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  • Query re: ankle joint stiffness

    I recently read a paper by Gabriel et al. (2008) titled, Dynamic joint stiffness of the ankle during walking: Gender-related differences. In this paper, the authors presented plots of ankle moment of force plotted against ankle joint angle during stance:

    Ankle_mom_vs_angle_1.jpg.

    I did a quick version of this with some data I had:

    Ankle_mom_vs_angle_2.jpg.

    Would I be correct in interpreting these curves as showing the hysteresis of the ankle joint plantarflexor muscles, in which case the region between the loading and unloading portions of the curves would represent the loss of energy during the stance phase (in the case of our data, that area is roughly 3.9 J/kg)? Would this energy be lost as heat or would it, in fact, be part of the energy that is transferred to the shank via the gastrocnemius? Or am I completely wrong here?

    Thanks for any discussion on this.

    Gabriel RC, Abrantes J, Granata K, Bulas-Cruz J, Melo-Pintod P, Filipe V. Dynamic joint stiffness of the ankle during walking: Gender-related differences, Physical Therapy in Sport 9 (2008) 1624

  • #2
    Re: Query re: ankle joint stiffness

    Hi
    -I have been doing the same experiment and have found the same loops and also published a case study paper on this. As I'm also going to calculate hysteresis , I guess it is the area between two loading and unloading curves which you can easily calculate it by Treapezoidal approximation approach.
    -Be carerful about the loop direction, If the unlaoding loop is upper , so it is not lost energy , it's the generated one by plantarflexors which occurs in fast speed walking. But if the unlaoding curve is under the loading , It is actually the lost energy, Which occurs in slow-normal walking speed.
    -Andrew Hansen in his work (2004) called this positive and negative hsyteresis, I also found it in Kreyszig. If you want to have more information, I propose to take a look at Hansen's works and also Frigo ,(2004-2012).

    I have faced a chalange which you might help: As hysteresis is actually the area between two curves I think we should subtract area under one curve from the other. but the part of curve which has negative angle values makes bias in calculation ( becuase area actually can not be negative!). Dont you think it's better to make all the curve values positive and then calculate the hsyteresis?
    Regards
    Zahra
    Last edited by Zahra Safaeepour; July 10th, 2012, 03:41 PM.

    Comment


    • #3
      Re: Query re: ankle joint stiffness

      Hi Zahra

      Thanks for your reply.

      Originally posted by safaee View Post
      Dont you think it's better to make all the curve values positive and then calculate the hsyteresis?
      My quick response is the choice of where the zero degrees (or radian) occurs is quite arbitrary: for relative joint angles, typically we choose the anatomical position, whereas for absolute segment angles we use either the vertical or horizontal as the reference. In the former case, it is quite useful when considering the power flows during movement as being able to differentiate when muscles are acting concentrically versus eccentrically have real functional implications. However, in the case we are considering here, I can't see why it would be incorrect to remove the negative bias from the angular data. And, I suppose the same could be said about the moment data, but perhaps other readers may have differing opinions.

      Comment


      • #4
        Re: Query re: ankle joint stiffness

        I'd advise quite against calling this "stiffness" and talking about "hysteresis". These are terms used in conventional mechanics to describe the behaviour of passive structures and these are active systems driven by muscles. (Anyone who doubts this should realise that the "hysteresis" at the ankle during normal walking represents energy gain rather than energy loss). The terminology we use in biomechanics is messy enough without corrupting terms that already have well defined meanings widely accepted through the rest of mechanics.

        Just a personal opinion of course.

        Richard

        Comment


        • #5
          Re: Query re: ankle joint stiffness

          Thanks, Richard, for your contribution.

          Originally posted by rbaker47 View Post
          I'd advise quite against calling this "stiffness" and talking about "hysteresis".
          As my original posting asked,
          Originally posted by dsmith94 View Post
          Would I be correct in interpreting these curves as showing the hysteresis of the ankle joint plantarflexor muscles ...
          I really wasn't sure what these curves were, just that they looked like hysteresis curves.

          Originally posted by rbaker47 View Post
          These are terms used in conventional mechanics to describe the behaviour of passive structures and these are active systems driven by muscles. (Anyone who doubts this should realise that the "hysteresis" at the ankle during normal walking represents energy gain rather than energy loss).
          Nevertheless, these terms are applied to active systems, particularly stiffness, for instance, in studies of quiet standing.

