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In Thought Experiment #3, the medially deviated STJ axis foot and centrally located STJ axis foot from Thought Experiment #2 are used to demonstrate the mechanical effects of STJ axis medial deviation on the tensile forces required within the posterior tibial muscle/tendon to initiate supination of the foot.

In both models, the posterior tibial muscle is illustrated as a superiorly directed force (F1 in the medially deviated STJ axis foot and F3 in the central STJ axis foot) that is attached to the medial aspect of the foot and exerts both a superiorly directed force on the medial foot and an inferiorly directed force on the tibia (it is attached to the medial-superior tibia by the dotted line). [It can be assumed that even though the posterior tibial muscle force will tend cause an valgus moment on the proximal tibia, this rotational force on the tibia should be ignored since the tibia is stabilized by the knee above it.]

Also, in both models, the individual has decided that they want to exert enough supination moment across the STJ by contracting their posterior tibial muscle so only 100 N of ground reaction force (GRF) is on the medial weightbearing surface of the foot. The total GRF on each foot is 400 N with 300 N of GRF on the lateral weightbearing surface of the foot.

The posterior tibial muscle is given to insert 3 cm medial to the STJ axis in the medially deviated STJ axis foot and 5 cm medial to the STJ axis in the central STJ axis foot. [The STJ axis is 2 cm more medial in the medially deviated foot than in the central STJ axis foot.]

The force acting vertically downward on the STJ axis in the medially deviated STJ axis foot, F2, and the central STJ axis foot, F4, can be calculated by assuming that the foot has no mass.

Here are my questions for Thought Experiment #3:

1. What is the posterior tibial muscle force, F1, required for the medially deviated STJ axis foot to allow the foot to stand with 300 N laterally and 100 N medially?

2. What will be the downward vertical force (F2) on the STJ axis (i.e. STJ axis compression force) in this foot once the posterior tibial muscle causes the lateral shift in the GRF as given?

3. What is the posterior tibial muscle force, F3, required for the central STJ axis axis foot to allow the foot to stand with 300 N laterally and 100 N medially?

4. What will be the downward vertical force (F4) on the STJ axis (i.e. STJ axis compression force) in this foot once the posterior tibial muscle causes the lateral shift in the GRF as given?

5. What mechanical factor(s) cause the medially deviated STJ axis foot to need such high magnitudes of PT muscle force to try to supinate the medial forefoot off of the ground?

6. Which foot would be most likely to develop posterior tibial dysfunction? Why?

7. Which foot would have more compressive force at the STJ axis when it tries to supinate the medial forefoot off of the ground? Why? What possible deletorious effects might this have on the joint surfaces of the STJ in each foot?

Good luck and happy calculating. :)

Attached Images

Thought Experiment 3.jpg (83.8 KB, 355 views)

__________________
Sincerely,

Kevin

**************************************************
Kevin A. Kirby, DPM
Adjunct Associate Professor
Department of Applied Biomechanics
California School of Podiatric Medicine at Samuel Merritt College

e-mail: kevinakirby@comcast.net

Private Practice:
107 Scripps Drive, Suite 200
Sacramento, CA 95825 USA
My location

Voice: (916) 925-8111 Fax: (916) 925-8136
**************************************************

Dear Kevin,

I said that I would have a go at this next one and not be so chicken...

I am having trouble working out the compression force at the STJ, so do you have any clues for how to calculate this?

1. F1 = 133.3N

2. ? 200N ?

3. F3 = 80N

4. ? 300N ?

5.The moment arm for the PT muscle is short (close to the STJ axis) so this creates a mechanical disadvantage, requiring the PT muscle to exert a much greater force to supinate the STJ (compared with a central or laterally deviated STJ axis). The pronatory force in a medially deviated STJ axis is also greater, (from Thought Experiment #2) so the PT muscle has to work harder to overcome this force and produce supination.

6. The medially deviated STJ - because the PT muscle has to constantly produce larger amounts of force through a mechanically disadvantaged position, which over time would lead to degeneration of the tendon.

7. The medially deviated STJ - because the PT muscle would be working less efficently and possibly causing more translational force/friction as well as compression force.

