Mathematical model of the neural functional relationship, based on the microstructure

Introduction. From studies of Ramon y Cajal to the most modern techniques for the study of the neuronal microstructure, it is evidenced that the organization of the neuronal cytoarchitecture corresponds to a potentially predictable spacetime order. Objective: To determine if there is a correlation between the anatomical arrangements of neurons in the human primary visual cortex with the vector distribution inferred in a mathematical model described previously. Methods: From 10 postmortem studies of pediatric patients who died from diseases that would not distort the normal architecture of the brain, equal fragments were taken from the right and left occipital cortex at the level of the calcarine fissure. The preparations were observed in an optical planar apochromatic microscope. Measurements were carried-out on the soma size, length of the apical dendrite, density of basal branches, density of dendritic spines in three segments of 50 mu m in the apical basal dendrites, length of the dendrite spine and head diameter, and diameter of apical and basal dendrites. These measures allowed to calculate the actual number of spines on each segment of 50 mu m. Results: The size of the soma, length of the apical dendrite and density of basal dendrites increase between 7 days to 14 years of age (p< 0.01). The density of spines (sp) in the apical dendrite presents significant changes in their pattern of distribution along the apical dendrite, with greater density in medial (1.14 sp/mu m) and terminal (1.13 sp/mu m) segments. The spines density in the 3 basal segments studied presented significant increases in children aged 7 days in an average of 1.5 sp/ mu m, in relation to 15-months old (0.63 sp/mu m) and to 14-years old (0.58 sp/mu m). The comparison between thorns density measured at 150 sp/mu m of the apical dendrite compared with baseline showed significant reductions of 59% at age 14 years and 31% at age 15 months. However, at an age of 7 days it is found a significant increase of a mean 29%. With this information a mathematical model is proposed that explains the correlation between the morphostructure of the primary visual cortex with its function, as a paradigm of study of the socalled higher cortical functions. Conclusion. Since the neural connections in the cerebral cortex of humans are morphologically distributed in a convergent/divergent manner, then cortical integration can be analyzed by the study of neuronal vector fields.