          Originally posted by rbaker47 View Post
          The terminology we use in biomechanics is messy enough without corrupting terms that already have well defined meanings widely accepted through the rest of mechanics.
          I agree that there are some confusing terms and I appreciate your input to this discussion.

          So, if in a passive system, e.g., a spring, the slope of the force-displacement curve is the stiffness of the spring, what, then, is the slope of a moment of force-angular displacement curve, say, at the ankle, during quiet standing, if it is not 'stiffness'? What is the correct way to interpret this?

          Comment


          • #6
            Re: Query re: ankle joint stiffness

            Originally posted by dsmith94 View Post
            So, if in a passive system, e.g., a spring, the slope of the force-displacement curve is the stiffness of the spring, what, then, is the slope of a moment of force-angular displacement curve, say, at the ankle, during quiet standing, if it is not 'stiffness'? What is the correct way to interpret this?
            We call the slope of a moment-angle curve as "rotational stiffness (Nm/deg)" in our studies.
            Wei F, Meyer EG, Braman JE, Powell JW, Haut RC. Rotational Stiffness of Football Shoes Influences Talus Motion during External Rotation of the Foot. J Biomech Eng. 2012;134(4):041002.

            Feng

            Comment


            • #7
              Re: Query re: ankle joint stiffness

              Hi Drew,

              There's a paper by Hof et al. (2002) on this topic that I like, although they did the analysis at the muscle level (soleus and gastrocnemius).

              Originally posted by dsmith94 View Post
              Would this energy be lost as heat or would it, in fact, be part of the energy that is transferred to the shank via the gastrocnemius?
              Hard to say re: gastroc. The concept of biarticular muscles acting as "energy straps" (Elftman, 1940) has been cautioned against (Zajac et al., 2002). Gastroc in Neptune et al. (2001) was the primary "swing initiator" in late stance whereas soleus didn't contribute much, but their roles were sometimes similar depending on the phase of the gait cycle and the task considered. Joint work and muscle fiber work were about equal in Sasaki et al. (2009) but they note that this was coincidence rather than a mechanical requirement. I would suspect the same is true of energy transfers by joint moments vs. individual muscles. I don't think you can say much about heat liberation purely from the joint work.

              - I agree with Dr. Baker that stiffness is maybe not the best term to use for moment-angle slopes or even muscle force-length slopes as active contributions can make things inconsistent with the formal definition of stiffness from mechanics (deformation in response to an applied force), which we should probably adopt. Maybe a better term is pseudo-/quasi-stiffness or something like that.

              - The lambda-model version of equilibrium point hypothesis centers on regulating muscle/joint stiffness in an active sense (Feldman 1974a,b; Gunther & Ruder, 2003; Feldman et al., 2011) but stiffness there also deviates from the "engineering" definition of stiffness.

              Ross

              References
              Elftman H (1940). The work done by muscles in running. American Journal of Physiology 129, 672-684.

              Feldman AG (1974a). Change in the length of muscle as a consequence of shift in equilibrium in the muscle-load system. Biophysics 19, 544-548.

              Feldman AG (1974b). Control of the length of the muscle. Biophysics 19, 766-771.

              Feldman AG, Krasovsky T, Banina MC, Lamontagne A, and Levin MF (2011). Changes in the referent body location and configuration may underlie human gait, as confirmed by findings of multi-muscle activity minimizations and phase resetting. Experimental Brain Research 210, 91-115.

              Gunther M and Ruder K (2003). Synthesis of two-dimensional human walking: a test of the lambda-model. Biological Cybernetics 89, 89-106.

              Hof AL, Van Zandwijk JP, and Bobbert MF (2002). Mechanics of human triceps surae muscle in walking, running and jumping. Acta Physiologica Scandinavica 174, 17-30.

              Neptune RR, Kautz SA, and Zajac FE (2001). Contributions of the individual ankle plantar flexors to support, forward progression and swing imitation during walking. Journal of Biomechanics 34, 1387-1398.

              Sasaki K, Neptune RR, and Kautz SA (2009). The relationships between muscle, external, internal and joint mechanical work during normal walking. Journal of Experimental Biology 212, 738-744.

              Zajac FE, Neptune RR, and Kautz SA (2002). Biomechanics and muscle coordination of human walking - Part I: Introduction to concepts, power transfer, dynamics and simulations. Gait & Posture 16, 215-232.

