Leg Stiffness

I said earlier in this thread that the spring mass model is not commonly employed to model walking, walking is usually modelled as a compound pendulum, compound pendulums don't have spring stiffness characteristics (I think), however I did link to this paper http://www.asbweb.org/conferences/2005/pdf/0035.pdf in which they had modelled walking and leg stiffness.

 

Mike,
Lets think about spring stiffness:two springs we add 100N load to each, one spring changes in length by 20mm, the other by 40mm, which is the stiffer spring? The one with the shorter change in length- right?

High arched feet tend not to pronate so much during gait- agreed? Pronation is effectively the equivalent to the spring compressing. So under the same load the low arched foot + leg compresses more (lower leg stiffness) than the high arched foot + leg (higher leg stiffness).

 

I remember the paper now you have posted it up again. Thanks.

lots of info

 

Or is it that we get more knee flexion in the low arched foot?

 

I was thinking sort of about this on the way home.

I´ve got a flex high arch foot ( to use terms similar to the paper) I was standing pronating and supinating my foot and trying to see if I could detect a flexion or extension moment at the knee in relation to each motion.

I came up with pronation - flexion at the knee
Supination - extension at the knee

But I thought Maybe thats what I want to see. Is there a relationship.
A STJ motion, knee joint motion coupling ?

Also Davis et al in 1 of their papers about patella femoral pain found a reduced leg stiffness and we know of relationship papers between pronation and patella femoral pain.

So maybe we do get more knee flexion with a low arch foot ?

 

Gastrocnemius creates internal knee joint flexion moment, increased gastrocnemius stiffness may result in ankle equinus, ankle equinus may result in increased foot pronation and increased knee flexion?

 

Here you go Mike, Irene Davis again (I wished she would contribute to this thread!)

http://www.sciencedirect.com/scienc...serid=10&md5=8cb7ed599b48c5050e0aeb8e54520d6c

"At the knee, the PR [excessive pronation]group demonstrated significantly less adduction and significantly greater flexion than the NL[normal group]. "

 

Yes it would great Irene if you have time.

So we have a joint coupling.

STJ pronation - Knee joint flexion all things being equal

 

I´ve been looking for away to get SALRE in to my thinking on the subject of leg stiffness. Maybe this is the answer.

 

Rebecca

In walking, this is probably because the heel strike transient is caused by the leg/foot dropping back just before heel strike. I.E. the leg swings thru to its forward apex then drops to the ground along the same arc. This gives a hammer strike type action. So unless the F-Scan insole was around the back of the heel (and it cannot record shear force ) there would be no sensors to record the force of the strike.

Dave

 

See also:
http://www.univie.ac.at/cga/teach-in/transient/index.html

 

My guess is that the reason the F-scan can't detect this high frequency spike at initial foot contact is that it's sampling rate isn't fast enough.

 

As Simon mentions above, running is modelled as a spring-mass whereas walking is modelled as an inverted pendulum. While I think that the discussion on leg stiffness is quite helpful in understanding the mechanics of running, it is probably not as helpful in trying to understand the mechanics of walking.

Remember that during running, the center of mass (CoM) rises from the middle of midstance (midsupport) until the apex of the CoM is reached at the middle of the double-float phase. Then the CoM again descends from the middle of the double-float phase to the middle of midsupport while impacting the ground, flexing the knee and dorsiflexing the ankle.

However, during walking, just the opposite happens. The CoM rises from heel contact to the middle of midstance and descends from the middle of midstance to toe-off. The potential energy-kinetic energy exchanges in running and walking are exactly opposite of each other which makes running and walking very different activities biomechanically. Therefore, please don't assume that what holds true for running will also hold true for walking, since the foot and lower extremity functions quite differently in each activity.

