September 2020

Overlooked Arch In The Foot Is Key To Its Evolution And Function

By William Weir

A long-overlooked part of the human foot is key to how the foot works, how it evolved, and how we walk and run, according to a Yale-led team of researchers.

The discovery upends nearly a century of conventional thinking about the human foot and could open new avenues to explore in evolutionary biology as well as guide new designs for robotic and prosthetic feet, said the study team.

The discovery, made by an international team of researchers and led by Yale engineer Madhusudhan Venkadesan, was published earlier this year in the journal Nature. The team was led jointly by Venkadesan, Shreyas Mandre from the University of Warwick, and Mahesh Bandi from the Okinawa Institute of Science & Technology.

When humans walk and run, the front of each foot repeatedly pushes on the ground with a force exceeding several times the body’s weight. Despite these strong forces, the human foot maintains its shape without severely bending. Such stiff feet — unique to humans among primates — were important for the evolution of bipedalism. (Watch this YouTube video on foot forces in running from the Yale group:

What makes human feet so stiff? According to conventional thinking, it’s mainly the longitudinal arch of the foot (Figure.). This arch runs from heel to forefoot and is reinforced by elastic tissues underneath it. The arch and tissues create a bow-and-string structure that for nearly a century was considered the main source of the foot’s stiffness.

But the foot has a second arch that runs across the width of the midfoot, known as the transverse arch. Venkadesan and his colleagues investigated the transverse arch, which had not been studied previously. They performed a series of experiments, using mechanical mimics of the foot, cadaveric human feet, and fossil samples from long-extinct human ancestors and relatives (hominins). Their results show that the transverse arch is the main source of the foot’s stiffness. (Watch this YouTube video for a demonstration of a mechanical structure that captures the essential features of the human foot.

The reason the transverse arch is so important can be found in your wallet. Take out a dollar bill, hold it at one end, and the dollar flops around. But press your thumb down to give the dollar some curvature, and it stands out straight.

“That type of effect also works in the foot,” said Venkadesan, assistant professor of mechanical engineering and materials science. “It’s not as simple as a sheet of paper because there are many other tissues and structures in the foot, but the principle turns out to be the same.”

Using mathematical analysis and experiments, the team gleaned the mechanical principle for why curvature induces stiffness — namely that bending a curved structure causes the material to also stretch. Even a thin sheet of paper is quite stiff if you try to stretch it. The transverse curvature engages this stretching stiffness to stiffen the whole structure, explained the researchers.

Because the foot is a complicated, multi-functional structure, it is not possible to modify just the transverse arch to test the theory without affecting other parts. So, using experiments on mechanical mimics of the foot, the researchers came up with a novel idea to see whether the transverse arch works the same way in real human feet.

“We found that transverse springs, which mimic tissues spanning the width of your foot, are crucial for curvature-induced stiffness,” said Ali Yawar, a Ph.D. student in Venkadesan’s lab. “So we expected that stiffness would decrease in real human feet if we were to remove the transverse tissues and leave everything else untouched.”

Together with Steven Tommasini, a research scientist at the Yale School of Medicine, they conducted experiments on the feet of human cadavers. “We found that the transverse arch, acting through the transverse tissues, is responsible for nearly half of the foot’s stiffness, considerably more than what the longitudinal arch contributes,” said Carolyn Eng, an associate research scientist in Venkadesan’s lab.

These results may also explain how the 3.66 million-year-old Australopithecus afarensis, the same species as the fossil Lucy, could have walked and left a human-like footprint despite having no apparent longitudinal arch. Working with Andrew Haims, a professor at the Yale School of Medicine, the researchers developed a new technique to measure transverse curvature using partial skeletons of the foot. By applying this technique to fossil samples, including A. afarensis, they traced how the transverse arch evolved among early hominins.

“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,” Venkadesan said.

The findings also open new lines of thought for podiatry, as well as the fields of evolutionary biology and robotics, the researchers said.

Source: Venkadesan, M., Yawar, A., Eng, C.M. et al. Stiffness of the human foot and evolution of the transverse arch. Nature 579, 97–100 (2020).

William Weir is a communications liaison with Yale University.

2 Responses to Overlooked Arch In The Foot Is Key To Its Evolution And Function

  1. The article above is based on a paper published in Nature which discussed the possible importance of the transverse arch of the midfoot to the stiffness of the longitudinal arch of the foot (Venkadesan M, Yawar A, Eng CM, Dias MA, Singh DK, Tommasini SM, Haims AH, Bandi MM, Mandre S:Stiffness of the human foot and evolution of the transverse arch. Nature, 26:1-4, 2020). Unfortunately, both the article above, and Venkadesan et al’s article published in nature, overestimates the biomechanical influence of the transverse arch of the foot on foot stiffness and whether Vendadesan et al’s ideas truly “have not been studied previously”.

