applied
sciences
A icle
Mechanical E alua ion o Implan -Assis ed Remo able Pa ial
Den u es in Kennedy Class I Pa ien s: Fini e Elemen
Design Conside a ions
Ana Messias 1, Ma ia A. Ne o 2,* , Ana M. Ama o 2, Ví o M. Lopes 3and Ped o Nicolau 1


Ci a ion: Messias, A.; Ne o, M.A.;
Ama o, A.M.; Lopes, V.M.; Nicolau, P.
Mechanical E alua ion o
Implan -Assis ed Remo able Pa ial
Den u es in Kennedy Class I Pa ien s:
Fini e Elemen Design Conside a ions.
Appl. Sci. 2021,11, 659. h ps://
doi.o g/10.3390/app11020659
Recei ed: 21 Decembe 2020
Accep ed: 8 Janua y 2021
Published: 12 Janua y 2021
Publishe ’s No e: MDPI s ays neu-
al wi h ega d o ju isdic ional clai-
ms in published maps and ins i u io-
nal a ilia ions.
Copy igh : © 2021 by he au ho s. Li-
censee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and con-
di ions o he C ea i e Commons A -
ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
1Depa men o Den is y, Cen e o Mechanical Enginee ing, Ma e ials and P ocesses (CEMMPRE),
Uni e si y o Coimb a, 3030-788 Coimb a, Po ugal; [email p o ec ed] (A.M.);
[email p o ec ed] (P.N.)
2Depa men o Mechanical Enginee ing, Cen e o Mechanical Enginee ing, Ma e ials and
P ocesses (CEMMPRE), Uni e si y o Coimb a, 3030-788 Coimb a, Po ugal; ana.ama [email p o ec ed]
3Depa men o Mechanical Enginee ing, Uni e si y o Coimb a, 3030-788 Coimb a, Po ugal;
[email p o ec ed]
*Co espondence: [email p o ec ed]; Tel.: +351-239790700
Abs ac :
The main pu pose o his wo k was o cons uc a clinically alid nume ical model o a
mandibula Kennedy class I pa ien ehabili a ed wi h a con en ional emo able pa ial den u e and
ano he wo wi h implan -assis ed emo able pa ial den u es a wo di e en implan loca ions. The
selec ed pa ien was classi ied as ASA I and i s mandible geome y econs uc ion was pe o med
by he con e sion o he Cone-Beam compu ed Tomog aphy (CBCT) scan aw medical da a in o a
3D model and subsequen con e sion o a CAD ile by e e se enginee ing me hods. The so issue
and emo able den u e geome ies we e also included in he CAD model as well as implan s, ball
a achmen s and ma ix. Mo eo e , pe iodon al ligamen was modelled by o se ing he mesh o
he oo su ace o each oo h. The ini e elemen esul s showed ha he ins alla ion o a den al
implan in each o he bila e al eden ulous egions helps p o iding suppo and e en ion o he
ex ension bases o he Remo able Pa ial Den u e (RPD) and signi ican ly educes he e ical and
an e io -pos e io displacemen s, ega dless o i s posi ion.
Keywo ds:
implan ; emo able pa ial den u es; ini e elemen me hod; Mandibula Kennedy Class I
1. In oduc ion
The use o clasp- e ained emo able pa ial den u es has been a popula op ion among
pa ien s and clinicians o ehabili a e pa ien s wi h pa ial eden ulism due o he non-
in asi e na u e o he ea men and ai cos -e iciency ela ionship on he sho - e m [
1
,
2
].
Howe e , on he long- e m, his cos -e iciency ela ionship is dis u bed by he limi a ions
o a emo able pa ial den u e, which ine i ably leads o pa ien dissa is ac ion and a d op
o he usage a e, pa icula ly, in he case o mandibula dis al ex ension den u es [3–5].
To educe some o hese limi a ions, he adjunc i e use o den al implan s wi h o
wi hou e en i e elemen s ha e been p oposed by se e al au ho s [
6
–
10
] and a e called
implan -assis ed emo able pa ial den u es. The ypical indica ions o implan -assis ed
emo able pa ial den u es a e si ua ions o Kennedy Class I and II eden ulism, pa icula ly
wi h long eden ulous spans, and Kennedy class IV si ua ions, o si ua ions o pa ien e usal
o wea den u es wi h comple e pala al co e age o isible clasp assemblies and insu icien
e en ion in he exis ing emo able pa ial den u es. In hese cases, he ype o implan o
use and he posi ion wi hin he eden ulous si es, as well as he ype o e en i e elemen s,
is a decision o he clinician, o en based on su gical, aes he ic o economic c i e ia [11].
The clinical guidelines and p inciples o he design o implan -assis ed emo able
pa ial den u es p oposed by G ossmann e al. [
12
] in pa ien si ua ions o Kennedy Class I
eden ulism indica e ha pe eden ulous a ea, one implan should be inse ed as dis ally as
Appl. Sci. 2021,11, 659. h ps://doi.o g/10.3390/app11020659 h ps://www.mdpi.com/jou nal/applsci
Appl. Sci. 2021,11, 659 2 o 18
possible o p o ide maximal suppo and s abili y, pa icula ly in he mandible. Howe e ,
hey also admi he possibili y o placing he implan s in a mesial posi ion adjacen o
he abu men ee h (na u al ee h suppo ing and e aining a emo able pa ial den u e),
whene e hese a e poo o p o ide suppo o o a oid unes he ic clasps in maxilla y
ehabili a ions. Only wo non-clinical s udies conside ed in he wo k o G ossmann e al.
comp ised he biomechanical e alua ion o he use o den al implan s in mandibula
Kennedy Class I si ua ions, ha is he s udy o mo emen and de o ma ion o he biological
s uc u es (abu men ee h, bone, mucosa, e c.) unde o ces applied o e he p os hesis and
implan s. One o hose s udies, pe o med by Ohkubo e al. [
13
], used an expe imen al se up
o measu e he p essu e unde a con en ional o an implan -assis ed emo able pa ial
den u e wi h he implan s placed dis ally. The esul s indica ed ha he implan suppo
con ibu ed o he educ ion o displacemen a he dis al ex ension o he emo able
pa ial den u es and dec eased he p essu e on so issues. The o he s udy [
14
] also
conside ed in he abo e-men ioned e ision, e alua ed he biomechanical e icacy o
placing implan s unde nea h he den u e base o ob ain s able occlusal suppo , using an
in-silico bi-dimensional model. The au ho s conside ed he possibili y o implan suppo
in he dis al (second mola ), mesial ( i s p emola ) o in e media e posi ion (second
p emola ). Compa ed o he con en ional emo able pa ial den u e op ion, he leas s ess
was ob ained a he empo omandibula join using he implan in he dis al posi ion,
ollowed by he in e media e and mesial posi ions.
The s udy o Maeda e al. was he i s o use he ini e elemen me hod (FEM)
o e alua e he biomechanical e ec o he implan suppo in he s uc u es in ol ed,
namely den u e, mandibula bone and empo omandibula join . In he ime ollowing
ha s udy, se e al esea che s ha e been using he ini e elemen me hod o e alua e he
s ess dis ibu ion o e he mandibula bone due o he sc ewed o e den u e posi ioned
on den al implan s [
15
–
20
]. In his s udy, h ee-dimensional ini e elemen analysis is also
used o cla i y he c i e ia o implan posi ioning wi hin he eden ulous span in p os he ic
ea men s wi h IARPD (implan assis ed emo able pa ial den u es). The p ima y aim
is achie ed by e alua ing he di e en pa e ns o s ess in he p os he ic s uc u e o
a ia ions o he implan posi ioning in he eden ulous a ea.