Am I heading in the right direction here with my answers or am I in the middle of nowhere ?

Regards

Donna

Donna:

I really like your interest and effort in trying to solve this problem. Compared to many others who have looked at the problem and have not attempted to solve it, I admire your courage.

My purpose in presenting these types of problems on Podiatry Arena is to begin introducing podiatrists to the concept of free body diagrams and modelling techniques which are used commonly within engineering and biomechanics to predict the internal forces within a structure/machine. I am trying to present some fairly simple problems that a first year engineering student should be able to "do in their sleep". However, for someone who has not been an engineering student or a graduate student in biomechanics and is not familiar with the conventions and "tricks" used to solve problems such as these, problems such as this seem unsolvable.

I like your answers to questions #5 and #6. However, your other answers are not correct. Instead of giving away the answers quite yet, let me give you some hints on how to solve the problem.

First of all, the best way to solve the problem such as this is to realize that all the vertically oriented forces must equal 0 (upward forces must equal downward forces) since the foot and leg are in equilibrium and not accelerating (this would also apply to horizonatal forces but I have conveniently removed them to simplify the problem in this case). In other words, in the medially deviated STJ axis foot the following equation applies and in the central STJ axis foot The next step is to find F1 and F3, the PT muscle/tendon tensile force. To find F1 and F3, you must make the counterclockwise moments acting around an arbitrary axis become equal in magnitude to the clockwise moments acting around the same axis. Since a moment is equal to force x moment arm, then in the medially deviated STJ axis foot, for example, the clockwise moment for the PT muscle/tendon tensile force across the STJ axis would be 3 cm x F1, and the counterclockwise moment across the STJ axis for the 300N lateral GRF would be 6 cm x 300N = 18.0 Nm. If you can construct an equation to make the counterclockwise moments be equal to the clockwise moments then you can solve for F1 and then question #1 will be answered for you. Then use the value for F1 to plug into the equation F1 + 100N + 300N = F2 and you will be able to solve for F2 and answer question #2. These same techniques can then be used to solve for the values in the central STJ axis location foot.

Keep up the good work, Donna. Others are also welcome to attempt to solve Thought Experiment #3.

__________________
Sincerely,

Kevin

**************************************************
Kevin A. Kirby, DPM
Adjunct Associate Professor
Department of Applied Biomechanics
California School of Podiatric Medicine at Samuel Merritt College

e-mail: kevinakirby@comcast.net

Private Practice:
107 Scripps Drive, Suite 200
Sacramento, CA 95825 USA
My location

Voice: (916) 925-8111 Fax: (916) 925-8136
**************************************************

Tomorrows lecture to the 2nd yrs is on 'planal dominance' - they ALL will be trying to solve the problem

CP

I would be interested in finding out how many of your students can solve this problem. Maybe extra credit??

__________________
Sincerely,

Kevin

**************************************************
Kevin A. Kirby, DPM
Adjunct Associate Professor
Department of Applied Biomechanics
California School of Podiatric Medicine at Samuel Merritt College

e-mail: kevinakirby@comcast.net

Private Practice:
107 Scripps Drive, Suite 200
Sacramento, CA 95825 USA
My location

Voice: (916) 925-8111 Fax: (916) 925-8136
**************************************************

Donna and Colleagues:

The force within the PT muscle/tendon is over 3 times greater in the medially deviated STJ axis than in the central STJ axis foot.

__________________
Sincerely,

Kevin

**************************************************
Kevin A. Kirby, DPM
Adjunct Associate Professor
Department of Applied Biomechanics
California School of Podiatric Medicine at Samuel Merritt College

e-mail: kevinakirby@comcast.net

Private Practice:
107 Scripps Drive, Suite 200
Sacramento, CA 95825 USA
My location

Voice: (916) 925-8111 Fax: (916) 925-8136
**************************************************

Dear Kevin,

I hope my maths/physics isn't as shocking this time around...it does make more sense the way you explained it, with clockwise vs counter-clockwise calculations...let's hope I can add and multiply

F1 = 533.3 N
F2 = 933.3N
F3 = 160N
F4 = 560N

Q7 is still stumping me, maybe it's my lack of spatial ability with interpreting diagrams

Donna :)

You are awesome, Donna. All values are correct.

The foot with the more medially deviated STJ axis would develop more STJ compression force when the PT muscle is used to attempt to supinate the medial forefoot off of the ground. This is due to the greater PT muscle force required to initiate STJ supination and the concomitantly greater downward pull from the PT muscle (from its origin), causing the tibia to be pulled harder downward onto the STJ.

Increased compression forces in joints lead to increased joint pressures [pressure = force/surface area) which is the most common cause of degenerative joint disease in weightbearing joints. Therefore, the STJ which is medially deviated may also have increased joint pressure due to the non-central alignment of the STJ which may, in turn, cause or accelerate the formation of DJD in the joint.

I wonder what the elastic limit is on stress-strain curve for the posterior tibial tendon (i.e. at what magnitude of tensile stress will the posterior tibial tendon start to show plastic deformation and/or failure)? This would help explain the mechanical etiology of posterior tibial tendon dysfunction.

__________________
Sincerely,

Kevin

**************************************************
Kevin A. Kirby, DPM
Adjunct Associate Professor
Department of Applied Biomechanics
California School of Podiatric Medicine at Samuel Merritt College

e-mail: kevinakirby@comcast.net

Private Practice:
107 Scripps Drive, Suite 200
Sacramento, CA 95825 USA
My location

Voice: (916) 925-8111 Fax: (916) 925-8136
**************************************************

Aww shucks you're embarrassing me! I did have a lot of clues after all...
Looking forward (kind of :p ) to the next one, my brain is slowly remembering bits and pieces of high school/uni physics!

To complete the questions that Donna correctly answered, here is the way I would have answered the questions:
F1 = 533.3 N


F2 = 933.3 N


F3 = 160 N


F4 = 560 N


First of all, the PT tendon has a decreased moment arm by which to produce STJ supination in the medially deviated STJ axis foot and the 300 N GRF plantar to the lateral weightbearing structure of the foot has a longer arm by which to produce STJ pronation. This combined with the vertically directed force from the talo-tibial unit (F2) acting on the STJ axis at a more medial location relative to the plantar foot causes the increased magnitude of PT muscle/tendon force required to unload the medial foot and attempt to supinate the medial foot off the ground.


The medially deviated STJ axis foot would be most likely to develop PT dysfunction since this foot requires 3.3 times the force within the PT tendon in order to shift the GRF more laterally under the plantar foot so that 300 N is lateral and only 100 N is medial. This increase in tensile force required to initiate supination in the medially deviated STJ axis foot would tend to lead to increased tensile stress within the PT tendon and would greatly increase the tendency for plastic deformation and/or tearing injuries of the PT tendon to occur during weightbearing activities.


The foot with the more medially deviated STJ axis would develop more STJ compression force when the PT muscle is used to attempt to supinate the medial forefoot off of the ground. This is due to the greater PT muscle force required to initiate STJ supination and the concomitantly greater downward pull from the PT muscle (from its origin), causing the tibia to be pulled harder downward onto the STJ.

Increased compression forces in joints lead to increased joint pressures [pressure = force/surface area) which is the most common cause of degenerative joint disease in weightbearing joints. Therefore, the STJ which is medially deviated may also have increased joint pressure due to the non-central alignment of the STJ which may, in turn, cause or accelerate the formation of DJD in the joint.

Hope this Thought Experiment has helped you all to better visualize the mechanical concepts of STJ axis deviation.

__________________
Sincerely,

Kevin

**************************************************
Kevin A. Kirby, DPM
Adjunct Associate Professor
Department of Applied Biomechanics
California School of Podiatric Medicine at Samuel Merritt College

e-mail: kevinakirby@comcast.net

Private Practice:
107 Scripps Drive, Suite 200
Sacramento, CA 95825 USA
My location

Voice: (916) 925-8111 Fax: (916) 925-8136
**************************************************

Colleagues:

I must remind you all that it is not extremely critical that you know how to solve these problems in order to effectively treat mechanical problems of the foot and lower extremity since it is the concepts that are important, not the calculations. However, I have always found that for myself, when I have forced myself to sit down and try to understand the physics principles and then develop the mathematical formulas to do the calculations, that I have gained a much deeper understanding of the mechanical nature of the foot.

I have been teaching this material now for over 20 years and am still trying to find a way to better educate a larger percentage of podiatrists on the mechanics of the foot using these concepts. I am hoping that this series of Thought Experiments in Podiatry Arena that utilize the concepts of modelling and modified versions of free body diagram analysis will allow the clinician to understnd these concepts more completely.

__________________
Sincerely,

Kevin

**************************************************
Kevin A. Kirby, DPM
Adjunct Associate Professor
Department of Applied Biomechanics
California School of Podiatric Medicine at Samuel Merritt College

e-mail: kevinakirby@comcast.net

Private Practice:
107 Scripps Drive, Suite 200
Sacramento, CA 95825 USA
My location

Voice: (916) 925-8111 Fax: (916) 925-8136
**************************************************

They are quite good. One question Kevin relating to your quote "This increase in tensile force required to initiate supination in the medially deviated STJ axis foot would tend to lead to increased tensile stress within the PT tendon and would greatly increase the tendency for plastic deformation and/or tearing injuries of the PT tendon to occur during weightbearing activities."

When would we use the term 'contractile forces' in relation to this? Does this relate to the muscle unit etc.? Or is it just much of a muchness.


And while we are here, your explanation for the onset of degenerative joint changes make some sense. But how does the compressive forces that a mechanically disadvantaged PT invoke, compare with average GRFs absorbed by an ADL such as walking on concrete for instance.

And dear I say, that your common sense theory would be at odds with a bulk of Australian physiotherapists (who probably confuse force with a pair of fours) who keep telling us that stronger active muscles provide "stability" to joints...which is the panacea of every mechanical problem.

Ron

Ron:

My example for the PT is not necessarily physiologic since the PT tendon can not probably withstand 533 N of tensile force without tearing. However, the point was to show how a medial axis location would increase the demands on the PT tendon to supinate the foot.

In addition, the point of me including the F2 and F4 compressive forces was for the reader to consider the effects of STJ axis deviation on the effects of the STJ compression force caused by increased demands on the muscles surrounding the STJ. I believe that a more centrally located, more normal STJ axis location would tend to decrease the STJ (and ankle joint) compression forces because of decreased demands on the invertors and evertors in order to supinate and pronate the foot during weightbearing activities.

Contractile forces refers to actively generated actin-myosin cross bridge forces and, in my example, would also include the serial elastic element passively generated tensile forces cause by muscle/tendon elongation. Of course these two factors always combine to cause the force within the tendon so I hope this convention is not confusing to the reader.

And, by the way, I would agree with your physiotherapist colleagues that stronger muscles do improve the "stability" of joints.....in fact, this sounds like a good topic for a future Thought Experiment. Thanks for that.

__________________
Sincerely,

Kevin

**************************************************
Kevin A. Kirby, DPM
Adjunct Associate Professor
Department of Applied Biomechanics
California School of Podiatric Medicine at Samuel Merritt College

e-mail: kevinakirby@comcast.net

Private Practice:
107 Scripps Drive, Suite 200
Sacramento, CA 95825 USA
My location

Voice: (916) 925-8111 Fax: (916) 925-8136
**************************************************

Oh no!.


I reckon a good thought experiment could be that you track through your patient histories, and pick out some case studies and approach them retrospectively...in a sequential problem solving manner.

Day 1. Signs and symptoms...tests...treatment........response.

Session 2... etc. Better/same/worse....tests....plan b....response


Of course, it would give us a chance to stand in your shoes, so that you may add bit by bit over days, to allow us to insert what we would do... or how we would approach the relevant obstacle.


To generalise, I don't think we know what to do when the textbook plan a fails. And most of us view non-conventional options like dracula views a wooden stake.


Sometime complex radical conditions require weird adjuncts. I am sure you have seen a few, and solved a few.

Bloody hell...

Evening all, sorry about the above, but it's quite late obe, oops, over, here. I'll have a more considered look and view in the near future. May I just take this opportunity to thank my good friend Mr Mark Russell for pointing out this really good thread. Rock'n'roll. Currently listening to Jason and the Scorchers. Thank you and Goodnight. Sammy