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The metatarsal parabola and the transverse arch of the foot .

Discussion in 'Biomechanics, Sports and Foot orthoses' started by scotfoot, May 28, 2020.

  1. scotfoot

    scotfoot Well-Known Member


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    Here is a thread from BiomchL ( which includes some early material of mine from Podiatry Arena ) which explains the importance of the metatarsal parabola in foot stiffness in later stance .
    • 1
      Foot stiffness and footwear

      June 28th, 2017, 04:43 AM
      1. The following proposes a hypothesis for a mechanism by which the foot becomes stiffer as the toes become more dorsiflexed during gait . If true ,one question the hypothesis raises is what effect close fitting footwear might have on foot function .

        So the hypothesis ,which may be old hat or even wrong is as follows .

        I began by looking at a radiograph of the human foot taken from the dorsal aspect . In the forefoot area , this clearly shows that the metatarsals extend distally to differing degrees . I have heard a line which connects the metatarsal heads called a" metatarsal parabola " so lets just go with that for now . This parabola is in the horizontal plane but is this arrangement which gives rise to the arch during the transition of the foot through late stance .

        Consider as an analogous structure to the metatarsals ,the fingers of the hand .
        Place your hand flat on a desk with the finger tips a few mm apart (ignore the thumb )
        Now keeping the finer tips in place on the desk ,lift the hand off the desk ,pivoting around the finger tips till you reach an angle between the fingers and the desk of about 70 degress . Now look at the fingers relative to each other . They have formed an arch structure . (Think of a piece of guttering about a foot long pushed into sand at an angle of 70 degrees .The part of the guttering you can see above the sand is similar to the finger structure you have created on the desk top and similar to the metatarsal arch formed when a foot , flat on the floor ,transitions towards toe off with the toes becoming more dorsiflexed .

        So how is energy stored in this system ? Back to the hand again .
        If you try the above hand /desk experiment you will notice that the middle fingers of the four need to bend to stay in the same spot on the desk . With a transitioning foot .this bending is probably replaced with a forward displacement of the second and third metatarsal heads and associated toes causing energy to be stored in the distal transverse ligament .

        So do the metatarsal heads of the first and second lesser toes move distally, relative to the other toes , as the toes move into a dorsilflexed position ? You can easily try this out for yourself by taking off your shoes and socks .sitting in a chair and moving your foot from a flat position to a position with the heel raised and observing toe movements ,but for me the answer was yes .

        The above also explains pressure distribution under the forefoot .

        So that is the theory in rough form .

        Any thoughts ?

      2. Regards
      3. Gerrard Farrell

        Glasgow
      4. scotfoot, Yesterday at 7:17 PM
      Tags: foot stiffnes, metatarsals, transverse arch
    • [​IMG]
      Karl Zelik[kzelik28]
      Senior Member
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    #2
    June 28th, 2017, 02:00 PM
    Re: Foot stiffness and footwear

    Hi Gerrard, I believe this recent article may be of interest and relevance:

    Yawar, Ali, et al. "Contribution of the transverse arch to foot stiffness in humans." arXiv preprint arXiv:1706.04610 (2017).
    https://arxiv.org/pdf/1706.04610.pdf

    All the best,
    • [​IMG]
      Gerrard Farrell[Gerrard Farrell]
      Senior Member
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    #3
    June 29th, 2017, 05:09 AM
    Re: Foot stiffness and footwear

    Hi Karl ,
    The paper you reference could not really be more relevant since it was when I was considering its contents that I came up with the theory outlined in the first post .
    I liked their currency bill idea and the comparison to a fishes fins (see below ) .The concept of a “geometrically flat ,yet functionally curved “ structure was new to me and might well account for some arch stiffness ,although as stance progresses through toe off I feel that the distal transverse arch will become structurally curved as well as functionally curved .

    I also liked their idea of energy storage in the transverse ligament but feel that more energy will be stored than they have calculated due to the metatarsal head movement detailed in my first post .

    Some time ago a paper was published that proposed that the intrinsic muscles of the foot helped stabilise the foots skeletal structures so that other larger muscle groups could operate more efficiently (1).

    If a currency bill arrangement of the metatarsals does come into being in the foot during gait , partly via the way the metatarsals are attached to the tarsal bones and partly due to the “metatarsal parabola” then I can see the value of stabilizing this structure and feel that Mckeons paper has real merit .

    I placed a few posts on the paper you mentioned on another site and have included these below

    Regards
    Gerry

    (1) The foot core system: a new paradigm for understanding intrinsic - NCBI
    https://www.ncbi.nlm.nih.gov/pubmed/24659509
    by PO McKeon - ‎2015 - ‎Cited by 60 - ‎Related articles
    21 Mar 2014 - The foot core system: a new paradigm for understanding intrinsic foot muscle function. McKeon PO(1), Hertel J(2), Bramble D(3), Davis I(4).



