High-Order Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for Euler Equations with Gravitation on Unstructured Meshes

In this paper, we propose a high-order accurate discontinuous Galerkin (DG) method for the compressible Euler equations under gravitational fields on unstructured meshes. The scheme preserves a general hydrostatic equilibrium state and provably guarantees the positivity of density and pressure at the same time. Comparing with the work on the well-balanced scheme for Euler equations with gravitation on rectangular meshes, the extension to triangular meshes is conceptually plausible but highly nontrivial. We first introduce a special way to recover the equilibrium state and then design a group of novel variables at the interface of two adjacent cells, which plays an important role in the well-balanced and positivity-preserving properties. One main challenge is that the well-balanced schemes may not have the weak positivity property. In order to achieve the well-balanced and positivity-preserving properties simultaneously while maintaining high-order accuracy, we carefully design DG spatial discretization with well-balanced numerical fluxes and suitable source term approximation. For the ideal gas, we prove that the resulting well-balanced scheme, coupled with strong stability preserving time discretizations, satisfies a weak positivity property. A simple existing limiter can be applied to enforce the positivity-preserving property, without losing high-order accuracy and conservation. Extensive one- and two-dimensional numerical examples demonstrate the desired properties of the proposed scheme, as well as its high resolution and robustness.     

Unconditional Positivity-Preserving and Energy Stable Schemes for a Reduced Poisson-Nernst-Planck System

The Poisson-Nernst-Planck (PNP) system is a widely accepted model for simulation of ionic channels. In this paper, we design, analyze, and numerically validate a second order unconditional positivity-preserving scheme for solving a reduced PNP system, which can well approximate the three dimensional ion channel problem. Positivity of numerical solutions is proven to hold true independent of the size of time steps and the choice of the Poisson solver. The scheme is easy to implement without resorting to any iteration method. Several numerical examples further confirm the positivity-preserving property, and demonstrate the accuracy, efficiency, and robustness of the proposed scheme, as well as the fast approach to steady states.     

Transcutaneous Blood Gas Measurement by Mass Spectrometry

A stainless steel, self heated, flat surface, skin surface probe, covered with a Mylar membrane, admits gases diffusing through the skin surface into a mass spectrometer at rates sufficiently low to provide reasonable measurement of blood P_o2 and P_co2. A second thermistor against the Mylar and insulated from the probe monitors skin temperature as an index of blood flow. Advantages of the mass spectrometer method compared to electrodes are that a single sensor detects all gases, including anaesthetics, the sensor is simple in design, the same mass spectrometer can monitor several patients simultaneously, anaesthetics do not interfere (as with halothane and the O₂ electrode), comparative checks with blood gas may be done using the same mass spectrometer, and perhaps, by summing all gases it may be possible to determine how fully arterialized the skin is.     

Continuous low-flow tracheal gas insufflation during partial liquid ventilation in rabbits

Background: Both partial liquid ventilation (PLV) and tracheal gas insufflation are novel techniques for mechanical ventilation. In this study we examined whether PLV superimposed by continuous low-flow tracheal gas insufflation (TGI) offers any advantage to the blood gases and lung mechanics in normal-lung rabbits compared to the use of PLV only.
Methods: Eighteen anesthetized, paralyzed and mechanically ventilated rabbits were used. After obtaining a baseline PaCO₂value between 29 and 39 mmHg (3.9 and 5.2 kPa), the animals were assigned to three equal groups according to the ventilation they received - A group: PLV superimposed by TGI; B group: PLV only; and C group: continuous mandatory ventilation (CMV) superimposed by TGI. Serial arterial blood gases, pH and lung mechanics were measured.
Results: The animals in each group were hemodynamically stable. In the case of the A group, PaO₂ continuously increased, and PaCO₂ stabilized around 40.8±5.5 mmHg (5.4±0.7 kPa, mean±SD, NS). In the B group, the tendency for PaO₂ to increase was not as definite; PaCO₂ continuously increased from 35.2±2.3 mmHg (4.7±0.3 kPa) to 56.3±12.7 mmHg (7.5±1.7 kPa, P < 0.05) at the end of the experiment. In the C group, PaO₂ and PaCO₂ were stable during the observation period. The superimposition of TGI on PLV did not decrease the airway pressures compared to PLV alone.
Conclusion: In summary, continuous low-flow TGI superimposed on PLV can decrease and stabilize the PaCO₂ elevation caused by the initiation of PLV.     

Effect of low fresh gas flow rates on inspired gas composition in a circle absorber system

Study Objective: To determine the effects of fresh gas f ow on inspired gas composition during low flow anesthesia.

