Determining insulin sensitivity from glucose tolerance tests in sheep.

A mathematical model of the dynamics of insulin and glucose during a frequently sampled intravenous glucose tolerance test (IVGTT) in sheep was developed that characterizes the large second-phase insulin secretion response in sheep during IVGTT. The model was fit to measurements of the glucose and insulin dynamics during standard IVGTT ( = 42) and modified IVGTT ( = 40), where insulin was injected 60 min after the initiation of the IVGTT. The correlation between log insulin sensitivity determined by hyperglycemic clamps (HGC) and standard IVGTT was = 0.43 ( = 0.005). The correlation between log insulin sensitivity determined by HGC and modified IVGTT was = 0.51 ( = 0.002). The model, therefore, provides a method to determine insulin sensitivity through a cheaper and more easily performed IVGTT. We validated our estimation procedure using 2 independent experiments on the effect of 1) pregnancy and 2) being born preterm and exposed to dextrose or dextrose with insulin on HGC-derived insulin sensitivity. The IVGTT-derived insulin sensitivity was significantly greater in pregnant ewes than in prepregnant ewes (difference of 0.39 ± 0.12 log n ng mL; < 0.05), and this was consistent with the significantly greater hyperinsulinemic euglycemic clamp-derived insulin sensitivity in pregnant ewes than in prepregnant ewes (difference of 4.03 ± 0.66 µmol mL kg min ng; < 0.001). There was no significant effect of being born preterm on IVGTT/HGC-derived insulin sensitivity. Basal insulin, insulin sensitivity, insulin production, and insulin clearance were lower in prepregnant ewes ( < 0.05). That is, prepregnant ewes have a lower insulin equilibrium status and less responsive insulin turnover. There was also a significant effect of insulin therapy on the rate of insulin clearance in preterm lambs ( < 0.05). This effect was independently significant of its covariance with all other model parameters. Therefore, it can be interpreted as a direct effect on the rate of insulin clearance by the insulin treatment. All other parameter responses to the insulin treatment effect can be regarded as being due to the covariance between these parameters. These analyses demonstrate that treatment effects on insulin sensitivity can be detected using IVGTT experiments.

A new, improved and generalizable approach for the analysis of biological data generated by -omic platforms.

The principles embodied by the Developmental Origins of Health and Disease (DOHaD) view of 'life history' trajectory are increasingly underpinned by biological data arising from molecular-based epigenomic and transcriptomic studies. Although a number of 'omic' platforms are now routinely and widely used in biology and medicine, data generation is frequently confounded by a frequency distribution in the measurement error (an inherent feature of the chemistry and physics of the measurement process), which adversely affect the accuracy of estimation and thus, the inference of relationships to other biological measures such as phenotype. Based on empirical derived data, we have previously derived a probability density function to capture such errors and thus improve the confidence of estimation and inference based on such data. Here we use published open source data sets to calculate parameter values relevant to the most widely used epigenomic and transcriptomic technologies Then by using our own data sets, we illustrate the benefits of this approach by specific application, to measurement of DNA methylation in this instance, in cases where levels of methylation at specific genomic sites represents either (1) a response variable or (2) an independent variable. Further, we extend this formulation to consideration of the 'bivariate' case, in which the co-dependency of methylation levels at two distinct genomic sites is tested for biological significance. These tools not only allow greater accuracy of measurement and improved confidence of functional inference, but in the case of epigenomic data at least, also reveal otherwise cryptic information.

The phenotype of an IVF child is associated with peri-conception measures of follicular characteristics and embryo quality.

