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Thought Experiment #4: Effect of STJ Axis Location on Sinus Tarsi Compression Forces

Discussion in 'Biomechanics, Sports and Foot orthoses' started by Kevin Kirby, Mar 25, 2006.


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    In Thought Experiment #4, the models of the foot have been modified from Thought Experiments #2 and #3 to now include a buttress of bone on the foot that is 2.0 cm lateral to the STJ axis in the area of the sinus tarsi of the foot. This buttress of bone on the foot acts as a "bumper" to prevent further STJ pronation past the maximally pronated position and is meant to model the approximate anatomical location of where the lateral process of the talus abuts against the floor of the sinus tarsi of the calcaneus when the maximally pronated position of the STJ is reached. [It would be very helpful to read the following 2 papers in order to better understand the clinical significance of this Thought Experiment: Kirby KA: Rotational equilibrium across the subtalar joint axis. JAPMA, 79: 1-14, 1989; Kirby KA: Subtalar joint axis location and rotational equilibrium theory of foot function. JAPMA, 91:465-488, 2001.]

    In the foot with the moderate medially deviated STJ axis (left), the STJ axis is 2 cm lateral to the medial weightbearing surface of the foot and 6 cm medial to the lateral weightbearing surface of the foot. In the foot with the mild medially deviated STJ axis (right), the STJ axis is 2.9 cm lateral to the medial weightbearing surface of the foot and 5.1 cm medial to the lateral weightbearing surface of the foot. In other words, the foot with the moderate medial STJ axis devation (left) is 9 mm more medial than the foot with mild STJ axis deviation (right).

    In the foot with the moderate medially deviated STJ axis, the vertically-directed compression force acting through the STJ axis is F1 and the vertically-directed compression force acting through the sinus tarsi is F2. In the foot with the mild medially deviated STJ axis, the compression force acting through the STJ axis is F3 and the compression force acting through the sinus tarsi is F4. In both of the feet, the ground reaction force (GRF) acting plantar to the medial weightbearing surface of the foot is 250 N and the GRF acting plantar to the lateral weightbearing surface of the foot is 150 N. Both feet are given to be in translational and rotational equilibrium.

    Here are my questions for Thought Experiment #4:

    1. Are compression forces from the talo-tibial unit (F2 and F4) acting vertically downward on the foot (i.e. calcaneus) causing a STJ pronation moment or a STJ supination moment? What motion would occur at the STJ if forces F2 and F4 were to suddenly be removed or dissapear?

    2. What is the magnitude of compression forces acting at the STJ axis (F1) and sinus tarsi (F2) in the foot with the moderate STJ axis deviation?

    3. What is the magnitude of compression forces acting at the STJ axis (F3) and sinus tarsi (F4) in the foot with the mild STJ axis deviation?

    4. Why does increased medial deviation of the STJ axis cause a change in the compression forces acting at the sinus tarsi (F2 and F4)?

    5. Why does a change in STJ axis position cause a change in the compression force acting across the STJ axis (F1 and F3)?

    6. What clinical symptoms in the area of the sinus tarsi might more likely to occur in a patient with a significantly medially deviated STJ axis when compared to a patient with a more normal STJ axis location? What mechanical stresses acting on which anatomical structures would be the most likely cause of these clinical symptoms?

    A much greater appreciation of the mechanical importance of this Thought Experiment will be gained by studying the anatomy of the sinus tarsi in both the maximally pronated STJ position and neutral position. It may be helpful to get out your foot skeleton and study it. Happy calculating!
     
  2. Anyone interested in taking a guess at this Thought Experiment? It's interesting to see how little the STJ axis needs to move relative to the plantar foot before it causes quite a difference in the internal forces within the foot.
     
  3. Donna

    Donna Active Member

    Hi Kevin,

    I have done a few calculations and am not sure if I have done it right or just made a big mess of it all... :( Every time I look at it I change my mind about the numbers and calculations :confused:

    I have been calculating it as:
    F1 = 250 + 150 +F2
    F3 = 250 + 150 + F4,
    but the numbers just look too wrong :confused:

    1. Supination moment...if F2 and F4 are removed then the STJ will pronate, more on the moderate than the mildly medially deviated STJ axis.

    2. F1 = 850N, F2 = 450N

    3. F3 = 782.5N, F4 = 382.5N

    Am I heading in the right direction here? Please stop me before I end up too far away from the answer! :eek:

    Regards

    Donna
     
  4. Donna:

    No you're not going the right direction.......

