Botox has become almost as famous as the celebrities who use it to iron out their wrinkles. But we could soon see an alternative approach to smoothing away those crow's feet, thanks to a pair of Cambridge University physicists who have found a formula that predicts how big wrinkles will be. Enrique Cerda and Lakshminarayanan Mahadevan reckon their theory might help cosmetic scientists design a new antiwrinkle cream that really works.
A thin sheet overlying a relatively stiff substance will form wrinkles if one or the other stretches or shrinks. When an apple dries out, its skin buckles; as human skin ages, the surface forms those character-building ripples. What Mahadevan and Cerda wanted to know was what controls the size, or wavelength, of those wrinkles.
In the 21 February issue of Physical Review Letters they report that the wavelength of wrinkles is a compromise between the skin and the firmer flesh underneath. Experimenting with thin elastic sheets that modeled human skin, the researchers found that a thin, skinlike sheet always prefers one large wave to many small wrinkles, while a relatively stiff, fleshlike underlay prefers the smallest waves possible. Their calculations indicate that the wrinkle wavelength is approximately equal to the fourth root of the ratio of the stiffness of skin to flesh. This means that to double the wavelength (and smooth a wrinkle), the underlay has to be 16 times as stiff.
The discovery could be used in helping to monitor and control manufacturing defect-free thin sheets of paper, glass, metal, and silicon, says Mahadevan. It could also help biologists understand how cells move around and help chemists measure the mechanical properties of membranes. And that world-weary skin? According to Mahadevan, crow's feet might be eliminated by treating carefully selected areas around the eyes to stiffen the skin and pull wrinkles flat. Botox has an altogether more drastic effect in that it paralyzes facial muscles.
"This work will help incrementally in making skin improvement products," says Tom Witten of the University of Chicago. "Its main significance, however, is in showing how the wavelength of the wrinkles grows with the strength of the substrate in a simple and surprising way."