STUDY QUESTION: Are childhood measures of phenotype associated with peri-conception parental, IVF treatment and/or embryonic characteristics of IVF children? SUMMARY ANSWER: Birthweight, childhood body mass index (BMI) and height of pre-pubertal IVF children were strongly associated with peri-conception factors, including follicular and embryonic characteristics. WHAT IS KNOWN ALREADY: A growing number of studies have identified a range of phenotypic differences between IVF and naturally conceived pre-pubertal children; for example, birthweights are lower following a fresh compared with a thawed embryo transfer. STUDY DESIGN, SIZE, DURATION: This retrospective cohort study included IVF children (n = 96) born at term (>37 weeks) after a singleton pregnancy from the transfer of either fresh or thawed embryos in New Zealand. Between March 2004 and November 2008, these children were subjected to clinical assessment before puberty. PARTICIPANTS/MATERIALS, SETTING, METHODS: Clinical assessment provided anthropometric measures of children aged 3.5-11 years old. Peri-conception factors (n = 36) derived retrospectively from parental, treatment, laboratory and embryonic variables (n = 69) were analysed using multiple stepwise regression with respect to standard deviation scores (SDSs) of the birthweight, mid-parental corrected BMI and height of the IVF children. Data from children conceived from fresh (n = 60) or thawed (n = 36) embryos, that met inclusion criteria and had high-quality data with >90% completeness, were analysed. MAIN RESULTS AND THE ROLE OF CHANCE: Embryo treatment at transfer was identified as a predictor of birthweight with thawed embryos resulting in heavier birthweights than fresh embryos [P = 0.02, 95% confidence interval (CI) fresh minus thawed: -1.047 to -0.006]. Birthweight SDS was positively associated with mid-parental corrected BMI SDS (P = 0.003, slope 0.339 ± 0.100). Four factors were related (P < 0.05) to mid-parental corrected height SDS. In particular, child height was inversely associated with the diameter of lead follicles at oocyte retrieval (P < 0.0001, slope -0.144 ± 0.040) and with the quality score of embryos at transfer (P = 0.0008, slope -0.425 ± 0.157), and directly associated with the number of follicles retrieved (P = 0.05, slope 1.011 ± 0.497). Child height was also positively associated with the transfer of a fresh as opposed to thawed embryo (P < 0.001, 95% CI 0.275-0.750). LIMITATIONS, REASONS FOR CAUTION: More than one embryo was transferred in most cycles so mean development and quality data were used. The large number of variables measured was on a relatively small sample size. Large cohorts from multiple clinics using a variety of treatment protocols and embryology methods are needed to confirm the associations identified and ultimately to test these factors as possible predictors of phenotype. WIDER IMPLICATIONS OF THE FINDINGS: This is the first study to directly associate peri-conception measures of IVF treatment with a pre-pubertal child's phenotype. Demonstration that peri-conception measures relate to a pre-pubertal child's phenotype extends the range of factors that may influence growth and development. These findings, if corroborated by larger studies, would provide invaluable information for practitioners, who may want to consider the impact of ovarian stimulation protocols as well as the quality of the embryo transferred on a child's growth and development, in addition to their impact on pregnancy rate. STUDY FUNDING/COMPETING INTERESTS: This work was supported by grants from the National Research Centre of Growth and Development New Zealand (grant 3682065) and the Australasian Paediatric Endocrine Group (APEG; grant 3621994), as well as a fellowship from Fertility Associates New Zealand awarded to M.P.G. In terms of competing interest, J.C.P is a shareholder of Fertility Associates. M.P.G. currently holds the position of Merck Serono Lecturer in Reproductive Biology. W.S.C. and P.L.H. have also received grants and non-financial support from Novo Nordisk, as well as personal fees from Pfizer that are unrelated to the current study. The other authors have no conflict of interest to declare.

The application of a model of glucose and insulin dynamics to explain an observed effect of leptin administration in reversal of developmental programming.

A dynamical model describing the glucose-insulin physiological system was applied to an experiment on the administration of the adipokine leptin between neonatal days 3 and 13 to rats whose dams were subject to different levels of nutrition during gestation. The effect of leptin treatment on the glucose-insulin equilibrium point and on the levels of other associated metabolites showed a significant change in direction that depended on the level of prenatal nutrition. Leptin has been shown to affect two factors that affect the equilibrium levels of glucose and insulin, gluconeogenesis and insulin sensitivity. Each effect is described by a parameter in the dynamical model. Mathematical analysis shows that changes in these parameters in the manner promoted by leptin would indeed increase or decrease the glucose-insulin equilibria depending on their initial equilibrium levels which might be induced by the level of prenatal nutrition. This analysis explains the results of the leptin experiment in the context of the dynamics of the glucocorticoid system. It also proposes a physiological mechanism for the expression of plasticity in the organism based on the status of the glucose and insulin equilibria.

