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Thought expt on distal to proximal effects of foot orthoses.

Discussion in 'Biomechanics, Sports and Foot orthoses' started by Simon Spooner, Jun 8, 2015.


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    This came about from a question I was asked in a private message.

    Imagine we place a set of weighing scales on the floor. We place a book on top of this; then we place another set of weighing scales on top of this; then another book on top of the second set of weighing scales. We continue adding layers of books and weighing scales until we have a stack of say 5 sets of scales and 5 books.

    Will all the weighing scales read the same?

    No. The weighing scale at the bottom of the stack will read the heighest and the weighing scale at the top will read the lowest, with decreasing readings as we move from the bottom of the stack to the top. This change is due to the decreasing mass of the books and weighing scales that are above each scale as we move up the stack- right?

    Now, let the books be the limb segments in the kinetic chain and let the weighing scales be force plates that we've introduced into the joints between the segments. In upright standing, the reaction force at the ankle should be higher than at the knee because the ankle has the additional mass of the shank segment acting upon it. Similarly, the reaction force at the knee should be higher than at the hip because the knee has the additional mass of the thigh segment acting upon it, and so on up the kinetic chain.

    Let us now introduce a foot orthosis that changes the magnitude of reaction forces at the foot-orthosis interface (for the sake of simplicity let the only component of the force vector altered by the foot orthosis be the magnitude), how will the segmental masses within the limb influence the kinetic effects (reaction force changes) from the foot orthosis as we move up the kinetic chain from distal to proximal?

    For simplicity, let the reaction forces without the orthosis be: at the hip = X, the knee 2X and the ankle 3X. Let the reduction in magnitude of the reaction force at the foot orthosis-interface be Y.

    Then, with the orthosis in-situ the ankle reaction force = 3X - Y... next...
     
  2. toomoon

    toomoon Well-Known Member

    But this will not be the case will it.. direction, velocity etc will be at least as important, so the equation is too simple.. burrp
     
  3. It's a simplified model Simon, designed to enable us to start to understand a complex system. We could argue that actually our orthosis is a flat sheet of material and as such the only change of interest is magnitude. Regardless, it's a model and I have stated that within this model the only change is magnitude. Any thoughts on the solution?

    Did you need me to pop you over my shoulder and pat your back to help you get that wind up?
     
  4. toomoon

    toomoon Well-Known Member

    Lentils mate.. never good..A solution you say..I certainly do not have one, and i am struggling to simplify this in my mind coz I cannot exclude things like muscle function, external stabilizers etc. The initial equation of the reaction forces at the ankle being 3x those of the hip might bear further scrutiny. If that were the case, I would suggest the most common site of degeneration at a joint level would be, in order, the ankle, the knee, and then the hip. In fact it is the knee, the hip, and then the ankle.. so there are other evil forces at play. But.. I am just a simple clinician.. wot would I know.. tooot
     
  5. Ian Drakard

    Ian Drakard Active Member

    ....2(X-Y), (X-Y)?
     
  6. That was my thought, Ian. But is it 3x -y, 2x -y , x-y, these would give different solutions ,could this be a factor for why foot orthoses might be progressively less effective as we move from distal to more proximal joints? Obviously magnitude is only one component of the reaction force vector, but interesting.
     
  7. toomoon

    toomoon Well-Known Member

    C'mon Spooner.. you know they work a treat for TMJ pain!!
     
  8. Well depending on which set of algebra is correct what this little model seems to suggest is that if the goal was to only reduce magnitude of joint reaction forces then the magnitude should be lowered progressively more as we move from distal to proximal by our foot orthosis here. So if this where the case, foot orthoses should be better at treating the hip than the ankle, I don't think this is the case... Or, foot orthoses should reduce magnitude by the same proportion of force as we move distal to proximal, I'm not sure this is the case either.
     
  9. Ian Drakard

    Ian Drakard Active Member

    Sorry. I'm wrong. It was bugging me all the way through last patient.

    I think it's Ankle = 3x -y, Knee= 2x - 2/3y, Hip= x -1/3y
     
  10. The implication of this being that the exact magnitude of the net GRF vector decreases as we move away from the point of application, distal to proximal through the limb.
     
  11. toomoon

    toomoon Well-Known Member

    I thought the same Ian. net reduction distal to proximal.. but.. obviously the reality is a lot more complex
     

  12. When we calculate joint moments, we should not be using the force recorded at the floor from a force plate, nor the same magnitude of force for our ankle, knee and hip calculations. Moreover, the more massive each joint segment, the greater reduction from segment to segment.

    However, when it comes to our foot orthosis the resultant change in the magnitude should be proportionally the same at all joints, i.e. if it reduces the magnitude by 10% at the ankle, it also reduces the magnitude by 10% at the knee and by 10% at the hip too.


    So, let's make the model slightly more sophisticated. Lets assume in our first model the GRF vector was orientated vertically, as was our limb. Now we introduce a different orthosis which results in the same point of application as our first orthosis, same change in magnitude, but with a line of action which is angled 5 degrees from the vertical. To take a joint moment we need to take the magnitude of the force vector at the point where it is perpendicular to the joint axis/ centre and multiply this by the perpendicular distance from the GRF vector to the joint axis/ centre. Basic trigonometry tells us that the further we move along the vector away from it's point of application then the bigger the moment arm when compared to our vertical GRF... quick back of the envelope sketch attached.
     

    Attached Files:

  13. efuller

    efuller MVP

    I'm still trying to figure out how an orthosis changes the magnitude of force at the foot orthotic interface. (Full length orthotic, static one legged stance) The force at the orthotic foot interface has to be exactly equal to the force of gravity acting on the body. If it wasn't, the body would be accelerating. So, ankle reaction force is = weight of body - weight of foot. Knee etc. Am I missing something in your question.

    Looking at joint reaction forces in gait is very interesting. Muscle contraction increases the joint reaction forces. Winter calculated the ankle joint reaction forces in a slow jog to be 11 times body weight. Winter also looked at something he called support moment. You need a certain amount of extensor activity to support the body. He found an inverse relationship to the amount of hip extensor versus knee extensor moments. Specifically, the more knee extension moment you have, the less hip extension you need. There was significant between day variation within individuals of the relative amount of hip moment versus knee moment. So, joint compressive forces will vary depending on which muscles are more active.

    Eric
     
  14. You seem to be missing that this is a thought experiement, Eric. In reality Einstein could not run along chasing a beam of light, but that didn't stop him employing this idea within a thought experiment in an attempt to work out fairly complex concepts.

    Would you be happier then if I said it was a quasi-static snapshot during gait, during which the GRF can be higher than body weight and a foot orthosis could reduce the magnitude of loading? It really doesn't make any difference here because that is not the point of this thought experiment thus far.

    Here are the points thus far:
    1) That the magnitude of the reaction force at the ground is not the same as the reaction force at the knee nor hip due to the influences of the segmental masses.- agree?

    2) Thus the use of the magnitude of reaction force at the ground to calculate knee and hip moments is erroneous. - agree?

    3) It should be possible to express an algebraic formula which represents the reduction in reaction force from distal to proximal when segmental masses are taken into consideration.- agree? What is the formula?

    4) Any change in magnitude of reaction forces which occurs due to foot orthosis use will not be the same at the ground as it will be when we move from distal to proximal through the limb and will similarly be expressed by the same algebraic formula as above. - agree? What is the formula?

    5) However, the percentage change in reaction force will be the same from distal to proximal- agree?

    And where we are just coming to:

    6) Angular change in the line of action of the net reaction force vector results in ever increasing changes in the lever arm of the joint moment as we move from distal to proximal. Agree?

    That's about as far as we are so far.
     
  15. Simon:

    I agree with Eric. The foot orthosis doesn't change the magnitude of ground reaction force (GRF) acting on the whole plantar foot, it only changes the magnitude of GRF acting at specific locations of the plantar foot. In other words, if the individual weighs 200 pounds, and during relaxed bipedal stance bears 100 pounds of GRF on each foot, the addition of orthoses will still mean that each foot bears 100 pounds of GRF.