    First of all, the vertical forces must all add up to be equal to 0 since the foot is in equilibrium. Therefore, for the moderate medially deviated STJ axis foot, the following is your first equation: F1 + F2 = 150N + 250 N = 400N.

    For the second equation for the moderate medially deviated STJ axi foot, produce another equation containing just F2, with the assumption that the pronation (counterclockwise) moments across the STJ axis must be equal to the supination (clockwise) moments acting across the STJ axis. This is really not much different than how you set up the equation for Thought Experiment #3 with the PT tendon.

    I know you can do this one!
     
  5. Donna

    Donna Active Member

    Hi Kevin,

    The first time I calculated these numbers, I got the results:

    F1 = 250 + 150 - F2
    F3 = 250 + 150 - F4

    F1 = 200N
    F2 = 200N
    F3 = 380N
    F4 = 20N

    Is this closer??? :confused:

    Regards

    Donna :eek:
     
  6. Donna:

    You are becoming a foot biomechanics wizard.....yes these are correct!! Now, give a go at the other questions when you have a chance.
     
  7. Donna

    Donna Active Member

    Hi Kevin

    Umm I don't know about being a wizard, I feel more like a trainee at the moment... :eek:

    1. To me it still looks like the F2 and F4 forces would be causing a supination moment as they are lateral to the STJ axis...am I maybe visualising this the wrong way? :confused:

    4. Increased medial deviation of STJ axis increases the lateral/supination moment arm length, which increases the compression force at the sinus tarsi because moment arm x GRF = moment torque,
    In the moderately medially deviated STJ, the lateral moment will be 150N x 0.06m = 9Nm...
    In the mildly medially deviated STJ, the lateral moment will be 150N x 0.051 = 7.65Nm...

    I'll get back to you on those other ones :p Need some more time to think about the others!

    Regards

    Donna :)
     
  8. Here are my questions for Thought Experiment #4:

    1. Are compression forces from the talo-tibial unit (F2 and F4) acting vertically downward on the foot (i.e. calcaneus) causing a STJ pronation moment or a STJ supination moment? The vertically downward directed sinus tarsi compression forces acting on the simulated floor of the sinus tarsi of the calcaneus (F2 and F4) cause a STJ supination moment.

    What motion would occur at the STJ if forces F2 and F4 were to suddenly be removed or dissapear?
    STJ pronation acceleration would occur. Since a sudden decrease in STJ supination moment would cause a net increase in STJ pronation moment, the conditions of rotational equilibrium would be violated since the pronation and supination moments would not be exactly counterbalanced, thus allowing an acceleration of pronation motion to occur.

    2. What is the magnitude of compression forces acting at the STJ axis (F1) and sinus tarsi (F2) in the foot with the moderate STJ axis deviation?
    F1 = 200N; F2 = 200N

    3. What is the magnitude of compression forces acting at the STJ axis (F3) and sinus tarsi (F4) in the foot with the mild STJ axis deviation?
    F3 = 380N; F4 = 20N

    4. Why does increased medial deviation of the STJ axis cause a change in the compression forces acting at the sinus tarsi (F2 and F4)?
    Increased medial deviation of the STJ axis has two very specific effects on the two forces acting on the plantar foot. First of all, the medial STJ axis deviation increases the pronation moment arm for the GRF acting on the lateral forefoot which will increase the magnitude of STJ pronation moment. Secondly, the medial STJ axis deviation decreases the supination moment arm for the GRF acting on the medial forefoot which will decrease the magnitude of STJ supination moment. These two effects, when combined, cause the net increase in STJ pronation moment that increases the compression force at the sinus tarsi (F2 and F4) that occurs with medial STJ axis deviation.

    Any more thoughts on the other questions??
     
  9. Donna

    Donna Active Member

    Hi Kevin,

    I'm not really sure exactly how to answer number 5...but I'll take a stab at it anyway... :eek:

    5. The STJ compression forces change because the amount of compression force in the sinus tarsi also changes. The differences in pronation moment is 10 times greater in the more medially deviated STJ axis foot (4Nm) compared with the mildly medially deviated STJ foot (0.4Nm), so the STJ has more compression forces through it in the mildly medially deviated foot as the sinus tarsi absorbs less compression force in this case (20N compared with 200N in the more medially deviated STJ foot).

    STJ compression = 250 + 150 - sinus tarsi compression
    So the greater sinus tarsi compression is, the less STJ compression is and vice versa.

