixed partial dentures based on the overload effect
of the abutment teeth and caused by the deformation process inside the intermediate section of prosthetic construction.

Key words: Dental rehabilitation, mathematical modeling, prosthetic bridges design

INTRODUCTION most widespread manipulation in the prosthodontic

practice.[2] Tan et al. found that the 10‑year probability
The prevalence of partial and full adentia among of survival for fixed partial dentures equals nearly
adults is one of the key problems of modern medicine. 89.1%  (being in rage of 81%–93.8%) while the
The WHO has even identified prerogative for the probability of success was found to be 71.1% (being
dental health development to ensure retention of at in range of 47.7%–85.2%).[3] Obviously, the prognosis
least 20 natural teeth among persons over 80 years old of dental bridge constructions depends on the
through the complex programs of dental prophylaxis adequacy of functional load distribution between
and preventive measures provided on different levels the abutment teeth and the intermediate part of the
of dental care system.[1] However, despite the key prosthesis.[4] Decisive role of such parameter, Lang
role of prevention, treatment of patients with already
existing partial defects of dentition remains one of the This is an open access article distributed under the terms of the Creative
Commons Attribution‑NonCommercial‑ShareAlike 3.0 License, which allows
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www.eurjdent.com Comparison of using different bridge prosthetic designs for partial defect
restoration through mathematical modeling. Eur J Dent 2017;11:345-51.

DOI: 10.4103/ejd.ejd_72_17

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Styranivska, et al.: Comparison of using different bridge prosthetic designs

et al. and Brägger et al. described in their recent papers, partial adentia. We have analyzed next three scenario
where they marked the importance of load distribution of possible prosthetic treatment of clinical situation
among natural teeth and dental implants during with adentia of the second premolar, first and second
different approaches of prosthetic rehabilitation.[5,6] molars on mandible:
The evaluation of elastically deformed states of bone • Restoration of partial adentia by the fixed prosthetic
near abutment teeth and implant infrastructure is denture supported by the first premolar and third
one of the key aspects to provide effective prognosis molar
of long‑term prosthetic success rate. Although the • Restoration of partial adentia by the fixed prosthetic
implant‑supported dentures remain common and denture supported by the first canine, premolar,
predictable method of prosthetic rehabilitation and third molar
during the partial adentia,[7] partial fixed prosthetic • Restoration of partial adentia by the demountable
designs with the support of natural teeth are prosthetic denture with the saddle‑shaped
more financially acceptable treatment option for a intermediate part fixed on the canine, first
significant number of patients. According to relevant premolar, and third molar with the use of rigid
research, dentists usually do not fully evaluate all locking fasteners.
of mucosa and bone support potential while using
fixed partial dentures.[8‑10] In some cases, the use of The total number of nodal points in the mathematical
demountable design of bridge structure can provide model for the first scenario was 216,734 and for the
an effective alternative for successful restoration of second and third 252,049. During the mathematical
adentia defect.[4,11] Relevant mathematical modeling simulation of those clinical situations, we assumed
approaches provide opportunities to argument the that all components of dentition are isotropic and
use of different designs of dental prostheses based on homogeneous. The use of tetrahedral volume elements
practically oriented objectives of treatment in different helped to form three‑dimensional mathematical
clinical situation.[12‑15] Such approaches also include models [Figure 1]. The main biochemical characteristics
evaluation of extent and topography of the defect, that were used during the modeling are present in
the state of supporting natural teeth, qualitative Table 1.
characteristics of bone, and features of interocclusal
relation with antagonist’s teeth. Therefore, the aim of Functional modeled load was applied tangentially to
this study was to analyze the stress–strain states of the occlusal surface of artificial teeth in the structure
bone and abutment teeth during the use of different of partial fixed denture because the force that is acting
prosthetic designs of fixed partial dentures with the at a distance from the abutment teeth has a more
use of relevant mathematical modeling principles. significant impact on the supporting teeth compare to
their direct load. Total load was 400 N. Such occlusal
MATERIALS AND METHODS load was chosen based on the results of previous
analogical studies published in peer‑reviewed
The use of Comsol Multiphysics 3.5 (Comsol AB, journals.[16,17] Analysis of stresses and strains at the
Sweden) software during the mathematical modeling
of stress–strain states provided numerical data for
analytical interpretation in three different clinical
scenarios. Initially three‑dimensional mathematical
model of normal condition included mandible with
continuous tooth row, consists of teeth, periodontium,
compact and spongy bone, and mucosa of the alveolar
process. The dimensions of the teeth, the thickness
and shape of the bone contours, deviation axis of the
teeth, alveolar bone, and mucosal thickness imitated
the average statistical data presented in the literature.
To simulate included partial dentition defect with the
absence of three teeth, we used only a lateral fragment
of mandible. Such kind of defect was found to be the
most prevalent  (27.4%) among randomly selected
256 patients of Prosthetic Department at Lviv National
Medical University Clinic, who had different forms of Figure 1: Tetrahedral volume elements used to build the model

