Rapid identification of elastic modulus of the interface tissue on dental implants surfaces using reduced-basis method and a neural network.

This paper proposes a rapid inverse analysis approach based on the reduced-basis method (RBM) and neural network (NN) to identify the "unknown" elastic modulus (Young's modulus) of the interfacial tissue between a dental implant and the surrounding bones. In the present RBM-NN approach, a RBM model is first built to compute displacement responses of dental implant-bone structures subjected to a harmonic loading for a set of "assumed" Young's moduli. The RBM model is then used to train a NN model that is used for actual inverse analysis in real-time. Actual experimental measurements of displacement responses are fed into the trained NN model to inversely determine the "true" elastic modulus of the interfacial tissue. As an example, a physical model of dental implant-bone structure is built and inverse analysis is conducted to verify the present RBM-NN approach. Based on numerical simulation and actual experiments, it is confirmed that the identified results are very accurate, reliable, and the computational saving is very significant. The present RBM-NN approach is found robust and efficient for inverse material characterizations in noninvasive and/or nondestructive evaluations.

[1]  Gui-Rong Liu,et al.  Computational Inverse Techniques for Material Characterization Using Dynamic Response , 2002 .

[2]  Guirong Liu A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS , 2008 .

[3]  T Jemt,et al.  Early failures in 4,641 consecutively placed Brånemark dental implants: a study from stage 1 surgery to the connection of completed prostheses. , 1991, The International journal of oral & maxillofacial implants.

[4]  N Meredith,et al.  Quantitative determination of the stability of the implant-tissue interface using resonance frequency analysis. , 1996, Clinical oral implants research.

[5]  Anthony T. Patera,et al.  Reduced basis approximation and a posteriori error estimation for a Boltzmann model , 2007 .

[6]  Gui-Rong Liu,et al.  A novel reduced-basis method with upper and lower bounds for real-time computation of linear elasticity problems , 2008 .

[7]  D. W. Noid,et al.  On the Design, Analysis, and Characterization of Materials Using Computational Neural Networks , 1996 .

[8]  A. Patera,et al.  Certified real‐time solution of the parametrized steady incompressible Navier–Stokes equations: rigorous reduced‐basis a posteriori error bounds , 2005 .

[9]  Gui-Rong Liu,et al.  Rapid inverse parameter estimation using reduced-basis approximation with asymptotic error estimation , 2008 .

[10]  S. Cowin,et al.  Wolff's law of trabecular architecture at remodeling equilibrium. , 1986, Journal of biomechanical engineering.

[11]  Anthony T. Patera,et al.  Reduced basis approximation and a posteriori error estimation for stress intensity factors , 2007 .

[12]  J B Brunski,et al.  Biomechanical factors affecting the bone-dental implant interface. , 1992, Clinical materials.

[13]  A. Patera,et al.  A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations , 2005 .

[14]  A. Wennerberg,et al.  Implant stability during initiation and resolution of experimental periimplantitis: an experimental study in the dog. , 2005, Clinical implant dentistry and related research.

[15]  K. Y. Lam,et al.  A combined genetic algorithm and nonlinear least squares method for material characterization using elastic waves , 2002 .

[16]  K. Lam,et al.  Material Characterization of FGM Plates Using Elastic Waves and an Inverse Procedure , 2001 .

[17]  S. Cowin Bone mechanics handbook , 2001 .

[18]  G. Liu,et al.  Application of finite element analysis in implant dentistry: a review of the literature. , 2001, The Journal of prosthetic dentistry.

[19]  Jian Zhang,et al.  Inverse identification of elastic modulus of dental implant–bone interfacial tissue using neural network and FEA model , 2009 .

[20]  Gui-Rong Liu,et al.  Influence of osseointegration degree and pattern on resonance frequency in the assessment of dental implant stability using finite element analysis. , 2008, The International Journal of Oral and Maxillofacial Implants.

[21]  Fook Fah Yap,et al.  On Determination of the Material Constants of Laminated Cylindrical Shells Based on an Inverse Optimal Approach , 2002 .

[22]  G. Rozza,et al.  On the stability of the reduced basis method for Stokes equations in parametrized domains , 2007 .

[23]  K. Y. Lam,et al.  Material characterization of functionally graded material by means of elastic waves and a progressive-learning neural network , 2001 .

[24]  Xu Han,et al.  A computational inverse technique for material characterization of a functionally graded cylinder using a progressive neural network , 2003, Neurocomputing.

[25]  Anthony T. Patera,et al.  10. Certified Rapid Solution of Partial Differential Equations for Real-Time Parameter Estimation and Optimization , 2007 .

[26]  Ch. Tsakmakis,et al.  Determination of constitutive properties fromspherical indentation data using neural networks. Part i:the case of pure kinematic hardening in plasticity laws , 1999 .

[27]  George A. Zarb,et al.  Tissue-Integrated Prostheses: Osseointegration in Clinical Dentistry , 1985 .

[28]  Gui-rong Liu,et al.  Computational Inverse Technique for Material Characterization of Functionally Graded Materials , 2003 .

[29]  Anthony T. Patera,et al.  Inverse identification of thermal parameters using reduced-basis method , 2005 .

[30]  D. Rovas,et al.  Reduced--Basis Output Bound Methods for Parametrized Partial Differential Equations , 2002 .

[31]  Gui-rong Liu,et al.  Computational Inverse Techniques in Nondestructive Evaluation , 2003 .