Brilliant 10: The Computational Contortionist

Rendering complex objects realistically requires a whole new kind of geometry

By Ryan Bradley

Complex Folding Computer scientist Eitan Grinspun studies how long, thin strands, such as spaghetti and undersea data cables, twist and coils John B. Carnett

When Eitan Grinspun’s adviser at the California Institute of Technology asked him to help develop a better way to model how cans bend when crushed, the young mathematician did not think it would be a major project. “He lured me into something that took years and years,” says Grinspun, now at Columbia University. But the journey to model a crushed Coke can ended with an entirely new field of geometry.

Differential geometry can describe how the curves and surfaces of a given object will bend and crease. The problem, Grinspun says, is “that differential geometry is built for smooth surfaces with infinite detail.” Computers can process only a finite amount of detail. For example, to describe a circle, computers must divide that circle into a series of connecting short sides—the greater the number of sides, the smoother the circle. Describing all of the curves and creases in a crushed can accurately takes a huge amount of processing power, so Grinspun—one of only a couple of mathematicians in the field with a background in computer science—set about translating the theorems into a more elegant set of instructions for the computer, allowing existing processors to break the infinite into discrete units far more efficiently.

Grinspun's method works by concentrating on the places where most of the movement will occur—in the case of the Coke can, the areas where it folds as it crumples. “There are a lot of flat regions where not much is happening,” he says. “If a computer spreads its attention equally, it’s not going to the interesting parts, where cracks are forming.”

Once Grinspun and his colleagues established this new approach, which they call discrete differential geometry, the queries from physicists, engineers and animators started arriving. Disney and Weta Digital use his theorems to make fabrics and hair move more convincingly. Physicists at MIT have created origami out of small sheets of plastic and water drops. Engineers can now far more accurately predict how cables will fall to the seafloor. “For me, [this field] is a playground,” he says. “I get to take any interesting physical problem—say, spaghetti movement. Toss it in the air, and it falls on the ground and it twists and coils. Why does it move that way?"

Brilliant 10: The Butterfly Pharmacist

Watching how insects use plants shows that self-medication isn’t just for complex animals

By Sarah Fecht

Checkmate Jaap de Roode studies how monarch butterflies use plant-based medicine to thwart parasites. John B. Carnett

“I didn’t start working with monarchs because I liked them,” says evolutionary biologist Jaap de Roode of Emory University. “I came to them because they have a really cool parasite.” That parasite, called Ophryocystis elektroscirrha, normally pokes holes in the butterflies’ skin, causing them to leak bodily fluids. But de Roode noticed that monarchs that ate the tropical milkweed plant did not suffer from parasitic infections as much as monarchs eating swamp milkweed did. This led him to suggest to his colleagues that the monarchs were self-medicating. “One of my reviewers said, ‘That’s completely ridiculous. There’s absolutely no way they could ever do that,’” de Roode recalls. Up until then, self-medication was seen as a complex cultural trait. Only a few animals, such as chimps and elephants, had been observed using medicine.

To test his hypothesis, first de Roode looked to see if infected larvae prefer to munch on the parasite-killing tropical milkweed species, rather than the swamp milkweed. They didn’t, so he concluded that the larvae do not use the tropical milkweed medicinally. But when he compared the behavior of healthy adult females with the behavior of infected adult females, a difference quickly became apparent. Infected females, which transmit the parasite to their offspring when they spawn, preferred to lay eggs on the tropical milkweed, showing that they can preemptively medicate their offspring. “Somehow, the mother knows what’s best,” de Roode says.

His findings challenge the view that only animals with cognitive complexity use medicine. If butterflies, which have a simple nervous system and no social structure, could preferentially use medicine, perhaps self-medication is pervasive in the animal kingdom and scientists just haven’t had the chance to find it yet.

Brilliant 10: The Chemical Catcher

Trapping and preserving biomarkers will help doctors detect cancer sooner

By Madhumita Venkataramanan

Protein Safari The nanoparticles built by Alessandra Luchini will catch cancer biomarkers the way nets catch fish John B. Carnett

When Alessandra Luchini was a girl growing up in Italy, she visited the Museo Galileo in Florence, where she saw the telescope that Galileo Galilei had invented four centuries before, in 1610. She was struck by its simplicity. with a just a couple of pieces of curved glass, anyone could see whole new worlds.

In 2005, Luchini, now an engineer at George Mason University, came to the U.S. on a grant from the Italian National Health Service to study ways to detect molecular signs of cancer. Some diseases, early on, release faint hints of their presence into our bodily fluids. These “biomarkers” are ephemeral—our enzymes chew them up within minutes, so they’re undetectable in most lab tests. If doctors had a way to catch and stabilize those biomarkers, they could detect diseases more quickly and begin treatment at a stage when the chances of recovery were much higher.

Luchini’s solution was to build a nanoparticle trap. The concept, like Galileo’s telescope, is simple: “It’s like a net for catching very small fishes,” Luchini says. The spherical nanoparticle, which took two years to perfect, uses hydrogel as its backbone. Inside, a crisscrossing polymer net holds bait, such as acid or dye, which chemically attracts various biomarkers. when lab technicians mix the nanoparticle in with a fresh blood sample, it traps the biomarkers and protects them from enzymes. The sample can then be tested at leisure. So far, Luchini has used nanoparticle traps to produce an early diagnosis of infectious diseases such as Lyme disease and tuberculosis. (The traps can also reveal the presence of human growth hormone in urine, and thus offer a novel way to reveal illegal doping by athletes.) She and her team are also working on nanotraps to find the skin-cancer biomarkers that exist in a person’s sweat.

Luchini’s next step is to modify the nanoparticles so they can trap biomarkers in a body, giving doctors a realtime view of what’s going on inside their patients.