Design: Randomized trial with 2-hour observation periods in patients assigned to one of three groups.

Setting: Inpatient surgery clinic at a medical center.

Patients: Thirty-six patients undergoing abdominal surgery with low flow anesthesia. Interventions: Fresh gas flow was given at a starting rate of 5 L/min for 6 minutes. Thereafter, the fresh gas flow setting was nitrous oxide (N₂O) 1 L/min and oxygen (O₂) 0.6 L/min (Group 1), N₂O 0.5 L/min and O₂ 0.5 L/min (Group 2), and with a moderate surplus of N₂O and O₂ with respect to the patient's O₂ consumption (Group 3).

Measurements and Main Results: The inspired O₂ concentration (FIO₂) was measured using a paramagnetic technique, and N₂O levels were measured with infrared sensors; the inspired nitrogen concentration (FIN₂) was calculated by the following formula: (FIN₂) = 1 - FIO₂ - FIN₂O, where FIN₂O is the inspired N₂O concentration. After 1 hour of anesthesia, FIO₂ was significantly lower in Group 1 than in Groups 2 and 3 (p < 0.01), and FIN₂ was significantly higher in Groups 2 and 3 than in Group 1 (p < 0.01). After 2 hours of anesthesia, (FIN₂) returned to normal in Group 2 but continued to increase in Group 3. FIN₂O was close to 0.7% only in Group 1.

Conclusions: The same initial period of denitrogenation is not adequate to denitrogenate the circle system in all cases. The lower the fresh gas flow, the longer the initial period of denitrogenation should be. Various levels of fresh gas flow for low-flow anesthesia have been suggested, but none guarantees adequate control of inspired gas composition unless f owmeters are continuously adjusted.     

Antiplane Wave Scattering from a Cylindrical Void in a Pre-Stressed Incompressible Neo-Hookean Material

An isolated cylindrical void is located inside an incompressible nonlinear-elastic medium whose constitutive behaviour is governed by a neo-Hookean strain energy function. In-plane hydrostatic pressure is applied in the far-field so that the void changes its radius and an inhomogeneous region of deformation arises in the vicinity of the void. We consider scattering from the void in the deformed configuration due to an incident field (of small amplitude) generated by a horizontally polarized shear (SH) line source, a distance r₀ (R₀) away from the centre of the void in the deformed (undeformed) configuration. We show that the scattering coefficients of this scattered field are unaffected by the pre-stress (initial deformation). In particular, they depend not on the deformed void radius a or distance r₀, but instead on the original void sizeA and original distance R₀.     

Haemodynamics during inhalation of a 50% nitrous-oxide-in-oxygen mixture with and without hypovolaemia

Background: Inhalation of a gas mixture containing 50% nitrous oxide in oxygen (N₂O/O₂) is widely used for pain relief in emergency situations, which may also be associated with blood loss. The aim of this study was to evaluate the haemodynamic effects of this gas mixture in normo- and hypovolaemic subjects.
Methods: Six healthy males were studied during inhalation of N₂O/O₂ before and after withdrawal of 900 ml of blood. On each occasion, we measured systemic and pulmonary arterial pressures, cardiac output, blood gases, extravascular lung water, and the blood flow and oxygen consumption in the whole body, liver and kidneys.
Results: Inhalation of N₂O/O₂ reduced the stroke volume and increased peripheral resistance. Oxygen uptake decreased in the liver (-30%) and in the whole body (-23%). Blood withdrawal reduced the pulmonary arterial and central venous pressures (-30 to -50%) and further decreased stroke volume and the blood flows to the liver and the kidney (-15%). The extravascular lung water tended to increase both during inhalation of N₂O/O₂ and during hypovolaemia.
Conclusion: N₂O/O₂ aggravated the hypokinetic circulation induced by hypovolaemia. However, the oxygen consumption decreased only during inhalation of N₂O/O₂. This opens up the possibility that the cardiodepression associated with N₂O/O₂ is caused by a change in metabolic demands.     

A Colocalized Scheme for Three-Temperature Grey Diffusion Radiation Hydrodynamics

A positivity-preserving, conservative and entropic numerical scheme is presented for the three-temperature grey diffusion radiation hydrodynamics model. More precisely, the dissipation matrices of the colocalized semi-Lagrangian scheme are defined in order to enforce the entropy production on each species (electron or ion) proportionally to its mass as prescribed in [34]. A reformulation of the model is then considered to enable the derivation of a robust convex combination based scheme. This yields the positivity-preserving property at each sub-iteration of the algorithm while the total energy conservation is reached at convergence. Numerous pure hydrodynamics and radiation hydrodynamics test cases are carried out to assess the accuracy of the method. The question of the stability of the scheme is also addressed. It is observed that the present numerical method is particularly robust.     