2. Ma e ials and Me hods
2.1. Geome ical Models
Th ee-dimensional ini e elemen models o IARPDs wi h wo di e en implan loca-
ions and one con en ional RPD, ha is, a oo h assis ed RPD, we e cons uc ed based on
he econs uc ion o he CBCT Kennedy Class I pa ien . The h ee ini e elemen models
we e iden i ied as: he con en ional RPD; he IARPD PREMOLARS (IARPD PM), p esen -
ing he implan s a he p emola egions; he IARPD MOLARS (IARPD MO), wi h he
implan s placed in he mola ’s egion. The selec ed pa ien showed no signs o ele an
sys emic o o al diseases, including se e e pe iodon al disease, and p esen ed mandibu-
la bila e al pos e io eden ulism missing h ee ee h pe eden ulous si e and mode a e
eso p ion o he esidual idges.
The geome ies o he compac and abecula bones o he mandible we e c ea ed
by he con e sion o he CBCT scan aw medical da a in o 3D models and subsequen
con e sion o a CAD ile by e e se enginee ing me hods. Simila ly, o he p ocess o
segmen a ion o he mandible bones, ee h segmen a ion allowed sepa a ing abu men
ee h (34, 33, 43, 44) om he emaining ee h, while pe iodon al ligamen s we e modelled
by o se ing he mesh o he oo su ace o each oo h (34, 33, 43, 44) by 0.25 o 0.3 mm. The
3D geome ical model o he ac ylic po ion o he RPD was ob ained om he scanning o
a con en ional den u e, which had been c ea ed o e he plas e mode o he pa ien , using
he inEOS
®
X5 labo a o y scanne (Si ona Den al Sys ems Inc., Long Island Ci y, NY, USA).
The 3D model o he me al amewo k o he RPD was c ea ed o e he scanned plas e
model using he 3Shape Den al Sys em
™
so wa e and, pos e io ly, assembled wi h he
ac ylics o he 3 d and 4 h quad an s. Mo eo e , he ex e nal su ace o he mandibula
Appl. Sci. 2021,11, 659 3 o 18
plas e model o he pa ien was also scanned o c ea e a 3D model o he co onal po ion
o he emaining ee h and so issue o he eden ulous a eas.
The implan s we e c ea ed using s CAD ools (Solidwo ks
®
2014, Dassaul Sys èmes
P e. L d., Singapo e) a e ea u e ex ac ion o he speci ic geome ical dimensions om
o icial images o S aumann S anda d Plus implan s (Ø 4.1 mm) wi h egula pla o m and
10 mm long p o ided by he manu ac u e (Ins i u S aumann AG, Basel, Swi ze land).
A ball a achmen (pa ix) and co esponding ma ix we e also c ea ed o es ablish he
connec ion be ween p os hesis and he implan . In he assemblage o IARPD models he
implan s we e placed as pa allel as possible o he abu men ee h in he egions o he
second p emola (Model IARPD PM) and o he ex emi y o me allic amewo k (Model
IARPD MO), which co esponded o he i ual posi ion o he i s mola . To model he
implan -bone con ac , he implan s we e hen immed om he co ical and cancellous
bone bodies using Boolean ope a ions. The same ope a ion was pe o med on he so
issue body o c ea e he space equi ed o he ansmucosal po ion o he implan . The
ma ices we e aligned wi h he ball a achmen s o he implan s and housed wi hin he
amewo k. The ac ylic po ions o he p os heses we e also modi ied o accommoda e he
implan s, ball a achmen s and ma ices.
A single pla e was c ea ed o apply he p esc ibed load uni o mly o e he ac ylic
ee h o he emo able pa ial den u e. The pla e was ske ched in he ho izon al plane
o he mandible (pa allel o he occlusal plane) and e ically ex uded o ob ain a inal
hickness o 10 mm. Addi ionally, a 10 mm diame e ci cle was included in he geome ic
cen e o he ske ch and ex uded 25 mm o o ce applica ion. A e he assembly o all
componen s o he models wi h implan -assis ed emo able pa ial den u es, he solid
bodies we e expo ed in he o ma o single Pa asolid bina y iles.
2.2. Nume ical Models
Each one o he h ee model iles was impo ed in o he ADINA sys em o linea and
nonlinea ini e elemen analysis (ADINA AUI e sion 9.3.1, ADINA R&D Inc., Wa e own,
WA, USA) including he ollowing bodies: co ical bone and non-abu men ee h; indi idu-
alized abu men ee h (34, 33, 43, 44); indi idualized pe iodon al ligamen s o he abu men
ee h (34, 33, 43, 44); cancellous bone; so issue (3 d and 4 h quad an s); me al amewo k
o he emo able pa ial den u e (including 2 ma ices in he case o he Models IARPD
PM and IARPD MO); ac ylic den u e bases wi h he missing ee h (3 d and 4 h quad an s);
implan s and ball a achmen s (Models IARPD PM and IARPD MO); loading pla e.
In bo h nume ical models o he IARPDs he implan s we e assumed bonded wi h
cancellous and co ical bones, simula ing comple e osseoin eg a ion. Mo eo e , he glue
mesh op ion was also used o model he a achmen o o he pai s o componen s o emain
pe ec ly bonded oge he , such as he inne su aces o he co ical bone and he ou e
su aces o he cancellous bone o he inne and ou e su aces o he pe iodon al ligamen
and he ee h and bone, espec i ely. Ne e heless, he Lag ange mul iplie echnique was
used o impose con ac cons ain condi ions, assu ing he possibili y o ela i e mo ion
be ween he su aces o he ollowing con ac pai s: implan /so - issue; so - issue/ac ylic;
so - issue/ amewo k; amewo k/ ee h; ee h-p emola / ee h-canine; ee h/co ical; and
ac ylic/implan .
Assignmen o he mesh densi y o he solid bodies o each model was made by
p omo ing equally spaced subdi isions o he bodies using he desi ed elemen edge leng h.
In some cases, he subdi ision o speci ic aces was ecalcula ed wi h smalle leng hs o
p omo e a mo e e ined mesh in a eas equi ing highe p ecision o he esul s. Table 1
p esen s he mesh densi y a ibu ed o each body and he e inemen a eas. Disc e iza ion
o he domains was assu ed by he Delaunay ee- o m meshing algo i hm o gene a e
8-node hexahed al (b ick) elemen s wi h mixed in e pola ion o mula ion (displacemen
and p essu e-based), conside ing a cons an p essu e (1 deg ee o eedom). Fo elemen s
wi h linea elas ic ma e ial p ope ies, addi ional displacemen deg ees o eedom we e
Appl. Sci. 2021,11, 659 4 o 18
allowed by selec ing he incompa ible modes op ion. The o al numbe o nodes and
elemen s o each model a e de ailed in Table 2.
Table 1.
Desc ip ion o he leng h o elemen edge a ibu ed o each body and he e inemen a eas.
Body Leng h (mm) Re inemen Zone (mm)
Co ical bone 1 Implan s egion (0.5)
Al eolus egion (0.25)
Cancellous bone 1 Implan s egion (0.5)
Tee h 0.5 Roo leng h (0.25)
Loading Pla e 1 Ac ylic con ac egion (0.5)
So issue 0.5 -
Implan s 0.5 -
Ac ylic 0.5 -
F amewo k 0.5 -
Pe iodon al Ligamen 0.25 -
Table 2. Desc ip ion o he o al numbe o elemen s and nodes pe model.
Con en ional IARPD PM IARPD MO
Elemen s 871,851 889,884 857,671
Nodes 506,375 472,936 478,075
2.3. Nume ical Models
This s udy assumed iso opic linea elas ic p ope ies o he co ical and cancellous
bones, ee h, amewo k, ac ylic, implan s, ball a achmen s and loading pla e bu no o
he o al so issues. These, i.e., o al mucosa and pe iodon al ligamen , we e modelled
conside ing non-linea hype elas ic p ope ies. Se e al models ha e been p oposed o
model he hype elas ic e ec s o biological so issues [
21
]. Ne e heless, he app oxi-
ma ion p oposed by Ogden [
22
,
23
] p o ides he closes ma ching o expe imen al da a
and was he ein conside ed o he modelling o bo h he o al mucosa and he pe iodon al
ligamen . The mechanical p ope ies o he ma e ials displaying a linea o ce-displacemen
ela ionship as implied in Hooke’s law a e p esen ed in Table 3.
