This paper presents simulations of a three-dimensional model of the bone remodelling process. The model consists of a set of variable order partial differential equations, in which the varying order depends on the presence of tumour cells. The simulations are of a two-dimensional bone, to make visualisation simpler. They show that this model corresponds to the known evolution of bone remodelling, and is simpler than integer order models found in the literature.

The paper presents a method of analysis of bone remodelling in the vicinity of implants. The authors aimed at building a model and numerical procedures which may be used as a tool in the prosthesis design process. The model proposed by the authors is based on the theory of adaptive elasticity and the lazy zone concept. It takes into consideration not only changes of the internal structure of the tissue (described by apparent density) but also surface remodelling and changes caused by the effects revealing some features of “creep”. Finite element analysis of a lumbar spinal segment with an artificial intervertebral disc was performed by means of the Ansys system with custom APDL code. The algorithms were in two variants: the so-called site-independent and site-specific. Resultant density distribution and modified shape of the vertebra are compared for both of them. It is shown that this two approaches predict the bone remodelling in different ways. A comparison with available clinical outcomes is also presented and similarities to the numerical results are pointed out.