The network structure of the corneal endothelium

Abstract

A generic network model is applied to study the structure of the mammalian corneal endothelium. The model has <p>been shown to reproduce the network properties of a wide range of systems, from low-dimensional inorganic glasses</p> <p>to colloidal nanoparticles deposited on a surface. Available extensive experimental microscopy results are analysed</p> <p>and combined to highlight the behaviour of two key metrics, the fraction of hexagonal rings ($p_6$) and the</p> <p>coefficient of variation of the area (CV). Their behaviour is analysed as a function of patient age, the onset of</p> <p>diabetes and contact lens wearing status. Wearing contact lenses for $\sim$10years is shown to change the endothelium</p> <p>structure by the equivalent of $\sim$30years contact lens-free. Model network configurations are obtained using a Monte Carlo bond switching</p> <p>algorithm with the resulting topologies controlled by two potential model parameters (the bond and angular force</p> <p>constants) and the Monte Carlo temperature. The effect of systematically varying these parameters is</p> <p>investigated. In addition, the effect of constraining the ring size distribution is investigated. The networks</p> <p>generated with relatively weak bond force constants are shown to correlate best with the experimental information. The</p> <p>importance of extracting the full ring size distribution (rather than simply the fraction of hexagons) is discussed.

Universality of Form: The Case of Retinal Cone Photoreceptor Mosaics

“…Lemaître's law is the virial equation of state for two-dimensional cellular networks, which relates two measures of disorder (i.e., thermodynamic variables), namely, the fraction of hexagons to the width of the polygon distribution [11,19,20,[39][40][41]. Although at first proposed for two-dimensional foams, it has been shown that a wide range of planar cellular networks in nature obey Lemaître's law, ranging from biology such as avian cones [30], epithelial cells [42], and mammalian corneal endothelium [43], to physics such as amorphous graphene [41], the Ising model [44], Bénard-Marangoni convection [45], silicon nanofoams [46], and silica bilayers [47]. It can be obtained by maximizing the entropy, H = − ∑ n≥3 p n ln p n , where p n is the probability, or the frequency of the appearance, of an n-sided polygon, while considering the following information:…”

Universality of Form: The Case of Retinal Cone Photoreceptor Mosaics

“…Lemaître’s law is the virial equation of state for two-dimensional cellular networks, which relates two measures of disorder (i.e., thermodynamic variables), namely, the fraction of hexagons to the width of the polygon distribution [11,18,19,31–33]. Although at first proposed for two-dimensional foams, it has been shown that a wide range of planar cellular networks in nature obeys Lemaître’s law, ranging from biology such as avian cones [23], epithelial cells [34], and mammalian corneal endothelium [35], to physics such as amorphous graphene [33], the Ising model [36], Bénard–Marangoni convection [37], silicon nanofoams [38], and silica bilayers [39]. It can be obtained by maximizing the entropy, H = − ∑ n ≥3 p n ln p n , where p n is the probability, or the frequency of appearance, of an n -sided polygon, while considering the following information: The first relation is the normalization condition, and the second one is a consequence of Euler’s relation concerning the topology of the structure, which assumes only three lines meet at a vertex.…”