Three-dimensional statistical modeling of neuronal populations: illustration with spatial localization of supernumerary neurons in the locus coeruleus of quaking mutant mice.

An algorithm for the three-dimensional statistical representation of neuronal populations was designed and implemented. Using this algorithm a series of 3D models, calculated from repeated histological experiments, can be combined to provide a synthetic vision of a population of neurons taking into account biological and experimental variability. Based on the point process theory, our algorithm allows computation of neuronal density maps from which isodensity surfaces can be readily extracted and visualized as surface models revealing the statistical organization of the neuronal population under study. This algorithm was applied to the spatial distribution of locus coeruleus (LC) neurons of 30- and 90-day-old control and quaking mice. By combining 12 3D models of the LC, a region of the nucleus in which a subpopulation of neurons loses its noradrenergic phenotype between 30 and 90 days postnatally was demonstrated in control mice but not in quaking mice, leading to the hyperplasia previously reported in adult mutants. Altogether, this algorithm allows computation of 3D statistical and graphical models of neuronal populations, providing a contribution to quantitative 3D neuroanatomical modeling.