"Wring Theory" of foot function - The Missing Link?

A nice thing about it is it helps explain why Dr Phillips got the results that he did in his quantitative analysis paper

 

Go here
http://www.podiatry-arena.com/podiatry-forum/showthread.php?t=82177 - post#3

Dave

 

No it is not. The lamina pedis model is 3 dimensional (3D) too. Indeed, Sarrafian built 3D physical models to illustrate this within his paper. Moreover, if we took the two long edges of Sarrafians model and removed the material between them, we should be left with a double helix.:morning: Similarly, if we took your two helices and connected them with a plane, we should have a spiral lamina- like Sarrafian's.:morning::morning:

In addition to Sarrafian's 3D lamina pedis model of the foot (which I think we've now established consists of a double helix connected by a lamina plane), Demp has modelled the foot as a 1/4 ellipsoid. How did you arrive at a double helix as being the best model? How did you decide upon the pitch of the helices and the geometry of the conic section? If we inserted bone pin markers into each of the osseous elements of the foot and tracked their motion's during dynamic function we should see that each bony element's displacement can be seen to follow the pathway of one or the other of the two helices, if the model is valid- right? What does the data Erin Ward and Chris Nester collected suggest with regard to this?

Sarrafian didn't mention 2nd moment of area, this is true, but then neither did you. Twisting a ruler is the same as the lamina pedis model. I'm just not sure how your model accommodates the change in 2nd moment of area either? Or, are you saying that a change in 2nd moment of area does not occur? Sarrafian did go on to describe how changes in the shape of the lamina pedis influenced the soft-tissue tensions, that led him to conclude, amongst other things, that the foot was close-packed in pronation. In the animation which I presume Noah Glaser did for you, your helices seem to "unwind" and separate from one another with pronation- is this indicative of close-packing? How does the spatial relationship between the two helices within your model relate to load/ deformation characteristics of the foot in-vivo?

OK, here's were it gets a bit messy in that midfoot function is pretty misunderstood, in no small part due to Tom Sgarlato making statements like: “When the STJ is neutral and the forefoot is forced to it’s maximal position of pronation, the plane of the plantar surface of the forefoot is perpendicular to the sagittal plane of the heel. In this position no amount of force directed upward against the plantar-lateral surface of the foot will cause any further dorsiflexion or eversion of the forefoot relative to the rearfoot as long as no STJ motion is allowed to occur.” Sgarlato TE: A compendium of podiatric biomechanics, 1971. This is patently nonsense; joints don't lock. End of story. What it does exemplify is the importance of the input force, which needs to be measured and controlled for in studies of joint motion. Speaking of which...

Secondly, Daryl's paper was called Phillips RD, Phillips RL Quantitative (not qualitative) analysis of the locking position of the midtarsal joint. JAPMA vol.73: 518-522, 1983. I haven't looked at that paper in many years, I remember Daryl telling me that he'd since spotted some problems within it. Just remind me, did Daryl measure range of motion in all three planes and how did he do that? How did he control the input force?

Here's an interesting study: Blackwood CB, Yuen TJ, Sangeorzan BJ, Ledoux WR.: The Midtarsal Joint Locking Mechanism. Foot Ankle Int. 2005 Dec;26(12):1074-80. They took nine cadaver specimens and tracked bone markers using 3D kinematics and found:

“Unexpectedly, we found a nonsignificant trend of increased range of motion of the navicular in the frontal plane from forefoot dorsiflexion to plantar flexion when the hindfoot was inverted compared to everted (p = 0.06). The cuboid data for the same loading conditions also increased when the hindfoot was inverted, but the difference was not significant (p = 0.3)."

Which seems to question the idea that rearfoot inversion decreases the range of and "locks" the midtarsal joint- indeed, it appears to support Sarrafian's position that the foot is close-packed with rearfoot pronation. How does it influence your model, Clint?

They go on:

"No significant difference in the frontal plane range of motion from forefoot eversion to inversion of either the navicular or cuboid while the hindfoot was everted or inverted was detected (p = 0.2 and 0.8, respectively).

This study supports the clinical observation that the foot is more flexible when the hindfoot is in valgus. However, the position of the midtarsal joint cannot fully explain the increased flexibility because the motion of the navicular and cuboid did not significantly increase.”

In other words, the change in foot flexibility which may have been observed in studies like: Phillips RD, Phillips RL Quantitative analysis of the locking position of the midtarsal joint. JAPMA vol.73: 518-522, 1983 do not appear to be due to changes in the range of motion at the midtarsal joints.

What are the implications here for your theories, Clint?

