Why are high arched orthoses stiffer than low arched orthoses?

Simon:

I know what you are driving toward here and I am, as you probably realize, playing a little bit of the devil's advocate role here. The ultimate purpose of me taking on this "exercise in debate" is so that we can better flesh out the proper terminology and concepts for us to use when we teach these basic principles of the biomechanics of foot orthoses and, when we are doing so, we are teaching with maximal clarity, minimal ambiguity and minimal confusion.

First of all, I believe when talking about the ability of an orthosis to support the loading forces from the foot and how the orthosis deforms in response to these loading forces, it is better to use the term "orthosis load versus deformation characteristics", rather than the term "orthosis stiffness". Since each orthosis may have multiple stiffnesses at each point along its load vs deformation curve and since this curve may be significantly affected by mechanical factors such as packing the arch of a shank independent orthosis to make it a shank dependent design, then I believe that the term "orthosis stiffness" oversimplifies this very complex load vs deformation curve too much for my taste.

Secondly, even though you are obviously not a big fan of the terms "shank dependent" and "shank independent", I believe that these terms [which I first heard Mike Burns, DPM, lecture on at a meeting in San Francisco when I was a third year podiatry student in about 1982] are exceedingly useful terms for the practicing clinician and podiatry student in allowing them to better understand how altering the geometry and construction of a foot orthosis may affect its load vs deformation characteristics. I have used these terms, shank dependent and shank independent in teaching now for over 27 years. In my use of these terms, I have never seen any ambiguity, any lack of clarity or any confusion be created when I use these terms to describe the basic mechanical differences between varying types of foot orthosis constructions to the thousands of clinicians and students I have taught them to.

Even though you can try contacting Mike Burns [since he is one of the smartest podiatrists I know.....you really should], I believe I know why Dr. Burns thought these terms were important since we have spoken multiple times on this subject. Dr. Burns thought that these terms were vitally important to get across the point to the clinician and student that it doesn't matter so much what the orthosis material is made of [Rohadur vs cork and leather during the early 1980s], but more important whether the orthosis, and its individual component materials, could resist deformation of the foot inside the shoe.

You must remember, Simon, at the time, many of Dr. Root's disciples were lecturing that only Rohadur could be made into a "functional orthosis" and that cork and leather orthoses could only be made into "accommodative orthoses" and could never be made into a "functional orthosis". Thank God for Dr. Burns in providing me that moment of biomechanical clarity by describing the concept of shank independent and shank dependent orthoses during my podiatry student years when I was starting to drown in the ocean of Root biomechanics dogma at CCPM. What a "breath of fresh air" that man gave me in my quest to make sense of the mechanical function of foot orthoses in this era when I was surrounded by the terms "locking of the midtarsal joint", "pronating to heel vertical", "forefoot to rearfoot relationship" and "flexible and rigid forefoot valgus".

Hopefully this better explains my perspective on this important issue in foot orthosis function. If I win this debate, then you need to buy me beers both in Manchester and in Orlando!!:drinks

 

Kevin, you can't win this debate, since you are wrong and I am right, on this occasion.:drinks I agree that load deformation in foot orthosis is neither constant nor consistent, hence I used the term "stiffness characteristics". I am not talking about a single foot orthosis having a single stiffness value, and you already know that I know that they don't. Equally you know that filling the arch of a foot orthosis just changes its stiffness characteristics, i.e. the gradient of the load/ deformation plot for a point on its surface in the area of the arch, nothing else in terms of effects on the reaction forces at the foot-orthosis interface.

 

By the way, the fact that you have been using them for 27 years, doesn't make them right. And moreover, these terms don't describe the basic mechanical differences between varying types of foot orthoses in terms of how they alter the location, magnitude nor timing of reaction forces at the foot orthosis interface- and that really is my point.

 

The question then becomes how does the variation in orthosis stiffness characteristics at the foot-orthois interface result in alteration of the location, magnitude and timing of reaction forces here?

I'll venture my thoughts, if anyone is interested... Or, does everyone already understand this and then it's just me that is enlightening my own self with this research?

 

Just puttin' it out there! But could the material strength and thickness, at any point along the orthosis, be determined by the supination resistance? More resistance--thicker material / less resistance--thinner material. Tricky to do, as either side of the thicker material would tend to flex more which would allow the thicker material section to move also. There's a formula there somewhere or am I totally off the mark? Maybe too many hits in the head!:boxing:

 

I for one would.

An idea, if the orthotic changes the shape of the medial and lateral longitudinal arch of the foot. Then the patients own arch stiffness will have changed. This change invivo change in stiffness will have direct mechanical results on the soft tissue.

