Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations

One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved spacetime. This canonical form is needed to apply the Whitham Lagrangian method. The latter method, unlike the WKB method, places no restriction on the magnitude of Planck's constant to obtain wave packets, and furthermore preserves the symmetries of the Dirac Lagrangian. We show using canonical Dirac fields in a curved spacetime, that the probability current has a Gordon decomposition into a convection current and a spin current, and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck's constant. We further discuss the classical-quantum correspondence in a curved spacetime based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved spacetime are a direct consequence of Whitham's Lagrangian method, and not just a physical hypothesis as introduced by Einstein and de Broglie, and by many quantum mechanics textbooks.Comment: PDF, 32 pages in referee format. Added significant material on canonical forms of Dirac equations. Simplified Theorem 1 for normal Dirac equations. Added section on Gordon decomposition of the probability current. Encapsulated main results in the statement of Theorem

Relations between lipoprotein(a) concentrations, LPA genetic variants, and the risk of mortality in patients with established coronary heart disease: a molecular and genetic association study

Background: Lipoprotein(a) concentrations in plasma are associated with cardiovascular risk in the general population. Whether lipoprotein(a) concentrations or LPA genetic variants predict long-term mortality in patients with established coronary heart disease remains less clear. Methods: We obtained data from 3313 patients with established coronary heart disease in the Ludwigshafen Risk and Cardiovascular Health (LURIC) study. We tested associations of tertiles of lipoprotein(a) concentration in plasma and two LPA single-nucleotide polymorphisms ([SNPs] rs10455872 and rs3798220) with all-cause mortality and cardiovascular mortality by Cox regression analysis and with severity of disease by generalised linear modelling, with and without adjustment for age, sex, diabetes diagnosis, systolic blood pressure, BMI, smoking status, estimated glomerular filtration rate, LDL-cholesterol concentration, and use of lipid-lowering therapy. Results for plasma lipoprotein(a) concentrations were validated in five independent studies involving 10 195 patients with established coronary heart disease. Results for genetic associations were replicated through large-scale collaborative analysis in the GENIUS-CHD consortium, comprising 106 353 patients with established coronary heart disease and 19 332 deaths in 22 studies or cohorts. Findings: The median follow-up was 9·9 years. Increased severity of coronary heart disease was associated with lipoprotein(a) concentrations in plasma in the highest tertile (adjusted hazard radio [HR] 1·44, 95% CI 1·14–1·83) and the presence of either LPA SNP (1·88, 1·40–2·53). No associations were found in LURIC with all-cause mortality (highest tertile of lipoprotein(a) concentration in plasma 0·95, 0·81–1·11 and either LPA SNP 1·10, 0·92–1·31) or cardiovascular mortality (0·99, 0·81–1·2 and 1·13, 0·90–1·40, respectively) or in the validation studies. Interpretation: In patients with prevalent coronary heart disease, lipoprotein(a) concentrations and genetic variants showed no associations with mortality. We conclude that these variables are not useful risk factors to measure to predict progression to death after coronary heart disease is established. Funding: Seventh Framework Programme for Research and Technical Development (AtheroRemo and RiskyCAD), INTERREG IV Oberrhein Programme, Deutsche Nierenstiftung, Else-Kroener Fresenius Foundation, Deutsche Stiftung für Herzforschung, Deutsche Forschungsgemeinschaft, Saarland University, German Federal Ministry of Education and Research, Willy Robert Pitzer Foundation, and Waldburg-Zeil Clinics Isny

Association of the coronary artery disease risk gene GUCY1A3 with ischaemic events after coronary intervention

