Fitting the Foot

[relferink]

DW and Fred,

I can't decide if I like the water balloon analogy you use. On the one hand it does help in describing some of the changes in shape, on the other hand it implies that there is a fluid like substance or volume if you like that can freely move around. The foot is such a structural object, nothing is moving around like that. The arteries and veins control blood supply and return it out of the foot precisely (in healthy feet). The bones do not change in shape or volume, only in orientation to each other. Muscles do contract and expand and a contracting muscle does indeed shorten and increase in width. Considering the size of the muscles in the foot I believe that for our discussion we can ignore the change in volume this brings to the circumference.

I do not agree that the change is girth defies logic and can only be explained by looking for shifting volumes. In my opinion the changes come from the change in shape of the foot, the widening of the ball is not just the spread of he metatarsals, the change of angulation between most bones in the foot at weight bearing is as much a factor. When you think of the foot as natures shock dampers just as in a a car you can imagine that when when loaded the foot "compresses" not unlike their counterparts in a car. The major difference, the bones do not compress into themselves, instead the structure does. It's hard to put into words but I hope this makes any sense.

To know how the change of shape can effect a girth measurement without the volume changing we look at a 2 dimensional circle. A circle is the smallest circumference in relation to the area (volume) inside the circle. If you change the shape, maintaining the same volume but a larger circumference.
So when the foot "stretches" out to carry weight the position of the basic structure (bone) changes with everything around it. Not that the ball of the foot is ever close to a circle but the change in shape adds circumference without added volume.

The volume changes as well when the toes bend in gait. Important in the functionality of the foot but not an issue when we talk about taking static measurements weight off or weight on or semi-weight bearing.
For the record I do the same Fred does, measure with the foot resting on the floor carrying it's own weight and the leg but with the customer seated.

Fred, as to your question about casting at heel height, I can only speak to a modest (max. 15/8) heel height but that's how I like to do it, it takes a lot of work and guessing out of the cast to last modification process. I still trace and measure the foot without a heel height and use those measurements on the last. Mostly because it is nearly impossible to record the position of the measurements otherwise and with poorly recorded measurements, no matter how well intentioned, your result will not be satisfactory.

My

Rob

[romango]

Rob,

I'm not sure I get this circle analogy. If you squeeze a circle, you don't change the area or circumference.

I think they are dependent. You cannot change one without the other.

Not to take away from the gist of your argument... I think the car shock dampeners part applies. Area across any given cross section may easily change as muscles contract - causing bulging in the middle body of the muscle.

- Rick

[lancepryor]

Rick:

I think your math is not correct. If you compress/change the shape of a circle, the girth/circumference will change while maintaining the same area. Think about a circle with a 1 inch radius (i.e. a 2 inch diameter). Its area is Pi square inches (about 3.14) because area = Pi * r^2. Circumference is 6.28 inches (2* Pi * r). Now, squish it into rectangle, with height of 1/2 inch, therefore length of 6.28 (because area is still 3.14 sq. inches, so with a 1/2 inch height, the length must be 6.28 [area = height * length].) Now, circumference =(1/2 * 2) + (6.28 * 2) = 13.56 inches [circumference = 2* height + 2 * length].

Thus, it is easy to see why the girth measurement changes as the joint spreads into a longer/wider position with weight on.

Lance

[fred_coencped]

Rob,
For any heel height a casting platform is incorporated .My question is utilzing the full weight foot print under foot on the same heel height platform and taking girth measurements while the foot is semi weight bearing while exactly plantar flexing the ankle joint for the intended heel height.Same for generic last.

That is what I am asking.So far I am using intuitive reasoning and instincts.I have contemplated this process since starting to cast the foot for many years and confess not having tried.

As we place the foot on the static weight bearing print over the casting platform with the intended heel height and ankle joint plantarflexed,marking the girth measurements to the print seem that would be exactly the same as the foot if the ankle joint were neutral.Seems like closer to reality in standing,e.g. womens high heels.

The reason I like DW`s balloon or bag theory is something called the double balloon or bag theory.
Meaning all organs,bones,tendons etc.have 2 layers of membranes.It is the connective tissue or the myo-fascial matrix both superficial and deepfascia.Physiologically bone to tendon to bone.But the tendons are continuous and connected as connective tissue and tendons in reality attach to periosteum,not the bone itself.

