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low propulsive forces but high velocity progression in walking?

Discussion in 'Biomechanics, Sports and Foot orthoses' started by David Smith, Apr 27, 2018.

  1. David Smith

    David Smith Well-Known Member


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    Hello Guys

    I have a 39 year old male client who has right -hip, groin, Achilles tendon and media ankle pain that stops him running but also is a landscape gardener and so walks a lot in his job and pain makes that difficult. This post is not so much about the pain or how to resolve it but rather the unusual finding in his MSK gait assessment.

    Hallux limitus and Ankle equinus both feet - very tight hamstrings, tight at about 30dgs hip flexion in straight leg raise, Slightly lateral stj axes rotated medially to 2nd MPJ. Both lateral rays stiff to dorsiflexion moments. Medial column flexible. Pronated foot posture in resting stance and thru stance phase in gait. Functional hallux limitus both. In all cases right is tighter and stiffer than left. Short right leg LLD -20mm.

    Below I have attached 2 graphics of plantar pressure FTC and the characterization of body CoM saggital plane acceleration as estimated by wearable IMU (accelerometer, Gyro, magnetometer). NB body weight 104kg

    You will note on the plantar pressure graph that the magnitude of the vertical force curve at propulsive / push off phase is only at 100N or so which is body weight equivalent indicating no vertical acceleration of the CoM. However the braking vertical force is high at 1.5+b/w.

    From the IMU output the saggital plane acceleration is very low in magnitude, the excursion range around zero is low and the slopes of the curves are shallow. This would indicate that A-P GRF at the foot were low and potentially apropulsive.

    there is a more normal graph attached also and normal slopes are between 8-10 and vary by about 0.5
    There are clear and wide variation between left and right that probably reflects the greater saggital plane progression perturbation on the right.

    double support phase is short (normal is 10% of stance)

    However he has a normal stride length of 1.3m at 1.84m tall - a forward velocity that is above average at 1.26m/s and average cadence of 119 steps/min

    I'm asking, is this evidence that, in this case, the forward propulsion is achieved by the forward leg swing rather than the A-P directed GRF? What are your thought and how would you explain those apparently unusual kinetics where there are apparently low propulsive forces but a high CoM velocity is maintained.
     

    Attached Files:

  2. efuller

    efuller MVP

    Which graphs are the normal and which are the subject's? Are the graphs from a single step or are they an average.
    I'm confused on a-p acceleration. How is this measured. Shouldn't the a-p acceleration have the same graph for both feet, but just time shifted. When you talk about saggittal plane accelerations you should make the distinction between vertical and horizontal. I'm assuming that when you talk about progression that you are speaking about horizontal accelerations.

    On the question of forward propulsion. Physics of gait. Winter had a great series of articles on this. Because of momentum there is not a lot of need of forward propulsion. Walking is just a series of vaults over the stance limb. You lose a bit of ap velocity as you climb up over the stance limb and then you accelerate forward once the center of mass is past the center of gravity and the body falls toward the next foot strike. With the vault over the stance foot, the ap accletration will be negative before the center of mass gets over the stance foot and will be positive after center of mass is past the stance foot.

    As for the energetics of the swing leg. Just before toe off there is a trade off between hip pull and ankle push. With hip pull, when the leg is behind the body, the body is pulling the leg forward and the equal and opposite reaction occurs of the leg pulling the body backward. Once the leg swings past the body, the body slows the leg down and the leg does accelerate the body forward.

    When there is ankle push there can be a net contribution from leg swing to forward acceleration. I'm not sure what happens with this trade off when you reach constant average velocity. However, for there to be positive a-p acceleration of the body, there has to have been, at some point, a-p ground reaction force.
     