    The longitudinal arch has been thought for many years to give most of the stiffness to the longitudinal arch of the foot to improve the mechanical efficiency of human bipedal gait. In their paper in Nature, Venkadesan et al make claims that the transverse arch of the midfoot contributes “more than 40% of the longitudinal stiffness of the foot”. Even though the authors have done their homework in modelling the transverse arch of the midfoot to estimate its contribution to longitudinal arch stiffness, the authors omitted important factors regarding the biomechanical importance of the longitudinal arch in increasing the mechanical efficiency of gait within the human bipedal animal. In other words, the estimate made by these authors that the midfoot transverse arch contributes “more than 40% of the longitudinal stiffness of the foot” appears to be wishful thinking on the part of these researchers.

    Why? Because these researchers didn’t take into consideration how the various tension load-bearing components of the longitudinal arch of the foot can all work together to reinforce each other and “load-share” to all increase the stiffness of the longitudinal arch of the foot. In 2017, I first described the Longitudinal Arch Load-Sharing System of the Foot which describes how the plantar fascia, plantar intrinsics, deep flexors, peroneus longus and plantar ligamenta all work together to contribute to longitudinal arch stiffness (Kirby KA: Longitudinal arch load-sharing system of the foot. Revista Española de Podología, 28(2), 2017).

    Unfortunately, Venkadesan et al seem to under-emphasize the importance of the central nervous system (CNS) controlled plantar intrinsic muscles and CNS-controlled posterior tibial peroneus longus, flexor hallucis longus or flexor digitorum longus muscles on how they may also increase the stiffness of the longitudinal arch. These strong muscles certainly provide very significant stiffening to the longitudinal arch of the foot. In addition, these authors seem to over-emphasize the importance of the slight curve of the midfoot bones within the frontal plane.

    Second, the authors also, for some unknown reason, did not reference other well-know authors who have also speculated on the importance of the midfoot transverse arch. 50 years ago, Kapandji modelled the midfoot transverse arch as being a part of the “vault” of the human foot. Kapandji even used a nearly identical “folded sheet” model to demonstrate the increased stability of the foot from the transverse midfoot arch that has also now been used ,a half-century later, by Venkadesan et al in their paper in Nature (Kapandji IA: The Physiology of the Joints. Volume 2. Lower Limb. 2nd Ed. Churchill Livingstone, New York, 1970). I would have thought that Kapandji’s well-known reference should have been included within the paper as the first reference to suggest how the transverse arch may increase the longitudinal arch stiffness of the foot. One would think that a half-century of introduction of an idea with multiple references to Kapandji’s work in the medical and scientific literature would rate it even a brief mention in a paper that claimed, somehow, that their idea was original.

    Third, there was little mention on the biomechanical significance of having a higher longitudinal arch height is on increasing the stiffness of the longitudinal arch. In 1998, Arangio et al demonstrated that raising the longitudinal arch of the foot from a flatter to higher-arched structure increased the stiffness of the longitudinal arch by over two-fold (Arangio GA, Chen C, Salathe EP: Effect of varying arch height with and without the plantar fascia on the mechanical properties of the foot. Foot Ankle Int, 19:705-709, 1998). Longitudinal arch height has a huge effect on longitudinal arch stiffness, a fact which was never mentioned within this paper by Venkadesan et al.

    In conclusion, I doubt that the transverse arch of the midfoot contributes “more than 40% of the longitudinal stiffness of the foot”, as the authors claim. The potential for the longitudinal arch to greatly increase the sagittal plane stiffness of the forefoot seemed to me to be marginalized within this paper, so that the transverse arch of the midfoot came out, in the view of the authors, as being a dominant factor in longitudinal arch stiffness.

    Kevin A. Kirby, DPM
    Adjunct Associate Professor, Department of Applied Biomechanics
    California School of Podiatric Medicine at Samuel Merritt College

    Private Practice, Sacramento, CA 95825 USA

  2. Dr Weir:
    Your theory is invalid in closed chain as there is no transverse arch at the level of the met heads, they are all on the ground.

    Your article is excellent if it is viewed a la Kapanji:

    would enjoy think tanking with you. Dennis (Dr Sha

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