Convolution roots and differentiability of isotropic positive definite functions on spheres

We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function. It is known that isotropic positive definite functions on d-dimensional Euclidean space admit a continuous derivative of order [(d − 1)/2]. We show that the same holds true for isotropic positive definite functions on spheres and prove that this result is optimal for all odd dimensions.

An integral conservative gridding--algorithm using Hermitian curve interpolation

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to significantly reduce these interpolation errors. The accuracy of the new algorithm was tested on a series of x-ray CT-images (head and neck, lung, pelvis). The new algorithm significantly improves the accuracy of the sampled images in terms of the mean square error and a quality index introduced by Wang and Bovik (2002 IEEE Signal Process. Lett. 9 81-4).

Physiologic response to changing positive end-expiratory pressure during neurally adjusted ventilatory assist in sedated, critically ill adults

Neurally adjusted ventilatory assist (NAVA) delivers airway pressure (Paw) in proportion to neural inspiratory drive as reflected by electrical activity of the diaphragm (EAdi). Changing positive end-expiratory pressure (PEEP) impacts respiratory muscle load and function and, hence, EAdi. We aimed to evaluate how PEEP affects the breathing pattern and neuroventilatory efficiency during NAVA.

High CD10 expression predicts favorable outcome in surgically treated lymph node-positive bladder cancer patients

CD10 predicts survival in different cancers. The prognostic significance in bladder cancer still has to be documented. One hundred fifty lymph node-positive bladder cancer patients were treated by cystectomy and standardized pelvic lymphadenectomy in curative intent. CD10 expression was evaluated in tissue microarrays (TMAs) constructed from histopathological normal urothelium, primary tumor (tumor center and invasion front), and corresponding lymph node metastases and correlated with tumor characteristics (stage, extracapsular extension, number, and total diameter of metastases) and survival. CD10 expression was successively lost from normal urothelium to primary tumor to metastases (P < .05) and decreased from the tumor center to the invasion front (P < .002). High CD10 expression in tumor center or invasion front (P < .05) but not in the metastases predicted favorable outcome; the prognostic information in the tumor center was independent from tumor stage and lymph node parameters. High CD10 expression level was not associated with specific tumor characteristics. A well-defined sampling strategy for TMAs allows detection of specific biomarker expression patterns and may generate prognostic information inherent in particular tumor areas. The favorable outcome in bladder cancer patients with high CD10 expression might suggest a tumor suppressive function of CD10.

Respiratory function during anesthesia: effects on gas exchange

Anaesthesia causes a respiratory impairment, whether the patient is breathing spontaneously or is ventilated mechanically. This impairment impedes the matching of alveolar ventilation and perfusion and thus the oxygenation of arterial blood. A triggering factor is loss of muscle tone that causes a fall in the resting lung volume, functional residual capacity. This fall promotes airway closure and gas adsorption, leading eventually to alveolar collapse, that is, atelectasis. The higher the oxygen concentration, the faster will the gas be adsorbed and the aleveoli collapse. Preoxygenation is a major cause of atelectasis and continuing use of high oxygen concentration maintains or increases the lung collapse, that typically is 10% or more of the lung tissue. It can exceed 25% to 40%. Perfusion of the atelectasis causes shunt and cyclic airway closure causes regions with low ventilation/perfusion ratios, that add to impaired oxygenation. Ventilation with positive end-expiratory pressure reduces the atelectasis but oxygenation need not improve, because of shift of blood flow down the lung to any remaining atelectatic tissue. Inflation of the lung to an airway pressure of 40 cmH2O recruits almost all collapsed lung and the lung remains open if ventilation is with moderate oxygen concentration (< 40%) but recollapses within a few minutes if ventilation is with 100% oxygen. Severe obesity increases the lung collapse and obstructive lung disease and one-lung anesthesia increase the mismatch of ventilation and perfusion. CO2 pneumoperitoneum increases atelectasis formation but not shunt, likely explained by enhanced hypoxic pulmonary vasoconstriction by CO2. Atelectasis may persist in the postoperative period and contribute to pneumonia.

