Multiphasic Modelling of the Vertebral Bone for Cement‐Injection Studies

Abstract

The stability of the human spine is highly dependent on the cancellous bone structure of the vertebra. In the case of osteoporosis and accompanied weaking of the vertebral structure, compression fractures and other lesions of the affected patient may occur. The reinforcement of the porous cancellous bone by the injection of bone-cement is a common procedure in order to overcome this issues. The modelling and computational simulation of vertebroplasty, i.e., bone-cement-injection into the vertebra, is of major interest to obtain valid and reliable predicitions for this surgery. A detailed micromechanical (and locally single-phasic) model exhibits the drawback that all geometrical and physical transition conditions of the individual parts and their complex microstructure have to be known. Therefore, this study considers a macro-scopic (and multi-constituent) continuum-mechanical model based on the Theory of Porous Media, where the homogenisation of the underlying microstructure results in a model of three constituents. In particular, these are the solid bone skeleton, which is saturated by bone marrow, where the latter may be displaced by the injected liquid bone cement. The micro-architecture is regarded by heterogeneous and anisotropic permeability tensors and the preferred directions of the trabecular bone structure. The presented strongly coupled macroscopic model offers the opportunity to not only simulate the flow of the pore fluids but also predicts the arising stresses and strains of the solid bone skeleton due to the numerical investigation of the injection process.