Skip to main content

2015 | OriginalPaper | Buchkapitel

On One Approach to the Simulation of the Periodontal Ligament Takes into Account Its Viscoelastic Properties

verfasst von : K. Yurkevich, S. Bosiakov

Erschienen in: Current Trends in Analysis and Its Applications

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The mathematical model of the viscoelastic periodontal ligament is presented. The relaxation kernel corresponds to the Maxwell model. Model describes the viscoelastic deformations of the periodontal membrane and the tooth movements. Analysis of premolar root movements in the form of an elliptical hyperboloid under the vertical load is performed.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat C. Bourauel, D. Vollmer, A. Jäger, Application of bone remodeling theories in the simulation of orthodontic tooth movements. J. Orofac. Orthop. 61, 266–279 (2000) CrossRef C. Bourauel, D. Vollmer, A. Jäger, Application of bone remodeling theories in the simulation of orthodontic tooth movements. J. Orofac. Orthop. 61, 266–279 (2000) CrossRef
2.
Zurück zum Zitat A.N. Wilson, J. Middleton, M.L. Jones, The role of the periodontal ligament in bone remodeling, in Recent Advances in Computer Methods in Biomechanics and Biomedical Engineering (Books and Journals International, Swansea, 1992), pp. 150–158 A.N. Wilson, J. Middleton, M.L. Jones, The role of the periodontal ligament in bone remodeling, in Recent Advances in Computer Methods in Biomechanics and Biomedical Engineering (Books and Journals International, Swansea, 1992), pp. 150–158
4.
Zurück zum Zitat M.G. Mullender, R. Huiskes, H.J. Weinans, A physiological approach to the simulation of bone remodeling as a self-organisational control process. J. Biomech. 27, 1389–1394 (1994) CrossRef M.G. Mullender, R. Huiskes, H.J. Weinans, A physiological approach to the simulation of bone remodeling as a self-organisational control process. J. Biomech. 27, 1389–1394 (1994) CrossRef
5.
Zurück zum Zitat H.J. Weinans, R. Huiskes, H.J. Grootenboer, The behavior of adaptive bone-remodeling simulation models. J. Biomech. 25, 1425–1441 (1992) CrossRef H.J. Weinans, R. Huiskes, H.J. Grootenboer, The behavior of adaptive bone-remodeling simulation models. J. Biomech. 25, 1425–1441 (1992) CrossRef
6.
Zurück zum Zitat B.J. Moxham, B.K.B. Berkovitz, The effects of external forces on the periodontal ligament, in The Periodontal Ligament in Health and Disease, ed. by B.J. Moxham, H.N. Newman (Mosby-Wolfe, London, 1995) B.J. Moxham, B.K.B. Berkovitz, The effects of external forces on the periodontal ligament, in The Periodontal Ligament in Health and Disease, ed. by B.J. Moxham, H.N. Newman (Mosby-Wolfe, London, 1995)
7.
Zurück zum Zitat T.S. Fill, R.W. Toogood, P.W. Major, J.P. Carey, Analytically determined mechanical properties of, and models for the periodontal ligament: critical review of literature. J. Biomech. 45, 9–16 (2012) CrossRef T.S. Fill, R.W. Toogood, P.W. Major, J.P. Carey, Analytically determined mechanical properties of, and models for the periodontal ligament: critical review of literature. J. Biomech. 45, 9–16 (2012) CrossRef
8.
Zurück zum Zitat K. Komatsu, Mechanical strength and viscoelastic response of the periodontal ligament in relation to structure. J. Dent. Biomech. 1, 1–18 (2010) K. Komatsu, Mechanical strength and viscoelastic response of the periodontal ligament in relation to structure. J. Dent. Biomech. 1, 1–18 (2010)
9.