So it is all about stiffness. Midfoot stiffness in this case. There is that paper - the spring in the arch of the arch of the foot, or something like that.

Does that make sense.

 

You may need to break it down more.

Medial deviated STJ thicker under the skive ie eva heel stabilizer will increase stiffness at that point.

Increased resistance to navicular lift -,thicker under this point or change the shape of the device - which is the point of discussion re heat molding prefabs. Yes most of the structural stiffness c omes from thickness, but the change in shape will also change stiffness

Etc etc

 

Or to expand that point thinking distially to proximally every time the foot comes in contact with the device the stiffness at that point has increased. Maybe ???? Im thinking especially the arch area.

 

Hang on guys

I've just come to this thread and had a quick read thru all the post and I don't think anyone has made this point.

The first moment of area relates to the distribution of an area about its centre. The area is a two dimensional space distributed about that point and establishes where that central point is.

The second moment of area / inertia relates to that area and any kind of virtual area represented by the curve of a material about an axis running thru that central point and its resistance to bending about that axis. The bending moment is relative only to the axis about which is contained within the virtual area. Therefore the bending moment at the central point within the virtual area is relative to the force applied times the angle of application to that axis of interest, i.e. if the force is at 90 degrees to the axis then the 1st moment of area = zero.

Hmmm! its quite difficult to describe that clearly but I hope you get my drift

apologies if someone already made that point

regards Dave Smith

 

Dave, what we really want to know is why are high arched orthoses stiffer than low arched orthoses?

 

Simon

How about a simple answer as this is the only type I can do!

The more vertical the surface geometry of the insole, the more parallel it is to the vertical component of the GRF, consequently it acts more like a pillar when loaded and experiences reduced bending moments when compared to a flat surface geometry.

Too simplistic?

Phil

 

Simon

Just another point re mechanical characteristics of insoles is its Hystereses properties. A material such as polyprop verses EVA should return energy more efficiently especially if it is shank independent.
The impact on the CoP should vary due to the 'spring' effect of the polyprop recoiling back to its original shape.

Phil

 

The point I was making (not very well) was that in this case the curve of the orthosis arch height due to the cavus MLA does not add to its stiffness in terms of its second moment of area.

The reason a high arched orthosis is stiffer to applied force than a low arched device is shown in the diagram below



Dave

 

Dave,
I'm at work and can't read your diagram very well on this little screen- can you put into words what you are trying to say in your diagram. Also, does you diagram apply to both a sold arch and a hollow arch?


Here's some load - deformation results for the highest point on the medial arch of a vasyli ~Dananberg. The interface of force gauge was circular with 10mm diameter. Orthotic was fixed centre of heel and centre of distal end of black "shell"

1mm = 7N
2mm = 13N
3mm = 20N
4mm = 24N
5mm = 28N
6mm = 32N
7mm = 36N
8mm = 42N
9mm = 48N
10mm = 53N

 

Simon
You wrote

Basically for the same arch length, measuring the arch and not the direct distance between points AB , the moment arm about a point on the arch apex to point A or B is longer on the low arch and so bending moments are higher so therefore greater deformation.

The low arch has the same vertical GRF at points AB, i.e. Their summation is equal to the applied vertical force. But, due to the trigonometrical effect of the reaction force vector the horizontal force applied to the ground is potentially greater on the low arch and so may overcome frictional forces and allow sliding which then allow orthosis deformation. (This is a conceptual explanation and not exactly true)

The percentage deformation of the low arch is greater than the high arch for the same absolute deformation.

Dave

PS yes Phil your conclusion in post 51 is exactly correct

 

Dave, I can't see your diagram, so forgive me if this is what you've said. What I've got is that:

Bending stiffness = bending moment / width of test piece (orthosis) x curvature (1/radius of curve).

As i asked previously: does this apply to a hollow arch and a solid arched shaped structure?

 

Simon

Just considering vertically applied force at the apex of the curve - There are effectively no bending moments about the solid arch since the GRF is distributed evenly along its base and so the net summation of moments about the apex or point of force application is Zero, or another way to think of it the centre of reaction force is directly below the line of action of the applied force.

Dave

 

Hesitate as I do to throw my hat into the ring on this one, I'm gonna.

I agree with Simon (assuming I've correctly understood his argument). I think it is mechanically irrelevant whether the stiffness of an orthoses is provided by compressive resistance in the Shank dependant (SD) insole or flexion stiffness in the Non shank dependant (NSD) insole. The foot cares only for what is going on underneath it, not why.

However I also agree with Kevin that the terms Shank dependant and non shank dependant are very important and provide useful information.

