Mathematical Model of Neuronal Morphology: Prenatal Development of the Human Dentate Nucleus

Abstract

The aim of the study was to quantify the morphological changes of the human dentate nucleus during prenatal development using mathematical models that take into account main morphometric parameters. The camera lucida drawings of Golgi impregnated neurons taken from human fetuses of gestational ages ranging from 14 to 41 weeks were analyzed. Four morphometric parameters, the size of the neuron, the dendritic complexity, maximum dendritic density, and the position of maximum density, were obtained using the modified Scholl method and fractal analysis. Their increase during the entire prenatal development can be adequately fitted with a simple exponential. The three parameters describing the evolution of branching complexity of the dendritic arbor positively correlated with the increase of the size of neurons, but with different rate constants, showing that the complex development of the dendritic arbor is complete during the prenatal period. The findings of the present study are in accordance with previous crude qualitative data on prenatal development of the human dentate nucleus, but provide much greater amount of fine details. The mathematical model developed here provides a sound foundation enabling further studies on natal development or analyzing neurological disorders during prenatal development.

Dynamics of Forest Fragmentation and Connectivity Using Particle and Fractal Analysis

“…Because the forests analysed here are morphologically complex, showing very often fragmented and non-uniform patterns and because the particle descriptors depend on the scale of observation 48 , the forest images were further examined by fractal analysis as this is a scale-invariant method. Fractal dimension (FD) as the main fractal parameter predominantly describes the degree of morphological complexity 49 .…”

Fractal Parameters of Tumour Microscopic Images as Prognostic Indicators of Clinical Outcome in Early Breast Cancer

“…By targeting specific features, primarily nuclei [21], even the studies using nonspecifically H&E-stained tissue sections [22][23][24][25][26] were in fact not analytically hypothesis-free. Although pathologists commonly use the pan-tissue H&E staining for pathologic assessment of histology specimens, it has been considered as suboptimal for fractal analysis27.…”

Fractal analysis in neuroanatomy and neurohistology

“…One of the first studies, which showed the usefulness of fractal analysis in neuroscience research, dealt with the morphological aspects of glial development (27). Following this research, further studies have concluded that FD of neuron and glial cells corresponds with the increase in their morphological complexity during development and maturation (2,28).…”