Stress distribution in the mouse-tibia loading model using analytical approaches together with correction factors

INTRODUCTION The mouse-tibia compression model (MTCM), is the gold standard for studying bone adaptation due to mechanical loading in vivo [1]. Often, experiments are replicated in silico through finite element (FE) modelling, providing insights into the link between adaption and localised loading (i.e. stress and strain) [2]. However, FE models of the MTCM are rather complex and computationally expensive. An alternative is to use analytical models (i.e. continuum mechanics) [3]. However, the latter assume the fibula is negligible, thus overestimating tibial load. This work explores the validity of this assumption and proposes correction factors for the use of analytical models. MATERIALS AND METHODS The tibia of a 16 week, female, C57BL/6 mouse was digitised via micro computed tomography (Skyscan 1172, 19 m voxel size). Both FE and analytical models were studied. The tibia was pin supported about the inferior articular surface. Load on the tibial head was represented by a point load at a given (x,y) location, 87 different load locations were investigated. For the FE model (ANSYS 19.2) a direct voxel to element meshing was used. For the analytical model, continuum-mechanics based beam equations were used (the fibula was neglected). An elastic modulus of 17 GPa and 10 GPa was used for bone and growth-plates respectively. RESULTS & DISCUSSION Figure 1 shows the proportion of load carried by the tibia, for different load locations. Studies suggest that in the MTCM, load is applied to the posterior edge of the condyles, thus approximately 88% of the load can be expected to be carried by the tibia. Comparison of the FE and analytical models shows error in the maximum axial stress to exceed 20% at the expected load location. Assuming skeletal similarity across C57BL/6 strain, we propose the load proportions from Figure 1 can be used as a general correction factor for the axial load in the analytical model. Through this correction factor, this error can be reduced below 10% at the expected load location. [Figure in PDF version]Figure 1: Proportion of load within the tibia for a given (x,y) load location. CONCLUSION Analytical models of the MTCM neglect the fibula. Dependent upon load location, it was found the fibula carries approximately 12% of the load, this can create sizable errors in the predicted stresses in the tibia. By correcting for the total load in the tibia, this error can be minimized.