A risk assessment approach applied to the growth of Erwinia carotovora in vegetable juice for variable temperature conditions.

Risk assessment for food spoilage relies on probabilistic models of microbial growth to predict the likelihood that microbial populations will exceed predefined spoilage levels. To assist in the design and management of industrial food quality systems, predictive microbiological models have to incorporate major risk factors such as the variability in the microbial strain, environment and initial contamination levels. In addition, the application of results measured under laboratory conditions to the less controlled environment of an industrial process usually also involves uncertainty. Extra information regarding this uncertainty must be factored into industrial microbial risk assessment. In this paper, based on our previous analysis of the growth of Erwinia carotovora we show how different factors contribute to the risk of microbial spoilage of vegetable juice and we demonstrate an effective way of including these factors into risk assessment models. The association of risk components with different unavoidable and manageable factors is also valuable for the development of optimal strategies for reducing microbial risk.

Estimation of microbial growth using population measurements subject to a detection limit.

In this paper we develop a maximum likelihood estimation procedure for determining the mean and variance in microbial population size from microbial population measurements subject to a detection limit. Existing estimation methods generally set non-detectable measurements equal to the detection limit and are highly biased. Because changes in the mean and variance in the microbial population size are typical in industrial processes we also outline statistical tests for detecting such changes when measurements are subject to a detection limit, which is critical for process control. In an industrial process there may also potentially be variability in the microbial growth rate due to variation in the microbial strain, environment, and food characteristics. Accordingly, we also present a maximum likelihood procedure for estimating microbial growth model parameters and their variance components from microbial population measurements subject to a detection limit. Such information can be used to generate the mean and variance through time of the microbial population size, which is vital for the application of predictive microbiological models to risk assessment and food product shelf-life estimation.

A dynamic model for ovulation rate reveals an effect of the estrogen receptor genotype on ovarian follicular development in the pig.

A mathematical model that describes the recruitment and growth of ovarian follicles was fitted to data on ovulation rate and the measurements of plasma estradiol collected at times during the estrous cycle for individual gilts. The method of least squares was used to obtain estimates of the parameters of the mathematical model. The estimated model parameters were the maximum estradiol production for a follicle, development of each follicle after commitment, and a function describing the initial estradiol production of committed follicles. The estimated parameters for each pig were classified by estrogen receptor (ER) genotype (AA or BB) and analyzed using a multivariate analysis of variance. There were differences between genotypes (P < 0.05) for the parameter that described the initial distribution of individual follicles at recruitment. Gilts with ER genotype BB recruited follicles that varied more in size but had fewer very small follicles, indicating that the ER gene affects the relative estradiol secretion of the follicles at commitment. This analysis is an example of a general approach to genetic studies that uses a mathematical model of the physiology as a statistical basis for estimating gene action.

Partitioning of the variance in the growth parameters of Erwinia carotovora on vegetable products.

The objective of this paper was to estimate and partition the variability in the microbial growth model parameters describing the growth of Erwinia carotovora on pasteurised and non-pasteurised vegetable juice from laboratory experiments performed under different temperature-varying conditions. We partitioned the model parameter variance and covariance components into effects due to temperature profile and replicate using a maximum likelihood technique. Temperature profile and replicate were treated as random effects and the food substrate was treated as a fixed effect. The replicate variance component was small indicating a high level of control in this experiment. Our analysis of the combined E. carotovora growth data sets used the Baranyi primary microbial growth model along with the Ratkowsky secondary growth model. The variability in the microbial growth parameters estimated from these microbial growth experiments is essential for predicting the mean and variance through time of the E. carotovora population size in a product supply chain and is the basis for microbiological risk assessment and food product shelf-life estimation. The variance partitioning made here also assists in the management of optimal product distribution networks by identifying elements of the supply chain contributing most to product variability.