Thus,in the heel spur where attachment of the plantar fascia to the calcaneous is the periosteum of the heel bone not the calcaneous.Therefore osteoblast cells biild up more bone at the distal site of attachment to the heel bone under the periosteum.Same throughout our bodies.

The foot is mostly water and dynamically changes shape.All the joints are moving and soft tissue follows the stuctures.Foot types and shapes are very dynamic in its changes.

Throw into the mix,things like swelling,activities,weight changes etc,then body types,bio-mechanics,individual preferences like tight shoes,roomy footwear,disease`s,etc.,now we have a huge variety of variables in fitting the foot.

I think we must pay attention to all of our evolution in fitting the foot and question why and how and keep open minds in an effort to design the footgear for all activities.

The foot is more then meets the eye it is a reflection of who and how we are.It is the human body re-iteratively repeating itself in the human race and in our selves from conception.

DW,I promise I will Take measurements on my next client for custom molded shoes with intended heel height casting platforms and compare to measuring at neutral ankles.I will let you know,but maybe someone else will get there first,unless anyone out there in the world has been there already, PLEASE ADVISE.....................

Fred

[dw]

Well, I'm not a foot doctor nor even a mathematician, but the logic still defies me.

If you draw that 2D circle, Rob, the area inside the circumference is wholly dependent on the circumference. This is a mathematical function: PI r squared. The area is fixed for any given radius and the circumference is a function of the radius. Thus you cannot increase the circumference without increasing the area. And vice versa...you cannot increase the area without an increase in the circumference.

Volume is a 3d version of area. In the same way that the circumference of a circle controls and constrains the area inside the circle, the outside surface of a sphere controls and constrains the volume contain therein.

So, even though we are not really talking about circles or spheres the same logic applies...at least to this old brain...I don't see how the simple spreading of the metatarsals can add volume. Volume cannot be added in a closed container...it can only be redistributed.

For the volume...and the circumference (girth)...to increase, something has to be added in the joint area--blood, tissue, substance, something.

Unless I am missing something fundamental--on the order of "properties of the physical universe" --it is not possible to measure an increase of girth in the forepart of the foot without a corresponding increase in volume. Where that extra volume comes from...well, tell me.

Tight Stitches
DWFII--HCC Member

[dw]

Lance,

Not so fast...I can't keep up.

Here's a simple test. Take a length of stainless steel wire and bend it into a perfect circle. Weld the ends together.

Now deform the circle...make it into an oval. Make it into a triangle, make it into a square. And just for kicks bend it back into a perfect circle.

Has the "circumference" changed...ever? I don't think so. Has the area inside the steel perimeter changed? Again, I doubt it.

The girth measurement around the ball of the foot is a little more variable due to the elasticity of the skin and tissue but the concept is still the same. Measure the foot in a resting position and the cross section will be mostly round (theoretically). Measure it weight-on and it will more nearly resemble an oval. Or, you can emulate that oval shape simply by squeezing the forepart.

But it's the same foot in either case and all things being equal the girth measurement should not change anymore than the circumference of the steel circle.

The fact that the girth does change when weight is place on the foot (and it's not even necessary to elevate the heel to observe this phenomenon) is at least partially due to that very elasticity of the skin and tissue. But not wholly...again simply because unless air is being pumped into the forefoot, the circumference cannot change without a corresponding change in volume/area.

The important thing to keep firmly in mind...at least for this mind...is that aside from the mechanics of the process, what we are really exploring is the change in circumference/girth. Volume is almost secondary.

If the circumference/girth does change...and I think we all admit that it does...then the volume must change. The only question is what is the nature of that additional volume? Air? Blood? What?

Tight Stitches
DWFII--HCC Member

[gshoes]

I think that this is rather obvious. The increase is easily due to water. But what do I know. I only say this because I watch my mother squeeze her feet into smaller and smaller shoes on the days she takes her water pill so that she can go shopping. There is a huge difference in volume. Maybe I don't really understand the question.

Geri

[lancepryor]

DW:

While your logic seems like common sense and is thus intuitively appealing, it is wrong! As noted by Rob and then in my previous post, you CAN change the circumference (i.e. girth) without changing the internal volume. I know this is counter-intuitive, but it is true!