Particle-in-Cell with Monte Carlo Collisions Gun Code Simulations of a Surface-Conversion H^− Ion Source

We present an extended update on the status of a particle-in-cell with Monte Carlo collisions (PIC-MCC) gun code developed at Los Alamos for the study of surface-converter H⁻ ion sources. The program is fully kinetic. Some of the program's features include: solution of arbitrary electrostatic and magnetostatic fields in an axisymmetric (r,z) geometry to describe the self-consistent time evolution of a plasma; simulation of a multi-species (e⁻, H⁺, H₂⁺, H₃⁺, H⁻) plasma discharge from a neutral hydrogen gas and filament-originated seed electrons; full 2-dimensional (r,z) 3-velocity (v_r, v_z, v_φ) dynamics for all species; detailed collision physics between charged particles and neutrals and the ability to represent multiple smooth (not stair-stepped) electrodes of arbitrary shape and voltage whose surfaces may be secondary-particle emitters (H⁻and e⁻). The status of this development is discussed in terms of its physics content and current implementation details.     

Bjorken Flow Revisited: Analytic and Numerical Solutions in Flat Space-Time Coordinates

In this work we provide analytic and numerical solutions for the Bjorken flow, a standard benchmark in relativistic hydrodynamics providing a simple model for the bulk evolution of matter created in collisions between heavy nuclei.We consider relativistic gases of both massive and massless particles, working in a (2+1) and (3+1) Minkowski space-time coordinate system. The numerical results from a recently developed lattice kinetic scheme show excellent agreement with the analytic solutions.     

The effects of multiple small doses of exogenous surfactant on experimental respiratory failure induced by lung lavage in rats

Aim: To test the effect on pulmonary gas exchange and mechanics of multiple small doses of exogenous surfactant as an alternative to bolus delivery in experimental respiratory failure induced by lung lavage.
Methods: After anesthesia, tracheostomy and constant volume ventilation, respiratory failure was induced by lung lavage in 20 rats. Animals were randomly assigned to an untreated control group or two experimental groups. Equal total doses of modified porcine surfactant (200 mg ·kg^-1 body weight,) were given by tracheal instillation, either as a single bolus or in four (50 mg·kg^-1 b.w.) fractional doses at 10-min intervals. Arterial pH and blood gases, and peak inspiratory pressure (PIP) were measured.
Results: After lavage, a rapid decrease in arterial pH and PaO₂, and an increase in PaCO₂ and PIP were observed in all animals. In both surfactant-treated groups, PaO₂ increased after surfactant instillation, and remained significantly higher than controls throughout the experiment. Arterial pH was significantly higher and PaCO₂ significantly lower only in the single bolus group. In the multiple dose group, these levels were similar to those of controls.
Conclusions: In surfactant-depleted rats with respiratory failure, instillation of four fractional surfactant doses did not result in the same enhancement on gas exchange and PIP, in the following 60 min, as same total dose given by a single bolus.     

Sweep Gas Flowrate and C02 Exchange in Artificial Lungs

Abstract A simple analysis and graphic result are presented for characterizing the dependence of CO₂ exchange on the sweep gas (ventilating gas) flowrate in artificial lungs. The analysis requires no knowledge of the device-specific mass transfer characteristics of an artificial lung, nor does it require detailed mathematical modeling or computer simulation. Rather, it uses appropriate normalization to establish generic features of the gas flow dependency of CO₂ exchange that are applicable to all artificial lung devices. Principal results are that the transition from relatively gas flow-sensitive to gas flow-insensitive CO₂, exchange occurs at sweep gas flowrates of approximately 40–60 times the CO₂ exchange rate. Achieving a CO₂ exchange rate within 85% of maximal (for a given oxygenator and blood-side conditions) requires a sweep gas flowrate of no less than approximately 50 times the nominal CO₂ exchange rate. When the sweep gas flowrate is less than 20 times the CO₂ exchange rate, CO₂ exchange is highly gas flow dependent and less than one-half the maximal possible rate.     

Halothane Anaesthesia with Spontaneous Respiration for Tonsillectomy in Children

Bain's anaesthetic circuit was used in 22 children undergoing tonsillectomy under halothane anaesthesia with spontaneous respiration. End-tidal CO₂ was monitored by capnography. The median maximum end-tidal CO₂ was 7%, and during surgery nine patients had an end-tidal CO₂ higher than 7%, corresponding to a Paco₂ close to 8 kPa when the arterial to end-tidal CO₂ difference is taken into consideration. Increase in fresh gas flow or change to a non-rebreathing system had virtually no effect on end-tidal CO₂. However, following discontinuation of halothane or during controlled respiration, acceptable values of end-tidal CO₂ were reached, leading to the conclusion that respiratory depression was responsible for the high values of end-tidal CO₂ rather than properties of Bain's circuit or too low gas flow rates.     

