A unifying theory of refractive error development

While retinal defocus is believed to be myopigenic in nature, the underlying mechanism has remained elusive. We recently constructed a theory of refractive error development to investigate its fundamental properties. Our Incremental Retinal-Defocus Theory is based on the principle that the change in retinal-defocus magnitude during an increment of genetically-programmed ocular growth provides the requisite sign for the appropriate alteration in subsequent environmentally-induced ocular growth. This theory was tested under five experimental conditions: lenses, diffusers, occlusion, crystalline lens removal, and prolonged nearwork. Predictions of the theory were consistent with previous animal and human experimental findings. In addition, simulations using a MATLAB/SIMULINK model supported our theory by demonstrating quantitatively the appropriate directional changes in ocular growth rate. Thus, our Incremental Retinal-Defocus Theory provides a simple and logical unifying concept underlying the mechanism for the development of refractive error.     

A detailed paraxial schematic eye for the White Leghorn chick

We studied the normal ocular development of the chick (Gallus gallus domesticus, White Leghorn) up to 15 days of age using both longitudinal and cross-sectional methods. The change in refractive error, corneal curvature and axial ocular distances were used to construct schematic eyes. Equations are presented which allow prediction of refractive error changes associated with changes in vitreous chamber depth. The mean refractive error was +3.2 D at hatching, which reduced by 66% over the first 3 days and stabilized by 11 days of age. The lens thickened and the anterior chamber deepened from hatching, but vitreal elongation and corneal flattening were delayed until after the first 3 days, suggesting that normal eye growth may be initially inhibited or inactive during an initial emmetropization period, and subsequently activated in response to myopic defocus arising from the continually expanding lens. Finally, when compared with published data on other chick strains, we find differences in the degree of hyperopia at hatching due to differences in lens thickness. However, the rate of ocular and vitreal expansion and the developmental changes in corneal power are similar, making the schematic eyes presented here generally applicable to different strains of chickens.     

Genomewide scan in Ashkenazi Jewish families demonstrates evidence of linkage of ocular refraction to a QTL on chromosome 1p36

The development of refractive error is mediated by both environmental and genetic factors. We performed regression-based quantitative trait locus (QTL) linkage analysis on Ashkenazi Jewish families to identify regions in the genome responsible for ocular refraction. We measured refractive error on individuals in 49 multi-generational American families of Ashkenazi Jewish descent. The average family size was 11.1 individuals and was composed of 2.7 generations. Recruitment criteria specified that each family contain at least two myopic members. The mean spherical equivalent refractive error in the sample was −3.46D (SD=3.29) and 87% of individuals were myopic. Microsatellite genotyping with 387 markers was performed on 411 individuals. We performed multipoint regression-based linkage analysis for ocular refraction and a log transformation of the trait using the statistical package Merlin-Regress. Empirical genomewide significance levels were estimated through gene-dropping simulations by generating random genotypes at each of the 387 markers in 200 replicates of our pedigrees. Maximum LOD scores of 9.5 for ocular refraction and 8.7 for log-transformed refraction (LTR) were observed at 49.1 cM on chromosome 1p36 between markers D1S552 and D1S1622. The empirical genomewide significance levels were P=0.065 for ocular refraction and P<0.005 for LTR, providing strong evidence for linkage of refraction to this locus. The inter-marker region containing the peak spans 11 Mb and contains approximately 189 genes. Conclusion: We found genomewide significant evidence for linkage of refractive error to a novel QTL on chromosome 1p36 in an Ashkenazi Jewish population.     

Prediction of the power of detection of marker-quantitative trait locus linkages using analysis of variance

Analysis of variance can be used to detect the linkage of segregating quantitative trait loci (QTLs) to molecular markers in outbred populations. Using independent full-sib families and assuming linkage equilibrium, equations to predict the power of detection of a QTL are described. These equations are based on an hierarchical analysis of variance assuming either a completely random model or a mixed model, in which the QTL effect is fixed. A simple prediction of power from the mean squares is used that assumes a random model so that in the mixed-model situation this is an approximation. Simulation is used to illustrate the failure of the random model to predict mean squares and, hence, the power. The mixed model is shown to provide accurate prediction of the mean squares and, using the approximation, of power.     

