The Influence of Load Magnitude on Fracture Repair in a Murine Model: a Fem Study

INTRODUCTION The treatment of bone fracture is an important public health problem in an ageing population. Healing involves a series of biological events that restores the tissue to its original shape and mechanical properties. It has been shown that the mechanical environment can modulate tissue differentiation. Several mechanoregulatory algorithms have been proposed to predict tissue differentiation during the repair process [1,2]. In this study, a murine fracture model with a stem cell seeded callus was studied with finite element models (FEM) to determine the effects of load magnitude on bone healing. METHODS An axisymmetric FEM of a proximal section of a murine tibia with a 0.4 mm fracture gap and external callus (Fig. 1a) was created (ABAQUS v6.10). It was assumed that the callus consisted of stem cell seeded granulation tissue initially. Progenitor cells from surrounding tissues (the marrow, periosteum and external soft tissues to the callus) were able to move into the callus. A biphasic theory regulated by shear strain and fluid flow was implemented into our simulation to investigate the tissue differentiation over healing time [2]. The mechanical stimuli applied to the stem cells over time results in a gradual change of the tissue material properties within the callus. The cells could differentiate into fibrous tissue, cartilage and bone. To simulate the movement of the cells through the regenerated tissue, a diffusion process coupled to the poroelastic stress analysis was developed. The diffusion coefficients were set such that after 3 weeks, the progenitor cells could spread throughout the entire callus [3]. A userdefined subroutine USDFLD was developed to update the material properties based on the average of computed mechanical stimuli in the previous 10 days, and on the cell concentration. The new material properties were finally computed using a rule of mixtures. The tissue mechanical properties were obtained from the literature [1]. The analysis was continued until tissue differentiation had reached a steadystate. To investigate the influence of load magnitude on fracture repair, axial compression loads of 0.5, 1, 2 N (1 Hz) were applied to the top of the cortical shaft, and the results were compared to reconstructed micro-CT images of a previously published experimental study [3]. In the experimental study, the healing response to different axial compression magnitudes was investigated in murine tibias with a transverse fracture over 2 weeks. RESULTS The FEM was initially validated by comparing the results to an axisymmetric human tibia fracture model of Isaksson et al. (2005) with the same geometry and loading regimes [1]. The predicted patterns of the regenerated tissue during the repair process were very similar. The predicted sequence of tissue regeneration in the murine fracture model occurred in the same pattern observed in vivo. After 14 steps (days), the interfragmentary gap still contained fibrous tissue for a load amplitude of 1 or 2 N whereas cartilage was predicted for the 0.5 N loading case (Fig. 1b & 1c). In all cases, the bone formation started from internal and external callus, independently. For the external callus the bone formation started at the tip of the callus and spread throughout the callus gradually. According to the obtained results, the bone healing rate was the highest under 0.5 N, intermediate under 1 N and the lowest under 2 N axial compression.