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Double support phase and leg stiffness

Discussion in 'Biomechanics, Sports and Foot orthoses' started by Simon Spooner, May 17, 2010.


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    All,
    Recognising that walking gait can be modelled as two springs in parallel, I wanted to explore the consequences of the timing of heel lift.

    If we accept that each limb can be modelled as a spring during walking, then the spring stiffness (k) of each limb would appear important. Dananberg talks about delayed heel lift as being a potential compensation for functional hallux limitus; so if the leg spring compresses and decompresses (rebounds) throughout each contact phase, then a delayed heel lift suggests a decrease in spring stiffness- right?- longer period- right? So lets say we have a left leg with delayed heel lift, this spring is not "decompressing" i.e. extending, until after the right foot strikes the ground and is foot flat, i.e. the right leg is compressing, while the left leg decompression is delayed- right? Since in the case of delayed heel lift, the left limbs decompression is delayed, if we model the frontal plane lower limbs as a double spring mass model (see picture), then the delayed decompression of the left leg spring should drive the right leg spring into the ground at a higher rate as the pelvis pivots about the spinal column?? However, n=1 experiment suggests that by delaying heel lift of the left leg this results in a decrease in the rate of loading (compression) of the right leg spring- right? i.e. we should see greater navicular drop in the right leg in this situation. Unless, of course, the left or right limbs compensate for this delayed upward driving force by reducing stiffness through increased knee flexion, viz. decreased leg stiffness... Indeed ,by delaying the offloading of the left leg the force applied to the right leg spring is reduced, therefore given a linear spring, it's compression is reduced. Think I've got it now, you ready for that paper Kirby?
     

    Attached Files:

  2. ie the knee will flex more( reduced ankle joint planatrflexion) due to the FnHL as a compensation mechanism in doing so the leg stiffness further decreases ?
     
  3. Put another way, if the knee flexes more, then we get a decrease in ankle dorsiflexion stiffness, i.e. the tibia can extend further over the planted foot before the heel is pulled off the floor by the achilles, i.e delayed heel lift. I was speaking more about the effects on the contra-lateral limb. However, if the leg stiffness of the contact limb decreases due to functional hallux limitus then the upward drive of that leg spring and its influence on the contra-lateral limb could be decreased and hence it's frequency might be decreased.
     
  4. Sorry, Simon. Don't know if I'll be able to help you now since I've completely transitioned over to Functional Foot Typing so I won't have to use physics any more in trying to understand how the human foot and lower extremity function during gait. It is quite a blissful experience......................if you know what I mean.:rolleyes::cool::drinks
     
  5. efuller

    efuller MVP

    Hi Simon,

    Just because it can be modeled as a spring, does not mean that it will always behave as a spring. I've always liked Winter's joint power analysis. I should go back and re read his papers. But, one of the points that really sticks out in my mind is that there is there can be more than one source of power and it can vary from day to day. But, we still can have some fun with spring models.


    decompressing = sproinging? = returning energy. This is where I have a problem with the spring model. We have to figure what part of the anatomy is providing the energy, or in the case of delayed heel lift, not supplying energy.

    As for the right leg compressing we can look at what is causing the compressing of the spring, or we can look at what anatomy is being compressed.

    In thinking about what is causing the compressing, isn't just loading the right leg going to compress it. It doesn't really need the push from the trailing (left) leg to compress it.

    In thinking about what anatomy is "compressed" at heel contact, you will see knee flexion, however the ankle is plantar flexing at heel contact and will not get compressed until the stance leg is pivoting at the ankle over the fully loaded foot. So, the "ankle spring" is basically loaded by the momentum of the body.


    That's a very good explanation of the sagittal plane model. Now, if the body only behaved as a spring. Another explanation of the n = 1 study you have is that when there is delayed heel lift, there is ankle joint power to propel the swing leg forward and the trunk has to lose energy to pull the swing leg forward.

    If I'm recalling the Winter papers correctly, in steady gait, most of the energy is going into moving the legs and the energy of the body doesn't change much. (There is a trade off between potential and kinetic energy as the body rises up over the stance leg and then falls forward to the next foot plant.

    It would be interesting to compare the spring model energetics tho those observed by Winter.

    Regards,

    Eric
     
  6. Simon:

    I liked Eric's response on Winter's ideas on power generation. Winter's analysis makes more sense to me than using springs to model the legs in walking.

