Chaos Theory, Whiplash, and the Role of ΔV
It’s been the raging question since whiplash was first recognized 80 years ago: is there a minimum speed where injury cannot occur during an auto collision?
The insurance industry is especially interested in this question, because if they can define this threshold high enough, they can easily reject all claims where the speed is lower than that “threshold of injury.”
Previous studies have attempted to answer this question, but these have invariably been flawed. The vast majority of these live crash test studies have conducted their experiments under idealized conditions:
- The test subjects are usually healthy, fit, middle-aged men of average height.
- The subjects have no pre-existing conditions.
- The subject was placed in the optimal position: head erect, facing straight forward, with excellent posture.
- The car seats have been set up to minimize injury, by making sure that headrests are at the correct height and the distance from the head.
Now, it’s understandable why the tests are conducted this way: you can’t ethically subject test participants to a crash that is likely to cause injury. But these ideal conditions in controlled crash tests bear little to no resemblance to a crash experienced by a harried soccer mom navigating 5 o’clock traffic while dealing with the needs of kids in the back seat.
A new study from Germany recognized the problem with controlled crash tests and set out to investigate real-world crashes to see if they could find this elusive “injury threshold.”
The researchers looked at 57 people who had been in a car crash. 21 of these were rear-end collisions, 19 were side impact crashes, and 13 were frontal crashes. Three of the collisions involved multiple impacts and there was one rollover crash.
Each crash victim was given a survey to assess neck injury and symptoms soon after the collision. Engineers investigated each crash to determine an estimate of the ΔV (pronounced delta-v, which means the change of velocity, or speed) of impact.
The authors found:
“For the rear-end collisions, individuals with and without cervical spine injuries were found in a DV range between 9 km/h and 37 km/h. This range was 15 km/h to 28 km/h for frontal collisions and 9 km/h to 36 km/h for side collisions.”
The researchers could not find any correlation between the speed of the crash and the chance of injury. In fact, some of the most severe injuries had occurred at what would consider a low speed crash:
“…we…observed a luxation fracture at C5/6 resulting from a frontal collision at a DV of 15 km/h and a facet joint fracture at C4 due to a side collision at a DV of 10 km/h. Both occupants had been wearing their seat belts, there had been no head contact, and the airbag had not deployed.”
On the other hand, some subjects had been involved in crashes with a delta v of 58 km/h, with no reports of symptoms!
(For perspective: 10 km/h = 6.2 mph; 15 km/h = 9 mph; 58 km/h = 36 mph.)
The researchers conclude that there is no correlation between ΔV and the risk of injury. Why? Because any particular crash literally involves hundreds of variable that can affect injury risk. In fact, there are so many different factors to take into consideration, that a car crash is a chaotic system that’s virtually unpredictable:
“It is tempting to speculate that the development of a cervical spine injury after whiplash is more like a complex system such as those described in chaos theory. Complex systems cannot be simplified into linear correlations. Even small variations of the initial conditions can affect the end result so that it is no longer predictable, such as in the case of the “butterfly effect”: the flapping of a butterfly’s wings can ultimately result in a different weather pattern. Taken together, it can be concluded that ΔV is an irrelevant predictive value for cervical spine injury after a MVA.”
Elbel M, Kramer M, Huber-Lang M, Hartwig E, Dehner C. Deceleration during ‘real-life’ motor vehicle collisions – a sensitive predictor for the risk of sustaining a cervical spine injury? Patient Safety in Surgery 2009;3:5.