Figure 1 shows the condensed version of the parameters (forces and moment arms) affecting movement and stability of the femur-acetabulum complex in the frontal plane during the closed kinetic chain. (A moment arm such as D1 and D2 is defined as the length of a line that extends from the axis of rotation to a point of right angle intersection with a respective force, in this case HAM or BW.)
In Figure 1 above we see several parameters. HAM represents the Hip Abductor Muscles, D1 represents the internal moment arm, D2 represents the external moment arm and BW represents the Body Weight of the individual. These factors all come into play when considering the frontal plane equilibrium of the hip joint. The equation representing the interaction of all of these parameters is HAM x D1 = D2 x BW. Both sides of this equation must be equal and balanced in order for the pelvis to remain stable and without movement when in the closed chain stance phase of gait. In this diagram, if the left side of the equation is greater than the right the net effect will be a counterclockwise hip moment and the patient will move their torso over the hip creating a hiking or lifting of the contralateral hip. This net movement will create abduction at the hip joint. If the right side of the equation is greater than the left the net effect will be a clockwise hip moment and the patient will move their torso away from the hip creating a dropping of the contralateral hip. This net movement will create adduction at the hip joint seen here and thus the classic Trendelenberg gait. We need to keep in mind that this is not a perfect model presented here since we are ignoring acceleration of the body in the forward sagittal plane and rotational planes. Investigating the equation further should bring the reader to further realization that if the body weight (BW) were to increase, mathematically the D2 external moment arm could decrease to keep the equation balanced. However, since the length of this D2 moment arm is rather fixed (unless the pelvis were to go through a counterclockwise rotation which would draw the body weight center closer to the hip joint center effectually abducting the stance hip, thus reducing the D2 moment arm) this is not a more likely scenario. Rather, the response would be to attempt to increase the left side of the mathematical equation thus increasing the HAM forces to attempt to keep the pelvis level and the equation from changing. In other words, when body weight increases we must increase the gain or contraction in the HAM group during each step to keep the pelvis level and balanced. Unfortunately the HAM strength has its limits of maximal contraction, sometimes far below any major increases in body weight. One must keep in mind that with increased HAM contraction there is a corresponding increase in joint compression across the hip articular surfaces which at reasonable levels is well embraced but at unreasonable levels can damage articular cartilage. One should thus conclude that maintaining a reasonable body weight for one’s bone structure keeps the right and left sides of the mathematical equation at tolerable levels, both for movement, stability and cartilage longevity. Fortunately the equation has a built in safety mechanism for these counterclockwise hip moments, one that is beneficial. In such scenarios, as the body is brought over the hip thus decreasing the D2 moment arm, the D1-internal moment arm increases in length and since the equation must be balanced the HAM force can decrease. Thus, the magnitude of the HAM force is inversely proportional to the length of the D1-internal moment arm. The whole equation can better be visualized and conceptualized by a teeter totter diagram with a sliding pivot point.
Shawn and Ivo, The Gait (and biomechanics) Guys
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