Aim: A common genetic variant at the GUCY1A3 coronary artery disease locus has been shown to influence platelet aggregation. The risk of ischaemic events including stent thrombosis varies with the efficacy of aspirin to inhibit platelet reactivity. This study sought to investigate whether homozygous GUCY1A3 (rs7692387) risk allele carriers display higher on-aspirin platelet reactivity and risk of ischaemic events early after coronary intervention. Methods and results: The association of GUCY1A3 genotype and on-aspirin platelet reactivity was analysed in the genetics substudy of the ISAR-ASPI registry (n = 1678) using impedance aggregometry. The clinical outcome cardiovascular death or stent thrombosis within 30 days after stenting was investigated in a meta-analysis of substudies of the ISAR-ASPI registry, the PLATO trial (n = 3236), and the Utrecht Coronary Biobank (n = 1003) comprising a total 5917 patients. Homozygous GUCY1A3 risk allele carriers (GG) displayed increased on-aspirin platelet reactivity compared with non-risk allele (AA/AG) carriers [150 (interquartile range 91–209) vs. 134 (85–194) AU⋅min, P 203 AU⋅min; 29.5 vs. 24.2%, P = 0.02). Homozygous risk allele carriers were also at higher risk for cardiovascular death or stent thrombosis (hazard ratio 1.70, 95% confidence interval 1.08–2.68; P = 0.02). Bleeding risk was not altered. Conclusion: We conclude that homozygous GUCY1A3 risk allele carriers are at increased risk of cardiovascular death or stent thrombosis within 30 days after coronary stenting, likely due to higher on-aspirin platelet reactivity. Whether GUCY1A3 genotype helps to tailor antiplatelet treatment remains to be investigated

Impact of fermentation, drying, roasting and Dutch processing on flavan-3-ol stereochemistry in cacao beans and cocoa ingredients

This paper reports a systematic study of the level of flavan-3-ol monomers during typical processing steps as cacao beans are dried, fermented and roasted and the results of Dutch-processing. Methods have been used that resolve the stereoisomers of epicatechin and catechin. In beans harvested from unripe and ripe cacao pods, we find only (-)-epicatechin and (+)-catechin with (-)-epicatechin being by far the predominant isomer. When beans are fermented there is a large loss of both (-)-epicatechin and (+)-catechin, but also the formation of (-)-catechin. We hypothesize that the heat of fermentation may, in part, be responsible for the formation of this enantiomer. When beans are progressively roasted at conditions described as low, medium and high roast conditions, there is a progressive loss of (-)-epicatechin and (+)-catechin and an increase in (-)-catechin with the higher roast levels. When natural and Dutch-processed cacao powders are analyzed, there is progressive loss of both (-)-epicatechin and (+)-catechin with lesser losses of (-)-catechin. We thus observe that in even lightly Dutch-processed powder, the level of (-)-catechin exceeds the level of (-)-epicatechin. The results indicate that much of the increase in the level of (-)-catechin observed during various processing steps may be the result of heat-related epimerization from (-)-epicatechin. These results are discussed with reference to the reported preferred order of absorption of (-)-epicatechin > (+)-catechin > (-)-catechin. These results are also discussed with respect to the balance that must be struck between the beneficial impact of fermentation and roasting on chocolate flavor and the healthful benefits of chocolate and cocoa powder that result in part from the flavan-3-ol monomers

Relations between lipoprotein(a) concentrations, LPA genetic variants, and the risk of mortality in patients with established coronary heart disease: a molecular and genetic association study

BACKGROUND: Lipoprotein(a) concentrations in plasma are associated with cardiovascular risk in the general population. Whether lipoprotein(a) concentrations or LPA genetic variants predict long-term mortality in patients with established coronary heart disease remains less clear. METHODS: We obtained data from 3313 patients with established coronary heart disease in the Ludwigshafen Risk and Cardiovascular Health (LURIC) study. We tested associations of tertiles of lipoprotein(a) concentration in plasma and two LPA single-nucleotide polymorphisms ([SNPs] rs10455872 and rs3798220) with all-cause mortality and cardiovascular mortality by Cox regression analysis and with severity of disease by generalised linear modelling, with and without adjustment for age, sex, diabetes diagnosis, systolic blood pressure, BMI, smoking status, estimated glomerular filtration rate, LDL-cholesterol concentration, and use of lipid-lowering therapy. Results for plasma lipoprotein(a) concentrations were validated in five independent studies involving 10 195 patients with established coronary heart disease. Results for genetic associations were replicated through large-scale collaborative analysis in the GENIUS-CHD consortium, comprising 106 353 patients with established coronary heart disease and 19 332 deaths in 22 studies or cohorts. FINDINGS: The median follow-up was 9·9 years. Increased severity of coronary heart disease was associated with lipoprotein(a) concentrations in plasma in the highest tertile (adjusted hazard radio [HR] 1·44, 95% CI 1·14-1·83) and the presence of either LPA SNP (1·88, 1·40-2·53). No associations were found in LURIC with all-cause mortality (highest tertile of lipoprotein(a) concentration in plasma 0·95, 0·81-1·11 and either LPA SNP 1·10, 0·92-1·31) or cardiovascular mortality (0·99, 0·81-1·2 and 1·13, 0·90-1·40, respectively) or in the validation studies. INTERPRETATION: In patients with prevalent coronary heart disease, lipoprotein(a) concentrations and genetic variants showed no associations with mortality. We conclude that these variables are not useful risk factors to measure to predict progression to death after coronary heart disease is established. FUNDING: Seventh Framework Programme for Research and Technical Development (AtheroRemo and RiskyCAD), INTERREG IV Oberrhein Programme, Deutsche Nierenstiftung, Else-Kroener Fresenius Foundation, Deutsche Stiftung für Herzforschung, Deutsche Forschungsgemeinschaft, Saarland University, German Federal Ministry of Education and Research, Willy Robert Pitzer Foundation, and Waldburg-Zeil Clinics Isny