Since the deceleration of the descent of the CoM from initial contact to the middle of midsupport is the period during the running gait cycle where the greatest eccentric loads are placed on the lower extremity, then the measurement of load-deformation characteristics of the lower extremity gives us a good idea of how the central nervous system and lower extremity are working together to regulate the descent of the CoM toward the middle of midsupport during running. In addition, since these eccentric loads during the first half of the support phase of running are thought to be the cause of the vast majority of running injuries, then the study of leg stiffness during running naturally makes very good sense in understanding the biomechanics of running injuries. However, since what allows an athlete to run faster in races is multifactorial, including muscle fiber type, psychological motivation, oxygen uptake ability, foot and lower extremity structure, strength and flexibility of the lower extremity joints, etc., I would seriously doubt that solely measuring leg stiffness will be predictive of racing ability in runners.

Hope this helps a little for this very good discussion.

 

Mike ignore my ramblings I was being a tool. In my mind leg stiffness was seperate to foot stiffness (hence my thoughts on a stiffer foot resulting in a reduction in leg stiffness). Hope I didn't throw you off. Luckily Simon is incredibly patient! Think I'm back on track now - we are talking leg stiffness (leg AND foot) and its relationship with surface stiffness (orthoses/footwear/ground)

 

Kevin,

Simon has inspired me to better understand stiffness and in my searching I came across this gem of a thread: Bending stiffness in the 1st metatarsophalangeal joint. It's funny you should make this excellent comment above today, as only last night (I know I know - not much of a Friday night...) I read a similar post you made back in 2007. Brilliant stuff.

Ian

 

If I think about Simons thought experiementin with these two posts it all makes much more sense, when considering the path of the bodies COM. COM will/can only load the spring (leg) only when travelling towards the ground.

 

All good Ian, its moved us on to discussing STJ position in relation to knee position so well played that man.

And yes it is great to have Simon stearing the ship.

 

The analysis of leg stiffness paper I linked to is interesting, I've not come across this approach for walking analysis before. Kevin is of course correct regarding differences in COM position between walking and running. If leg stiffness is significant during the CoM downward displacement, then there are two periods during waking when it should be significant: From heel strike to the top of the first peak in the force time graph and from the bottom of the trough to the top of the 2nd peak. I think this approach to examining leg stiffness during walking may shed some light on sagittal plane biomechanics and pathomechanics.

 

Now thats an intersting thought, I wonder what Craig, Howard,Bruce and Graham etc would think of that?

I´ve also been thinking more on leg stiffness and SALRE as well in relation to tissue stress.

I´ve seen many times in discussion between the Sagittial and SALRE groups at the end of the discussions, the conclusion is made that were are not that far away from each other maybe leg stiffness is the glue ? Time will tell.

 

Lets take that first peak- too little leg stiffness = "excessive" pronation= muscles work harder to stiffen the leg= PT dysfunction- right?

Try this: walk with your knees locked out extended (stiff leg)- how much do you pronate at heel strike? In me I get very, very little. Now walk with very flexed knees- in me lots of pronation... Hmmmm. n =1 but I'm on it! Vary your knee flexion, one pound says there is more pronation with more knee flexion. Why is that? Too little stiffness at heel strike = the body tries to stiffen that segment through increased activation of muscles. Muscles have to work too hard = PT dysfunction.

Now that second peak:
Functional hallux limitus = too much stiffness in the 1st met/ hallux segments = the body tries to reduce stiffness by decreased activation of muscles = flexed posture, delayed heel lift etc- Howard?

The more I think about this, the more I think that those flat spots are the limb adapting it's stiffness. Dave, the inspiration is with me- shall we get writing now, or am I talking out of my hat?

 

N=2 Me as well

School of funny walks

 

I think I've got this sussed and the paradigm is called "zone of optimal limb stiffness (ZOOLS) theory". As I was quoted as saying in a recent edition of Podiatry Now: "stiffness appears to be the new black this season"....... bring on the :bash::sinking: And the couple of years trying to get the paper accepted- right Kevin?

 

So, if I understand well, when the orthoses are not prescribed for running [or other sport activities], the leg stiffness, probably, doesn't influence the clinical decisions related to device's material ie hard/soft ?
Respectfully,
Daniel

 

you could be right Kevin but the heel strike transient occurs within 50ms, which equates to a frequency of >20hz, which is high compared to the stance phase frequency but, as Nyquist states, a minimum sample rate of 2 x the signal frequency is required to capture a reliable characterisation (although I wrote a research paper that recommended 7 x signal rate as optimum for resolution v's noise v's data saturation) then the sample rate of an F-scan at up to 500hz should give excellent resolution of this. Even old systems at 60hz should capture the force spike. Anyway that's digressing from the discussion somewhat.

