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D r . C l a u d i o G a n d a r i l l a s F .
FACTORES MECÁNICOS EN PREPARACIONES DENTARIAS
U n i v e r s i d a d A n d r é s B e l l o - F a c u l t a d d e o d o n t o l o g í a - V i ñ a d e l M a r
RESTAURACIONES
Lesiones de CariesLesiones No Cariosas
MalformacionesProblemas Estéticos
Reemplazo de restauracionesIatogrenia
Objetivos de restauraciones:
1. Restaurar forma/función y estética.
2. Promover la integridad de los tejidos duros y blandos de la cavidad oral.
3. Promover salud y bienestar de los pacientes.
Adecuado diagnósticoBiomaterialesTécnica clínica
Preparación dentaria
RESTAURACIONESEXITOSAS
Forma artificial que se da a un diente para poder reconstruirlo con materiales y técnicas adecuadas que devuelvan su función
dentro del aparato masticatorio.
Preparación Dentaria
Cavidad Muñón Planos radiculares Biseles
Asperización
Preparación Dentaria Tipos de Preparaciones / Restauraciones
ExtracoronariaIntracoronaria
OPERATORIA PROTESIS FIJA
Restauraciones de cobertura no completaRestauraciones Intracoronarias Restauraciones Extracoronarias
DIRECTAS INDIRECTAS
!
!
!
!
!
!
INDIRECTAS
Amalgamas
Resinas
Inlays
Onlays
Coronas
Carillas
RESTAURACIONES DENTARIAS
INDIRECTAS
Forma de Anclaje
DIRECTAS
Forma de Retención
!!
!!
• Eliminar todos los defectos y dar la protección necesaria a la pulpa dental.
• Situar los márgenes de la restauración de la forma más conservadora posible.
• Dar forma adecuada de modo que las fuerzas masticatorias sobre el diente,
restauración o ambos no produzcan fracturas ni desplacen la restauración.
• Permitir la aplicación estética y funcional de un material restaurador.
OBJETIVOS:
Preparación Dentaria Preparación Dentaria
Factores Biológicos
Factores MecánicosPrincipios biomecánicos
Planimetria cavitaria
Mecánica: Parte de la física que estudia el movimiento y el equilibrio de los cuerpos, así como de las fuerzas que los producen.
RETENCIÓN
Principio Biomecánico definido como:
Fuerzas que se oponen a la extrusión de la restauración a lo largo del eje de inserción de la restauración.
• Paredes axiales de una cavidad• Paredes axiales de un muñón• Paredes internas de conducto protésico• Anclajes complementarios
Dada por fricción o roce entre las paredes axiales de la preparación dentaria y la restauración:
RETENCIÓN
La Retención depende de:
• Conicidad/paralelismo de paredes contrapuestas• Longitud de paredes opuestas• Diámetro de la preparación• Retenciones auxiliares
La Retención es Potenciada por:
• Paredes largas, lisas y paralelas• Ángulos Marcados• Correcta correspondencia de superficies
¿Que otorga principalmente la retención en cavidades expulsivas?
El elemento esencial de la retención lo constituyen el paralelismo entre dos superficies dentarias verticales opuestas entre si que pertenecen a la misma preparación dentaria.
PARALELISMO ENTRE PAREDES
Paralelismo
FORMAS DE RETENCIÓN
Por retención (socavado)
FORMAS DE RETENCIÓN
Compresión
FORMAS DE RETENCIÓN
Profundización
FORMAS DE RETENCIÓN
/ Mortaja
! !
Cola de Milano
D M
Vista Oclusal
FORMAS DE RETENCIÓN
Principio biomecánico definido como toda FUERZA que se opone a la intrusión de la
restauración.
Lo otorgan las superficies de la preparación dentaria que no son paralelas a las fuerzas de intrusión (paredes oblicuas y perpendiculares)
SOPORTE
!
ANCLAJE
Lo que impide que una restauración se desaloje o se mueva de su posición sin estar sometida a cargas funcionales.
