The spines of apical dendrites of the layer V pyramidal cells of the area striata in the mouse represent a sequence of post-synaptic structures receiving a variety of contacts from terminal fibers derived fundamentally from short axon cells and superficial pyramidal cells. The study of Golgi preparations of mice 180 days old shows the existence of the most complicated terminal structures over portions of apical dendrites at the levels of layers III and IV. Observations on young mice reveals the terminations of the specific afferent fibers on the dendrites of short axon cells. A mathematical model which defines the distribution of spines along the apical dendrites is introduced. The principal equation of the model has been adjusted from the data processing of microscope countings through a series of programs written for an IBM 7070. The equation defines satisfactorily the different distributions of dendritic spines in mice 10-180 days old raised in normal conditions and in complete darkness. The equation defines also the distribution of dendritic spines in the visual cortex of mice enucleated at birth on one side, and the distribution along the apical dendrites of various cortical areas of the hamster, cat and man. The number of dendritic spines increases with the age of the subject and their distribution varies significantly according to the values of the parameters of the model. © 1969 Springer-Verlag.

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