  3. David Smith

    David Smith Well-Known Member

     
  4. efuller

    efuller MVP

    Where is the accelerometer placed? If you are measuring whole body acceleration they should be the same for both limbs. When I said time shifted I meant that the acceleration during swing of one leg should be the same as during stance of the other leg. The left and right a-p acceleration curves were not the same when one was in stance and the other in swing. (They were very close to the same in the normal acceleration curves. The were very different for this subject)



    Where I was coming from on this was Newton's first law. Momentum. Once you have achieved velocity, no energy input is required. For example a bicycle rolling on a flat street. It would be one strange gait though if there was not some vertical displacement. If there is little deceleration, you don't need much acceleration to maintain constant velocity..

    I'm not sure what you mean when you said the forward position of the leg also moves the CoM forward. At the initation of swing the leg, the leg is decelerating the body.

    Did I miss the graph where you meassured horizontal force? graph. Could you go through your thinking on correlation of acceleration and plantar ground reaction force.
     
  5. David Smith

    David Smith Well-Known Member

    Eric, no there is no direct measure of horizontal force but perhaps one can imply A-P force impulse from horizontal A-P accelerations of the CoM. (The accelerometer array (IMU) was placed on the posterior pelvis approximating the position of the CoM. ) the vertical force measured by the pressure mat cannot directly imply any forward acceleration of the CoM, we could just be jumping up and down, but we often assume some correlation between Vf and horizontal braking and propulsive forces because we know that in gait we do have a forward velocity. we do have a high vertical force implying heavy braking of progression and yet no propulsive peak that might imply a propulsive force to recover CoM velocity.
    With regard to the horizontal A-P CoM accelerations - We could just say a=f/m and since mass is constant a change in acceleration must = a change in force applied. But then we could consider that Force = ma therefore force time = mass x change in velocity. Momentum = mass x velocity and if the mass is constant, e.g. as in body weight, then the change in velocity must be a change in momentum. Since Kinetic energy is 1/2mxv^2 and in this example the mass is constant then any change in momentum must indicate a change in kinetic energy. If the average velocity of gait progression is constant but there is a change in kinetic energy within each gait cycle then there must be an exchange of energy from potential to kinetic and back and this must be facilitated by a force to enable the energy for work to be done. Therefore if we are not seeing either a vertical force impulse and the horizontal acceleration impulse/integral is low, then how does he maintain a relatively high forward velocity where this exchange of kinetic to potential energy does not seem to be occurring or at least is quite attenuated.
    The type of gait progression model you describe earlier Eric could only work if we always walked down hill and the additional input energy required for forward motion came from gravity. since the CoM move thru and arc with each step there must be some energy input to recover the height of the CoM with the next step otherwise we just crash into the ground, but you know that of course so maybe I'm misunderstanding your description of how gait can progress without a horizontal application of force with each step.
     
  6. Dananberg

    Dananberg Active Member

    These graph shapes are consistent with equinis gait when hallux limitus is present. Heel fit is premature, and then there is a delay in forward progression as CoM has to catch up and surpass the planted foot. Once the CoM advances beyond this point, falling body weight will again drive propulsion. The delay in propulsion is also related to the time required to invert and avoid the limited 1st MTP joint. Otherwise, advancement is impossible.
     
  7. David Smith

    David Smith Well-Known Member

    Howard, yes I agree if this was one side equinus with low propulsive forces but I would usually expect and do see that the CoM velocity is maintained by a larger propulsive FTC on the contralateral side. Do you often see this pattern of both feet high braking FTC and non existent propulsive FTC?
     
  8. efuller

    efuller MVP

    In the subject you are asking about, there is very little ap deceleration so there is very little need for aceleration to maintain constant velocity. It is possibe to have a high vertical force without breaking or acceleration. It wouldn't look like the gait that we are used to seeing.


    There doesn't have to be a change of potential to kinetic. Energy can be added or removed by the muscles.



    There was some energy of gait research done on Groucho walking. Groucho walking can be done fairly fast with minimal vertical accelerations. It is interesting to work backwards from the accelerations and ground reactive force to try and figure out the kinematics of the gait. What did you see when watching the subject walk?
     
