Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

Crystallographic characterization of the first reported crystalline form of the potent hallucinogen (R)-2-amino-1-(8-bromobenzo[1,2-b;5,4-b']difuran-4-yl)propane or `bromodragonfly': the 1:1 anhydrous proton-transfer compound with 3,5-dinitrosalicylic acid

The 1:1 proton-transfer compound of the potent substituted amphetamine hallucinogen (R)-1-(8-bromobenzo[1,2-b; 4,5-b']difuran-4-yl)-2-aminopropane (common trivial name 'bromodragonfly') with 3,5-dinitrosalicylic acid, 1-(8-bromobenzo[1,2-b;4,5-b']difuran-4-yl)-2-mmoniopropane 2-carboxy-4,6-dinitrophenolate, C13H13BrNO2+ C7H3N2O7- forms hydrogen-bonded cation-anion chain substructures comprising undulating head-to-tail anion chains formed through C(8) carboxyl O-H...O(nitro) associations and incorporating the aminium groups of the cations. The intra-chain cation-anion hydrogen-bonding associations feature proximal cyclic R33(8) interactions involving both a N+-H...O(phenolate) and the carboxyl O--H...O(nitro)associations. Also present are aromatic pi-pi ring interactions [minimum ring centroid separation, 3.566(2)A; inter-plane dihedral angle, 5.13(1)deg]. A lateral hydrogen-bonding interaction between the third aminium proton and a carboxyl O acceptor link the chain substructures giving a two-dimensional sheet structure. This determination represents the first of any form of this compound and confirms that it has the (R) absolute configuration. The atypical crystal stability is attributed both to the hydrogen-bonded chain substructures provided by the anions, which accommodate the aminium proton-donor groups of the cations and give cross-linking, and to the presence of cation--anion aromatic ring pi-pi interactions.

Transition of synthetic chromium oxide gel to crystalline chromium oxide : a hot stage Raman spectroscopic study

Chromium oxide gel material was synthesised and appeared to be X-ray amorphous. The changes in the structure of the synthetic chromium oxide gel were investigated using hot-stage Raman spectroscopy based upon the results of thermogravimetric analysis. The thermally decomposed product of the synthetic chromium oxide gel in nitrogen atmosphere was confirmed to be crystalline Cr2O3 as determined by the hot-stage Raman spectra. Two bands were observed at 849 and 735 cm-1 in the Raman spectrum at 25 °C, which were attributed to the symmetric stretching modes of O-CrIII-OH and O-CrIII-O. With temperature increase, the intensity of the band at 849 cm-1 decreased, while the band at 735 cm-1 increased. These changes in intensity are attributed to the loss of OH groups and formation of O-CrIII-O units in the structure. A strongly hydrogen bonded water H-O-H bending band was found at 1704 cm-1 in the Raman spectrum of the chromium oxide gel, however this band shifted to around 1590 cm-1 due to destruction of the hydrogen bonds upon thermal treatment. Six new Raman bands were observed at 578, 540, 513, 390, 342 and 303 cm-1 attributed to the thermal decomposed product Cr2O3. The use of the hot-stage Raman microscope enabled low-temperature phase changes brought about through dehydration and dehydroxylation to be studied.

A solvothermal route to crystalline lithium niobate

A solvothermal route for the preparation of crystalline state lithium niobate using Li2 CO3 and Nb2 O5 is developed. Oxalic acid is employed as solvent, which coordinates with niobium oxide to stimulate the main reaction. Scanning electron microscopy images show that the as-prepared sample displays a cubic morphology. X-ray diffraction and IR spectrum of the as-prepared sample indicate that the sample is well crystalline.

Advanced numerical characterization of mono-crystalline copper with defects

Based on the embedded atom method (EAM) and molecular dynamics (MD) method, the mono-crystalline copper with different defects is investigated through tension and nanoindentation simulation. The single-crystal copper nanowire with surface defects is firstly studied through tension. For validation, the tension simulations for nanowire without defect are carried out under different temperatures and strain rates. The defects on nanowires are then systematically studied in considering different defects orientation distribution. It is found that the Young’s modulus is insensitive of surface defects and centro-plane defects. However, the yield strength and yield point show a significant decrease due to the different defects. Specially, the 〖45〗^° defect in surface and in (200) plane exerts the biggest influence to the yield strength, about 34.20% and 51.45% decrease are observed, respectively. Different defects are observed to serve as a dislocation source and different necking positions of the nanowires during tension are found. During nanoindentation simulation, dislocation is found nucleating below the contact area, but no obvious dislocation is generated around the nano-cavity. Comparing with the perfect substrate during nanoindentation, the substrate with nano-cavities emerged less dislocations, it is supposed that the nano-cavity absorbed part of the indent energy, and less plastic deformation happened in the defected substrate.