Aquatic therapies in patients with compromised left ventricular function and heart failure

With water immersion, gravity is partly eliminated, and the water exerts a pressure on the body surface. Consequently there is a blood volume shift from the periphery to the central circulation, resulting in marked volume loading of the thorax and heart. This paper presents a selection of published literature on water immersion, balneotherapy, aqua exercises, and swimming, in patients with left ventricular dysfunction (LVD) and/or stable chronic heart failure (CHF). Based on exploratory studies, central hemodynamic and neurohumoral responses of aquatic therapies will be illustrated. Major findings are: 1. In LVD and CHF, a positive effect of therapeutic warm-water tub bathing has been observed, which is assumed to be from afterload reduction due to peripheral vasodilatation caused by the warm water. 2. In coronary patients with LVD, at low-level water cycling the heart is working more efficiently than at lowlevel cycling outside of water. 3. In patients with previous extensive myocardial infarction, upright immersion to the neck resulted in temporary pathological increases in mean pulmonary artery pressure (mPAP) and mean pulmonary capillary pressures (mPCP). 4. Additionally, during slow swimming (20-25m/min) the mPAP and/or PCP were higher than during supine cycling outside water at a 100W load. 5. In CHF patients, neck- deep immersion resulted in a decrease or no change in stroke volume. 6. Although patients are hemodynamically compromised, they usually maintain a feeling of well-being during aquatic therapy. Based on these findings, clinical indications for aquatic therapies are proposed and ideas are presented to provoke further research.

Oxidized low density lipoprotein impairs endothelial progenitor cell function by downregulation of E-selectin and integrin alpha(v)beta5

BACKGROUND: Oxidized low density lipoprotein (oxLDL) has been shown to induce apoptosis and senescence of endothelial progenitor cells (EPC). In the present study, we hypothesized that even sub-apoptotic concentrations of oxLDL impair the angiogenic potential of EPC and investigated if this effect is mediated by affecting adhesion and incorporation. METHODS: A co-culture system of human microvascular endothelial cells and EPC was used to study the effect of sub-apoptotic concentrations of native (nLDL) and oxLDL on cell-cell interaction. The expression and the functional role of angiogenic adhesion molecules and integrins was monitored by FACS and neutralizing assay, respectively. RESULTS: We observed an inhibition of tube formation and impairment of EPC integration into the vascular network of mature endothelial cells by oxLDL. In contrast, nLDL did not affect angiogenic properties of EPC. Incubation of EPC with sub-apoptotic oxLDL concentrations significantly decreased E-selectin and integrin alpha(v)beta(5) expression (37.6% positive events vs. 71.5% and 24.3% vs. 49.9% compared to control culture media without oxLDL). Interestingly, expression of alpha(v)beta(3), VE-cadherin and CD31 remained unchanged. Blocking of E-selectin and integrin alpha(v)beta(5) by neutralizing antibody effectively inhibited adhesion of EPC to differentiated endothelial cells (56.5% and 41.9% of control; p<0.001). CONCLUSION: In conclusion, oxidative alteration of LDL impairs angiogenic properties of EPC at sub-apoptotic levels by downregulation of E-selectin and integrin alpha(v)beta(5), both substantial mediators of EPC-endothelial cell interaction.

Effect of fluid resuscitation on mortality and organ function in experimental sepsis models

