Influence of guiding tooth geometry on contact forces distribution in the human masticatory system: a FEM study/ Vedanciojo danties geometrines formos itakos salycio jegu pasiskirstymui zmogaus kramtymo sistemoje tyrimas baigtiniu elementu metodu.
Pileicikiene, G. ; Surna, A. ; Skirbutis, G. 等
1. Introduction
The finite element method (FEM) has become the prevalent technique
used as an effective tool for analyzing all kinds of physical phenomena
in structural, solid and fluid mechanics. Moreover it is used for
simulating various processes in engineering in the last four decades. A
remarkable advantage of the FEM is the chance to study areas that are
difficult or impossible to access without any risks to a human sample
[1]. The FEM has been frequently used in various fields of medical
studies such as cardiovascular mechanics [2, 3], biomechanics of
musculoskeletal system [5], radiofrequency ablation of liver tumors
[5-7] as well as in ophthalmology [8], neurosurgery [9] and of course,
dentistry [10]. Dentistry is an area of medicine where the study of
human biomechanics such as chewing has the potential to improve patient
care [11]. The use of FEM allows studying a single tooth, a set of
teeth, or even the relationship between maxillary and mandibular dental
arches; furthermore, finite element methods can be applied with the aim
of improving the design of materials, structures and manufacturing
procedures, leading to improved clinical results in dentistry [12].
There are already plenty reports on the modeling and stress analysis of
different constituent parts of human masticatory system [10]. But still
there have been very few reports that took FEM as a tool for the study
of relationship between occlusal surfaces geometry and forces
distribution in the whole masticatory system. Geometrical form of
occlusal surfaces, spatial arrangement of teeth in dental arches and
condition of supporting structures has crucial influence on masticatory
function efficiency. Furthermore, proper geometry of occlusal surfaces
of posterior teeth determines appropriate distribution of occlusal load
to the supporting structures and normal activity of masticatory muscles
and temporomandibular joints. Most of previously performed studies were
directed to the relation between form of occlusal surfaces and chewing
efficiency [13, 14] as well as temporomandibular joint pathology [15,
16], whereas the influence of geometrical form of occlusal surfaces in
guiding teeth on forces distribution in constituent parts of masticatory
system is still a little investigated field. Therefore it was decided in
this study to analyze by means of FEM the influence of geometrical form
of a guiding tooth on the distribution of contact forces in constituent
parts of human masticatory system.
2. Three-dimensional reconstruction of skeletal and dental
morphology
In order to create high accuracy three dimensional geometrical
models of the main components of the investigative person masticatory
system, we used our original hybrid modeling technique based on computed
tomography images and three-dimensional optical scanning data [17-19].
3. The biomechanical model of masticatory system
LS-DYNA 970 finite element software (Livermore Software Technology
Corporation, USA) was employed for creation of mathematical model of
masticatory system. By means of surfaces triangulation hard parts
comprising the biomechanical system have been created: mandibular dental
arch, maxillary dental arch, right and left mandibular condyles and
mandibular fossae of temporal bone. Based on accurate three-dimensional
coordinates the models of individual hard parts of masticatory system
were interconnected into one entirety according to general system of
axes. Models of mandibular and maxillary dental arches were assumed to
be whole and rigid. The model of maxillary dental arch was fixed in
space. The model of the mandibular dental arch was able to move in space
synchronically with the mandibular condyles under the action of applied
forces. Clenching was simulated by the action of resultant force vectors
of four bilateral masticatory muscles, responsible for the elevation of
the mandible, which was assumed as static occlusal load. Models of
temporomandibular joint discs were generated mathematically by using a
mathematical "material forming" procedure. The reasonable
level of refinement of the model enabled to save computational
resources, simultaneously preserving all important geometrical
properties of the investigated biomechanical structure. The created
biomechanical model representing entire masticatory system consisted of
eight basic parts: two rigid structures representing the mandibular and
maxillary dental arches, two mandibular condyles, two mandibular fossae
of temporal bone, and solid models of two articular discs. The final
view of computational model with applied muscle force system
(represented by arrow triplets) and mathematically generated articular
discs, ready for numerical experiments is presented in Fig. 1. Creation
of computational biomechanical model of the human masticatory system was
described, in detail, previously [20].