  9. David Smith

    David Smith Well-Known Member

    Like this

    https://www.coachseye.com/v/ea62a9036186400aa6634a15c24cf401
     
  10. Dananberg

    Dananberg Active Member

    Dave,

    When hallux limitus is present, lack of propulsion should be rather obvious. The foot must invert (or abduct...depending on morphology) as a method of avoidance. This is a time consuming event, so the progression of the CoM is unable to use the foot's progression through the sagittal plane to magnify its thrust potential, hence the limited acceleration visible on the graphs.

    Howard
     
  11. David Smith

    David Smith Well-Known Member

    Eric, yes the muscles do act to add energy but usually that is to restore potential energy ie to raise the CoM ie the propulsive leg pushes the body CoM over the standing leg or the muscles of the swinging leg can move that legs CoM forward to give it the potential energy or fmg to move the whole body forward into the next step. This allows the potential energy of the body CoM to become kinetic as it fall thru and arc about the pivot of the standing foot.
    This can be seen by a simple experiment -
    Take one step, lift the back leg off the ground but remain stationary for a second, then swing the back leg thru to a forward position and you will tip forward onto the next step. Even better bring the back leg forward by first flexing the knee so the heel comes to the bum and then flex the hip and then extend the knee, thus reducing the moment of inertia of the leg during swing and the contralateral equal and opposite forces at the standing foot. If after extending the knee you do not rotate onto the next step then just nod your head forward to displace the total CoM slightly forward of the CoF on the standing leg and then you will rotate onto the next step. No need for any propulsive muscle action from the standing leg.
    Or we can swing the the leg forward with high angular velocity and as it brakes in the forward position then the inertial force of the leg CoM, combined with the change of potential energy to kinetic or fmg as in the previous example, will drive the whole body CoM forward.
    How ever this type of 'walking' does not allow for very high forward velocities because we are relying on small forces acting on relatively large masses to cause an acceleration of the CoM into the next step (a=f/m)
    You say that maybe if the velocity of the CoM is high then we could maintain it with small accelerations during the gait cycle because of the principle of conservation of mechanical energy. However while this principle works with conservative forces, non conservative forces will slow add negative or positive acceleration and so change the mechanical energy equation. The front foot hitting the ground produces non conservative forces that reduce the total kinetic energy in terms of forward motion. so we need another source of non conservative forces, ie the propulsive foot, for which the energy required comes from the muscles. This gives us the 'normal sinusodial wave progression of the CoM moving thru the energy changes potential to kinetic and back, thereby utilising gravity, a conservative force in the mechanical energy equation, combined with non conservative forces to maintain forward velocity of the CoM.
    As you mention Eric, we can adopt this Grouch Marx type gait whereby the CoM is kept at a constant height from the ground

    but since there is no use of conservative forces then this gait style only relies on non conservative forces to maintain CoM forward velocity. Since there are no up and down displacements then the vertical forces of the GRF are minimalised but the horizontal forces are necessarily increased.
    So, I experimented with the Groucho walk using the accelerometer imu array mounted on the posterior pelvis and yes what we see is that horizontal A-P acelerations are much higher than in a normal gait style. Normal gait with average CoM velocity of 1.25m/s returns a mean acceleration slope of 8-10 - reducing CoM velocity to about 1m/s also reduces the slope of the CoM A-P accelerations to 4-6 but with Groucho walking style the A-P slope is 15-18 at a forward CoM velocity of 0.95m/s. Reducing CoM velocity in normal walking is achieved by a combination of reducing stride length and cadence (although it could be achieved by one or the other) but with Groucho walking CoM velocity of 0.95m/s is achieved by reduced cadence and maintaining or increasing stride length. This results in increased force impulses (integrals) both in propulsion and braking during walking.
    In the example of interest in this thread tho, I am stuggling to understand how he can prgress forward at a relatively high velocity with low vertical displacement, as implied by low vertical forces (on the pressure mat) in the second half of the stance phase combined with high vertical forces on the first half of stance phase, implying heavy braking and then low horizontal A-P force excursions around zero (shown by the IMU output) implying low propulsive force.
    Maybe the high apparent braking forces are not just braking but also muscle forces returning the height of the CoM during the first half of stance (like the stance phase of running) and then just rolling over the planted foot for the rest of the stance phase?? This might be possible and would be consistent with avoiding loading of the medial f/foot to avoind SPPP (saggital plane progression perturbation) due to FncHL.
    What do you think Eric and Howard - thanks for your input btw.

