Numerical modelling of cancellous bone damage using an orthotropic failure criterion and tissue elastic properties as a function of the mineral content and microporosity

Megías, Raquel; Vercher-Martínez, Ana; Belda, Ricardo; Peris, José Luis; Larrainzar-Garijo, Ricardo; Giner, Eugenio; Fuenmayor, F. Javier

Affiliations

¹Dept. de Ingeniería Mecánica y de Materiales. Instituto de Ingeniería Mecánica y Biomecánica de Valencia - I2MB, Universitat Politècnica de València, Camino de Vera, Building 5E-9C, Valencia 46022, Spain

²Instituto de Ingeniería Mecánica y Biomecánica de Valencia - I2MB, Healthcare Technology Group (GTS-IBV), Universitat Politècnica de València, Camino de Vera, Building 5E-9C, Valencia 46022, Spain

³Orthopedic and Trauma Department, Hospital Universitario Infanta Leonor, Medical School, Universidad Complutense Madrid, Spain

Abstract and keywords

Background and objective: Elastic and strength properties of lamellar tissue are essential to analyze the mechanical behaviour of bone at the meso- or macro-scale. Although many efforts have been made to model the architecture of cancellous bone, in general, isotropic elastic constants are assumed for tissue modelling, neglecting its non-isotropic behaviour. Therefore, isotropic damage laws are often used to estimate the bone failure. The main goals of this work are: (1) to present a new model for the estimation of the elastic properties of lamellar tissue which includes the bone mineral density (BMD) and the microporosity, (2) to address the numerical modelling of cancellous bone damage using an orthotropic failure criterion and a discrete damage mechanics analysis, including the novel approach for the tissue elastic properties aforementioned.

Methods: Numerical homogenization has been used to estimate the elastic properties of lamellar bone considering BMD and microporosity. Microcomputed Tomography ( μ-CT) scans have been performed to obtain the micro-finite element (μ-FE) model of cancellous bone from a vertebra of swine. In this model, lamellar tissue is orientated by considering a unidirectional layer pattern being the mineralized collagen fibrils aligned with the most representative geometrical feature of the trabeculae network. We have considered the Hashin’s failure criterion and the Material Property Degradation (MPDG) method for simulating the onset and evolution of bone damage.

Results: The terms of the stiffness matrix for lamellar tissue are derived as functions of the BMD and microporosity at tissue scale. Results obtained for the apparent yield strain values agree with experimental values found in the literature. The influence of the damage parameters on the bone mechanics behaviour is also presented.

Conclusions: Stiffness matrix of lamellar tissue depends on both BMD and microporosity. The new approach presented in this work enables to analyze the influence of the BMD and porosity on the mechanical response of bone. Lamellar tissue orientation has to be considered in the mechanical analysis of the cancellous bone. An orthotropic failure criterion can be used to analyze the bone failure onset instead of isotropic criteria. The elastic property degradation method is an efficient procedure to analyze the failure propagation in a 3D numerical model.

Keywords: Lamellar bone porosity; Cancellous bone numerical modelling; Finite element method; Damage initiation; Material property degradation; Orthotropic failure criterion

Links

DOI: 10.1016/j.cmpb.2022.106764

PubMed: 35366593

WoS: 000821201900008

History

Received: 2021-09-22

Revised: 2022-03-07

Accepted: 2022-03-18

Cited Works (28)

