Thermal Load and Heat Transfer in Dental Titanium Implants: an Ex Vivo-Based Exact Analytical/Numerical Solution to the ‘Heat Equation’

Grigorios P. Panotopoulos; Ziyad S. Haidar

doi:10.3390/dj10030043

Thermal Load and Heat Transfer in Dental Titanium Implants: an Ex Vivo-Based Exact Analytical/Numerical Solution to the ‘Heat Equation’

Grigorios P. Panotopoulos^*, Ziyad S. Haidar^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Introduction: Heat is a kinetic process whereby energy flows from between two systems, hot-to-cold objects. In oro-dental implantology, conductive heat transfer/(or thermal stress) is a complex physical phenomenon to analyze and consider in treatment planning. Hence, ample research has attempted to measure heat-production to avoid over-heating during bone-cutting and drilling for titanium (Ti) implant-site preparation and insertion, thereby preventing/minimizing early (as well as delayed) implant-related complications and failure. Objective: Given the low bone-thermal conductivity whereby heat generated by osteotomies is not effectively dissipated and tends to remain within the surrounding tissue (peri-implant), increasing the possibility of thermal-injury, this work attempts to obtain an exact analytical solution of the heat equation under exponential thermal-stress, modeling transient heat transfer and temperature changes in Ti implants (fixtures) upon hot-liquid oral intake. Materials and Methods: We, via an ex vivo-based model, investigated the impact of the (a) material, (b) location point along implant length, and (c) exposure time of the thermal load on localized temperature changes. Results: Despite its simplicity, the presented solution contains all the physics and reproduces the key features obtained in previous numerical analyses studies. To the best of our knowledge, this is the first introduction of the intrinsic time, a "proper" time that characterizes the geometry of the dental implant fixture, where we show, mathematically and graphically, how the interplay between "proper" time and exposure time influences temperature changes in Ti implants, under the suitable initial and boundary conditions. This fills the current gap in the literature by obtaining a simplified yet exact analytical solution, assuming an exponential thermal load model relevant to cold/hot beverage or food intake. Conclusions: This work aspires to accurately complement the overall clinical diagnostic and treatment plan for enhanced bone-implant interface, implant stability, and success rates, whether for immediate or delayed loading strategies.

Original language	English
Article number	43
Pages (from-to)	1-14
Number of pages	14
Journal	Dentistry Journal
Volume	10
Issue number	3
DOIs	https://doi.org/10.3390/dj10030043
State	Published - 10 Mar 2022