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
In order to evaluate distribution of contact forces in masticatory
system of healthy subject using created model the distribution of
reaction forces in maxillary dental arch and temporomandibular joint
discs, generated during simulated clenching into central occlusion with
non-modified geometry dental arches under action of applied force
system, imitating activity of jaw closing muscles was investigated.
4. Investigation of guiding tooth geometry influence on contact
forces distribution
4.1. Numerical experiments
In order to investigate ability of the created model of human
masticatory system for the evaluation of guiding teeth geometry
influence on contact forces distribution in the masticatory system we
performed two numerical experiments. Based on assumption that maximum
occlusal forces are generated and their redistribution is determined by
the character of occlusal contacts in central occlusion, numerical
experiments were performed with the created model's dental arches
set into central occlusion position. Spatial relation of computational
model's dental arches in the position of central occlusion was
calculated mathematically, according to the nature of occlusal contacts,
marked in central occlusion position on gypsum models, made by alginate
impressions of the dental arches of the investigative person.
To evaluate the influence of guiding tooth geometry on contact
forces distribution numerical experiment simulating adjustment of
occlusal interference on the surface of one guiding tooth was performed.
It was assumed that canine guidance is specific to the investigative
subject, therefore occlusal interference on guiding surface of maxillary
right canine (tooth 13) was simulated and redistributions of forces
during the stages of its adjustment were investigated. Initially guiding
elements on palatal surface of tooth 13 were determined and marked based
on occlusal relations of gypsum models of dental arches. According to
markings on gypsum model of the maxillary dental arch corrective plane
involving guiding elements of tooth 13 was delineated on corresponding
tooth in the computational model (Fig. 2, a). It was assumed that
simulated occlusal interference was 0.8 mm height in axis Y if measured
from central occlusion point on the palatal surface of the tooth.
Accordingly, two points of corrective plane were uplifted in axis Y by
0.8 mm (Fig. 2, b). Adjustment of occlusal interference was simulated by
changing the inclination of corrective plane; it was achieved by
lowering two points of the plane in axis Y by 0.2 and 0.5 mm (Fig. 2, c
and d). Therefore, simulating adjustment stages of occlusal interference
on maxillary right canine, calculations were performed and force
redistribution investigated with given height of 0.8, 0.6 and 0.3 mm of
occlusal interference on guiding surface of tooth 13.
4.2. Results
Results of numerical experiment, performed to evaluate the
influence of guiding teeth geometry on contact forces distribution in
masticatory system of healthy subject with non modified geometry dental
arches are presented in Fig. 3 and Table 1.
It is obvious from Fig. 3 that supreme forces acted on the
posterior teeth in both sides of dental arch, articular discs were
loaded nearly symmetrically and with less force; ultimate force vectors
were directed along the axes of teeth, lateral vectors were negligible;
and rotational moments in the centers of resistance of maxillary teeth
were insignificant.
Results of numerical experiment, performed to evaluate the
influence of guiding teeth geometry on contact forces distribution in
simulated clinical situation with simulated occlusal interference on
surface of tooth 13 are presented in Fig. 4 and Tables 2, 3 and 4.
Based on changes of reaction forces and total moments presented in
Table 2 it can be stated that even minimal modification (0.3 mm) of
tooth 13 guiding surface determined significant alterations of reaction
forces and total moments acting the particular tooth. Among three
simulated situations the most beneficial distribution of reaction forces
was established when simulated occlusal interference was of height 0.3
mm, because forces acting on the tooth in axis Z decreased and
proportions between forces acting in axes X and Y persisted similar as
were estimated without modification of tooth's geometry. However,
even such small occlusal interference (0.3 mm) caused approximately
three times increment of forces acting in axes X and Y. Values of
tooth's 13 rotational moment's components in three axes
indicated that diminishing of simulated occlusal interference changed
not only spatial orientation of tooth's rotational axis but also
its tendency of rotation; while strong tendency of driftage forward was
observed during all the stages of numerical experiment.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
Evaluation of total reaction forces showed that with lowering the
simulated occlusal interference total reaction forces of maxillary
dental arch gradually decreased in axis X and increased in axis Y, while
their effects in axis Z changed unevenly; this was caused by significant
change of magnitude and direction of lateral force arisen in teeth 13
when simulated occlusal interference was of height 0.6 mm (Table 3).