In vitro, it won't. But we don't use insoles on a work bench or in a testing rig, we use them in shoes. Shoes with shanks of various shapes and, yes, stiffnesses. If the shank of the shoe has a shape already built into it, and the insole is SD, then the surface topography of the insole in vivo will have been changed. The same surface geometry in the same shoe in an NSD insole, will not be changed by the shape of the shank.

By the same token, if we fit an SD insole to a shoe, the the patient places the same insole into a shoe which is narrower in the midfoot, the SD insole cannot sit on the shank of the shoe and must ride up onto the side of the shoe, probably on the medial side. Thus will the surface topography be changed. A NSD insole which is the same width on the surface may still sit in the same position because the contact points are only on the heel and forefoot, which are less likely to vary so much.

There are also important considerations with SD vs NSD in terms of the plasticity / stiffness of the shank of the shoe. If the inferior weight bearing surface area of the insole is smaller, it will exert greater deforming force on the shoe. In simple terms, a NSD insole is more likely to "sink" into a soft shoeliner than a SD insole because it has a smaller "footprint".

As Simon said, Shank dependant or non shank dependant tells you nothing the stiffness of the device, nor the foot-orthosis interface topography, nor the frictional characteristics at the foot-orthosis interface. But conversly the stiffness / load deformation information alone do not tell us if the insole will have its shape changed by a different shaped shoe, or whether it is suitable for a shoe with a very soft lining, or whether the width of the insole should be measured at the shank of the shoe or a little way up it. That, for me, is the usefulness of these terms. They tell us nothing about stiffness, but give us several useful pieces of pragmatic information in terms of how the insole might behave in situ in different shoes.

Sorry. Off topic for the high arch / low arch bit but relevant to the Shank dependant terminolgy debate.

 

Mike, Neil,
I was talking in more general terms. Lets ignore (as much as we can) changes in surface geometry and the influence that has on stiffness characteristics of the orthosis and focus on the stiffness characteristics per se.


When a person is in motion and impacts with the ground during the contact phase of gait the momentum of their body is transmitted through the foot, transferred to the foot orthosis, through the shoe, and ultimately to the ground.
With a relatively compliant foot orthosis in situ, the body’s momentum is transferred relatively slowly through the orthosis, and the force of the impact is consequently relatively small. If, however, the person walks upon a relatively stiff foot orthoses their momentum is transferred more rapidly to the orthosis, and the force of impact is consequently greater. The stiffer the foot orthosis the more rapidly the dynamics of the foot will be decelerated and equilibrium between the foot and orthosis reached. Thus, in the presence of a less stiff (more compliant) foot orthoses the time from initial impact to complete deceleration of motion to zero velocity and equilibrium will be longer, the force of impact lower, and the rate of loading slower, all other factors being equal. Conversely, in the presence of a stiffer foot orthosis, the time from initial impact to zero velocity and equilibrium will be shorter, the force of impact higher, and the rate of loading faster.

It is important to realise that neither the orthosis stiffness nor the foot’s stiffness is consistent nor constant across the foot-orthosis interface and that the loading magnitude and rate of loading vary with time during the contact phase of gait across the foot-orthosis interface too. So areas in which the foot-orthosis are stiffer will have a higher rate of change of momentum and consequently higher reaction forces compared to areas in which the foot orthosis is more compliant. Then consider how centre of pressure is calculated.

The other way I've been thinking about this is to assume that each point on the orthosis surface is similar to a spring. So, lets say we have flat insole made up of blocks of foam, each block of foam works like a spring. Hookes law says: F = -k x
Where:
x is the displacement of the end of the spring from its equilibrium position
F is the restoring force exerted by the material
k is the force constant (or spring constant)

So in picture 1 we have a section of this device which is basically 5x blocks of foam. If all of the foam blocks had the same stiffness (K1-5) then when we loaded them they should all deform the same amount under load and the restoring (reaction) force should be the same at each block of foam (picture 2)

If however the stiffness was not equal in all blocks and was reduced as we moved from K1-K5 (K1 is stiffer than K2>K3>K4>k5) then under loading we might get the situation in picture 3, and the restoring forces.....????? Help! My brain has turned to jam....

Anyone?

 

K5 would be 5 times the restoring force of k1

so we would have k1= rf(restoring force) at the point k1
k1 = rf
k2= rf+rf
k3= rf+rf+rf
k4=rf+rf+rf+rf
k5= rf+rf+rf+rf+rf

I think ?????