Introduction Several recent studies have shown that a positive fluid balance in critical illness is associated with worse outcome. We tested the effects of moderate vs. high-volume resuscitation strategies on mortality, systemic and regional blood flows, mitochondrial respiration, and organ function in two experimental sepsis models. Methods 48 pigs were randomized to continuous endotoxin infusion, fecal peritonitis, and a control group (n = 16 each), and each group further to two different basal rates of volume supply for 24 hours [moderate-volume (10 ml/kg/h, Ringer's lactate, n = 8); high-volume (15 + 5 ml/kg/h, Ringer's lactate and hydroxyethyl starch (HES), n = 8)], both supplemented by additional volume boli, as guided by urinary output, filling pressures, and responses in stroke volume. Systemic and regional hemodynamics were measured and tissue specimens taken for mitochondrial function assessment and histological analysis. Results Mortality in high-volume groups was 87% (peritonitis), 75% (endotoxemia), and 13% (controls). In moderate-volume groups mortality was 50% (peritonitis), 13% (endotoxemia) and 0% (controls). Both septic groups became hyperdynamic. While neither sepsis nor volume resuscitation strategy was associated with altered hepatic or muscle mitochondrial complex I- and II-dependent respiration, non-survivors had lower hepatic complex II-dependent respiratory control ratios (2.6 +/- 0.7, vs. 3.3 +/- 0.9 in survivors; P = 0.01). Histology revealed moderate damage in all organs, colloid plaques in lung tissue of high-volume groups, and severe kidney damage in endotoxin high-volume animals. Conclusions High-volume resuscitation including HES in experimental peritonitis and endotoxemia increased mortality despite better initial hemodynamic stability. This suggests that the strategy of early fluid management influences outcome in sepsis. The high mortality was not associated with reduced mitochondrial complex I- or II-dependent muscle and hepatic respiration.

Effects of GDNF pretreatment on function and survival of transplanted fetal ventral mesencephalic cells in the 6-OHDA rat model of Parkinson's disease

Transplantation of fetal dopaminergic (DA) neurons offers an experimental therapy for Parkinson's disease (PD). The low availability and the poor survival and integration of transplanted cells in the host brain are major obstacles in this approach. Glial cell line-derived neurotrophic factor (GDNF) is a potent neurotrophic factor with growth- and survival-promoting capabilities for developing DA neurons. In the present study, we examined whether pretreatment of ventral mesencephalic (VM) free-floating roller tube (FFRT) cultures with GDNF would improve graft survival and function. For that purpose organotypic cultures of E14 rat VM were grown for 2, 4 or 8 days in the absence (control) or presence of GDNF [10 ng/ml] and transplanted into the striatum of 6-hydroxydopamine-lesioned rats. While all groups of rats showed a significant reduction in d-amphetamine-induced rotations at 6 weeks posttransplantation a significantly improved graft function was observed only in the days in vitro (DIV) 4 GDNF pretreated group compared to the control group. In addition, no statistical significant differences between groups were found in the number of surviving tyrosine hydroxylase-immunoreactive (TH-ir) neurons assessed at 9 weeks posttransplantation. However, a tendency for higher TH-ir fiber outgrowth from the transplants in the GDNF pretreated groups as compared to corresponding controls was observed. Furthermore, GDNF pretreatment showed a tendency for a higher number of GIRK2 positive neurons in the grafts. In sum, our findings demonstrate that GDNF pretreatment was not disadvantageous for transplants of embryonic rat VM with the FFRT culture technique but only marginally improved graft survival and function.

Biomechanical evaluation of the stabilizing function of the atlantoaxial ligaments under shear loading: A canine cadaveric study

OBJECTIVES To evaluate the stabilizing function of atlanto-axial ligaments in dogs. STUDY DESIGN Cadaveric biomechanical study. ANIMALS Beagle dog cadavers (n = 10). METHODS The craniocervical region was collected from 10 Beagle cadavers, and the occipito-atlanto-axial region was prepared and freed from the surrounding muscles. Care was taken to preserve integrity of the atlantoaxial ligaments and atlantoaxial joint capsule. The atlanto-occipital joints were blocked with 2 diverging transarticular 1.8 mm positive threaded K-wires. Specimen extremities were embedded in polymethylmethacrylate (PMMA) and mounted on a simulator testing shear load at the atlantoaxial joint. Range of motion (ROM) and neutral zone (NZ) were determined with all ligaments intact, after cutting the apical ligament, both alar ligaments, the transverse ligaments and finally after cutting the dorsal atlantoaxial ligament. RESULTS ROM increased similarly and stepwise during testing. The most significant increase was observed after transection of the alar ligaments. CONCLUSION The alar ligaments seem to be the most important ligamentous structures for stabilization of the atlantoaxial joint under shear load.