Bibliographical note

Funding Information:
Acknowledgments: ZS Haidar (DDS, Cert Implantol, MSc OMFS, FRCS (C), MBA, PhD) acknowledges the generous funding and operating grants that supported this work via providing the necessary resources to the BioMAT’X I+D+I Research Group (Haidar Lab), part of CiiB (Centro de Investigación e Innovación Biomédica), through the Faculty of Dentistry (F-ODO) and Department for Research, Development and Innovation I+D+i, Universidad de los Andes, Santiago, Chile.
Funding Information:
Figure 8. Experimental Set‐up; developed in‐House (at the BioMAT’X R&D&I Laboratory—Haidar Lab, CiiB, Faculties of Medicine and Dentistry, Universidad de los Andes, Santiago de Chile) as an ex‐vivo heat distribution model employ‐ ing human patient‐grade titanium dental implants placed into porcine ribs (without coolant) and thermal changes moni‐ tored/recorded (quantified) using a CorDEX TP3R ToughPix DigiTherm Digital Thermal Camera (an ongoing investiga‐ tion). into porcine ribs (without coolant) and thermal changes monitored/recorded (quantified) using a CorDEX TP3R ToughPix DigiTherm Digital Thermal Camera (an ongoing investigation). Author Contributions: Conceptualization, Z.S.H.; methodology, Z.S.H. and G.P.P.; software, AGu.Pt.hPo.;r vCaolindtaritibount,i oGn.Ps:.PC. oanncde pZtu.Sa.Hliz.;a tfioornm, aZl. Sa.nHa.l;ymsies,t hGo.dPo.Plo. gayn,dZ Z.S..SH.H. a.;n idnvGe.sPt.iPg.;astioofntw, Zar.Se.,HG..;P r.Pe.‐; vsoaulirdcaetsio, nG,.GP..PP..P a. nandd ZZ.S.S.H.H.;. ;dfoartma acul arantaiolyns,i sZ, .GS..PH.P. .aanndd GZ..SP..HP..;; iwnvrietsintigg—atioornig, iZn.aSl. Hd.r;arfets opurercpeasr,aGti.oPn.P,. aZn.Sd.HZ.. Sa.Hnd.; dGa.tPa.Pcu.; rawtiroitnin, Zg—.S.rHev. aienwd Gan.Pd.P .e; dwitriintign,g —Z.So.rHig. inaanldd rGaf.Pt p.Pr.e; pvairsautaiolinz,aZti.oSn.H, .Za.Sn.dHG. .aPn.Pd.; wG.rPit.iPn.g; —surpeevriveiwsioann,d Ze.dS.iHtin.;g p, rZo.jSe.cHt .aadnmdiGni.sPt.rPa.;tivoinsu, aZl.iSz.aHti.o; nfu, nZd.Si.nHg. aacnqduGis.iPti.oP.n;,s uZp.Se.rHv.i sAiolln ,aZut.Sh.oHrs.; phraovjee crteaadd manindi satgraretieodn t,oZ t.hS.eH p.;ufbulnisdhiendg vaecrqsuioisni toiof nth, eZ m.S.aHn.uAsclrliaput.t hors have read and agreed to the published version of the manuscript. Funding: Author (G.P.P.) acknowledges the Fundaçao para a Ciencia e Tecnologia (FCT) in Portu‐ Fgualn fdoirn tgh:eA fuinthanorci(aGl .sPu.Pp.)paocrkt nporwovleiddegdes toth Ce EFuNnTdRaAça o(Cpeanrtaera fCoire nAcsitaroepTheycnsioclso agniad( FGCrTav) iitnatPioonrt)u, gIna‐l fsotirtuthtoe fSinuapnecriioalr sTuépcpnoicrot ,p UronviivdeerdsitdoaCdeE NdeT RLAisb(Coae,n ttherrofourghA stthreo pGhryasnict sNano.d UGIrDaBvi/t0a0t0io9n9/)2, 0In2s0t.i tTuhtoe Sauutpheorrio arlsToé wcniischoe,sU ton iavcekrnsiodwaldeeddgee tLhies bfouan,dtehdr ooupgphorthtuenGitrya tnot wNoor.kU oInD tBh/is0 0m0u99lt/i‐2d0i2sc0i.pTlihnearayu pthroor‐ ajelcsto wwiitshh eBsiotoMaAcTk’nXo wI+lDed+gi e(Hthaeidfaurn dLeadb) oupnpdoertru tnhiety stuopwerovriskioonn othf isthme uCltoir-dreisspciopnlidnianrgy Apruothjeocrt (Z.S.H.). The corresponding author (Z.S.H.) acknowledges supplementary operating funding pro‐ vided from CONICYT‐FONDEF Chile under awarded project/grant (national) #ID16I10366 (2016– 2020), Fondo de Ayuda a la Investigacion (FAI)—Universidad de los Andes No. INV‐IN‐2015‐101 (2015–2020) and Fondos de Apoyo a la Innovación (FAIN), Dirección de Innovación—Universidad de los Andes, Project X’PLANT 3Ss Dental Implant Solutions, No. Oco ZFAIN2019005 (2018‐2022). Project X’PLANT 3Ss Dental Implant Solutions, No. Oco ZFAIN2019005 (2018-2022).
Publisher Copyright:
© 2022 by the authors.

Keywords

Dental implants
Thermal stress
Modeling of heat transfer
Temperature changes
Heat equation
Analytical solution

Access to Document

10.3390/dj10030043

Cite this

@article{7bb522d2acb0412e97ffafc3b0f044bd,

title = "Thermal Load and Heat Transfer in Dental Titanium Implants: an Ex Vivo-Based Exact Analytical/Numerical Solution to the {\textquoteleft}Heat Equation{\textquoteright}",