 

Simon wrote

Full size

 

That's where I got lost, the restoring force should be higher in K5 than in K1, but the reaction force due to rate of change of momentum should be higher in the stiffer foam (K1) than the less stiff foam (K5)- David, your help please. I'm sure I'm getting this wrong for a reason.

 

Here's something else that's bugging me. If we double the initial length of a spring, it doubles the amount of compression produced for a given load. Lets say we have a foam block of material which acts like a spring under loading, if we double the thickness, it should deform twice the amount for a given load, if it behaves in a linear fashion. ~So how do we get from this to: "stiffness characteristics being increased in thicker materials?"

So (and this is what I was hoping Kevin would tell me yesterday): lets take four orthosis:

1) Linear material within the loading range, "shank independent" low arch
2) Linear material within the loading range, "shank independent" high arch 2x higher than low arch
3) Linear material within the loading range, "shank dependent"- filled low arch
4) Linear material within the loading range, "shank dependent" filled high arch 2x higher than low arch

Orthoses 1 and 3 have the same surface topography and orthoses 2 and 4 have the same surface topography.

Lets load the highest point on the medial longitudinal arches of these devices vertically downward... in number 4) the material is twice as thick (2x longer spring beneath point of loading) as it is in number 3) thus it should deform twice as much under a given load as number 3).... if it's linear and behaves like a spring.

In orthoses 1) and 2) the material thickness is the same but their curvature differs. They should behave like beams supported at either end, thus: bending stiffness = bending moment / width of test piece (orthosis) x curvature (1/radius of curve). So if the span length is the same, but the radius of the curve to the point of loading is different......

Where's Simon? He's lost in space...

"What's going on- Jesus Jones"

 

It's the thickness of the wire that makes up the spring thats changed when we "thicken the orthosis" not the length of the spring- right. Got it now.

 

Dumb kid out the back question........

Ive drawn a picture. A - B represents length of device - Is this the spring length ? (or is X - Y ? )

Black line represents the original shank independent device

Blue represents EVA fill - which is the thickness of the wire changing ? Which would be the measurement of the thickness of material on the X- Y line 6 mm for Poly and the full distance when EVA is added

Which would mean in this case the orthotic stiffness has increased, by the spring wire increasing.

this would also mean change in restoring force as well my guess an increase , however the reaction force would not change due to the fact that it can only react to the "downward" force from the foot.

is this what you mean ? if not can you, Dave, Kevin anyone use very small words and help out the kids in the back row.

 

Did you get your son to colour that in for you Mike?

 

Your just lucky I didn´t go all Jackson Pollock on you on do the free hand.

Colors http://www.youtube.com/watch?v=EqkS5dVMbNc&NR=1

 

Double post- delete

 

Mike, I was thinking for a filled in arch under vertical loading it should be X-Y. I just took some blocks of eva and quickly put them in the materials testing jig, compressing single 10mm thick block by 2mm = 122N, double layer 20mm thick compressed by 2mm = 97N. Is this an issue of percentage of compression to resting thickness? i.e. I compressed the first block by 20% whereas I compressed the double layer by 10%

 

Got it now, Fanks

I will say that this is now way above my pay grade and may have this all wrong... Just putting it out there.

I was looking at Youngs Modulus yesterday I guess it´s a question in this area of elasticity linear or non linear - right ? how much force for 30 mm 2mm ?

 

Like I said, I was hoping someone would bring this up in the shank dependent / independent discussion (that'll be you Kevin ). When the foot is on top of a shank dependent device the device is in compression across pretty much its entire form, the body weight acting downwards and the shoe pushing up beneath it. Lets take our point at the apex of the medial longitudinal arch area of the device. The amount of compression caused by a given load will be dependent upon three factors:

1) the original height of the material- at tall piece of material will compress more than a short piece of material- so if we make two shank dependent devices out of identical eva foam, and load our point at the apex of the the medial longitudinal arches of the two devices, the higher arched device should compress more than the low arched devices. Thus we have greater deformation per unit load in the high arched device this the slope of the load deformation curve will be less steep, thus this point should exhibit lower stiffness characteristics than the low arched device.

2) It's cross section area (a small piece will compress more than a big piece because in the latter case the load is more spread out). Still trying to get my head around this, lets say the our point on the surface of the orthotic to which the load is applied is 1cm x 1cm square, then the cross sectional area is the same regardless of arch height. if we took out the column of material from the device in kind of a free body diagram way

3) The compressibility of the material. If both the low arched and high arched devices are made from the same material, this is not relevant.

So it seems to me that shank dependent devices are under compression across their entire form, whereas shank independent devices must resist the foot via a combination of compression (in the areas which the device contact the shoe) and bending where the device is not in contact with the shoe- In which case beam theory applies to this portion. I am amazed Kevin didn't bring this up, since he wrote it in his newsletter on the topic.