During all the stages of numerical experiment the character of
reaction forces in temporomandibular joint articular discs changed
together with the modification of simulated adjustment of occlusal
interference height (Table 4). With non modified geometry of tooth 13 it
was established that both articular discs were loaded nearly equally in
axes X and Y; while magnitudes of forces in axis Z differed almost
twice. The higher was the simulated occlusal interference the stronger
vertical forces (in axis Y) affected right articular disc and the
slighter vertical forces acted on left articular disc; forces in axis X
decreased in both articular discs while lateral forces in axis Z
increased almost twice in right and decreased almost three times in left
articular disc.
5. Conclusions
In accordance with results of the performed numerical experiments
it can be stated that simulated occlusal interference on guiding surface
of tooth 13 determined significant changes of magnitudes and directions
of forces acting the tooth and influenced its tendency for driftage;
also caused changes in loading of the temporomandibular joint discs and
alternated character of total forces acting on the whole maxillary
dental arch. The evaluation of forces alternations during simulated
stages of occlusal interference adjustment demonstrated that the most
beneficial distribution of reaction forces was established when
simulated occlusal interference was reduced to minimal height of 0.3 mm.
However, even such diminutive occlusal interference (0.3 mm) caused
significant increment of deleterious lateral forces. Consequently, the
created three-dimensional finite element model of masticatory system
showed satisfactory efficiency for the evaluation of forces, acting on
guiding tooth when its geometry is modified, because even minimal error
(0.3 mm) of simulated occlusal adjustment caused non physiological
redistribution of forces both in guiding tooth and in temporomandibular
joint discs.
Received February 10, 2010
Accepted May 20, 2010
References
[1.] Jeon, P.D., Turley, P.K., Ting, K. Three-dimensional finite
element analysis of stress in the periodontal ligament of the maxillary
first molar with simulated bone loss. -Am J Orthod Dentofacial Orthop,
2001, 119, p.498-504.
[2.] Mackerle, J. Finite element modelling and simulations in
cardiovascular mechanics and cardiology: A bibliography 1993-2004.
-Computer Methods in Biomechanics & Biomedical Engineering, 2005, 8,
p.59 -581.
[3.] Sermesant, M., Forest, C., Pennec, X., Delingette, H., Ayache,
N. Deformable biomechanical models: Application to 4D cardiac image
analysis. -Medical Image Analysis, 2003, 7, p.475-488.
[4.] Michnik, R., Jurkoj?, J., Pauk, J. Identification of muscles
forces during gait of children with foot disabilities. -Mechanika.
-Kaunas: Technologija, 2009, Nr.6(80), p.48-51.
[5.] Barauskas, R., Gulbinas, A., Barauskas, G., Vanagas, T. Finite
element modeling of cooled-tip probe radiofrequency ablation processes
in liver tissue. Computers in Biology and Medicine, 2008, 38(6),
p.694-708.
[6.] Barauskas, R., Gulbinas, A., Barauskas, G. Investigation of
radiofrequency ablation process in liver tissue by finite element
modeling and experiment. -Medicina. -Kaunas, 2007, 43(4), p.310-325.
[7.] Barauskas, R., Gulbinas, A., Barauskas, G. Finite element
modeling and experimental investigation of infiltration of sodium
chloride solution into in-vitro liver tissue. -Medicina. -Kaunas, 2007,
43(5), p.399-411.
[8.] Sukhun, J.A., Lindqvist, C., Kontio, R. Modelling of orbital
deformation using finite-element analysis. - J. R. Soc. Interface, 2006,
3, p.255-262.
[9.] Gao, C., Tay, F.E.H., Nowinski, W.L. A Finite Element Method
Based Deformable Brain Atlas Suited for Surgery Simulation. -Engineering
in Medicine and Biology Society, 2005, p.4337-4340.
