An hp-version discontinuous Galerkin method for integro-differential equations of parabolic type

We study the numerical solution of a class of parabolic integro-differential equations with weakly singular kernels. We use an $hp$-version discontinuous Galerkin (DG) method for the discretization in time. We derive optimal $hp$-version error estimates and show that exponential rates of convergence can be achieved for solutions with singular (temporal) behavior near $t=0$ caused by the weakly singular kernel. Moreover, we prove that by using nonuniformly refined time steps, optimal algebraic convergence rates can be achieved for the $h$-version DG method. We then combine the DG time-stepping method with a standard finite element discretization in space, and present an optimal error analysis of the resulting fully discrete scheme. Our theoretical results are numerically validated in a series of test problems

Routine clinical cardiovascular magnetic resonance in paediatric and adult congenital heart disease: patients, protocols, questions asked and contributions made

<p>Abstract</p> <p>Background</p> <p>Cardiovascular Magnetic Resonance (CMR) of patients with congenital heart disease (CHD) has become routine clinical practice. However, existing CMR protocols focus predominantly on patients with ischemic heart disease, and information is limited on the types of patient with CHD who benefit from CMR investigation, and in what ways. Therefore the aim of this study was to answer the questions: What type of patients were studied by CMR in a centre specializing in paediatric and adult CHD management? What questions were asked, which protocols were used and were the questions successfully answered? To answer these questions, we conducted a cohort study of all 362 patients that received routine clinical CMR during 2007 at the Department of Paediatric Cardiology and Congenital Heart Disease at the Deutsches Herzzentrum München.</p> <p>Results</p> <p>Underlying diagnosis was in 33% Fallot's tetralogy, 17% aortic coarctation, 8% Ebstein's disease, 6% Marfan's disease, 4% single ventricle with Fontan-like circulation, and 32% others. Median age was 26 years (7 days – 75 years). Ventricular volumes were assessed in 67% of the patients; flow in 74%; unknown anatomy only in 9%; specific individual morphology of known anatomy in 83%; myocardial fibrosis in 8%; stress-induced myocardial perfusion defects in 1%. Only in 3% of the cases the question could not be fully answered.</p> <p>Conclusion</p> <p>Contrary to common belief, routine CMR of patients with CHD was not requested to address global anatomical questions so much as to clarify specific questions of morphology and function of known anatomy. The CMR protocols used differed markedly from those widely used in patients with ischemic heart disease.</p

First-trimester cesarean scar pregnancy: a comparative analysis of treatment options from the international registry

Background: A cesarean scar pregnancy is an iatrogenic consequence of a previous cesarean delivery. The gestational sac implants into a niche created by the incision of the previous cesarean delivery, and this carries a substantial risk for major maternal complications. The aim of this study was to report, analyze, and compare the effectiveness and safety of different treatments options for cesarean scar pregnancies managed in the first trimester through a registry. Objective: This study aimed to evaluated the ultrasound findings, disease behavior, and management of first-trimester cesarean scar pregnancies. Study design: We created an international registry of cesarean scar pregnancy cases to study the ultrasound findings, disease behavior, and management of cesarean scar pregnancies. The Cesarean Scar Pregnancy Registry collects anonymized ultrasound and clinical data of individual patients with a cesarean scar pregnancy on a secure, digital information platform. Cases were uploaded by 31 participating centers across 19 countries. In this study, we only included live and failing cesarean scar pregnancies (with or without a positive fetal heart beat) that received active treatment (medical or surgical) before 12+6 weeks' gestation to evaluate the effectiveness and safety of the different management options. Patients managed expectantly were not included in this study and will be reported separately. Treatment was classified as successful if it led to a complete resolution of the pregnancy without the need for any additional medical interventions. Results: Between August 29, 2018, and February 28, 2023, we recorded 460 patients with cesarean scar pregnancies (281 live, 179 failing cesarean scar pregnancy) who fulfilled the inclusion criteria and were registered. A total of 270 of 460 (58.7%) patients were managed surgically, 123 of 460 (26.7%) patients underwent medical management, 46 of 460 (10%) patients underwent balloon management, and 21 of 460 (4.6%) patients received other, less frequently used treatment options. Suction evacuation was very effective with a success rate of 202 of 221 (91.5%; 95% confidence interval, 87.8-95.2), whereas systemic methotrexate was least effective with only 38 of 64 (59.4%; 95% confidence interval, 48.4-70.4) patients not requiring additional treatment. Overall, surgical treatment of cesarean scar pregnancies was successful in 236 of 258 (91.5%, 95% confidence interval, 88.4-94.5) patients and complications were observed in 24 of 258 patients (9.3%; 95% confidence interval, 6.6-11.9). Conclusion: A cesarean scar pregnancy can be managed effectively in the first trimester of pregnancy in more than 90% of cases with either suction evacuation, balloon treatment, or surgical excision. The effectiveness of all treatment options decreases with advancing gestational age, and cesarean scar pregnancies should be treated as early as possible after confirmation of the diagnosis. Local medical treatment with potassium chloride or methotrexate is less efficient and has higher rates of complications than the other treatment options. Systemic methotrexate has a substantial risk of failing and a higher complication rate and should not be recommended as first-line treatment