Thirdly, as Nester and co-workers pointed out: axes of rotation are not a physical or anatomical entity but a kinematic parameter that is used to describe the characteristics of the motion of one rigid body (eg, a body segment) relative to a reference rigid body.
Axes of rotation do not determine the motion at a joint; rather, the motion determines the axis (Nester C.J., Findlow A., Bowker P.: Scientific Approach to the Axis of Rotation at the Midtarsal Joint. J Am Podiatr Med Assoc 91(2): 68-73, 2001) in their work they described three mean axial positions for the midfoot during gait: one for the period corresponding to loading response; one for midstance and one from propulsion. According to Nester and co-workers, during loading response and from heel off to toe off the motion of the forefoot on the rearfoot about the midtarsal joint generated axes which were due to either: inversion, dorsiflexion and abduction or eversion, plantarflexion and adduction. Viz, neither pronation nor supination.

How does this sit with your model, Clint?

The motion of the rearfoot relative to the forefoot is also dependent upon whether these segments are moving in-phase or anti-phase with one another, which varies between and perhaps within individuals (Chang R, Van Emerick R, Hamill J: Quantifying rearfoot-forefoot coordination in Human Walking. Journal of Biomechanics (41) 3101-3105, 2008)

What say you, Clint?

Which is all very interesting but skirts around and doesn't really answer the question posed, which to reiterate was:

do the structures you describe within your "paper" have compression or moments at the joints between the structural elements and/ or any bending moments acting on the structural elements?

The answer, as I think we all know, is that compression does occur at the structural joints, along with moments at the joints and bending moments within the structural elements. Thus, tensegrity can be of little importance at this level of structural modelling and serves only to obfuscate here. Do you agree, Clint? Indeed, has anyone ever managed to build a dynamic structure which obeys the laws of tensegrity while changing it's structural shape? There's the key, it not about modelling the foot in 3D, it's all about modelling it in 4D.

There's more, but that'll do for now.

 

Here's a little devil's advocate for those following along: why do we need models like Clint's double helix representation of the foot, when we already have models which accurately portray the anatomy of the foot, with each of it's structural elements that allow us to perform simulations with finite element analyses etc?

 

I think Clint is exploring established knowledge from a fresh perspective that has the potential to be a useful intuitive model for the clinician. I get the feeling this is a sincere investigation, as opposed to a bogus idea to sell a new product, and should be encouraged, although a little reigning in is also helpful and you are asking some searching questions based on some good research.
Fresh perspectives make us all put our thinking caps on tho and even if turns out that this theory adds little to our useful knowledge it will still be useful to explore and check what we think we know.
Finite element models are great and ultimately our best detailed analysis system but simple more elementary models can be more readily available for intuitive learning, SALRE being a good example of such.

I'm not sure about the actual existence of the double helix but the idea of winding up a spring is useful in that it indicates stiffening and not locking and the actions of a shortening cylindrical structure as it is wound up and lengthening as its unwound. I think this winding and unwinding is misleading in terms of the stiffness of the foot during propulsion since a pronated foot can be just as stiff and propulsive as a supinated one, it just becomes stiff in a different position. You only have to look at the propulsive foot of a high jumper to recognise that. (it isn't supinated for sure). This might indicate that the fully pronated foot is also winding up the spring to become stiff again it certainly isn't a bag of bones or pile of pickup sticks.

Regards Dave

 

Hence my earlier point:

How is this useful to the clinician, Dave? Particularly if, as you intimate, it is inaccurate?

Like I said when you started talking about the twisted ruler- I needed to check the starting position of Sarrafian's "ruler"- a better starting position (Neutral- ouch) might be the untwisted, yet longitudinally bent ruler, such that pronation induces a twist in one direction, while supination indices a twist in the other direction.

 

I am glad to see I have sparked some interest. If one tries to over simplify the situation. Nature is a complex simplicity. It will accomplish the complex things with the simplest, most efficient ways possible. In Geometry, I was taught a plane (plate) is different from a helix. I can take a flat beam and shave away the sides and now I have a I-beam. If you look at it right,they look the same, but they have different properties. They are not the same. A plate has an X and a Y coordinate. Twist it or not, it will have different properties from a spiral. I have not been satisfied with the results of a twisted plane. Obviously, many others have not been either.

 

In rereading Sarrafian's paper on his Twisted Plate Model of the foot, I appreciate Sarrafian's work even more now. However, I still have difficulty seeing: 1) how the Wring Model is any better than Sarrafian's Twisted Plate Model in describing foot biomechanics, and 2) how the Wring Model helps the clinician any more than the Twisted Plate Model in treating patients.

In fact, as far as naming a model, I think Sarrafian has done a much better job than Clint has since a "twisted plate" conjures up an object that itself can act as a model, whereas the term "wring" has multiple meanings, none of which conjures up an image, at least to me, to serve as a useful model.

Instead of "Wring Theory", I would have named the paper, "The Modified Twisted Plate Theory", or better yet, "The Modified Twisted Plate Model of Foot Function".

 

what is your email. Will forward Daryls paper to you.