    However, even though the orthosis can't change the magnitude of force acting on the whole plantar foot, the orthosis can change the center of pressure (CoP) acting on the plantar foot and can change the direction and plantar location of the resultant GRF vector acting on each foot during relaxed bipedal stance. However, again, since the segmental masses of the shank and thigh have not been changed by the addition of an orthosis to the plantar foot, the addition of an orthosis under the foot would again not change the total magnitude of joint reaction force at the ankle, knee or hip, but may indeed change the CoP of that reaction force within the joint surfaces within the ankle, knee and possibly even the hip.

    That's my two cents.:drinks
     
  16. I started this thread because when I was asked the original question about how ground reaction forces are dissipated as they pass up the limb, I realised it was not something I'd given any real thought, so I wrongly thought that others might not have either and would find it useful. Then I listened to the podcast that Griff participated in and I heard comments along the lines of "I don't think foot orthoses are that useful with more proximal problems"- so I thought it was worthy of further exploration in a thread here. Clearly, I was wrong to assume these things. I won't bother anyone again with such silly thoughts. Instead, you'll find me running after beams of light like Einstein, since the vast makority of comments thus far have told me how it is too simplistic and does not reflect reality etc. I suspect the point is being missed.

    Forget the relaxed standing bit, I was just trying to keep things really, really simple in a thought experiment that I thought might be useful. You don't think that cushioning in a running shoe alters the magnitude of the net ground reaction force vector during running as a function of time, Kevin? Does a foot orthosis alter the magnitude of the net GRF vector at time t during the stance period of walking gait? I could have talked about a quasi-static analysis during gait, but instead I tried to keep things really, really simple so that those following, who don't know what quasi-static analysis is, might understand it. This was obviously a mistake and I should have instead presented a full-blown dynamic model, rather than try to explore highly complex ideas by stripping them back to simplisitc thought experiments in which we can ignore accelerations.

    The reality is, the magnitude of the reaction force vector is not the same at ascending locations within the joints of the lower limb due to the influence of segmental masses. Taking moments using magnitudes at the floor are erroneous when we wish to calculate moments at the knee, hip etc. I was hoping we could increase complexity with discussion and eventually get onto the subject of wave propogation through different tissues, but I can see there is no point. Forget the simple thought experiment I posted, it's obviously not complex enough for those reading here.

    You're right about one thing though Kevin, the segmental masses haven't changed, which is why we see the same proportional change from proximal to distal in our static model (of course, in a dynamic situation the accelerations of the segments has changed- but that makes things overly complicated at the moment for my mind- hence I talked about a static situation, but lets go with quasi-static for now where, as you know, acceleration = 0). But that doesn't seem to support the hypothesis that foot orthoses should be less useful when treating more proximal problems. Neither does the increasing lever arm changes with change in the angular position of the line of action of the net GRF vector as we move from distal to proximal either. So, maybe foot orthoses should be most effective at treating more proximal joints, not less effective?
     
  17. Let me go back a post:

    I should be grateful if we could answer these points: (I'll add the qualifier: in a quasi-static situation)

    1) That the magnitude of the reaction force at the ground is not the same as the reaction force at the knee nor hip due to the influences of the segmental masses.- agree?

    2) Thus the use of the magnitude of reaction force at the ground to calculate knee and hip moments is erroneous. - agree?

    3) It should be possible to express an algebraic formula which represents the reduction in reaction force from distal to proximal when segmental masses are taken into consideration.- agree? What is the formula?

    4) Any change in magnitude of reaction forces which occurs due to foot orthosis use will not be the same at the ground as it will be when we move from distal to proximal through the limb and will similarly be expressed by the same algebraic formula as above. - agree? What is the formula?

    5) However, the percentage change in reaction force will be the same from distal to proximal- agree?

    6) Angular change in the line of action of the net reaction force vector results in ever increasing changes in the lever arm of the joint moment as we move from distal to proximal, the longer the limb segments the greater this effect. Agree?

    To these I will add:

    7) Since there is a reduction in the magnitude of the reaction force in the limb segments from distal to proximal, yet there is simultaneously an increase in the change in lever arm from distal to proximal when the reaction force is non-vertical, then when we introduce a foot orthosis which changes the angle of the line of action of the net reaction force and also decreases the magnitude of the net ground reaction force at that point in time, then there is a "balancing point" at which the angular change negates the magnitude change in terms of the resultant joint moment. I hope that makes sense.- agree?
     