Volunteer Bias in Recruitment, Retention, and Blood Sample Donation in a Randomised Controlled Trial Involving Mothers and Their Children at Six Months and Two Years: A Longitudinal Analysis

BACKGROUND: The vulnerability of clinical trials to volunteer bias is under-reported. Volunteer bias is systematic error due to differences between those who choose to participate in studies and those who do not. METHODS AND RESULTS: This paper extends the applications of the concept of volunteer bias by using data from a trial of probiotic supplementation for childhood atopy in healthy dyads to explore 1) differences between a) trial participants and aggregated data from publicly available databases b) participants and non-participants as the trial progressed 2) impact on trial findings of weighting data according to deprivation (Townsend) fifths in the sample and target populations. 1) a) Recruits (n = 454) were less deprived than the target population, matched for area of residence and delivery dates (n = 6,893) (mean [SD] deprivation scores 0.09[4.21] and 0.79[4.08], t = 3.44, df = 511, p<0.001). b) i) As the trial progressed, representation of the most deprived decreased. These participants and smokers were less likely to be retained at 6 months (n = 430[95%]) (OR 0.29,0.13-0.67 and 0.20,0.09-0.46), and 2 years (n = 380[84%]) (aOR 0.68,0.50-0.93 and 0.55,0.28-1.09), and consent to infant blood sample donation (n = 220[48%]) (aOR 0.72,0.57-0.92 and 0.43,0.22-0.83). ii) Mothers interested in probiotics or research or reporting infants' adverse events or rashes were more likely to attend research clinics and consent to skin-prick testing. Mothers participating to help children were more likely to consent to infant blood sample donation. 2) In one trial outcome, atopic eczema, the intervention had a positive effect only in the over-represented, least deprived group. Here, data weighting attenuated risk reduction from 6.9%(0.9-13.1%) to 4.6%(-1.4-+10.5%), and OR from 0.40(0.18-0.91) to 0.56(0.26-1.21). Other findings were unchanged. CONCLUSIONS: Potential for volunteer bias intensified during the trial, due to non-participation of the most deprived and smokers. However, these were not the only predictors of non-participation. Data weighting quantified volunteer bias and modified one important trial outcome. TRIAL REGISTRATION: This randomised, double blind, parallel group, placebo controlled trial is registered with the International Standard Randomised Controlled Trials Register, Number (ISRCTN) 26287422. Registered title: Probiotics in the prevention of atopy in infants and children

The local discontinuous Galerkin method for linear incompressible fluid flow: A review

SIGLEAvailable from TIB Hannover: RR1606(2003,1) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman