α

Cobb angle

The Ferguson angle is slightly more complicated to measure than Cobb due to the three landmark points (rather than two endplates in the Cobb technique). There can be difficulties in identifying the centres of the vertebrae, depending on their shape. The diagonals of the vertebra, as used in the standard Ferguson method, do not intersect at its geometric centre. The intersection of perpendicular lines drawn through the midpoints of the upper and lower endplates of a vertebra, proposed as a more accurate method of obtaining the geometric centre especially with prominently wedge-shaped vertebrae [32], is also flawed since it assumes that the four corners of the vertebral body lie on a circle. An alternative, more reliable method of finding the geometric centres has been proposed [33]. It has been shown that the Ferguson angle is closely related to the Cobb angle, with the ratio between Cobb and Ferguson angles for the same curve being 1.35 [34]. Measurement variability for the Ferguson angle appears to be comparable with, or slightly higher than that of the Cobb angle [32, 34, 35].

10.3 Image Processing Methods

The increasing adoption of digital imaging provides a growing opportunity to (a) develop more detailed metrics for spinal deformity assessment which consider all vertebral levels in a scoliotic curve rather than just the two end vertebrae, (b) implement these metrics quickly and accurately using semiand fully-automated image processing tools, and (c) measure scoliosis curvature using 3D datasets from modalities such as biplanar radiography, CT and MR. The remainder of this chapter presents details of image processing applications which are being developed by the authors in an attempt to avoid the manual measurement variability mentioned above, and also to allow development of new metrics which may in the longer term improve surgical planning and treatment decision making for spinal deformity patients.

10.3.1 Previous Studies

Development of medical image processing algorithms for assessment of scoliosis has been sparse to date. Several studies have used algorithms to perform computeraided measurement of Cobb angle and other standard measures based on digitized anatomical landmarks manually selected by a user on a computer screen [36–39]. Gerard et al. [40] developed a semi-automated algorithm for scoliotic deformity measurement using dynamic programming optimisation. An automated algorithm for measuring vertebral rotation from a CT slices using the inherent symmetry of the vertebral cross-section was developed by Adam et al. [10]. Algorithms have also been developed to process back surface topography images (see Sect. 10.2), including a recent non-rigid registration algorithm [41]. However, as mentioned previously, back shape approaches are limited in their ability to assess the underlying spinal deformity and so are not widely used clinically.

10.3.2 Discrete and Continuum Functions for Spinal Curvature

A key aspect of developing more detailed metrics for spinal deformity assessment is measuring all vertebrae in a scoliotic curve, not just the end or apical vertebrae (as in the Cobb and Ferguson methods). Measuring all vertebrae provides a fuller understanding of how deformities affect each vertebral level before treatment, and also captures changes in spinal configuration after surgical treatment which may occur over only one or two vertebral levels (such as decompensation at the top of an implant construct). However, the challenges in measuring all vertebral levels are

(a) defining appropriate anatomical landmarks for reliable, semior fully-automated detection from radiographic images, and (b) processing these landmark coordinates to obtain meaningful measures of deformity shape which will assist in diagnosis and treatment.

One approach being developed by the authors for use with low dose CT datasets of AIS patients is to use the edge of the vertebral canal as a robust anatomical landmark suitable for semi-automated detection. Figure 10.7 shows a transverse CT slice of a scoliosis patient, which demonstrates the clearly defined, high contrast, enclosed inner boundary of the vertebral canal.

Even though individual vertebrae may be substantially tilted relative to the transverse CT slices, even in large scoliosis curves (Cobb angle 60◦), one or more CT slices will contain an enclosed vertebral canal such as that shown in Fig. 10.7. From these images, a spinal canal tracking algorithm has been developed using the ImageJ software (version 1.43u, National Institutes of Health, USA), which uses ImageJ’s automatic edge tracing command to locate the inner boundary of the vertebral canal, and determine the canal centroid coordinates. By applying this algorithm for each vertebral level in a scoliosis curve, a series of 17 x,y,z datapoints for the entire thoracolumbar spine can be generated, and pairs of x,z and y,z data points define spinal curvature in the coronal and sagittal planes respectively.

Fig. 10.7 Left: Axial CT slice showing the enclosed vertebral canal which is used as a landmark detection point by the semi-automated ‘canal tracker’ algorithm. Note that the anterior vertebral column is more rotated and deviated away from the mid-sagittal plane than the posterior part of the vertebra. Right: Close-up view of vertebral canal showing outline traced by the ImageJ edge detection algorithm and geometric centre of the detected outline which is used as the vertebral canal landmark

Having measured vertebral canal landmark coordinates for each vertebral level, these coordinates (which represent a ‘discrete’ representation of the scoliotic spine curvature) can then be used to generate a ‘continuum’ representation of scoliotic spinal curvature by fitting a mathematical function to the 17 sets of landmark coordinates. The approach used here is to fit two sixth order polynomial functions to pairs of x, z (coronal plane) and y, z (sagittal plane) coordinates respectively,

where cn and sn are the coronal and sagittal polynomial coefficients, respectively. Of course, other mathematical functions could be used. Figure 10.8 shows examples of two scoliosis patients where vertebral canal landmarks have been measured and continuum representations of the spinal curvature generated using this approach.

To show the relationship of the vertebral canal landmarks (which are located posteriorly in the vertebral canal) to the anterior vertebral column (where the Cobb and Ferguson angles are measured), Fig. 10.8 overlays the vertebral canal landmark points on CT reconstructions of the anterior vertebral columns. From these images it is apparent that first, while the vertebral canal landmarks and continuum curves closely follow the anterior column contours, the vertebral canal curvature tends to be less severe than that of the anterior column. This is to be expected because the anterior column is more rotated and displaced relative to the mid-sagittal plane than the vertebral canal (Fig. 10.7). Second, the vertebral canal landmark points do not always lie at mid-height relative to the anterior vertebral bodies.

Fig. 10.8 Coronal CT reconstructions of two scoliosis patients showing the vertebral canal landmark points (dark blue diamonds) and polynomial fits (pink lines) to the vertebral canal landmark points which provide a continuum mathematical description of the spinal curvature

This can occur firstly because the vertebra may be tilted in the sagittal plane (with the anterior vertebral body higher than the posterior vertebral canal – see the sagittal CT view in Fig. 10.1), and also because the current implementation of the algorithm is semi-automated, so there may be a choice of several axial CT slices in which an enclosed vertebral canal can be clearly seen by the user, leading to a user variability in slice selection. We note, however, that the resulting continuum mathematical representation is insensitive to variations in the CT slice chosen within a particular vertebrae for spinal canal landmark detection.

Having obtained discrete landmark points and a continuum representation of the spinal curvature, various curve metrics can be extracted. In particular, the inflection points of the coronal plane polynomial can be readily located by finding the zeros of the second derivative of the polynomial (i.e. the roots of a fourth order polynomial),

and the angle between the normals to the coronal curve at two neighboring inflection points can then be determined to provide a ‘Cobb-equivalent angle’. This approach is analogous with the clinical definition of the coronal Cobb angle, which is based on locating the ‘most tilted’ endplates in a scoliotic curve.

In some cases, the coronal polynomial curve has only one inflection point, and in these cases an alternative approach must be used to generate the ‘Cobb-equivalent’