IN: PROCEEDINGS OF II. WORLD CONGRESS OF IBRO, BUDAPEST, 1987 (NEUROSCIENCE)
TENSOR MODEL OF THE MUSCULO-SKELETAL HEAD-NECK SYSTEM OF THE MONKEY. F. Lestienne, P. Liverneaux (CNRS Lab. Neurosensorielle, Paris), J. Laczkó (KFKI, Budapest), A. Pellionisz (NYU Physiol. & Biophys. New York)
The understanding of structuro-functional principles of sensorimotor systems hinges on a proper quantitative knowledge of the complex anatomical features of the system and on the power of the mathematical concepts and formalisms applied to the explanation of its functioning. While oculomotor systems can be approximated by three pairs of quasi-orthogonally arranged muscles (permitting an almost separate pitch- yaw- roll analysis), one of the most obvious features of the neck-head musculo-skeletal apparatus is the overcomplete number of non-orthogonally arranged set of muscles, built upon a multisegmented skeletal cervical column (see the accompanying abstract). Recently, the multidimensional geometrical approach, tensor theory was applied to model such headcontrol systems in the cat (Pellionisz & Peterson, 1986), in which case the muscle origin and insertion-points have been quantitatively measured (Baker, Wickland & Peterson, 1986).
Since the approach is based on the quantitated availability of the coordinates intrinsic to movements (i.e. the skeletal and muscular elements), a computer modeling technique was developed that is applicable if such data are available only in graphical form and the computer is utilized to extract the quantitative information. As the first step of such modeling, 2-D diagrams of the cervical column and the neck-muscles of macaca fascilularis were inputed to the widely available graphical processor (Apple Macintosh).
By selecting joint-points and muscle origin and insertion-points, the overcomplete and non-orthogonal system of coordinates of individual muscle-contractions were automatically calculated. Since tensor network theory postulates (by means of the Moore-Penrose generalized inverse of the covariant metric tensor, cf. Pellionisz 1984), a unique distribution of muscle-activities even in such overdetermined systems, activations of muscles ("EMG") and movements, according to any movement-intentions in the 2D, could be calculated arid displayed. With the increasing availability of potent graphic work-stations, such computerized tensor models are expected to develop into a valuable research tool for the interpretation of sensorimotor experimental data.