abstract = "Introduction: Heat is a kinetic process whereby energy flows from between two systems, hot-to-cold objects. In oro-dental implantology, conductive heat transfer/(or thermal stress) is a complex physical phenomenon to analyze and consider in treatment planning. Hence, ample research has attempted to measure heat-production to avoid over-heating during bone-cutting and drilling for titanium (Ti) implant-site preparation and insertion, thereby preventing/minimizing early (as well as delayed) implant-related complications and failure. Objective: Given the low bone-thermal conductivity whereby heat generated by osteotomies is not effectively dissipated and tends to remain within the surrounding tissue (peri-implant), increasing the possibility of thermal-injury, this work attempts to obtain an exact analytical solution of the heat equation under exponential thermal-stress, modeling transient heat transfer and temperature changes in Ti implants (fixtures) upon hot-liquid oral intake. Materials and Methods: We, via an ex vivo-based model, investigated the impact of the (a) material, (b) location point along implant length, and (c) exposure time of the thermal load on localized temperature changes. Results: Despite its simplicity, the presented solution contains all the physics and reproduces the key features obtained in previous numerical analyses studies. To the best of our knowledge, this is the first introduction of the intrinsic time, a {"}proper{"} time that characterizes the geometry of the dental implant fixture, where we show, mathematically and graphically, how the interplay between {"}proper{"} time and exposure time influences temperature changes in Ti implants, under the suitable initial and boundary conditions. This fills the current gap in the literature by obtaining a simplified yet exact analytical solution, assuming an exponential thermal load model relevant to cold/hot beverage or food intake. Conclusions: This work aspires to accurately complement the overall clinical diagnostic and treatment plan for enhanced bone-implant interface, implant stability, and success rates, whether for immediate or delayed loading strategies.",

keywords = "Dental implants, Thermal stress, Modeling of heat transfer, Temperature changes, Heat equation, Analytical solution",

