Modeling of a non-local stimulus for bone remodeling process under cyclic load: Application to a dental implant using a bioresorbable porous material

In this paper, a numerical method based on finite elements is used to study the phenomena of resorption and growth of bone tissue and resorption of the biomaterial in the neighborhood of a dental implant fixture of the type IntraMobil Zylinder. The mechanical stimulus that drives these processes is a linear combination of strain energy and viscous dissipation. To simulate the implant, an axisymmetric model has been used from the point of view of the geometry; the material behavior is described in the poro-visco-elastic frame. The external action is represented by a load variable with sinusoidal law characterized by different frequencies. Investigated aspects are the influence of the load frequency and of the lazy zone on the remodeling process.

[1]  Leopoldo Greco,et al.  Wave propagation in pantographic 2D lattices with internal discontinuities , 2014, 1412.3926.

[2]  Pierre Seppecher,et al.  Second-gradient theory : application to Cahn-Hilliard fluids , 2000 .

[3]  Jonathan A. Dantzig,et al.  Mechanics of Materials and Structures DISSIPATION ENERGY AS A STIMULUS FOR CORTICAL BONE ADAPTATION , 2011 .

[4]  Luisa Pagnini,et al.  The three-hinged arch as an example of piezomechanic passive controlled structure , 2016 .

[5]  On the role of grain growth, recrystallization and polygonization in a continuum theory for anisotropic ice sheets , 2004, Annals of Glaciology.

[6]  In Gwun Jang,et al.  Application of design space optimization to bone remodeling simulation of trabecular architecture in human proximal femur for higher computational efficiency , 2010 .

[7]  Giuseppe Ruta,et al.  A beam model for the flexural–torsional buckling of thin-walled members with some applications , 2008 .

[8]  E. Sedlin,et al.  A rheologic model for cortical bone. A study of the physical properties of human femoral samples. , 1965, Acta orthopaedica Scandinavica. Supplementum.

[9]  Luca Placidi,et al.  An anisotropic flow law for incompressible polycrystalline materials , 2005 .

[10]  A. Gjelsvik,et al.  Mechanical properties of hydrated cortical bone. , 1974, Journal of biomechanics.

[11]  K. Hutter,et al.  What are the dominant thermomechanical processes in the basal sediment layer of large ice sheets? , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[12]  Ugo Andreaus,et al.  Optimal bone density distributions: Numerical analysis of the osteocyte spatial influence in bone remodeling , 2014, Comput. Methods Programs Biomed..

[14]  Dionisio Del Vescovo,et al.  Comparison of piezoelectronic networks acting as distributed vibration absorbers , 2004 .

[15]  F. dell’Isola,et al.  On phase transition layers in certain micro-damaged two-phase solids , 1997 .

[16]  Nicola Rizzi,et al.  The effects of warping constraints on the buckling of thin-walled structures , 2010 .

[17]  Ivan Giorgio,et al.  The influence of different loads on the remodeling process of a bone and bioresorbable material mixture with voids , 2016 .

[18]  D R Carter,et al.  Bone creep-fatigue damage accumulation. , 1989, Journal of biomechanics.

[19]  Giuseppe Piccardo,et al.  On the effect of twist angle on nonlinear galloping of suspended cables , 2009 .

[20]  N. Roveri,et al.  Fractional dissipation generated by hidden wave-fields , 2015 .

[21]  S. Cowin Bone poroelasticity. , 1999, Journal of biomechanics.

[22]  M. Biot,et al.  Generalized Theory of Acoustic Propagation in Porous Dissipative Media * , 1998 .

[23]  A. Akay,et al.  Dissipation in a finite-size bath. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  F. dell’Isola,et al.  A phenomenological approach to phase transition in classical field theory , 1987 .

[25]  Gabriel Wittum,et al.  Evolution of a fibre-reinforced growing mixture , 2009 .

[26]  Francesco dell’Isola,et al.  Variational formulation of pre-stressed solid-fluid mixture theory, with an application to wave phenomena , 2008 .

[27]  Victor A. Eremeyev,et al.  Phase transitions in thermoelastic and thermoviscoelastic shells , 2008 .

[28]  Luca Placidi,et al.  Thermodynamics of polycrystalline materials treated by the theory of mixtures with continuous diversity , 2006 .

[29]  Tomasz Lekszycki,et al.  A 2‐D continuum model of a mixture of bone tissue and bio‐resorbable material for simulating mass density redistribution under load slowly variable in time , 2014 .

[30]  Dionisio Del Vescovo,et al.  Dynamic problems for metamaterials: Review of existing models and ideas for further research , 2014 .

