Mathematical Modeling of Retinal Mosaic Formation by Mechanical Interactions and Dendritic Overlap

Abstract

The retina is a complex assembly of neurons packed into a three-layer structure containing five classes of cells. Each class of retinal cells is regularly arranged within its layer in an orderly configuration called the retinal mosaic. We have set up a mathematical model of retinal mosaic formation focusing on the actions of local mechanical forces on the neuron's cytoskeleton. The cytoskeleton has been modeled according to two approaches, one based on the tensegrity concept (a structure made of elastic and rigid elements), and the other based on a simple model with viscoelastic features. We have assumed causing deformation of their cytoskeleton, overlap of dendritic areas and movement of the neuron. Simulations based on these two models indicate that a random distribution of neurons reaches an orderly configuration by local and mechanical neuron interaction in the case in which the cytoskeleton is modeled using the tensegrity approach, but not when the neuron is modeled as a purely viscoelastic system. Considering that the main structural difference between the Maxwell model and the tensegrity model is that the latter model contains rigid elements whereas the former does not, this suggests that the presence of rigid components in the cytoskeleton of retinal neurons plays a key role in the formation processes of the retinal mosaic.

Stretch to See: Lateral Tension Strongly Determines Cell Survival in Long-Term Cultures of Adult Porcine Retina

“…The morphology of porcine adult in vivo retina has already been described in detail, 23,24 but is of importance, and will therefore be briefly summarized. Hematoxylin and eosin staining of adult normal retina displayed well-defined nuclear layers, with larger cell bodies in the INL compared with the ONL (Fig.…”

“…Free-floating cultured specimens show regional specialization such as areas of high visual acuity and the orderly cellular mosaic. 3,22,23 The full significance of prevailing retinal tension in the normal eye is largely unknown. However, further understanding may be provided by conditions in vivo and in vitro in which tensility is lost.…”

Semi-Supervised Learning Method of U-Net Deep Learning Network for Blood Vessel Segmentation in Retinal Images

“…The task of segmenting the blood vessels aims to obtain the complete blood vessel tree in the retinal image. The blood vessel tree can be used to achieve many tasks, including retinal blood vessel quantification [1], retinal image registration [2], retinal mosaic [3] and biometric identification [4].…”

“…This proposed semi-supervised learning method provides a new, general, high-performance learning framework for blood vessel segmentation with limited labeled data. (3) We discussed the relationship between the number of hand-labeled retinal images and segmentation accuracy, which was helpful for reducing the costs of labeling the retinal images.…”

Bivariate spatial point patterns in the retina: a reproducible review

“…Given that the d min model is a phenomenological model, it suggests only that local exclusion zones are sufficient to recreate global order, but cannot tell us which developmental mechanisms are responsible. To assess which mechanisms might be responsible, we need to examine mechanistic models (Eglen et al, 2000;Eglen and Willshaw, 2002;Ruggiero et al, 2007). However, although we cannot use the current methods to understand the mechanisms of development, the existence of retinal mosaics is often used as an indicator of an independent cell type (Cook, 2003;Seung and Sümbül, 2014).…”