author = "Panotopoulos, {Grigorios P.} and Haidar, {Ziyad S.}",

note = "Funding Information: Acknowledgments: ZS Haidar (DDS, Cert Implantol, MSc OMFS, FRCS (C), MBA, PhD) acknowledges the generous funding and operating grants that supported this work via providing the necessary resources to the BioMAT{\textquoteright}X I+D+I Research Group (Haidar Lab), part of CiiB (Centro de Investigaci{\'o}n e Innovaci{\'o}n Biom{\'e}dica), through the Faculty of Dentistry (F-ODO) and Department for Research, Development and Innovation I+D+i, Universidad de los Andes, Santiago, Chile. Funding Information: Figure 8. Experimental Set‐up; developed in‐House (at the BioMAT{\textquoteright}X R&D&I Laboratory—Haidar Lab, CiiB, Faculties of Medicine and Dentistry, Universidad de los Andes, Santiago de Chile) as an ex‐vivo heat distribution model employ‐ ing human patient‐grade titanium dental implants placed into porcine ribs (without coolant) and thermal changes moni‐ tored/recorded (quantified) using a CorDEX TP3R ToughPix DigiTherm Digital Thermal Camera (an ongoing investiga‐ tion). into porcine ribs (without coolant) and thermal changes monitored/recorded (quantified) using a CorDEX TP3R ToughPix DigiTherm Digital Thermal Camera (an ongoing investigation). Author Contributions: Conceptualization, Z.S.H.; methodology, Z.S.H. and G.P.P.; software, AGu.Pt.hPo.;r vCaolindtaritibount,i oGn.Ps:.PC. oanncde pZtu.Sa.Hliz.;a tfioornm, aZl. Sa.nHa.l;ymsies,t hGo.dPo.Plo. gayn,dZ Z.S..SH.H. a.;n idnvGe.sPt.iPg.;astioofntw, Zar.Se.,HG..;P r.Pe.‐; vsoaulirdcaetsio, nG,.GP..PP..P a. nandd ZZ.S.S.H.H.;. ;dfoartma acul arantaiolyns,i sZ, .GS..PH.P. .aanndd GZ..SP..HP..;; iwnvrietsintigg—atioornig, iZn.aSl. Hd.r;arfets opurercpeasr,aGti.oPn.P,. aZn.Sd.HZ.. Sa.Hnd.; dGa.tPa.Pcu.; rawtiroitnin, Zg—.S.rHev. aienwd Gan.Pd.P .e; dwitriintign,g —Z.So.rHig. inaanldd rGaf.Pt p.Pr.e; pvairsautaiolinz,aZti.oSn.H, .Za.Sn.dHG. .aPn.Pd.; wG.rPit.iPn.g; —surpeevriveiwsioann,d Ze.dS.iHtin.;g p, rZo.jSe.cHt .aadnmdiGni.sPt.rPa.;tivoinsu, aZl.iSz.aHti.o; nfu, nZd.Si.nHg. aacnqduGis.iPti.oP.n;,s uZp.Se.rHv.i sAiolln ,aZut.Sh.oHrs.; phraovjee crteaadd manindi satgraretieodn t,oZ t.hS.eH p.;ufbulnisdhiendg vaecrqsuioisni toiof nth, eZ m.S.aHn.uAsclrliaput.t hors have read and agreed to the published version of the manuscript. Funding: Author (G.P.P.) acknowledges the Funda{\c c}ao para a Ciencia e Tecnologia (FCT) in Portu‐ Fgualn fdoirn tgh:eA fuinthanorci(aGl .sPu.Pp.)paocrkt nporwovleiddegdes toth Ce EFuNnTdRaA{\c c}a o(Cpeanrtaera fCoire nAcsitaroepTheycnsioclso agniad( FGCrTav) iitnatPioonrt)u, gIna‐l fsotirtuthtoe fSinuapnecriioalr sTu{\'e}pcpnoicrot ,p UronviivdeerdsitdoaCdeE NdeT RLAisb(Coae,n ttherrofourghA stthreo pGhryasnict sNano.d UGIrDaBvi/t0a0t0io9n9/)2, 0In2s0t.i tTuhtoe Sauutpheorrio arlsTo{\'e} wcniischoe,sU ton iavcekrnsiodwaldeeddgee tLhies bfouan,dtehdr ooupgphorthtuenGitrya tnot wNoor.kU oInD tBh/is0 0m0u99lt/i‐2d0i2sc0i.pTlihnearayu pthroor‐ ajelcsto wwiitshh eBsiotoMaAcTk{\textquoteright}nXo wI+lDed+gi e(Hthaeidfaurn dLeadb) oupnpdoertru tnhiety stuopwerovriskioonn othf isthme uCltoir-dreisspciopnlidnianrgy Apruothjeocrt (Z.S.H.). The corresponding author (Z.S.H.) acknowledges supplementary operating funding pro‐ vided from CONICYT‐FONDEF Chile under awarded project/grant (national) #ID16I10366 (2016– 2020), Fondo de Ayuda a la Investigacion (FAI)—Universidad de los Andes No. INV‐IN‐2015‐101 (2015–2020) and Fondos de Apoyo a la Innovaci{\'o}n (FAIN), Direcci{\'o}n de Innovaci{\'o}n—Universidad de los Andes, Project X{\textquoteright}PLANT 3Ss Dental Implant Solutions, No. Oco ZFAIN2019005 (2018‐2022). Project X{\textquoteright}PLANT 3Ss Dental Implant Solutions, No. Oco ZFAIN2019005 (2018-2022). Publisher Copyright: {\textcopyright} 2022 by the authors.",

year = "2022",

month = mar,

day = "10",

doi = "10.3390/dj10030043",

language = "English",

volume = "10",

pages = "1--14",

journal = "Dentistry Journal",

issn = "2304-6767",

publisher = "MDPI Multidisciplinary Digital Publishing Institute",

number = "3",

}

TY - JOUR

T1 - Thermal Load and Heat Transfer in Dental Titanium Implants

T2 - an Ex Vivo-Based Exact Analytical/Numerical Solution to the ‘Heat Equation’

AU - Panotopoulos, Grigorios P.

AU - Haidar, Ziyad S.