    1.
    Contribution of the transverse arch to foot stiffness in humans
    Ali Yawar, Lucia Korpas, Maria Lugo-Bolanos, Shreyas Mandre, Madhusudhan Venkadesan
    (source)
    #scotfootActive Member
    So appendages can be "geometrically flat, yet functionally curved " . So does the human foot have a functional , distally placed ,transverse arch ?

    Gerry
    Gerrard Farrell
    Glasgow

    2.
    scotfootActive Member
    Further to posts 3 and 4 above ,some time ago I wrote the following -

    Extract
    "First I found myself a suitable surface such as linoleum . Next I took off my shoes and socks and stood next to a wall for support . Then , taking most of my weight initially on the right foot which was kept flat on the ground ,I put my left foot into toe off position so that only the ball of the foot and the toes were in contact with the ground . Then I carefully transferred some weight onto the left foot and finally,with the ball of the foot and toes under some pressure , rotated the foot outwards producing torque . I found that the toes played an important part in resisting the outward rotation and that they also began to become spaced out from each other possibly engaging the adductors .( please note that I am not suggesting that anyone copy the above exercise sequence or injury may result )
    So perhaps the toes can significantly aid grip on a flat rigid surface ? "

    After reading the paper mentioned in post 3 (1) , it now seems plausible to me that toe and hence metatarsal head splaying caused by the torque produced during the foot movement detailed in the extract above ,might produce a more marked currency bill folding effect than forefoot weight bearing alone . Hence increasing foot stiffness in response to increased foot torque during walking /running .

    Gerry
    (1)
    (Contribution of the transverse arch to foot stiffness in humans
    Ali Yawar, Lucia Korpas, Maria Lugo-Bolanos, Shreyas Mandre, Madhusudhan Venkadesan
    (source)
    Gerrard Farrell

    Glasgow





    3.
    scotfootActive Member
    This video analysis (1) of a fishes fin helps to explain their hypothesis . For my part , although the hypothesis as it applies to the foot may account for a small part of the stiffening of the foot , I believe that the distal transverse arch makes the majority of its contribution to arch stiffness via a different mechanism .

    Gerry
    (1) Video illustrating the mechanism underlying curvature-induced ...

    [​IMG] ▶ 1:04

    29 May 2017 - Uploaded by Shreyas Mandre
    Curvature-induced stiffening of a fish fin, Khoi Nguyen, Ning Yu, Mahesh M. Bandi, Madhusudhan Venkadesan ...
    Gerrard Farrell

    Glasgow






    4.
    scotfootActive Member
    I do think the theory proposed in the Ali Yawar et al study, above, may have some validity but I do not believe their study protocol is a valid way of testing it .Nor do I believe the mechanism they describe plays a major role in foot stiffness .

    In addition ,in my opinion the study below (1) and all such studies do not show that there is no distal transverse arch function but instead show that there IS .
    1
    Z Orthop Ihre Grenzgeb. 1995 Jul-Aug;133(4):335-40.
    Ultrasonic measurements (n = 172) and plantar pressure investigations (n = 119) are performed on the forefeet of healthy adults, in order to constitute a correlation between shape and function of the anterior metatarsal arch. The thickness of the sole of the foot has its maximum beneath the 2nd metatarsal head and its minimum beneath the 1st and 5th ray. The highest pressure values are found at the 2nd and 3rd metatarsal head. It is concluded that despite the arch like configuration of the forefoot there is no structural arch function. The biological principle of adequate padding of pressure points results-depending on the load-in a different thickness of the soft tissues of the sole of the foot. The higher pressure under the central metatarsal heads is accompanied by thicker soft tissue pads and a more dorsal position of these rays.
    Gerrard Farrell

    Glasgow
    Last edited by Gerrard Farrell; July 1st, 2017, 01:35 PM. Reason: Spacing of text
    • [​IMG]
      Gerrard Farrell[Gerrard Farrell]
      Senior Member
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      • Posts: 116
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    #4
    June 30th, 2017, 03:34 PM
    Re: Foot stiffness and footwear

    Taking the content of the previous posts as a whole , it seems quite possible that the transverse arch of the foot provides the majority of the foot stiffness required for energy efficient gait . It also seems likely that the distal transverse arch becomes more pronounced as the forefoot is loaded and the toes become more dorsiflexed .
    With regard to maintaining foot structure then , perhaps the primary role of the intrinsic muscles of the foot is to help maintain the integrity of the transverse arch of the foot and not the longitudinal arch .
    For example the oblique head of the adductor hallucis could be viewed as a torsion resistant cross strut of the transverse system .

