TRABECULAR SURFACE REMODELING SIMULATION USING MICROSTRUCTURAL FINITE ELEMENT MODELS

Participants: T. Adachi, K. Tsubota*, Y. Tomita*, N. J. Caldwell, S. J. Hollister,

Keywords: bone remodeling, trabecular microstructure, computational biomechanics

Introduction

Since local mechanical signals play an important role in stimulating and regulating cellular activities in bone remodeling, it is essential to relate the morphological changes of trabecular architecture to the trabecular-level mechanical stress/strain in modeling and simulation of mechanically induced trabecular bone remodeling. Digital image-based finite element models are useful not only for estimating microstructural stress/strain, but also for simulating the trabecular surface movement due to osteoclastic resorption and osteoblastic formation by removing and adding surface elements. The purposes of this study were to investigate basic features of the trabecular remodeling based on a uniform stress hypothesis and to demonstrate the applicability of the simulation method for trabecular bone remodeling using microstructural finite element models.

Materials and Methods

A rate equation was used for trabecular surface remodeling, based on a uniform stress hypothesis, in which producing uniform tissue stress is the driving force for adaptation, :

where .

The parameter , in Fig.1(a), regulates the spatial sensitivity, the size of the area where cells can sense the mechanical stimuli. The parameters and which are in the rate equation, shown in Fig.1(b), are the threshold values that regulate the rate of volumetric changes.

Trabeculae were modeled as an assemblage of voxel elements, as shown in Fig.1(c) and the morphological changes were accomplished by removal/addition of the voxel elements from/to the trabecular surface. Trabecular bone was assumed to be a homogeneous and isotropic elastic material with Young's modulus E = 20 GPa and Poisson's ratio = 0.3. The parameters were set as 1.0mm, 4.0, and 5.0.

(a) (b) Rate equation and , (c) Discretized surface

Figure 1: Trabecular surface remodeling driven by local mechanical stimulus

To investigate the primary features of the proposed remodeling rate equation at the trabecular structural level, remodeling simulations was conducted for 555 mm cube trabecular bone specimen, obtained by 3D micro-CT image from the distal femoral metaphysis of a dog, as shown in Fig.2. The cube was assumed to be loaded in compression. The each voxel size was 50m, and the total volume contains 1 million voxel elements.

Results

The progression of morphological changes of trabecular bone by surface remodeling under compressive loading is shown in Fig.2. From the initial architecture, as shown in Fig.2(a), trabecular architecture changed by resorption and formation driven by the nonuniformity of the trabecular surface stress and started aligning along the compressive axis as shown in Fig.2(b). This reorientation is due to the resorption of the trabecula, perpendicular to the compressive axis, an example of which is indicated by a circle in Fig.2, and the formation, along the axis indicated by a rectangle in Fig.2. Finally, trabecular architecture changed into that shown in Fig.2(c) at the 20th step.

(a) Initial (b) 8th step (c) 20th step

Figure 2: Remodeling simulation of trabecular cubic under compressive loading.

In this case, trabeculae changed their morphology to align along the loading direction, showing adaptation to support mechanical loading. During the remodeling process, total trabecular volume decreased, however, the total strain energy also decreased. This result indicated that the stiffer structure against applied load was accomplished by adaptive remodeling. The expression of a remodeling rate equation could be extended to consider the nonuniformity of the stress in the trabeculae by integrating over the volume element dV for the case when the role of the osteocyte is taken into account. The equivalent stress was used as the scalar function of a mechanical stimulus. If other positive values, such as strain energy density, are used, similar result could be expected at the equilibrium state.