N1 - Funding Information: Acknowledgments: ZS Haidar (DDS, Cert Implantol, MSc OMFS, FRCS (C), MBA, PhD) acknowledges the generous funding and operating grants that supported this work via providing the necessary resources to the BioMAT’X I+D+I Research Group (Haidar Lab), part of CiiB (Centro de Investigación e Innovación Biomédica), through the Faculty of Dentistry (F-ODO) and Department for Research, Development and Innovation I+D+i, Universidad de los Andes, Santiago, Chile. Funding Information: Figure 8. Experimental Set‐up; developed in‐House (at the BioMAT’X R&D&I Laboratory—Haidar Lab, CiiB, Faculties of Medicine and Dentistry, Universidad de los Andes, Santiago de Chile) as an ex‐vivo heat distribution model employ‐ ing human patient‐grade titanium dental implants placed into porcine ribs (without coolant) and thermal changes moni‐ tored/recorded (quantified) using a CorDEX TP3R ToughPix DigiTherm Digital Thermal Camera (an ongoing investiga‐ tion). into porcine ribs (without coolant) and thermal changes monitored/recorded (quantified) using a CorDEX TP3R ToughPix DigiTherm Digital Thermal Camera (an ongoing investigation). Author Contributions: Conceptualization, Z.S.H.; methodology, Z.S.H. and G.P.P.; software, AGu.Pt.hPo.;r vCaolindtaritibount,i oGn.Ps:.PC. oanncde pZtu.Sa.Hliz.;a tfioornm, aZl. Sa.nHa.l;ymsies,t hGo.dPo.Plo. gayn,dZ Z.S..SH.H. a.;n idnvGe.sPt.iPg.;astioofntw, Zar.Se.,HG..;P r.Pe.‐; vsoaulirdcaetsio, nG,.GP..PP..P a. nandd ZZ.S.S.H.H.;. ;dfoartma acul arantaiolyns,i sZ, .GS..PH.P. .aanndd GZ..SP..HP..;; iwnvrietsintigg—atioornig, iZn.aSl. Hd.r;arfets opurercpeasr,aGti.oPn.P,. aZn.Sd.HZ.. Sa.Hnd.; dGa.tPa.Pcu.; rawtiroitnin, Zg—.S.rHev. aienwd Gan.Pd.P .e; dwitriintign,g —Z.So.rHig. inaanldd rGaf.Pt p.Pr.e; pvairsautaiolinz,aZti.oSn.H, .Za.Sn.dHG. .aPn.Pd.; wG.rPit.iPn.g; —surpeevriveiwsioann,d Ze.dS.iHtin.;g p, rZo.jSe.cHt .aadnmdiGni.sPt.rPa.;tivoinsu, aZl.iSz.aHti.o; nfu, nZd.Si.nHg. aacnqduGis.iPti.oP.n;,s uZp.Se.rHv.i sAiolln ,aZut.Sh.oHrs.; phraovjee crteaadd manindi satgraretieodn t,oZ t.hS.eH p.;ufbulnisdhiendg vaecrqsuioisni toiof nth, eZ m.S.aHn.uAsclrliaput.t hors have read and agreed to the published version of the manuscript. Funding: Author (G.P.P.) acknowledges the Fundaçao para a Ciencia e Tecnologia (FCT) in Portu‐ Fgualn fdoirn tgh:eA fuinthanorci(aGl .sPu.Pp.)paocrkt nporwovleiddegdes toth Ce EFuNnTdRaAça o(Cpeanrtaera fCoire nAcsitaroepTheycnsioclso agniad( FGCrTav) iitnatPioonrt)u, gIna‐l fsotirtuthtoe fSinuapnecriioalr sTuépcpnoicrot ,p UronviivdeerdsitdoaCdeE NdeT RLAisb(Coae,n ttherrofourghA stthreo pGhryasnict sNano.d UGIrDaBvi/t0a0t0io9n9/)2, 0In2s0t.i tTuhtoe Sauutpheorrio arlsToé wcniischoe,sU ton iavcekrnsiodwaldeeddgee tLhies bfouan,dtehdr ooupgphorthtuenGitrya tnot wNoor.kU oInD tBh/is0 0m0u99lt/i‐2d0i2sc0i.pTlihnearayu pthroor‐ ajelcsto wwiitshh eBsiotoMaAcTk’nXo wI+lDed+gi e(Hthaeidfaurn dLeadb) oupnpdoertru tnhiety stuopwerovriskioonn othf isthme uCltoir-dreisspciopnlidnianrgy Apruothjeocrt (Z.S.H.). The corresponding author (Z.S.H.) acknowledges supplementary operating funding pro‐ vided from CONICYT‐FONDEF Chile under awarded project/grant (national) #ID16I10366 (2016– 2020), Fondo de Ayuda a la Investigacion (FAI)—Universidad de los Andes No. INV‐IN‐2015‐101 (2015–2020) and Fondos de Apoyo a la Innovación (FAIN), Dirección de Innovación—Universidad de los Andes, Project X’PLANT 3Ss Dental Implant Solutions, No. Oco ZFAIN2019005 (2018‐2022). Project X’PLANT 3Ss Dental Implant Solutions, No. Oco ZFAIN2019005 (2018-2022). Publisher Copyright: © 2022 by the authors.

