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The transverse arch of the foot -Venkadesan et al

Discussion in 'Biomechanics, Sports and Foot orthoses' started by scotfoot, Mar 1, 2020.

  1. scotfoot

    scotfoot Well-Known Member

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    This thread is about a recent paper published in Nature by Venkasen et al ( see link below ) and an important error that affects some , but not all aspects of the paper .

    In a nutshell , as the ball of the foot begins to bear weight during gait ,the metatarsal heads splay mediolaterally ,the transverse ligament comes under increased tension , and the ball of the foot broadens .

    However , and critically , as gait progresses and the heel comes clear of the ground , the ball of the foot begins to narrow again , giving a more pronounced metatarsal arch in the distal aspect of the foot which is vital to foot stiffness during push off .

    The narrowing is a product of the different lengths of the metatarsals which gives rise to the metatarsal parabola .

    The narrowing of the ball of the foot is easy to prove by simply using a couple of thick paperback books and a flat surface . Just stand with both feet on the floor with the books touching either side of the ball area of the bare reference foot (the majority of your weight should be on the contralateral foot at this stage ).

    Now transfer 70 of your weight onto the reference foot with a careful emphasis of the ball of the foot . You should find that the books move apart as the met heads and ball of the foot splay . Now , keeping some weight on the contralateral foot for balance , lift the heel of the reference foot off the flat surface by about 45 degrees so that the ball of that foot supports about 70 % of your weight .

    Now look down at your reference foot and the books . Daylight has appeared between them . The foot has narrowed from is splayed configuration .

    In summary , as the heel clears the ground , relative to each other the met heads move apart anteroposteriorly and together mediolaterally .

    Stiffness of the human foot and evolution of the transverse ...

    www.nature.com › nature › articles
    4 days ago - In the foot, the material properties of the inter-metatarsal tissues and the mobility ... the plantar fascia and other longitudinally oriented ligaments and muscles, and do ... Therefore, the transverse curvature has the effect of amplifying the intrinsic ..
  2. scotfoot

    scotfoot Well-Known Member

    Further to the post above , Venkadesan found that cutting the transverse ligaments reduced foot stiffness by 40% . This figure would have been much higher had he considered a "heel up" "mets closer " foot position .
  3. NewsBot

    NewsBot The Admin that posts the news.

    NEWS RELEASE 26-FEB-2020
    Mathematician identifies new tricks for the old arch in our foot

    A stiff mid-foot is essential for withstanding excessive force when pushing off on the ground for walking and running
    The arch along the length of the foot was believed to be responsible for mid-foot stiffness. Now, a research collaboration between the University of Warwick and two other universities has illustrated the greater importance of a lesser studied foot arch - the transverse arch.
    Our research opens new ways to study the foot for future researchers on foot health. Even the definitions of flatfoot are based upon the longitudinal arch and do not consider the transverse arch. Our work throws these standard practices into question but more work is needed to know how to update them.
    Walking and running subjects our feet to forces in excess of body weight. The longitudinal arch of the feet was thought to be the reason the feet do not deform under such load. However, researchers from the University of Warwick, Okinawa Institute of Science and Technology Graduate University in Japan and Yale University have illustrated that the transverse arch may be more important for this stiffness.

    Past theories of the foot stiffness look at the longitudinal arch, however in the paper 'Stiffness of the human foot and evolution of the transverse arch' published today, the 26th of February in the journal Nature, researchers from the University of Warwick working in collaboration with Yale University and OIST Graduate University, propose the transverse arch may play an equally important role.

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

    This collaboration between Dr Shreyas Mandre, from the Department of Maths at the University of Warwick, Professor Mahesh Bandi, from the Nonlinear and Non-equilibrium Physics Unit at the Okinawa Institute of Science and Technology Graduate University (OIST) and Professor Madhusudhan Venkadesan, from Yale University was funded by a Young Investigator award by the Human Frontiers Science Program.

    The authors say that this research motivates further work into the role of the transverse arches in the disciplines of podiatry and evolutionary anthropology. These insights could also inspire new designs for prosthetic and robotic feet.

    The role of the transverse arch may be understood in simpler terms by looking at a thin paper sheet. When the short edge is held 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," Dr. Mandre explains. "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."

    But because the foot serves multiple mechanical functions, 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 ingeniously 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 Ali Yawar, a co-author of the study.

    "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," said Carolyn Eng, another co-author of the article. In comparison, experiments in the 1980's 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 accounts 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 Prof. 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 that were discovered in Laetoli.
  4. NewsBot

    NewsBot The Admin that posts the news.

    Stiffness of the human foot and evolution of the transverse arch
    Madhusudhan Venkadesan, Ali Yawar, Carolyn M. Eng, Marcelo A. Dias, Dhiraj K. Singh, Steven M. Tommasini, Andrew H. Haims, Mahesh M. Bandi & Shreyas Mandre
    Nature (2020)
  5. NewsBot

    NewsBot The Admin that posts the news.

  6. scotfoot

    scotfoot Well-Known Member

    Very simply , you cannot properly understand the transverse arch of the foot unless you understand the role of the metatarsal parabola .

    Take the dollar bill analogy . Give such a geometric shape a transverse curve and then lever it ,convexity upward , onto a desk at 45 degress and it will fold up as the free end corner touch the desk first . However take the same dollar bill and , with scissors , make the free end into an arch . Now give it a transverse curve , lever against the desk and it resists collapsing .

    Going back to the foot , the greater the convexity /transverse curve of the arch the stronger the structure , so gait progression and heel lift gives a stronger structure over a given time as the met heads are pulled together mediolaterally and pushed apart anteroposteriorly by ground reaction forces and tension within transverse ligament .