Table 3. Mechanical p ope ies o he iso opic linea elas ic ma e ials.
Ma e ial Young’s Modulus (GPa) Poisson’ Ra io
Co ical Bone 20.0 [24–26] 0.30
Cancellous bone 1.37 [24,27] 0.30
Tee h (den in) 13.0 [28] 0.37
Ch omium-cobal 211 [29] 0.30
Ac ylic 2.20 [29] 0.31
Ti anium g ade 4 110 0.32
S ainless s eel 180 0.30
The nonlinea cons i u i e models o he o al mucosa and o pe iodon al ligamen s
we e de i ed om a s ain ene gy densi y unc ion (SEDF), W, which is de ined pe
uni o e e ence olume (ADINA R&D 2012). This model is based di ec ly on p incipal
s e ches ins ead o in a ian s o de e mine he de ia o ic s ain ene gy unc ion (WD)
and accoun s o olume ic comp essibili y by he inclusion o a e m o he olume ic
s ain ene gy densi y (ADINA R&D 2012). In he case o he o al mucosa, he s ain
ene gy densi y unc ion was se based on he i ing o a uniaxial s ess–s ain cu e om
expe imen al da a epo ed by Kishi e al. in 1972 ci ed in Chen e al. [
30
], using a Ogden 9 h
Appl. Sci. 2021,11, 659 5 o 18
o de app oxima ion ob ained by he me hod o singula alue decomposi ion. Simila ly,
he pe iodon al ligamen ma e ial p ope ies we e ob ained om he da a o po cine
pe iodon al ligamen s subjec ed o uniaxial ensile es s ha we e pe o med along he
ibbe di ec ion, as epo ed by Na ali e al. [
31
] and Nishihi a e al. [
32
]. The cu e i ing
p ocedu e o he Ogden unc ion was also ob ained by singula alue decomposi ion and
9 h o de app oxima ion.
2.4. Loading and Bounda y Condi ions
Bounda y condi ions we e applied in he condyles o he mandible and in he inse ion
a eas o he mas ica ion muscles. Thus, as shown in Figu e 1, all h ee nodal deg ees o
eedom we e ixed in he inse ion o he masse e muscle in he lowe bo de o he
mandible and in he inse ion o he medial p e ygoid, he middle empo alis, and he
la e al p e ygoid muscles in he co onoid p ocess.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 o 18
The nonlinea cons i u i e models o he o al mucosa and o pe iodon al ligamen s
we e de i ed om a s ain ene gy densi y unc ion (SEDF), W, which is de ined pe uni
o e e ence olume (ADINA R&D 2012). This model is based di ec ly on p incipal
s e ches ins ead o in a ian s o de e mine he de ia o ic s ain ene gy unc ion (WD)
and accoun s o olume ic comp essibili y by he inclusion o a e m o he olume ic
s ain ene gy densi y (ADINA R&D 2012). In he case o he o al mucosa, he s ain ene gy
densi y unc ion was se based on he i ing o a uniaxial s ess–s ain cu e om expe -
imen al da a epo ed by Kishi e al. in 1972 ci ed in Chen e al. [30], using a Ogden 9 h
o de app oxima ion ob ained by he me hod o singula alue decomposi ion. Simila ly,
he pe iodon al ligamen ma e ial p ope ies we e ob ained om he da a o po cine pe -
iodon al ligamen s subjec ed o uniaxial ensile es s ha we e pe o med along he ibbe
di ec ion, as epo ed by Na ali e al. [31] and Nishihi a e al. [32]. The cu e i ing p o-
cedu e o he Ogden unc ion was also ob ained by singula alue decomposi ion and
9 h o de app oxima ion.
2.4. Loading and Bounda y Condi ions
Bounda y condi ions we e applied in he condyles o he mandible and in he inse -
ion a eas o he mas ica ion muscles. Thus, as shown in Figu e 1, all h ee nodal deg ees
o eedom we e ixed in he inse ion o he masse e muscle in he lowe bo de o he
mandible and in he inse ion o he medial p e ygoid, he middle empo alis, and he
la e al p e ygoid muscles in he co onoid p ocess.
Figu e 1. Bounda y condi ions applied o he model as all deg ees o eedom ixi y o he nodes
loca ed a he heo e ical inse ion o he mas ica ion muscles masse e , middle empo alis and
medial p e ygoid, as well as comple e ixi y o he condyles.
The load was applied on a 78.5 mm
2
ci cle in he geome ic cen e o he loading pla e
as a homogenously dis ibu ed p essu e co esponding o a 240 N load in he Z di ec ion,
as shown in Figu e 2. The loads we e applied g adually o a oid dynamic e ec s and con-
e gence p oblems. The au oma ic ime s epping p ocedu e was used o he model CON-
VENTIONAL RPD o imp o e he con e gence a e.
Figu e 1.
Bounda y condi ions applied o he model as all deg ees o eedom ixi y o he nodes
loca ed a he heo e ical inse ion o he mas ica ion muscles masse e , middle empo alis and medial
p e ygoid, as well as comple e ixi y o he condyles.
The load was applied on a 78.5 mm
2
ci cle in he geome ic cen e o he loading pla e
as a homogenously dis ibu ed p essu e co esponding o a 240 N load in he Z di ec ion,
as shown in Figu e 2. The loads we e applied g adually o a oid dynamic e ec s and
con e gence p oblems. The au oma ic ime s epping p ocedu e was used o he model
CONVENTIONAL RPD o imp o e he con e gence a e.

Appl. Sci. 2021,11, 659 6 o 18
Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 o 18
Figu e 2. Loading condi ions applied o all h ee models as a uni o m p essu e equi alen o a 240
N o ce along he Z di ec ion (pu ely e ical), applied o a 78.5 mm
2
ci cle in he geome ic cen e
o he loading pla e, designed by CAD o pe ec i ing o he occlusal su aces o he ac ylic
ee h.
3. Resul s
Simula ions o bo h models o IARPD success ully comple ed all ime s eps o he
compu a ion, whe eas he simula ion o he CONVENTIONAL RPD s opped a he inc e-
men al 66-s ep, due o excessi e de o ma ion o he issue. Hence, he s ep 50, co espond-
ing o a 120 N load, was he basis o compa isons among models. These compa isons
we e based on he quali a i e in e p e a ion o he band plo s and quan i a i e analysis o
he alues o displacemen , s ain and s ess o di e en elemen g oups a he same load
s ep.
The dis ibu ion o alues o he h ee models was s a is ically analysed using he
one-way ANOVA es o he S a is ical Package o Social Sciences (SPSS) e sion 23.0.
Pos -hoc compa isons we e made using he - es o independen samples wi h Bon e -
oni co ec ion. The signi icance le el was se a 0.05.
3.1. O e al Displacemen s
The CONVENTIONAL RPD model e ealed signi ican displacemen in he sagi al
plane, pa icula ly no iced on he bo om o he ac ylic whe e he highes absolu e alues
we e iden i ied. All displacemen occu ed in he pos e io –an e io di ec ion ( owa ds
he na u al ee h) and showed he leas alue in he occlusal su aces o he ac ylic ee h
and on he occlusal es s ha sea on he p emola s Figu e 3, wi h a mean alue o −190 ±
36 μm. The same pa e n was iden i ied in he IARPD PM model. Ne e heless, compa i-
son o he alues egis e ed o he wo homologous bands e eals ha he displacemen s
in he IARPD PM occu a a scale o hund ed imes smalle . The mean displacemen in he
sagi al plane o he IARPD PM model was −6.30 ± 2.33 μm.
