Sample Preparation and Imaging

With Institutional Review Board approval, clinical CT scans were obtained from 6 patients (range: 3.9–11.9 years; mean: 8.2 years) with tibial torsion abnormalities but morphologically normal distal femora at 0.4 to 0.6 mm in-plane resolution and 0.63 mm slice thickness (GE Lightspeed VCT; GE Healthcare, Piscataway, NJ, USA).

The structure of mouse knee joints was assessed by micro–computed tomography (μCT) and histology. With Institutional Animal Care and Use Committee approval, both hindlimbs of 21 C57BL/6 male mice, n = 3 pairs each at 12, 16, 20, 24, 30, 60, and 120 days postnatal, were harvested, fixed in 10% neutral buffered formalin, and scanned intact by μCT at (9 μm) isotropic voxel resolution (SkyScan 1076; SkyScan, Kontich, Belgium; 70 kVp, 140 μA, 1750 ms exposure). Following μCT, 1 femur at each age point was randomly selected for histologic processing. Proximal and distal femora were decalcified in 10% formic acid and paraffin-embedded. Sagittal sections (5 μm thick) were obtained approximately through the center of the medial femoral condyle of the distal femur. Sections were stained with Safranin-O and digitized at 20× magnification (0.5 μm resolution) with an Aperio ScanScope (Aperio Technologies, Vista, CA, USA).

Gross Morphology

Human and mouse CT images were qualitatively analyzed for morphologic changes at the bone-cartilage interface during developmental growth in 2-D coronal and sagittal planes through the center of the load-bearing region of the condyle and in 3-D reconstructions. Distal femora were assessed for contour of the condyles, posterior condyle prominence, medial femoral condyle (MFC) versus lateral femoral condyle (LFC) size, and trochlear ridge development, as well as location and morphology of the growth plate. Contour of the opposing tibial plateau, as well as joint space width between the distal femoral and proximal tibial secondary ossification centers (SOCs), were also noted.

Histology

Safranin-O sections were compared with matching μCT sections of mouse femora to interpret the bone-cartilage interface of the SOC relative to the overlying articular-epiphyseal cartilage. In addition, histology sections were assessed for chondrocyte hypertrophy and organization.

Image Processing

All CT and μCT scans were imported into Mimics (Materialise, Leuven, Belgium) for surface segmentation and 3-D reconstruction. Left femora were flipped in orientation to match right femora. Bone-cartilage interfaces were identified by thresholding for bone, segmented, and exported as point clouds.

Width and Thickness Measurements

Transepicondylar widths were determined in human and mouse distal femora as a measure of growth. In 3-D reconstructed models, transepicondylar width was measured as the nearest distance from the edge of the lateral epicondyle to the edge of the medial epicondyle. In the mouse, the overall length of the femur was also determined from the most proximal point on the femoral head to the most distal point on the femoral condyles.

Thicknesses of the articular-epiphyseal and growth plate cartilage were calculated from 2-D histology images. Articular-epiphyseal cartilage was defined from the articular surface to the calcified cartilage tidemark, or to the distal edge of large hypertrophic cells for young joints with no tidemark. Growth plate cartilage was defined from the epiphyseal side of reserve zone chondrocytes to the metaphyseal side of terminal hypertrophic zone chondrocytes. Because articular-epiphyseal and growth plate cartilage contours were highly curved in the mouse distal femur, making it difficult to estimate thickness directly, cartilage thickness was calculated as the area of the cartilage divided by the average width of the cartilage.

Statistical Shape Modeling

Both femora of 15 mice, n = 3 pairs each at days 12, 24, 30, 60, and 120, were used as the initial training samples for SSM. Training samples were rigidly registered and isotropically scaled to the largest femur (day 120 sample). Point-to-point correspondences between coordinates of each femur were defined automatically, following previously established methods by first constructing a normalized average atlas shape and then extrapolating points (landmark coordinates), in corresponding locations to each femur. Each distal femur was described by 412 landmarks, located from the femoral condyles to the proximal edge of the trochlea.

The statistical shape model was built from the landmarks of the training samples using principal component analysis. A mean shape was calculated from training sample landmarks, and deviations of each shape from the mean were determined. Singular value decomposition of the covariance matrix was performed to obtain the eigenvectors and corresponding eigenvalues (in descending order). The eigenvectors represent the modes of variation within the training set, analogous to the principal axes of an ellipse. The eigenvalues represent the variance explained by each mode, or the amount of contribution of each mode to overall joint shape variation. Using the modes of variation from the model, the shape parameters, b , of each sample was calculated by X=ˉX+Pb
X = X ¯ + Pb
, whereˉXisthemeanshape
where X ¯ is the mean shape
, P=(p1|p2|…|pt)
P = ( p 1 | p 2 | … | p t )
are the first t modes of variation that explain greater than 90% of the total shape variance, and X is the sample shape. Shape parameters are analogous to principal radii of an ellipse. Parameters were normalized to 1 standard deviation of the mode, calculated as the square root of the corresponding eigenvalue.

Additional samples at days 16 and 20 were analyzed by applying the SSM. Samples were segmented in Mimics, rigidly aligned to the same reference femur from the training set, and nonrigidly aligned to the model atlas shape to extrapolate landmarks. Shape parameters were then determined as described above.

Growth Maps: Deformation Rates, Strain Rates, and Strain Directions

Deformation and principal surface strain rates between ages were calculated from corresponding landmark coordinates of the average shape at each age. Here, landmark coordinates represented non-scaled shapes. Samples were aligned at the centroid of the growth plate to determine deformations during growth. Magnitudes of deformation were calculated as the distance between corresponding landmarks, and deformations in the same direction as the outward surface normal vector were defined as positive. The 2-D components of Green’s strain E _ij were calculated from ds ² − ds ₀ ² = 2E _ij dX _i dX _j for i,j = 1:2, where ds ₀ ² = dX _i dX _j is the squared segment length of a pair of landmarks at the first age point, and ds ² is the squared length at the second age point. Maximum principal strain rates and directions were calculated from the Green strain components.

Deformation and strain rates were mapped in 3-D onto the triangulated surfaces of the average shape at each age point. Surface patches intersecting the transverse plane and sagittal plane through the medial condyle were determined, and the 3-D principal strain directions of those patches were projected onto each plane to illustrate strain directions along the 2-D surface contour.

Statistics

Differences in mode parameters between age points were assessed by a one-way analysis of variance with post hoc Tukey test. All data are expressed as mean ± SD.