Three-Dimensional Quantification of Bone Mineral Density in the Distal Femur and Proximal Tibia Based on Computed Tomography: In Vitro Evaluation of an Extended Standardization Method

Abstract

While alterations in bone mineral density (BMD) are of interest in a number of musculoskeletal conditions affecting the knee, their analysis is limited by a lack of tools able to take full advantage of modern imaging modalities. This study introduced a new method, combining computed tomography (CT) and computational anatomy algorithms, to produce standardized three-dimensional BMD quantification in the distal femur and proximal tibia. The method was evaluated on ten cadaveric knees CT-scanned twice and processed following three different experimental settings to assess the influence of different scans and operators. The median reliability (intraclass correlation coefficient (ICC)) ranged from 0.96 to 0.99 and the median reproducibility (precision error (RMSSD)) ranged from 3.97 to 10.75 mg/cc for the different experimental settings. In conclusion, this paper presented a method to standardize three-dimensional knee BMD with excellent reliability and adequate reproducibility to be used in research and clinical applications. The perspectives offered by this novel method are further reinforced by the fact it relies on conventional CT scan of the knee. The standardization method introduced in this work is not limited to BMD and could be adapted to quantify other bone parameters in three dimension based on CT images or images acquired using different modalities.

Keywords: bone mineral density; computational anatomy; knee; osteoarthritis; osteoporosis; quantitative computed tomography; registration.

Figure 1

Segmentation of the femoral and tibial bones and identification of the subchondral bone areas (left), and resulting three-dimensional femoral and tibial bone meshes (right). In both plots, the subchondral bones are in red and the non-subchondral bones are in blue.

Figure 2

Flowchart of the first phase consisting of bone surface registration. ICP: Iterative Closest Point, TPS: Thin Plate Splines.

Figure 3

Illustration of the first phase of the registration procedure for the distal femur (see Figure 2 for an overall Figure 1. (a): the cylinder fitted to the subchondral bone area of the moving femur is aligned and scaled to coincide with the cylinder of the reference femur. Step 1. (b): the moving femur is scaled around and along the cylinder axis to match the size of the reference femur. Step 1. (c): the moving femur is rotated around the cylinder axis in order to align its subchondral bone area to the subchondral area of the reference femur. Step 2: not necessary for the femur. Step 3: a nonrigid transformation is applied to the moving femur to locally match the reference femur.

Figure 4

Histogram of the reliability for the 12,000 femoral (top) and 7000 tibial (bottom) cells in the three settings.

Figure 5

Illustration of the spatial variations in reliability: (left) reference distal femur and proximal tibia bone models with two representative coronal slices and (right) intraclass correlation (ICC) maps for the three settings at the coronal slices for the tibia (top) and the femur (bottom).