              Comment


              • #8
                Re: Query re: ankle joint stiffness

                Hi Drew,

                Originally posted by rbaker47 View Post
                These are terms used in conventional mechanics to describe the behaviour of passive structures and these are active systems driven by muscles. Richard
                Thank you Drew for bringing up a very relevant and important issue! I agree with Richard in that these terms (stiffness, hysteresis, etc.) are traditionally used to describe the dynamics of passive systems, and thus must be used carefully.

                Originally posted by dsmith94 View Post
                So, if in a passive system, e.g., a spring, the slope of the force-displacement curve is the stiffness of the spring, what, then, is the slope of a moment of force-angular displacement curve, say, at the ankle, during quiet standing, if it is not 'stiffness'? What is the correct way to interpret this?
                As a result of the powered nature of human joints, the torque-angle relationship of the ankle cannot necessarily be used to determine the joint system dynamics (i.e. impedance, often represented in terms of stiffness, damping and inertia). In order to determine these properties, the joint must be perturbed and there are countless interesting studies using these techniques to determine joint stiffness (see Kearney & Hunter [1990] for an excellent review). Thus, during walking, the torque-angle relationship, or quasi-stiffness, is a description of the task but not necessarily representative of the joint stiffness properties.

                Therefore, it would be helpful to distinguish between these concepts in the biomechanics literature. We've recently submitted a modeling paper that delineates the concepts of stiffness and quasi-stiffness to hopefully aid in preventing confusion regarding their definitions/usages. Additionally, we've recently published preliminary stiffness and damping values of the ankle during the stance phase of walking (Rouse et al. IEEE International Conference on Biomedical Robotics and Biomechatronics [2012]).

                I hope this helps!

                Elliott Rouse

                Biomedical Engineering
                Northwestern University
                Center for Bionic Medicine
                Rehabilitation Institute of Chicago

                Comment


                • #9
                  Re: Query re: ankle joint stiffness

                  Originally posted by dsmith94 View Post
                  I recently read a paper by Gabriel et al. (2008) titled, Dynamic joint stiffness of the ankle during walking: Gender-related differences. In this paper, the authors presented plots of ankle moment of force plotted against ankle joint angle during stance:

                  [ATTACH]160[/ATTACH].

                  I did a quick version of this with some data I had:

                  [ATTACH]161[/ATTACH].

                  Would I be correct in interpreting these curves as showing the hysteresis of the ankle joint plantarflexor muscles, in which case the region between the loading and unloading portions of the curves would represent the loss of energy during the stance phase (in the case of our data, that area is roughly 3.9 J/kg)? Would this energy be lost as heat or would it, in fact, be part of the energy that is transferred to the shank via the gastrocnemius? Or am I completely wrong here?

                  Thanks for any discussion on this.

                  Gabriel RC, Abrantes J, Granata K, Bulas-Cruz J, Melo-Pintod P, Filipe V. Dynamic joint stiffness of the ankle during walking: Gender-related differences, Physical Therapy in Sport 9 (2008) 1624
                  I would like to make a slight diversion from the main thrust of your comment. I can not see how gender related differences can be of value and that is a matter I could easily be corrected. However, what I would find of vlaue is to see if the ankle anatomy makes a difference to these graphs (i.e. the angle-moment profiles). By ankle anatomy I mean for example the squatting facet. So would people with the squatting facet have a different profile compared to those who may be similar in other ways.

                  As you are in HK you probably have access to many people with the squatting facet.

                  thanks

                  Hamid Rassoulian

                  Comment


                  • #10
                    Re: Query re: ankle joint stiffness

                    Hi,
                    Thank you for reply. I really apprecite for making this discution happen as it is my reasrech line theses days.
                    I would suggest this article "Joint stiffness: Myth or reality by Mrak Latash" as he recommended using quasi-stiffness instead of stiffness in biological system.
                    However, human ankle can both damp and generate energy . I have collected data from 21 subjects at three different gait speed calling slow/normal and fast and I could see following behaviour( not surprisingly as I saw it in other litrature too) . The moment-angle loop had counter clockwise direction in fast walking( > 1.4 m/s) and in normal walking it had nearly zero hysteresis , while in slow walking the loop was clockwise ! So what do you recommend the best word to explain this behaviour?
                    I also recommend " The human ankle during walking: implications for design of biomimetic ankle prostheses by Hansen et al" which has explained why to use quassi-stiffness and hysteresis terms in ankle moment-angle curve.
                    Regards
                    Zahra

