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 multi-segmented skeletal cervical column (see  the 
accompanying abstract). Recently, the multidimensional geometrical 
approach, tensor theory was applied to model  such head-control 
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 and 
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.