A coupled computational framework for bone fracture healing and long-term remodelling: Investigating the role of internal fixation on bone fractures

Abstract

In this study, a coupled computational modelling framework for bone fracture repair is presented that enables predictions of both healing and remodelling phases of the fracture region and is used to investigate the role of an internal fixation plate on the long-term healing performance of a fracture tibia under a range of different conditions. It was found that introduction of a titanium plate allowed the tibia to undergo successful healing at higher loading conditions and fracture gaps, compared with the non-plated versions. While these plated cases showed faster rates of repair in the healing phase, their performance was substantially different once they entered the remodelling phase, with substantial regions of stress shielding predicted. This framework is one of the few implementations of both fracture healing and remodelling phases of bone repair and includes several innovative approaches to smoothing, time-averaging and time incrementation in its implementation, thereby avoiding any unwanted abrupt changes between tissue phenotypes. This provides a better representation of tissue development in the fracture site when compared with fracture healing models alone and provides a suitable platform to investigate the long-term performance of orthopaedic fixation devices. This would enable the more effective design of permanent fixation devices and optimisation of the spatial and temporal performance of bioabsorbable implants.

Keywords: bone fracture healing; finite element modelling; orthopaedic implants.

FIGURE 1

Geometric information on human tibia implanted and external fixator; (A) bone plate; (B) callus regions; (C) top‐down view of plate without pins; (D) side view of plate with pins. All measurements were recorded in millimetres

FIGURE 2

Iterative calculations for tissue development for bone fracture repair and bone remodelling; (A) Bone fracture repair algorithm and (B) SED/damage‐based bone remodelling

FIGURE 3

Overview of diffusion model used to describe the infiltration of MSCs/development of blood vessels; (A) MSCs invading the fracture callus from the surrounding soft tissue, bone marrow and inner cambial of the periosteum; (B) Cellular concentration magnitude applied to surface shown in (A)

FIGURE 4

(A) The mechano‐regulation model based on deviatoric strain and fluid velocity. (B) Smoothed mechanobiological regulation based on Sapotnick et al.

FIGURE 5

(A) Bone remodelling algorithm using SED as the mechanical stimulus for the implant; (B) Surface area density of bone $\left(\mathrm{a}\left(\mathrm{\rho }\right)\right)$ as a function of bone density

FIGURE 6

Post‐operative loading conditions

FIGURE 7

(A) Predicted IFM by FE‐model versus healing time of an osteotomy of a sheep. (B) Histology section of a well‐healed mouse at day 26. (C) Histology section of a mouse with mixed healing at day 26. Stained with Hall's and Brunt's Quadruple (HBQ) stain and false‐coloured. Blue = cartilage, yellow = trabecular bone, purple = fibrous/amorphous tissue, red = cortical bone, black/white = bone marrow.(D) Geometrical dimensions of one quarter of FE‐model of the callus region used fracture healing model calibration

FIGURE 8

Elastic modulus of fractured tibia over a 1‐year time period with a constant fracture gap and different loading conditions; (A) fracture callus healing performance over 1 year; (B) fracture callus healing performance over 112 days; (C–E) contour plots of fracture callus; (F) SED/micro‐damage based remodelling

FIGURE 9

Elastic modulus of fractured tibia over a 1‐year time period with a constant loading condition and different fracture gaps; (A) fracture callus healing performance over 1 year; (B) fracture callus healing performance over 112 days; (C–E) contour plots of fracture callus; (F) SED/micro‐damage based remodelling

FIGURE 10

Contour plots of plated fracture callus; (A–C) fracture callus with a constant fracture gap and different conditions; (D–E) fracture callus with a constant loading condition and different fracture gaps; (E) wireframe representation of callus and plate positions

FIGURE 11

Elastic modulus within cortical bone and fracture callus focus for plated tibia with 3 mm fracture gap under LC(A) at 150, 200, 250, 300 and 350 days. Simulations were ran with damage (D) and with the no damage (ND)