Distribution of Expiratory Gas and Rebreathing in T-piece Modifications Used in Weaning

The simple T-piece is frequently used as a weaning system during respirator treatment. It is modified with an expiratory non-compliant reservoir (EnCR), an inspiratory compliant reservoir (ICR) and/or an expiratory one-way valve. The distribution of expiratory gases and rebreathing were studied in a model set-up in the corresponding systems at different fresh gas flows (FGF) and tidal volumes (V_T). An EnCR produces no change, whereas an ICR causes the expiratory gas to flow into the inspiratory limb, an effect which is intensified by the presence of an expiratory valve. With a falling FGF and a rising V_T, increasing amounts of expiratory gas are found in the inspiratory limb in the modifications with an ICR. However, this only gives rise to rebreathing in the valve modification with a low FGF and high V_T. The modification of the T-piece with an ICR but without a one-way valve is advantageous, as this system combines only slight dilution via the expiratory limb and a minimal risk of rebreathing.     

Preliminary evaluation of a new continuous intra-arterial blood gas monitoring device

Continuous intra-arterial blood gas monitoring is a new technique, possibly offering therapeutic advantages through improved monitoring in patients prone to hypoxaemia, hypercapnia and/or respiratory acidosis. Therefore, we studied the clinical applicability, reliability, precision and side effect of long-term continuous intraarterial blood gas monitoring in patients suffering from severe acute respiratory distress syndrome.
In 10 patients continuous intra-arterial blood gas monitoring based on fluorescent optodes technique was performed. At 4 h intervals, arterial blood samples for in vitro blood gas analyses were drawn, stored in ice, and analysed within 3 min. Evaluation of data retrieved from the continuous intra-arterial blood gas monitoring and in vitro blood gas analysis was based on 596 data points using 10 catheters. Average length of insertion was 281±215 h, max. lengths of stay was 750 h. Arterial blood gas data obtained in vivo were compared to the mean of in vivo and in vitro arterial blood gases.
Inter-catheter bias, expressed as percent difference between continuous intra-arterial blood gas and mean in vitro blood gas analysis was 0. 19±0. 23% for pH, 1. 1 ±5. 2% for PaCO₂ and 1. 6±5. 7% for PaO₂. No significant gas partial pressure dependent change in precision was demonstrable. There was no significant time dependent drift in sensor precision over the study period. No negative side-effects related to IABG monitoring were observed.
We conclude that long-term use of this new device is possible in patients and represents a reliable alternative to conventional in vitro arterial blood gas analysis, when continuous monitoring of blood gases and/or acid-base balance is critical.     

Pulmonary sympathetic denervation does not increase airway resistance in patients with chronic obstructive pulmonary disease (COPD)

Whether or not neural blockade of pulmonary sympathetic innervation is of relevance for airway resistance in patients with chronic obstructive pulmonary disease (COPD) is unknown. Accordingly we evaluated airway resistance during sympathetic blockade by high thoracic epidural anaesthesia in patients with COPD. Before and 45 min after thoracic epidural injection of bupivacaine 0.75% (6–8 ml; n=10) total respiratory resistance (oscillometry, R_os), vital capacity (VC), forced expiratory vital capacity in 1 s (FEV₁, [% VC]), functional residual capacity (FRC; helium dilution method), and arterial blood gases were measured. Three additional patients received bupivacaine intravenously (1.2 mg . min^-1 for 45 min), another three received saline epidurally. Sensory blockade covered segment C₅ through T₈. As an indicator of widespread sympathetic blockade including the lungs, skin temperature increased significantly on thumb and little toe. Despite pulmonary sympathetic denervation R_os, FEV₁, and FRC remained unchanged, while VC decreased slightly, probably due to intercostal muscle blockade. Blood gases remained constant. Neither intravenous bupivacaine nor epidural saline evoked directional changes. Since, in contrast to β-adre-noceptor blockade, pulmonary sympathetic denervation did not increase airway resistance in patients with COPD, neural sympathetic blockade seems to be of no relevance for airway resistance in these patients.     