In he IARPD MO model, displacemen s we e egis e ed om pos e io o an e io
wi h app oxima ion o he emaining ee h (nega i e alues), bu also om an e io o
pos e io , howe e , mos elemen s showed no displacemen (as ep esen ed in ligh
g een). The highes mo emen o app oxima ion o he emaining ee h was obse ed in
he clasps and occlusal es s whe eas he opposi e mo emen was de ec ed in he po ion
o he lowe bo de o he ac ylic be ween he abu men oo h and he implan .
Figu e 2.
Loading condi ions applied o all h ee models as a uni o m p essu e equi alen o a 240 N
o ce along he Z di ec ion (pu ely e ical), applied o a 78.5 mm
2
ci cle in he geome ic cen e o
he loading pla e, designed by CAD o pe ec i ing o he occlusal su aces o he ac ylic ee h.
3. Resul s
Simula ions o bo h models o IARPD success ully comple ed all ime s eps o he com-
pu a ion, whe eas he simula ion o he CONVENTIONAL RPD s opped a he inc emen al
66-s ep, due o excessi e de o ma ion o he issue. Hence, he s ep 50, co esponding o a
120 N load, was he basis o compa isons among models. These compa isons we e based
on he quali a i e in e p e a ion o he band plo s and quan i a i e analysis o he alues o
displacemen , s ain and s ess o di e en elemen g oups a he same load s ep.
The dis ibu ion o alues o he h ee models was s a is ically analysed using he
one-way ANOVA es o he S a is ical Package o Social Sciences (SPSS) e sion 23.0.
Pos -hoc compa isons we e made using he - es o independen samples wi h Bon e oni
co ec ion. The signi icance le el was se a 0.05.
3.1. O e al Displacemen s
The CONVENTIONAL RPD model e ealed signi ican displacemen in he sagi al
plane, pa icula ly no iced on he bo om o he ac ylic whe e he highes absolu e alues
we e iden i ied. All displacemen occu ed in he pos e io –an e io di ec ion ( owa ds he
na u al ee h) and showed he leas alue in he occlusal su aces o he ac ylic ee h and on
he occlusal es s ha sea on he p emola s Figu e 3, wi h a mean alue o
−190 ±36 µm
.
The same pa e n was iden i ied in he IARPD PM model. Ne e heless, compa ison o
he alues egis e ed o he wo homologous bands e eals ha he displacemen s in he
IARPD PM occu a a scale o hund ed imes smalle . The mean displacemen in he sagi al
plane o he IARPD PM model was −6.30 ±2.33 µm.
In he IARPD MO model, displacemen s we e egis e ed om pos e io o an e io
wi h app oxima ion o he emaining ee h (nega i e alues), bu also om an e io o
pos e io , howe e , mos elemen s showed no displacemen (as ep esen ed in ligh g een).
The highes mo emen o app oxima ion o he emaining ee h was obse ed in he clasps
and occlusal es s whe eas he opposi e mo emen was de ec ed in he po ion o he lowe
bo de o he ac ylic be ween he abu men oo h and he implan .
Appl. Sci. 2021,11, 659 7 o 18
Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 o 18
Figu e 3. Band plo o he displacemen in he Y di ec ion o he h ee models analysed: CONVENTIONAL Remo able
pa ial den u e (RPD) (le ), implan -assis ed emo able pa ial den u e) IARPD PM (cen e ), IARPD MO ( igh ). Non-
ma ching colou scales. Homologous bands o he CONVENTIONAL RPD and IARPD PM models ha e 100 imes dis-
c epancy in alues.
Displacemen in he Z di ec ion was mainly esponsible o he displacemen magni-
ude o he RPDs, accompanying he di ec ion o he applied o ce, i.e., downwa ds, in he
di ec ion o he unde lying so issues. Fo CONVENTIONAL and IARPD PM models
he e was a no iceable end o sinking o he ac ylic po ion o he RPD wi h displace-
men s inc easing wi h he inc ease o he dis ance o he suppo s ( ee h o implan ). De-
spi e he simila pa e n o e ical displacemen o hese wo models, he issue wa d
mo emen was highe in he CONVENTIONAL RPD model and he di e ence be ween
models educed om being 250 imes highe in he mos an e io po ion o he ame-
wo k and ac ylic o 40 imes in he dis al ex eme o he wo p os heses. In he IARPD MO
model, on he con a y, he leas e ical displacemen was egis e ed in he egion o he
implan s and he la ges displacemen s in he apical di ec ion we e associa ed wi h he
an e io egion, whe e he amewo k con ac s he abu men ee h. Mean alues o he
h ee models we e, espec i ely, −710 ± 84 μm, −14 ± 6.4 μm and −4 ± 0.81 μm. The co e-
sponding maximum alues we e −900, −28.4 and −5.5 μm.
The magni ude o displacemen s is plo ed in Figu e 4. In con o mi y wi h he e-
po ed magni udes o he ho izon al and e ical displacemen s, he CONVENTIONAL
and IARPD PM models p esen ed simila dis ibu ions. O e all, hese dis ibu ions we e
symme ical and he highes displacemen aking place in he ac ylic po ions, inc easing
om mesial o he dis al ee end o he ac ylic lange. Though also symme ical, he
IARPD MO model e ealed he highes displacemen s in he mos p oximal po ion o he
ac ylic and in he clasp assembly and indi ec e aine . The lowes displacemen s we e
ound in he icini y o he implan a achmen .
Figu e 4. Dis ibu ion o he global displacemen s o he elemen s in each o he h ee models:
CONVENTIONAL RPD (le ), IARPD PREMOLARS (cen e ), IARPD MOLARS ( igh ). Non-
ma ching colou scales. Homologous bands o he CONVENTIONAL RPD and IARPD PM models
ha e 100 imes disc epancy in alues.
Figu e 3.
Band plo o he displacemen in he Y di ec ion o he h ee models analysed: CONVENTIONAL Remo able
pa ial den u e (RPD) (
le
), implan -assis ed emo able pa ial den u e) IARPD PM (
cen e
), IARPD MO (
igh
). Non-
ma ching colou scales. Homologous bands o he CONVENTIONAL RPD and IARPD PM models ha e 100 imes
disc epancy in alues.
Displacemen in he Z di ec ion was mainly esponsible o he displacemen mag-
ni ude o he RPDs, accompanying he di ec ion o he applied o ce, i.e., downwa ds,
in he di ec ion o he unde lying so issues. Fo CONVENTIONAL and IARPD PM
models he e was a no iceable end o sinking o he ac ylic po ion o he RPD wi h dis-
placemen s inc easing wi h he inc ease o he dis ance o he suppo s ( ee h o implan ).
Despi e he simila pa e n o e ical displacemen o hese wo models, he issue wa d
mo emen was highe in he CONVENTIONAL RPD model and he di e ence be ween
models educed om being 250 imes highe in he mos an e io po ion o he amewo k
and ac ylic o 40 imes in he dis al ex eme o he wo p os heses. In he IARPD MO
model, on he con a y, he leas e ical displacemen was egis e ed in he egion o he
implan s and he la ges displacemen s in he apical di ec ion we e associa ed wi h he
an e io egion, whe e he amewo k con ac s he abu men ee h. Mean alues o he
h ee models we e, espec i ely,
−
710
±
84
µ
m,
−
14
±
6.4
µ
m and
−
4
±
0.81
µ
m. The
co esponding maximum alues we e −900, −28.4 and −5.5 µm.
