1. Global geometric variables represent high-order parameters in the control of cat posture. In particular, limb length and orientation are accurately controlled in response to tilts of the support platform. There is now electrophysiological evidence, obtained in anesthetized cats, that spinal sensory neurons projecting to the cerebellum are broadly tuned to limb length and orientation. Limb length and orientation specify the position of the limb end-points in body-centered polar coordinates. They define an intended posture in a global manner, leaving the detailed geometric configuration of the limbs undetermined. The planar covariation of limb joint angles described in the accompanying paper suggests the existence of an intermediate processing stage that transforms endpoint coordinates into the angular coordinates of the joints (inverse mapping). In this paper we address the question of the nature of this coordinate transformation. Because the number of degrees of freedom of angular motion in each limb exceeds that of endpoint motion in world space, several different angular configurations are compatible with any given endpoint position in world space. Thus the problem of coordinate transformation is a priori indeterminate. We have tested a number of different hypotheses. 2. Coordinate transformation could be accomplished implicitly by means of discrete kinematic synergies. Any given geometric configuration of the limb would result from a weighed combination of only two distinct patterns of angular covariations, the first pattern affecting selectively limb length and the second pattern affecting limb orientation. This decomposition, however, was found in only a few sporadic cases. 3. We also tested the possibility that the coordinate transformation involves the Moore-Penrose generalized inverse. We found that this algorithm produces a planar covariation of the joint angles, but with an orientation orthogonal to the experimental plane. By contrast, a linear transformation with constant, position-independent terms can fit the experimental plane of angular covariations but predicts large errors in endpoint position. 4. The particular orientation in joint space of the experimental plane, coupled with the scatter of data points around the plane, bears a specific implication for the problem of inverse mapping. The experimental plane crosses the constant position lines (the loci of all possible changes of the joint angles that correspond with an invariant position of the endpoint) at an acute angle. Consequently the specification of limb orientation is little sensitive to joint configurations: relatively small changes in orientation can be produced by large changes in joint configurations.(ABSTRACT TRUNCATED AT 400 WORDS)

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Spine biomechanics represents a traditional area of research by orthopaedists, neurosurgeons, bioengineers and physicists. Working in an emergency setting and managing spinal traumas every day we began a study on extended literature devoted to biomechanics of the spine, to see beyond the usual static evaluation of neuroimaging patterns. After our earlier paper on biomechanics of the spine16, we have reviewed and broadened some topics such as the role of the ligaments and introduced the main mechanisms of primary spinal traumas and deformations. The spine is a multiarticular complex structure controlled by the muscles whose correct function presupposes its stability. Several “stability factors” ensure spinal stability and correct movements. A number of biomechanical studies analysed the contribution of individual bony and soft spinal elements to stability and the effects of traumas. Several theories have been derived from these studies to account for the distribution of loads and vector forces, including failure-producing loads, among the components of functional spinal units (FSU). Holdsworth's initial two column concept, the three column models by Louis and Denis up to most recent four column theory by Cartolari all represent evolutions in assessing the distribution of loads and the presence and degree of instability in spinal traumas. Whether acute or chronic spinal instability means a partial or complete loss of one or both functions of the spine: load-bearing and cord protection. The diagnosis of spinal instability is crucial to establish the most appropriate strategy of management, namely in acute conditions. Biomechanical concepts are fundamental to understand the factors deciding the type, location and extent of spinal traumas, possible instability and the primary mechanism of the main types of injuries.

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