    However, I do believe that spring models can be used to effectively explain foot function in functional hallux limitus (FnHL). I would use a foot model that had a more compliant medial longitudinal arch (MLA) which created a more stiff 1st metatarso-phalangeal joint (MPJ) for FnHL. One could also use a more stiff MLA and a more compliant 1st MPJ for a foot that had normal 1st MPJ dorsiflexion.

    In the foot with FnHL modeled in such a fashion, the more compliant spring at the MLA would delay heel off due to the increased magnitude of forefoot dorsiflexion and the corresponding prolonged duration of forefoot dorsiflexion on the rearfoot during late midstance. This, in turn, would cause an increase in 1st MPJ stiffness which would further delay heel off and cause increased hallux plantar load for a given amount of hallux dorsiflexion.

    Once we get to propulsion strategies, I like Winter's papers on ankle push-off versus hip pull. I don't see how a spring model could explain this dynamic, central nervous system-mediated phenomenon better.
     
  7. I´ve not read Winters stuff

    anyone got a full copy of this ?

    but found these 2
     
  8. Griff

    Griff Moderator

    Here you go Mike

    IG
     

    Attached Files:

  9. See figure 3 of the attached paper.
     

    Attached Files:

  10. The paper attached provides an interesting analysis of pushing and pulling.

    They state that: "The energetic advantages of a toe-off impulse are
    likely to be realized in the human only if toe-off occurs slightly
    ahead of, and potentially overlapping with, heel strike. Therefore,
    it is quite possible that one foot performs positive external work
    and the other negative work during double support "

    This would fit with the double spring mass model; one spring extending while the other is compressing: one spring doing negative work and the other doing positive work
     

    Attached Files:

  11. Moreover, the longer the duration of double limb support the greater the potential for one limb to be doing positive work and the other to be doing negative work on the centre of mass. So the question arises, does a delayed heel lift result in a longer period of double limb support? What factors may influence the duration of double support?

    Here is what Geyer said in his PhD about double support:
    "the COM dynamics during walking may well be described
    by purely elastic leg operation with the double support phase having an essential
    contribution. In fact, considering a complete stance phase of one spring leg of the
    spring-mass walking model, the effective load (mass) on this spring only gradually
    increases after touch-down as the opposite spring still is partially supporting the
    COM. Due to sufficient stiffness, the spring quickly reaches its peak compression
    leading to a corresponding initial force peak in the vertical GRF. In contrast to
    running, the spring does not relax completely afterwards since, following take-off of
    the opposite spring, the stance spring has to bear the full body weight. Consequently,
    the stance spring starts to oscillate and further force peaks occur until the ongoing
    rotational motion allows the opposite spring again to contact the ground initiating
    the next double support. From this instant on, the effective load on the spring under
    consideration gradually decreases (as the opposite spring takes over in supporting
    the COM) and, finally, the spring leg completely relaxes terminating the stance
    phase."
     
  12. Firstly, sorry for the multiple posts in this thread due to a stream of thoughts not coming all at once.

    I agree with your analysis above, but what decreases the foot spring stiffness (kfoot)?
    (Bringing us back to whether the foot is driving the leg or the leg is driving the foot. Craig suggested that the leg is driving the foot, I'm not sure where he got that from- Craig?) Isn't it possible that a decrease in the spring stiffness of the leg segments proximal to the foot are responsible for the observations you make above? We know that the leg stiffness is reduced via increased knee flexion and internal rotation, which as Eric points out: during walking occurs prior to the ankle and foot spring coming into play. Internal rotation of the leg allows / drives greater vertical displacement of the navicular via rearfoot pronation. Increased knee flexion reduces achilles tendon tension; decreased achilles tendon tension decreases plantar fascial tension, allowing greater rearfoot pronation, navicular drop etc. reducing kfoot. In order to understand the biomechanics, we need to look at the system as a whole, not just the foot in isolation- agreed?

    So the question is: are the compensation patterns described by Howard in Gait style as an etiology to chronic postural pain part 2, really compensations patterns or are they the etiologies of functional halllux limitus? Kevin, you have previously made the argument that foot pronation is a cause not a compensation of functional hallux limitus, I am merely extending that argument up the kinetic chain. Decreased leg stiffness via increased knee and hip flexion could cause functional hallux limitus and what causes decreased leg stiffness.... increased surface stiffness and...? So if we have a leg functioning at the lower limits of it's zone of optimal leg stiffness (ZOOLS), locomotion on a stiff surface may just push the leg outside of it's ZOOLS and cause functional hallux limitus.