If you 'squish' a circle with area of 3.14 (thus with a radius of 1 and a diameter of 2) into a long oval, the circumference/girth WILL change, even while the interior area does not change. Using my example above, but changing the rectangle to a long oval with a height of 1 (versus a height of 2 for the circle), the circumference/girth/perimeter of the oval would be about 10 (vs. 6.28 for the circle), even though the interior volume remains unchanged!

Or, think about it this way: if you tried to maintain the same interior volume as you flattened/'squished' a circle to a flatter and flatter oval, obviously the length of the oval would have to get longer and longer to maintain the same interior volume. Imagine you start to flatten the oval so the top and bottom almost meet -- then, how long would the oval have to be? VERY long. Therefore, the circumference/girth/perimeter would also be very big, because it would be slightly more than 2X the length of the oval. Thus, circumference/girth/perimeter has changed even though the interior area has not.

What allows this to happen in a foot, or something like a balloon, is that the skin/container can stretch, thus accommodating changes in girth while interior volume does not change.

So, to summarize, contrary to common sense, when the foot flattens and the joint elongates with pressure, the girth will increase even if the interior volume of the joint does not change! (I'm not saying that the interior volume does not change at all, but I agree with Rob that the interior volume can't be changing nearly as much as the girth is changing).

Lance

[donrwalker]

Lance you need to get you terms straight. A circle does not have volume. A circle has area. That area can change if you change the shape of the line inclosing the area. To use DW's example, if you pull the wire until the sides nearly touch the area is obviously smaller.

Don

[erickgeer]

10968.jpg

[lancepryor]

Donald:
You are correct; however, the point remains that the perimeter (i.e. girth) will change while the interior areas remains unchanged.

Your example proves my point -- if changing the shape changes the enclosed are, then in order to maintain a constant area we need to change the length of the wire, ie. change the perimeter (or, the 'girth')!

DW:

You posted while I was composing my previous message.

The flaw in your logic is that your in your example with the wire, the internal volume does in fact change when you change the shape of the wire!

to quote you: "Has the "circumference" changed...ever? I don't think so. Has the area inside the steel perimeter changed? Again, I doubt it."


Here are some areas for the same perimeter/girth/circumference (wire is 6.28 inches long):

circle: 3.14 Sq. inches
Equilateral triangle: 1.89 Sq. inches
Square: 2.46 Sq. inches
Oval (1 inch high, 3.6 inches long) approximately 2.3 sq inches
Rectangle (1/2 inch high, 2.64 inches long): 1.32 Sq. inches


Thus, to maintain a constant interior volume, the girth has to change as we move away from a circle.

Lance

(Message edited by lancepryor on February 04, 2010)

(Message edited by lancepryor on February 04, 2010)

[dw]

Lance,

I see your point. I will have to think on this a while. But I don't see any flaws in your thinking...about the area/volume.

The problem is that the whole issue is about circumference not area or volume. Volume got brought into this as a way of explaining the change of girth.

I just don't believe that the circumference/girth will change all that much just due to the elasticity of the skin. Even in the flattened oval...to the point where the sides are touching...the circumference (if we can call it that) never changes.

My reasoning is still valid, I believe, on one score: if the circumference of the forefoot changes the internal volume has to change...something has to be added.

Take our proverbial water balloon again. Tie it so that you have a sphere (this creates a perfectly contained volume with no outside additions or subtractions possible). Now flatten it as much as you want. Even with the elasticity of the rubber, the circumference cannot change. Without an addition of more water or air the "skin" of the balloon cannot go anywhere. Or am I wrong?

Tight Stitches
DWFII--HCC Member

[romango]

Back to my original proposal.. When muscles contract, they bulge in the middle. This could account for a change in girth. But I think there are many other possible mechanisms.

[dw]

Eric,

That's cheating!

Seriously...you're bending the perimeter back on itself. Take it to its logical conclusion and the circumferential line will ultimately merge with itself...and you'll end up with a "kink". Fundamentally, you're foreshortening the circumference.


Tight Stitches
DWFII--HCC Member

[lancepryor]

DW:

I am not sure what you mean by 'circumference,' but I think you are wrong.

