## Group theory and spinal injuries

Medical science is stuck in the middle ages when it comes to understanding the causes of back pain and how to prevent it. If you want advice, “bend your knees when lifting” is all you’re likely to get.

The standard theory describing spinal injuries is known as the principal loading hypothesis and assumes that any damage is caused by one of either tension, compression, bending or shear forces on the spine.

But Vladimir Ivancevic from the Defence Science & Technology Organisation in Edinburgh, Australia, says this is a vast simplification of what is really going on and has developed a far more sophisticated model to describe spinal damage.

In his model, each vertebrae is able to undergo a range of rotations–pitch, yaw and roll–as well as a range of translations. In the language of group theory, these can be described by the Special Euclidean group SE(3).

(An element of SE(3) is a pair (A, a) where A ∈ SO(3), the special orthogonal group of rotations,  and a ∈ R3. The action of SE(3) on R3 is the rotation A followed by translation by the vector a.)

The overall motion of the spine can then be described by composing the SE(3) groups for all 19 vertebrae.

The key to Ivancevic’s theory is that it is not the ordinary motion of the vertebrae that causes injury or even their acceleration but the rate of change of acceleration, the second derivative of velocity which he calls an SE(3)-jolt. He says that a certain class of the SE(3)-jolts cause tissue damage which results in pain.

His group theory method could be powerfully employed to determine what classes of SE(3)-jolts are unacceptable. It would then be relatively straightforward to design car seats, webbing for soldiers and office chairs specifically to prevent these movements.

This paper doesn’t go that far, however. And here’s where I think Ivancevic is stuck. Not all vertebrae have the same range of movement: lumbar vertebrae movement at the base of the spine is much less pronounced than cervical vertebrae movement at the top, and obviously this has to be allowed for in the model. But measuring and incorporating these idiosyncrasies is going to be tricky.

So although his model may capture the behaviour of a perfect spine made from ideal building blocks, I can’t help wondering whether translating this in to a real world model will be much harder than even Ivancevic anticipates.

Ref: arxiv.org/abs/0806.3340: New Mechanics of Spinal Injury