ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation

Pregnancy-Associated Hypertension in Glucose-Intolerant Pregnancy and Subsequent Metabolic Syndrome

To evaluate whether pregnancy-associated hypertension (preeclampsia or gestational hypertension), among women with varying degrees of glucose intolerance during pregnancy is associated with maternal metabolic syndrome 5-10 years later

On the fourth-order accurate compact ADI scheme for solving the unsteady Nonlinear Coupled Burgers' Equations

The two-dimensional unsteady coupled Burgers' equations with moderate to severe gradients, are solved numerically using higher-order accurate finite difference schemes; namely the fourth-order accurate compact ADI scheme, and the fourth-order accurate Du Fort Frankel scheme. The question of numerical stability and convergence are presented. Comparisons are made between the present schemes in terms of accuracy and computational efficiency for solving problems with severe internal and boundary gradients. The present study shows that the fourth-order compact ADI scheme is stable and efficient

Association of Cervical Effacement With the Rate of Cervical Change in Labor Among Nulliparous Women

OBJECTIVE: To assess the association of cervical effacement with the rate of intrapartum cervical change among nulliparous women. METHODS: We conducted a secondary analysis of a prospective trial of intrapartum fetal pulse oximetry. For women who had vaginal deliveries, interval-censored regression was used to estimate the time to dilate at 1-cm intervals. For each given centimeter of progressive cervical dilation, women were divided into those who had achieved 100% cervical effacement and those who had not. The analysis was performed separately for women in spontaneous labor and those who were given oxytocin. RESULTS: A total of 3,902 women were included in this analysis, 1,466 (38%) who underwent labor induction, 1,948 (50%) who underwent labor augmentation (combined for the analysis), and 488 (13%) who labored spontaneously. For women in spontaneous labor, the time to dilate 1 cm was shorter for those who were 100% effaced starting at 4 cm of cervical dilation (P=.01 to <.001). For women who received oxytocin, the time to dilate 1 cm was shorter for those who were 100% effaced throughout labor (P<.001). CONCLUSION: The rate of cervical dilation among nulliparous women is associated with not only the degree of cervical dilation, but also with cervical effacement. CLINICAL TRIAL REGISTRATION: ClinicalTrials.gov, www.clinicaltrials.gov, NCT00098709

Carpenter-Coustan Compared With National Diabetes Data Group Criteria for Diagnosing Gestational Diabetes

Use of Carpenter-Coustan compared to National Diabetes Data Group (NDDG) criteria increases the number of women diagnosed with GDM by 30-50%, but whether treatment of this milder GDM reduces adverse outcomes is unknown. We explored the effects of the diagnostic criteria used on the benefits of GDM treatment

Haptoglobin Phenotype, Preeclampsia Risk and the Efficacy of Vitamin C and E Supplementation to Prevent Preeclampsia in a Racially Diverse Population

Haptoglobin's (Hp) antioxidant and pro-angiogenic properties differ between the 1-1, 2-1, and 2-2 phenotypes. Hp phenotype affects cardiovascular disease risk and treatment response to antioxidant vitamins in some non-pregnant populations. We previously demonstrated that preeclampsia risk was doubled in white Hp 2-1 women, compared to Hp 1-1 women. Our objectives were to determine whether we could reproduce this finding in a larger cohort, and to determine whether Hp phenotype influences lack of efficacy of antioxidant vitamins in preventing preeclampsia and serious complications of pregnancy-associated hypertension (PAH). This is a secondary analysis of a randomized controlled trial in which 10,154 low-risk women received daily vitamin C and E, or placebo, from 9-16 weeks gestation until delivery. Hp phenotype was determined in the study prediction cohort (n = 2,393) and a case-control cohort (703 cases, 1,406 controls). The primary outcome was severe PAH, or mild or severe PAH with elevated liver enzymes, elevated serum creatinine, thrombocytopenia, eclampsia, fetal growth restriction, medically indicated preterm birth or perinatal death. Preeclampsia was a secondary outcome. Odds ratios were estimated by logistic regression. Sampling weights were used to reduce bias from an overrepresentation of women with preeclampsia or the primary outcome. There was no relationship between Hp phenotype and the primary outcome or preeclampsia in Hispanic, white/other or black women. Vitamin supplementation did not reduce the risk of the primary outcome or preeclampsia in women of any phenotype. Supplementation increased preeclampsia risk (odds ratio 3.30; 95% confidence interval 1.61-6.82, p<0.01) in Hispanic Hp 2-2 women. Hp phenotype does not influence preeclampsia risk, or identify a subset of women who may benefit from vitamin C and E supplementation to prevent preeclampsia

Flux-splitting schemes for parabolic problems

To solve numerically boundary value problems for parabolic equations with mixed derivatives, the construction of difference schemes with prescribed quality faces essential difficulties. In parabolic problems, some possibilities are associated with the transition to a new formulation of the problem, where the fluxes (derivatives with respect to a spatial direction) are treated as unknown quantities. In this case, the original problem is rewritten in the form of a boundary value problem for the system of equations in the fluxes. This work deals with studying schemes with weights for parabolic equations written in the flux coordinates. Unconditionally stable flux locally one-dimensional schemes of the first and second order of approximation in time are constructed for parabolic equations without mixed derivatives. A peculiarity of the system of equations written in flux variables for equations with mixed derivatives is that there do exist coupled terms with time derivatives

Vitamin D status and recurrent preterm birth: a nested case-control study in high-risk women

OBJECTIVE: To determine whether vitamin D status is associated with recurrent preterm birth, and any interactions between vitamin D levels and fish consumption. DESIGN: A nested case-control study, using data from a randomised trial of omega-3 fatty acid supplementation to prevent recurrent preterm birth. SETTING: Fourteen academic health centres in the USA. POPULATION: Women with prior spontaneous preterm birth. METHODS: In 131 cases (preterm delivery at <35 weeks of gestation) and 134 term controls, we measured serum 25-hydroxyvitamin D [25(OH)D] concentrations by liquid chromatography-tandem mass spectrometry (LC-MS) from samples collected at baseline (16-22 weeks of gestation). Logistic regression models controlled for study centre, maternal age, race/ethnicity, number of prior preterm deliveries, smoking status, body mass index, and treatment. MAIN OUTCOME MEASURES: Recurrent preterm birth at <37 and <32 weeks of gestation. RESULTS: The median mid-gestation serum 25(OH)D concentration was 67 nmol/l, and 27% had concentrations of <50 nmol/l. Serum 25(OH)D concentration was not significantly associated with preterm birth (OR 1.33; 95% CI 0.48-3.70 for lowest versus highest quartiles). Likewise, comparing women with 25(OH)D concentrations of 50 nmol/l, or higher, with those with <50 nmol/l generated an odds ratio of 0.80 (95% CI 0.38-1.69). Contrary to our expectation, a negative correlation was observed between fish consumption and serum 25(OH)D concentration (-0.18, P < 0.01). CONCLUSIONS: In a cohort of women with a prior preterm birth, vitamin D status at mid-pregnancy was not associated with recurrent preterm birth

Does Maternal BMI Influence Treatment Effect in Women with Mild Gestational Diabetes?

To determine whether maternal body mass index (BMI) influences the beneficial effects of diabetes treatment in women with gestational diabetes (GDM)

Fish Consumption, Erythrocyte Fatty Acids, and Preterm Birth

To estimate the association between fish consumption and erythrocyte omega-3 long chain polyunsaturated fatty acids and preterm birth in a high-risk cohort