Year	Entry
2010	Reisinger AG, Pahr DH, Zysset PK. Sensitivity analysis and parametric study of elastic properties of an unidirectional mineralized bone fibril-array using mean field methods. Biomech Model Mechanobiol. October 2010;9(5):499-510.
1988	Schaffler MB, Burr DB. Stiffness of compact bone: effects of porosity and density. J Biomech. 1988;21(1):13-16.
2018	Hammond MA, Wallace JM, Allen MR, Siegmund T. Incorporating tissue anisotropy and heterogeneity in finite element models of trabecular bone altered predicted local stress distributions. Biomech Model Mechanobiol. April 2018;17(2):605-614.
2019	Hammond MA, Wallace JM, Allen MR, Siegmund T. Mechanics of linear microcracking in trabecular bone. J Biomech. January 23, 2019;83:34-42.
2006	Donnelly E, Williams RM, Downs SA, Dickinson ME, Baker SP, van der Meulen MCH. Quasistatic and dynamic nanomechanical properties of cancellous bone tissue relate to collagen content and organization. J Mater Res. August 2006;21(8):2106-2117.
1967	Ascenzi A, Bonucci E. The tensile properties of single osteons. Acta Anat. 1967;158(4):375-386.
1998	Zioupos P. Recent developments in the study of failure of solid biomaterials and bone: “fracture” and “pre-fracture” toughness. Mater Sci Eng C Mater Biol Appl. September 1998;6(1):33-40.
2008	Renders GAP, Mulder L, Langenbach GEJ, van Ruijven LJ, van Eijden TMGJ. Biomechanical effect of mineral heterogeneity in trabecular bone. J Biomech. August 2008;41(13):2793-2798.
2011	Wolfram U, Wilke H-J, Zysset PK. Damage accumulation in vertebral trabecular bone depends on loading mode and direction. J Biomech. April 7, 2011;44(7):1164-1169.
2013	Hambli R. Micro-CT finite element model and experimental validation of trabecular bone damage and fracture. Bone. October 2013;56(2):363-374.
1968	Ascenzi A, Bonucci E. The compressive properties of single osteons. Anat Rec. July 1968;161(3):377-392.
2011	Hambli R. Multiscale prediction of crack density and crack length accumulation in trabecular bone based on neural networks and finite element simulation. Int J Num Meth Biomed Eng. April 2011;27(4):461-475.
1999	Cowin SC. Bone poroelasticity. J Biomech. March 1999;32(3):217-238.
2015	Oftadeh R, Perez-Viloria M, Villa-Camacho JC, Vaziri A, Nazarian A. Biomechanics and mechanobiology of trabecular bone: a review. J Biomech Eng. January 2015;137(1):010802.
1998	Kopperdahl DL, Keaveny TM. Yield strain behavior of trabecular bone. J Biomech. July 1998;31(7):601-608.
2005	Nagaraja S, Couse TL, Guldberg RE. Trabecular bone microdamage and microstructural stresses under uniaxial compression. J Biomech. 2005;38(4):707-716.
1989	Turner CH. Yield behavior of bovine cancellous bone [published correction appears in J Biomech Eng. 1989;111(4):335]. J Biomech Eng. August 1989;111(3):256-260.
1986	Currey JD. Power law models for the mechanical properties of cancellous bone. Eng Med. July 1986;15(3):153-154.
2006	Nazarian A, Stauber M, Zurakowski D, Snyder BD, Müller R. The interaction of microstructure and volume fraction in predicting failure in cancellous bone. Bone. December 2006;39(6):1196-1202.
1988	Currey JD. The effect of porosity and mineral content on the Young's modulus of elasticity of compact bone. J Biomech. 1988;21(2):131-139.
1987	Parfitt AM. Bone remodeling and bone loss: understanding the pathophysiology of osteoporosis. Clin Obstet Gynecol. December 1987;30(4):789-811.
2016	Torres AM, Matheny JB, Keaveny TM, Taylor D, Rimnac CM, Hernandez CJ. Material heterogeneity in cancellous bone promotes deformation recovery after mechanical failure. Proc Natl Acad Sci USA. March 15, 2016;113(11):2892-2897.
1984	Parfitt AM. Age-related structural changes in trabecular and cortical bone: cellular mechanisms and biomechanical consequences. Calcif Tiss Int. 1984;36(suppl 1):S123-S128.
2016	Georgiadis M, Guizar-Sicairos M, Gschwend O, Hangartner P, Bunk O, Müller R, Schneider P. Ultrastructure organization of human trabeculae assessed by 3D sSAXS and relation to bone microarchitecture. PLoS One. August 22, 2016;11(8):e0159838.
1972	Ascenzi A, Bonucci E. The shearing properties of single osteons. Anat Rec. March 1972;172B(3):499-510.
1990	Mosekilde L. Consequences of the remodelling process for vertebral trabecular bone structure: a scanning electron microscopy study (uncoupling of unloaded structures). Bone Miner. July 1990;10(1):13-35.
1985	Lemaitre J. A continuous damage mechanics model for ductile fracture. J Eng Mater Technol. January 1985;107(1):83-89.
2009	Garcia D, Zysset PK, Charlebois M, Curnier A. A three-dimensional elastic plastic damage constitutive law for bone tissue. Biomech Model Mechanobiol. April 2009;8(2):149-165.