Cheers Dave

 

Quote : Mr. Hartmut Geyer - PhD Dissertation
"Chapter 1 ...But, although the inverted pendulum renders the simplest walking model conceivable, it generates GRF patterns notably inconsistent with experimental observations (Full and Koditschek,1999; Pandy, 2003). Correspondingly, investigations on human walking revealed that, instead of vaulting over rigid legs, the COM experiences much less vertical excursion necessitating significant stance-limb compression (Lee and Farley, 1998;Gard et al., 2004).
Chapter 6 - Change of walking gait paradigm - Although both the inverted pendulum and the spring-mass model have largely shaped our principal understanding of legged locomotion in the past, they rank differently when assessing their value as basic gait templates encoding parsimoniously the characteristic whole body dynamics as identified by the corresponding GRF patterns. In this respect, only the spring-mass model for running prevails and the inverted pendulum must be refuted as template for walking. Consequently, the identification of a walking template represents one of the major challenges in biomechanics."

http://www.lauflabor.uni-jena.de/files/HartmutData/Geyer05PhDThesis.pdf

Could this work to change the view of leg stiffness related to walking ?

Respectfully,
Daniel

 

This is a good point to keep in mind. Especially when considering the CoM displacement as a spring mass model. Since the acceleration, velocity and displacement curves are each 90dgs out of phase. See walking graph example below (ref Dr Chris Kirley) The running graph would be reversed.



attached is an excel example of the total data that makes the above graph clearer. Its a Chris Kirtley work that is a clearer simplified version of some that I have been working on lately. The black curve represents the force time curve for both feet combined i.e. the GRF applied to the CoM thru a whole gait cycle. Fz 1 2 and 3 are the individual GRF for each stance phase.

 

Dave and Simon. It seems you two have been discussing alot of what we have been in this thread.

I´ve never used a force plate/scan and am pretty much :sinking:. I´m sure I´m not the only one If you have time some very basic reading or more expanded post might help get my head around it all. I´m very visual in my understanding of stuff and graphs and number usually lead to a brain melt down. ( thats why the spring with COM idea no problems show a graph with the same thing lost.)

Only if you have time


Thanks in advance

EDIT : In the excel example COM by displacement - COM affected by GRF ? and COM by Kinematics - COM affected by leg stiffness regulation?

 

Try this:
http://jeb.biologists.org/cgi/reprint/201/21/2935.pdf

 

So to summarize.

may not be totally correct. There maybe phases during walking gait when the spring-mass module maybe incorporated in relation to leg stiffness ?

 

Yeah.

 

I think I need an arvo at the Uni playing around with foot scans and the resultant info.

Could we then go as far as saying that the changes in the foot interface
( shoes,orthotics,etc ) that we make as part of our treatment plan will be most effective during the times of COM vertical displacement ?

So a running patient could have a specific device which will be more effective on foot kinematics at certain stages of there gait cycle when they have the vertical displacement moving. As part of why,when type thinking ?

 

Mike, there is always a vertical displacement of the CoM unless we have a point of equilibrium, i.e. the top and bottom of the com displacement = equilibrium, or a flat spot

 

ok thanks, lots of new info/thinking for me - Time to digest again.

 

I think I´m getting a bit snowed in by the terms. I´ll get there.

I was thinking about this example this morning.

If we have 3 triplets. the only difference between them is leg stiffness.

A= Reduced leg stiffness

B= perfect leg stiffness (what ever that is)

C= Increased leg stiffness

We get them to run over the exact same surface at the exact same speed with the exact same foot strike.

Triplet A COM will travel up and down more and faster ( increased rate and distance of vertical displacement of COM?). They will have greater knee flexion( and maybe hip fexion and ankle plantarflexion), increased stj pronation moments, increased muscle use.

