The wrong arch may have gotten credit for foot stiffness

The transverse arch may be more important for foot stiffness than the longitudinal arch, researchers report.

Walking and running subjects our feet to forces in excess of body weight. Scientists have thought the foot’s longitudinal arch was why our feet don’t deform under such load. The new research, however, suggests the transverse arch may play an equally important role.

The researchers found that the transverse arch is a bigger source of foot stiffness than what researchers previously found was due to the longitudinal arch. They also discovered that the transverse arch evolved to become almost human-like over 3.5 million years ago.

This research motivates further work into the role of the transverse arches in podiatry and evolutionary anthropology, the researchers say. These insights could also inspire new designs for prosthetic and robotic feet.

A schematic of the foot skeleton showing the arches and typical loading pattern. The image at the top right is a sheet of paper bending under a 5g weight. The bottom right shows the same sheet but with a transverse arch supporting 500g of weight. (Credit: U. Warwick)

The role of the transverse arch may be understood in simpler terms by looking at a thin paper sheet. When you hold the short edge flat, the sheet is floppy and droops under a little weight. But curl the edge a little and even 100 times as much weight is not excessive.

“Flat thin objects like paper sheets bend easily, but are much difficult to stretch,” says Shreyas Mandre from the math department at the University of Warwick. “The transverse curvature of the sheet engages its transverse stretching when attempting to bend it. This coupling of bending and stretching due to curvature is the principle underlying the stiffening role of the transverse arch.”

Because the foot serves multiple mechanical functions, however, its structure is more complicated than the paper sheet. Therefore, “flattening” the foot to test the hypothesis of curvature-induced stiffening may have unidentified confounding variables. To overcome this difficulty, the researchers disrupted the underlying principle while keeping the transverse arch intact.

“Understanding of the underlying principle enabled us to build mechanical mimics of the foot comprising springs that imitated the elastic tissue of the foot. Disrupting the transversely oriented springs in these mimics had the same effect as flattening them,” explains coauthor Ali Yawar of Yale University.

“We disrupted the underlying principle of curvature-induced stiffening in human cadaveric feet by transecting the transverse tissue, which reduced the mid-foot stiffness by nearly half,” says coauthor Carolyn Eng of Yale. In comparison, experiments in the 1980s on disrupting the stiffening mechanism due to the longitudinal arch only showed a reduction in stiffness by about 25%.

This research also injects new interpretation of the fossil record of human ancestral species, especially pertaining to the emergence of bipedalism. The researchers formulated a measure of the transverse arch to account for variations in the length and thickness of the feet. They used the measure to compare related species such as the great apes, human ancestral species, and some distantly related primates.

“Our evidence suggests that a human-like transverse arch may have evolved over 3.5 million years ago, a whole 1.5 million years before the emergence of the genus Homo and was a key step in the evolution of modern humans,” explains coauthor Madhusudhan Venkadesan.

It also provides a hypothesis for how Australopithecus afarensis, the same species as the fossil Lucy, thought to not possess longitudinally arched feet, could generate footprints like humans researchers discovered in Laetoli.

The work appears in Nature.

Funding for the work came from a Young Investigator award by the Human Frontiers Science Program. Additional researchers from the University of Warwick, the Nonlinear and Non-equilibrium Physics Unit at the Okinawa Institute of Science and Technology Graduate University, and Yale contributed to the work.

Source: University of Warwick

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