The magni ude o displacemen s is plo ed in Figu e 4. In con o mi y wi h he epo ed
magni udes o he ho izon al and e ical displacemen s, he CONVENTIONAL and
IARPD PM models p esen ed simila dis ibu ions. O e all, hese dis ibu ions we e
symme ical and he highes displacemen aking place in he ac ylic po ions, inc easing
om mesial o he dis al ee end o he ac ylic lange. Though also symme ical, he IARPD
MO model e ealed he highes displacemen s in he mos p oximal po ion o he ac ylic
and in he clasp assembly and indi ec e aine . The lowes displacemen s we e ound in
he icini y o he implan a achmen .
Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 o 18
Figu e 3. Band plo o he displacemen in he Y di ec ion o he h ee models analysed: CONVENTIONAL Remo able
pa ial den u e (RPD) (le ), implan -assis ed emo able pa ial den u e) IARPD PM (cen e ), IARPD MO ( igh ). Non-
ma ching colou scales. Homologous bands o he CONVENTIONAL RPD and IARPD PM models ha e 100 imes dis-
c epancy in alues.
Displacemen in he Z di ec ion was mainly esponsible o he displacemen magni-
ude o he RPDs, accompanying he di ec ion o he applied o ce, i.e., downwa ds, in he
di ec ion o he unde lying so issues. Fo CONVENTIONAL and IARPD PM models
he e was a no iceable end o sinking o he ac ylic po ion o he RPD wi h displace-
men s inc easing wi h he inc ease o he dis ance o he suppo s ( ee h o implan ). De-
spi e he simila pa e n o e ical displacemen o hese wo models, he issue wa d
mo emen was highe in he CONVENTIONAL RPD model and he di e ence be ween
models educed om being 250 imes highe in he mos an e io po ion o he ame-
wo k and ac ylic o 40 imes in he dis al ex eme o he wo p os heses. In he IARPD MO
model, on he con a y, he leas e ical displacemen was egis e ed in he egion o he
implan s and he la ges displacemen s in he apical di ec ion we e associa ed wi h he
an e io egion, whe e he amewo k con ac s he abu men ee h. Mean alues o he
h ee models we e, espec i ely, −710 ± 84 μm, −14 ± 6.4 μm and −4 ± 0.81 μm. The co e-
sponding maximum alues we e −900, −28.4 and −5.5 μm.
The magni ude o displacemen s is plo ed in Figu e 4. In con o mi y wi h he e-
po ed magni udes o he ho izon al and e ical displacemen s, he CONVENTIONAL
and IARPD PM models p esen ed simila dis ibu ions. O e all, hese dis ibu ions we e
symme ical and he highes displacemen aking place in he ac ylic po ions, inc easing
om mesial o he dis al ee end o he ac ylic lange. Though also symme ical, he
IARPD MO model e ealed he highes displacemen s in he mos p oximal po ion o he
ac ylic and in he clasp assembly and indi ec e aine . The lowes displacemen s we e
ound in he icini y o he implan a achmen .
Figu e 4. Dis ibu ion o he global displacemen s o he elemen s in each o he h ee models:
CONVENTIONAL RPD (le ), IARPD PREMOLARS (cen e ), IARPD MOLARS ( igh ). Non-
ma ching colou scales. Homologous bands o he CONVENTIONAL RPD and IARPD PM models
ha e 100 imes disc epancy in alues.
Figu e 4.
Dis ibu ion o he global displacemen s o he elemen s in each o he h ee models: CONVENTIONAL RPD
(
le
), IARPD PREMOLARS (
cen e
), IARPD MOLARS (
igh
). Non-ma ching colou scales. Homologous bands o he
CONVENTIONAL RPD and IARPD PM models ha e 100 imes disc epancy in alues.
Appl. Sci. 2021,11, 659 8 o 18
S a is ically signi ican di e ences we e ound be ween he mean alues o displace-
men o he h ee g oups (p< 0.001), Table 4. Mean alues o displacemen o he IARPD
MO we e 4
±
0.8
µ
m, anging om 2 o 6
µ
ms and we e signi ican ly lowe han any o he
model. Despi e he simila i ies in dis ibu ion o displacemen s in he CONVENTIONAL
and he IARPD PM models, he alues o hose g oups we e also s a is ically di e en ,
wi h means o 730
±
80
µ
m and 20
±
6
µ
m espec i ely. Pai wise compa isons o he h ee
models a e de ailed in Table 5.
Table 4.
Mean alues and ange o he magni ude o displacemen o each model. S a is ical analysis
wi h one-way ANOVA. SD- s anda d de ia ion; min- minimum; max- maximum.
Model Mean ±SD (µm) Range (Min-Max) ANOVA
Con en ional RPD 730.0 ±80 530–910 F(2, 320686) = 7825410,
p< 0.001
IARPD PM 20.0 ±6.0 3–30
IARPD MO 4.0 ±0.8 2–6
Table 5.
Mean di e ences in he magni ude o displacemen o he p os hesis ( amewo k and ac ylic)
be ween pai s o models. S a is ical analysis wi h wo sample - es s, assuming unequal a iances
and Bon e oni co ec ion. 95% CI−95% con idence in e al o he di e ence.
Pai Mean Di e ence (µm) 95% CI pValue
Con en ional RPD/IARPD PM 718 (717,718) <0.001
Con en ional RPD/IARPD MO 730 (729–731) <0.001
IARPD PM/IARPD MO 12 (11–13) <0.001
Loading o he ac ylic po ion o he p os hesis induced displacemen o he abu men
ee h by means o he con ac wi h he amewo k, h ough he occlusal and cingulum
es s. Fo he wo implan -assis ed models he la ges componen o he displacemen was
e ical and in he di ec ion o he load, whe eas o he CONVENTIONAL RPD model, he
la ges displacemen s we e consis en ly dis ibu ed be ween e ical and an e io -pos e io ,
as can be seen in Table 6. In his case, he abu men ee h no only mo e in he di ec ion o
he load bu also p esen ipping owa ds he eden ulous span.
Table 6.
Displacemen s o he abu men ee h in all h ee di ec ions, X, Y and Z, co esponding
o lingual–buccal, pos e io –an e io and e ical, espec i ely, and he co esponding magni ude.
Mean ±SD (Min–Max) (µm).
Model Ling.-Buc. Pos .-An . Ve ical Magni ude
Con en ional RPD 2.2 ±9.0
(−33.6 o 39.7)
−14.4 ±16.9
(−104.4 o 24.0)
12.0 ±5.2
(−40.2 o −1.0)
22.4 ±15.7
(6.5 o 110.0)
IARPD PM 0.4 ±0.1
(0.08 o 0.7)
−4.4 ±1.2
(−7.8 o −1.5)
−9.8 ±0.8
(−12 o −7.9)
10.9 ±0.9
(9.1 o 13.8)
IARPD MO 0.1 ±0.5
(−1.0 o 1.6)
−0.5 ±0.05
(−2.2 o 0.5)
−2.2 ±0.4
(−3.2 o −1.3)
2.3 ±0.4
(1.3 o 3.3)
The addi ion o he implan s o he ehabili a ion ha e signi ican ly educed he
magni ude o displacemen s o he abu men ee h and he lowes displacemen s we e
egis e ed in he IARPD MO model.
3.2. O e all S esses
The s ess dis ibu ion in he amewo ks was di e en o all h ee models. The
CONVENTIONAL RPD model p esen ed he highes alues o e ec i e s ess, showing
ex ensi e a eas wi h alues supe io o 10 MPa, as p esen ed in Figu e 5a. The mean on
Mises s ess was 11.3
±
14 MPa, anging om 0.8 MPa o 200 MPa. C i ical a eas we e a he
Appl. Sci. 2021,11, 659 9 o 18
di ec e aine s, namely he igid po ion o he e en i e clasp and he mino connec o s,
as well as he majo connec o , whe e he maximum p incipal s esses a e o ensile ype,
as can be seen in Figu e 5b.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 o 18
he di ec e aine s, namely he igid po ion o he e en i e clasp and he mino connec -
o s, as well as he majo connec o , whe e he maximum p incipal s esses a e o ensile
ype, as can be seen in Figu e 5b.