[10.] Mackerle, J. Finite element modelling and simulations in
dentistry: a bibliography 1990-2003. -Comput Methods Biomech Biomed Eng,
2004. 7, p.277-303.
[11.] Correia, A., Piloto, P., Campos, J.C.R., Vaz, M. Finite
element analysis of the mechanical behavior of a partially edentulous
mandible as a function of cancellous bone density. -Rev. Odonto Cienc,
2009, 24(1), p.22-27.
[12.] Alemzadeh, K. Dento-Munch and dento-OS inventions. Digital
Dental News, 2009, 3, p.28-33.
[13.] Bourdiol, P., Mioche, L. Correlations between functional and
occlusal tooth-surface areas and food texture during natural chewing
sequences in humans. -Arch Oral Biol, 2000, 45(8), p.691-699.
[14.] Ciancaglini, R., Gherlone, E.F., Radaelli, G. Association
between loss of occlusal support and symptoms of functional disturbances
of the masticatory system. -J Oral Rehabil, 1999, 26, p.248-253.
[15.] Sato, S., Ohta, M., Sawatari, M., Kawamura, H., Motegi, K.
Occlusal contact areas, occlusal pressure, bite force and masticatory
efficiency in patients with anterior disc displacement of the
temporomandibular joint. -J Oral Rehabil, 1999, 26, p.908-911.
[16.] Tanaka, E., Tanaka, M., Watanabe, M., Del Pozo, R., Tanne, K.
Influences of occlusal and skeletal discrepancies on biomechanical
environment in the TMJ during maximum clenching: an analytic approach
with the finite element method. -J Oral Rehabil, 2001, 28, p.888-894.
[17.] Surna, R. A three-dimensional model of the masticatory
system. -Proc. of 12th Int. Conf. "Mechanika 2007". -Kaunas,
2007, p.203-207.
[18.] Surna, R. Creation of 3D model of human masticatory system.
-Proc. of 13th Int. Conf. "Mechanika 2008". -Kaunas, 2008,
p.213-217.
[19.] Pilei?ikiene, G., Surna, A., Skirbutis, G., Surna, R.,
Barauskas, R. A new technique for the creation of a higher accuracy 3D
geometrical model of the human masticatory system. -Mechanika. -Kaunas:
Technologi ja, 2009, Nr.4(78), p.44-50.
[20.] Pilei?ikiene, G., Surna, A., Barauskas, R., Surna, R.,
Basevicius, A. Finite element analysis of stresses in the maxillary and
mandibular dental arches and TMJ articular discs during clenching into
maximum intercuspation, anterior and unilateral posterior occlusion.
-Stomatologija, Baltic Dental and Maxillofacial Journal, 2007, 9,
p.121-128.
G. Pileicikiene *, A. Surna **, G. Skirbutis ***, R. Barauskas
****, R. Surna *****
* Kaunas University of Medicine, Sukileliii 51, 50106 Kaunas,
Lithuania, E-mail g.pileicikiene@gmail.com
** Kaunas University of Medicine, Sukileliii 51, 50106Kaunas,
Lithuania, E-mail: surna@dent.kmu.lt
*** Kaunas University of Medicine, Sukileliii 51, 50106Kaunas,
Lithuania, E-mail: gediminasskirbutis@yahoo.com
**** Kaunas University of Technology, Studenti 50, 51368 Kaunas,
Lithuania, E-mail: rimantas.barauskas@ktu.lt
***** Kaunas University of Technology, Studenti 50, 51368 Kaunas,
Lithuania, E-mail: surna@ktu.lt
Table 1
Reaction forces of maxillary teeth and temporomandibular joint discs,
calculated during simulated clenching with nonmodified geometry
dental arches
Location of Total reaction Total reaction
force/moment in force in axis force in axis
masticatory system X, N Y,N
Right articular disc -65.154 -125.211