 

Given that the foot is wringing and unwringing itself, this is the name I figured would be best. Finding fault with the name has nothing to do with the discussion of the "Wring Theory." If one wanted to describe it from the standpoint of its geometry, "The twisting, and untwisting of the Foot Helix" would be more appropriate, but since you already said that the Lamina Pedis was a bogus model in the first place, why is this a discussion?

 

I do not have the paper by Demp. Can you send it to me?
The lamina plane does not have the mobility of a helix that is reflected in the foot. Therefore I am not comfortable of attaching such to my described model.
Looking at figure 6-d that is exactly what I did. I believe the macroform is a Double Helix, but I still had to let the anatomy define how it achieved such a form at its individual components ie. joints. As for the Conical part of the Double Helix, this was follow the fact that the the medial and lateral legs, of the Conical Double Helix, converge at the subtalar joint. Sarafian, had a nice picture of this in his paper. I do not have specifics as to the exact pitch and that will require further studies. The nice thing is we now how the capability to test these things in the living model. The gold foot you see at the very beginning is an actual CAD modeling of my foot. That is why you see an OCD of the medial talar dome. The video, every model, and every figure you see is my own personal work. (I have ninja skills.) Shareware is pretty powerful nowadays You can calmly leave Noah out of this whole thing. Where he contributed is when I was trying to understand how to measure plantar fascial tension given the height of the arch. Figures 15-a,b,c,d, were what I finally settled on and that came from a consulting NASA engineer. I can put you in contact with him if you should need the information. He even showed me what I was screwing up on in building the toggle joint of 16-a,b. Pretty smart guy.

I would love to measure all this stuff. I do not have Erin Wards information, but I have been in contact with him and he and his crew found it interesting. The paper has alot more in it than when I first spoke with Erin.
There is the technology to measure this stuff in 4-D and I have been in contact with them. I would like to volunteer my feet. I am currently working on coming up with the $75,000 it costs to do it.

Can you break up your posting, so I can make sure I address them all. Lunch is over and I have to get back to work. Enjoying the conversation.
Clint

 

Clint:

Can you point out, in any of my many comments here on Podiatry Arena, where I said that "the Lamina Pedis was a bogus model"?

In addition, by commenting on your use of the term "Wring" to describe your "theory", I wanted to point out the fact that the term "Wring", was a somewhat unusual name with multiple meanings. I suggested what I thought was a better idea for a name for your "theory" since it seemed rather to be a modification of Sarrafian's Twisted Plate model, rather than a new "theory" of foot function.

I didn't expect you to like my suggestion, but I thought I would throw it out there anyway since I think it is a valid point.

My comment wasn't a discussion, it was a comment. However, if you want to make it a discussion, then we can certainly proceed in that direction.

 

I gave all my copies to a research colleague some years ago. Try the one at the bottom of the list first, but I've got a feeling it may have been in his master thesis- why not contact him?

Demp, PH: A mathematical model for the study of metatarsal length patterns. JAPA 54:2 1964 p.107-110

Demp PH: Mathematical medicine. JAPA 60:9 1970 p352-353

Demp PH: The metatarsal hyperbola and the pathomechanical forefoot. Currrent Podiatry 20:3 1971 p15-17

Demp PH: A numerical taxonomy for evaluating the angular biomechanics of the human metatarsus. Current Podiatry 24:5 1975 p.9-11

Demp PH: Biomechanical optimality and the mathematical measurement of diagnostic patterns in the human foot. Arch Pod Med Foot Surg 3:1 1976 p.11-21

Demp PH: Biomechanical foot roentgenometry. Yearbook of podiatry 1978-1979. Ed: TH Clarke. Futura Publ. Co. New York 1978 p. 64-70

Demp PH: An anthropometric index for screening foot dysfunction. Current Podiatry. 28:6 1979a p.11-13

Demp PH: A mathematical taxonomy to evaluate the biomechanical quality of the human foot. M.S. Thesis (unpublished) Polytechnic Institute of New York, USA June 1979b

Demp PH: A correlation of length, width, height and pathomechanical quality in the human foot. Current Podiatry 31:8 1982 p23

Demp PH: Biomechanical profile analysis of the foot radiograph based on mathematical modelling. Current Podiatry 32:10 1983a p15-17

Demp PH:Mathematical modelling in podiatric surgery. A new approach to biomechanical evaluation. J Acad Amb Foot Surg 1:1 1983b p72-73

Demp PH: A mathematical taxonomy to evaluate the biomechanical quality of the human foot. Mathl Comput Modelling 11 1988 p341-345

Demp PH: A mathematical taxonomy to evaluate the biomechanical quality of the human foot. Mathl Comput Modelling 12 1989 p777-790

Demp PH: Using conic curves to classify pathomechanical biostructure of the metatarsus. Mathl Comput Modelling 14 1990a p668-673

Demp PH: Pathomechanical metatarsal arc: radiographic evaluation of its geometric configuration. Clin Pod Med Surg 7:4 1990b p765-776

Demp PH: Numerical diagnosis of pathoanatomy in the human forefoot: A pilot study. The Lower Extremity 1:2 1994 p133-138

Demp PH: Geometric models that classify structural variation of the foot. JAPMA 88:9 1998 437-441

I've now got a horrible feeling that it might have been Hiss that used a 1/4 ellipsoid first. To be honest it was really just to point out that others have used 3D geometric models of the foot.

