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Thought Experiment #8: Multiple Joint Moments from CoP

Discussion in 'Biomechanics, Sports and Foot orthoses' started by Kevin Kirby, Dec 5, 2007.

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    Thought Experiment 8

    In the continuing series of Thought Experiments (Gedankenexperiment), we will be considering the mechanical effects that a single isolated force acting on the plantar foot may have on the multiple joints of the foot and ankle.

    In the illustration below, a single isolated force, Force A, is shown to be acting on the plantar aspect of the second metatarsal head. As a result of Force A, there will multiple moments acting across the joint axes of the foot and lower extremity. In this case, how does the foot respond to Force A? Assume the Achilles tendon is exerting a passive tensile force on the posterior calcaneus in response to Force A.

    1) What is the direction of external moment at the subtalar joint (STJ) from Force A?

    2) What is the net moment acting across the STJ? (Consider the effects from Achilles tendon also.)

    3) What is the direction of external moment at the 2nd metatarsal-2nd cuneiform joint from Force A?

    4) What is the direction of external moment at the 2nd cuneiform-navicular joint from Force A?

    5) What is the direction of external moment at the talo-navicular joint from Force A?

    6) What is the direction of external moment at the ankle joint from Force A?

    7) Do these moments occur simultaneously or does the force "flow" from one joint to the other (i.e. one joint first experiencing its moment, then the next joint, then the next, in response to Force A)?

    8) If these multiple moments are occurring, and the foot is in relaxed bipedal stance, what do we know regarding the direction and magnitude of the moments occurring within the foot (i.e. internal moments) that keep the joints of the foot stable, and at rest in the standing position? In other words, what are the direction and magnitude of the internal moments at these joints during relaxed bipedal stance?
    Last edited: Dec 5, 2007
  2. Admin2

    Admin2 Administrator Staff Member

  3. Dean Hartley

    Dean Hartley Active Member

    Kevin I thought I would have a go at these. Be gentle, I only finished my degree 2 weeks ago! The middle questions have me slightly confused, but have attempted them.

    Q1) Force A would result in a pronation moment at the STJ

    Q2) The net moment occurring would depend on the antagonistic pull here of the achilles tendon. If this was occurring in late midstance when the tendo-achilles (TA) is contracting I would suspect the net moment would be a supination moment as the TA would be likely to be overriding the force through the forefoot. If force A is greater then the pull of the TA, then a pronation moment would occur. If both forces were equal, equilibrium would result.

    Q3) A dorsiflexion moment would occur at the 2nd met-2nd cuneiform joint from force A

    For Q4 & Q5 I am not completely sure. I will have a go and say it results in a plantarflexion moment at the 2nd cuneiform-navicular joint. Dorsiflexion and possible adduction moment of the talonavicular joint.

    Q6) Force A will cause a dorsiflexion (with some abduction) moment at the ankle joint.

    Q7) I would believe these moments to occur one after another (but very closely followed) as the distal force would act like a chain reaction to the more proximal joints as the force is applied.

    Q8) The internal moments of the foot will antagonise the external moments of the foot to obtain equilibrium and this results in static bipedal standing.
    Again not completely sure, but those are some of my thoughts on paper.

  4. DaVinci

    DaVinci Well-Known Member

    Where else in the world can a new graduate intertact like this with some of the best brains in the Podiatry world?
  5. Dean Hartley

    Dean Hartley Active Member

    Been thinking of that lately, its really quite amazing how podiatry arena works. Ill just try to not make a fool of myself!
  6. Very impressive, Dean. You must possess good confidence in your ability to attempt to publicly answer these questions at such an early stage in your career. Hopefully your professors didn't find you as annoying as mine did. :rolleyes:

    Correct. Since Force A is lateral to the STJ axis, it will cause a STJ pronation moment.

    Not quite right. The Achilles tendon force is critical here. Here are a few more questions for you, Dean: A) Assume that Force A = 300 N, that the ankle joint is in rotational equilibrium, that Force A is 14.0 cm anterior to the ankle joint axis and that Achilles tendon is 7.0 cm posterior to the ankle joint axis. What would be the tensile force within the Achilles tendon, assuming no other muscle forces are present?


    Not right. How could a dorsiflexion force on the 2nd metatarsal and 2nd cuneiform cause a plantarflexion moment at the 2nd cuneiform-navicular joint? Why would an adduction moment occur at the talonavicular joint?