Nitric oxide administration after the ventilator: evaluation of mixing conditions

Background: Because of the potential toxicity of nitric oxide (NO) and its oxidising product nitrogen dioxide (NO₂), any system for the delivery of inhaled NO must aim at stable and predictable levels of NO and as low concentrations as possible of NO₂.
Methods: In a laboratory set-up, we have evaluated mixing conditions in a system where NO is added after the ventilator with continuous flow. Mixing was studied by using carbon dioxide (CO₂) as a tracer gas since capnography has a short response time (360 ms) in comparison with measurements of NO with electrochemical fuel cells (response time of 18s). CO₂ (in volumes corresponding to an ideal mixture of 1,3 and 6%) was fed, after the ventilator, either into plain breathing tubing, into one or two soda lime absorbers, or into an empty and a soda lime-filled canister, at different ventilatory rates and different I: E ratios. Samples were drawn from the inspiratory limb close to the Y-piece. NO was added in the same way and in the same volume as the highest concentration of CO₂.
Results: CO₂ added to plain tubing resulted in peak levels up to five times the set levels, while addition to a mixing box with an empty and a soda lime-filled canister resulted in even mixing with gas concentrations close to the ideal. When NO was fed into plain tubing, low levels were measured at the Y-piece, indicating poor mixing. Gas supply to a mixing chamber resulted in even concentrations.
Conclusions: Even and predictable levels of NO can be obtained with continuous flow of NO to the inspiratory limb, after the ventilator, if a mixing chamber is used. To obtain adequate mixing, the volume of the mixing box should be greater than the tidal volume.     

Predictable nitrous oxide uptake enables simple oxygen uptake monitoring during low flow anaesthesia

The uptake rate of oxygen and nitrous oxide were studied during low flow anaesthesia with enflurane or isoflurane in nitrous oxide with either spontaneous or controlled ventilation. The excess gas flow and composition were analysed. The nitrous oxide uptake rate was in agreement with Severinghaus'formula _N20 1000.t^-0.5. The composition of excess gas was predictable and the following formula for oxygen uptake could be derived: O₂=fgO₂ -0.45 (fgN²O -(kg: 70.1000.t^-0.5)) where oxygen uptake rate (O₂, ml.min^-1) equals oxygen fresh gas flow (fgO₂) minus 0.45 times the difference between the fresh gas flow of nitrous oxide (fgN₂O), ml.min^-1 and estimated uptake of nitrous oxide. The equation assumes constant inspired gas concentrations of 30% oxygen and 65–70% nitrous oxide. The oxygen uptake rates calculated from this formula were in good agreement with measured uptake rates. Thus, continuous monitoring of oxygen uptake rates is possible by using only reliable flowmeters and analysis of inspried oxygen concentration.     

The Flow Requirement in a Non-Polluting Mapleson C Circuit

Capnography and measurement of the respiratory minute volume were carried out on normal, conscious subjects during breathing of pure O₂ via a Mapleson C modification of a Magill attachment, with and without continuous gas evacuation. The measurements were performed in two series, with intermittent discharge and with continuous evacuation. Rebreathing was calculated in relation to the test subject's basal respiratory minute volume, measured at the commencement of the test. The measurements indicated CO₂ accumulation at a flow below 200% of the respiratory minute volume. There was no significant difference between the systems with and without evacuation.     

Two Nonlinear Positivity-Preserving Finite Volume Schemes for Three-Dimensional Heat Conduction Equations on General Polyhedral Meshes

In this article we present two types of nonlinear positivity-preserving finite volume (PPFV) schemes for a class of three-dimensional heat conduction equations on general polyhedral meshes. First, we present a new parameter selection strategy on the one-sided flux and establish a nonlinear PPFV scheme based on a two-point flux with higher efficiency. By comparing with the scheme proposed in [H. Xie, X. Xu, C. Zhai, H. Yong, Commun. Comput. Phys. 24 (2018) 1375–1408], our scheme avoids the assumption that the values of auxiliary unknowns are nonnegative, which makes our interpolation formulae suitable to be constructed by existing approaches with high accuracy and well robustness (e.g., the finite element method), thus enhancing the adaptability to distorted meshes with large deformations. Then we derive a linear multi-point flux involving combination coefficients and, via the Patankar trick, obtain another nonlinear PPFV scheme that is concise and easy to implement. The selection strategy of combination coefficients is also provided to improve the convergence behavior of the Picard procedure. Furthermore, the existence and positivity-preserving properties of these two nonlinear PPFV solutions are proved. Numerical experiments with the discontinuous diffusion scalar as well as discontinuous and anisotropic diffusion tensors are given to confirm our theoretical findings and demonstrate that our schemes both can achieve ideal-order accuracy even on severely distorted meshes.