    (The more medially deviated STJ axis creates a resultant of 4Nm pronation moment (250N x 0.02m = 5Nm supination moment and 150N x 0.06m = 9 Nm pronation moment), and the mildly medially deviated STJ axis creates a resultant of 0.4Nm pronation moment (250 x 0.029m = 7.25Nm supination moment and 150 x 0.051 = 7.65 Nm pronation moment).)

    I know that my expression of physics is shocking, but hopefully some of my thought processes are decipherable from all that jumble up there^ :confused:

    Regards

    Donna
     
  10. Donna:

    I like your answer. However, the answer that I was looking for was this: the STJ compression force added to the sinus compression force will always equal the GRF on the plantar foot (assuming equilibrium conditions). Therefore, as the sinus tarsi compression force increases with medial STJ axis deviation, the STJ compression force will need to decrease since both of these forces must add up to equal 400N. When there are no sinus tarsi compression forces present, such as when there is a more normal STJ axis location, then 400 N of STJ compression force will be present.

    I hope that others have been able to follow these Thought Experiments and understand the models. It is a lot of work on my part, but I think if these little mental exercises are stimulating a number of podiatrists and other clinicians to start thinking in this fashion, then maybe we will be making some headway in improving the knowledge level of those who treat mechanical dysfunction of the foot and lower extremity on a daily basis.

    By the way, when we start adding foot orthoses to the model, then it should get even more interesting and clinically relevant.
     
  11. Donna

    Donna Active Member

    Thanks Kevin, it sounds so much more sensible when you put it that way :D

    Still thinking about how different mechanical stresses would be affecting the sinus tarsi pain, I'm thinking there may be talocalcaneal ligament strain secondary to pronation :eek: ...I haven't seen many cases of sinus tarsi pain myself though :confused: ...maybe someone else might like to do Q6 since I am kind of hogging the answer box here! :cool:

    Regards

    Donna
     
  12. Donna:

    You seem to be the only one interested enough or brave enough to attempt an answer. Without your interest, I wouldn't bother spending the time doing all of this for Podiatry Arena. It has been a pleasure working with you.

    Here's question #6:

    6. What clinical symptoms in the area of the sinus tarsi might more likely to occur in a patient with a significantly medially deviated STJ axis when compared to a patient with a more normal STJ axis location? The increased compression forces within the sinus tarsi will tend to cause sinus tarsi syndrome or pain within the sinus tarsi during weightbearing activities.

    What mechanical stresses acting on which anatomical structures would be the most likely cause of these clinical symptoms?Compression stress on either the floor of the sinus tarsi of the calcaneus or at the lateral process of the talus and/or compresion stress on the multiple soft tissue structures of the sinus tarsi (i.e. capsule of posterior talocalcaneal joint, interosseous talocalcaneal ligament, cervical ligament, root of inferior extensor retinaculum, extensor digitorum brevis origin) would be the most likely cause of the symptoms that we call "sinus tarsi syndrome" or "sinus tarsitis".
     
  13. Donna

    Donna Active Member

    Hi Kevin,

    I'm sure I'm not the only one who's interested in the Thought Experiments :eek: , judging by the number of views that each one has had! :) It's interesting to see the concepts broken down into physics equations, makes you think outside the square... :D

    Regards

    Donna
     
  14. Donna:

    I guess you may be right. However the numbers may indicate simply those people who visited the discussion, saw the physics and math involved, and then quickly exited before their brains had a melt-down. ;)
     
  15. Donna

    Donna Active Member

    Brain meltdown is not as painful as it sounds :eek: and it is nice to get positive feedback at the end of it all :cool:

    Bring on the next brain meltdown! :D

    Regards

    Donna
     
  16. David Smith

    David Smith Well-Known Member

    Kevin and Donna

    I would say there are two catagories of non contributors in this thread.
    Those who have no difficulty with the problems and don't want to spoil the 'fun'.
    Those who would like to join in but are too embarrased to be wrong 'on air'.

    To that second group I would say " you only win when your prepared to lose"
    and at the moment Donna is winning hands down.

    Forums like this, with all the learned contributors like Craig and Jeff and Eric and Simon and Kevin M and Kevin K et al, are a wonderful source of education
    Prof Kevin K is putting in time and effort to pass on his knowledge FREE of CHARGE, grab with both hands these opportunities that come your way, many have paid top dollar for such learning. This is almost a free lunch you just have to be prepared to pay with a little effort and possible embarrasment.

    So if there are interested parties out there? if I may, here are some tips which may help.