Depende principalmente de la Retención.
Lo que impide que una restauración se desaloje o se mueva de su posición bajo la acción de fuerzas funcionales o parafuncionales.
Este principio también se conoce como “estabilidad funcional”
ESTABILIDAD (RESISTENCIA) Fuerzas que actúan sobre los dientes
Comprensivas Traccionales Tangenciales
ESTABILIDAD (RESISTENCIA)Fuerzas que actúan sobre los dientes
f: fuerza masticatoria
ESTABILIDAD (RESISTENCIA)Fuerzas que actúan sobre los dientes
f: fuerza masticatoria
L = f tang. alfa
FUERZA LATERAL (L)
alfa=8f: fuerza=10 kg.
fuerza lateral = 70 kg.
Efecto Cuña
A mayor Altura cuspídea plano inclinado de mayor ángulo
Mayor posibilidad de fractura
Teoría de Robinson
Estudio de las tensiones con diferentes diseños cavitarios
Estudio del efecto cuña de las restauraciones sobre lo dientes:
Recubrimiento cuspídeoDisminución de la altura cuspídea.Ángulos diedros redondedos
FOTO
ELAS
TICI
DAD
542 d e n t a l m a t e r i a l s 2 3 ( 2 0 0 7 ) 539–548
(enamel and dentin) are automatically created in the form ofmasks by growing a threshold region on the entire stack ofscans (Fig. 1B). Using MIMICS STL+ module, enamel (Fig. 2A)and dentin were then separately converted into stereolithog-raphy files (STL, bilinear and interplane interpolation algo-rithm). Native STLs are improper for use in FEA because ofthe aspect ratio and connectivity of the triangles in these files.The REMESH module attached to MIMICS was therefore usedto automatically reduce the amount of triangles and simulta-neously improve the quality of the triangles while maintainingthe geometry (Fig. 2B). During remesh, the tolerance variationfrom the original data can be specified (quality of trianglesdoes not mean tolerance variation from the original data). Thequality is defined as a measure of triangle height/base ratioso that the file can be imported in the finite element anal-
Fig. 2 – (A) Stereolithography triangulated (STL) file ofenamel obtained through the STL+ module within MIMICS.The density and quality (aspect ratio and connectivity) ofthe triangles is not appropriate for use in finite elementanalysis. (B) Enamel STL file optimized for FEA using theREMESH module within MIMICS. Note the improvedtriangle shape and the intact geometry compared to Fig. 2Ain spite of a significant reduction in number of triangles.
Tabl
e2
–FE
Age
omet
ryan
dch
arac
teri
stic
sfo
rth
edi
ffer
ent
mod
els
Mod
ella
bel
Des
crip
tion
Spec
ific
feat
ure
sV
olu
met
ric
mes
h
No.
ofel
emen
tsa
No.
ofn
odes
a
NA
TIn
tact
nat
ura
ltoo
th(u
nre
stor
ed)
Man
dib
ula
rm
olar
1293
7427
223
CA
VM
OU
nre
stor
edto
oth
wit
hM
Op
rep
arat
ion
Occ
lusa
lwid
th:1
/2in
terc
usp
.wid
th;o
cclu
sald
epth
:>3
mm
;p
roxi
mal
dep
th:1
mm
abov
eC
EJ;d
ista
lmar
gin
alri
dge
inta
ct10
6817
2351
9
CA
VM
OD
Un
rest
ored
toot
hw
ith
MO
Dp
rep
arat
ion
Occ
lusa
lwid
th:1
/2in
terc
usp
.wid
th;o
cclu
sald
epth
:>3
mm
;p
roxi
mal
dep
th:1
mm
abov
eC
EJ95
826
2151
0
END
OM
OU
nre
stor
edto
oth
wit
hM
Op
rep
arat
ion
and
end
odon
tic
acce
ssp
rep
arat
ion
End
odon
tic
acce
ssca
vity
rem
ovin
gin
tact
wal
lwit
had
jace
nt
box.