Identification of apolipoprotein A-I as a "STOP" signal for myopia

Good visual acuity requires that the axial length of the ocular globe is matched to the refractive power of the cornea and lens to focus the images of distant objects onto the retina. During the growth of the juvenile eye, this is achieved through the emmetropization process that adjusts the ocular axial length to compensate for the refractive changes that occur in the anterior segment. A failure of the emmetropization process can result in either excessive or insufficient axial growth, leading to myopia or hyperopia, respectively. Emmetropization is mainly regulated by the retina, which generates two opposite signals: "GO/GROW" signals to increase axial growth and "STOP" signals to block it. The presence of GO/GROW and STOP signals was investigated by a proteomics analysis of the retinas from chicken with experimental myopia and hyperopia. Of 18 differentially expressed proteins that were identified, five displayed an expression profile corresponding to GO/GROW signals, and two corresponded to STOP signals. Western blotting confirmed that apolipoprotein A-I (apoA-I) has the characteristics of a STOP signal both in the retina as well as in the fibrous sclera. In accordance with this, intraocular application of the peroxisome proliferator-activated receptor alpha agonist GW7647 resulted in up-regulation of apoA-I levels and in a significant reduction of experimental myopia. In conclusion, using a comprehensive functional proteomics analysis of chicken ocular growth models we identified targets for ocular growth control. The correlation of elevated apoA-I levels with reduced ocular axial growth points toward a functional relationship with the observed morphological changes of the eye.     

The refractive development of the eye of the American kestrel (Falco sparverius): a new avian model

Summary Most measures of avian visual performance are carried out on commonly available domestic species such as the chicken, and most of the data on avian induced refractive error deals with chickens. Raptors are predatory birds in which good visual resolving ability is particularly important. Behavioral studies indicate that the eyes of raptors have two to three times the resolving ability of the human eye. The domestic chicken is precocial at hatching whereas most raptors are semi-altricial. This study was an effort to determine if the effect of early visual deprivation on the refractive development of the chicken eye can be reproduced in the American kestrel, a species which is not domesticated and in which the need for acute vision is particularly important.Visual deprivation was achieved by unilaterally applying translucent plastic goggles over the eyes of kestrels two days after hatching. Refractive error was measured using a retinoscope and trial lenses. Ocular growth was monitored by A-scan ultrasonography, and frozen ocular sections of sacrificed birds. The effect of the experimental manipulation on the contralateral control eye and body weight was evaluated each day over a 42-day period. The goggles did not significantly affect the normal changes in body weight or the normal pattern of ocular growth and refractive development in the untreated eyes. An analysis of the refractive state changes as a result of form deprivation was made each week for 6 weeks after hatching on both the treated and untreated eyes in a separate group of experimental birds. Visual form deprivation caused a significant myopic shift in refractive error and a significant increase in the vitreous chamber depth in the treated eyes at 3 and 6 weeks of age. However, the amount of myopia produced is much less than that induced in chicks, and in certain cases hyperopia is produced. The kestrels recover from myopia and hyperopia within 10 days of goggle removal, after 3 to 4 weeks of deprivation.This study is the first indication that chickens may not be a representative bird model for studying form deprivation myopia. First, myopia is not always produced in kestrels in response to form deprivation. Second, kestrels are severely myopic at hatching and therefore, the direction of emmetropization is opposite to that found in hatchling chicks.     

