Mechanobiochemical bone remodelling around an uncemented acetabular component: influence of bone orthotropy

Abstract

Mechanical loosening of an implant is often caused by bone resorption, owing to stress/strain shielding. Adaptive bone remodelling elucidates the response of bone tissue to alterations in mechanical and biochemical environments. This study aims to propose a novel framework of bone remodelling based on the combined effects of bone orthotropy and mechanobiochemical stimulus. The proposed remodelling framework was employed in the finite element model of an implanted hemipelvis to predict evolutionary changes in bone density and associated orthotropic bone material properties. In order to account for variations in load transfer during common daily activities, several musculoskeletal loading conditions of hip joint corresponding to sitting down/up, stairs ascend/descend and normal walking were considered. The bone remodelling predictions were compared with those of isotropic strain energy density (SED)-based, isotropic mechanobiochemical and orthotropic strain-based bone remodelling formulations. Although similar trends of bone resorption were predicted by orthotropic mechanobiochemical (MBC) and orthotropic strain-based models across implanted acetabulum, more volume (10–20%) of bone elements was subjected to bone resorption for the orthotropic MBC model. Higher bone resorption (75–85%) was predicted by the orthotropic strain-based and orthotropic MBC models compared to the isotropic MBC and SED-based models. Higher bone apposition (35–160%) across the implanted acetabulum was predicted by the isotropic MBC model, compared to the SED-based model. The remodelling predictions indicated that a reduction in estrogen level might lead to an increase in bone resorption. The study highlighted the importance of including mechanobiochemical stimulus and bone anisotropy to predict bone remodelling adequately.

Graphical Abstract

Appendices

Appendix 1. Biochemical reactions

The biochemical reactions considered in the mechanobiochemical model are briefly mentioned in this section. These reactions involve mononuclear cells (MCELL), multinucleated osteoclasts (MNOC), old bone (OldB), activator osteoblasts (ActivOB), osteoblasts (OB) and osteoids (Osteoid)) [17]. The biochemical reactions are represented by α (1 to 5). The formation of the MNOC is the first step of bone remodelling process (α = 1), as follows:

$${N}_{1} +\mathrm{ MCELL }\rightleftharpoons \mathrm{ MNOC }+ {N}_{4}$$

Where N₁ is the mixture of substances which initiate the reaction with MCELL. In the subsequent reaction (α = 2), MNOC reacts with the old bone and the remaining products are the resultant of the bone resorption:

$$\mathrm{MNOC }+\mathrm{ OldB}\rightleftharpoons {N}_{6} + {N}_{7}$$

The N₇ reacts with OldB to produce ActivOB (α = 3) which is responsible for activating the osteoblasts (α = 4).

$${N}_{7} + {\text{OldB}}\rightleftharpoons \mathrm{ActivOB }+ {N}_{9}$$

The ActivOB acts on the OB, which causes them produce the Osteoid (collagen type 1; unmineralized bone):

$${\text{ActivOB}} + {\text{OB}}\rightleftharpoons {\text{Osteoid}}+{N}_{12}$$

The last reaction (α = 5) in bone remodelling process involves the mineralization of Osteoid by N₁₃ to form the NewB, as described in the following reaction.

$${N}_{13}+{\text{Osteoid}}\rightleftharpoons {\text{NewB}}+{N}_{15}$$

The NewB represents the mineralized collagen that eventually forms the new bone. N₁₅ is the remaining substrates of the biochemical reactions.

Appendix 2. Predictions of trabecular orientations in femur

In order to evaluate the efficacy of the model in predicting the orthotropic material orientations, a FE model of intact femur was used [44]. An intact femur was chosen over a hemipelvis, since the trabecular architecture is clearly distinguishable in a μCT dataset of a proximal femur [28]. These predictions were then compared to the μCT data of a proximal femur in a coronal section, as depicted in Fig. 9. The intact femur was meshed using 10-node tetrahedral elements of edge length ranging from 0.3 to 0.8 mm, and the FE model consisted ≈ 113,000 number of elements. The site-specific apparent density and Young’s modulus of the bone were obtained from the greyscale values of CT scan data. The orthotropic orientations of the model, corresponding to the absolute value of maximum principal stress, were computed and visualized using the scientific visualization software ParaView 5.11.1 (Sandia National Labs, Kitware Inc, www.paraview.org).

The orthotropic material orientations predicted for a natural femur model were comparable to the trabecular architecture of the μCT image of a healthy femur [28], as evident in Fig. 9. The principal compressive group, which originates from the medial femur shaft and directing towards the femoral head, was distinguishable in the coronal plane. However, the primary tensile group which originates from the lateral femur shaft and ending in the femoral head was not very well distinguishable from the directional arrows. Nevertheless, other trabecular groups such as greater trochanter, secondary tensile and secondary compressive groups were predicted adequately by the orthotropic MBC framework. The predictions of trabecular orientations in an intact femur model were in agreement with that of earlier in silico studies [4, 26, 45]. The material orientations of bone elements adapted orthotropically, leading to an optimally structured trabecular design for an efficient load transfer. The agreement of the orthotropic orientation with the trabecular bone architecture confirms the suitability of the novel framework for predicting bone adaptation, adequately.