Zurück zum Zitat M. Ferrari, R. Sorrentino, F. Zarone, D. Apicella, R. Aversa, A. Apicella, Non-linear viscoelastic finite element analysis of the effect of the length of glass fiber posts on the biomechanical behaviour of directly restored incisors and surrounding alveolar bone. Dent. Mater. 27, 485–498 (2008) CrossRef M. Ferrari, R. Sorrentino, F. Zarone, D. Apicella, R. Aversa, A. Apicella, Non-linear viscoelastic finite element analysis of the effect of the length of glass fiber posts on the biomechanical behaviour of directly restored incisors and surrounding alveolar bone. Dent. Mater. 27, 485–498 (2008) CrossRef
10.
Zurück zum Zitat S.M. Bien, Fluid dynamic mechanisms which regulate tooth movement, in Advances in Oral Biology, vol. 2, ed. by E.H. Staple (1966), pp. 173–201 S.M. Bien, Fluid dynamic mechanisms which regulate tooth movement, in Advances in Oral Biology, vol. 2, ed. by E.H. Staple (1966), pp. 173–201
11.
Zurück zum Zitat D.C. Picton, D.J. Wills, Viscoelastic properties of the periodontal ligament and mucous membrane. J. Prosthet. Dent. 40, 263–272 (1978) CrossRef D.C. Picton, D.J. Wills, Viscoelastic properties of the periodontal ligament and mucous membrane. J. Prosthet. Dent. 40, 263–272 (1978) CrossRef
12.
Zurück zum Zitat D.J. Wills, D.C. Picton, W.I. Davies, An investigation of the viscoelastic properties of the periodontium in monkeys. J. Periodontal Res. 7, 42–51 (1972) CrossRef D.J. Wills, D.C. Picton, W.I. Davies, An investigation of the viscoelastic properties of the periodontium in monkeys. J. Periodontal Res. 7, 42–51 (1972) CrossRef
13.
Zurück zum Zitat G.G. Ross, C.S. Lear, R. De Cou, Modeling the lateral movement of teeth. J. Biomech. 9, 723–734 (1976) CrossRef G.G. Ross, C.S. Lear, R. De Cou, Modeling the lateral movement of teeth. J. Biomech. 9, 723–734 (1976) CrossRef
14.
Zurück zum Zitat J.R. Funk, G.W. Hall, J.R. Grandall, W.D. Pilkey, Linear and quasi-linear viscoelastic characterization of ankle ligaments. J. Biomech. Eng. 122, 15–22 (2000) CrossRef J.R. Funk, G.W. Hall, J.R. Grandall, W.D. Pilkey, Linear and quasi-linear viscoelastic characterization of ankle ligaments. J. Biomech. Eng. 122, 15–22 (2000) CrossRef
15.
Zurück zum Zitat J. Middleton, M.L. Jones, A.N. Wilson, Three-dimensional analysis of orthodontic tooth movement. J. Biomed. Eng. 12, 319–327 (1990) CrossRef J. Middleton, M.L. Jones, A.N. Wilson, Three-dimensional analysis of orthodontic tooth movement. J. Biomed. Eng. 12, 319–327 (1990) CrossRef
16.
Zurück zum Zitat M. Pini, P. Zysset, J. Botsis, R. Contro, Tensile and compressive behavior of the bovine periodontal ligament. J. Biomech. 37, 111–119 (2004) CrossRef M. Pini, P. Zysset, J. Botsis, R. Contro, Tensile and compressive behavior of the bovine periodontal ligament. J. Biomech. 37, 111–119 (2004) CrossRef
17.
Zurück zum Zitat H. Körber, Electronic registration of tooth movements. Int. Dent. J. 21, 466–477 (1971) H. Körber, Electronic registration of tooth movements. Int. Dent. J. 21, 466–477 (1971)
18.
Zurück zum Zitat H.R. Mühlemann, Tooth mobility: a review of clinical aspects and research findings. J. Periodontol. 38, 686–713 (1967) H.R. Mühlemann, Tooth mobility: a review of clinical aspects and research findings. J. Periodontol. 38, 686–713 (1967)
19.
Zurück zum Zitat D.C. Picton, Extrusive mobility of teeth in adult monkeys (Macaca fascicularis). Arch. Oral Biol. 31, 369–372 (1986) CrossRef D.C. Picton, Extrusive mobility of teeth in adult monkeys (Macaca fascicularis). Arch. Oral Biol. 31, 369–372 (1986) CrossRef
20.
Zurück zum Zitat D.C. Picton, Tooth mobility—an update. Eur. J. Orthod. 12, 109–115 (1990) CrossRef D.C. Picton, Tooth mobility—an update. Eur. J. Orthod. 12, 109–115 (1990) CrossRef
21.