I don't really have time to split up my post from last night for you, Clint. Try to work through it point by point.

 

However, your contention was that Sarrafian's model was two dimensional. I have merely pointed out to you that it is not. Do you still believe that Sarrafian's model is two dimensional?

When you say that you have not been satisfied with the results of a twisted plane, what do you mean? How are you testing the results of a double helix? This is my point, you have not demonstrated the validity of your double helix model- as I said previously, if we inserted bone pin markers into each of the osseous elements of the foot and tracked their motion's during dynamic function we should see that each bony element's displacement can be seen to follow the pathway of one or the other of the two helices, if the model is valid. But you have not done this.

More later, work now.

 

This one: http://www.sciencedirect.com/science/article/pii/0895717789901337

 

Attached (it's open-access). I'll avoid the temptation to post more until Clint has had chance to work through all of the questions I asked of him yesterday.

 

Clint’s paper is clearly a work in progress. It appears to have been written in phases, and the sections are somewhat discontinuous. Poor grammar and writing as one were talking….vs. writing, are glaring issues for this to be acceptable. That said, there has been considerable effort put to this concept, and while some of these principles are not new ones, enough has been added to combine many biomechanical principles into an interesting and cohesive thought process.

It is the helical design component which I find most intriguing about Clint’s thesis. Good thinking. This conforms well with the rotational changes seen during evolution of the foot structures. OJ Lewis wrote how the lateral column actually rotated to come “in line” with the adaphistic medial column of the ape to human foot progression. Essentially the same bones….only oriented on a different axis….with striking functional and morphological variation. How helical! I would be curious to hear Bob Kidd’s take.

Clint’s suggestion that the design on the midfoot support via the peroneals and posterior tibial muscles/tendons is a windlass in origin bypasses the purely mechanical effect of the Hick’s Windlass Effect. The beauty of the Hick’s Windlass is its basis in NON-MUSCULAR function. It would seem counter to Hick’s description to give the “windlass” name to a muscular structure. This is not to suggest that there is no support function between the peroneals and posterior tibial groups, just that using nomenclature which was reserved for a non-muscular entity is misplaced.

Clint has raised the issue of tensegrity again. PA has had some interesting discussions regarding the use of the tensegrity model to describe foot function. Kevin Kirby’s comment about the forces acting across the midfoot joints negating it being a true tensegrity structure would be accurate, if this was in fact the case. However, and as a point for discussion, X-rays of normal feet in weight bearing, show clear spaces between the midfoot joints…..ie, no contact. The calcaneus does not even touch the floor, but appears suspended above the fat pad. An orthopedic surgeon I know once described to me that during knee reconstruction, he repeatedly observed, that once adequate tension was restored to the knee joint ligaments….the knee joint space OPENED! This would be difficult to reconcile if it were not routinely ignored.

If the joint surfaces are not touching…..than perhaps the tensegrity concept of continuous tension with discontinuous compression components does reflect an effective model to understand postural integrity, the foot included.

Howard

 

Hello Howard,

This old stump again...

What do they show during dynamic function? (anyone got a copy of Don Green's fluoroscopy video?)

Here's a study which looked at joint surface contact at the subtalar joint: http://www.sciencedirect.com/science/article/pii/002192909400076G

Here's one that looked at the contact at the talonavicular and calcaneocuboid joint too: http://www.ncbi.nlm.nih.gov/pubmed/17257548

Notwithstanding, tensegrity isn't just about discontinuous tension and compression, it also requires that:

"no structural member experiences a bending moment."- Wikipedia http://en.wikipedia.org/wiki/Tensegrity

The reality is, that the structural elements of the foot do experience bending moments.
Ian Stokes demonstrated this in 1979: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1233023/pdf/janat00239-0128.pdf
Sharkey et al., among others, have demonstrated this more recently: http://jbjs.org/data/Journals/JBJS/741/1050.pdf

Thus, it appears that joint surfaces in the foot compress against one another (i.e. compression is not discontinuous) and/ or that the structural members of the foot do exhibit bending moments. Viz. the tensegrity model is not valid here.

Regards,
Simon

 

Hi Simon,

Let’s review the studies you used to support your position that the foot cannot be a tensegrity structure.

”Contact areas and pressure distributions in the subtalar joint” Journal of Biomechanics,1995. In this study, disarticulated specimens were used. Pressure sensing films were inserted to assess STJ loads. If tensegrity requires a continuous tension network, wouldn’t you agree that this could NOT be the condition, once the ligaments were incised to permit insertion of the pressure sensors.