MRI study of the changes in crystalline lens shape with accommodation and ageing in humans

Magnetic Resonance Imaging was used to study changes in the crystalline lens and ciliary body with accommodation and aging. Monocular images were obtained in 15 young (19-29 years) and 15 older (60-70 years) emmetropes when viewing at far (6m) and at individual near points (14.5 to 20.9 cm) in the younger group. With accommodation, lens thickness increased (mean±95% CI: 0.33±0.06mm) by a similar magnitude to the decrease in anterior chamber depth (0.31±0.07mm) and equatorial diameter (0.32±0.04mm) with a decrease in the radius of curvature of the posterior lens surface (0.58±0.30mm). Anterior lens surface shape could not be determined due to the overlapping region with the iris. Ciliary ring diameter decreased (0.44±0.17mm) with no decrease in circumlental space or forward ciliary body movement. With aging, lens thickness increased (mean±95% CI: 0.97±0.24mm) similar in magnitude to the sum of the decrease in anterior chamber depth (0.45±0.21mm) and increase in anterior segment depth (0.52±0.23mm). Equatorial lens diameter increased (0.28±0.23mm) with no change in the posterior lens surface radius of curvature. Ciliary ring diameter decreased (0.57±0.41mm) with reduced circumlental space (0.43±0.15mm) and no forward ciliary body movement. Accommodative changes support the Helmholtz theory of accommodation including an increase in posterior lens surface curvature. Certain aspects of aging changes mimic accommodation.

Molecular dynamics studies of the effects of branching characteristics on the crystalline structure of polyethylene

Molecular dynamics simulations were carried out on single chain models of linear low-density polyethylene in vacuum to study the effects of branch length, branch content, and branch distribution on the polymer’s crystalline structure at 300 K. The trans/gauche (t/g) ratios of the backbones of the modeled molecules were calculated and utilized to characterize their degree of crystallinity. The results show that the t/g ratio decreases with increasing branch content regardless of branch length and branch distribution, indicating that branch content is the key molecular parameter that controls the degree of crystallinity. Although t/g ratios of the models with the same branch content vary, they are of secondary importance. However, our data suggests that branch distribution (regular or random) has a significant effect on the degree of crystallinity for models containing 10 hexyl branches/1,000 backbone carbons. The fractions of branches that resided in the equilibrium crystalline structures of the models were also calculated. On average, 9.8% and 2.5% of the branches were found in the crystallites of the molecules with ethyl and hexyl branches while C13 NMR experiments showed that the respective probabilities of branch inclusion for ethyl and hexyl branches are 10% and 6% [Hosoda et al., Polymer 1990, 31, 1999–2005]. However, the degree of branch inclusion seems to be insensitive to the branch content and branch distribution.

A comparative study on the mineralogy, chemistry and chronology of the Apollo 16 crystalline impact melt breccias. Part II: Chronology.

The controversy on how to interpret the ages of lunar highland breccias has recently been discussed by James [1]. Are the measured ages testimony of true events in lunar history; do they represent the age of the ancient crustal rocks, mixed ages of unequilibrated matrix-phenocryst relationships, or merely thermal events subsequent to the formational event ? It is certain from analyses of terrestrial impact melt breccias that the melt matrix of whole impact melt sheets is isotopically equilibrated due to the extensive mixing process of the early cratering stage [2,3]. It has been shown that isotopic equilibration takes place between impact melt matrix and target rock clasts therein, with the intensity of isotopic exchange depending on the degree of shock metamorphism, thermal metamorphism and the size of the clasts [4]. Therefore, impact melt breccias - if they are relatively clast-poor and mineralogically well studied - can be considered to be the most reliable source for information on the impact history of the lunar highland.

Gradients of refractive index in the crystalline lens and transient changes in refraction among patients with diabetes

Transient hyperopic refractive shifts occur on a timescale of weeks in some patients after initiation of therapy for hyperglycemia, and are usually followed by recovery to the original refraction. Possible lenticular origin of these changes is considered in terms of a paraxial gradient index model. Assuming that the lens thickness and curvatures remain unchanged, as observed in practice, it appears possible to account for initial hyperopic refractive shifts of up to a few diopters by reduction in refractive index near the lens center and alteration in the rate of change between center and surface, so that most of the index change occurs closer to the lens surface. Restoration of the original refraction depends on further change in the refractive index distribution with more gradual changes in refractive index from the lens center to its surface. Modeling limitations are discussed.

Methods to estimate the size and shape of the unaccommodated crystalline lens in vivo

Purpose. The purpose of this article was to present methods capable of estimating the size and shape of the human eye lens without resorting to phakometry or magnetic resonance imaging (MRI). Methods. Previously published biometry and phakometry data of 66 emmetropic eyes of 66 subjects (age range [18, 63] years, spherical equivalent range [−0.75, +0.75] D) were used to define multiple linear regressions for the radii of curvature and thickness of the lens, from which the lens refractive index could be derived. MRI biometry was also available for a subset of 30 subjects, from which regressions could be determined for the vertex radii of curvature, conic constants, equatorial diameter, volume, and surface area. All regressions were compared with the phakometry and MRI data; the radii of curvature regressions were also compared with a method proposed by Bennett and Royston et al. Results. The regressions were in good agreement with the original measurements. This was especially the case for the regressions of lens thickness, volume, and surface area, which each had an R2 > 0.6. The regression for the posterior radius of curvature had an R2 < 0.2, making this regression unreliable. For all other regressions we found 0.25 < R2 < 0.6. The Bennett-Royston method also produced a good estimation of the radii of curvature, provided its parameters were adjusted appropriately. Conclusions. The regressions presented in this article offer a valuable alternative in case no measured lens biometry values are available; however care must be taken for possible outliers.