    Lets look at the treatment for functional hallux limitus: for example, a foot orthosis shell with kinetic wedge forefoot extension: the foot orthosis shell limits the downward displacement of the navicular, increasing kfoot; the kinetic wedge pre-loads the hallux increasing plantar fascial tension = increasing kfoot (remember leg stiffness, kleg includes the foots contribution to that net stiffness). A more compliant shell under the heel section should result in an increase in leg stiffness at heel strike. Take a look at the anatomy of the Vasyli Dananberg........ Good luck or good judgement?

    Check out the shoes and the surface this chap is walking on- stiff or compliant?
     

    Attached Files:

  13. Another paper of interest attached.

    Ever get the feeling you're talking to yourself?
     

    Attached Files:

  14. Probably happens when there is only people like Dave, Eric and Kevin can discuss things at the same level as you have got to now, if their busy then your talking to the mirror.

    I´m still here but following along and when I get time read Winters stuff with more detail see if I´ve got anything to offer.

    PS this is not a request to "dumb" it down
     
  15. Of course this is possible, however, unlikely, in my opinion. I believe much of functional hallux limitus (FnHL) is caused by the passive characteristics of the plantar ligaments, plantar fascia and morphology of the weightbearing foot, which would be relatively unaffected by knee joint stiffness. Knee joint stiffness will, of course, influence foot function, but probably not make a foot go from having normal 1st MPJ dorsiflexion to having FnHL.

    Don't think you can necessarily make these generalizations, Dr. Spooner. Slight knee flexion will decrease gastrocnemius length and thereby decrease Achilles tendon tensile force, but increased knee flexion will also increase soleus length and thereby increase Achilles tendon tensile force. Additionally, increased Achilles tendon tensile force will increase subtalar joint (STJ) pronation moment in most feet, however, in some feet, increased Achilles tendon tensile force will increase STJ supination moment (e.g. laterally deviated STJ axis). Therefore, while we always want to look at the system as a whole, ignoring the inter-individual variability of foot structure and function while trying to make generalizations about the effect of knee stiffness on overall foot function probably isn't a good idea also.

    Honestly, Simon, I think you are reaching here, but, of course, I could be wrong. I believe a much better explanation and model for the treatment of FnHL can be made using the idea of STJ pronation moments, STJ axis location, medial longitidinal arch height, first ray/first MPJ biomechanics and compliance/stiffness of the medial longitudinal arch and plantar fascia.

    Hey....no fair.....I didn't say you could take a photo of me walking in the morning before my coffee!!:drinks
     
  16. But what if all the above in influenced/controlled by knee flexion which causes/enables the tibia to internally rotated and then STJ pronates - then there is a decrease in Meidal logitudinal arch stiffness etc. = FHnL

    Its then comes back to the discussion Simon has been trying to get Craig involved in ie does the tibia movements drive STJ pronation

    Chicken or Egg ?
     
  17. and to add a little to this that Ive just thought about while grinding some devices, a FHnL does not become a sagittial plane blockage until the heel begins to leave the ground so there is opportunity for a CNS response to leg stiffness regulation..... I think !
     
  18. We can agree to disagree on this final point, Kevin. Maybe not in everyone, but in some people it may. Nice research project for someone. In fact, I'll test that hypothesis tomorrow at work, if I measure hallux dorsiflexion stiffness with a force gauge with the knee extended and in varying degrees of knee flexion, we should see no change in the hallux dorsiflexion stiffness if your contention is correct, but if we do see change then knee flexion has potential to influence 1st MTPJ stiffness, at least in static stance- right? If anyone has pressure measurement kit, try walking over the the mat with knees locked out straight and in varying degrees of knee flexion- let us know if the data you get shows changes that might be associated with functional hallux limitus.


    Only if the ankle dorsiflexion is increased, if it is not, how does soleus increase achilles tendon tension with greater knee flexion? This might explain the delayed heel lift with the tibia having to travel further over the planted foot in order to generate enough ankle joint plantarflexion moment to pull the heel off the ground.

    I think you've got that the wrong way around? Unless we are talking about external moment from centre of pressure passing anterior and lateral to the STJ axis?
    I'm not saying foot structure is not important, I just trying to work out the sequence of the chain. What role does leg stiffness have in determining all of the things you list above? Indeed, what role do all of the things you list above have in determining leg stiffness proximal to the foot?

    As Mike has recognised, it's about chickens and eggs- Craig?

    Read a good paper today, I'll upload it when the arena lets me.
     