“Effect of tibiotalar joint arthrodesis on adjacent tarsal joint pressure in a cadaver model”. In this paper, changes in CC and TN joint pressures are assessed in disarticulated cadaver foot/ankle specimens. Pressures substantially increased when the ankle joint was fused vs. normal. While I would argue the same way about loss of ligamentous integrity causing a loss of the tensegrity structure, I would point out that when the ankle was fused, the loss of the discontinuous compression member effect overloaded the adjacent structure. Fuller (Buckminster….not Eric) described this effect in Synergetics II. Once the structural integrity of the tension network is disturbed, the structure will collapse at 90 degrees to the forces applied. Prehaps this study proved this concept!

The ’79 Stokes represents a series of calculations to determine forces acting on the foot. It does NOT directly measure the bending moment, it only alludes to it based on the mathematics used in the paper. In consideration of its mathematics, the paper itself includes the following disclaimer “The accuracy of these results depends upon the accuracy of the measurements, and of the assumptions in the mechanical model. The major source of error in the measurements is in the distribution of force under the foot (± 30 %). The overall accuracy of the calculated results is estimated to be about ± 50%.”

So, the papers used to support the contention that the foot cannot possibly a tensegrity structure fail to do so. An intact, in-vivo foot, visible on x-ray, demonstrate spacing between joint surfaces not explained via the studies you have cited. What is known is that removing tension from the foot, ie, cut the plantar fascia, causes the foot’s arch structure to lower. (Kevin has a terrific lecture on this topic.) The more ligaments that are incised, the lower the structure will become. Thus, removal of the continuous tension supplied by the ligamentous/fascia structure causes loss of structural integrity. This seems to support the concept that the foot (and body) are tensegrity structures vs. series of levers and pulleys.

Howard

 

What papers do you use to support your position, Howard? Show me the studies which demonstrate that there are no joint compression forces and no bending moments acting about the structural elements of the foot in-vivo...

Sure my evidence has limitations: it's pretty hard, if not impossible, to measure these thing in-vivo without causing some disruption.

Do you honestly believe that there are no bending moments acting across the metatarsals or other structural elements of the foot in-vivo? Here you go: http://www.staffs.ac.uk/isb-fw/Manuscr/Arndt15.PDF ( http://www.sciencedirect.com/science/article/pii/S0966636202001911 ). I guess now your going to say that putting the titanium staple into these subjects means that it is not a good representation of those without the staple, even though bending moments were observed in-vivo using bone mounted strain-gauges with minimal anatomical disruption :bash:.

Does that study count? If not, then I guess this doesn't either: http://www.sciencedirect.com/science/article/pii/S002192900100241X

What if I posted an x-ray picture of the foot with joints contacting (non-discontinuous compression between the structural members) would that sway you? Here you go, do you think there are any areas here where compression is not discontinuous? :

 

Thank you for the insight

 

It all comes down to the direction of force in the tension members. For the rigid members to be discontinuous, the tension members have to be pulling them apart. In the foot the collateral ligaments would have to be positioned in such a way that they would be pulling the ends of the contacting bones apart. To do this you would need a little outrigger on bone A that extends beyond the joint surface and ligament would have to run back towards the rest of bone A and attach to bone B in order to pull the joint surfaces away from each other.

The ligaments can only support tension, they cannot push the bones apart. They can only pull the bones toward each other. The foot is not a tensegrity structure.

Eric

 

This paper from JBJS clearly shows that the joints of the foot bear compression forces which, therefore, invalidates the idea that tensegrity can be used to model foot mechanics (Lakin RC, DeGnore LT, Pienkowski D. Contact mechanics of normal tarsometatarsal joints. JBJS 83-A(4):520-8, 2001). See attached paper. Also, just because radiographs show the osseous structures of a normal foot to have an apparent "space" between them at the joints (I hope we all know that articular cartilage is radiolucent), does also not mean that the articular cartilage is not bearing significant compression forces and compression forces within the joint. Osteoarthritis just doesn't occur by itself....it is caused by compression forces acting on joints.

In addition, 67 years ago, John Hicks clearly demonstrated, by using mirrors drilled into each metatarsal ray of cadaver specimens, that the metatarsals are each subjected to bending moments under weightbearing conditions. Hicks showed a bend in the second metatarsal of about 0.5 degrees under simulated loading conditions. The bend in each metatarsal ray that Hicks demonstrated over a half century ago, is caused by bending moments. Bending moments cannot occur on the compression elements of a tensegrity structure which also clearly invalidates the idea that "tensegrity" can be used to accurately analyze and model foot mechanics (Hicks JH: The foot as a support. Acta Anatomica, 25:34-45, 1955). See attached paper.