Loss-of-function mutation of the SCN3B-encoded sodium channel {beta}3 subunit associated with a case of idiopathic ventricular fibrillation.

AIMS Loss-of-function mutations in the SCN5A-encoded sodium channel SCN5A or Nav1.5 have been identified in idiopathic ventricular fibrillation (IVF) in the absence of Brugada syndrome phenotype. Nav1.5 is regulated by four sodium channel auxiliary beta subunits. Here, we report a case with IVF and a novel mutation in the SCN3B-encoded sodium channel beta subunit Navbeta3 that causes a loss of function of Nav1.5 channels in vitro. METHODS AND RESULTS Comprehensive open reading frame mutational analysis of KCNQ1, KCNH2, SCN5A, KCNE1, KCNE2, GPD1L, four sodium channel beta subunit genes (SCN1-4B), and targeted scan of RYR2 was performed. A novel missense mutation, Navbeta3-V54G, was identified in a 20-year-old male following witnessed collapse and defibrillation from VF. The ECG exhibited epsilon waves, and imaging studies demonstrated a structurally normal heart. The mutated residue was highly conserved across species, localized to the Navbeta3 extracellular domain, and absent in 800 reference alleles. We found that HEK-293 cells had endogenous Navbeta3, but COS cells did not. Co-expression of Nav1.5 with Navbeta3-V54G (with or without co-expression of the Navbeta1 subunit) in both HEK-293 cells and COS cells revealed a significant decrease in peak sodium current and a positive shift of inactivation compared with WT. Co-immunoprecipitation experiments showed association of Navbeta3 with Nav1.5, and immunocytochemistry demonstrated a dramatic decrease in trafficking to the plasma membrane when co-expressed with mutant Navbeta3-V54G. CONCLUSION This study provides molecular and cellular evidence implicating mutations in Navbeta3 as a cause of IVF.

The effect of heart rate reduction by ivabradine on collateral function in patients with chronic stable coronary artery disease

Objective To evaluate the effect of heart rate reduction by ivabradine on coronary collateral function in patients with chronic stable coronary artery disease (CAD). Methods This was a prospective randomised placebo-controlled monocentre trial in a university hospital setting. 46 patients with chronic stable CAD received placebo (n=23) or ivabradine (n=23) for the duration of 6 months. The main outcome measure was collateral flow index (CFI) as obtained during a 1 min coronary artery balloon occlusion at study inclusion (baseline) and at the 6-month follow-up examination. CFI is the ratio between simultaneously recorded mean coronary occlusive pressure divided by mean aortic pressure both subtracted by mean central venous pressure. Results During follow-up, heart rate changed by +0.2±7.8 beats/min in the placebo group, and by –8.1±11.6 beats/min in the ivabradine group (p=0.0089). In the placebo group, CFI decreased from 0.140±0.097 at baseline to 0.109±0.067 at follow-up (p=0.12); it increased from 0.107±0.077 at baseline to 0.152±0.090 at follow-up in the ivabradine group (p=0.0461). The difference in CFI between the 6-month follow-up and baseline examination amounted to −0.031±0.090 in the placebo group and to +0.040±0.094 in the ivabradine group (p=0.0113). Conclusions Heart rate reduction by ivabradine appears to have a positive effect on coronary collateral function in patients with chronic stable CAD.

Minimizing the Threat of a Positive Majority Deficit in Two-tier Voting Systems with Equipopulous Units

The mean majority deficit in a two-tier voting system is a function of the partition of the population. We derive a new square-root rule: For odd-numbered population sizes and equipopulous units the mean majority deficit is maximal when the member size of the units in the partition is close to the square root of the population size. Furthermore, within the partitions into roughly equipopulous units, partitions with small even numbers of units or small even-sized units yield high mean majority deficits. We discuss the implications for the winner-takes-all system in the US Electoral College.

Increasing mean arterial blood pressure in sepsis: effects on fluid balance, vasopressor load and renal function.