A fully continuous individual-based model of tumor cell evolution

The aim of this work is to develop and study a fully continuous individual-based model (IBM) for cancer tumor invasion into a spatial environment of surrounding tissue. The IBM improves previous spatially discrete models, because it is continuous in all variables (including spatial variables), and thus not constrained to lattice frameworks. The IBM includes four types of individual elements: tumor cells, extracellular macromolecules (MM), a matrix degradative enzyme (MDE), and oxygen. The algorithm underlying the IBM is based on the dynamic interaction of these four elements in the spatial environment, with special consideration of mutation phenotypes. A set of stochastic differential equations is formulated to describe the evolution of the IBM in an equivalent way. The IBM is scaled up to a system of partial differential equations (PDE) representing the limiting behavior of the IBM as the number of cells and molecules approaches infinity. Both models (IBM and PDE) are numerically simulated with two kinds of initial conditions: homogeneous MM distribution and heterogeneous MM distribution. With both kinds of initial MM distributions spatial fingering patterns appear in the tumor growth. The output of both simulations is quite similar.     

A New Evaluation Method for 2‐D Fluorescence Spectra Based on Theoretical Modeling

This article presents a new evaluation procedure of 2‐D fluorescence spectra obtained during a yeast cultivation without performing a calibration measurement. The 2‐D fluorescence spectra are used to predict the process variables biomass, glucose and ethanol. The new calibration procedure uses a theoretical model of these process variables, i.e., differential equations, to replace any calibration measurement. The theoretical model parameters are identified simultaneously during the calculation of the chemometric models. The root mean square error of prediction of the chemometric models with respect to off‐line measurements are 1.5 g/L, 0.40 g/L and 0.56 g/L for glucose, biomass and ethanol, respectively.     

Adequate Examination of the Eye

A concise outline of the methodology of an adequate examination of the eye is presented so that the ocular findings may be used properly in establishing a diagnosis. An accurate ocular history is important. Visual acuity at a distance and at the reading point should be measured in such a way as to avoid the introduction of error. A pinhole disc can be used to differentiate a refractive error from organic pathology. Clinical methods of performing the visual field examination, estimating the lacrimal tear production, and determining intraocular pressure are described and illustrated.     

Differential distribution of some elements in a camera type eye-lens as revealed by energy dispersive x-ray micro-analysis

Differential distribution of some elements have been detected in the cortex and medulla of the camera type eye-lens in a fresh water fish, Notopterus sp., using energy dispersive X-ray spectroscopy. This unique pattern of elemental distribution explains the less understood mechanism by which the optical properties of different parts of the fish lens are altered continuously and differentially during growth. The study also suggests the possible optical roles of some elements in ocular refractive structures.     

Bayesian Dynamical Systems Modelling in the Social Sciences

Data arising from social systems is often highly complex, involving non-linear relationships between the macro-level variables that characterize these systems. We present a method for analyzing this type of longitudinal or panel data using differential equations. We identify the best non-linear functions that capture interactions between variables, employing Bayes factor to decide how many interaction terms should be included in the model. This method punishes overly complicated models and identifies models with the most explanatory power. We illustrate our approach on the classic example of relating democracy and economic growth, identifying non-linear relationships between these two variables. We show how multiple variables and variable lags can be accounted for and provide a toolbox in R to implement our approach.     

Refractive Status at Birth: Its Relation to Newborn Physical Parameters at Birth and Gestational Age

Background

Refractive status at birth is related to gestational age. Preterm babies have myopia which decreases as gestational age increases and term babies are known to be hypermetropic. This study looked at the correlation of refractive status with birth weight in term and preterm babies, and with physical indicators of intra-uterine growth such as the head circumference and length of the baby at birth.

Methods

All babies delivered at St. Stephens Hospital and admitted in the nursery were eligible for the study. Refraction was performed within the first week of life. 0.8% tropicamide with 0.5% phenylephrine was used to achieve cycloplegia and paralysis of accommodation. 599 newborn babies participated in the study. Data pertaining to the right eye is utilized for all the analyses except that for anisometropia where the two eyes were compared. Growth parameters were measured soon after birth. Simple linear regression analysis was performed to see the association of refractive status, (mean spherical equivalent (MSE), astigmatism and anisometropia) with each of the study variables, namely gestation, length, weight and head circumference. Subsequently, multiple linear regression was carried out to identify the independent predictors for each of the outcome parameters.