  18. Very short on time now, Simon, getting ready for Manchester. However, on #2, the standard method of calculating moments at the ankle, STJ, knee and hip joints is by using the GRF vector which acts on the plantar foot. Why do you think this standardly method of calculating knee and hip moments is erroneous?
     
  19. Kevin, the reasoning for this was provided in the intitial part of this thought experiment, in the first post within the thread:


     
  20. I've tried to explain my thinking with some diagrams in the attached file. Hope it helps.
     

    Attached Files:

    • grf.pdf
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  21. Simon,

    The illustrations provided do help and I now understand what you are trying to get at.

    However, the external moment at the "+" joint would still be calculated by the GRF vector (i.s. its magnitude and perpendicular distance relative to the joint center) since the two segments below the "+" joint act as lever arms for GRF to modify the external joint moment and their masses are not part of the calculation of external joint moments. We don't need segmental masses to calculate external joint moments, we only need the magnitude, direction and line of action of the GRF vector and the axis of rotation of the joint to calculate external joint moments.

    Said another way, the external forces caused by GRF and the external joint moments that this GRF creates about the knee need to be counterbalanced by the internal forces and internal joint moments within the knee in order to maintain rotational equilibrium. The compression forces within the knee and internal joint moments within the knee will likely be affected by the relative mass of the segments above the knee, but this will still not necessarily always affect the GRF vector, its magnitude and its location within space relative to the knee joint.

    Hope this helps. By the way, this is a great thought experiment and I think it really helps delineate external from internal moments and how they are calculated. Thanks!:drinks
     
  22. I'm glad they help and thank you for your response.


    But their masses are part of the calculation for external joint moment since their masses influence the magnitude of the force registered at the force plate on the floor, F=ma. In the model F = (M1 + M2 + M3) X G , at the floor.

    What you are saying is that within the model the external moment (Mext) should be given by Mext = ((M1 + M2 + M3 x G) x d); What would the internal moment (Mint) be given by, given that the system is in equilibrium? We know that the internal moment must be Mint= ((M1 x G) x d)

    To be in equilibrium the internal and external moments must be equal and opposite so that ((M1 x G) x d) = ((M1 + M2 + M3 x G) x d). Since the force, M1 x G is smaller than the force, (M1 + M2 + M3) x G, the lever arm (d) for the internal moment has to be much larger to negate the increased magnitude of the force component of the external moment- right?
     
  23. efuller

    efuller MVP

    In a book he wrote, David Winter specifically warned against extending ground reaction force vector up through multiple joint segments. He used a thought experiment to explain why you could not use the ground reaction force vector to calculate the moments at the more superior joints. He had a person walking in a sagittal view and had a heel contact ground reaction force vector. The line of action was extended and there was a huge lever arm of the ground reaction force vector at the neck vertebra and we obviously don't feel a huge moment from ground reaction force at the neck. I'm trying to recall if this was only in a dynamic situation. The internal moments from muscles at the joints don't allow the lever arm of ground reaction force to be transmitted up the kinetic chain.

    Thinking statically about the diagram, there is a moment acting on the whole body. So, there must be some other forces present that counteract that moment or a rotation of the whole body would occur (assuming gravity acting on the center of mass of the uniform segment). So for the purposes of this discussion, we are missing some external forces.


    Eric
     
  24. Extending the ground reaction force vector from the foot to the knee is the standardly accepted method of determining external knee joint moments in all the papers I have read on knee joint moments that have been published by the International Biomechanics Community over the past two decades.

    I can see, however, the errors that may occur in extending the GRF vector from the plantar foot to determine external joint moments in any joint above the hip.
     
  25. As I said previously, popularity is not a good measure of validity.

    Why the hip?
     
  26. I'm all for popularity when the papers I have been mentioning are published in the Journal of Biomechanics and other respected biomechanics journals.

    Simon, do you know of any research papers published in the Journal of Biomechanics in the last decade that determine the external knee joint moments acting on the knee using your "segment mass subtraction" method that you described in your thought experiment?