Zurück zum Zitat S.R. Toms, G.J. Dakin, J.E. Lemons, A.W. Eberhardt, Quasi-linear viscoelastic behavior of the human periodontal ligament. J. Biomech. 35, 1411–1415 (2002) CrossRef S.R. Toms, G.J. Dakin, J.E. Lemons, A.W. Eberhardt, Quasi-linear viscoelastic behavior of the human periodontal ligament. J. Biomech. 35, 1411–1415 (2002) CrossRef
22.
Zurück zum Zitat J. Hazrati, F. Ghalichi, B. Mirzakouchaki, Strain dependent stress relaxation behavior of periodontal ligament. J. Biomech. 41(1), S471 (2008) CrossRef J. Hazrati, F. Ghalichi, B. Mirzakouchaki, Strain dependent stress relaxation behavior of periodontal ligament. J. Biomech. 41(1), S471 (2008) CrossRef
23.
Zurück zum Zitat F. Maceri, M. Marino, G. Vairo, Mechanical behaviour of endodontic restorations with multiple prefabricated posts: a finite-element approach. J. Biomech. 40, 2386–2398 (2007) CrossRef F. Maceri, M. Marino, G. Vairo, Mechanical behaviour of endodontic restorations with multiple prefabricated posts: a finite-element approach. J. Biomech. 40, 2386–2398 (2007) CrossRef
24.
Zurück zum Zitat A.N. Natali, E.L. Carniel, P.G. Pavan, C. Bourauel, A. Ziegler, L. Keilig, Experimental-numerical analysis of minipig’s multi-rooted teeth. J. Biomech. 40, 1701–1708 (2007) CrossRef A.N. Natali, E.L. Carniel, P.G. Pavan, C. Bourauel, A. Ziegler, L. Keilig, Experimental-numerical analysis of minipig’s multi-rooted teeth. J. Biomech. 40, 1701–1708 (2007) CrossRef
25.
Zurück zum Zitat E. Peña, B. Calvo, M.A. Martińez, M. Doblaré, An anisotropic viscohyperelastic model for ligaments at finite strains. Formulation and computational aspects. Int. J. Solids Struct. 44, 760–778 (2007) CrossRefMATH E. Peña, B. Calvo, M.A. Martińez, M. Doblaré, An anisotropic viscohyperelastic model for ligaments at finite strains. Formulation and computational aspects. Int. J. Solids Struct. 44, 760–778 (2007) CrossRefMATH
26.
Zurück zum Zitat E. Peña, J.A. Peña, M. Doblaré, On modeling nonlinear viscoelastic effects in ligaments. J. Biomech. 41, 2659–2666 (2008) CrossRef E. Peña, J.A. Peña, M. Doblaré, On modeling nonlinear viscoelastic effects in ligaments. J. Biomech. 41, 2659–2666 (2008) CrossRef
27.
Zurück zum Zitat S.M. Bosiakov, K.S. Yurkevich, Mathematical modelling of initial tooth root displacements in bone tissue under action of instant static loading. Rus. J. Biomech. 15, 22–29 (2011) S.M. Bosiakov, K.S. Yurkevich, Mathematical modelling of initial tooth root displacements in bone tissue under action of instant static loading. Rus. J. Biomech. 15, 22–29 (2011)
28.
Zurück zum Zitat S.R. Toms, A.W. Eberhardt, A nonlinear finite element analysis of the periodontal ligament under orthodontic tooth loading. Am. J. Orthod. Dentofac. Orthop. 123, 657–665 (2003) CrossRef S.R. Toms, A.W. Eberhardt, A nonlinear finite element analysis of the periodontal ligament under orthodontic tooth loading. Am. J. Orthod. Dentofac. Orthop. 123, 657–665 (2003) CrossRef
29.
Zurück zum Zitat M. Poppe, C. Bourauel, A. Jäger, Determination of the elasticity parameters of the human periodontal ligament and the location of the center of resistance of single-rooted teeth. A study of autopsy specimens and their conversion into finite element models. J. Orofac. Orthop. 63, 358–370 (2002) CrossRef M. Poppe, C. Bourauel, A. Jäger, Determination of the elasticity parameters of the human periodontal ligament and the location of the center of resistance of single-rooted teeth. A study of autopsy specimens and their conversion into finite element models. J. Orofac. Orthop. 63, 358–370 (2002) CrossRef
Metadaten
Titel
On One Approach to the Simulation of the Periodontal Ligament Takes into Account Its Viscoelastic Properties
verfasst von
K. Yurkevich
S. Bosiakov
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-12577-0_86