If I'm right, the idea that higher arched devices show increased stiffness characteristics compared to low arched devices only applies to shank independent devices and in fact the reverse will be true of shank dependent devices.

 

Simon

A certain material will have a given young's modulus, open cell eva foam in compression is about 3mPa, compared to polyprop at about 3gPa. This is a representation of the resistance to deformation assuming Hookes law i.e. linearity.
Young's modulus (E) = Stress/Strain. Stress = Force/area and strain = change in length divided by original length.

You are interested in strain (in terms of change in length) but a change in the area that a given force is applied to will change the change the stress and therefore also the change in length ( L1 -Lo) because there is less force per unit area. E.G. a thick rubber band V's a thin rubber band.

So to know the amount of deformation of a certain material you need to know the force applied, the area the original length and E.

Force = 850N area = 5cm^2 Lo = 4cm E = 3mPa (Lo = original length and L1 = final length)

Find change in length

E= (F/A)/(L1-Lo/Lo)

if L1-Lo = change in length = c

and so E = (FLo)/(Ac)

and so Ac = FLo/E => 0.0005*c = (850*0.04)/3^6

and c= ((850*0.04)/3^6) / 0.0005

c=0.00001133/0.0005 = 0.02266667m

c= 2.27cm

Now change area to 15cm^2

c = 0.00001133/0.0015 and then c= 0.76cm

Now change length to 8cm but original area of 5cm^2

c = ((850*0.08)/3^6) / 0.0005 = 0.00002267 / 0.0005

c = 4.53cm

Therefore you can see that, for the same force applied, as area increases deformation is decreased inversely proportional and as length increases deformation increases proportionally

To intuitively test this take one long elastic band and stretch it to maximum before breaking. Then fold to double it up and stretch it to maximum again. You will notice the change in characteristics in line with what was shown above, i.e. the single band stretches easily and much longer than the double band.

Does this help to clear your head??

Regards Dave

 

Simon

The moments about a point at the apex of each curve will be the same but there is potentially more deformation of the low arch because the structure is less stable due to increased horizontal forces compared to the vertical forces. If they both rely on the frictional forces to maintain stability then the low arch will tend to move i.e. increase in length with less vertical applied force. This is why I wrote in my diagram that the illustration was more intuitive the actual true. This because as you apply force to the top of the arch the arch will deform i.e. move away from the force and so the force applied will be less than an arch that does not so easily tend to move away from the applied force i.e. the high arch that is more stable, the ultimate of this would be a square arch which is entirely stable until there is material failure.

Regards dave

 

Dave, let me check my understanding, lets say I have a block of eva foam which is 1cm x 1cm x 1cm, I apply a load vertically downwards the load is applied to the whole area of the top face of the block (thus the area of the load = 1cm x 1cm) under this load the block will compress by a certain amount. If I keep the base area of the block as 1cm x 1cm, but increase the height to 2cm and apply the same load to the top face of the block, the block will again compress but by a greater amount than the shorter block- right?

Basically, going back to springs- we've effectively doubled the length of the spring- so if eva was linear we'd see twice the compression under the same load in the tall block compared to the short block, the fact that we don't see exactly double is due to the non-linearity of the material.

 

So, in a shank independent device a higher arch will deform less per unit load than a lower arched device, but in a shank dependent device a higher arch = thicker material (longer column of material beneath the applied force), so it will deform more per unit load than a low arched device, assuming the materials are the same and the area of loading is the same- right?

 

I'm trying to illustrate my thinking on this. If we assume that we have a shank dependent device then we can divide it up into a series of columnar elements of material, say eva. This is rather like a histogram then, the top of the columns being the foot-orthosis interface, the base of the columns being the orthosis-shoe interface. if the columns have equal cross sectional area, but vary in length, like in the histogram and then we loaded each column with equal loading, say 10N on each, the longer the column the more it would compress under it's 10N loading- right?

 

One more....

 

If EVA is linear should be the same at all 5 points I think ?

 

Surely not, since the column of material is longer under area 5... If I had 2 springs, identical except that ones resting length is five cm and the others resting length is 10 cm, and I hang 10N load off each, which one would displace the most under load (hint: the long one). I'll pull a java app that illustrates this if I can find it.

 

Was on the way to edit my reply too much reading and writing re elastic nature of tendons,fascia,EVA in the last few days.

I agree the spring in area 5 is longer and so should compress more than area 1, but i am triple guessing myself again.

Dave help ?