Teach-in 2003: Lombard's paradox

by Chris Kirtley, The Catholic University of America, Washington DC

A muscle can cause the extension of a joint which it can flex

By means of an ingenious apparatus that he designed to record simultaneously the contractions of as many as fifteen muscles, Warren Plimpton Lombard (1855-1939) sought to explain why the quadriceps and hamstring muscles contracted simultaneously during the sit-to-stand motion. Rectus femoris and the hamstrings are antagonistic, and this coactivation is known as Lombard's paradox (Lombard & Abbott, 1907).

The paradox is classically explained by noting the relative moment arms of the hamstrings and rectus femoris at either the hip or
the knee, and their effects on the magnitude of the moments produced by either muscle group at each of the two joints (Rasch
& Burke, 1978, pp. 296-7).

Muscles cannot develop different amounts of force in their different parts. The hamstrings, for instance, cannot selectively extend the hip without acting with equal force at the knee. Thus, the only way for hip extension and knee extension to occur simultaneously in the act of standing (or eccentrically in the act of sitting) is for the net moment to be an extensor moment at both the hip and knee joints. Lombard suggested three necessary conditions for such paradoxical co-contraction:

In 1989, Felix Zajac & co-workers pointed out that the role of muscles, particularly two-joint muscles, was much more complex than has traditionally been assumed. For example, in certain situations, the gastrocnemius could act as a knee extensor. It is clear now that the direction in which a joint is accelerated depends on the dynamic state of all body segments, making it difficult to predict the effect of an individual muscle contraction without extensive and accurate biomechanical models (Zajac et al, 2003).

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