Thought Experiment #10: External vs Internal Moments
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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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