    Here's a good article on knee joint forces for those still following along.


    http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3324308/
     
  27. I was aware of Winter's argument which Eric referred to because the guy that asked me the original question provided me with his data, unfortunately I seem to have deleted it, so I may need to request it from him again. Kevin, so all of those papers published within the journal of biomechanics that employed the long axis of the foot to equal the subtalar joint axis are valid? Does this mean this long axis approximation was correct? Like I said, popularity is not validity Kevin, as well you know. I thought you and I were agreed on pushing the boundaries here, not just accepting that which has been said before?

    Why the hip?
     
  28. efuller

    efuller MVP

    I agree with Simon. We should attempt to figure out whether David Winter was correct or whether the standard accepted method is correct. I believe David Winter's argument was that internal joint moments prevent the direct transference of forces up the kinetic chain. I can see if there is no acceleration of a joint then the line of action of ground reaction force could be applied more proximally. However, if there is a net ankle joint moment and ankle joint acceleration, the foot will be applying a moment to the leg and the leg will be applying a moment to the foot. The moment that foot applies to the leg will be creating a rotation, that will affect the knee, that one does not see when one is treating the lower leg as a rigid body. To use the ground reaction force vector to calculate the moment of ground reaction force at the knee, you would have to assume that foot and leg are a rigid body.

    Eric
     
  29. Simon:

    I believe using the GRF vector relative to the knee makes the most biomechanical sense when using inverse dynamics to determine external knee joint moments. Do you have any references which use the method you are proposing to determine knee joint moments, or was this just something you thought up for the thought experiment?

    I don't mind "pushing the boundaries" for something that seems to not make good biomechanical sense. However, using force plates, linked segment models, 3D video gait analysis and inverse dynamics to determine external knee joint moments during gait seems to make the most sense to me biomechanically. Do you have any specific reason why the above method, which is used in nearly all biomechanical studies of knee joint external moments, is not accurate? Do you have a better method by which to determine external knee joint moments?

    The hip seems to be a likely stopping place for using inverse dynamics from GRF to determine external moments since I imagine that the GRF vector working across any of the long bones of the lower extremity should be able to be used to model joint moments up to the hip well. Once the pelvic-vertebral, vertebral-vertebral joints are reached,however, the GRF vector is likely to be "less direct" or "more distorted" to be useful (I'm looking for the right words here but need to become more educated on this subject). Unfortunately, I am guessing here and would appreciate reading Winter's article on this subject if anyone has it available so I can bring myself up to speed on the latest thinking on this subject. Where's Bart Van Gheluwe when you need him?!

    I've answered your questions, Dr. Spooner now it's time for you to answer mine.:drinks
     
  30. Eric:

    I believe that quasi-static modelling is the solution to your questions. However, using the inertial properties of the limb segments should allow a good approximation of knee joint moments even during dynamic gait.

    The problem is that we will have a good idea of what the direction and magnitude of the internal knee joint moments are with inverse dynamics, but we will not know which anatomical structure(s) is causing these internal moments at the knee. I believe inverse dynamics gives us a good approximation of the external knee joint moments during dynamic activities, and, from what I know, seems better than any other method we have available for dynamic gait.

    Eric, do you know of any more accurate method of determining external knee joint moments during gait other than inverse dynamics, GRF vectors from force plates and 3D motion analysis?
     
  31. Kevin, I honestly had never given this any thought prior to being asked the question, at which time I designed the thought experiment with the weighing sscales and books.

    However, others have obviously considered the problem of projecting the GRF vector and ignoring segmental masses before me, see:
    http://www.rehab.research.va.gov/jour/81/18/1/pdf/wells.pdf

    "It has been noted that projecting the line of action of the ground reaction force to obtain a measure of joint moment is an approximate measure because it neglects the weight and inertia force contributions of the limbs between the ground and the joint under consideration. From above it would be expected that the joint moment estimates would become poorer as the inertia forces increase (higher accelerations associated with velocity/ cadence) and as the forces due to segment weight between the ground and the joint increase (estimating at the knee and, worse at the hip)."
     