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Styranivska, et al.: Comparison of using different bridge prosthetic designs

different components of the model was carried out by RESULTS

colorful representation of stress distribution and the
numerical data to provide objective comparison; the During the first scenario of modeling fixed partial
stress–strain state of dentition in the normal condition dentures supported by the first premolar and third
without any defect was determined. All the original molar, maximum stress occurred in the abutment
data, such as the geometric structure of the model, crowns and places of their connection with the
properties of tissues, size, direction, and load location, intermediate part of the denture. The greatest stresses
were preserved for further comparison with all three were located at the area of distal tooth that reached
mentioned above scenarios of possible prosthetic 190.88 MPa, and the lowest of 29.94 MPa registered
rehabilitation.[2,15,18] at the intermediate part of fixed prostheses, where
the load was applied. Mesial abutment tooth reached
To provide clinical evidences of effective use of stress of 122.98 MPa while strain of mesial and distal
demountable prosthetic denture with the saddle‑shaped abutment tooth was nearly the same and stated
intermediate part fixed on the canine, first premolar, for 85.36 and 84.39 µm, respectively. Deformation
and third molar with the use of rigid locking fasteners, level of intermediate denture part reached
we approbate such scenario on 16 patients with partial 115.00 µm [Figure 2]. In the area of abutment teeth,
adentia of the second premolar, first and second molar maximum stress occurred in the cervical region and
at mandible. These 16 patients represented study group. was gradually decreasing while going along vestibular
Other 16 patients with partial adentia of the second side to half of the roots length and along oral side to
premolar, first and second molar were treated by fixed
partial denture placed on the canine, first premolar,
and third molar. Inclusion criteria for patients from
study and control group were partial adentia of the
second premolar, first and second molar at mandible
without any somatic, periodontal, or other medical
conditions that can influenced results of prosthetic
treatment. Observation of bone resorption was
provided using spot‑film radiography method after 1
and 3 years of prosthetic treatment. Standardization of
bone state analysis based on radiographical results was
provided by superimposition method of saddle‑shaped
intermediate part of prosthetic construction, which was
used as a reference line for bone reduction registration.

Microsoft Excel Software (Microsoft Office 2016,

Developed by Microsoft) helped to evaluate absolute
mistakes of stress and strain parameters of each
abutment tooth during three modeled scenarios and
normal condition and to summarize data into the
forms of tables.

Table 1: Biochemical parameters used during the

mathematical modeling
Element of the model Е (МPa) ν σc (MPa) σр (MPa)
Tooth 1.56×104 0.3 230-310 2-104
Mandible bone 4.9×103 0.3 26-160 10-20
Mucosa 75 0.4 ‑ ‑
Metal part of fixed 22×104 0.33 ‑ 700-970
partial denture
Saddle‑shaped 5×103 0.3 ‑ ‑
Figure 2: Representation of stress and strain states of denture elements,
intermediate part of
abutment teeth, and bone structure during the first scenario modeling
demountable prosthetic
with the use of fixed prosthetic denture on the first premolar and
denture
third molar

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Styranivska, et al.: Comparison of using different bridge prosthetic designs

2/3 of roots length. The greatest stress was defined

in the area of distal abutment tooth (44.97 MPa) and
the greatest strain in contrast was registered at mesial
abutment tooth (66.15 µm). Due to such scenario,
stress that occurred in mesial abutment tooth was
8 times higher compare to normal condition of natural
denture and 20 times higher in the area of distal
abutment tooth. The deformation of abutment teeth
was also increased at the first premolar by 23 times
and for the third molar by 26 times compare to the
normal condition. The stressed in the bone structure
around the mesial tooth (29.48 MPa) was lower than
at the distal abutment tooth (41.04 MPa). Comparative
analysis of stress–strain state of bone around abutment
teeth (first premolar and third molar) in condition of
defect and during normal state of teeth row obtained
that such parameter was 20 times higher in the area
of premolar and 31 times higher in the area of molar,
while strain parameters were also increased by 17 and
14 times, respectively, for each area of abutment teeth.

