Reliable Patient-Specific Simulations of the Femur. In: Gefen A, editor. Patient-Specific Modeling in Tomorrow's Medicine. Berlin: Springer Berlin Heidelberg; 2012. pp. 3-26. [DOI: 10.1007/8415_2011_89]

Time Dependent Behaviour of Trabecular Bone at Multiple Load Levels

The deformation of bone when subjected to loads is not instantaneous but varies with time. To investigate this time-dependent behaviour sixteen bovine trabecular bone specimens were subjected to compressive loading, creep, unloading and recovery at multiple load levels corresponding to apparent strains of 2000-25,000 με. We found that: the time-dependent response of trabecular bone comprises of both recoverable and irrecoverable strains; the strain response is nonlinearly related to applied load levels; and the response is linked to bone volume fraction. Although majority of strain is recovered after the load-creep-unload-recovery cycle some residual strain always exists. The analysis of results indicates that trabecular bone becomes stiffer initially and then experiences stiffness degradation with the increasing load levels. Steady state creep rate was found to be dependent on applied stress level and bone volume fraction with a power law relationship.

Linear viscoelasticity - bone volume fraction relationships of bovine trabecular bone

Trabecular bone has been previously recognized as time-dependent (viscoelastic) material, but the relationships of its viscoelastic behaviour with bone volume fraction (BV/TV) have not been investigated so far. Therefore, the aim of the present study was to quantify the time-dependent viscoelastic behaviour of trabecular bone and relate it to BV/TV. Uniaxial compressive creep experiments were performed on cylindrical bovine trabecular bone samples (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textit{n}\,{=}\,13$$\end{document}n=13) at loads corresponding to physiological strain level of 2000 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upmu }{\upvarepsilon }$$\end{document}με. We assumed that the bone behaves in a linear viscoelastic manner at this low strain level and the corresponding linear viscoelastic parameters were estimated by fitting a generalized Kelvin–Voigt rheological model to the experimental creep strain response. Strong and significant power law relationships (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r^2\,{=}\,0.73,\ p\,{<}\,0.001$$\end{document}r2=0.73,p<0.001) were found between time-dependent creep compliance function and BV/TV of the bone. These BV/TV-based material properties can be used in finite element models involving trabecular bone to predict time-dependent response. For users’ convenience, the creep compliance functions were also converted to relaxation functions by using numerical interconversion methods and similar power law relationships were reported between time-dependent relaxation modulus function and BV/TV.

Patient-specific modelling of bone and bone-implant systems: the challenges

In the past three decades, finite element (FE) modelling has provided considerable understanding to the area of musculoskeletal biomechanics. However, most of this understanding has been generated using generic, standardised or idealised models. Patient-specific modelling (PSM) is almost never used for making clinical decisions. Imaging technologies have made it possible to create patient-specific geometries and FE meshes for modelling. While these have brought us closer to PSM, several challenges associated with the definition of material properties, loads, boundary conditions and interaction between components still need to be overcome. This study reviews the current status of PSM with respect to defining material behaviour and prescribing boundary conditions and interactions. With regard to the constitutive modelling of bone, it is seen that imaging is being increasingly used to define elastic properties (isotropic as well as anisotropic). However, the post-elastic and time-dependent behaviour, important for several modelling situations, is mostly obtained from in vitro experiments. Strain-based plasticity, not commonly available in FE codes, appears to have the potential of reducing an element of patient-specificity in modelling the yielding behaviour of bone. PSM of real boundary conditions that include muscles and ligaments continues to remain a challenge; many clinically relevant questions can be, however, answered without their inclusion. Simulation techniques to undertake PSM of interactions between bone and uncemented implants are available. Interference fit employed in both joint replacement fracture treatments induces considerable preload whose inclusion in models is important for the prediction of interface behaviour.