Rehabilitating Low Back Disorders - Fundamentals and Assessment Tools for Occupational Ergonomics - page 458

potential energy is calculated from stiffness (k) and deformation (x) in the elastic element:

x 2

PE ¼ 1 = 2 k :

In other words the greater the stiffness (k) the greater the steepness of the sides of the bowl (from the
previous analogy), and the more stable the structure. Thus stiffness creates stability (see Figure 20.3).
Active muscle produces a stiff member and in fact the greater the activation of the muscle, the greater
this stiffness — it has long been known that joint stiffness increases rapidly and nonlinearly with
muscle activation such that only very modest levels of muscle activity create sufficiently stiff and stable
joints. Furthermore, joints possess inherent joint stiffness as the passive capsules and ligaments contribute
stiffness particularly at the end range of motion. The motor control system is able to control stability of the
joints through coordinated muscle coactivation and to a lesser degree by placing joints in positions,
which modulate passive stiffness contribution. However, a faulty motor control system can lead to
inappropriate magnitudes of muscle force and stiffness, allowing a “valley” for the “ball to roll out” or
clinically, for a joint to buckle or undergo shear translation. But mechanical systems and particularly mus-
culoskeletal linkages, are limited to the analysis of “local stability” since the energy wells are not infinitely
deep and the many anatomical components contribute force and stiffness in synchrony to create “surfaces”
of potential energy where there are many local wells. Thus local minima are located from examination of
the derivative of the energy surface (see Reference 13 for mathematical details). Spine stability then,
is quantified by forming a matrix where the total “stiffness energy” for each degree of freedom of joint
motion is represented by a number (or eigenvalue) and the magnitude of that number represents its
contribution to forming the “height of the bowl” in that particular dimension. Eigenvalues less than
zero indicate the potential for instability. The eigenvector (different from the eigenvalue) can then identify
the mode in which the instability occurred while sensitivity analysis may reveal the possible contributors
allowing unstable behavior. Gardner-Morse et al. 18 have initiated interesting investigations into eigenvectors
by predicting patterns of spine deformation due to impaired muscular intersegmental control) or for
clinical relevance — what muscular pattern would have prevented the instability?
Activating a group of muscle synergists and antagonists in the optimal way now becomes a critical
issue. In clinical terms the full complement of the stabilizing musculature must work harmoniously to
both ensure stability together with generation of the required moment and desired joint movement.
But only one muscle with inappropriate activation amplitude may produce instability, or at least unstable
behavior could result at lower applied loads.
How much stability is necessary — obviously insufficient stiffness renders the joint unstable but too
much stiffness and coactivation imposes massive load penalties on the joints and prevents motion.

FIGURE 20.3 (a) Increasing the stiffness of the cables (muscles) increases the stability (or deepens the bowl) and
increases the ability to support larger applied loads “p” without falling. (b) Spine stiffness (and stability) is achieved
by a complex interaction of stiffening structures along the spine and (c) those forming the torso wall (right panel).