Stefan Talu

Surface roughness of intraocular lenses with different dioptric powers assessed by atomic force microscopy

PURPOSE: To analyze the optic surface roughness and morphology of 2 types of hydrophobic acrylic intraocular lenses (IOLs) with various dioptric powers using atomic force microscopy (AFM). SETTING: Technical University of Cluj‐Napoca, Faculty of Mechanics, Cluj‐Napoca, Romania. METHODS: Atomic force microscopy was used to characterize the topography of 2 types of hydrophobic acrylic IOLs from a single manufacturer (SN60AT and SA30AL) with dioptric powers ranging from 10.0 diopters (D) to 30.0 D. The AFM analysis was performed in contact mode using a V‐shaped silicon nitride cantilever with a pyramidal tip curvature of 15 nm and a nominal spring constant of 0.2 N/m. Detailed surface characterization of the IOL optic was obtained using 6 quantitative parameters provided by the AFM software. RESULTS: Five of 6 roughness parameters indicated statistically significant differences (P<.05) between IOLs with different dioptric powers, with the 10.0 D IOL in both models providing the smoothest optic surface. Between models with the same dioptric power, the SN60AT model had lower values of each surface roughness parameter than the SA30AL model. CONCLUSIONS: Atomic force microscopy was an accurate tool for assessing the surface properties of IOL optics. Manufacturing processes were responsible for introducing detectable differences in the topography of IOL biomaterials with identical copolymer constituents but different dioptric powers. Nanometric analysis may assist IOL manufacturers in developing IOLs with optimal surface characteristics. Financial Disclosure: No author has a financial or proprietary interest in any material or method mentioned.

Evaluation of equations for describing the human crystalline lens

Accurate mathematical descriptions of the human crystalline lens surface shape are required to properly understand the nature of functional adaptations that occur when the lens shape alters to changes in refractive power. Using least squares method, the total mean normal distance, smoothness, rate of change of the transverse and sagittal radii of curvatures and continuity at the lens equator between eight mathematical functions: conic, figuring conicoid, generalized conic, Hermans conic patch, Urs polynomial, Urs 10th order Fourier series, Chien, and Giovanzana, and 17 human crystalline lenses were evaluated. The mean differences of the fits of all the equations to the whole lens and to the central 8 mm of the lens surfaces were >24 μm with comparable standard deviations. When considering fit smoothness and continuity at the equator, the Giovanzana and Chien functions are most representative of the lens surface.

Multifractal analysis of human peripapillary atrophy

Multifractal characteristics of the retinal vascular networks in healthy patients and patients with peripapillary atrophy (PPA) are compared in the paper. Segmented and skeletonized fundus images from the DRIVE database were analyzed over the image region corresponding to the macular area and over the whole image. The regional and overall multifractal characteristics of fundi could serve as further clues in detecting human PPA and for quantifying the pathological stages of PPA cases.

Mathematical models for the shape analysis of human crystalline lens

The objective of this paper is to present an analysis of mathematical models of the human crystalline lens. Seven existing models presented in the literature were investigated: conic, figuring conicoid, generalized conic, Hermans conic patch, Kasprzak hyperbolic cosine, Urs 10th-order Fourier series and Giovanzana parametric models. The analyzed models describe the shape for a data set of human crystalline lenses with ages from 6 to 82 years. The results highlight the difficulty and complexity of the task of choosing the most appropriate model for the crystalline lens shape.

On Approximation of Human Corneal Surface with Superellipsoids

The objective of this paper is to present results of the theoretical and experimental researches for determination of an approximation of human corneal surface with superellipsoids using computational geometry. The mathematical formula permits a complex representation and the tool allowing exploring the physical and optical characteristics of the cornea. The spatial shape of the cornea can be described using different mathematical models with particular parameters for different subjects (women and men). These researches are applied in geometric constructions and computer aided design used in corneal refractive surgery, human vision studies, solid modelling and biomechanical behavior of the cornea.

An Overview on Mathematical Models of Human Crystalline Lens

To describe the human crystalline lens, mathematical models are required. Advanced mathematical models are applied for human vision studies and biomechanical behavior of the crystalline lens. The accurate modeling of the crystalline lens is important in the development of intraocular lenses. This paper presents an overview of researches for human crystalline lens modeling using mathematical models.

Mathematical Analysis of the Human Crystalline Lens in Giovanzana Parametric Model

The objective of this paper is to present a mathematical analysis of the human crystalline lens in Giovanzana parametric model. This model can serve to improve computational modeling, such as finite element modeling of the human crystalline lens.