    Dave Smith
     
  12. efuller

    efuller MVP

    Hi Dave, Long post so I'm going to comment on parts.

    The best example of muscles absorbing energy is at the knee at heel contact. The quadriceps are active creating an extensor moment at time the knee is flexing. When the moment is opposite to the direction of motion energy is absorbed into the muscles. So, the muscles removing energy does happen in most steps.

    As for your thought experiment, a lot depends on the length of the step and the velocity. And if you stay stationary for a second and then lift your trailing leg, you will fall backwards. The center of pressure of ground reaction force is anterior to the center of mass and in that situation the force couple of ground reaction force and the force of gravity on the center of mass will cause you to accelerate backwards. This is why you usually see deceleration (a-p) up until the point the center of mass passes the stance foot.

    As to explain why there is little a-p deceleration and acceleration with your patient, he could have walked with midstance knee flexion that reduced the amount of vertical height gain and that could decrease both the deceleration and acceleration (a-p). There was not an unusual amount of knee flexion when he was on the treadmill. Was he walking differently when on the treadmill as opposed to when he had the accelerometer and was walking over the force platform?
     
  13. efuller

    efuller MVP

    Dave, are you saying that leg swing is changing force on the contralateral foot? The force applied to the pelvis by the swing leg is completely independent from the force applied to the pelvis from ground reaction force on the stance leg.
     
  14. David Smith

    David Smith Well-Known Member

    Quote "As for your thought experiment, a lot depends on the length of the step and the velocity. And if you stay stationary for a second and then lift your trailing leg, you will fall backwards. The center of pressure of ground reaction force is anterior to the center of mass and in that situation the force couple of ground reaction force and the force of gravity on the center of mass will cause you to accelerate backwards. This is why you usually see deceleration (a-p) up until the point the center of mass passes the stance foot."

    Eric, Yes that would be true if you didn't lean forward slightly to balance the CoM over the standing foot as you raise the back leg but if you do and then swing the back leg to the front without compensating by leaning back a little then you will fall into the next step because the CoM is forward of the GRF CoF on the foot. The point of lifting the back leg and waiting a second is so that it is clear that there is no push or residual momentum from the rear leg/foot.

    I didn't note a difference between treadmill walking and floor walking although I expect there would be if closely scrutinised.

    Dave
     
  15. David Smith

    David Smith Well-Known Member

    Here's an example of my Groucho walk at 0.97m/s velocity and a cadence of 100steps/min and stride length 1.2m My Groucho walk.png
     
  16. David Smith

    David Smith Well-Known Member

    Here's my normal walking gait. Cadence 94spm velocity 1.11m/s stride length 1.4m 2018-05-03 (2).png
     
  17. efuller

    efuller MVP

    Looking at the video, it appears that groucho walking can be done rapidly (high velocity) and with little a-p accelerations. It is also possible to do groucho walking with high a-p accelerations and decelerations.
     
  18. efuller

    efuller MVP

    Try groucho walking with a shorter stride length higher cadence.
     