(a)
(b)
Figu e 5. Smoo hed s esses dis ibu ion on he amewo k o he CONVENTIONAL RPD model: (a) on Mises s ess,
bo om iew on he le , op iew on he igh ; (b) p incipal s esses in he di ec e aine , wi h all non-pu ple colo s
ep esen ing ensile s esses and he a eas in pink wi h alues supe io o 100 MPa.
In he case o he IARPD PM and IARPD MO models, he e was no high s ess accu-
mula ion in he di ec e aine s o majo connec o . The highes s ess accumula ion was
in he in e io po ion o he ma ix and su ounding ma e ial, as obse ed in Figu e 6,
and, gene ally, was lowe han in he CONVENTIONAL RPD model. Fo he IARPD PM
model, he mean on Mises s ess alue was 3.04 ± 4.96 MPa, anging om 462 Pa o 68
MPa, while in he IARPD MO model he on Mises s ess alue was o 1.81 ± 2.37 MPa,
anging om 651 Pa o 43 MPa. The alues dis ibu ion o he h ee models a e shown in
he box plo g aphic p esen ed a Figu e 7. One-way ANOVA de ec ed signi ican di e -
ences be ween models, F(2, 77087) = 8740, p < 0.001. All h ee models we e ound o be
di e en in he pai wise compa isons p esen ed a Table 7.
Figu e 5.
Smoo hed s esses dis ibu ion on he amewo k o he CONVENTIONAL RPD model: (
a
) on Mises s ess,
bo om iew on he le , op iew on he igh ; (
b
) p incipal s esses in he di ec e aine , wi h all non-pu ple colo s
ep esen ing ensile s esses and he a eas in pink wi h alues supe io o 100 MPa.
In he case o he IARPD PM and IARPD MO models, he e was no high s ess
accumula ion in he di ec e aine s o majo connec o . The highes s ess accumula ion
was in he in e io po ion o he ma ix and su ounding ma e ial, as obse ed in
Figu e 6
,
and, gene ally, was lowe han in he CONVENTIONAL RPD model. Fo he IARPD PM
model, he mean on Mises s ess alue was 3.04
±
4.96 MPa, anging om 462 Pa o
68 MPa, while in he IARPD MO model he on Mises s ess alue was o
1.81 ±2.37 MPa
,
anging om 651 Pa o 43 MPa. The alues dis ibu ion o he h ee models a e shown in he
box plo g aphic p esen ed a Figu e 7. One-way ANOVA de ec ed signi ican di e ences
be ween models, F(2, 77087) = 8740, p< 0.001. All h ee models we e ound o be di e en
in he pai wise compa isons p esen ed a Table 7.
Appl. Sci. 2021,11, 659 16 o 18
isk o ailu e, which should be conside ed in he case o ex ensi e eden ulism, namely
when 4 ee h a e missing pe eden ulous span.
Limi a ions o he p esen wo k a e mainly ela ed o he na u e o he s udy and
possibili y o ansposi ion o he clinical se ing. Fo ins ance, in his s udy he beha io o
RPDs in he o al ca i y was simula ed assuming ha he amewo k and abu men ee h
we e no igidly bonded, allowing sliding, whe eas he ball a achmen and he ma ix
inco po a ed in he amewo k we e igidly a ached, ensu ing a o al ansmission o
loads om he con ac o o he a ge su aces. This was a echnical op ion o imp o e
con e gence o esul s and app oxima ion accu acy bu limi ed he possibili y o ee
o a ion a ound he ball a achmen which is clinically obse ed [
52
–
54
] when he ac ylic
ee h a e loaded. Fu u e esea ch should add ess o he pa ame e s ha migh change he
magni ude o all e ec s emphasized in his wo k, namely he ype o a achmen sys em, he
heigh o he co esponding abu men [
55
–
57
] and he ype o implan (one o wo-piece).
No wi hs anding his, i is e y clea ha he addi ion o one implan o he den u e bea ing
a eas, ega dless o he posi ion, is pa amoun o he educ ion o he displacemen s o he
p os hesis and, consequen ly, o he abu men ee h mobili y.
5. Conclusions
Wi hin he limi a ions o a s a ic ini e elemen analysis, i is possible o conclude ha
he loading o con en ional Kennedy class I RPDs leads o signi ican e ical displacemen
o he ex ension bases owa ds he unde lying so issues, like a can ile e beam unde
lexion. The ins alla ion o a den al implan in each o he bila e al eden ulous egions
o p o ide suppo and e en ion o he ex ension bases o he RPD signi ican ly educes
he e ical and an e io -pos e io displacemen s, ega dless o he posi ion. Howe e ,
implan -assis ed emo able pa ial den u es (IARPDs) wi h he implan placed in he mos
mesial/an e io posi ion, adjacen o he abu men ee h e ain a pa e n o displacemen s
compa able o ha o he con en ional RPDs. In he con en ional RPDs he a eas o he
highes e ec i e s ess o he amewo ks sp ead h ough he di ec e aine s, auxilia y
es s and majo connec o . In he IARPDs he highes s ess accumula ion is shi ed o
he in e io po ion o he ma ix and su ounding ma e ial, ega dless o he implan
posi ion. The lowes e ec i e s ess o he amewo k is ob ained wi h he implan in he
mos dis al/pos e io posi ion. The indings o his wo k migh be used o helping he
design o implan assis ed emo able pa ial den u es (IARPDs).
Au ho Con ibu ions:
Concep ualiza ion, P.N.; me hodology, P.N. and M.A.N.; so wa e, A.M.,
V.M.L. and M.A.N.; alida ion, A.M., M.A.N. and A.M.A.; w i ing—o iginal d a p epa a ion, A.M.;
w i ing— e iew and edi ing, M.A.N., P.N. and A.M.A. All au ho s ha e ead and ag eed o he
published e sion o he manusc ip .
Funding:
This esea ch was sponso ed by FEDER unds h ough he p og am COMPETE–P og ama
Ope acional Fac o es de Compe i i idade–and by na ional unds h ough FCT–Fundação pa a a
Ciência e a Tecnologia, unde he p ojec UIDB/00285/2020 and unde a PhD ellowship om he
Po uguese awa ded o Ana Messias (SFRH/BD/82442/2011).
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen :
The da a p esen ed in his s udy a e a ailable on eques om he
co esponding au ho .
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Re e ences
1.
Wos mann, B.; Bud z-Jo gensen, E.; Jepson, N.; Mushimo o, E.; Palmq is , S.; So ou, A.; Öwall, B. Indica ions o emo able
pa ial den u es: A li e a u e e iew. J. P os he . Den . 2006,95, 70. [C ossRe ]
2.
Rehmann, P.; O bach, K.; Fe ge , P.; Wös mann, B. T ea men Ou comes wi h Remo able Pa ial Den u es: A Re ospec i e
Analysis. In . J. P os hodon . 2013,26, 147–150. [C ossRe ] [PubMed]

Appl. Sci. 2021,11, 659 17 o 18
3.
Koyama, S.; Sasaki, K.; Yokoyama, M.; Sasaki, T.; Hanawa, S. E alua ion o ac o s a ec ing he con inuing use and pa ien
sa is ac ion wi h emo able pa ial den u es o e 5 yea s. J. P os hodon . Res. 2010,54, 97–101. [C ossRe ] [PubMed]
4.