                    Comment


                    • #11
                      Re: Query re: ankle joint stiffness

                      Originally posted by rbaker47 View Post
                      The terminology we use in biomechanics is messy enough without corrupting terms that already have well defined meanings widely accepted through the rest of mechanics.
                      Unfortunately, one just has to do a simple search on the terms "stiffness" and "balance" or "gait" to see that very few authors, or editors, seem to differentiate between terms for passive and active systems. I've just had a paper on ankle joint 'stiffness' published in the Journal of Biomechanics (http://www.sciencedirect.com/science...21929012003338) and throughout the review process, our choice of the term 'stiffness' was never questioned by the reviewers or the editor. Having read the comments in this thread, I am not sure I understand the whole passive vs active issue, but perhaps it would be clearer (or possibly easier) to use the terms "passive stiffness" and "active stiffness" rather than stiffness and quasi-stiffness? The article I mentioned in my original posting called it "dynamic joint stiffness", which would be another alternative.

                      Comment


                      • #12
                        Re: Query re: ankle joint stiffness

                        Hi
                        What about ''visco-elastic stiffness" ? Since this quantity differes with speed?
                        Last edited by Zahra Safaeepour; July 14th, 2012, 11:35 AM.

                        Comment


                        • #13
                          Re: Query re: ankle joint stiffness

                          Originally posted by safaee View Post
                          Hi
                          What about ''visco-elastic stiffness" ? Since this quantity differes with speed?
                          I remember that the ISB had a workgroup on standards in biomechanics some years back. Does anyone know if the terminology that is the subject of this thread was ever discussed in that workgroup's final report?

                          Comment


                          • #14
                            Re: Query re: ankle joint stiffness

                            Hi Drew,

                            Originally posted by dsmith94 View Post
                            I am not sure I understand the whole passive vs active issue, but perhaps it would be clearer (or possibly easier) to use the terms "passive stiffness" and "active stiffness" rather than stiffness and quasi-stiffness?
                            Under the assumption that the ankle joint is behaving with passive dynamics, the slope of the torque-angle curve denotes the stiffness (under these assumptions, any deviation in angle can be considered a 'perturbation') This is typically the assumption in sway studies during quiet standing. However, during walking, there is a prescribed torque-angle relationship and quasi-stiffness. But, since the ankle joint is active rather than passive, many different ankle stiffness profiles could result in the prescribed walking torque-angle relationship. Imagine co-contraction while walking, as is the case on slippery surfaces. This would increase stiffness, but not necessarily alter the torque-angle relationship.

                            Thus, the quasi-stiffness is not necessarily a stiffness at all. The aforementioned Latash & Zatsiorsky [1993] paper distinguishes between these concepts by the storage of potential energy--the quasi-stiffness does not store energy and cannot therefore be considered a 'stiffness.'

                            Perhaps an example can help me be clear: Consider an inverted pendulum with a spring at the base with a stiffness greater than the small angle destabilizing torque relationship (i.e. the pendulum will remain inverted, even if disturbed slightly). Now, if the pendulum is perturbed, the torque-angle relationship will always reflect the stiffness of the spring. This is a passive system and this behavior is assumed during sway estimations of stiffness during quiet standing.

                            Now consider the same pendulum, but with a motor at the base, rather than a spring. Imagine the pendulum angle is being driven by the motor. The only way to determine the "stiffness" of the motor controller would be to interact with, or perturb, the pendulum. Furthermore, the specific torque-angle relationship no longer reflects the stiffness dynamics, unless the torque-angle information is in response to a perturbation. In automation applications, it's common to have a very high stiffness to preserve position fidelity--but these systems still have torque-angle relationships defined by their tasks that do not reflect the stiffness of their control systems, whether the stiffness values are high or low.

                            I hope this is more clear! Thanks and please let me know your thoughts.

                            Elliott Rouse

                            Biomedical Engineering
                            Northwestern University
                            Center for Bionic Medicine
                            Rehabilitation Institute of Chicago

                            Comment


                            • #15
                              Re: Query re: ankle joint stiffness

                              Hi
                              Thank you for explanation. It means as ankle behaves actively for example by the concentic contraction of muscles , so the term of stiffness would not be correct here but "quasi-stiffness" is approprate?
                              So, would you please explain more about " quasi-stiffness"? I could not understand what you explained with Latash work.

                              Comment

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