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Windlass mechanism kinetics and 1st met compression

Discussion in 'Biomechanics, Sports and Foot orthoses' started by Robertisaacs, Apr 4, 2010.

  1. Members do not see these Ads. Sign Up.
    This one has been floating around in the back of my head for a few weeks. I can't make it jump any higher, perhaps someone better at physics than me can help. Eric's thread gave me a prod.

    Lets consider the 1st MPJ as a simple hinge joint, leaving aside (for starters) any irregularities in joint surface.

    Internal PF moments from the PF (loads) and the flexor hallucis muscles (less).

    External DF moments from the GRF in the digit. In spades again.

    What is the relationship / equation for compressive force in the joint itself (X-)

    I will stress that I take to physics like a duck to archery, thats why I'm struggling. I just don't have the physics.

    This would appear to be one of those where we have to convert rotational force into translational

    I started with, If there is equilibrium then IPF / lever arm + EDF / lever arm yields the total translational force X-. But that did'nt seem right because (in this model) without any IPF, EDF will exert no X- force that I could see. But then of course the system would not be in Rotational equilibrium.

    Also to make this model anything approximating to clinically useful (or even mildly interesting) I guess we would need to know the lever arm information (where grf is exerted and where tendons insert). Got myself well confused there as well.

    Any chance anyone can give me a nudge? I've got a nasty case of mathematicians block.

  2. Robert:

    First of all, why don't you explain all of these abbreviations you used in your post above so that everyone understands what you mean:

    PF (plantarflexion and plantar fascia??)

    Since I don't know what you mean, then this means that probably more than 50% of everyone trying to read your post here on Podiatry Arena also doesn't know what you mean when you use abbreviations without first spelling them out.

    Maybe you should ask the mystic Guru Bob what these abbreviations mean??:confused::cool:
  3. Guru bob is better at cosmic wisdom. This is a bit prosaic for him.

    I was meaning

    df - dorsiflexion
    pf - plantarflexion ( and yes I did slip and use it for plantar fascia as well)
    grf - ground reaction force
    mpj -. Oh c'mon, that one is pretty standard.
    Ipf - internal plantarflexion moment
    edf - external dorsiflexion moment

    X- - force in a "backward" direction, viz how hard the prox phalanx is pushing on the metatarsal head.

    Sorry, I get acronym happy sometimes.
  4. Now I think though it's got to be more complex still because the size of the "drum" about which the windlass winds will also affect things won't it.
  5. In which case the dorsiflexion moment and range at the base of the 1st met will also be significant.
  6. efuller

    efuller MVP

    The use of center of pressure is very helpful in determining lever arms. First off don't consider the joint as a hinge. You have to analyze the joint surfaces. Once you find the center of pressure on the joint surface you can figure out where the force from one bone can be considered to act on the other bone. (As an aside, this is the assumption that is made when you calculate moments about joints using joint axes. The assumption is made that the center of pressure at joint the joint surface is where the axis is.) If you actually wanted to measure this there are pressure sensitive films that could be placed in a cadaver joint and then the pressure digitized and the center of pressure calculated.

    Now you have to do the free body diagram. Easiest done in static stance. You have tension in the fascia and compression at the joint surface acting on the base of the proximal phalanx. This is creating a plantar flexion moment. Ground reaction force on the hallux will be considered to act at the center of pressure under the hallux. Hmmmm. I'll have to think about this one for a while. The upward force from the ground will have to a measurement from its line of action to some point. I'm not quite sure what that point would be. It could be the joint line, it could be the axis of rotation of the joint. In practice the difference between those two may not be that great. Once you choose that distance you can make the calculations. Joint compressive force = tendon force (e.g. FHL tendon) + tension from the sesamoids.

    In equilibrium the plantar flexion moment on the hallux is equal to the dorsiflexion moment, acting on the hallux, from the ground. Dorsiflexion moment from the ground = magnitude of force from ground (GRF hallux) x distance from center of pressure to joint axis (d ground). Plantar flexion moment = joint compression force (Jnt Force) x distance from center of pressure of joint surface to middle of sesamoids (Jnt distance).

    (GRF hallux) x (d ground) = (Jnt F) (Jnt Dist)

    Algebra to get

    (GRF hallux) x (d ground) / (Jnt Dist) =(Jnt F)

    You can estimate error for the assumptions of the distances by plugging in the high and low possible estimates.

    I hope this helps,

  7. Robert:

    I've taken the liberty of adding in the meanings of your many abbreviations above so that more people can follow along.

    As Eric stated, the best way to approach this problem is by drawing a diagram of what you are looking for and go from there. To determine the compression force within the 1st metatarsophalangeal joint (MPJ), we must first determine what the known forces and dimensions of the model are? We have very many unknowns here to try and determine the compression force within the 1st MPJ since we can't determine the tensile forces within the plantar fascia, flexor hallucis longus, flexor hallucis brevis, abductor hallucis, adductor hallucis or flexor hallucis brevis. All of these structures may directly add to the compression force within the 1st MPJ during weightbearing activities since all of these structures will tend to pull on the proximal phalanx or distal phalanx of the hallux toward the first metatarsal head.

    However, by measuring the ground reaction force (GRF) plantar to the hallux and assuming that all of these tension forces acting across the 1st MPJ will also create an internal 1st MPJ plantarflexion moment, then one may be able to approximate the 1st MPJ compression force from measuring the plantarflexion moment arms for each of these muscles/fascia to the proximal phalanx and distal phalanx and comparing it to the center of the first MPJ for determining compression force. There was a nice paper done on type of modelling, in addition to Eric's fine paper, from a few years ago but I don't have time now to track it down since my first patient just showed up.
  8. HansMassage

    HansMassage Active Member

    Could be a valuable calculation. In my past experience an engineer turned chiropractor was able to establish a formula that every degree of lost cervical lordosis increased the cervical rotation force requirements 2.5%. Because the insurance adjusters love statistical models of loss and improvement it helped us get paid to track it on progress reports.

    Hans Albert Quistorff, LMP
    Antalgic Posture Pain Specialist

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