In the case of the second scenario, the use of canine

as an additional abutment tooth was found that the
greatest stresses were located in the area of distal
tooth (113.21 MPa) and the smallest in the intermediate
part of prosthetic denture (23.23 MPa). However, the
value of the maximum stress was lower compare
to the first modeling scenario: in the area of mesial
supporting crowns just by 1.5 times higher, in the
Figure 3: Representation of stress and strain states of denture elements,
area of distal crown by 1.7 times higher, and in the abutment teeth, and bone structure during the first scenario modeling
intermediate part by 1.3 times higher. Deformation of with the use of fixed prosthetic denture on the canine, first premolar,
prosthetic elements had inverse representation: the and third molar
greatest deformation was observed in the intermediate
part of denture (68.53 µm) and the smallest at the maximum stress in the bone tissue around the
abutment crown fixed on the third molar (32.37 µm). abutment teeth located at the cervical area of alveolus
The magnitude of the deformations was also lower and was gradually decreasing toward the roots apices
compare to the first scenario, especially in the area of and toward the defect space. The stress level at the
supporting crown by 2.6 times. Maximum stress in the mesial abutment teeth (17.07 MPa) was lower than at
area of abutment teeth occurred in the cervical region the distal abutment teeth (23.83 MPa). The greatest
and gradually decreasing through the vestibular side bone deformation observed at the first premolar
to 1/3 the length of roots and from oral side to the two (14.03  µm) that was characterized by orally distal
half of the roots length. The greatest stress was stated in direction. Deformations occur near the third molar
the distal abutment tooth (26.55 MPa), and the smallest (12.61  µm), distributed in the mesial‑oral direction,
was observed near canine that served as additional toward the defect space. The maximum stresses of
abutment tooth (9.50 MPa) [Figure 3]. Compared with bone tissue in the area of abutment teeth decreased
the first modeled scenario, the maximum stress in the by 1.7 and the strain decreases by 2 times compare
first premolar decreased by 1.6 times and in the third to the first modeled scenario. However, such values
molar by 1.7 times. However, these values were higher were higher than at the areas of corresponding teeth
than the corresponding parameters at the natural with no partial defect [Figure 4].
integral state of dentition (by the 5 and 12 times,
respectively). Loading of the intermediate part caused During the third modeled scenario, the stresses of
the greatest strain in the first premolar  (35.57  µm) the mesial crowns (28.05 MPa) were noted to be
and the smallest in the canine area (17.05 µm). The higher than at distal abutments (15.74 MPa). The

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Styranivska, et al.: Comparison of using different bridge prosthetic designs

lowest stress was registered in the saddle‑shaped first premolar, and third molar with the use of
basis of demountable prosthesis construction (2.07 rigid locking fasteners, we approbate such scenario
MPa). Deformation of structural denture elements on 16 patients with partial adentia of the second
had an inverse relationship to previous scenarios: premolar, first and second molar. These 16 patients
the most deformed was saddle‑shaped basis of represented study group. Other 16 patients with
prostheses (46.36 µm), and the least deformed was partial adentia of the second premolar, first and second
abutment mesial crown (14.58 µm). In comparison with
molar were treated by fixed partial denture placed on
fixed prosthetic denture supported by the canine, first
the canine, first premolar, and third molar  (control
premolar, and third molar, stresses at the abutment
group). After 1 year of functioning, the atrophy
teeth in third modeled scenario were smaller: at the
mesial abutment tooth by 2.8 times, at distal crown by progress of the alveolar bone under saddle‑base
6.1 times, and at the intermediate part by at 11.1 times, demountable prosthesis in study group was noticed
respectively, the deformation levels decreased by to be uniform and amounted to 0.2 mm. After 3 years
3.1, 1.9, and 1.4 times. Values of maximum stresses
exceeded defined stress maximums of normal state by
2.2 times at the canine, by 2.9 times at the premolar,
and by 3.1 times at the third molar. Because the canine
served as additional abutment, its stress and strain
were minimal compared with other supporting teeth.
The maximum deformation of abutment teeth were
higher than normal state by 3.5, 4.2, and 6.2 times,
respectively. The use of demountable prosthesis at
third clinical scenario helped to decrease the stresses
in bone tissues around the mesial abutment teeth by
3.0 times, around distal abutment teeth by 3.4 time,
and level of deformation – by 1.5 and 1.2 times,
respectively [Figure 5 and Table 2].

To provide clinical evidences of effective use of

such demountable prosthetic denture with the
saddle‑shaped intermediate part fixed on the canine,

Figure 5: Representation of stress and strain states of denture elements,

abutment teeth, and bone structure during the third scenario modeling
Figure 4: The comparison of stress and strains values during the first with the use of demountable prosthetic denture with the saddle‑shaped
and second modeled scenarios and normal state of dentition intermediate part