Left articular disc -77.031 -120.901
Tooth 17 19.227 122.091
Tooth 27 20.496 67.718
Tooth 16 0 0
Tooth 26 4.511 233.101
Tooth 15 17.335 44.237
Tooth 25 0 0
Tooth 14 10.331 88.087
Tooth 24 0 0
Tooth 13 12.928 10.078
Teeth 23, 12, 22, 0 0
11, 21
Total force on 84.827 565.311
dental arch
Location of Total reaction Total moment Total moment
force/moment in force in axis in axis in axis
masticatory system Z,N X, Nm Y, Nm
Right articular disc 27.459 -- --
Left articular disc -15.531 -- --
Tooth 17 2.289 0.2129 -0.0392
Tooth 27 -3.606 -0.0447 0.0412
Tooth 16 0 0 0
Tooth 26 32.372 -0.9707 0.0157
Tooth 15 2.637 0.0871 -0.0397
Tooth 25 0 0 0
Tooth 14 -31.499 0.3386 -0.0576
Tooth 24 0 0 0
Tooth 13 9.863 -0.1295 0.0409
Teeth 23, 12, 22, 0 0 0
11, 21
Total force on 12.057 -- --
dental arch
Location of Total moment
force/moment in in axis
masticatory system Z, Nm
Right articular disc --
Left articular disc --
Tooth 17 0.1941
Tooth 27 0.2731
Tooth 16 0
Tooth 26 0.2867
Tooth 15 0.1045
Tooth 25 0
Tooth 14 -0.0435
Tooth 24 0
Tooth 13 0.1279
Teeth 23, 12, 22, 0
11, 21
Total force on --
dental arch
Table 2
Alternations of reaction forces and total moments estimated during
simulated adjustment of occlusal interference (OI) on guiding
surface of tooth 13
Character of Total reaction Total reaction
tooth's geometry force in axis X, N force in axis
modification Y, N
OI=0.8 mm 86.644 51.064
OI=0.6 mm 44.656 51.472
OI=0.3mm 30.511 28.286
Nonmodified 12.928 10.078
Character of Total reaction Total moment Total moment in
tooth's geometry force in axis in axis X, Nm axis Y, Nm
modification Z, N
OI=0.8 mm 10.687 -0.2605 0.1696
OI=0.6 mm -33.646 0.3632 -0.0568
OI=0.3mm 4.921 -0.0602 0.0112
Nonmodified 9.863 -0.1295 0.0409
Character of Total moment
tooth's geometry in axis Z, Nm
modification
OI=0.8 mm 0.8346
OI=0.6 mm 0.3875
OI=0.3mm 0.3074
Nonmodified 0.1279
Table 3
Alternations of total reaction forces on whole maxillary dental arch
estimated during simulated adjustment of occlusal interference (OI)
on guiding surface of tooth 13
Character of Total reaction Total reaction
tooth's geometry force in axis force in axis
modification X, N Y, N
OI=0.8 mm 126.611 545.531
OI=0.6 mm 125.211 542.165
OI=0.3mm 82.629 559.221
Nonmodified 84.827 565.311
Character of Total reaction
tooth's geometry force in axis
modification Z, N
OI=0.8 mm 33.361
OI=0.6 mm -1.253
OI=0.3mm 14.121
Nonmodified 12.057
Table 4
Alternations of reaction forces in temporomandibular joint articular
discs estimated during simulated adjustment of occlusal interference
(OI) on guiding surface of tooth 13
Right articular disc
Character of Total reaction Total reaction
tooth's geometry force in axis force in axis
modification X, N Y, N
OI=0.8 mm -40.157 -159.891
OI=0.6 mm -25.597 -116.35
OI=0.3mm -64.881 -128.61
Character of Total reaction Total reaction
tooth's geometry force in axis force in axis
modification Z, N X, N
OI=0.8 mm 38.873 -60.617
OI=0.6 mm 4.769 -79.239
OI=0.3mm 30.561 -79.941
Left articular disc
Character of Total reaction Total reaction
tooth's geometry force in axis force in axis
modification Y, N Z, N
OI=0.8 mm -106.311 -5.737
OI=0.6 mm -153.111 -15.568
OI=0.3mm -123.591 -17.004