Triplet B will have some COM movement, but will be more contolled. Again there will be some knee flexion etc but this person body system-CNS response to the surface stiffness will keep the leg in ZOOLS.

Triplet C COM will have less travel up and down and will occur at a slower pace
( decreased rate and distance of vertical displacement of COM?), we will see less knee flexion, reduced STJ pronation moment/mnaybe STJ supination moments and reduce muscle use.

Triplet A is more likely to get soft tissue type injuries such as patella femoral syndrome and plantar fasciitis.

Triplet B- all good in a perfect work

Triplet C is more likly to get bone related problems such as stress fractures.

Now we get the triplets A and C to run in different shoes on the same surface. We have worked out how to use shoe sole to help the body control leg stiffness ie Nigg tuning effect.

We give Triplet A a soft shoe with increased cushing. This should all things being equal will mean the CNS works in such away to increase leg stiffness. If the tuning is perfect Triplet A will have the same COM displacement, etc as Triplet B.

WE now take Triplet C a harder shoe/minimilist. This all things being equal will mean the CNS works is such away to decrease leg stiffness. If the tuning is perfect Triplet C will have the same COM displacement, etc as Triplet B.

The problem occurs with this in the real world are that, muscle length,strength, Joints ROM and QOM (quaility of motion), STJ axis position ( there is probably more that Ive missed) will all effect the bodies ability to control leg stiffness.

What also must be considered which Daniel has asked what effect an orthotic ( of different design and material) will have on our ability to effect a patients leg stiffness.

Of to find some reading on orthotics and leg stiffness.

 

The rate of loading is interesting, since with a faster rate of loading we should get stiffer tissues. Does the stiff leg load faster or slower than the compliant leg?

Basically by adding interfaces, we are adding springs in series. So the shoe adds a "spring" and the orthosis adds another "spring", each with their own stiffness characteristics. Remember the system: leg + ground, or, leg + shoe + ground, or, leg + orthosis + shoe + ground, always wants to maintain the same net stiffness. So, if the shoe is compliant and the orthosis is stiff, they may actually cancel each other out.

 

In your example we are expecting the CNS to respond to the change in surface stiffness. So compliant leg + compliant surface = body stiffens up the leg. This is good as long as the body has the ability to stiffen the leg, what if it is already working as stiff as it can? If it is the net leg stiffness + surface stiffness that is key, and the leg is already functioning as stiff as it can be (but is still too compliant), then our only option would be to stiffen the surface- right?

If we assume that by the time an overuse pathology occurs the body has tried and failed to adapt it's stiffness to within the ZOOLS, then we have to take the latter approach, at least initially. However, if we were trying to improve performance in an un-injured athlete, the first approach may be more beneficial. However, we need to look at metabolic cost etc.

This leads me to the conclusion that if we want to see kinematic change from our orthosis we would most likely see this with compliant limb + compliant orthosis (or vice versa). But if we are interested in only changing kinetics at foot-orthosis this would most likely be observed with compliant limb + stiff orthosis (or vice-versa). However, in the pathologic state (assuming the CNS has tried and failed to maintain the ZOOLS), these "kinetic pairings" of compliant limb + stiff orthosis or stiff limb + compliant orthoses, may well generate the best short-term outcomes for the patient.

 

I would assume that the leg with the increased stiffness to have increased loading rate on the foot scan, due to the face the knee will flex more in a compliant leg which I´m guess would slow down the loading rate.

 

Now that is intersting and may explain some results of experiments with stiffness and orthotics that Ive read but can´t seem to find today.

 

I added to my post above while you were replying -sorry Mike. It feels counter-intuitive that a compliant leg + compliant device should result in greater kinematic effects than a compliant leg + stiff device. I think this is where the surface topography and posting of the device come in to play. But if we consider just a flat insole "tuned" to the leg stiffness, this should hold true, all other factors being equal. This seems to be partly supported by the studies of running of different surface stiffness. Remember too that the main stiffness "adjusters" seem to be the hip and the knee, so it's the kinematic / kinetic effects at these joints I am principally talking about.