Estimation of growth parameters from multiple-recapture data

This article develops a method for analysis of growth data with multiple recaptures when the initial ages for all individuals are unknown. The existing approaches either impute the initial ages or model them as random effects. Assumptions about the initial age are not verifiable because all the initial ages are unknown. We present an alternative approach that treats all the lengths including the length at first capture as correlated repeated measures for each individual. Optimal estimating equations are developed using the generalized estimating equations approach that only requires the first two moment assumptions. Explicit expressions for estimation of both mean growth parameters and variance components are given to minimize the computational complexity. Simulation studies indicate that the proposed method works well. Two real data sets are analyzed for illustration, one from whelks (Dicathais aegaota) and the other from southern rock lobster (Jasus edwardsii) in South Australia.

Exact solutions of coupled multispecies linear reaction–diffusion equations on a uniformly growing domain

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

Cord blood 25-hydroxyvitamin D and fetal growth in the China-Anhui birth cohort study

We determined the association of cord blood 25-hydroxyvitamin D [25(OH)D] with birth weight and the risk of small for gestational age (SGA). As part of the China-Anhui Birth Cohort (C-ABC) study, we measured cord blood levels of 25(OH)D in 1491 neonates in Hefei, China. The data on maternal sociodemographic characteristics, health status, lifestyle, birth outcomes were prospectively collected. Multiple regression models were used to estimate the association of 25(OH)D levels with birth weight and the risk of SGA. Compared with neonates in the lowest decile of cord blood 25(OH)D levels, neonates in four deciles (the fourth, fifth, sixth and seventh deciles) had significantly increased birth weight and decreased risk of SGA. Multiple linear regression models showed that per 10 nmol/L increase in cord blood 25(OH)D, birth weight increased by 61.0 g (95% CI: 31.9, 89.9) at concentrations less than 40 nmol/L, and then decreased by 68.5 g (95% CI: −110.5, −26.6) at concentrations from 40 to 70 nmol/L. This study provides the first epidemiological evidence that there was an inverted U shaped relationship between neonatal vitamin D status and fetal growth, and the risk of SGA reduced at moderate concentration.

Longitudinal changes in choroidal thickness and eye growth in childhood

PURPOSE To examine longitudinal changes in choroidal thickness and axial length in a population of children with a range of refractive errors. METHODS One hundred and one children (41 myopes and 60 nonmyopes) aged 10 to 15 years participated in this prospective, observational longitudinal study. For each child, 6-month measures of choroidal thickness (using enhanced depth imaging optical coherence tomography) and axial ocular biometry were collected four times over an 18-month period. Linear mixed-models were used to examine the longitudinal changes in choroidal thickness and the relationship between changes in choroidal thickness and axial eye growth over the study period. RESULTS A significant group mean increase in subfoveal choroidal thickness was observed over 18 months (mean increase 13 6 22 lm, P < 0.001). Myopic children exhibited significantly thinner choroids compared with nonmyopic children (P < 0.001), although there was no significant time by refractive group interaction (P ¼ 0.46), indicating similar changes in choroidal thickness over time in myopes and nonmyopes. However, a significant association between the change in choroidal thickness and the change in axial length over time was found (P < 0.001, β = −0.14). Children showing faster axial eye growth exhibited significantly less choroidal thickening over time compared with children showing slower axial eye growth. CONCLUSIONS A significant increase in choroidal thickness occurs over an 18-month period in normal 10- to 15-year-old children. Children undergoing faster axial eye growth exhibited less thickening and, in some cases, a thinning of the choroid. These findings support a potential role for the choroid in the mechanisms regulating eye growth in childhood.

Growth of boehmite nanofibers by assembling nanoparticles with surfactant micelles

It is known that boehmite (AlOOH) nanofibers formed in the presence of nonionic poly(ethylene oxide) (PEO) surfactant at 373 K. A novel approach is proposed in this study for the growth of the boehmite nanofibers: when fresh aluminum hydrate precipitate was added at regular interval to initial mixture of boehmite and PEO surfactant at 373 K, the nanofibers grow from 40 to 50 nm long to over 100 nm. It is believed that the surfactant micelles play an important role in the nanofiber growth: directing the assembly of aluminum hydrate particles through hydrogen bonding with the hydroxyls on the surface of aluminum hydrate particles. Meanwhile a gradual improvement in the crystallinity of the fibers during growth is observed and attributed to the Ostwald ripening process. This approach allows us to precisely control the size and morphology of boehmite nanofibers using soft chemical methods and could be useful for low temperature, aqueous syntheses of other oxide nanomaterials with tailorable structural specificity such as size, dimension and morphology.