  19. David Smith

    David Smith Well-Known Member

    So this is me trying to reproduce the subjects outputs by walking flat midfoot strike and bent knee, propulsing early from the knee and using no ankle plantarflexion in late stance and inverting foot as if to avoid FncHL You can see that I achieved the low A-P accelerations (while maintaining a forward velocity of 1.44m/s cadence 122spm and stride length 1.48m) but the vertical forces characterised by the pressure mat are the good old M shape with peaks at 1.4b/w and trough at 0.6b/w which would imply large fluctuations of CoM sine wave action ie utilising the conservative forces in exchange of potential to kinetic energy.
    Me low propulsion.png Me AM3 bent knee flat foot.png
     
  20. David Smith

    David Smith Well-Known Member

    Run out of time right now but will get back to it soon - its useful and fun to experiment and discuss like this
     
  21. efuller

    efuller MVP

    The video that you posted of the subject, he looked quite propulsive. You could see the entire plantar surface of his foot in the video. There is also some ankle plantar flexion while the foot is still on the ground. In apropulsive gait, you don't see ankle plantar flexion and you rarely see much of the sole of the foot.

    The essence of the question that you are asking is what causes the usual 2nd hump in the force time curve for a stance foot. I'm not sure. but theorizing, I would guess it is stance knee extension in propulsion. If someone was avoiding a painful first mpj they might choose to extend their knee less.
     
  22. David Smith

    David Smith Well-Known Member

    "The essence of the question that you are asking is what causes the usual 2nd hump in the force time curve for a stance foot. I'm not sure. but theorizing, I would guess it is stance knee extension in propulsion. If someone was avoiding a painful first mpj they might choose to extend their knee less."

    yes exactly Eric, I've tried reproducing the gait that produces that pressure FTC and A-P acceleration curve but can't and I can't explain in theory how it might occur. Howard seems to be saying that a compensation for FncHL (which this patient does have) would produce that output but I haven't seen it before even tho I see many patients with FncHL.
     
  23. David Smith

    David Smith Well-Known Member

    Aha! so Groucho walk with higher cadence and shorter stride - Cadence 105spm, stride 1.2m velocity 1.06m/s - Pressure FTC single high first half stance peak of 1.6-1.7b/w and no second peak. Low A-P acceleration at 6, This is quite close to the subjects gait parameters. So maybe we've cracked it guys!?
    Groucho short step.png Groucho AM3 short step.png
     
  24. Dananberg

    Dananberg Active Member

    In order to have the 2nd peaks in the force/time curve, motion of the metatarsal bases about the heads is required. When hallux limitus (as you described) is present, the lack of motion is not in the toe, but in the metatarsals themselves. They are therefore unable to transmit increasing loads through the forefoot to the support surface, hence the lack of a 2nd peak and a period of limited to no acceleration during terminal single support phase.

    Howard
     
  25. David Smith

    David Smith Well-Known Member

    Not quite up to the forward velocity of the subject of interest ie 1.06 Vs 1.26 - pushing the velocity up toward that results in increased acceleration slopes, ie 1.11m/s = slope of 7.4 plus
     
  26. David Smith

    David Smith Well-Known Member

    Update -- AM3 pressure mat FTC after mobilising foot and ankle and 1st MPJs, releasing hammies and GCS to gett increased hip RoM in SLR from 40dgs to 80dgs. Plus wearing shoes with OTC skive orthsoes with heel lifts and 1st MPJ c/o right. (NB the right hallux is abducted (away from the foot midline) as the foot pronates in w/bearing barefoot stance)
    Accelerometer array IMU - output showed similar Acceleration slopes a previous but with higher forward velocity, slower cadence and longer stride indicating reduce saggital plane progression purtubation which can be assumed to be because of reduced FncHL - Gold Star to Howard Dananberg :) Now I can make his bespoke orthoses with confidence in the desing and knowing what I'm trying to change and achieve. Good Data is good!! EL propulsive AM3.png
     
  27. kcookphysio

    kcookphysio Welcome New Poster

    “You will note on the plantar pressure graph that the magnitude of the vertical force curve at propulsive / push off phase is only at 100N or so which is body weight equivalent indicating no vertical acceleration of the CoM.”
    Two quick points..... I believe that pressure plate systems are known to underestimate ground reaction forces so this needs to be taken into account. I would also think that using accelerometer near CoM would be better used to discuss vertical acceleration of COM rather than using calculations from plantar pressure sensors?
     
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