In vivo estimation of bone stiffness at the distal femur and proximal tibia using ultra-high-field 7-Tesla magnetic resonance imaging and micro-finite element analysis

Abstract

The goal of this study was to demonstrate the feasibility of using 7-Tesla (7T) magnetic resonance imaging (MRI) and micro-finite element analysis (µFEA) to evaluate mechanical and structural properties of whole, cortical, and trabecular bone at the distal femur and proximal tibia in vivo. 14 healthy subjects were recruited (age 40.7 ± 15.7 years). The right knee was scanned on a 7T MRI scanner using a 28 channel-receive knee coil and a three-dimensional fast low-angle shot sequence (TR/TE 20 ms/5.02 ms, 0.234 mm × 0.234 mm × 1 mm, 80 axial images, 7 min 9 s). Bone was analyzed at the distal femoral metaphysis, femoral condyles, and tibial plateau. Whole, cortical, and trabecular bone stiffness was computed using µFEA. Bone volume fraction (BVF), bone areas, and cortical thickness were measured. Trabecular bone stiffness (933.7 ± 433.3 MPa) was greater than cortical bone stiffness (216 ± 152 MPa) at all three locations (P < 0.05). Across locations, there were no differences in bone stiffness (whole, cortical, or trabecular). Whole, cortical, and trabecular bone stiffness correlated with BVF (R ≥ 0.69, P < 0.05) and inversely correlated with corresponding whole, cortical, and trabecular areas (R ≤ -0.54, P < 0.05), but not with cortical thickness (R < -0.11, P > 0.05). Whole, cortical, and trabecular stiffness correlated with body mass index (R ≥ 0.62, P < 0.05). In conclusion, at the distal femur and proximal tibia, trabecular bone contributes 66-74% of whole bone stiffness. 7T MRI and µFEA may be used as a method to provide insight into how structural properties of cortical or trabecular bone affect bone mechanical competence in vivo.

Fig. 1

a Sagittal MRI localizer image showing the locations of analysis at the distal femoral metaphysis, femoral condyles, and tibial plateau. To compute bone stiffness, μ-FEA was performed using an axial compression simulation. b Representative axial 7T MR image at the level of the distal femoral metaphysis with corresponding segmentation shown in (c). (In MR images of bone, marrow spaces are white and bone is dark.) d Representative axial 7T MR image at the level of the femoral condyles with corresponding segmentation shown in (e). f Representative axial 7T MR image at the level of the tibial plateau with corresponding segmentation shown in (g). The outer segmentation border indicates the periosteal border of bone. The inner segmentation border indicates the endosteal border of bone.

Fig. 2

a Boxplots of data from Table 1 comparing whole, cortical, and trabecular bone stiffness at the distal femoral metaphysis, the femoral condyles, and the tibial plateau. At all locations, trabecular bone stiffness was greater than cortical bone stiffness (P < 0.0001). There were no differences in whole, cortical, or trabecular bone stiffness when comparisons were performed between locations (P > 0.40). b Boxplots comparing the proportion of BVF due to trabecular versus cortical bone at the distal femoral metaphysis, the femoral condyles, and the tibial plateau. At all locations, trabecular bone represented a greater proportion of BVF compared to cortical bone (P < 0.0001)

Fig. 3

Graphs illustrating the relationship between whole, cortical, and trabecular bone stiffness and BVF at the distal femoral metaphysis, femoral condyles, and the tibial plateau. With the exception of cortical bone at the tibial plateau (R = 0.29, P > 0.31), there was a positive correlation between bone stiffness and BVF (R = 0.74−0.85, P ≤ 0.004 for all)

Fig. 4

Graphs illustrating the negative correlation between whole, trabecular, and cortical bone stiffness and corresponding whole, trabecular, and cortical bone areas at the proximal tibia and distal femoral metaphysis (R = −0.54 to −0.6, P < 0.05)

Fig. 5

Graphs illustrating the relationship between whole, trabecular, and cortical bone stiffness and BMI. Whole, trabecular, and cortical bone stiffness positively correlated with BMI at the distal femoral metaphysis and at the femoral condyles (R = 0.55−0.67, P < 0.05), but not at the tibial plateau (R = −0.12 to 0.42, P ≥ 0.14)