1136
0325
554
END
OM
OD
Un
rest
ored
toot
hw
ith
MO
Dp
rep
arat
ion
and
end
odon
tic
acce
ssp
rep
arat
ion
End
odon
tic
acce
ssca
vity
rem
ovin
gin
tact
wal
lsw
ith
both
adja
cen
tbo
xes
1026
1223
432
CPR
Toot
hre
stor
edw
ith
MO
Dco
mp
osit
ere
stor
atio
nR
esto
rati
onsi
zesi
mila
rto
CA
V12
9374
2722
3
CER
Toot
hre
stor
edw
ith
MO
Dfe
ldsp
ath
icce
ram
icre
stor
atio
nR
esto
rati
onsi
zesi
mila
rto
CA
V12
9374
2722
3
aSt
one
base
excl
ud
ed.
d e n t a l m a t e r i a l s 2 3 ( 2 0 0 7 ) 539–548 543
ysis software package without generating any problem. Theremesh operations were also applied to the dentin STL. Seg-mentation of enamel and dentin may be accomplished by atrained operator in ca. 90 min (including remesh of the STLfiles).
Third, a strereolithography handling software (MAGICS 9.9,Materialise, Leuven Belgium) was used in order to reestab-lish the congruence of the interfacial mesh between enameland dentin (this congruence being lost during the previousremeshing process) using Boolean operations (addition, inter-
Fig. 3 – (A) Cross-sectional view of the enamel–dentin assembly as seen in MAGICS. Both enamel and dentin STLs share theexact same geometry at their interface (dentinoenamel junction). (B). Congruent enamel (white) and dentin (yellow) meshesalong with CAD objects used to simulate a stone base (cylinder) and different cavity designs (red inserts). Mesh congruencebetween the root portion and the stone base was obtained through a Boolean subtraction process (stone cylinder minusdentin). (C). Congruent STL parts of enamel (white) and dentin (yellow) resulting from Boolean intersections andsubstractions between the original enamel/dentin STLs and different CAD inserts (right side). The assembly of the differentparts result in five possible models (left side), i.e. the natural tooth (NAT), MO and MOD cavities (CAV), MO and MODendodontic access preparations (ENDO). The NAT model was also used to simulate a composite resin inlay (CPR) and aporcelain inlay (CER) by attributing different material properties to the enamel and dentin inserts (see Table 2).
section or subtraction of volumes). Once a congruent mesh atthe dentinoenamel junction was obtained (Fig. 3A), additionalBoolean operations with CAD objects (Fig. 3B and C) were usedto simulate a cylindrical fixation base (embedding the rootwithin 2 mm of the cementoenamel junction), as well as dif-ferent cavity preparations (MO and MOD cavities, endodonticaccess cavities) and restorations. The exact design and dimen-sions of the MO, MOD and endodontic access cavities aredescribed in Table 2. These successive restorative situationswere chosen because they reproduce existing experiments
ANALISIS DE ELEMENTO FINITO546 d e n t a l m a t e r i a l s 2 3 ( 2 0 0 7 ) 539–548
Fig. 6 – First principal stress distribution in four of the seven models studied. To allow for better comparison of the stresspattern, the MOD insert of enamel and dentin (model NAT) or the MOD ceramic restoration (model CER) were made invisible.Colors, tensile stresses; gray, compressive stresses. Note the similarity between NAT and CER.
approaches were proposed to access the inner anatomicaldetail without extrapolation and accelerate the productionof the models. Verdonschot et al. [13] might have been thefirst authors to describe the development of a 3D finite ele-ment model of a restored tooth based on a microscale CTdata-acquisition technique. The tooth was scanned after beingrestored with an MOD composite and the 3D geometry wasobtained through the stacking of traced 2D sections, stillinvolving a significant amount of manual work. An interest-ing semi-automated method was proposed [6–8] to generatesolid models of bones without internal boundaries (plain auto-matic volumetric mesh), then using the Hounsfield unit (HU)to attribute a specific Young’s modulus to each element basedon scan density. When applied to small structures like teeth(with thin anatomical details such as the enamel shell), thistechnique does not allow the fine control of internal bound-aries (e.g. dentinoenamel junction), the exact geometry ofwhich will have to follow the automatic volumetric meshingprocess.