[31]  T. Lekszycki Modelling of Bone Adaptation Based on an Optimal Response Hypothesis* , 2002 .

[32]  Leopoldo Greco,et al.  An isogeometric implicit G1 mixed finite element for Kirchhoff space rods , 2016 .

[33]  Leopoldo Greco,et al.  A variational model based on isogeometric interpolation for the analysis of cracked bodies , 2014 .

[34]  P J Mentag,et al.  Intramobile cylinder (IMZ) two-stage osteointegrated implant system with the intramobile element (IME): part I. Its ratinale and procedure for use. , 1987, The International journal of oral & maxillofacial implants.

[35]  A. Misra,et al.  Physico-mechanical properties determination using microscale homotopic measurements: application to sound and caries-affected primary tooth dentin. , 2009, Acta biomaterialia.

[36]  A. Della Corte,et al.  The postulations á la D’Alembert and á la Cauchy for higher gradient continuum theories are equivalent: a review of existing results , 2015, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[37]  S. Cowin,et al.  Bone remodeling I: theory of adaptive elasticity , 1976 .

[38]  Angelo Luongo,et al.  Linear and non-linear interactions between static and dynamic bifurcations of damped planar beams , 2007 .

[39]  P. Seppecher,et al.  Cauchy Tetrahedron Argument Applied to Higher Contact Interactions , 2015, Archive for Rational Mechanics and Analysis.

[40]  Stephen C. Cowin,et al.  Linear elastic materials with voids , 1983 .

[41]  Alessandro Della Corte,et al.  Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof , 2015 .

[42]  Francesco dell’Isola,et al.  A mixture model with evolving mass densities for describing synthesis and resorption phenomena in bones reconstructed with bio‐resorbable materials , 2012 .

[43]  Francesco dell’Isola,et al.  Plane bias extension test for a continuum with two inextensible families of fibers: A variational treatment with Lagrange multipliers and a perturbation solution , 2016 .

[44]  Flavio Stochino,et al.  Constitutive models for strongly curved beams in the frame of isogeometric analysis , 2016 .

[45]  Ivan Giorgio,et al.  Modeling of the interaction between bone tissue and resorbable biomaterial as linear elastic materials with voids , 2015 .

[46]  Luisa Pagnini,et al.  A numerical algorithm for the aerodynamic identification of structures , 1997 .

[47]  Alfio Grillo,et al.  An energetic approach to the analysis of anisotropic hyperelastic materials , 2008 .

[48]  H. Grootenboer,et al.  The behavior of adaptive bone-remodeling simulation models. , 1992, Journal of biomechanics.

[49]  Luca Placidi,et al.  A variational approach for a nonlinear 1-dimensional second gradient continuum damage model , 2015 .

[50]  H. Altenbach,et al.  Acceleration waves and ellipticity in thermoelastic micropolar media , 2010 .

[51]  M. Biot MECHANICS OF DEFORMATION AND ACOUSTIC PROPAGATION IN POROUS MEDIA , 1962 .

[52]  Ugo Andreaus,et al.  Finite element analysis of the stress state produced by an orthodontic skeletal anchorage system based on miniscrews , 2013 .

[53]  F. dell'Isola,et al.  A micro-structured continuum modelling compacting fluid-saturated grounds: the effects of pore-size scale parameter , 1998 .

[54]  P. D'Asdia,et al.  Damage modelling and seismic response of simple degrading systems , 1987 .

[55]  A. Freidin,et al.  The stability of the equilibrium of two-phase elastic solids , 2007 .

[56]  Ugo Andreaus,et al.  Optimal-tuning PID control of adaptive materials for structural efficiency , 2011 .

[57]  Francesco dell’Isola,et al.  Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence , 2015 .

[58]  F. Darve,et al.  A Continuum Model for Deformable, Second Gradient Porous Media Partially Saturated with Compressible Fluids , 2013 .

[59]  D R Carter,et al.  A cumulative damage model for bone fracture , 1985, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[60]  Stefano Gabriele,et al.  Initial postbuckling behavior of thin-walled frames under mode interaction , 2013 .

[61]  G. Niznick Achieving Osseointegration in Soft Bone: The Search for Improved Results , 2000 .

[62]  T. Lekszycki,et al.  Application of Variational Methods in Analysis and Synthesis of Viscoelastic Continuous Systems , 1991 .

[63]  Antonio Cazzani,et al.  Isogeometric analysis of plane-curved beams , 2016 .

[64]  Jean-François Ganghoffer,et al.  Mechanical modeling of growth considering domain variation―Part II: Volumetric and surface growth involving Eshelby tensors , 2010 .

