## A mathematical analysis of the initial stability of a short femoral prosthesis

Student thesis: Master thesis (including HD thesis)

• Sandi Hupfeld
Purpose:
Hip arthroplasty is a common surgical procedure to relieve pain caused by disease or hip
fractions etc.. The durability of the procedure is finite, which makes treatment of younger
patients challenging. Based on this, research with short femoral stems in order to preserve
bone for multiple revisions have been made. One of these is the newly developed Primoris
stem. This is fixated by bone compaction, which in theory provides a good initial stability. But
the preconditions of the host bone are crucial for obtaining a successful result, however no
studies have been made in order to investigate this.
The aim of this thesis was to analyse the initial stability of Primoris, based on the compressive
behaviour of bone tissue and thereby create representative mathematical models to analyse
the effect of different preconditions of the host bone.
Methods:
As themechanical behaviour of bone tissue depends on the relative density ½r and additionally
changes during compaction, a mathematical expression was derived for pr = 0.2 to pr = 0.6, in
order to obtain results which rely on the true behaviour of the bone tissue. For analysing the
stability by estimating the pull-out force, a Finite Element (FE) model was developed using LSDYNA.
This method allows a simulation of the insertion process in 3D of where the impact of
different preconditions of the host bone can be estimated. But as the reliability of the results
fromthe FEmodel is difficult to determine, a simplified analytical model was created to provide
a basic understanding of the process and thereby be able to develop the FE model.
Results:
The initial process of developing a mathematical expression in order to describe the
compressive behaviour of the bone tissue, followed the trend found in the literature and
provided the basis for the two models. The analytical model showed that the lowest contact
pressure obtained was at pr = 0.2, where only 7 % compaction was obtained compared with
94.7 % at pr= 0.6. It was also found that the friction between the bone and stem had a major
impact on the pull-out force. Both the analytical model and the FE model showed that various
pr are of great importance for succes, as an increase in pr contributes with a higher pull-out
force. They also showed higher pull-out force when changing the conical angle from µ=3.5°to
µ=3.5°.
Conclusion:
There were a significant similarity between the results obtained from the models when
changing the preconditions, of which it can be concluded that the FE model demonstrated
the ability of analysing different preconditions and thereby estimating the initial stability. This
can be useful for a qualitative prediction of the surgical procedure. The parameter effecting the
stability the most was pr , as a lower pr resulted in lower pull-out force, and thereby an inferior
stability. But it was also seen that the geometry of the stem had an impact of the result.
Language English 1 Jun 2016 89 Aalborg Universitetshospital Poul Torben Nielsen ptn@rn.dkOther
ID: 234513003