The approach used in the present study suggests thatmaximum anatomical detail is obtained by surface/interface-based meshing using stereolithography (STL) surface data.The different parts of the model featuring different mechan-ical properties are identified first (segmentation process) andmeshed accordingly. Elements do not overlap the differentstructures but strictly follow the internal boundaries, resulting
in a smooth and very well controlled representation of inter-faces like the dentinoenamel junction (Fig. 3A). Significantadvantages, when using STLs, are the sophisticated visual-ization tools (shaded wireframe 3D views, section views etc.)and possibilities offered by the Boolean operations. The gen-eral principle of Boolean operations is that a new object can beformed by combining two 3D objects. Objects can be united,intersected or subtracted. When intersecting or subtractingtwo overlapping objects, a congruent mesh is assured at theinterface between the new objects. This property is essen-tial to assure the continuity of the resulting volumetric mesh.Boolean operations with predefined CAD objects (box, cylin-der, cone or inserts as in Fig. 3B) constitute an importantfeature. It allowed us to “digitally” simulate successive restora-tive procedures (Fig. 3C), unlike Verdonschot et al. [13] whohad to “physically” restore the tooth before scanning it. In thepresent study, the geometry of the unaltered tooth remains,allowing for direct comparison with the different experimen-tal conditions. The very user-friendly graphic interface allowsfor rapid modifications of the different parts and generationsof new STLs that can be instantly exported and volumetricallymeshed the FEA program. It must be pointed out that micro-CTis not suitable for human teeth in live patients. However, con-sidering that only 81 slices were necessary to generate thesevalid FEA models, one can easily foresee that the exponentialdevelopment of commercial dental CT-scanners, computer
544 d e n t a l m a t e r i a l s 2 3 ( 2 0 0 7 ) 539–548
Table 3 – Material properties
Elastic modulus (GPa) Poisson’s ratio
Enamel 84.1a 0.30b
Dentin 18.6c 0.31d
Composite 10.0e 0.24f
Ceramic 78.0g 0.28a
a Craig et al. [25].b Anusavice and Hojjatie [24].c McGuiness et al. [28].d Farah et al. [27].e Eldiwany et al. [26].f Nakayama et al. [29].g Data from manuftacturer of Creation-Willi Geller dental porcelain
(Klema, Meiningen, Austria).
[14–16], which will be used in the validation process of the FEAmodel (see Section 3). Two additional experimental conditionswere generated by attributing different material properties tothe enamel and dentin inserts included in model NAT: a com-posite resin inlay (CPR) and a feldspathic ceramic inlay (CER).The treatment of the STL files in MAGICS may be accomplishedby a trained operator in ca. 30–60 min per model (including allBoolean operations).
Fourth, the optimized STL files of the segmented enameland dentin parts were then imported in a finite element anal-ysis software package (MSC.Marc/MSC.Mentat, MSC.Software,Santa Ana, CA) for the generation of a volumetric mesh andattribution of material properties (Table 3). The triangulatedSTL files are ideal for automatic mesh generation using atetrahedral mesher (tetrahedron elements with pyramid-likeshape and 4 nodal points). This last step may be accomplishedby a trained operator in ca. 30–60 min per model (includingattribution of boundary conditions and 17 min to run the anal-ysis).