    Simple .

    Actually , even more simple is as follows .
    Take a thin piece of rectangular card , give it a transverse curve and it will form a poor scoop for getting ice cream out of a tub .
    Flatten out the card , tear the free end it in such a way that it becomes curved , reform the card to give a transverse arch and you have a better scoop .
  7. efuller

    efuller MVP

  8. efuller

    efuller MVP

    Definition of arch
    1. a curved symmetrical structure spanning an opening and typically supporting the weight of a bridge, roof, or wall above it.
  9. scotfoot

    scotfoot Well-Known Member

    I understand what you are saying Eric and know you dont understand what I am saying . Dont worry about it .
  10. scotfoot

    scotfoot Well-Known Member

    " Actually , even more simple is as follows .
    Take a thin piece of rectangular card , give it a transverse curve and it will form a poor scoop for getting ice cream out of a tub .
    Flatten out the card , tear the free end it in such a way that it becomes curved , reform the card to give a transverse arch and you have a better scoop . "

    Expanding on the above , if you again flatten the card and make the curve more pronounced , then when you reintroduce a transverse arch to the card you have an even stiffener scoop than with the lesser curvature .

    Thus the foot becomes stiffer through transverse arching as the heel lifts during later stance .

    Can't believe this mechanism has been missed by all . Including Venkadesan et al and their advisers . And I will likely never get a mention in connection with this .

    Generally , there seems to be a tendency in academia not to give credit where credit is due if you can possibly avoid it . In my opinion , this does nothing other than damage the credibility of the individuals concerned and of the research community in general .
    Last edited: Mar 3, 2020
  11. scotfoot

    scotfoot Well-Known Member

    In summary then and with regard to the papers of Venkadesan on foot stiffness -

    1 Fish fins - nope , red herring

    2 "as the heel clears the ground , relative to each other the met heads move apart anteroposteriorly and together mediolaterally ." A key to foot stiffness and far , as I know , first proposed by me .

    3 Implications - footwear which causes the forefoot to rest on a concave surface likely reduces foot stiffness .
    Glycation likely impedes met head movement causing increased pressure under second met head . Solution - see work of prof Isabel Sacco .

    Eric , forget arches and just think card ice cream scoop with variable end scoop curvature .

    I await researchers "discovering" point 2 and look forward to the press announcement .
  12. efuller

    efuller MVP

    Just don't call it transverse arching. A beam, or arch, resists bending better when there is greater distance between the tension part of the structure and compression part of the structure. (This explains the folded piece of paper scoop.) This was probably discovered by pre historic builders. It has been in engineering textbooks for over a century. You could call this the joist effect, like I have in the past. With supination of the STJ the talus rotates more on top of the calcaneus, creating more distance between the compression elements (dorsal bones) and tension elements (plantar ligaments and plantar fascia). Hicks, in the 1950's, applied beam theory concepts to the longitudinal arch of the foot. These ideas are not new. Neither you, nor I, can take credit for being the first one to apply engineering principles to the structures of the foot.

    There are other possible explanations of the observation that foot stiffness decreases with cutting of the transverse intermetatarsal ligament than the transverse arch. For example, cutting the transverse intermetatarsal ligament could lead to less ability to keep the first metatarsal in line with the fascia and tension in the fascia would cause medial deviation of the first met head and less resistance to dorsiflexion of the metatarsal.

    By the way, I question their observation that the foot gets narrower with heel lift. In some feet it gets wider. There are feet, in static stance, when the examiner attempts to dorsiflex the big toe, the first metatarsal head becomes more prominent medially. This is the motion that occurs at the first metatarsal phalangeal joint with heel lift. The foot will not get narrower for all feet.

    The other problem in connecting the experimental observations seen with cutting the transverse intermetatarsal ligament is that structures proximal to the metatarsal heads were not mentioned in the experiment. This is a problem for both the joist effect and the transverse arch explanation. This experimental design is very, very, weak evidence for the transverse arch explanation. Jumping to a conclusion can cloud your search for the truth of what is really going on.
  13. scotfoot

    scotfoot Well-Known Member

    Hi Eric
    I am claiming to be the first to point out that the geometry of the metatarsal parabola causes the tension and compression elements in the distal foot to move further apart in a vertical direction as the heel lifts during gait , giving inceased stiffness .
    Until I a proved wrong I am taking the liberty of calling this the " arena effect " .

    The authors did not say that the foot narrowed in gait ,I did . They in fact thought distal stiffness came from a widening of the forefoot and a fish fin effect .
    Admittedly my observations are based only on 3 pairs of feet including my own .

    Re the cadaver work , the tested feet should have had the toes in a dorsiflexed position and only one incision was required .
    That incision should have been a severing of the transverse ligament between the second and third met heads to decouple the the lateral and medial longitudinal arches . There are reasons for this which include the stability issues which you raised in your post .

    So the arena effect then . You will have to forgive me blowing my own trumpet but people keep nicking my tunes!
  14. scotfoot

    scotfoot Well-Known Member

    Eric ,
    Here is a good picture of " arena effect " Note the concavity of the metatarsal arrangement which becomes accentuated as the heel lifts .

    Attached Files:

  15. scotfoot

    scotfoot Well-Known Member

    Here is a link to a 10 second video which explains how the metatarsal parabola, where the metatarsals extend to different distances distally , causes the met heads to move relative to each other anteroposteriorly as the heel lifts during later stance .
    This causes the transverse arch to be more pronounced distally and helps to turn the foot into a rigid lever at push off .

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