A much better and more accurate way of modelling the foot is to use the known shapes and anatomical locations of the compression load-bearing structures (bones and articular cartilage) and tension load-bearing structures of the foot, along with the external forces on those structures and perform either finite element analysis (as Simon mentioned earlier) or even simple free body diagrams (as Eric has been describing to us for a few decades) to determine the internal forces within those structures. In order to better determine load vs deformation response of the foot, it is best to model the medial longitudinal arch, lateral longitudinal arch and/or each of the metatarsal rays as a type of spring with a constantly varying spring stiffness, depending on load acting on that structure. I have included an illustration of such an example that I made up three years ago about the load-deformation characteristics of the medial and lateral longitudinal arches and metatarsal rays.

I still don't see how the "Wring Model" gives us new information that we didn't already have before in the existing medical literature. Can someone please tell me how the "Wring Model" is a signficant improvement over Sarrafian's Twisted Plate Model or how it is "The Missing Link"? I just can't see it.

 

For those interested in Sarrafian's "Twisted Plate" model, here is his paper from 25 years ago where he so nicely describes it (Sarrafian SK: Functional characteristics of the foot and plantar aponeurosis under tibiotalar loading. Foot & Ankle, 8(1):4-18, 1987). Thanks to Clint for sharing the paper with me.:drinks

 

After digging through my boxes of old journals, I found the paper by Daryl Phillips and his father which I have included for all of your reading pleasure (Phillips, R.D., Phillips, R.L.: Quantitative analysis of the locking position of the midtarsal joint. JAPA, 73(10):518-522, 1983).

Just one question for anyone out there familiar with mathematics....how can you possibly determine that a curve is "exponential" with only three data points determining the shape of that curve.

 

I'm more concerned with the methodology employed versus the inferences being made: Daryl made inferences regarding the talonavicular and calcaneocuboid articulations. He didn't directly measure the motion occurring at either of these articulations, made no statement regarding how the input force was controlled for, and measured only the frontal plane "locked" position of the forefoot to the rearfoot.

As I mentioned previously, the concept of joints "locking" is just nonsense and is dependent upon the input force (See Nester too). Moreover, the Blackwood study begs serious questions as to the role of the talonavicular and calcaneocuboid articulations in modulation of forefoot to rearfoot stiffness observed in-vivo. http://www.amputation.research.va.gov/limb_loss_prevention/Midtarsal_Joint_Locking.asp

Daryl assumed that the forefoot either pronated or supinated about fixed "oblique" and "longitudinal" axes at the midtarsal joint. Again, as I previously discussed, this is questioned by Nester's data- Nester recorded resultant axes which were due to triplanar combined motions which were neither pronation nor supination. Daryl, like Root before him, ignores the other joints twixt the midtarsal joints and his measurement position, which (we are left to guess) was probably similar to Root's- at a point just proximal to the MTPJ's. Blackwood's data suggests that it is at these more distal joints (those distal to the calcaneocuboid and talonavicular joint) that the change in forefoot to rearfoot stiffness is truly modulated with modification of rearfoot position, not at the talonavicular nor calcaneocuboid articulations. So, how does this fit with Clint's "lasso's" and "windlasses"? Over to you, Clint...

 

Yes it is valid but tenuous at best unless you know for sure that they are the only data points available in the sample range otherwise you have no idea about what went on in between the data point, (or after the last one) which is always true but there is less probability of random excursion within the range if the data points are close i.e. if the sample resolution is high.

Excel characterisation of 3 data expressed as a linear and exponential curve.




Just to make that more clear the growth of the exponential curve is proportional to its current value so with only 3 data points you can only make a rough assumption that this is the case as can be seen by comparing the two curves and assuming that there are straight lines between data. having said that the best fit trend line in this example is the exponential with R^2 value close to one, so take what you will from that.

Dave

 

I would imagine that we all agree that the foot is a complex structure which cannot be completely pigeon-holed into any specific type of mechanical design. Newtonian physics cannot be used as the only method of analysis to determine how and why feet function and actually work (most of the time). A gymnast performing an iron cross would have their arms torn apart by the forces present if not for the tension network surrounding the shoulder girdle.

Kevin wrote on a different thread in relation to calcaneal stress fractures in barefoot or minimalist runners. “The calcaneal stress fractures could very well be due to shear stresses, and not either to impact loads or bending moments.”

The case to which Kevin refers, when a calcaneus fractures during forefoot running, would be consistent with a failure of the tensegrity system with component fracture at 90 degrees to the force applied (Fuller, B, Synergenics II).

Kevin also described that compressive forces across joints are the likely cause of osteoarthritis. From my clinical perspective, I have always viewed osteoarthritis as more of a chronic repair process that a true degenerative one (vs. rheumatoid arthritis, for instance). If the injury is actually related to repetitive strain (as present in walking), would not the normal repair process be instituted on a repetitive basis? Further, why wouldn’t all joints become degenerated if it is strictly compressive load being applied? The normal function of a tensegrity structure requires flexible hinges at the discontinuous compression component interfaces. Loss of motion would result in a constant compressive force at a single location within any joint, thus causing damage repetitively. It would also cause the failure of the tensegrity structure. In the hundreds of hallux limitus cases I have treated over the years, joint DJD reduces when motion is restored to the 1st MTP joint.