PY - 2022/3/10

Y1 - 2022/3/10

N2 - Introduction: Heat is a kinetic process whereby energy flows from between two systems, hot-to-cold objects. In oro-dental implantology, conductive heat transfer/(or thermal stress) is a complex physical phenomenon to analyze and consider in treatment planning. Hence, ample research has attempted to measure heat-production to avoid over-heating during bone-cutting and drilling for titanium (Ti) implant-site preparation and insertion, thereby preventing/minimizing early (as well as delayed) implant-related complications and failure. Objective: Given the low bone-thermal conductivity whereby heat generated by osteotomies is not effectively dissipated and tends to remain within the surrounding tissue (peri-implant), increasing the possibility of thermal-injury, this work attempts to obtain an exact analytical solution of the heat equation under exponential thermal-stress, modeling transient heat transfer and temperature changes in Ti implants (fixtures) upon hot-liquid oral intake. Materials and Methods: We, via an ex vivo-based model, investigated the impact of the (a) material, (b) location point along implant length, and (c) exposure time of the thermal load on localized temperature changes. Results: Despite its simplicity, the presented solution contains all the physics and reproduces the key features obtained in previous numerical analyses studies. To the best of our knowledge, this is the first introduction of the intrinsic time, a "proper" time that characterizes the geometry of the dental implant fixture, where we show, mathematically and graphically, how the interplay between "proper" time and exposure time influences temperature changes in Ti implants, under the suitable initial and boundary conditions. This fills the current gap in the literature by obtaining a simplified yet exact analytical solution, assuming an exponential thermal load model relevant to cold/hot beverage or food intake. Conclusions: This work aspires to accurately complement the overall clinical diagnostic and treatment plan for enhanced bone-implant interface, implant stability, and success rates, whether for immediate or delayed loading strategies.

AB - Introduction: Heat is a kinetic process whereby energy flows from between two systems, hot-to-cold objects. In oro-dental implantology, conductive heat transfer/(or thermal stress) is a complex physical phenomenon to analyze and consider in treatment planning. Hence, ample research has attempted to measure heat-production to avoid over-heating during bone-cutting and drilling for titanium (Ti) implant-site preparation and insertion, thereby preventing/minimizing early (as well as delayed) implant-related complications and failure. Objective: Given the low bone-thermal conductivity whereby heat generated by osteotomies is not effectively dissipated and tends to remain within the surrounding tissue (peri-implant), increasing the possibility of thermal-injury, this work attempts to obtain an exact analytical solution of the heat equation under exponential thermal-stress, modeling transient heat transfer and temperature changes in Ti implants (fixtures) upon hot-liquid oral intake. Materials and Methods: We, via an ex vivo-based model, investigated the impact of the (a) material, (b) location point along implant length, and (c) exposure time of the thermal load on localized temperature changes. Results: Despite its simplicity, the presented solution contains all the physics and reproduces the key features obtained in previous numerical analyses studies. To the best of our knowledge, this is the first introduction of the intrinsic time, a "proper" time that characterizes the geometry of the dental implant fixture, where we show, mathematically and graphically, how the interplay between "proper" time and exposure time influences temperature changes in Ti implants, under the suitable initial and boundary conditions. This fills the current gap in the literature by obtaining a simplified yet exact analytical solution, assuming an exponential thermal load model relevant to cold/hot beverage or food intake. Conclusions: This work aspires to accurately complement the overall clinical diagnostic and treatment plan for enhanced bone-implant interface, implant stability, and success rates, whether for immediate or delayed loading strategies.

KW - Dental implants

KW - Thermal stress

KW - Modeling of heat transfer

KW - Temperature changes

KW - Heat equation

KW - Analytical solution

UR - http://www.scopus.com/inward/record.url?scp=85129687084&partnerID=8YFLogxK

U2 - 10.3390/dj10030043

DO - 10.3390/dj10030043

M3 - Article

C2 - 35323245

SN - 2304-6767

VL - 10

SP - 1

EP - 14

JO - Dentistry Journal

JF - Dentistry Journal

IS - 3

M1 - 43

ER -

Thermal Load and Heat Transfer in Dental Titanium Implants: an Ex Vivo-Based Exact Analytical/Numerical Solution to the ‘Heat Equation’

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