The Human Cornea as a Micro Multilayers Crystal Lattice. Bio- Mechanical and Tensile Properties According to the “hall-petch” Relationship

This paper is proposing to the scientific community a new, original approach to the problem of the bio-mechanical and tensile study of the human cornea. By overturning the traditional “classic” approach, focusing mainly on the analysis of the collagen fibril composition and distribution, and on the yield stress of the Stroma only (in the wrong assumption of its alleged “major importance”, as a layer making 90% of corneal thickness), we introduce herewith a new approach, considering the human cornea as a micro multilayers crystal lattice, in which the whole bio-mechanical yield stress of the 5 layers (membranes) can be simultaneously and precisely calculated according to the “Hall-Petch” relationship for micro and nano multilayers materials. Introduction One of the main problem, in the analysis of the human cornea for medical and surgical purposes, and in the recent evolution of bio-mechanical studies, for manufacturing of bio-synthetic corneas, was mainly the “optical” and “biological” approach to the analysis of the human cornea. In other words, for too many years and decades, the human cornea was analyzed mainly from an optical and medical approach (refractive defects and organic diseases), and from a purely “biological” standpoint, i.e, analysis of the cells and fibrils making the composition of the 5 corneal layers (Epithelium, Bowman’s membrane, Stroma, Descemet’s membrane, Endothelium). However, strange as it may seem, for too long a physics and engineering full analysis of the human cornea was lacking, an analysis trying to better clarify the mechanical and tensile behavior of the corneal structure, and with a yield stress analysis, in order to better and precisely understand the mechanical strength of the corneal structure, and to plan more precisely new biosyntetic tissues and/or medical/surgical interventions. 1) The importance of studies on corneal yield stress. A meaningful progress in this direction was made with the more recent studies on yield stress, by J. Hjortdal in 1996,regarding the central area of the cornea then followed by A. Pandolfi, G. Holzapfel in 2008, on the whole corneal structure. The only flaws, in pioneering works handling the study of the yield stress of the human cornea, were in the misuse of the von Mises yield stress tensor (Pandolfi, Holzapfel), that is correct to calculate the yield stress of steel and concrete beams and structures, but is not suitable to analyze a colloidal structure as the human cornea, undergoing huge hydrostatic/volumetric changes, leading thereby to theoretical conclusions that were often mismatching with experimental results. Moreover, all the papers handling the human cornea, so far, are always focusing mainly on the central stroma, as the most thick corneal layer, almost totally disregarding the other “smaller” layers, for a yield stress analysis. In a study of 2010: “Biomechanics: principles, trends and applications”, one of the authors, Ahmed Elsheikh, wrote at p. 60: “The mechanical behavior of the human cornea is dominated by the stroma, that forms 90% of its thickness.”. 2) New model. The human cornea as a micro multilayers crystal lattice. Bio mechanical and tensile properties according to the Hall-Petch relationship. Therefore, after realizing that the “path” (full analysis of corneal yield stress) showed by the first studies on yield stress was correct, but maybe it was necessary to choose a better corneal model, I tried to devise it. I realized that the main drawback of the current bio-mechanical models is in their failure to grasp the peculiar, and somehow unique structural and morphological features of human cornea. 1) From a structural point of view our human cornea is a crystal lattice (collagen fibrils + endothelial/epithelial cells) 2) From a morphological standpoint, our human cornea is a micro-film (whose average thickness is around 560/600 μm) made of 5 micro-layers (Epithelium, Bowman’s membrane, Stroma, Descemet’s membrane, Basement/Endothelium). After coupling the fundamental features above, the question is: Is there a model, in Physics, whose ability to mathematically describe the behavior of micro multilayers crystal lattices has succesfully and experimentally been tested in recent times? Of course there is! According to the “ Hall-Petch relationship” (that was discovered almost 60 years ago, but curiously it was never applied so far to make a model of human cornea) , we know that in a crystal lattice there is an inverse relationship between a grain size and its yield stress , as follows: (1)