The tension components with in the foot are vast and complex. The ability to distribute forces through the individual osseous components while managing the loads across an entire tension network (tendons, ligaments, fascia) represents an explanation to what we see daily. I can accept that this is not a tensegrity structure in its purest sense….but what then is it?

Howard

 

99% of the variance in Y is explained by the variance in X. Viz. the exponential model fits the data very well in this instance. But then, I'm guessing you designed it that way.:drinks

 

Simon

Yes;

so if in the same time frame +1 and you had double the sample rate (plus an additional one at the end) you might see that this curve, that contains the original data points, is not exponential.



Dave

 

Newtonian mechanics includes the concept of tension, and can along with the other mechanical laws explain the mechanical function of the foot, as it can that of tensegrity structures. I should sincerely hope that we can all agree that a gymnast performing the iron cross is not breaking the laws of mechanical physics, Howard.

 

Agreed, it comes down to the resolution, as you stated previously and the number of nodes that you fit the line to. So you could have a hundred co-ordinates but if you fit your line to only two of these, you'd get a linear equation, but the r square value might be low, i.e. the linear model does not fit the data very well (this is why I often complain when papers report poor correlations, but have only attempted to model the relationship between two variables using a linear model, and a statistical test which measures only the linear fit). As you add X terms to the equation, you increase the fit of the model (and obviously change it's geometric form), but at the expense of a degree of freedom per X term in your statistical analysis of the fit. No problem, if you've got lots of n=, but not so clever when your statistically analysing n=3.

What I should have liked to have seen in Daryl's paper should have been a plot of x versus y for all of the subjects together, with a line of best fit applied to the data for the whole sample, not a selected case by case, as was presented (in typical Daryl style, he seems to have done his calculations on the back of a fag packet! He's an excellent mathematician. Here's a true story- I was working through his linear equation for the STJ axis paper with a mate of mine who's also an excellent mathematician back in about 1993 when we came upon an error in one of the equations in the paper, I phoned Daryl to ask him about this- I was young and he was the first American podiatrist I had ever spoken with. I asked about it and he said, something along the lines of "Oh, I don't know, I just did it on my pocket calculator"- here was me with another now PhD scientist racking our brains to work out the maths and write a programme to solve the maths that Daryl had just knocked up on his pocket calculator- doh!). All the raw data seems to be there though in Daryl's paper, which Daryl is to be commended for. If I get time I might stick it into SPSS and see what's in there.

 

Howard could you clarify this please? Are you saying that DJD reduces as in a hyaline cartilage change (I assume that you are discussing foot orthoses and not cheilectomy?) or does not progress? How would you quantify this in vivo?

Sincerely,

 

My point is that you cannot determine, from a set of three data ponits, whether a relationship is "exponential" or not. Instead of an "exponential curve" the data could just as well represent two straight lines, both intersecting at the second data point. I think this was a very big assumption in this paper that three data points in an experiment could lead one to so confidently state the following:

1. "In 48 feet, showing a high degree of biomechanical variation, all demonstrated an exponential increase in the eversion of the forefoot to the rearfoot as the subtalar joint moved from its fully supinated position to its fully pronated position."

2. "An attempt was made to correlate the values of pronation to be a linear increase, not the exponential increase that we found."

3. "We have presented a study that was conducted in a clinical situation in which we quantitated the increase in the eversion of the locked position of the midtarsal joint as the subtalar joint was moved through its full range of motion. We established that the eversion increases in a natural exponential manner. Every degree of subtalar pronation produces an exponential increase in midtarsal joint instability."

Why couldn't the authors, just as well, have made the following statements in their paper from analyzing the data from their experiment?

1. "In 48 feet, showing a high degree of biomechanical variation, all demonstrated an intersecting straight line increase in the eversion of the forefoot to the rearfoot as the subtalar joint moved from its fully supinated position to its fully pronated position."

2. "An attempt was made to correlate the values of pronation to be a linear increase, not the intersecting straight line increase that we found."

3. "We have presented a study that was conducted in a clinical situation in which we quantitated the increase in the eversion of the locked position of the midtarsal joint as the subtalar joint was moved through its full range of motion. We established that the eversion increases in a natural intersecting straight line manner. Every degree of subtalar pronation produces an intersecting straight line increase in midtarsal joint instability."

So for all those who have confidently stated in the past that the "midtarsal joint range of motion increases exponentially with pronation of the subtalar joint"....I say....show me the data!!

 

The Iron Cross in rings in gymnastics can easily be analyzed using the principles of Newtonian mechanics (see attachment).

In addition, the combining of tension load-bearing elements and compression load-bearing elements to make more functional tools and structures are nothing new. The bow (i.e. bow and arrow) combines the tension load-bearing element of a bow string along with the compression load-bearing element of a bow to make a very useful tool that has been used probably for at least 10,000 years. Neither the Iron Cross nor the Bow and Arrow are examples of tensegrity.