INTRODUCTION: The objective of this study was to evaluate the effects of two different mean arterial blood pressure (MAP) targets on needs for resuscitation, organ dysfunction, mitochondrial respiration and inflammatory response in a long-term model of fecal peritonitis. METHODS: Twenty-four anesthetized and mechanically ventilated pigs were randomly assigned (n = 8/group) to a septic control group (septic-CG) without resuscitation until death or one of two groups with resuscitation performed after 12 hours of untreated sepsis for 48 hours, targeting MAP 50-60 mmHg (low-MAP) or 75-85 mmHg (high-MAP). RESULTS: MAP at the end of resuscitation was 56 ± 13 mmHg (mean ± SD) and 76 ± 17 mmHg respectively, for low-MAP and high-MAP groups. One animal each in high- and low-MAP groups, and all animals in septic-CG died (median survival time: 21.8 hours, inter-quartile range: 16.3-27.5 hours). Norepinephrine was administered to all animals of the high-MAP group (0.38 (0.21-0.56) mcg/kg/min), and to three animals of the low-MAP group (0.00 (0.00-0.25) mcg/kg/min; P = 0.009). The high-MAP group had a more positive fluid balance (3.3 ± 1.0 mL/kg/h vs. 2.3 ± 0.7 mL/kg/h; P = 0.001). Inflammatory markers, skeletal muscle ATP content and hemodynamics other than MAP did not differ between low- and high-MAP groups. The incidence of acute kidney injury (AKI) after 12 hours of untreated sepsis was, respectively for low- and high-MAP groups, 50% (4/8) and 38% (3/8), and in the end of the study 57% (4/7) and 0% (P = 0.026). In septic-CG, maximal isolated skeletal muscle mitochondrial Complex I, State 3 respiration increased from 1357 ± 149 pmol/s/mg to 1822 ± 385 pmol/s/mg, (P = 0.020). In high- and low-MAP groups, permeabilized skeletal muscle fibers Complex IV-state 3 respiration increased during resuscitation (P = 0.003). CONCLUSIONS: The MAP targets during resuscitation did not alter the inflammatory response, nor affected skeletal muscle ATP content and mitochondrial respiration. While targeting a lower MAP was associated with increased incidence of AKI, targeting a higher MAP resulted in increased net positive fluid balance and vasopressor load during resuscitation. The long-term effects of different MAP targets need to be evaluated in further studies.

Function of Natural Internal Mammary-to-Coronary Artery Bypasses and Its Effect on Myocardial Ischemia.

BACKGROUND The function of naturally existing internal mammary (IMA)-to-coronary artery bypasses and their quantitative effect on myocardial ischemia are unknown. METHODS AND RESULTS The primary end point of this study was collateral flow index (CFI) obtained during two 1-minute coronary artery balloon occlusions, the first with and the second without simultaneous distal IMA occlusion. The secondary study end point was the quantitatively determined intracoronary ECG ST-segment elevation. CFI is the ratio of simultaneously recorded mean coronary occlusive pressure divided by mean aortic pressure both subtracted by mean central venous pressure. A total of 180 pairs of CFI measurements were performed among 120 patients. With and without IMA occlusion, CFI was 0.110±0.074 and 0.096±0.072, respectively (P<0.0001). The difference of CFI obtained in the presence minus CFI obtained in the absence of IMA occlusion was highest and most consistently positive during left IMA with left anterior descending artery occlusion and during right IMA with right coronary artery occlusion (ipsilateral occlusions): 0.033±0.044 and 0.025±0.027, respectively. This CFI difference was absent during right IMA with left anterior descending artery occlusion and during left IMA with right coronary artery occlusion (contralateral occlusions): -0.007±0.034 and 0.001±0.023, respectively (P=0.0002 versus ipsilateral occlusions). The respective CFI differences during either IMA with left circumflex artery occlusion were inconsistently positive. Intracoronary ECG ST-segment elevations were significantly reduced during ipsilateral IMA occlusions but not during contralateral or left circumflex artery occlusions. CONCLUSION There is a functional, ischemia-reducing extracardiac coronary artery supply via ipsilateral but not via contralateral natural IMA bypasses. CLINICAL TRIAL REGISTRATION URL http://www.clinicaltrials.gov. Unique identifier: NCTO1676207.