  32. Simon,

    I never had given this much consideration either so I am glad you introduced this thought experiment to force me to consider the mechanics of estimating internal and external forces and moments at the knee. It has been good for me to consider your points but I am not yet certain of how the thought experiment can best be answered.

    On another note, Pam and I are flying out of Sacramento early this afternoon, heading to Heathrow for a short vacation in London before Biomechanics Summer School in Manchester later next week. Since I still need to do some polishing up on my lectures during that time and since I will also be occupied with enjoying the sights and sounds of London (last time we vacationed in London was 2007), my time will be somewhat limited. But, I will give it some thought over the next week as time allows.

    All in all, it's a good discussion and I believe we will all learn something from it. Thanks!:drinks
     
  33. Found these lecture notes from Brigham Young University, not sure of the author.

    "Projection of the GRF Vector
    Can joint moments during gait be calculated by simply multiplying the resultant GRF vector times the perpendicular distance to each of the relevant joint center?
    No!
    This approach has been used, primarily in the clinical arena, but is inappropriate for many reasons (see Winter 1990 reading)"

    http://biomech.byu.edu/Portals/83/docs/exsc663/part04/663_inversedynamics.pdf
     
  34. Just picked up a copy of Winter's book: Biomechanics and motor control of human movement from Amazon @ £3. Happy days- I'll let you know his rationale for why projection of the GRF vector is not valid once it arrives, although I suspect that it will be a similar argument to that which I described in the thought experiment here. Kevin's argument of internal versus eternal moment notwithstanding. Hint: calculate the internal moment first, rather than the external moment first.
     
  35. David Winter's editorial here is confusing to me.

    Someone please explain this statement from Winter's editorial???

    Since when do ground reaction forces not contribute to the net moments acting across the ankle or knee joint?!
     
  36. efuller

    efuller MVP

    That letter to the editor did raise an interesting point. Winter said that reactive forces are the result of gravity and muscular action. Muscular action is obvious when you stand on a bathroom scale and flex and extend your knees. Knee extension will increase ground reaction force and cause the body to accelerate upward. Winter also said that the reaction forces don't cause a moment, but are the result of a moment. The author's response letter quoted Winter back to himself. "At heel contact, the ground reaction force vector is posterior to the ankle joint and would tend to cause foot slap unless the anterior tibial muscle were not active" (apologies for imperfect quote. it was done from memory. I think the gist is representative of what he said.)

    What I think this makes us do is think about the sources of joint moment. At heel contact the floor reactive force vector (that is reactive to gravity) will still cause an ankle plantar flexion moment. As the anterior tibial muscle contracts, it would tend to shift the center of pressure under the foot posteriorly. The ankle plantarflexes, so we know that the moment, at the ankle, from floor reactive forces (from gravity) will create a larger plantar flexion moment than the dorsiflexion moment from the anterior tibial muscle. So, if we know the ground reaction force vector and the location of the ankle joint axis, the calculated moment would be larger than just the contribution of ground reaction force alone.

    Where this affects us clinically is when we look at center of pressure paths relative to where the STJ axis is. If we see a far lateral center of pressure path, and we are not looking at all the inverse dynamics, then we don't know if that high pronation moment from the ground is just from reaction to gravity or reaction to supination moment from the posterior tibial muscle. (Looking at Kevin's rotational equilibrium paper one can easily see how the posterior tibial muscle can create a "reactive" pronation moment from the ground.

    My take from the discussion is that Winter was right, you should not look at ground reaction force vector alone because its location could be altered by muscular contraction.

    What say you?

    Eric
     
  37. My take from the discussion is that Winter was wrong. Net moments do include the ground reaction force vector. Winter said the GRF vector wasn't a part of the net moments!
     
  38. Internal forces are generated by "active tissues", i.e. muscles. By definition, the "reaction forces" are simply the grounds reactions to the forces being applied to it, the forces being applied to the ground are due to the segmental masses x intrinsic (muscle generated) + gravitational accelerations. F=ma. The ground just applies an equal and opposite force. Newton's third, Cauchy and Hooke.
     
  39. So, in Eric's paper on position of the center of pressure relative to the STJ axis, according to Winter, we can ignore the GRF which is causing external pronation or supination moments at the STJ axis?
     
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