Finite element analysis of bone mechanical properties using MRI-derived bound and pore water concentration maps

Abstract

Ultrashort echo time (UTE) MRI techniques can be used to image the concentration of water in bones. Particularly, quantitative MRI imaging of collagen-bound water concentration (C_bw) and pore water concentration (C_pw) in cortical bone have been shown as potential biomarkers for bone fracture risk. To investigate the effect of C_bw and C_pw on the evaluation of bone mechanical properties, MRI-based finite element models of cadaver radii were generated with tissue material properties derived from 3 D maps of C_bw and C_pw measurements. Three-point bending tests were simulated by means of the finite element method to predict bending properties of the bone and the results were compared with those from direct mechanical testing. The study results demonstrate that these MRI-derived measures of C_bw and C_pw improve the prediction of bone mechanical properties in cadaver radii and have the potential to be useful in assessing patient-specific bone fragility risk.

Keywords: MRI; bone; bound water; finite element analysis; pore water.

Figure 1.

The experiment overview. For the ith bone, i = 1 to N_b, material properties, Ei and Yi, were iteratively adjusted until the root mean square difference between the simulated and experimentally measured force-displacement curves was minimized.

Figure 2.

Three-point bending test setup (left) and force-displacement curve of a representative radius. From the force-displacement data, stiffness, yield force (15% loss in stiffness), pre-yield work (area under the force-vs.-displacement curve until the yield point), and work-to-fracture (area under the force-vs.- displacement curve until the failure point) were calculated (Manhard et al. 2016). Failure was defined as 5% decrease from the ultimate force.

Figure 3.

MRI images of a representative radius acquired at distal third site. The left image shows the conventional UTE image with red box indicating the radius bone. The middle and right images show the maps of C_bw and C_pw overlaid on the corresponding AIR and DAFP images, respectively.

Figure 4.

Experimental (solid line) and simulated (dashed line) force-displacement curves using $\{{\widehat{E}}_i,{\widehat{Y}}_i\}$ (blue) and {E_A, Y_A} (orange) parameters from two representative bones.

Figure 5.

Correlations of elastic modulus (left) and yield stress (right) with MRI-derived C_bw and C_pw.

Figure 6.

Experimental (solid line) and model-based (dashed line) simulated force-displacement curves from case A (orange), case B (green), and case C (blue) of two representative bones.

Figure 7.

Correlations between measured mechanical data (x-axis) and predicted mechanical data (y-axis) of three different models. Case A: Homogeneous tissue properties, Case B: Homogeneous tissue properties derived from C_bw and C_pw, and Case C: Heterogeneous tissue properties derived from C_bw and C_pw.