    Gerry

    Gerrard Farrell

    Glasgow

    • [​IMG]
      Gerrard Farrell[Gerrard Farrell]
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      #5
      July 10th, 2017, 04:51 AM
      Re: Foot stiffness and footwear

      The following thought experiment may help explain how a transverse arch extending from the tarsals ,along the metatarsals and into the forefoot can help increase foot stiffness during gait .

      First take a disc of wood with a thickness of 1 inch and a diameter of six inches and divide this into two equal semicircular parts . Next orientate the two arched sections vertically and directly facing each other and about six inches apart . Next create 5 equally spaced holes in the two facing surfaces about one inch up from the bases . Next take a length of bamboo cane ,of about six inches in length and fix its ends into hole 1 of the two facing arched sections .Do the same with the remaining 4 facing holes in the arched sections . Now imagine the whole thing glued together ( or ,if you prefer , fastened together with gut or some such material to better represent ligaments)

      You should now have a mental picture of something resembling a toast rack .
      Now pick up the construction by the two ,arched end pieces ,one in each hand . Rotate the hands inwards ,applying force and the construction flexes .

      Now picture a second construction but this time the holes are NOT placed along a straight line one inch up from the bases of the arched end pieces (respectively , the under tension transverse ligament and tarsals ) but instead place them following the curvature of the arch so that bamboo connectors (the metatarsals ) help form part of a transversely arched structure which better resists flexion (like a piece of guttering ) .

      It is also worth noting that in the first construction the sections of cane (metatarsals ) flex along their lengths but in the second example the cane is subject to compression and stretch which it is better able to resist .


      Gerry
      Last edited by Gerrard Farrell; July 10th, 2017, 04:54 AM.
    • [​IMG]
      Gerrard Farrell[Gerrard Farrell]
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      #6
      July 13th, 2017, 05:29 AM
      Re: Foot stiffness and footwear

      In summary then , the transverse arch can be viewed as being composed of five saggital sections ,each of which corresponds to a metatarsal and a component of the transverse arch of the tarsals . Each of these sections is further composed of ligaments and by a component of the plantar fascia ( overall , the foot can be thought of as having five longitudinal arches each composed of a metatarsal ,tarsal arch , calcaneus and talus supported by ligaments and the plantar fascia )

      The most medial of the saggital sections ( which is a part of the medial longitudinal arch ) is composed of tarsal arch ,the first metatarsal ,ligaments and the plantar fascia .

      So we have five metatarsals in the transverse arch ,which are in turn united by common proximal and distal sites of attachment (tarsal arch and transverse ligament -see previous post ) .

      During later stance the existence of a "metatarsal parabola " causes the metatarsals to give rise to a distally placed transverse arch which ,when taken as together with the rest of the transverse arch , provides the necessary stiffness for this phase of gait .

      I have omitted the intrinsic foot muscles from the system because increasingly I see their role (other than helping to control toe movement ) as being pivotal in maintaining the transverse arch of the foot during later stance . However they do this not primarily by resisting body weight but rather by controlling the configuration of the transverse arch . That is they make adjustments to the bony/ligamentous framework of the foot and this framework ,aided by the extrinsic foot muscles , supports the body during gait . (see PO Mckeon et al above post 3 ) .

      If all of the above is true then weak or " under educated " intrinsics will eventually lead to major problems with the entire system leading perhaps to more proximal tissue failure .

      If this is all starting to look like very similar Mckenzies " half dome" and Mckeons (1) "foot core " expansion of the same , then that is because I think both ideas are valid since the existence of a metatarsal parabola would extend the half dome into the forefoot when foot stiffness is most required .


      Any thoughts ?
      Gerry
      (1)The foot core system: a new paradigm for understanding intrinsic foot ...

      bjsm.bmj.com › Archive › Volume 49, Issue 5
      by PO McKeon - ‎2015 - ‎Cited by 63 - ‎Related articles
      We then integrate the concept of the foot core into the assessment and treatment of the foot. Finally, we call for an increased awareness of the importance of the ...
      Last edited by Gerrard Farrell; July 17th,


    • Gerrard Farrell[Gerrard Farrell]
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      #9
      September 14th, 2017, 07:14 AM
      Re: Foot stiffness and footwear

      Much of the above seems to have been neatly summarized in pictures with this link . Look at the first two figures ,from left to right , and the metatarsals in particular .

      Link https://www.biomedcentral.com/collections/footwear
    • [​IMG]
      Gerrard Farrell[Gerrard Farrell]
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      #10
      September 16th, 2017, 06:47 AM
      Re: Foot stiffness and footwear
      With regard to the previous posts the linked to paper below (1) may be of interest , especially "Other factors may be responsible for. the observed pressure increase, such as reduced range of motion of the metatarsophalangeal joints and increased stiffness of plantar soft tissues ".
      So looking at this phrase has started me wondering about increased stiffness in the feet of diabetic patients and the possible impact this might have on plantar pressures under met heads #2 and #3 in particular .
      Earlier in the thread I wrote "Metatarsal parabola + terminal stance = distal transverse arch . Can't be any other way . "

      For this to be true the met heads must be able to move relative to each other thus allowing a spread of pressure across the forefoot during gait . But what if diabetes induced stiffness prevents this from happening ? With the met heads unable to move relative the each other , then ,during late stance ,the pressure under head #2 in particular may cause repeated ulceration .