Modeling the effect of energy status on mammary gland growth and lactation.

The impact of nutrition on lactation can be separated into acute effects, affecting day-to-day yield, and chronic effects, which govern the persistency of lactation and rate of decline of the lactation curve. A mathematical model of the mammary gland was constructed to investigate both acute and chronic effects. Mammary growth is expressed in terms of the dynamics of populations of active (secreting) and quiescent (engorged) alveoli. The secretion rate of active alveoli is expressed in terms of the energy status of the dam. The model was fitted to data from a 2 x 2 factorial trial in which lactation curves were measured for heifers of two different genotypes (North American and New Zealand Holstein-Friesians) fed two different diets [grass and total mixed rations (TMR)]. Total formation of alveoli during pregnancy and lactation was statistically the same across all groups despite differences between diets, in the rate of formation of alveoli at parturition. The senescence rate of alveoli was significantly higher for heifers fed grass compared with heifers fed TMR, which corresponds to better persistency for heifers fed TMR. Heifers fed TMR had a higher rate of reactivation of quiescent alveoli than heifers fed grass, which also contributes to increased persistence for heifers fed TMR. There was a genotype x diet interaction in the rate of quiescence of active alveoli: the North American-Grass group had a higher rate of quiescence than the other three groups, perhaps reflecting differences in selection pressures between the New Zealand and North American genotypes.

Stochastic modelling of the growth of a microbial population under changing temperature regimes.

The application of models of microbial growth to the design of food safety systems requires consideration of the effect of arbitrary changes in external variables on growth of bacteria. In particular, the effect of changes in external variables, such as temperature, on the probability that the microbial population size will not exceed acceptable levels at a given time needs to be predicted. This paper presents a method of calculating the time-dependent probability distribution of the microbial population size under arbitrary changes of temperature through time. To illustrate this method, the effect of a sudden temporary increase in temperature on the evolution of the probability distribution of Lactobacillus plantarum population size is presented. The effect of this change in temperature on the time taken for the population to reach a critical size, with a given probability, is also calculated and the application of this calculation to the design of HACCP protocols is discussed.

Predictive microbiology and food safety.

The evaluation of risk in food safety requires knowledge of the probability that microbial population sizes will not exceed defined levels. This probability is evaluated assuming that the growth of the microbial population can be described by the Gompertz equation with the variance of growth depending on the population size. It is shown that the probability density associated with this phenomenon is skewed, so that the risk of a high microbial population is greater than that which would be estimated using a symmetrical probability distribution such as the Gaussian. Maximum likelihood estimates of the parameters of the Gompertz equation based on the derived probability density are calculated using data published by Zwietering et al. [23] for the growth of Lactobacillus plantarum under different temperatures. The probability that a microbial population of a given size will exceed an unacceptable level within a given time is calculated for growth at two temperatures, 10 and 25 degrees C. The implication of these theoretical results for the management of risk in food safety and in the design of hazard analysis critical control point procedures is discussed.

A model of follicular development and ovulation in sheep and cattle.

A dynamic model to describe ovarian follicular development following commitment has been developed. It identifies follicular growth with oestradiol production and assumes that this growth is the result of intra-ovarian stimulation, gonadotrophin stimulation, and inhibitory interactions among the follicles, where larger follicles suppress the growth of the smaller follicles. The variables of the model are the levels of oestradiol in each follicle at commitment, the rate of change of oestradiol production by individual follicles during follicular development, and the level of oestradiol that will induce luteinizing hormone (LH) surge. Changes in the variables of the model could be associated with both genetic and environmental effects. The behaviour of the model is consistent with experimental observations. The model can be expanded to include exogenous follicle-stimulating hormone (FSH) administration assuming that FSH is associated with advancing the maturation of gonadotrophin-dependent follicles without affecting the number of committed follicles. The use of the model to explore FSH administration strategies is demonstrated. The model confirms that the response to FSH administration depends on both the amount of FSH and the time of administration. The largest number of double ovulations occurred when FSH was given at the time of the deviation of the dominant and subordinate follicles.