The approach described here is based on cross-sectional images obtained with CT. The field of view and energy of the radio source are handled as necessary for the individual case, but kept constant throughout the CT scan. As in the presented case, the scan should cover the area between the acetabulum and minor trochanter with contiguous 3-mm slices. In addition, one cross-section of the femoral knee condyles is acquired. During the 3D measurement, this cross-section provides important information about the rotation of the femoral neck relative to the knee. Digital copies of all images are transferred to a network of workstations for further postprocessing.

The goal of the postprocessing is to delineate the structures of interest within the scanned volume. Initial segmentation of the femur and pelvis is done with commonly used intensity thresholding techniques [1]. Operator interaction is needed to ensure proper separation of pelvis and femur and to determine the border between femoral head and neck. The latter is equivalent to the growth plate, which appears less dense than calcified bone in CT images. Because of this contrast, a reliable and quick segmentation of the growth plate can be achieved manually. The final segmented volume contains pelvis, femoral head, proximal femoral metaphysis, and a cross-section of the condyle, for the left and the right sides (Fig. 5).

The segmented images are used to reconstruct 3D models (Fig. 1) using marching cubes [9], an algorithm described in the Visualization section of this book and available in "The Visualization Toolkit" (VTK) [12] (Fig. 6). During the 3D reconstruction process, the border of an anatomical structure on one cross-section is connected to the next with triangles. Surface models of the reconstructed structures typically consist of about 50,000 triangles, after application of a triangle reduction algorithm [13]. The rendering process uses the VTK libraries as well [12]. Display is performed on Sun workstations with 3D graphic hardware acceleration.

The software development platform for the interactive 3D measurement tool is the Tcl/Tk language in combination with the programming languages C and C + +. Tcl/Tk is a script language that provides the capabilities of standard C/C + + coding and supports socket programming, input/output handling, looping, and mathematical manipulation. Tk is a popular extension of Tcl designed for graphical user interface (GUI) construction with convenient features for interface layout and associated event handling. Both Tcl and Tk have interfaces that enable developers to implement custom C/C + + code for arbitrary extensions. For 3D computer graphics representation, a graphics programming environment such as VTK can be used along with a graphics library such as OpenGL (Sun Microsystems).

The 3D graphics part of the interface depicts a scene of the

FIGURE 6 Using triangulation, the edges of the outlined structures are connected throughout the cross-sections, thereby building a 3D reconstruction. See also Plate 43.

3D models and an axis tool that consists of an axis and a plane perpendicularly placed on one end of the axis. Point of view and sizing of the whole 3D scene can be changed by direct mouse interaction on the display window. In addition, the axis tool can be positioned independently of the anatomical bone structures. A GUI window allows this manipulation in six degrees of freedom. One can determine an anatomical axis on the 3D bone structures interactively by positioning the axis tool along the presumed anatomical axis. A mouse click on the save buttons in the GUI window stores the vector information for the appropriate anatomical axis. Buttons and anatomical 3D structures are accordingly color-coded to prevent user errors. After all necessary axes are determined and stored, the required angles can be computed and displayed.

For pathoanatomical analysis and accurate planning of surgical treatment, it is essential to know the following angles: shaft-neck (Fig. 7), physis-neck, femoral neck torsion (Fig. 8), physeal torsion, and acetabular anteversion and inclination (Fig. 14) [2].

(Remark: in general, shaft-neck angle is called caput-collum-diaphysis angle (CCD). In this chapter, this term is not used in order to prevent misinterpretations; in severe cases of SCFE it is not useful to determine the proximal end of the neck (lat.: collum) as the center point of the femoral head (lat.: caput) because of its misplacement.)

FIGURE 6 Using triangulation, the edges of the outlined structures are connected throughout the cross-sections, thereby building a 3D reconstruction. See also Plate 43.

FIGURE 7 Depiction of a femoral shaft-neck angle measurement (blue) on the shaft-neck plane (green). See also Plate 44.

Femoral neck axis (acetabular axis I): n

Capital femoral physis: g

Femoral shaft axis (pelvis axis I): s Femoral condyle axis (pelvis axis II): k

When S is the plane with normal vector s, the shaft-neck angle is the angle formed by the projection of the femoral neck axis n and condyle axis k onto S, defined as n' and k' respectively.

In the same manner, the shaft-physis angle is formed by the projection of condyle axis k and the CFE g axis, namely g'.

Absolute values of each angle is formulated as follows:

Shaft-neck angle: | ¿N' OK'| = |cos_l(n' • k') |

Shaft-physis angle: |/S'OG'| = |cos"^g' • k') |

FIGURE 7 Depiction of a femoral shaft-neck angle measurement (blue) on the shaft-neck plane (green). See also Plate 44.

The angles computed in (1) and (2) are absolute values; thus, we have to evaluate the positive and negative factor of shaft-neck and shaft-physis angles separately.

The femoral neck can be ante- or retrotorted with respect to the knee condyles. This correlates with either positive or negative positioning of n' with respect to k'. Here, n" is the outer product of s and n', and k'' is that of s and k'. If the n' is in positive (or counterclockwise) side of the k', the angle formed by nl and k'' is greater than the angle formed by n'' and k'. In cases where n' is in the negative (or clockwise) side, the same angle should be smaller.

Consequently, shaft-neck and shaft-physis angles are formulated as

These angles describe the geometry of the proximal femur, the degree of slippage, and the acetabulum orientation. For the measurement of these angles it is necessary to determine the axis of the femoral shaft (Fig. 9, left image), condyles (Fig. 9, right image), capital femoral physis (which is interpreted as the base of the slipped femoral head, Fig. 10, left image), neck (Fig. 10, right image), acetabulum (Fig. 11), and the pelvis (I + II) (Figs 12 and 13). The principal axes are vectors:

FIGURE 8 Depiction of a femoral neck torsion measurement (blue) between the shaft-neck plane (green) and the shaft-condyle plane (red). See also Plate 45.

FIGURE 11 Determination of the acetabular axis (left image, anterior aspect; right image, posterior aspect).

where jcos"^(gx n) ■ (gx fe)) |, I¿N'OK''I < I¿K'ON''I -Icos"^(gx n) ■ (Vx fe)) |, I¿N'OK''I > I¿K'ON''

where cos"1| (gx g) ■ (sxfe) ) , I¿GOK'I < I¿KOG'I

The torsional angles (neck torsion and physeal torsion) and the angles against the diaphyseal axis were assessed for the neck and the growth plate, respectively:

FIGURE 12 Determination of the pelvis axis I (left image, superior aspect; right image, posterio-lateral aspect).

¿SON = cos"1 (V ■ n) ¿SOG = cos"1 (g ■ g)

Acetabular anteversion was determined analogously to the torsional angles and acetabular inclination analogously to the shaft-neck angle.

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