SOME sportspeople are more prone to injury than others, despite being fully fit. A new mathematical model of the body shows that these athletes rely on a fixed combination of movements that they cannot easily modify. The discovery might help in spotting injury-prone athletes early on.
Sports injuries are extremely difficult to study because of the huge range of body movements involved; the complex shape of the bones, cartilage and muscle tissue; and the difficulty in determining how the body handles large forces. Traditional models of the body use differential equations, and tracking the motion of just one or two joints requires tremendous computer power. Add more joints to the mix, and the calculations become fiendishly difficult even for a powerful computer.
Now mathematicians Rudi Penne of the Karel de Grote School in Antwerp, Belgium, and Henri Laurie of the University of Cape Town in South Africa, have found a way to simplify analysis of the body鈥檚 movement by using a technique called projective geometry. This is a way of studying the relationship between two lines in terms of their orientation, but without having to deal with their coordinates.
Advertisement
Using projective geometry, Penne and Laurie modelled the actions of cricket bowlers, who are notorious for their frequent injuries. After making some assumptions about a bowler鈥檚 action 鈥� for instance, they ignored any rotations of the wrist and elbow 鈥� the researchers modelled all the ways in which joint movements could be combined to deliver a cricket ball. They found that most combinations allowed the bowler to make small adjustments to the action, but that a few combinations gave no room for manoeuvre. The researchers call this phenomenon 鈥渞educed redundancy鈥� and say that it may play a special role in sports injuries.
Many injuries begin as small problems such as a micro-tear or fracture that becomes larger with repeated action. A bowler鈥檚 ability to modify his action while remaining effective avoids aggravating any injuries.
But if any change in movement is not possible because of the requirements of a bowler鈥檚 action, the micro injury is much more likely to become serious ().
The mathematicians tested their idea on two bowlers, one of whom is prone to injury. Their study showed that a critical component of his action had reduced redundancy while the other bowler鈥檚 action did not. 鈥淭his may help us make an early diagnosis of injury-prone cricketers,鈥� Laurie says.
鈥淚t is an elegant approach which has a lot of appeal, but considerably more work is needed to apply it more generally,鈥� says Kit Vaughan, a biomedical engineer at the University of Cape Town. Penne and Laurie now hope to test their ideas on a larger group of cricketers and to model other sporting actions such as the way footballers take free kicks or how rugby union players scrummage.