      So what can be done ? Professor Isabel Sacco has done a lot of work in the area of mobilizing foot and ankle tissues made stiffer by the effects of diabetes , and she has shown that these tissues respond well and become less stiff , using physiotherapy methods such as strengthening and stretching .

      So how can you stretch the forefoot across the met heads ,their associated capsules and the deep metatarsal ligament .

      Possibly as follows . First an extract from earlier in this thread -

      "First I found myself a suitable surface such as linoleum . Next I took off my shoes and socks and stood next to a wall for support . Then , taking most of my weight initially on the right foot which was kept flat on the ground ,I put my left foot into toe off position so that only the ball of the foot and the toes were in contact with the ground . Then I carefully transferred some weight onto the left foot and finally,with the ball of the foot and toes under some pressure , rotated the foot outwards producing torque . I found that the toes played an important part in resisting the outward rotation and that they also began to become spaced out from each other possibly engaging the adductors .( please note that I am not suggesting that anyone copy the above exercise sequence or injury may result )
      So perhaps the toes can significantly aid grip on a flat rigid surface ? "

      This stretch might work to mobilize the tissues in question allowing met head movement and the avoidance of very large pressure under #2 , causing ulceration . However the stretching method could easily cause tissue tears between the toes if not done under expert supervision , at least during a learning process for the patient , and so should not be attempted without supervision by a qualified health care professional (and even then only following proper trials ) .

      Can the risks eventually be reduced if the exercise is found to be beneficial ?
      This might be possible by only carrying out the exercise in a seated position to reduce the stretching forces involved . Also ,instead of a material like linoleum being used underfoot a suitable gel like material might be used ,the consistency of which would allow the gel to distort or even tear , if a patient ,perhaps with sensory neuropthy , is applying stretching forces likely to case tissue damage .
      Gerrard Farrell


     
  2. scotfoot

    scotfoot Well-Known Member

    Further to the above post it would appear that a number of podiatrist now agree with my assessment .
    For those still not convinced here is a very brief video explaining how the metatarsal parabola is key to foot stiffness in later stance .
    Note that in the video the area arched by the elastic represents the tarsal transverse arch and the fingers the metatarsals of the foot .
     
  3. scotfoot

    scotfoot Well-Known Member

    Back in 2017 we had a thread on the transverse arch of the foot here on podiatry arena ( See below )in which I argued the existence of the arena effect

    With regard to Vankendesan et al and Yawar et al here is quote from one of my posts back then.

    "Its probably much easier to understand the above if you ignore all the stuff about fish fins . Its a red herring .
    Metatarsal parabola + terminal stance = distal transverse arch . Can't be any other way .


    Done ."

    I am greatly heartened to hear that what I call the arena effect ,and which I appear to have been the first to identify and describe , is now being taught by some in UK podiatry schools , all be it under another name.

    Also to Davidh . I was in no way trying to be rude in that old thread from 2017 and hopefully , if you still read posts on Podiatry arena , the video will illustrate what I was trying to explain .
    Old thread title from 2017
    Transverse arch stiffness and ankle and hip joint moments
     
  4. scotfoot

    scotfoot Well-Known Member

    Also mentioned in post # 1 from 2017 is the splaying apart of the metatarsal heads which occurs during unshod gait just as the heel lifts clear of the ground and the foot tends to externally rotate .

    Strong toe flexors are required to press the toes into the ground to resist external rotation of the foot .
    The torque produced puts strain on the transverse ligament which is assisted by the intrinsic muscles including the adductor hallucis .
    In later stance the "arena effect "begins to dominate, stiffening the foot prior to push off by generation of a more marked transverse arch through the geometry of the metatarsal parabola .
    Here is a very short , 6 sec ,video.

     
  5. scotfoot

    scotfoot Well-Known Member

    So how might you test the "arena effect "( exaggeration of transverse arch ) on foot stiffness .
    Why not take the rig of Welte et al 2018 and then introduce convexity / concavity , mediolaterally ,under the met heads . A concave surface under the met heads and the arena effect is reduced ,convex and it is increased .
    Dorsiflexing the toes with a flat surface under the met heads and you get some anteroposterior displacement of the met heads relative to each other increasing stiffness

    A concave surface under met heads reduces this relative displacement and convex increases displacement .
    Huge implications for shoe design , met fracture rate , diabetic feet etc . Very much worth investigating.
    Gerry
     
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