  19. efuller

    efuller MVP

    Quote:
    Originally Posted by Kevin Kirby View Post
    Of course this is possible, however, unlikely, in my opinion. I believe much of functional hallux limitus (FnHL) is caused by the passive characteristics of the plantar ligaments, plantar fascia and morphology of the weightbearing foot, which would be relatively unaffected by knee joint stiffness. Knee joint stiffness will, of course, influence foot function, but probably not make a foot go from having normal 1st MPJ dorsiflexion to having FnHL.​

    Simon Replied
    We can agree to disagree on this final point, Kevin. Maybe not in everyone, but in some people it may. Nice research project for someone. In fact, I'll test that hypothesis tomorrow at work, if I measure hallux dorsiflexion stiffness with a force gauge with the knee extended and in varying degrees of knee flexion, we should see no change in the hallux dorsiflexion stiffness if your contention is correct, but if we do see change then knee flexion has potential to influence 1st MTPJ stiffness, at least in static stance- right? If anyone has pressure measurement kit, try walking over the the mat with knees locked out straight and in varying degrees of knee flexion- let us know if the data you get shows changes that might be associated with functional hallux limitus.

    The Hicks paper showed that the location of the center of pressure was very important for fascial tightness (which I believe is the cause of functional hallux limitus. This makes sense in that a further distal center of pressure will increase first ray dorsiflexion moment. So, leg stiffness may alter 1st MPJ stiffness, but it may be because of how location of center of pressure is changed by the leg stiffness.

    Kevin Wrote:
    Quote:
    Originally Posted by Kevin Kirby View Post
    Don't think you can necessarily make these generalizations, Dr. Spooner. Slight knee flexion will decrease gastrocnemius length and thereby decrease Achilles tendon tensile force, but increased knee flexion will also increase soleus length and thereby increase Achilles tendon tensile force.​

    Simon replied
    Only if the ankle dorsiflexion is increased, if it is not, how does soleus increase achilles tendon tension with greater knee flexion? This might explain the delayed heel lift with the tibia having to travel further over the planted foot in order to generate enough ankle joint plantarflexion moment to pull the heel off the ground.


    Agreed, but how do you increase knee flexion without increasing ankle dorsiflexion and still stand upright. We also have to look at the length tension characteristics of the Soleus muscle. There is CNS control over its length up to a point. The question is whether the soleus muscle starts to add in passive force as it nears the end of range of motion in dorsiflexion of the ankle. If I were designing it, I would want the soleus to be able to develop near its maximum force at the end of range of motion of the ankle joint. If it was weak at this point in the range of motion it would be very easy to damage structures of the joint like the talar neck as it hits the anterior inferior aspect of the tibia. It's been a while since I poked electrodes into frog muscles and measured length tension characteristics. As I recall, the passive tension was just starting to ramp up as the active tension decreased.

    What I'm trying to say is that passive tension may be a very small factor in this discussion and that the CNS will be responsible for tension developed in this kind of experiment. This won't be a straight mechanical effect.

    Kevin wrote:
    Quote:
    Originally Posted by Kevin Kirby View Post
    Additionally, increased Achilles tendon tensile force will increase subtalar joint (STJ) pronation moment in most feet, however, in some feet, increased Achilles tendon tensile force will increase STJ supination moment (e.g. laterally deviated STJ axis).​

    Simon replied
    I think you've got that the wrong way around? Unless we are talking about external moment from centre of pressure passing anterior and lateral to the STJ axis?​

    I think that he is referring to the location of the center of pressure. In weight bearing activity the tension in the Achilles tendon will cause an anterior shift in the center of pressure. With a more medially positioned axis, the center of pressure will be farther lateral than in a laterally positioned STJ axis. The Hicks paper on the action of muscles is good for exploring where the "balance point" ends up with Achilles tendon tension.

    Quote:
    Originally Posted by Kevin Kirby View Post
    Therefore, while we always want to look at the system as a whole, ignoring the inter-individual variability of foot structure and function while trying to make generalizations about the effect of knee stiffness on overall foot function probably isn't a good idea also.

    Honestly, Simon, I think you are reaching here, but, of course, I could be wrong. I believe a much better explanation and model for the treatment of FnHL can be made using the idea of STJ pronation moments, STJ axis location, medial longitidinal arch height, first ray/first MPJ biomechanics and compliance/stiffness of the medial longitudinal arch and plantar fascia.​

    Simon replied
    I'm not saying foot structure is not important, I just trying to work out the sequence of the chain. What role does leg stiffness have in determining all of the things you list above? Indeed, what role do all of the things you list above have in determining leg stiffness proximal to the foot?