I think we can agree that water is more or less non-compressable -- i.e. if you put it in a balloon (or your perfect container) and you squish the container to change its shape, the interior volume won't change.

If that perfect container stars out as a perfect sphere, it will have a given surface area. If you then change the shape of the container, the surface (and hence 'cirumference'?) area WILL change, even as the interior volume does not change (this is analagous to the two dimensional examples we were using earlier, but this time we're talking 3 dimensions). Thus, it is NOT true that interior volume has to change when shape changes. Shape can change with the same interior volume. What this requires is a skin/container that can stretch, since more surface area is required when the container is no longer a perfect sphere.

To Rob's point earlier: a circle is the most efficient way to contain a given area, and a perfect sphere is the most efficient way to contain a given volume, when efficiency is defined as the minimum necessary perimeter (2 D) or surface area (3 D). Thus, as we move away from a circle (2 D) or perfect sphere (3 D), we need a longer perimeter -- i.e. girth -- in 2 D and more surface area (material) in 3 D.

Hope that makes sense.

Lance

[lancepryor]

DW:

Erick's picture is a brilliant demonstration of the proposition. Obviously, the 'girth' or perimeter hasn't changed when he changed the circle into his shape, but the enclosed area has changed (been diminished). This proves that the SAME perimeter (i.e. girth) can have different enclosed areas -- thus, logically, for the SAME enclosed area, you would need different perimeters -- girths -- to enclose the same internal area. Hence, when you CHANGE the shape enclosing a constant area, you change the necessary perimeter -- girth. So, if the area of the joint remains unchanged, changing the foot's shape will change the perimeter measurement -- i.e. its girth measurement.

Lance

[erickgeer]

DW,

Ha! I can't quite pars what you've said, but I think the image demonstrates how the area can be altered significantly while keeping a constant outer measurement. The reorganizing of the circumference is fundamental to contouring the last from short heel to the ball. If you look at a cross-section of a last, it is anything but a circle (especially in the cone).

Back to the difference between weight-bearing and non-weight-bearing. I'm trying to think through changing measurements and the elasticity of the skin and tissues are requirements for the dynamic nature of the foot.

Weight off, the ligaments are neutral, weight-on, the tissues stretch or contract. Those with better knowledge of foot tissues than I can correct me here, but this is my line of thinking:

The transverse arch flattens on weight bearing. The connective tissue towards the plantar side will stretch from side to side, while the tissue towards the dorsal side will get compressed. I think the tissue won't compress as much as it can stretch, thus accounting for the increased measurement of the outer girth on weight bearing.

I can picture this in my head pretty well, but it would take too long to create an image.

I really need to get going, so I'll look forward to seeing where this goes this evening.

Erick

[lancepryor]

Rick:

Yes, muscles when contracting do get bigger in the middle, but they also get shorter. Yet, the foot when having weight on it gets longer!

Also, the girth of the foot changes with simple addition of the weight of the body, without any significant contraction of the muscles. This change, I would suggest, is largely due to the change in shape of the joint, with its attendant impact on the measured girth.

Certainly, the foot also changes due to changes in muscle contraction/relaxation, blood and fluid content, etc. We all know that the foot changes size during the day.

However, I think we've been largely discussing the difference in measurement between a weight-on and weight-off measurement, taken at basically the same time. I don't think a static, weight-on foot has that much contraction of the muscles in the area of the joint (unlike when going through a stride cycle). Thus, something else is causing the difference we experience in these two measurements. Rob (I think!) and I suggest it is largely the geometric consequence of the change in shape (but not volume) of the foot that occurs when weight is put on the foot.

Lance

[chuck_deats]

Excellent discussion, but have to agree with Lance. An extreme example: Take DW's wire circle and squish it completely together so the wires are touching. The enclosed area would aproach zero. Conversly, as the circle (or foot) is flattened, the girth would have to increase to keep the same area. I think that is what Lance said.

Don't think I will change the way I measure, but it is good to understand "why".

[lancepryor]

Thanks Chuck!

I actually do think this has been a vary valuable conversation and has made me think about the topic in a way I never have before.