 

Howard:

Good to see you contributing again on Podiatry Arena.

I basically agree with you here, Howard, but think we can more accurately model the foot and lower extremity not as a "tension network" but rather as a "tension-compression network". The tension forces within the muscles, tendons, ligaments and fascia could not occur without compression forces within the bones and joints. Therefore, to just analyze the foot and lower extremity as a "tension network" is really only looking at about one half of the whole picture. In order to analyze and model the biomechanical function of the foot and lower extremity properly and more completely, the mechanical effects of soft tissue tension foreces on bone and joint compression forces and the mechanical effects of bone and joint compression forces on the tension forces within the muscles, tendons, ligaments and fascia must also be considered.

I do agree with you that the concept of "tensegrity" is a very interesting concept and certainly is important to understand when one starts to consider how tension-compression networks can be utlized either in both inanimate and biological systems to allow certain structural and functional properties to occur. However, in the human body, the concept of "tensegrity" is much too constraining, in my opinion, to scientifically analyze the biomechanical function of any of the joints of the body since a true "tensegrity structure" does not allow any "joint" compression forces between its compression elements and does not also allow any bending moments on its compression elements.

I prefer to analyze the mechanical interplay between compression and tension forces within the human body, along with the shear forces, in order to gain a more complete and accurate model of the biomechanical function of the foot and lower extremity.:drinks

 

I will try to state this as simple as I can. Refering to my article, figures 23-a,b, should answer a lot. Joint surfaces are slippery. It is hard to stop motion on ice. When the joint is wrung, it does something very interesting. It takes objects(ligaments, bones) that are static in length and size and shortens/lengthens their position relative to one another. This tension induces compression and bottoms out the Range of motion. If one where to measure the amount of motion of joints, combined in series, the total amount of motion would be a sum of the degrees of motion of each of the joints in series. i.e. 5 degrees of motion in the first joint, plus five degrees of motion in the next joint, equals a combined degrees of motion of 10. In the foot, with progressive, STJ supinatory motion, we see a progressive decrease in the amount of forefoot motion. Simply stated, this is a result of a progressive reduction of slack in the static length of the surrounding joint ligaments, in the series. This is why the wringing effect is so important. Twisting is a uniplanar motion. Wringing, on the other hand, takes into effect all 3 planes at once. A 3D model has to be functional in all 3 planes at once. That will include a translation/shifting on itself. That is why the conical double helix fits so well. The helix will allow its opposing legs to basically occupy the same relative space, at the same time. They can slide and rotate past each other. For sake of an overly simplified example, this is what a nut and bolt interface is. It is a simple machine. This fits with the open/closed pack position described in the glossary of the paper. As for the conical nature, I believe this is part of what changes the amount of motion or bottoming out of the foot range of motion. It creates compression between the legs, as it wrings together. One example, that I forgot to mention, is tapered threads, as seen on an oil drilling rig. This tapered approach allow the meshing of the full amount of threads in less than a full 360 degree turn, rather than, say, 8 full rotations. The bite on the full length of threads is just as strong as a regular straight thread, but only took a partial rotation to engage all the threads.
As for the 4-D studies, I have been researching this for about two years. It is available and I have been in contact with individuals that can do this. It is cost prohibitive at this time. About $50-75,000.
As for why do we need to be precise, as to the functional model of the foot? For one, the confusion as to how to talk with one another, about foot function ,will certainly not be clarified, until we do. Also, "we dont know what we dont know." To declare it all settled, would be overly presumptive.

 

Even though I am not getting a lot out of Paul's explanations of his Wring Model, I did attend a good lecture this weekend on the Twisted Plate Theory of Sarrafian at Paul Scherer's Learning in the Vineyards Seminar in Napa, California.

Doug Richie gave a well-received lecture on Sarrafian's Twisted Plate Theory and also mentioned the Lamina Pedis from MacConnaill in 1954. However, I didn't hear him mention anything about a "Wring Theory" or a "Wring Model".

I'm sending an e-mail to Doug today to see if he wants to come on to Podiatry Arena to give us his opinions on what he thinks of the "Wring Model" and to better explain how the "Twisted Plate Model" might help the clinician better understand foot function.

 

I will refer you to figure 28-a,b,c. In this example, I am holding a beaded necklace in my hands. Without the twisting, my hands can slide freely. By simple twisting of the necklace in my hands 180 degrees, the amount motion between my hands is significantly reduced. This is why the wring theory is very important to understanding foot function.

 

What's the difference between saying the above and saying that when a ligament becomes tight it limits further motion in a direction. There is still plenty of motion in the opposite direction to the twist. I prefer talk abut specific anatomical structures and specific directions of forces applied to those structures. If you get to far away from the anatomy there is the danger of magical thinking, for example locked and unlocked joints.

Eric