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The geometric principles of the COBB angle
For more than 50 years, the severity of adolescent scoliosis has been determined using the COBB angle. The COBB angle construction technique still determines our view of the statics of the spine today. It has contributed to a significant standardization of treatment decisions in spinal deformity surgery. Derived angles are used to determine (regional) cervical and lumbar lordosis and thoracic kyphosis.
by Kmhkmh – Own work, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=48897686
So how do you get from the curvature to the angle? Let’s imagine that a circle is placed inside the scoliosis. The circle can be clearly described by its radius. The contact distance of the circle with the spine is the arc length Δs. We create tangents at the points where the circle loses contact with the spine. These outer tangents together form an angle Δφ. The geometric basis of the COBB angle is ultimately the relationship of the outer tangent angle Δφ to the arc length and radius of the created circle of curvature:
The COBB angle and its weaknesses
The construction of the COBB angle on the X-ray image
For scoliosis on the PA X-ray of the entire spine (and thus exemplary for kyphosis and lordosis on the lateral X-ray)
- identify neutral vertebrae
- the legs of the angle to be determined are drawn on the end plates of the neutral vertebrae
- the angle is either constructed manually (via 2 orthogonals) or output by the computer
All 3 process steps are subject to errors and lead to deviations of up to 10° between different examiners.1Bernstein P, Metzler J, Weinzierl M, Seifert C, Kisel W, Wacker M. Radiographic scoliosis angle estimation: spline-based measurement reveals superior reliability compared to traditional COBB method. Eur Spine J. 2021 Mar;30(3):676-685. doi: 10.1007/s00586-020-06577-3. Epub 2020 Aug 27. PMID: 32856177.
With the current treatment cut-offs for idiopathic adolescent scoliosis of 10°/25°/40°, this is an intolerable deviation. The clinically active physician then usually helps himself with the important aspect of progression. If two x-rays of different dates from the same patient are placed next to each other, the error in step 1 (selection of the neutral vertebrae) can almost be ruled out. Step 3 is not critical nowadays due to the use of computers. Thus, the 10° error in the individual patient may not lead to a clinically incorrect decision.
But – the comparability of different patients is not given, unless the error can be averaged out over several examiners. Also, the COBB angle alone does not reflect the extent of the clinical deformity and thus the patient’s level of suffering.
For example, large-arched single-curve 40° scolioses can lead to a considerable deformity with trunk imbalance, while double- or triple-arched scolioses only cause (externally barely perceptible) trunk shortening. Another observation is that external measurement methods such as moirée or raster stereography correlate quite well with the progression behavior of the deformity on an intra-individual basis, but cannot be converted 1:1 to the COBB angle. 2Schulte TL, Hierholzer E, Boerke A, Lerner T, Liljenqvist U, Bullmann V, Hackenberg L. Raster stereography versus radiography in the long-term follow-up of idiopathic scoliosis. J Spinal Disord Tech. 2008 Feb;21(1):23-8. doi: 10.1097/BSD.0b013e318057529b. PMID: 18418132. Raster stereographic data can only be correlated with Cobb-angles at values below 20° 3Thometz JG, Lamdan R, Liu XC, Lyon R. Relationship between Quantec measurement and Cobb angle in patients with idiopathic scoliosis. J Pediatr Orthop. 2000 Jul-Aug;20(4):512-6. PMID: 10912610.
Unclear error in the transfer of the COBB angle construction to other deformities
In idiopathic scolioses, we find relatively harmonious relationships, i.e. the arc lengths span several segments – so there are also correspondingly large circles of curvature. Visually visible deformity and the outer angles of the tangents and thus also the COBB angle are at least approximately the same.
The situation is more difficult with degenerative scoliosis. Due to disc changes, the vertebral segments develop their own curvature dynamics, which can be completely different in the lower and upper lumbar spine. Proximal curves tend to be large-arched, while the distal lumbar spine produces short segmental curves. The effect of the measured COBB angles on the statics of the spine can therefore no longer be predicted, as different curvature circles and therefore different deformities are present at different locations.
Greater precision thanks to a spline-based approach
Our current geometric description of scoliosis is inaccurate because at least 2 errors can occur when constructing the angles. In addition, it probably does not reflect the reality of the deformity forces as soon as curvatures of different sizes are encountered.
The solution to this problem is to return to the actual angle-determining step: the tangents. These could also be drawn directly on the spine – bypassing the COBB construction. However, this is difficult to do by hand, as the reference line is difficult to determine. However, a computer algorithm can interpolate an artificial reference line from the vertebral bodies. This creates the geometric figure of the spline, which is also known from computer graphics. Cubic interpolation of the line to the plotted points produces an approximation of the scoliosis that is capable of reducing the measurement error by a power of ten. 4Bernstein P, Metzler J, Weinzierl M, Seifert C, Kisel W, Wacker M. Radiographic scoliosis angle estimation: spline-based measurement reveals superior reliability compared to traditional COBB method. Eur Spine J. 2021 Mar;30(3):676-685. doi: 10.1007/s00586-020-06577-3. Epub 2020 Aug 27. PMID: 32856177.
If we go one step further, a spline contains significantly more information than a single angle value. Distribution of curvature and imbalances of curvature circles can be represented much better than a construct of angles and classifications (Lenke, King,…). For an algorithmically driven understanding of scoliosis, there is therefore no alternative to switching to a spline-based measurement method.
The technical implementation of this step is very simple. Vertebrae can be marked semi-automatically or fully automatically and the spline can be constructed from them – done. Implant manufacturers already offer such solutions as fully automated AI gadgets, and even surgical planning can be carried out to the exact degree.
With the xray-annotator, I would like to offer a free tool for anyone interested. The tool allows spline-based measurement in addition to the classic regional and segmental COBB angle measurement. It is also possible for several examiners in one institution to measure the images.
