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Thought Experiment #10: External vs Internal Moments

Discussion in 'Biomechanics, Sports and Foot orthoses' started by Kevin Kirby, Oct 11, 2009.


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    Thought Experiment #10: External vs Internal Moments

    An external moment may be defined as a moment caused by forces acting external to the foot that causes moments across a joint axis. An example of an external moment would be a moment caused by the force between the plantar foot and the ground, which is called ground reaction force (GRF). An internal moment may be defined as a moment caused by forces acting internally within the foot that causes moments across a joint axis. When communicating the concepts of joint moments acting either on or within the foot and lower extremity, it is important to describe whether the moments acting that joint axis are external or internal moments since the convention within the international biomechanics community for biomechanics studies using inverse dynamics is to describe internal moments, whereas the convention that I, and others, have used over the past 20+ years to describe moments of the foot and lower extremity have been to use external moments (Kirby KA: Methods for determination of positional variations in the subtalar joint axis. JAPMA, 77: 228-234, 1987; Kirby KA: Rotational equilibrium across the subtalar joint axis. JAPMA, 79: 1-14, 1989; Kirby KA, Green DR: Evaluation and Nonoperative Management of Pes Valgus, pp. 295-327, in DeValentine, S.(ed), Foot and Ankle Disorders in Children. Churchill-Livingstone, New York, 1992; Kirby KA: The medial heel skive technique: improving pronation control in foot orthoses. JAPMA, 82: 177-188, 1992; Kirby KA: Biomechanics of the normal and abnormal foot. JAPMA, 90:30-34, 2000; Kirby KA: Subtalar joint axis location and rotational equilibrium theory of foot function. JAPMA, 91:465-488, 2001, Kirby KA: Foot and Lower Extremity Biomechanics: A Ten Year Collection of Precision Intricast Newsletters. Precision Intricast, Inc., Payson, Arizona, 1997; Kirby KA: Foot and Lower Extremity Biomechanics II: Precision Intricast Newsletters, 1997-2002. Precision Intricast, Inc., Payson, AZ, 2002; Kirby KA: Foot and Lower Extremity Biomechanics III: Precision Intricast Newsletters, 2002-2008. Precision Intricast, Inc., Payson, AZ, 2009).

    The problem is, that during a static situation, where rotational equilibrium and translational equilibrium are in effect, the internal moments acting across a joint axis will be equal and opposite to the external moments acting across the same joint axis. Therefore, unless one knows beforehand whether the moments are external or internal that are being described or reported, the meaning of the moments may be totally reversed, causing confusion and poor communication of ideas.

    In the example illustrated below, the posterior aspect of the right leg/foot is modeled as having a subtalar joint (STJ) axis that is parallel to the transverse and sagittal planes with GRF only being born on the forefoot, not the heel. On the left, there is 200 newtons (N) of GRF acting on the 1st metatarsal head and 200 N of GRF acting on the 5th metatarsal head. This creates a total of 400 N of superiorly directed GRF acting on the plantar forefoot which is counter balanced by 400 N of inferiorly directed joint compression force acting at the STJ. Since the 200 N of GRF at the 1st MPJ has a 4 cm (0.04 m) moment arm to the STJ axis, then this medial force will produce 8 Nm of STJ supination moment. Since the 200 N of GRF at the 5th MPJ has a 4 cm (0.04 m) moment arm to the STJ axis, then this lateral force will produce 8 Nm of STJ pronation moment. Therefore, in the illustration on the left, 8 Nm of supination moment equals 8 Nm of pronation moment, causing STJ rotational equilibrium so that no net external STJ supination moments nor external pronation moments are acting across the STJ axis. In addition, since the 400 N of vertical force from body weight acting on the STJ axis has no moment arm, then there is also no net internal supination moments nor internal pronation moments.

    In the illustration on the right, however, the center of pressure (CoP) has shifted laterally on the plantar foot so that 150 N of GRF now acts on the 1st metatarsal head and 250 N of GRF now acts on the 5th metatarsal head. GRF at the 1st metatarsal head causes (150 N x 0.04 m =) 6 Nm of supination moment and GRF at the 5th metatarsal head causes (250 N x 0.04 m =) 10 Nm of pronation moment so that a net external STJ pronation moment of (10 Nm - 6 Nm =) 4 Nm is acting on the foot.

    Assuming now that the posterior tibial muscle is the only muscle that is undergoing contractile activity to maintain the CoP in a more lateral position on the plantar foot, and that it is acting with a moment arm of 2 cm from the STJ axis with a magnitude of 200 N of tensile force, the net internal STJ supination moment from the posterior tibial muscle will be (200 N x 0.02 m =) 4 Nm. Note also that the vertical joint compression force acting on the STJ will now increase to 600 N since the superiorly directed force being exerted from the posterior tibial muscle pulling downward on the tibia will increase the STJ compression force by an extra 200 N when compared to the illustration on the left.

    Therefore, the 4 Nm of external STJ pronation moment caused by the CoP being laterally positioned relative to the STJ axis must be exactly counterbalanced by 4 Nm of internal STJ supination moment caused by the posterior tibial muscle pulling vertically upward on the medial foot in order for the foot to rest quietly in this position, with the lateral forefoot having more GRF acting on it than the medial forefoot. The external joint moments and internal joint moments acting across the STJ axis are equal but opposite to each other. For the biomechanics researcher, using inverse dynamics and the using the convention of reporting internal rearfoot inversion moments, they would report that the foot has 4 Nm of rearfoot inversion moment acting on it. However, from the convention that we clinicians commonly use to discuss rearfoot moments, we would report that the foot has 4 Nm of rearfoot eversion moments acting on it. Both are correct, but using different conventions for discussing the moments acting across the joint axes of the foot and lower extremity. Thus we all must be careful when we are discussing moments or reading research articles to be certain whether external or internal moments are being discussed so that we can all understand each other and not all become confused by different conventions of moments when we are communicating with each other.