I just did a quick set of measurements. For my foot, simply changing from weight-off to weight-on increases my girths in the following ways:
Joint: +3/8"
Waist: +1/4"
Instep: +1/8"

These changes are instantaneous when applying the weight, and the measurements immediately revert when removing the weight. Because of the instantaneous character of the change, and because our feet are made up of materials which are fundamentally not compressable (i.e. solids and liquids, not gasses), there is no way the total volume of my feet change that quickly (blood isn't flowing in and out of my feet instantaneously as weight is applied and removed). Hence, I think this proves the change in girth measurement must be due to the change in shape of our feet when weight is applied. When the foot flattens in the forefoot as weight is applied, the girth will increase even if the cross-sectional area and the total volume of the foot remains constant!

Lance

[erickgeer]

I can't leave with a bug in my brain-

The volume is three-dimensional, but a girth measurement only creates a two-dimensional figure. What Rick is describing I "think" is right when you assume that there are tissues that can stretch or compress. The volume is staying the same, but the measures at specific locations are changing due to the stretch/compress. Very minute alterations can greatly change the measurements. The "mass" of the tissues is probably being very subtly shifted fore and aft of the specific place being measured (sorry if I'm mixing terminology)

Hopefully, that actually made sense- I'm going to have to re-read all of this later when my head clears.

Erick

[dw]

I think I'm beginning to see it...I'll have to let it sit and mull awhile.

Meantime...I guess we are all in agreement that, for whatever reason, girth measurement will increase with weight bearing.

Now we need to decide whether this is an advantage or not when measuring the foot. In other words, will a weight on girth yield a good fit without any addition or subtraction?

Or will it, as some claim (myself included), result in too much room in the forepart of the shoe.

BTW, I want to thank all of you for a great discussion. I think it is extremely useful.

Tight Stitches
DWFII--HCC Member

[janne_melkersson]

Wow, what an outpouring!

Here are my two cents;

I can not make a last just by knowing the clients measurements I need it in a context which is together with the tracing of the feet. I believe that with these facilities you have all the data you need for the making of lasts.

I get the best result measuring with what I call weight of i.e. with the client sitting on a cheer with the knee in 90 degree angle. If the tape and the tracing consistently are followed then the result will in most cases be a good fit.

Unless you do what I did some weeks ago that is!
By mistake I cut the measuring tape in two and since it was the only tape I had I put it together with duct tape. I thought I had secured it and I made a pair of lasts using it. When it was delivering time the shoes ended up way to big. I couldn't figure out what was wrong so I took the tape to re-check the measure and suddenly I got it in two again! During the making of the lasts the tape started to separate which caused the last to be pretty over measured.

I am still convinced that the tape and the measurements is all you need for making lasts but next time I will be sure the tape is in good shape :-) Anyway, the client was in good mood and we laughed about it and I got me a lesson

[paul]

It is good to wonder why.
It is good to wonder why.
It is good to wonder why.


But I wll add that I do acknowledge the phenomena of girth change.

Personally, I like the results I get taking measurements "semi-weight bearing", that is, with the customer seated, with their knees at 90 degrees, as mentioned by others.

And as we all seem to agree, at least, that's what matters most, being happy with the results.

However I am sure that somehow, this phenomena serves a very good purpose, for the foot to expand with weight.

How might be a better question for us to explore. It may lead to clues to the question of why. You know, exploring the mechanics, as someone suggested.

Just some random thoughts,
Paul

[relferink]

All;

I post a quick reply before hopping on a 19 hour flight and imagine my shock upon arrival across the globe by all the confusion I caused. (and also very happy with the level of discussion taking place)

Lance, thank you for explaining the concept in a mathematical way much better than I could have. You understand exactly the point I was trying to make. In addition we have to remember that this is ONE of the elements, in my opinion one of the main ones but only one of many.

It is logically nearly impossible to grasp that one can measure a 3D object as complex as the foot with just a hand full of girth measurements in a static state and still get a reasonable result that also functions when the foot becomes dynamic in gait.

For what it's worth, in my initial reply to Jeff I wanted to offer a different way to look at and approach the subject, not to change how to measure or to invalidate any method that obviously has worked for many years and many different makers.

Give me the weekend to get over my yet-leg and let all the posts foment in my brain before I respond any more.

Rob