2.2. Boundary conditions, loadcase and dataprocessing
Fixed zero-displacement in the three spatial dimensions wasassigned to the nodes at the bottom surface of the stone base.The tooth and restorative materials were taken as bonded,which simulate usage of adhesive luting cements. A uniformlyramp loading was applied to the mesial cusps through a rigidbody, i.e. a 9.5-mm diameter ball positioned as close as possi-ble to the tooth (Fig. 4). The tooth was defined as deformablecontact body. Contact between these bodies was determinedautomatically by the FEA simulation during the static mechan-ical loadcase (no inertia effects) with a uniform stepping pro-cedure of 10 steps. A motion was applied to the rigid ball alongthe Z-axis through a negative velocity of 0.02 mm per step.Only one step was required to reach contact in both cusps. Themotion continued for the remaining steps to reach a total force100–200 N on the ball (depending on the model). The stress andstrain distributions were solved using the MSC.Marc solver. Asmentioned before, these specific boundary conditions, loadprotocol and configuration were chosen because they repro-duce existing experiments by Panitvisai and Messer [14], andJantarat et al. [15,16].
Fig. 4 – Load protocol and configuration as seen in Mentat,i.e. a nonlinear contact analysis between a rigid body(9.5-mm diameter load sphere moving along Z-axis againstthe tooth) and a deformable tooth (CAV MOD shown here).The widening of the cusps (!v) was calculated from theoutput values of displacement along the Y-axis for selectednodes near the cusp tip.
3. Results
The post-processing file was accessed through MENTAT toselect specific nodes on the buccal and lingual enamel nearthe cusp tip and to collect the values of displacement inthe Y direction for each loading step (Y+ denotes displace-ment in lingual direction and Y− in buccal direction). Theforce along the Z-axis on the rigid ball was also collectedfor each step. After the transfer of these data to a spread-sheet, the widening (deformation) of the cusp was calculated(by summing the displacement of each cusp) and plottedagainst the force along Z-axis on the ball (Fig. 5). As expectedin an elastic simulation, there is a quasi-linear relationshipbetween load and deformation. The progressive loss of toothsubstance (MO to MOD to ENDO) translates into a progres-sive loss of cuspal stiffness (decreased slope of the force vs.deformation plot). The unrestored tooth (NAT) and the toothwith the MOD ceramic inlay (CER) display the same con-duct (100% recovery of cuspal stiffness), while the more flex-ible composite inlay allowed for partial of recovery of cuspalstiffness.
ANALISIS DE ELEMENTO FINITO
Concepto de Ingraham
Preparaciones dentarias para incrustaciones metálicas de clase I y II que no protegen las cúspides favorecen la fractura dentaria
Concepto de Ingraham Concepto de IngrahamConcepto de Vigas
Tipos de vigas Viga simple apoyada
Viga fija y libre Viga a extremo libre
cantilever - voladizo
Viga empotrada en sus extremos
P3
Tensión máxima que resiste una viga:
Proporcional a su ancho en sentido horizontal
Proporcional al cuadrado de su espesor en sentido vertical
Resistencia de las vigas:
a b c
1x 2x4x
en Preparaciones DentariasAPLICACIÓN PRINCIPIOS BIOMECÁNICOS Tamaño cavitario y resistencia de paredes
• Cavidades conservadoras aumentan resistencia del remanente
• Resistencia de paredes: determina el tipo de restauración
• Concepto de esmalte sostenido idealmente (no valido para RC)
• Seguir la dirección de los prismas (ángulo cavo superficial).
a)
b)
c)
Ángulo Cavo Superficial
Ángulo Cervical FLEXIÓN DE PISO
• La flexión es mayor cuando el espesor dentinario es menor.
• Siempre deben existir puntos de
apoyo en tejido firme.• Piso cavitario plano.
dolor y/o fractura
FLEXIÓN DE PISO CONCLUSIÓN
• Siempre tener presente que una cavidad implica perdida de integridad dentaria.
• Capacidad de determinar mejor opción de tratamiento de acuerdo a la pérdida de tejido (intracoronaria, extracoronaria, recubrimiento cuspideo)
• Aplicar conceptos básicos de mecánica aplicados al diente al momento de tallar nuestra cavidad.
• Aplicar siempre lo aprendido en relación a las características cavitarias para cada tipo de restauración.