By Damien Mearns.
The Cobb angle was invented by John Robert Cobb. It passes itself off as being the measurement of a scoliosis curve, but it is only the measurement of the shadow of the curve that the X-ray makes; and there is a difference, sometimes a significant one.
To get more accurate value for the curve of the spine in Scoliosis I’ve invented the Mearns Angle.
What’s wrong with the Cobb Angle ?
When you walk along a beach near Sunset you can see your shadow on the sand and that shadow makes you look like a disproportioned giant. This is due to the angle of the light source – the Sun – being low in the sky and so you, the Sun & the screen – in this case the beach – are not lined up perfectly square on with each other. The result is distortion of the image.
An X-ray works in the same way: unless the X-ray source, you and the screen are lined up perfectly square on then the X-ray image will be distorted. Scoliosis X-rays in hospital settings are not going to be as distorted as an evening beach shadow but there will be significant distortion – to a clinically relevant level nevertheless. The Mearns angle corrects for this distortion to give you a more accurate measurement than the Cobb angle.
A the angle of a scoliosis curve is at base “How much to the side does it go compared to how high it goes” so if a curve moves to the side by 3 inches on someone with a back length of 3 feet, then this will be a smaller curve than someone whose curve goes out to the side 3 inches but has a back length of 1 foot.
When you lean forward (or backwards – anything off-centre) an X-ray beam coming at you will see your scoliosis curve move out to the side by the same amount than if you stand up perfectly vertical, but the X-ray beam will see your spine as shorter – and hence the Cobb angle will be larger than the true angle of your scoliosis.
It is a common tale that scoliosis patients tell of being told off during their childhood for “not standing up straight”. A non-Scoliosis person will classically have a kyphosis of the upper back of 20 to 40 degrees, a lordosis of the lumber spine of 40 to 60 degrees and might stand leaning forward by 5 to 10 degrees. Patients with scoliosis might have have all these number exaggerated and any part of the spine over which the Cobb angle is measured will be effected by all of these numbers.
So to get from the Cobb Angle to the Mearns Angle an adjustment needs to be made to account for the height loss of the image due to the combined angle of tilt. The combined angle of tilt includes the physical forward from the feet and hips with any lordosis or kyphosis angles along the area used to measure the Cobb angle. As this is not an easy thing to measure, it is a ball park number – which will be adequate.
In Microsoft’s Excel, the formula to get the Mearns Angle is, (on a techy level, behind the scenes):
The Mearns Angle = 180-(DEGREES(ATAN(TAN(RADIANS((180-Cobb_Angle)/2))/COS(RADIANS(Tilt_Angle))))*2)
Below is a table showing the relationship.
How to use the table: Do a side-on picture of your body and-or use a side-on X-Ray) and estimate the angle you are off from centre along the area where your scoliosis cobb angle was measured.
Look up your Mearns Angle in the central table by looking up your Cobb angle in the left hand column and going across to the column with your tilt angle in.
| Tilt | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 | 80 | |
| Cobb | Mearns | ||||||||||||||||
| 10 | 10.0 | 9.8 | 9.7 | 9.4 | 9.1 | 8.7 | 8.2 | 7.7 | 7.1 | 6.4 | 5.7 | 5.0 | 4.2 | 3.4 | 2.6 | 1.7 | |
| 15 | 14.9 | 14.8 | 14.5 | 14.1 | 13.6 | 13.0 | 12.3 | 11.5 | 10.6 | 9.7 | 8.6 | 7.5 | 6.4 | 5.2 | 3.9 | 2.6 | |
| 20 | 19.9 | 19.7 | 19.3 | 18.8 | 18.2 | 17.4 | 16.4 | 15.4 | 14.2 | 12.9 | 11.6 | 10.1 | 8.5 | 6.9 | 5.2 | 3.5 | |
| 25 | 24.9 | 24.6 | 24.2 | 23.5 | 22.7 | 21.7 | 20.6 | 19.3 | 17.8 | 16.2 | 14.5 | 12.7 | 10.7 | 8.7 | 6.6 | 4.4 | |
