Porous‐media simulation of bone‐cement spreading during vertebroplasty

Abstract

The reinforcement of porous vertebral cancellous bone by the injection of bone cement is a practical procedure for the stabilisation of osteoporotic compression fractures and other weakening lesions. This contribution concerns the reproduction and prediction of the resulting bone-cement distribution during the injection procedure by means of numerical simulation. A detailed micromechanical (locally single-phasic) model exhibits the drawback that all geometrical and physical transition conditions of the individual parts of the complex aggregate have to be known. Therefore, we rather proceed from a macroscopic (and multi-constituent) continuum-mechanical model based on the Theory of Porous Media. In this regard, the homogenisation of the underlying micro-structure results in a model of three constituents: these are the solid bone skeleton, which is saturated by the liquid bone marrow that may be displaced by the injected liquid bone cement. The influence of the microarchitecture of the pore space on the spreading of the bone cement is considered by a spatial diversification of the anisotropic permeability tensors, obtained through image processing techniques applied to medical imaging data (µCT). The numerical investigation of the strongly coupled problem enables the study of vertebroplasty and allows for the comparison between the simulation results and the experimentally determined bone-cement distribution that were imaged during injections.

Multiphasic Modelling of the Vertebral Bone for Cement‐Injection Studies

“…Thus, the overall aggregrate of superimposed and interacting continua is given by ϕ = α ϕ α with α = {S, C, M } being the set of constituents and ϕ F = β ϕ β denoting the pore space with the subset of pore-liquids β = {C, M }, cf. [2] for more details. The motion of the solid constituent ϕ S is described with a Lagrangean description via the displacement u S = x−X S , whereas the liquid constituents are formulated in a modified Eulerian description via the seepage velocities…”

“…Further, the seepage velocities w β of the pore liquids are obtained by an evaluation of the dissipation principle and are expressed by Darcy-like filter laws, hence, they depend on the effective pressures p βR and contain the intrinsic permeability tensor K S , cf. [2].…”