Results

Simple linear regression showed a significant relation between all 4 study variables and refractive error but in multiple regression only gestational age and weight were related to refractive error. The partial correlation of weight with MSE adjusted for gestation was 0.28 and that of gestation with MSE adjusted for weight was 0.10. Birth weight had a higher correlation to MSE than gestational age.

Conclusion

This is the first study to look at refractive error against all these growth parameters, in preterm and term babies at birth. It would appear from this study that birth weight rather than gestation should be used as criteria for screening for refractive error, especially in developing countries where the incidence of intrauterine malnutrition is higher.     

Graphical rules for non-steady state enzyme kinetic

The exiting graphical methods in enzyme kinetics can be used only within the scope of steady state reactions. In this paper, two graphical rules are presented to deal with the non-steady state enzyme catalysed reaction systems. According to Rule 1 we can immediately write out the phase concentration of enzyme species. The calculation work such as setting up differential equations, making Laplace transformation, expanding determinants, which are both tedious and liable to error, are completely saved. By means of Rule 2 the secular equations for the consecutive first-order reactions can be written out directly without need of setting up differential equations, expanding determinants, etc., that would otherwise be laborious and prone to errors. In addition, two check formulae are also presented for these two graphical methods, respectively. They are useful in order for avoiding the omission of terms during calculations, especially, for complicated mechanisms.     

包含哑变量的黑龙江省落叶松人工林碳储量预测模型系统

利用2005—2010年两期黑龙江省落叶松人工林固定监测样地数据,分析黑龙江省落叶松人工林各林分变量因子之间的关系,建立地位级指数曲线模型和林分密度指数模型,采用两步最小二乘的方法建立预测包含林分平均断面积和林分碳储量的联立方程组,将以上所构建的模型统称为黑龙江省落叶松人工林碳储量预测模型系统.同时将龄组和区域作为哑变量加入到预测模型中.结果表明: 模型系统中除地位级指数曲线模型之外,剩余模型的确定系数(R²)均大于0.98,均方根误差均小于4,而加入哑变量的模型R²有所增加,均方根误差均小于3,说明模型稳定性较好,预估参数较为精确.各模型的平均相对误差均小于2%,大部分模型平均相对误差绝对值小于15%,模型精度均在95%以上,研究结果可以对黑龙江省不同区域和龄组的落叶松人工林林分平均树高进行精确拟合.根据地位级指数曲线模型和联立方程组的拟合参数进行分析,当调查样地在同一区域时,林分年龄越大,林分平均树高、林分平均断面积和林分碳储量越大,符合实际生长规律;而在林分年龄相同、区域不同时,不同区域林分平均树高由大到小的排列顺序为: 平原地区、小兴安岭南坡地区、张广才岭东坡地区、完达山地区、张广才岭西坡地区、小兴安岭北坡地区.不同区域林分断面积和林分碳储量由多到少的排列顺序为: 张广才岭东坡地区、小兴安岭北坡地区、张广才岭西坡地区、小兴安岭南坡地区、完达山地区、平原地区.     

Patient-specific modeling of corneal refractive surgery outcomes and inverse estimation of elastic property changes

The purpose of this study is to develop a 3D patient-specific finite element model (FEM) of the cornea and sclera to compare predicted and in vivo refractive outcomes and to estimate the corneal elastic property changes associated with each procedure. Both eyes of a patient who underwent laser-assisted in situ keratomileusis (LASIK) for myopic astigmatism were modeled. Pre- and postoperative Scheimpflug anterior and posterior corneal elevation maps were imported into a 3D corneo-scleral FEM with an unrestrained limbus. Preoperative corneal hyperelastic properties were chosen to account for meridional anisotropy. Inverse FEM was used to determine the undeformed corneal state that produced <0.1% error in anterior elevation between simulated and in vivo preoperative geometries. Case-specific 3D aspheric ablation profiles were simulated, and corneal topography and spherical aberration were compared at clinical intraocular pressure. The magnitude of elastic weakening of the residual corneal bed required to maximize the agreement with clinical axial power was calculated and compared with the changes in ocular response analyzer (ORA) measurements. The models produced curvature maps and spherical aberrations equivalent to in vivo measurements. For the preoperative property values used in this study, predicted elastic weakening with LASIK was as high as 55% for a radially uniform model of residual corneal weakening and 65% at the point of maximum ablation in a spatially varying model of weakening. Reductions in ORA variables were also observed. A patient-specific FEM of corneal refractive surgery is presented, which allows the estimation of surgically induced changes in corneal elastic properties. Significant elastic weakening after LASIK was required to replicate clinical topographic outcomes in this two-eye pilot study.     