Shaghaghian, S.; Tagh a, M.; Abduo, J.; Baghe i, R. O al heal h- ela ed quali y o li e o emo able pa ial den u e wea e s and
ela ed ac o s. J. O al Rehabil. 2015,42, 40–48. [C ossRe ] [PubMed]
5. Moldo an, O.; Rudolph, H.; Lu ha d , R.G. Biological complica ions o emo able den al p os heses in he mode a ely educed
den i ion: A sys ema ic li e a u e e iew. Clin. O al In es ig. 2018,22, 2439–2461. [C ossRe ]
6.
Pellecchia, M.; Pellecchia, R.; Em iaz, S. Dis al ex ension mandibula emo able pa ial den u e connec ed o an an e io ixed
implan -suppo ed p os hesis: A clinical epo . J. P os he . Den . 2000,83, 607–612. [C ossRe ]
7.
Ch onopoulos, V.; Sa a ianou, A.; Kou is, S. The Use o Den al Implan s in Combina ion wi h Remo able Pa ial Den u es.
A Case Repo . J. Es he . Res o . Den . 2008,20, 355–364. [C ossRe ]
8.
Fugazzo o, P.A.; Ligh oo , W.S. Maximizing ea men ou comes wi h emo able pa ial p os hesis h ough he inclusion o
implan s and loca o a achmen s. J. Mass. Den . Soc. 2010,59, 20–22.
9.
Kim, J.H.; Lee, J.H. An implan -suppo ed emo able pa ial den u e on milled ba s o comp omise he inadequa e ea men
plan: A clinical epo . J. Ad . P os hodon . 2010,2, 58–60. [C ossRe ]
10.
Pimen el, M.J.; A éllaga, J.P.; Bacchi, A.; Del Bel Cu y, A.A. The Use o Implan s o Imp o e Remo able Pa ial Den u e Func ion.
J. Indian P os hodon . Soc. 2014,14, 243–247. [C ossRe ]
11.
Bo olini, S.; Na ali, A.; F anchi, M.; Coggiola, A.; Consolo, U. Implan -Re ained Remo able Pa ial Den u es: An 8-Yea
Re ospec i e S udy. J. P os hodon . 2011,20, 168–172. [C ossRe ] [PubMed]
12.
G ossmann, Y.; Nissan, J.; Le in, L. Clinical E ec i eness o Implan -Suppo ed Remo able Pa ial Den u es-A Re iew o he
Li e a u e and Re ospec i e Case E alua ion. J. O al Maxillo ac. Su g. 2009,67, 1941–1946. [C ossRe ] [PubMed]
13.
Ohkubo, C.; Ku iha a, D.; Shimpo, H.; Suzuki, Y.; Kokubo, Y.; Hosoi, T. E ec o implan suppo on dis al ex ension emo able
pa ial den u es: In i o assessmen . J. O al Rehabil. 2007,34, 52–56. [C ossRe ]
14.
Maeda, Y.; Sogo, M.; Tsu sumi, S. E icacy o a pos e io implan suppo o ex a sho ened den al a ches: A biomechanical
model analysis. J. O al Rehabil. 2005,32, 656–660. [C ossRe ] [PubMed]
15.
Huang, H.L.; Hsu, J.T.; Fuh, L.J.; Tu, M.G.; Ko, C.C.; Shen, Y.W. Bone s ess and in e acial sliding analysis o implan designs on
an immedia ely loaded maxilla y implan : A non-linea ini e elemen s udy. J. Den . 2008,36, 409–417. [C ossRe ]
16.
Del’A co Pigna a Cunha, L.; Pellizze , E.P.; Ve i, F.R.; Pe ei a, J.A. E alua ion o he in luence o loca ion o osseoin eg a ed
implan s associa ed wi h mandibula emo able pa ial den u es. Implan Den . 2008,17, 278–287. [C ossRe ]
17.
Mema i, Y.; Ge amy, A.; Fayaz, A.; Rez ani Habib Abadi, S.; Mansou i, Y.; Rez ani Habib Abadi, S. In luence o Implan Posi ion on
S ess Dis ibu ion in Implan -Assis ed Dis al Ex ension Remo able Pa ial Den u es: A 3D Fini e Elemen Analysis; Teh an Uni e si y o
Medical Sciences: Teh an, I an, 2014; Volume 11.
18.
Eom, J.W.; Lim, Y.J.; Kim, M.J.; Kwon, H.B. Th ee-dimensional ini e elemen analysis o implan -assis ed emo able pa ial
den u es. J. P os he . Den . 2017,117, 735–742. [C ossRe ]
19.
Cicciù, M.; Ce ino, G.; Milone, D.; Risi ano, G. FEM in es iga ion o he s ess dis ibu ion o e mandibula bone due o sc ewed
o e den u e posi ioned on den al implan s. Ma e ials 2018,11, 1512. [C ossRe ]
20.
Pa k, S.M.; Pa k, S.; Shin, S.; Lee, H.; Ahn, S.J.; Kim, L.; Lee, S.H.; Noh, G. Designing a mandibula ad ancemen de ice wi h
opology op imiza ion o a pa ially eden ulous pa ien . J. P os he . Den . 2020,123, 850–859. [C ossRe ]
21.
Chagnon, G.; Rebouah, M.; Fa ie , D.; Chagnon, G.; Rebouah, M.; Fa ie , D. Hype elas ic Ene gy Densi ies o So Biological
Tissues: A Re iew. Hype elas ic Ene gy Densi ies So Biol. Tissues A Re . J. Elas . 2015,120, 129–160. [C ossRe ]
22.
Ogden, R.W. Nonlinea Elas ici y wi h Applica ion o Ma e ial Modelling; Cen e o Excellence o Ad anced Ma e ials and S uc u es:
Hong Kong, China, 2003.
23.
Ogden, R.W.; Saccomandi, G.; Sgu a, I. Fi ing hype elas ic models o expe imen al da a. Compu . Mech.
2004
,34, 484–502.
[C ossRe ]
24.
Schwa z-Dabney, C.L.; Dechow, P.C. Eden ula ion al e s ma e ial p ope ies o co ical bone in he human mandible. J. Den . Res.
2002,81, 613–617. [C ossRe ]
25.
Rapo , A.J.; Rinaldi, R.G.; Ho zman, J.L.; Daegling, D.J. Elas ic modulus a ia ion in mandibula bone: A mic oinden a ion s udy
o Macaca ascicula is. Am. J. Phys. An h opol. 2008,135, 100–109. [C ossRe ]
26.
Odin, G.; Sa oldelli, C.; Boucha d, P.O.; Tillie , Y. De e mina ion o Young’s modulus o mandibula bone using in e se analysis.
Med. Eng. Phys. 2010,32, 630–637. [C ossRe ]
27.
Schwa z-Dabney, C.L.; Dechow, P.C. Va ia ions in co ical ma e ial p ope ies h oughou he human den a e mandible. Am. J.
Phys. An h opol. 2003,120, 252–277. [C ossRe ]
28.
Zhang, Y.R.; Du, W.; Zhou, X.D.; Yu, H.Y. Re iew o esea ch on he mechanical p ope ies o he human oo h. In . J. O al Sci.
2014,6, 61–69. [C ossRe ]
29.
Shahmi i, R.; Aa s, J.M.; Bennani, V.; Das, R.; Swain, M.V. S ain dis ibu ion in a Kennedy class i implan assis ed emo able
pa ial den u e unde a ious loading condi ions. In . J. Den . 2013,2013, 351279. [C ossRe ]
30.
Chen, J.; Ahmad, R.; Suenaga, H.; Li, W.; Swain, M.; Li, Q. A compa a i e s udy on comple e and implan e ained den u e
ea men s—A biomechanics pe spec i e. J. Biomech. 2015,48, 512–519. [C ossRe ]
31.
Na ali, A.N.; Ca niel, E.L.; Pa an, P.G. Cons i u i e modelling o inelas ic beha iou o co ical bone. Med. Eng. Phys.
2008
,30,
905–912. [C ossRe ]
Appl. Sci. 2021,11, 659 18 o 18
32.