    Force A will cause a ankle joint dorsiflexion moment but could cause an abduction moment of the ankle joint only if the Force A was also directed laterally.

    Not quite right. What is Sir Isaac Newton's Third Law of Motion? Could this famous 17th and 18th century scientist's Laws of Motion be used to understand whether forces occur simultaneously or in rapid sequence or possibly flow from one bone to the other? In other words, can a force exist in the distal segment without as large of a force in the proximal segment?

    That is correct. If the external force, Force A, caused 30 Newton-meter (Nm) of dorsiflexion moment across the talo-navicular joint, and it was seen that the foot was standing still, with no movement across the talo-navicular joint, then what would be the direction and magnitude of the net internal moment acting across the talo-navicular joint?

    By the way, Dean, instead of using the word "antagonize", I would use the word "counterbalance" to describe the actions of opposing moments to attain rotational equilibrium.

    Good job.......so far.
  7. Dean Hartley

    Dean Hartley Active Member


    Tensile force in the Achilles tendon would be 600N....?

    Not exactly sure what I was thinking here, was going to say simply dorsiflexion moment for these joints, then I think I confused myself.

    I said abducted here due to the angle of the ankle joint axis (around 20degrees from the frontal plane?) not being perpendicular to the central bisection of the foot. I just thought it wouldn't be purely dorsiflexion.

    Would the moments occur simultaneously but the force would be of different magnitudes?

    30 Nm of plantarflexion moment would be occurring simultaneously by internal moments to result in equilibrium at the talo-navicular joint.

    I hope I am on the right track. I didn't do physics in high school, although did a higher level of maths, so I hope some of my mathematical reasoning is correct.

  8. Dean:

    All your responses are correct. There needs to be an abuction force on the foot in order to have an abduction moment at the ankle joint. Excellent work!!
  9. But how is force transmitted at an atomic level? :p;)
  10. Simon:

    A little bit out of my area of expertise, but it is my understanding that when one object contacts another object, the atoms of each respective object never touch the other, but rather are repelled from each other by molecular forces and by their "electron clouds".
  11. So is force passed atom by atom?
  12. Good question, Simon. What do you think?
  13. I think that at this atomic level if repulsion between atoms exists, as you have suggested, then there is likely to be a knock on effect from atom to atom. This might be seen as force "flowing" from atom to atom and therefore passing through a body over a finite time period. However, at the level in which we are dealing in clinical biomechanics, it is acceptable to think of forces acting instantaneously across such a body since the time periods involved are likely to be very, very small. But I could be wrong. I could blame George Lucas for my obsession with "The force". Since at the age of 7 I was rather impressionable and I have spent the rest of my life trying to control objects by waving my hands at them. I also make weird light sabre noises at inappropriate times. You may have noticed this occasionally.

    What do you think?

    BTW I seem to remember reading that a Gecko was able to hang on to vertical sheets of glass, because the atoms of it's feet merged with those of the glass??????? Not quite but Van da Vaals forces attracting the atoms together.
    Last edited: Dec 5, 2007
  14. Dean:

    You aren't off the hook quite yet. Now, if the force plantar to the second metatarsal head in the illustration from my initial posting was moved to being directly plantar to the subtalar joint (STJ) axis, considering also the effects from Achilles tendon tension, would the STJ supinate, pronate or be stable in rotational equilbrium?
  15. Dean Hartley

    Dean Hartley Active Member

    In the first illustration the Achilles tendon you said was applying a passive tensile force, from my understanding this was to 'counterbalance' the effects of force A and to keep the STJ in rotational equilibrium. Therefore I would believe if force A moved directly plantar to the STJ axis (the moment arm of force A would be reduced to 0), resulting in the inability of force A to produce any moment upon the STJ, resulting in the Achilles tendon overpowering Force A (as it would be unopposed) and causing a net supination moment at the STJ.

    However if the Achilles tendon was simply creating a passive tensile force to the calcaneus originally to obtain rotational equilibrium, then this external force of the Achilles tendon may also be reduced along with force A to enable equilibrium at the STJ.

    I hope you could understand that Kevin.

    Last edited: Dec 6, 2007
  16. Dean:

    Your answer above is perfect. Therefore, if Force A was directly plantar to the STJ axis, and the Achilles tendon was placed under tensile force because of Force A in my illustration, then a net STJ supination moment would occur, tending to cause STJ supination. This occurs because tensile force within the Achilles tendon causes a STJ supination moment in this foot. Lesson? You cannot just look at the center of pressure relative to the STJ axis to determine net STJ moments.

