2 resultados para Non-complete extended p-sum (NEPS)
em Universidad de Alicante
Resumo:
Let T be a given subset of ℝ n , whose elements are called sites, and let s∈T. The Voronoi cell of s with respect to T consists of all points closer to s than to any other site. In many real applications, the position of some elements of T is uncertain due to either random external causes or to measurement errors. In this paper we analyze the effect on the Voronoi cell of small changes in s or in a given non-empty set P⊂T\{s}. Two types of perturbations of P are considered, one of them not increasing the cardinality of T. More in detail, the paper provides conditions for the corresponding Voronoi cell mappings to be closed, lower and upper semicontinuous. All the involved conditions are expressed in terms of the data.
Resumo:
The mechanical response of the cornea subjected to a non-contact air-jet tonometry diagnostic test represents an interplay between its geometry, the corneal material behavior and the loading. The objective is to study this interplay to better understand and interpret the results obtained with a non-contact tonometry test. A patient-specific finite element model of a healthy eye, accounting for the load free configuration, was used. The corneal tissue was modeled as an anisotropic hyperelastic material with two preferential directions. Three different sets of parameters within the human experimental range obtained from inflation tests were considered. The influence of the IOP was studied by considering four pressure levels (10–28 mmHg) whereas the influence of corneal thickness was studied by inducing a uniform variation (300–600 microns). A Computer Fluid Dynamics (CFD) air-jet simulation determined pressure loading exerted on the anterior corneal surface. The maximum apex displacement showed a linear variation with IOP for all materials examined. On the contrary, the maximum apex displacement followed a cubic relation with corneal thickness. In addition, a significant sensitivity of the apical displacement to the corneal stiffness was also obtained. Explanation to this behavior was found in the fact that the cornea experiences bending when subjected to an air-puff loading, causing the anterior surface to work in compression whereas the posterior surface works in tension. Hence, collagen fibers located at the anterior surface do not contribute to load bearing. Non-contact tonometry devices give useful information that could be misleading since the corneal deformation is the result of the interaction between the mechanical properties, IOP, and geometry. Therefore, a non-contact tonometry test is not sufficient to evaluate their individual contribution and a complete in-vivo characterization would require more than one test to independently determine the membrane and bending corneal behavior.