Weak convergence of a sequence of stochastic difference equations to a stochastic ordinary differential equation

We consider a sequence of discrete parameter stochastic processes defined by solutions to stochastic difference equations. A condition is given that this sequence converges weakly to a continuous parameter process defined by solutions to a stochastic ordinary differential equation. Applying this result, two limit theorems related to population biology are proved. Random parameters in stochastic difference equations are autocorrelated stationary Gaussian processes in the first case. They are jump-type Markov processes in the second case. We discuss a problem of continuous time approximations for discrete time models in random environments.     

Mathematical Models of the Kinetics of the Cultivation of Microorganisms

Various equations of mathematical models for the kinetics of the development of various biological processes were obtained on the basis of the generalized differential equation of biomass growth. Aerobic periodic cultivation of the yeast Saccharomyces cerevisiae was carried out to provide a comparative evaluation of advantages and disadvantages of four types of mathematical models. It is shown that the exponential model is a particular solution to the generalized differential equation. The developed mathematical model can be used to predict the course of biological processes in time and can serve as a tool for a computational experiment in order to clarify the dependence of the rate of a biological process on changes in certain parameters that affect the development of cells.     

A study of some diffusion models of population growth

The stochastic differential equations of many diffusion processes which arise in studies of population growth in random environments can be transformed, if the Stratonovich stochastic calculus is employed, to the equation of the Wiener process. If the transformation function has certain properties then the transition probability density function and quantities relating to the time to first attain a given population size can be obtained from the known results for the Wiener process. Some other random growth processes can be derived from the Ornstein-Uhlenbeck process. These transformation methods are applied to the random processes of Malthusian growth, Pearl-Verhulst logistic growth and a recent model of density independent growth due to Levins.     

Prevalence and associations of steep cornea/keratoconus in Greater Beijing. The Beijing Eye Study

Purpose

To evaluate the prevalence and associated factors of steep cornea/keratoconus in the adult Chinese population.

Methods

The population-based Beijing Eye Study 2011 included 3468 individuals with a mean age of 64.6±9.8 years (range: 50–93 years). A detailed ophthalmic examination was performed including optical low-coherence reflectometry. Steep cornea/keratoconus were defined as an anterior corneal refractive power exceeding 48 diopters.

Results

Mean refractive power of the cornea was 43.16±1.45 diopters (range: 36.51 to 48.46 diopters; flattest meridian) and 43.98±1.52 diopters (range: 37.00 to 52.88 diopters; steepest meridian). A steep cornea/keratoconus defined as corneal refractive power of ≥48 diopters and ≥49 diopters was detected in 27 subjects (prevalence rate: 0.9±0.2%) and 6 (0.2± 0.1%) subjects, respectively. Presence of steep cornea/keratoconus was associated with shorter axial length (P<0.001), smaller interpupillary distance (P = 0.038), lower best corrected visual acuity (P = 0.021), higher cylindrical refractive error (P<0.001) and more myopic refractive error (P<0.001). It was not significantly associated with gender, body height, psychic depression, cognitive function, blood concentrations of glucose, lipids, creatinine and C-reactive protein, blood pressure and quality of life score, nor with intraocular pressure, dry eye feeling, and lens thickness.

Conclusions

A steep cornea/keratoconus defined as corneal refractive power of 48+ diopters has a prevalence of 0.9±0.2% among Chinese aged 50 years and above. Its prevalence was significantly associated with the ocular parameters of shorter axial length, smaller interpupillary distance, higher cylindrical and myopic refractive error and lower best corrected visual acuity, however, with none of the systemic parameters tested.