Keywords: spine, kinematics, kinetics, joint clearance, control, model.

Morphologic complexity of the spine is evident [4]. A complex system of ligaments and muscles specifies the intervertebral kinetics. Their structural redundancy is evident but still unexplained. From the technical mechanics standpoint, it is an evidently overdetermined system. An unambiguous idea about the mechanical role of the intervertebral discs of the intervertebral articulation has not existed so far. There is experimental proof about a wide variability of intervertebral kinematics within the same individual, which is manifested already on the first level, i.e., on the position of its instantaneous axis of revolution, [3]. This phenomenon can be observed with all vertebrates, not excluding man. Morphology of the intervertebral articulation forms sufficient arguments for legitimacy of the hypothesis that the intervertebral articulation, which is situated markedly close to the vertebral canal, can be considered as a dominant element defining the intervertebral kinematics. This element defines a two-armed lever, when the spinal process is situated on the dorsal end with a huge ligamentary and muscular set-up. On the ventral end, the body of the vertebra dominates, to which the intervertebral disc is connected and as well as a system of ligaments and muscles. The intervertebral joints define by their shape intervertebral mobility that differs not only depending on its position on the spine but is also intra-individually variable. The contact surfaces of the joints are covered with deformable cartilage, which, consequently complicates "the accuracy" of the relative mobility definition considerably. From this reality, it follows at least that the intervertebral kinematics will be strongly dependant on the load pattern. The authors aimed at defining such a model interpretation that would enable the phenomena mentioned to be judged and, in addition, that would create a tool to analyze the vertebral force transfer and the role of the intervertebral disc. Since the skeletal part of the spine provides a protection of the spinal cord, located in the vertebral canal, the optimalizing criteria for the control of kinetics of the whole linked complex shall take into account the biological aspects [4].

Our interpretation of the model issues from imagining a two-stage securing of the actual (current, etc) intervertebral kinetics. The first hierarchic superior factor is the shape of the intervertebral joint facets and the geometry of the whole vertebra. Further it is assumed that the variability of the problem, resulting from the inter-articular clearance, is trimmed by a complex interplay of the spinal musculature and ligamentary system effects including the intervertebral disc. However, "the tuning ability" necessarily requires the existence of a collaborating perceptive system that would primarily inform the supervising control system about the whole system conditions. At the first approximation to the problem solution, we have created a linear four-member model of a series consisting of rigid members (bone components). These are mutually connected by kinematic couples with a "preferred" rotation, and have also a certain internal flexibility causing an inter- articular clearance. The intervertebral disc is simulated by a visco-elastic element that is deformable both in tension and compression and has a decisive influence on damping dynamic processes in the intervertebral kinetics [1,2,3]. Its role is defined by elements simulating the ligaments which are also visco-elastic but present only a tensile effect when stretched. The muscle is considered to be an active externally controlled element in the model. It presents a controlled visco-elasticity. The whole configuration of these elements in the system accepts a material structural redundancy of the biologic pattern. The elementary intervertebral mobility is ensured by mutually antagonic couples of intervertebral muscles and ligaments. The simultaneous bendings of the vertebra 4-2, 3-1, 4-1 are then independently ensured by the muscular-ligament couples. The model has been created for a reduced 2D variant without the articular clearance. An extended, "tuned", 3D variant (with the articular clearance consideration) has been partially developed. The active role of the muscle net will be studied in the next stage. Passive behavior of the primary variant was tested in the condition of a bending moment in the form of a Dirrac impulse.

Acknowledgement

This project was supported by grants No. 106/03/0958 and No. 106/03/0464 of the Czech Grant Agency.

1

Giles L.G.F., Singer K.P., "Clinical Anatomy and Management of Low Back Pain", Reed Educational and Professional Publishong Ltd., The Bath Press, GB, Rochaester, 1997.

2

Wite A.A., Panjabi M.M., "Clinical Biomechanics of the Spine", Lippincott Williams & Wilkins, London, 1990.

3

Zemanová P., Zeman J., "Torsion stiffness of intervertebral disc and its identification", Proceedings of International Conference Biomechanice of Man 2002 in Cejkovice, Prague, 55 - 57, 2002.

4

Otáhal, S., Otáhal J., "Subarachnoidal interspace and cerebrospinal fluid transportation", In: Complexity of biomaterials and tissue structures, Charles University, Prague, 125 - 134, ISBN 80-86317-20-X, 2002.

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