Subsequent Event Risk in Individuals with Established Coronary Heart Disease:Design and Rationale of the GENIUS-CHD Consortium

BACKGROUND: The "GENetIcs of sUbSequent Coronary Heart Disease" (GENIUS-CHD) consortium was established to facilitate discovery and validation of genetic variants and biomarkers for risk of subsequent CHD events, in individuals with established CHD. METHODS: The consortium currently includes 57 studies from 18 countries, recruiting 185,614 participants with either acute coronary syndrome, stable CHD or a mixture of both at baseline. All studies collected biological samples and followed-up study participants prospectively for subsequent events. RESULTS: Enrollment into the individual studies took place between 1985 to present day with duration of follow up ranging from 9 months to 15 years. Within each study, participants with CHD are predominantly of self-reported European descent (38%-100%), mostly male (44%-91%) with mean ages at recruitment ranging from 40 to 75 years. Initial feasibility analyses, using a federated analysis approach, yielded expected associations between age (HR 1.15 95% CI 1.14-1.16) per 5-year increase, male sex (HR 1.17, 95% CI 1.13-1.21) and smoking (HR 1.43, 95% CI 1.35-1.51) with risk of subsequent CHD death or myocardial infarction, and differing associations with other individual and composite cardiovascular endpoints. CONCLUSIONS: GENIUS-CHD is a global collaboration seeking to elucidate genetic and non-genetic determinants of subsequent event risk in individuals with established CHD, in order to improve residual risk prediction and identify novel drug targets for secondary prevention. Initial analyses demonstrate the feasibility and reliability of a federated analysis approach. The consortium now plans to initiate and test novel hypotheses as well as supporting replication and validation analyses for other investigators

Association of Chromosome 9p21 with Subsequent Coronary Heart Disease events:A GENIUS-CHD study of individual participant data

BACKGROUND:Genetic variation at chromosome 9p21 is a recognized risk factor for coronary heart disease (CHD). However, its effect on disease progression and subsequent events is unclear, raising questions about its value for stratification of residual risk. METHODS:A variant at chromosome 9p21 (rs1333049) was tested for association with subsequent events during follow-up in 103,357 Europeans with established CHD at baseline from the GENIUS-CHD Consortium (73.1% male, mean age 62.9 years). The primary outcome, subsequent CHD death or myocardial infarction (CHD death/MI), occurred in 13,040 of the 93,115 participants with available outcome data. Effect estimates were compared to case/control risk obtained from CARDIoGRAMPlusC4D including 47,222 CHD cases and 122,264 controls free of CHD. RESULTS:Meta-analyses revealed no significant association between chromosome 9p21 and the primary outcome of CHD death/MI among those with established CHD at baseline (GENIUS-CHD OR 1.02; 95% CI 0.99-1.05). This contrasted with a strong association in CARDIoGRAMPlusC4D OR 1.20; 95% CI 1.18-1.22; p for interaction Conclusions: In contrast to studies comparing individuals with CHD to disease free controls, we found no clear association between genetic variation at chromosome 9p21 and risk of subsequent acute CHD events when all individuals had CHD at baseline. However, the association with subsequent revascularization may support the postulated mechanism of chromosome 9p21 for promoting atheroma development