    In 2D analysis there are three equations of eqilibrium.That is, all forces must add up to zero. There must always be equilibrium.
    2 for translational (straight line) forces and one for rotational forces (moments)

    I think to more easily calculate these forces it is better to forget the cardinal planes and axes and use a global reference frame.
    Therefore instead of saggital, coronal/frontal, transverse and flexion/extension, adduction/abduction, internal and external rotation, Just imagine a global (ground reference) orthoganal ( right angle ) axes set of X, Y, Z. So in a 2D analysis there are two translational forces Y vertical and X horizontal and one rotational Z.
    Then forces and moments can have a positive or negative value in terms of direction.
    Y forces in an upward direction are positive, X forces from left to right are positive. The Z axis is imagined coming straight out of your screen or paper and moments are positive in the anticlockwise direction.

    The equations therefore are

    (Sum of +Fy) + (Sum of -FY) = 0 .... F = Force M= Moment * = multiply
    (Sum of +Fx) + (Sum of -Fx) = 0
    (Sum of +Mz) + (Sum of -Mz) = 0

    Moments = [Net sum of (all individual FY*their moment arms)] + [Net sum of (all individual FX * their moment arms)]= 0

    Or some find it easier to think in terms of Anticlockwise and clockwise moments which =

    (Sum of (+)acw forces * moment arms) + (sum of (-)cw forces *moment arms) = 0

    It is assumed in static analysis that there are no accelerations or inertial forces.

    So then make a simple diagram of the segment you are intersted in eg the foot (and nothing else). Put in the point of rotation of interest eg the STJ then add in the forces applied to the segment and relevant dimensions (already done for you in Kevins diagrams except Kevin has added the lower leg segment for clarity)
    This is a freebody diagram and is a MOST EXCELLENT tool for analysis type problems Dude.
    In this way it does not matter if your analysis is of a foot or banana or a bridge the calculation of forces and moments are the same


    Hope this is not taken as patronising, just trying help.

    Cheers Dave Smith
     
    Last edited: Mar 30, 2006
  17. Dave:

    Thanks for the comments. I don't think there are many like you, with a prior engineering background, reading these Thought Experiments so I assume that most of those looking at these problems don't want to attempt the problem since they find the problem too difficult to solve. The math is not that difficult...it is more a problem of setting up the equations correctly which you have so nicely detailed.

    Maybe when I get a chance (probably in another lifetime) it would be nice to take some engineering classes to more fully learn engineering concepts, rather than having to learn them on my own by reading books.

    And I absolutely love one of your last comments "In this way it does not matter if your analysis is of a foot or banana or a bridge the calculation of forces and moments are the same." I think that a free body diagram of a banana under 400N of load would be an interesting Thought Experiment. Maybe a graphite-laminate banana would be able to handle that type of load....even though it would probably drive a hungry chimpanzee crazy. ;)
     
  18. MikeM

    MikeM Member

    Kevin:

    I have been working on this problem for the last few days and came to the same answer as Donna for the rotational forces acting around the sinus tarsi and STJ axis ie. (The more medially deviated STJ axis creates a resultant of 4Nm pronation moment (250N x 0.02m = 5Nm supination moment and 150N x 0.06m = 9 Nm pronation moment), and the mildly medially deviated STJ axis creates a resultant of 0.4Nm pronation moment (250 x 0.029m = 7.25Nm supination moment and 150 x 0.051 = 7.65 Nm pronation moment).)
    I also came to the same conclusions on questions 1, 4, 5 and 6. But could you please explain how you came about the answers for questions 2 and 3. I am having trouble understanding how F1 and F2 can be the same (200N), as F2 is actually working with a 2cm lever arm whereas F1 is working perpendicular through the STJ axis. The same is also occurring with F3 and F4 (F3 through the STJ axis and F4 through the sinus tarsi) so really the actual location of the STJ axis shouldn't be having a bearing on the downward forces. It should only affect the GRF's as these are the forces that the change in STJ axis location affects due to the changes in moment arms.

    Thanks,
    Mike
     
  19. Mike:

    In this problem, the STJ axis, since it is modelled as a hinge, may have either a compression force or a tensile force acting on it, whereas, the sinus tarsi may only have a compression force, since it is not modelled as a hinge. Depending on the relative distribution of GRF on the plantar foot, the values for F1 and F2 (or F3 and F4) will change. The value for F1 or F3 could actually be a negative value indicating a tensile force at the STJ axis if most the GRF was laterally. Therefore, having F1 = F2 is not unusual considering I set up the experiment to be that way.

    You could also solve for the rotational forces when setting up your equations by choosing the sinus tarsi, or any point between the GRFs, as being an "axis of rotation". Go ahead and try using the sinus tarsi as the axis of rotation and solve the equation, and you will get the same results for the unknowns.
    Remember, F1 + F2 and F3 + F4 will always equal 400N since the vertically acting forces on the foot must always equal zero in this equilibrium (i.e. static) analysis.

    The location of the STJ axis does have a bearing on the vertical compression/tensile forces acting through the STJ axis since I have now added the sinus tarsi, in this Thought Experiment #4, as a potential compression-bearing structure of the foot. As the STJ axis and sinus tarsi are moved medially and/or laterally in the foot the values for the STJ axis force and sinus tarsi force will change, which will also be affected by the relative distribution of GRF on the plantar foot. There will be some positions of where the STJ axis is bearing all the forces and the sinus tarsi none, other positions where they will bear the same compression forces, other positions where the sinus tarsi is bearing more compression force than the sinus tarsi, and finally, other positions where the STJ axis might have a tensile force in it and the sinus tarsi will have a compression force. You can demonstrate this by playing with the GRFs and STJ/sinus tarsi positions in my model to see this for yourself.

    These are excellent questions Mark. You will learn more as you "play" with the model by plugging in your own GRFs and STJ/sinus tarsi positions into the model and finding out how these change the relative forces through the sinus tarsi and STJ.
     
  20. MikeM

    MikeM Member

    Kevin:

    I can understand the theory behind how the forces are working around the STJ axis and how changing the location of the STJ axis changes the forces required to supinate or pronate the foot. I'm having a problem, however, understanding the maths involved in working out the forces in questions 2 and 3. Could you please tell me what formula you are using to get these answers (ie. F1 200N, F2 200N, F3 380N, F4 20N). I've had a look at Thought Exp #5 and need to make sure I understand the physics/math behind this Experiment first before I try the next one.

    Thanks
    Mike
     
  21. Donna

    Donna Active Member

    Hi Mike

    The formulae that I used are:

    F1 + F2 = 250 + 150, and F3 + F4 = 250 + 150 ie. total GRF is equal to compression force in STJ + compression force in sinus tarsi

    Basically all forces medial to the STJ axis must equal all forces lateral to the STJ axis as the model is in equilibrium. The GRF act in an upwards direction and the F1, F2, F3 and F4 forces act in a downward direction as the diagram is 2D only. :cool:

    So to find F2...

    Sum of torques medial to STJ = sum of torques lateral to STJ
    which breaks down to...

    Moment arm x Force medial = Moment arm x Force Lateral - Moment arm x F2
    and to find F4...

    Moment arm x Force medial = Moment arm x Force lateral - Moment arm x F4

    and to then find F1 use the formula above F1 = 250 + 150 - F2
    and for F3 use F3 = 250 + 150 - F4

    So if you fiddle with these numbers plugging in the Force in "N" and Moment Arm Length in "m", you will arrive at torque values in "Nm". You then convert the Torques back into "N" by dividing by the sinus tarsi Moment Arm in "m" to find the missing values F1, F2, F3 and F4...

    Hope this helps a bit...hoping not to confuse you any more! :eek:

    Regards

    Donna
     
  22. MikeM

    MikeM Member

    Kevin:

    Thanks for that. I understand now. Forgot that force is a vector therefore had my plus and minus in the wrong places in my equations. Makes sense now when you put it that way.

    Thanks
    Mike :)
     
  23. Donna

    Donna Active Member

    Sweet...glad to hear I didn't cause extra brain meltdown :D
     
  24. Mike, you should thank Donna for her well-done reply to your query. I was asleep while her fingers were busy at work. :)

    Remember that vectors can be either positive or minus in value, depending on the reference frame of the problem and the conventions chosen for directions. I like to set up the equation for rotational equilibrium of these free body diagrams so that:

    Summation of counterclockwise moments - Summation of clockwise moments = 0

    Or, alternatively:

    Summation of counterclockwise moments = Summation of clockwise moments

    Either way, the same answer will occur. Now, time for you to move onto Thought Experiment #5 before I cook up another one (#6), this one being a little more complex.
     
  25. MikeM

    MikeM Member

    Donna:

    Sorry Donna, I was too busy concentrating on the message and missed the name. Thanks for sharing your wisdom :)
     
  26. Donna

    Donna Active Member

    That's ok... I can forgive this once :p Especially since I could think of much worse names to be called ;)

    Regards

    Donna (a.k.a Kevin?) :cool:
     
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