    As Mike has recognised, it's about chickens and eggs- Craig?


    I'm inclined to agree with Kevin. I feel that leg stiffness is an abstraction that is getting away from force on individual anatomical structures. There may be correlations between leg stiffness and something clinically relevant, but until that is found I would prefer to keep it simple and look directly at the anatomy.

    Regards,

    Eric
     
  20. Agreed, I tried this tonight, if I keep ankle dorsiflexion fixed my ass goes out backward to achieve increased knee flexion, CoP drops backard toward the heel. If I allow the tibia to drop forward, then Cop shifts anteriorly. The question is which has the bigger effect, passive tension in the achilles or CoP shifting forward, depends on axial positions, does it not?



    The length/ tension relationship is interesting Janda's work comes into play here. So it depends on whether the muscle is "short and strong" or "long and weak" as to where within the range maximal force is exerted.

    He has to be, or else he is wrong. ;)
    Indeed, but what causes the medially deviated axis? Can you say with certainty that greater knee flexion and internal rotation would not cause an increase in the medial deviation of the STJ axis?

    Stiffness and force are inseparable via Hookes Law, the question is whether we look at tissue or more global level. Leg stiffness has been demonstrated to be related to pathology, foot type has been demonstrated to be related to leg stiffness. Which is why it is commanding the interest of some of the best biomechanics researchers. If you want the references I'll add the papers -when the arena will let me!!!! :bang: If not I can mail them to you, Eric.
     
  21. Hi Folks got an answer from Craig .Here

    Here is the paper he got the info from.

    and I found the 2nd paper the transfer of movement between calc and tibia when looking for the 1st (Ian was too fast for me to upload the 1st though) I´ve not read it but it is by Nigg.
     
  22. Slightly off topic but there is a neat little java app here: http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1665.0

    Two masses connected by two springs in series. Lets say that M1 and K1 represent the foot and that M2 and K2 represent the leg. Initially, the masses (m) and spring stiffness (k) are set the same, untick the f_ext box and the simulation will start. Observe!

    Now reduce the foot stiffness by reducing K1 to its minimum setting and increase the mass of the leg (m2) to it's maximum. Observe!

    Try maximising K1 and minimising K2, etc.
    Have a play!

    I guess we could also say M1 and K1 represent a foot orthosis + shoe and that M2 + K2 represent the foot- this goes back to what Kevin and I were discussing in the MASS thread.
     
  23. Managed to get one attached, not the original one I wanted to, but hey.
     

    Attached Files:

  24. Thanks Mike.

    So the question then becomes: if the leg is driving the foot as reported in the paper by Bellchamber and Van den Bogert, not the foot driving the leg, how do you explain the "compensation patterns" in kinematics that Dananberg described to be associated with functional hallux limitus? Here's one explanation: they are not compensation patterns, they are aetiolgical factors... What's your explanation?
     
  25. I´m not sure there a lot of chickens and eggs running around my hen house at the moment.

    But I will ring one of the guys who does the bone pin studies in the next couple of work days and ask if they had Tibia pins and measured movement timing paterns get some more data.

    If they are aetiological factors then people with no FHnL would develop a FHnL when walking like the marx brothers.

    N = 1 bent knee increased hallux dorsiflexion stiffness straight leg reduced hallux dorsiflexion stiffness.

    Intersting
     
  26. Interesting. I'd like to think that will be my epitaph. I don't know if any of this is right or wrong, anymore than the rest of the contributors do, but I would like to think it makes you stop to think. Would we see any functional hallux limitus if we all walked barefoot on the beach and measured for functional hallux limitus while walking in such an environment- I doubt it.
     
  27. Just don´t get me to write it, I did not think it was possible but my spelling is getting worse .:dizzy:
     
  28. But maybe the FHnL limitus is of use for the body in energy storage and return. Ie as discussed before 100 m final olympics all had limited ROM 1st.

    so the knee flexion may help increase dorsiflxion stiffness of the 1st well all Metatarsalphalageal joints at various stages of the gait cycle to increase energy storage and return..... maybe
     
  29. Isn't this the same as the cheetah keeping it's claws extended?
     
  30. There was a thread about spiked runing shoes, cheetah and lever arms of the foot that Eric and I discussed last year. I´ll try look for it tomorrow.
     
  31. Don't worry about that on my account, I was referring to that research.
     
  32. Sorry Simon I did not check my personal email for the last 24 hours. Just got your email the file won´t load for me as well . :confused:

    EDIT :No for 3 attempts
     
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