    Next question:

    If the STJ axis in my illustration was laterally deviated, so that the STJ axis passed between the 2nd and 3rd metatarsal heads, would the foot tend to pronate, supinate or be stable? Why?
  17. Dean Hartley

    Dean Hartley Active Member

    Kevin, if the STJ axis was to be laterally deviated in this foot, passing through the 2nd and 3rd metatarsals heads, force A would be medial to the STJ axis causing a supination moment. This coupled with the tensile force of the Achilles tendon (if the Achilles tendon is still applying force to the posterior aspect of the calcaneus) could result in the foot being quite laterally unstable. No pronation moment will be present if these were the two sole external forces. For the foot to be stable in this case, pronation moment would need to be applied lateral to the STJ axis, if this was in a real foot I would suspect the peroneals to be working very hard to maintain rotational equilibirium, but the dreaded lateral ankle sprain may be a common occurrence!

  18. Dean:

    Excellent! Another perfect answer. I am impressed.

    Here's another question:

    If Force A in the illustration is non-vertical, and directed superior-medially, will this change in angle of the vector of Force A cause increased STJ supination moment, increased STJ pronation moment or cause STJ rotational stability? Also, will the inclination angle of the STJ axis have any affect on this?
  19. Dean Hartley

    Dean Hartley Active Member

    Kevin, getting a little bit more complicated, but think I have my head around it. I hope.

    If Force A was directed superior-medially I would believe this would result in less pronation moment at the STJ axis, leading to an overall increase in STJ supination moment occurring. I say this because isn't force the greatest when it is applied perpendicular to the point of rotation. The angle of the force vector as you now suggested would decrease the ability of this external moment to create a pronation moment at the STJ axis, and the amount of force would need to be increased to obtain rotational equilibrium here.

    The inclination angle of the STJ axis would play an affect. If the angle is increased a greater moment arm would be present for Force A, increasing the amount of pronation moment. And vice versa if the inclination angle was decreased. Furthermore I believe if the inclination angle changed it would also change the direction of motion occuring at the STJ. For example if the inclination angle increased, more transverse plane motion would occur with a decrease in the frontal plane motion.


  20. Good show again, Dean. The more medial direction of Force A would cause Force A to either have less magnitude of STJ pronation moment or would cause Force A to now cause a STJ supination moment, since the line of action of the vector of Force A would lie medial to the STJ axis, which is positioned approximately 10-20 cm superior from the ground at the level of the 2nd metatarsal head. A lower inclination angle of the STJ axis would tend to cause this medially directed Force A to have less of a STJ supination effect than would a higher inclination angle of the STJ axis since the medial-lateral shear force (from a more medially directed Force A) will cause more of a rotational effect on a joint axis which is oriented vertically (i.e. at the intersections of the sagittal and frontal planes) than horizontally (i.e. at the intersections of the transverse and sagittal planes).

    Attached is a paper that I did with Bart Van Gheluwe and Friso Hagman (two biomechanics researchers from Belgium) that uses this concept to determine the mechanical effects of simulated genu valgum on the foot (Van Gheluwe B, Kirby KA, Hagman F: Effects of simulated genu valgum and genu varum on ground reaction forces and subtalar joint function during gait. JAPMA, 95:531-541, 2005).

    Next questions for you:

    How would one orient the line of action and vector of Force A on the second metatarsal head so that it would have the maximum potential to cause a STJ pronation moment?

    How would one orient the line of action and vector of Force A on the second metatarsal head so that it would have the maximum potential to cause a pure compression force at the subtalar joint?
    Last edited: Dec 7, 2007
  21. Dean Hartley

    Dean Hartley Active Member

    I am assuming Kevin you are talking about Force A being directed superior-medially again, as in the first diagram the Force A would be at its greatest mechanical advantage being located perpendicular to the axis of rotation. In this instance I would assume the only way to increase the pronation moment of Force A would be to either increase the force applied or increase the moment arm of Force A by artificially creating a larger area between the foot and the point of contact of the force vector on the foot or shoe.

