A technique to grow any target shape from any starting shape has been demonstrated by scientists from the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS). This development has potential applications in tissue engineering.
In a paper published in the Proceedings of the National Academy of Sciences, the team from SEAS and the Wyss Institute for Biologically Inspired Engineering reverse engineered nature’s ability to grow a diverse array of shapes.
"The challenge was how to do the inverse problem," said Wim van Rees, a postdoctoral fellow at SEAS and first author of the paper. "There's a lot of research on the experimental side but there's not enough on the theoretical side to explain what's actually happening. The question is, if I want to end with a specific shape, how do I design my initial structure?"
Inspired by the growth of leaves, the researchers developed a theory for how to pattern the growth orientations and magnitudes of a bilayer, two different layers of elastic materials glued together that respond differently to the same stimuli. By programming one layer to swell more and/or in a different direction than the other, the overall shape and curvature of the bilayer can be fully controlled. In principle, the bilayer can be made of any material, in any shape, and respond to any stimuli from heat to light, swelling, or even biological growth.
The team unraveled the mathematical connection between the behavior of the bilayer and that of a single layer. "We found a very elegant relationship in a material that consists of these two layers," said van Rees. "You can take the growth of a bilayer and write its energy directly in terms of a curved monolayer."
That means that if you know the curvatures of any shape you can reverse engineer the energy and growth patterns needed to grow that shape using a bilayer.
"This kind of reverse engineering problem is notoriously difficult to solve, even using days of computation on a supercomputer," said Etienne Vouga, former postdoctoral fellow in the group, now an assistant professor of computer science at the University of Texas at Austin. "By elucidating how the physics and geometry of bilayers are intimately coupled, we were able to construct an algorithm that solves for the needed growth pattern in seconds, even on a laptop, no matter how complicated the target shape."
Image: A new technique to grow any target shape from any starting shape is demonstrated by "growing" the face of the father of quantum physics, Max Planck, from a flat disk. Image courtesy of Harvard SEAS.