| 30 | 29.9 | 29.6 | 29.0 | 28.3 | 27.3 | 26.1 | 24.8 | 23.2 | 21.5 | 19.5 | 17.5 | 15.3 | 12.9 | 10.5 | 7.9 | 5.3 | |
| 35 | 34.9 | 34.5 | 33.9 | 33.0 | 31.9 | 30.5 | 29.0 | 27.2 | 25.1 | 22.9 | 20.5 | 17.9 | 15.2 | 12.3 | 9.3 | 6.3 | |
| 40 | 39.9 | 39.4 | 38.7 | 37.8 | 36.5 | 35.0 | 33.2 | 31.2 | 28.9 | 26.3 | 23.6 | 20.6 | 17.5 | 14.2 | 10.8 | 7.2 | |
| 45 | 44.8 | 44.4 | 43.6 | 42.5 | 41.2 | 39.5 | 37.5 | 35.2 | 32.6 | 29.8 | 26.7 | 23.4 | 19.9 | 16.1 | 12.2 | 8.2 | |
| 50 | 49.8 | 49.3 | 48.5 | 47.3 | 45.8 | 44.0 | 41.8 | 39.3 | 36.5 | 33.4 | 29.9 | 26.2 | 22.3 | 18.1 | 13.8 | 9.3 | |
| 55 | 54.8 | 54.3 | 53.4 | 52.1 | 50.5 | 48.5 | 46.2 | 43.5 | 40.4 | 37.0 | 33.2 | 29.2 | 24.8 | 20.2 | 15.3 | 10.3 | |
| 60 | 59.8 | 59.2 | 58.3 | 57.0 | 55.2 | 53.1 | 50.6 | 47.7 | 44.4 | 40.7 | 36.6 | 32.2 | 27.4 | 22.3 | 17.0 | 11.5 | |
| 65 | 64.8 | 64.2 | 63.2 | 61.8 | 60.0 | 57.8 | 55.1 | 52.0 | 48.5 | 44.5 | 40.1 | 35.3 | 30.1 | 24.6 | 18.7 | 12.6 | |
| 70 | 69.8 | 69.2 | 68.1 | 66.7 | 64.8 | 62.5 | 59.7 | 56.4 | 52.7 | 48.5 | 43.8 | 38.6 | 33.0 | 26.9 | 20.5 | 13.9 | |
| 75 | 74.8 | 74.2 | 73.1 | 71.6 | 69.6 | 67.2 | 64.3 | 60.9 | 57.0 | 52.5 | 47.5 | 42.0 | 35.9 | 29.4 | 22.5 | 15.2 | |
| 80 | 79.8 | 79.1 | 78.1 | 76.5 | 74.5 | 72.0 | 69.0 | 65.5 | 61.4 | 56.7 | 51.4 | 45.5 | 39.1 | 32.0 | 24.5 | 16.6 | |
| 85 | 84.8 | 84.1 | 83.0 | 81.5 | 79.4 | 76.9 | 73.8 | 70.1 | 65.9 | 61.0 | 55.5 | 49.2 | 42.3 | 34.8 | 26.7 | 18.1 | |
| 90 | 89.8 | 89.1 | 88.0 | 86.4 | 84.4 | 81.8 | 78.6 | 74.9 | 70.5 | 65.5 | 59.7 | 53.1 | 45.8 | 37.8 | 29.0 | 19.7 | |
| 95 | 94.8 | 94.1 | 93.0 | 91.4 | 89.4 | 86.8 | 83.6 | 79.8 | 75.3 | 70.1 | 64.1 | 57.2 | 49.5 | 40.9 | 31.5 | 21.5 | |
| 100 | 99.8 | 99.1 | 98.0 | 96.5 | 94.4 | 91.8 | 88.6 | 84.8 | 80.2 | 74.9 | 68.7 | 61.6 | 53.5 | 44.4 | 34.3 | 23.4 | |
| 105 | 104.8 | 104.2 | 103.1 | 101.5 | 99.5 | 96.9 | 93.7 | 89.9 | 85.3 | 79.9 | 73.6 | 66.2 | 57.7 | 48.0 | 37.3 | 25.5 | |
| 110 | 109.8 | 109.2 | 108.1 | 106.6 | 104.6 | 102.1 | 99.0 | 95.1 | 90.6 | 85.1 | 78.6 | 71.1 | 62.2 | 52.1 | 40.6 | 27.9 | |
| 115 | 114.8 | 114.2 | 113.2 | 111.7 | 109.8 | 107.3 | 104.3 | 100.5 | 96.0 | 90.5 | 84.0 | 76.3 | 67.1 | 56.5 | 44.2 | 30.5 | |
| 120 | 119.8 | 119.2 | 118.3 | 116.9 | 115.0 | 112.6 | 109.6 | 106.0 | 101.5 | 96.1 | 89.6 | 81.8 | 72.4 | 61.3 | 48.3 | 33.5 | |
| 125 | 124.8 | 124.3 | 123.4 | 122.0 | 120.3 | 118.0 | 115.1 | 111.6 | 107.3 | 102.0 | 95.5 | 87.7 | 78.1 | 66.6 | 52.9 | 36.9 |
Is this significant ? Yes. Tilts of 40 degrees+ are not uncommon and a 50 degree Cobb angle at a 40 degree tilt shows a Mearns Angle of 40 degrees.
Excel Spreadsheet with Mearns Angle Calculator here: Mearns Angle
- Download the spreadsheet and open it. Just enter your Cobb Angle and an estimate of your Tilt Angle to see your Mearns Angle – the more accurate angle of your scoliosis.
The other big problem with using the Cobb Angle to define scoliosis totally – which is how it is used, is Goodhart’s Law, which states that when a metric becomes a target, it loses its value as a good measure. A standard example is in colonial India. British officials offered a bounty on cobra skins to reduce the cobra population.
However, citizens began breeding cobras for their skins and then releasing them when they were discovered, which actually increased the cobra population.
In scoliosis, the metric and target is the Cobb angle. The Cobb angle is not the angle of the scoliosis curve. It is the angle of the x-ray of the curve, which is a shadow finger puppet of the spine. The result if this is bracing which squashes spines into braces to “make the x-ray look better” and surgery where patients afterwards can no longer turn their head to cross the road or tie their shoe laces – other metrics that are rather important, but which are ignored.
All other aspects of the back are ignored : https://youtu.be/9oB4mlv3P1U
“X-rays are the gold standard” – no they are not.