Nishihi a, M.; Yamamo o, K.; Sa o, Y.; Ishikawa, H.; Na ali, A.N. Mechanics o pe iodon al ligamen m nishihi a, k yamamo o,
y sa o, h ishikawa, an na ali. In Den al Biomechanics; CRC P ess: Boca Ra on, FL, USA, 2003; pp. 38–52.
33.
Shahmi i, R.; Aa s, J.M.; Bennani, V.; A ieh, M.A.; Swain, M.V. Fini e elemen analysis o an implan -assis ed emo able pa ial
den u e. J. P os hodon . 2013,22, 550–555. [C ossRe ]
34.
Shahmi i, R.; Das, R.; Aa s, J.M.; Bennani, V. Fini e elemen analysis o an implan -assis ed emo able pa ial den u e du ing
bila e al loading: Occlusal es s posi ion. J. P os he . Den . 2014,112, 1126–1133. [C ossRe ]
35. Shahmi i, R.; Das, R. Fini e elemen analysis o implan -assis ed emo able pa ial den u es: F amewo k design conside a ions.
J. P os he . Den . 2017,118, 177–186. [C ossRe ]
36.
Pa k, J.; Ahn, S.-J.; Lee, H.; Noh, G. Implan placemen in he emo able mandibula ad ancemen de ice o comple ely
eden ulous pa ien s: A ini e elemen s udy. J. Compu . Des. Eng. 2020,2020, 1–9. [C ossRe ]
37.
Jo ge, J.H.; Quishida, C.C.C.; Ve gani, C.E.; Machado, A.L.; Pa a ina, A.C.; Giampaolo, E.T. Clinical e alua ion o ailu es in
emo able pa ial den u es. J. O al Sci. 2012,54, 337–342. [C ossRe ]
38.
F ank, R.P.; B ud ik, J.S.; Noonan, C.J. Clinical ou come o he al e ed cas imp ession p ocedu e compa ed wi h use o a one-piece
cas . J. P os he . Den . 2004,91. [C ossRe ]
39.
Jin, X.; Sa o, M.; Nishiyama, A.; Ohyama, T. In luence o loading posi ions o mandibula unila e al dis al ex ension emo able
pa ial den u es on mo emen s o abu men oo h and den u e base. J. Med. Den . Sci. 2004,51, 155–163.
40. I oh, H.; Baba, K.; A idome, K.; Okada, D.; Tokuda, A.; Nishiyama, A.; Miu a, H.; Iga ashi, Y. E ec o di ec e aine and majo
connec o designs on RPD and abu men oo h mo emen dynamics. J. O al Rehabil. 2008,35, 810–815. [C ossRe ]
41.
Labuschagne, A.; an Rensbu g, N.F.J.; an de Me we, A.J. Compa ison o linea beam heo ies. Ma h. Compu . Model.
2009
,49,
20–30. [C ossRe ]
42.
Ne o, M.A.; Ama o, A.; Luis, R.; Ci ne, J.; Leal, R. Enginee ing Compu a ion o S uc u es: The Fini e Elemen Me hod; Sp inge :
Cham, Swi ze land, 2015; ISBN1 9783319177106. ISBN2 9783319177090.
43.
Helal, M.A.; Ba aka, O.A.; Sanad, M.E.; Al-Khia y, Y.; Ludwig, K.; Ke n, M. E ec o Clasp Design on Re en ion a Di e en
In e als Using Di e en Abu men Ma e ials and in a Simula ed O al Condi ion. J. P os hodon . 2014,23, 140–145. [C ossRe ]
44.
Valli u, P.K.; Kokkonen, M. De lec ion a igue o cobal -ch omium, i anium, and gold alloy cas den u e clasp. J. P os he . Den .
1995,74, 412–419. [C ossRe ]
45.
Lassila, L.V.; Valli u, P.K. E ec o wa e and a i icial sali a on he low cycle a igue esis ance o cobal -ch omium den al alloy.
J. P os he . Den . 1998,80, 708–713. [C ossRe ]
46.
Mahmoud, A.; Wakabayashi, N.; Takahashi, H.; Ohyama, T. De lec ion a igue o Ti-6Al-7Nb, Co-C , and gold alloy cas clasps.
J. P os he . Den . 2005,93, 183–188. [C ossRe ]
47.
Shahmi i, R.; Das, R. Fini e Elemen Analysis o Implan -Assis ed Remo able Pa ial Den u e A achmen wi h Di e en Ma ix
Designs Du ing Bila e al Loading. In . J. O al Maxillo ac. Implan s 2016,31, e116–e127. [C ossRe ]
48.
Miji i sky, E.; Lo ean, A.; Mazo , Z.; Le in, L. Implan Too h-Suppo ed Remo able Pa ial Den u e wi h a Leas 15-Yea
Long-Te m Follow-Up. Clin. Implan Den . Rela . Res. 2015,17, 917–922. [C ossRe ]
49.
Payne, A.G.T.; Tawse-Smi h, A.; Wismeije , D.; De Sil a, R.K.; Ma, S. Mul icen e p ospec i e e alua ion o implan -assis ed
mandibula emo able pa ial den u es: Su gical and p os hodon ic ou comes. Clin. O al Implan s Res.
2017
,28, 116–125.
[C ossRe ]
50.
Jensen, C.; Meije , H.J.A.; Raghoeba , G.M.; Ke dijk, W.; Cune, M.S. Implan -suppo ed emo able pa ial den u es in he
mandible: A 3–16 yea e ospec i e s udy. J. P os hodon . Res. 2017,61, 98–105. [C ossRe ]
51.
Bon an e, E.A.; Coelho, P.G. A C i ical Pe spec i e on Mechanical Tes ing o Implan s and P os heses. Ad . Den . Res.
2016
,28,
18–27. [C ossRe ]
52.
Alsabeeha, N.; Payne, A.G.T.; De Sil a, R.K.; Swain, M.V. Mandibula single-implan o e den u es: A e iew wi h su gical and
p os hodon ic pe spec i es o a no el app oach. Clin. O al Implan s Res. 2009,20, 356–365. [C ossRe ]
53.
Cicciù, M.; Ce ino, G.; Milone, D.; Risi ano, G. FEM analysis o den al implan -abu men in e ace o e den u e componen s and
pa ame ic e alua ion o Equa o ®and Loca o ®p os hodon ics a achmen s. Ma e ials 2019,12, 592. [C ossRe ]
54.
Nogawa, T.; Sai o, M.; Mu ashima, N.; Takayama, Y.; Yokoyama, A. In luence o igidi y o e aine s on dynamic beha io o
implan -suppo ed emo able pa ial den u es. In . J. Implan Den . 2020,6, 60. [C ossRe ]
55.
Spina o, S.; S acchi, C.; Lomba di, T.; Be na dello, F.; Messina, M.; Za e, D. Biological wid h es ablishmen a ound den al implan s
is in luenced by abu men heigh i espec i e o e ical mucosal hickness: A clus e andomized con olled ial. Clin. O al
Implan s Res. 2019,30, 649–659. [C ossRe ]
56.
Spina o, S.; S acchi, C.; Lomba di, T.; Be na dello, F.; Messina, M.; Do igo, S.; Za e, D. In luence o abu men heigh and e ical
mucosal hickness on ea ly ma ginal bone loss a ound implan s: A andomised clinical ial wi h an 18-mon h pos -loading
clinical and adiog aphic e alua ion. In . J. O al Implan ol. 2020,13, 279–290.
57.
Ohyama, T.; Nakabayashi, S.; Yasuda, H.; Kase, T.; Namaki, S. Mechanical analysis o he e ec s o implan posi ion and abu men
heigh on implan -assis ed emo able pa ial den u es. J. P os hodon . Res. 2020,64, 340–345. [C ossRe ]