Table 2: Comparison of stress and strain parameters of each abutment tooth during three modeled scenarios
and normal condition
Parameters Fixed partial denture Normal parameters Fixed partial Demountable partial
(3 abutment teeth) denture denture (3 abutment teeth)
(2 abutment teeth)
Canine First Third Canine First Third First Third Canine First Third
premolar molar premolar molar premolar molar premolar molar
Stress (Мpa) 9.5±0.8 20.0±1.1 26.5±1.2 1.9±0.2 3.8±0.3 2.2±0.1 31.7±1.4 44.9±1.6 4.1±0.3 8.9±0.2 7.2±0.4
Strain (µm) 17.0±1.2 35.5±1.5 26.0±1.1 1.9±0.2 2.8±0.2 2.1±0.2 66.1±1.8 56.7±1.4 6.9±0.4 12.2±0.4 15.0±0.3

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Styranivska, et al.: Comparison of using different bridge prosthetic designs

of functioning, the reduction of the alveolar process important role of optimal support and adequate
reached just 0.35 mm. In the second control group, distribution of functional loading.[3,8] To reduce
radiographical expansion of periodontal gap and negative impacts of saddle base of prostheses in
signs of osteoporosis were detected in 7.7% ± 4.3% of defect area, an elastic lining could be used as an
cases at the defect area of teeth row. The level of bone additional layer between prosthetic inner surface and
resorption at defect area after 3 years of functioning soft tissue interface. The use of demountable prosthetic
reached the range of 1.2–1.8 mm. In 23.1% ± 6.8% of appliances supported by three abutment teeth
cases, periodontal complications such as localized decreases the levels of stresses and strains compare
periodontitis or chronic gum inflammation have been to nonremovable prosthetic design. Consequently, the
developed due to overload of abutment teeth. use of mountable prosthetic appliances with saddle
base transmitted functional load to the abutment
DISCUSSIONS teeth in a greater manner that to the soft tissue in
defect area due to the use of rigid locking fasteners.
Fixed prosthetic rehabilitation of the second premolar, Less load on the toothless area reduces atrophic
first and second molar adentia seems to be challenging processes under the saddle base. On the other hand,
task for practical dentist due to the appearance of the proposed design eliminates the overloading of
considerable stresses and strains in the supporting abutment teeth that occurs during the use of classic
tissues that varies based on different prosthetic nonremovable prosthetics, reducing their stress and
designs.[6,11,19,20] Within the possibility to provide strains. Analysis of stress–strain state components
restoration of adentia region with construction of the models showed that the use of prosthetic
supported by dental implants, it can be stated that appliances supported by two or three teeth marked
retention parameters are definitely influencing not inverse relationship between stress values and strains:
only stability of supra constructions but also a changes in the areas, the greatest stresses were found the
at peri‑implant bone.[21,22] Finite element model (FEM) minimal deformations values. During the second and
analytical researches dedicated to the evaluation of third modeling scenarios, the horizontal component
masticatory load distribution due to the different of stresses and strains was directed orally and toward
form and shapes of dental implants found that not the defect. In addition, the stress inside the bone near
all modification of dental screws are argumented by abutment teeth spreads in the opposite direction from
the prognosed functional results; thus, the question the defect, except areas of mesial abutment teeth in
of choosing adequate materials and methods for the second modeled situation, which indicates about
prosthetic treatment is a primary question of planning the splinting effect of additional abutment tooth. Due
procedures.[23] Previous studies of different types to the limitations of this study, we can conclude that
of single‑tooth crown prosthesis with the FEM and the use of a demountable prosthetic denture with the
Von Mises analyses found that cemented retained saddle‑shaped intermediate part fixed on the canine,
prostheses offer a better and more homogeneous first premolar, and third molar with the use of rigid
distribution of the load forces compared to screwed locking fasteners appeared to be considerable due to
prostheses. Such point could be transferred on the the obtained stress and strains values.
prosthetic designs with natural teeth support, but
different effects of strain and stress distribution[24] CONCLUSIONS
could also influence functional prognosis of abutment
teeth. Such effects increase with the convergence of The methods of mathematical modeling proved
abutment teeth, which presented in such cases by the that the causes of complications during the use of
first premolar and third molar. Inadequate prosthetic fixed partial dentures based on overload effect of
can cause the periodontal tissues alteration in future, the abutment teeth and deformation process inside
the problems with appropriate crown fixation, and the intermediate section of prosthetic construction.
fracture of abutment teeth.[5,25,26] Additional support Inclusion of the additional abutment tooth leads to a
of prosthetic constructions with the mesial tooth such decrease of stress–strain values in all the component
as canine improves the effectiveness of prosthodontic elements of the mathematical model and provides a
treatment, reducing the horizontal component of splinting effect of construction. Design of demountable
stresses and strains, but not completely resolving the prosthetic construction eliminates the overload effect
problem of abutment teeth overload. Hard and soft of abutment teeth under the functional loading and
tissue of partial defects with the appropriate design helps to decrease the degree of bone structure atrophy
of intermediate prosthetic construction can play an during the prolonged functioning of the prostheses.

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