Arterial blood pressure during early sepsis and outcome

OBJECTIVE: To evaluate the association between arterial blood pressure (ABP) during the first 24 h and mortality in sepsis. DESIGN: Retrospective cohort study. SETTING: Multidisciplinary intensive care unit (ICU). PATIENTS AND PARTICIPANTS: A total of 274 septic patients. INTERVENTIONS: None. MEASUREMENTS AND RESULTS: Hemodynamic, and laboratory parameters were extracted from a PDMS database. The hourly time integral of ABP drops below clinically relevant systolic arterial pressure (SAP), mean arterial pressure (MAP), and mean perfusion pressure (MPP = MAP - central venous pressure) levels was calculated for the first 24 h after ICU admission and compared with 28-day-mortality. Binary and linear regression models (adjusted for SAPS II as a measure of disease severity), and a receiver operating characteristic (ROC) analysis were applied. The areas under the ROC curve were largest for the hourly time integrals of ABP drops below MAP 60 mmHg (0.779 vs. 0.764 for ABP drops below MAP 55 mmHg; P < or = 0.01) and MPP 45 mmHg. No association between the hourly time integrals of ABP drops below certain SAP levels and mortality was detected. One or more episodes of MAP < 60 mmHg increased the risk of death by 2.96 (CI 95%, 1.06-10.36, P = 0.04). The area under the ROC curve to predict the need for renal replacement therapy was highest for the hourly time integral of ABP drops below MAP 75 mmHg. CONCLUSIONS: A MAP level > or = 60 mmHg may be as safe as higher MAP levels during the first 24 h of ICU therapy in septic patients. A higher MAP may be required to maintain kidney function.

Pulmonary venous flow velocity patterns in 404 individuals without cardiovascular disease

OBJECTIVE To determine the pulmonary venous flow velocity (PVFV) values in a large normal population. DESIGN Prospective study in consecutive individuals. SETTING University hospital. METHODS Among 404 normal individuals, the flow velocity pattern in the right upper pulmonary vein was recorded in 315 subjects using transthoracic echocardiography, and in both upper pulmonary veins in 100 subjects using transoesophageal echocardiography. Subjects were divided into five age groups. The PVFV values were compared between transthoracic and transoesophageal echocardiography within the age groups, and intraindividually between the right and left upper pulmonary veins in transoesophageal echocardiography. RESULTS Normal PVFV values for the right upper pulmonary vein in transthoracic and transoesophageal echocardiography are presented. The duration of flow reversal at atrial contraction was overestimated using transthoracic echocardiography (mean (SD): 96 (21) ms in transoesophageal echocardiography, 120 (28) ms in transthoracic echocardiography, p < 0.0001). Systolic to diastolic peak flow velocity ratio (S:D) increased earlier with advancing age with transoesophageal echocardiography than with transthoracic echocardiography. Similar results were found for the corresponding time-velocity integrals. Data from the left and right upper pulmonary veins differed with respect to onset and deceleration of flow velocities, but not for flow durations or peak velocities. CONCLUSIONS Normal PVFV values generally show a wide range. The data presented will be of value in assessing left ventricular diastolic function and mitral regurgitation using the PVFV pattern.

A Stieltjes approach to static hedges

Static hedging of complicated payoff structures by standard instruments becomes increasingly popular in finance. The classical approach is developed for quite regular functions, while for less regular cases, generalized functions and approximation arguments are used. In this note, we discuss the regularity conditions in the classical decomposition formula due to P. Carr and D. Madan (in Jarrow ed, Volatility, pp. 417–427, Risk Publ., London, 1998) if the integrals in this formula are interpreted as Lebesgue integrals with respect to the Lebesgue measure. Furthermore, we show that if we replace these integrals by Lebesgue–Stieltjes integrals, the family of representable functions can be extended considerably with a direct approach.

A scrutiny of hard pion chiral perturbation theory

In the recently proposed framework of hard pion chiral perturbation theory, the leading chiral logarithms are predicted to factorize with respect to the energy dependence in the chiral limit. We have scrutinized this assumption in the case of vector and scalar pion form factors FV;S(s) by means of standard chiral perturbation theory and dispersion relations. We show that this factorization property is valid for the elastic contribution to the dispersion integrals for FV;S(s) but it is violated starting at three loops when the inelastic four-pion contributions arise.

Factorization of leading chiral logarithms in the pion form factors

In the recently proposed framework of hard pion chiral perturbation theory, the leading chiral logarithms are predicted to factorize with respect to the energy dependence in the chiral limit. We have scrutinized this assumption in the case of vector and scalar pion form factors FV;S(s) by means of standard chiral perturbation theory and dispersion relations. We show that this factorization property is valid for the elastic contribution to the dispersion integrals for FV;S(s) but it is violated starting at three loops when the inelastic four-pion contributions arise.

Effect of surface restoring on subsurface variability in a climate model during 1949–2005

Initializing the ocean for decadal predictability studies is a challenge, as it requires reconstructing the little observed subsurface trajectory of ocean variability. In this study we explore to what extent surface nudging using well-observed sea surface temperature (SST) can reconstruct the deeper ocean variations for the 1949–2005 period. An ensemble made with a nudged version of the IPSLCM5A model and compared to ocean reanalyses and reconstructed datasets. The SST is restored to observations using a physically-based relaxation coefficient, in contrast to earlier studies, which use a much larger value. The assessment is restricted to the regions where the ocean reanalyses agree, i.e. in the upper 500 m of the ocean, although this can be latitude and basin dependent. Significant reconstruction of the subsurface is achieved in specific regions, namely region of subduction in the subtropical Atlantic, below the thermocline in the equatorial Pacific and, in some cases, in the North Atlantic deep convection regions. Beyond the mean correlations, ocean integrals are used to explore the time evolution of the correlation over 20-year windows. Classical fixed depth heat content diagnostics do not exhibit any significant reconstruction between the different existing bservation-based references and can therefore not be used to assess global average time-varying correlations in the nudged simulations. Using the physically based average temperature above an isotherm (14°C) alleviates this issue in the tropics and subtropics and shows significant reconstruction of these quantities in the nudged simulations for several decades. This skill is attributed to the wind stress reconstruction in the tropics, as already demonstrated in a perfect model study using the same model. Thus, we also show here the robustness of this result in an historical and observational context.

Steiner’s formula in the Heisenberg group

Steiner’s tube formula states that the volume of an ϵ-neighborhood of a smooth regular domain in Rn is a polynomial of degree n in the variable ϵ whose coefficients are curvature integrals (also called quermassintegrals). We prove a similar result in the sub-Riemannian setting of the first Heisenberg group. In contrast to the Euclidean setting, we find that the volume of an ϵ-neighborhood with respect to the Heisenberg metric is an analytic function of ϵ that is generally not a polynomial. The coefficients of the series expansion can be explicitly written in terms of integrals of iteratively defined canonical polynomials of just five curvature terms.