    Now for the thought experiment: If the illustration on the right had 180 N of GRF acting plantar to the 1st metatarsal head, with 220 N of GRF acting plantar to the 5th metatarsal head, what would the posterior tibial muscle force need to become and what would the vertical compression force through the STJ need to become, with this new STJ equilibrium situation? What would the external rearfoot inversion/eversion moments become? What would the internal rearfoot inversion/eversion moments become? Finally, if a foot orthosis was placed plantar to the foot in this new situation and exerted an extra 70 Nm of external rearfoot inversion moment, what would the new posterior tibial muscle force, STJ compression force, and external and internal inversion/eversion moments become?
     

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  2. Tom Quinton

    Tom Quinton Member

    Thanks for the post Kevin.

    If the illustration on the right had 180 N of GRF acting plantar to the 1st metatarsal head, with 220 N of GRF acting plantar to the 5th metatarsal head, what would the posterior tibial muscle force need to become? 80 N.

    What would the vertical compression force through the STJ need to become? 480 N.

    What would the external rearfoot inversion/eversion moments become? There would be an external eversion moment of 1.6 Nm.

    What would the internal rearfoot inversion/eversion moments become? There would be an internal inversion moment of 1.6 Nm.

    Finally, if a foot orthosis was placed plantar to the foot in this new situation and exerted an extra 70 Nm of external rearfoot inversion moment, what would the new posterior tibial muscle force, STJ compression force, and external and internal inversion/eversion moments become? Hmmm???? 70 Nm seems like a lot. I'm not sure?
     
  3. Tom:

    That was excellent! You got those quick.

    My mistake. It should have been 0.7 Nm of external rearfoot inversion moment, not 70 Nm of external rearfoot inversion moment. I wrote that one in a little bit of haste....sorry about that.....maybe now it makes more sense so one of you can calculate the correct final answer.
     
  4. Gedankenexperiment fans: the last question still has not been answered

    probably because I made a typing error on my initial post.

    Here goes again:

    Finally, if a foot orthosis was placed plantar to the foot in this new situation and exerted an extra 0.7 Nm of external rearfoot inversion moment, what would the new posterior tibial muscle force, STJ compression force, and external and internal inversion/eversion moments become?

    Certainly some one other than Tom have a go at it.:drinks
     
  5. markjohconley

    markjohconley Well-Known Member

    I'll give it a go Prof. Kirby, I don't get embarrassed much nowadays

    45 N new Posterior Tibialis mm force
    445 N new STJ compression force
    0.9 Nm new external eversion moment
    0.9 Nm new internal inversion moment

    mark
     
  6. Mark:

    Excellent.....all answers are right!

    Now, hopefully the concepts of internal and external moments are a little more clear for everyone. In addition, hopefully the example of how a foot orthosis can decrease external STJ pronation moments and decrease internal STJ supination moments at the same time is helpful in better understanding some of the current confusion that is being caused in interpreting the latest biomechanical research on wedges and orthoses on foot and lower extremity function.
     
  7. markjohconley

    markjohconley Well-Known Member

    Thanks Kevin, an excellent teaching exercise. I for one needed it.

    "Master Po: Close your eyes. What do you see?
    Young Caine: I see the water, I hear the birds.
    Po: Do you hear your own heartbeat?
    Caine: No.
    Po: Do you hear the grasshopper that is at your feet?
    Caine: Old man, how is it that you hear these things?
    Po: Young man, how is it that you do not?"
     
  8. hakimgonzalez

    hakimgonzalez Welcome New Poster

    What if in the diagram on the left the posterior tibial muscle force was 100N. The internal moment would be 2Nm. This would mean that the net moment about the STJ is 2Nm causing eversion. How is this moment classified? Is it an external moment or an internal moment or just the net moment (neither internal or external)?
     
  9. efuller

    efuller MVP

    If, in the left diagram, the PT muscle force was 100N, and the lever arm is still 4units, so the internal supination moment would have to be a 400 Nxlength units. At a particular instant you may see these forces and moments, but it would not be in equilibrium because there is no moment from ground reaction force and there is a moment from muscle. So, there should be an acceleration occuring at that instant in time.

    Also, the muscle moment would be a supination moment not a pronation moment. A lot of the confusion comes from the convention of defining a system and then looking at whether the forces are external to that system or internal to that system. This nomenclature can be avoided by just describing each force. For example, the 100N force in the posterior tibial tendon creates a 400Ncm or 4Nm supination moment at the STJ axis. That way you get around having to figure out whether the force is internal or external. The difficulty comes when you are reading a paper where they report that there is a knee abduction moment. The moment is not fully described and you still have know what authors of papers are thinking if you want to understand their research results. Is the moment that they are describing from ground reaction force, or from joint compression and ligamentous tension. Those two moments are the equal and opposite reactions from Newton's law. It is also important to describe what body those forces are applied to. Forces and moments are applied to bodies and not about imaginary lines. So, ground reaction force creates an adduction moment on the lower leg and foot and not really the knee. The equal and opposite moment appled to the lower leg and foot is from collateral ligaments and compression forces at the knee.
    So, in my example above, to make my explanation more clear, I should have said that the posterior tibial muscle applies a supination moment to the foot about the STJ axis. You need the structure applying the moment, the direction of the moment and the structure that to which the moment is applied to fully describe the situation.

    Eric

    Cheers,
    Eric
     
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