[65]  S Belouettar,et al.  A micropolar anisotropic constitutive model of cancellous bone from discrete homogenization. , 2012, Journal of the mechanical behavior of biomedical materials.

[66]  Tomasz Lekszycki,et al.  A continuum model for the bio-mechanical interactions between living tissue and bio-resorbable graft after bone reconstructive surgery , 2011 .

[67]  M. Pulvirenti,et al.  Macroscopic Description of Microscopically Strongly Inhomogenous Systems: A Mathematical Basis for the Synthesis of Higher Gradients Metamaterials , 2015, 1504.08015.

[68]  Ridha Hambli,et al.  Connecting Mechanics and Bone Cell Activities in the Bone Remodeling Process: An Integrated Finite Element Modeling , 2014, Front. Bioeng. Biotechnol..

[69]  Alfio Grillo,et al.  Poroelastic materials reinforced by statistically oriented fibres—numerical implementation and application to articular cartilage , 2014 .

[70]  M. Pikos Fundamentals of Implant Dentistry: Surgical Principles , 2017 .

[71]  G. Wittum,et al.  A poroplastic model of structural reorganisation in porous media of biomechanical interest , 2016 .

[72]  Ugo Andreaus,et al.  Modeling of Trabecular Architecture as Result of an Optimal Control Procedure , 2013 .

[73]  Dionisio Del Vescovo,et al.  Piezo-electromechanical smart materials with distributed arrays of piezoelectric transducers: Current and upcoming applications , 2015 .

[74]  Emilio Turco,et al.  A three-dimensional B-spline boundary element , 1998 .

[75]  Ugo Andreaus,et al.  Coupling image processing and stress analysis for damage identification in a human premolar tooth , 2011, Comput. Methods Programs Biomed..

[76]  Luca Placidi,et al.  A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model , 2016 .

[77]  F. dell'Isola,et al.  Modeling and design of passive electric networks interconnecting piezoelectric transducers for distributed vibration control , 2003 .

[78]  R. Huiskes,et al.  Proposal for the regulatory mechanism of Wolff's law , 1995, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[79]  Antonio Cazzani,et al.  Isogeometric analysis: a powerful numerical tool for the elastic analysis of historical masonry arches , 2016 .

[80]  L E Lanyon,et al.  Static vs dynamic loads as an influence on bone remodelling. , 1984, Journal of biomechanics.

[81]  Ugo Andreaus,et al.  An optimal control procedure for bone adaptation under mechanical stimulus , 2012 .

[82]  N. Rizzi,et al.  A one-dimensional continuum with microstructure for single-wall carbon nanotubes bifurcation analysis , 2016 .

[83]  Possible Approaches in Modelling Rearrangement in a Microstructured Material , 2007 .

[84]  A. Misra,et al.  Higher-Order Stress-Strain Theory for Damage Modeling Implemented in an Element-free Galerkin Formulation , 2010 .

[85]  F. dell’Isola,et al.  Dynamics of solids with microperiodic nonconnected fluid inclusions , 1997 .

[86]  Dionisio Del Vescovo,et al.  Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network , 2009 .

[87]  Francesco dell’Isola,et al.  A visco-poroelastic model of functional adaptation in bones reconstructed with bio-resorbable materials , 2016, Biomechanics and Modeling in Mechanobiology.

[88]  Luca Placidi,et al.  A microscale second gradient approximation of the damage parameter of quasi‐brittle heterogeneous lattices , 2014 .

[89]  Leopoldo Greco,et al.  B-Spline interpolation of Kirchhoff-Love space rods , 2013 .

[90]  Jean-François Ganghoffer,et al.  A contribution to the mechanics and thermodynamics of surface growth. Application to bone external remodeling , 2012 .

[91]  Leopoldo Greco,et al.  An implicit G1 multi patch B-spline interpolation for Kirchhoff–Love space rod , 2014 .

[92]  Victor A. Eremeyev,et al.  Analysis of the viscoelastic behavior of plates made of functionally graded materials , 2008 .

[93]  Alessandro Della Corte,et al.  Referential description of the evolution of a 2D swarm of robots interacting with the closer neighbors: Perspectives of continuum modeling via higher gradient continua , 2016 .

[94]  C H Turner,et al.  Homeostatic control of bone structure: an application of feedback theory. , 1991, Bone.

[95]  Yang Yang,et al.  Higher-Order Continuum Theory Applied to Fracture Simulation of Nanoscale Intergranular Glassy Film , 2011 .

[96]  A Staines,et al.  Bone adaptation to load: microdamage as a stimulus for bone remodelling , 2002, Journal of anatomy.

[97]  C H Turner,et al.  Three rules for bone adaptation to mechanical stimuli. , 1998, Bone.