    However if you are talking about the force vector being superior-medially directed, then to increase the pronation moment, this vector would need to manipulated so it would be applied closer to perpendicular to the axis of rotation. In this instance conservatively you could use a forefoot valgus pad or full length valgus pad (such as those used for lateral knee OA). This type of padding would not only aid in orienting the force vector more perpendicular to the axis of rotation but also increase its moment arm, resulting in an increase net pronation moment. (A diagram would help here to show you what exactly I mean, although Iam not great at putting my mind on paper with a drawing).

    My understanding of the pure compression force of the subtalar joint axis you mean a force which is neither pronating or supinating the STJ. Therefore to obtain this in this situation increased supination moment would need to occur. This could be done by something similar as previously stated but the opposite of; a forefoot varus pad (which I wouldn't think would be ideal in aiding propulsion). This would reduce the affects of the force vector from Force A at causing a pronation moment, resulting in increased supination moment (from the Achilles tendon and shifting the GRF more medially), ideally to the state of compression on the STJ axis, so there is no over-riding supination or pronation moment occurring.

    I hope you can decipher that. A diagram would of really helped, but I'm not computer friendly when it comes to them.

    Last edited: Dec 7, 2007
  22. Excellent again, Dean. In order for a force to have maximum rotational effect on the STJ then the force needs to have a line of action which is exactly perpendicular, or at a right angle, to the STJ axis. In order for a force to have maximum compression effect on the STJ, then it needs to have a line of action which is pointed directly toward the STJ axis.

    Final questions:

    When an amputation of the distal half of the 5th metatarsal occurs, would one expect there to be an increase in STJ pronation moments, an increase in STJ supination moments or no change in STJ moments during weightbearing activities?


    What might happen to a foot clinically over time that has such an operation?
  23. Dean Hartley

    Dean Hartley Active Member


    The amputation of the distal half of the 5th MPJ would reduce STJ pronation moments during weightbearing activities. This is because ground reaction force lateral to the STJ axis causing a pronation moment would be decreased significantly. Leading to STJ supination moments being unopposed.

    I would believe several things could happen to this foot over time. As a result of the overwhelming STJ supination moments, chronic peroneal overuse would occur. Lateral ankle sprains would be a problem. This could also lead to a plantarflexed 1st ray due to the increased tension of the peroneus longus and to promote ground contact of the medial forefoot. The peri-amputation area would be a high pressure area as the ground reaction force would be applied to a lesser area, possible resulting in hyperkeratotic disorders etc. The centre of pressure line would also be disrupted, I'm gathering it would be delayed in going medially in the forefoot due to loss of the effect of ground reaction force on the lateral forefoot (???).

    I guess the list could be endless, depending on foot type and other biomechanical factors??.


  24. Dean:

    Again, your are right on. The removal of the distal half of the second metatarsal would lessen the contribution of this segment of bone to the STJ pronation moments acting on the foot so that, all other factors being equal, reduced magnitudes of STJ pronation moment and a more supinated foot would tend to result. The likely scenario of this net gain in STJ supination moment from 5th metatarsal partial amputation would be the following:

    1. A shift in the center of pressure to a more lateral position on the plantar foot.

    2. A significant increase in ground reaction force on the 4th metatarsal head (may lead to hyperkeratotic lesion/ulcer at 4th metatarsal head).

    3. An increase in supination instability of the foot (may lead to increased tendency toward inversion ankle sprains).

    4. Increased contractile force in the peroneal muscles during weightbearing activities (may lead to peroneal tendinopathy).

    5. Increased external dorsiflexion moments at the calcaneo-cuboid and 4th metatarsal-cuboid joints (may lead to lateral dorsal midfoot interosseous compression syndrome).

    You only finished your degree a few weeks ago, Dean?? I just wish I had a classroom full of students like you over the past 22+ years that I have been teaching these same subjects both here in the States and internationally. I guess I'm going to have to come up with some harder questions for you next time!
  25. Dean Hartley

    Dean Hartley Active Member

    Thanks for spending time with me Kevin, thoroughly enjoyed it. My knowledge in this area is a result of Podiatry Arena and your Precision Intricast texts. Maybe you could sign them if I see you at a conference one time down under!! haha:p. Seriously though, great texts, very useful, I recommend them to colleauges all the time.

    Again thankyou for the time spent. Look forward to further discussions.

  26. Dean:

    When you get around to wanting to do something useful with your superior knowledge in biomechanics, you should consider writing a paper for publication in one of the podiatry journals. I am serious....no joke.

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