On the numerical treatment of viscous and convective effects in relative pressure reconstruction methods

The mechanism of many cardiovascular diseases can be understood by studying the pressure distribution in blood vessels. Direct pressure measurements, however, require invasive probing and provide only single‐point data. Alternatively, relative pressure fields can be reconstructed from imaging‐based velocity measurements by considering viscous and inertial forces. Both contributions can be potential troublemakers in pressure reconstruction: the former due to its higher‐order derivatives, and the latter because of the quadratic nonlinearity in the convective acceleration. Viscous and convective terms can be treated in various forms, which, although equivalent for ideal measurements, can perform differently in practice. In fact, multiple versions are often used in literature, with no apparent consensus on the more suitable variants. In this context, the present work investigates the performance of different versions of relative pressure estimators. For viscous effects, in particular, two new modified estimators are presented to circumvent second‐order differentiation without requiring surface integrals. In‐silico and in‐vitro data in the typical regime of cerebrovascular flows are considered, allowing a systematic noise sensitivity study. Convective terms are shown to be the main source of error, even for flows with pronounced viscous component. Moreover, the conservation (often integrated) form of convection exhibits higher noise sensitivity than the standard convective description, in all three families of estimators considered here. For the classical pressure Poisson estimator, the present modified version of the viscous term tends to yield better accuracy than the (recently introduced) integrated form, although this effect is in most cases negligible when compared to convection‐related errors

Implicit-explicit schemes for incompressible flow problems with variable viscosity

In this work we study different Implicit-Explicit (IMEX) schemes for incompressible flow problems with variable viscosity. Unlike most previous work on IMEX schemes, which focuses on the convective part, we here focus on treating parts of the diffusive term explicitly to reduce the coupling between the velocity components. We present different, both monolithic and fractional-step, IMEX alternatives for the variable-viscosity Navier--Stokes system, analysing their theoretical and algorithmic properties. Stability results are proven for all the methods presented, with all these results being unconditional, except for one of the discretisations using a fractional-step scheme, where a CFL condition (in terms of the problem data) is required for showing stability. Our analysis is supported by a series of numerical experiments

An efficient split-step framework for non-Newtonian incompressible flow problems with consistent pressure boundary conditions

Incompressible flow problems with nonlinear viscosity, as they often appear in biomedical and industrial applications, impose several numerical challenges related to regularity requirements, boundary conditions, matrix preconditioning, among other aspects. In particular, standard split-step or projection schemes decoupling velocity and pressure are not as efficient for generalised Newtonian fluids, since the additional terms due to the non-zero viscosity gradient couple all velocity components again. Moreover, classical pressure correction methods are not consistent with the non-Newtonian setting, which can cause numerical artifacts such as spurious pressure boundary layers. Although consistent reformulations have been recently developed, the additional projection steps needed for the viscous stress tensor incur considerable computational overhead. In this work, we present a new time-splitting framework that handles such important issues, leading to an efficient and accurate numerical tool. Two key factors for achieving this are an appropriate explicit–implicit treatment of the viscous and convective nonlinearities, as well as the derivation of a pressure Poisson problem with fully consistent boundary conditions and finite-element-suitable regularity requirements. We present first- and higher-order stepping schemes tailored for this purpose, as well as various numerical examples showcasing the stability, accuracy and efficiency of the proposed framework

Robust stabilised finite element solvers for generalised Newtonian fluid flows

Various materials and solid-fluid mixtures of engineering and biomedical interest can be modelled as generalised Newtonian fluids, as their apparent viscosity depends locally on the flow field. Despite the particular features of such models, it is common practice to combine them with numerical techniques originally conceived for Newtonian fluids, which can bring several issues such as spurious pressure boundary layers, unsuitable natural boundary conditions and coupling terms spoiling the efficiency of nonlinear solvers and preconditioners. In this work, we present a finite element framework dealing with such issues while maintaining low computational cost and simple implementation. The building blocks of our algorithm are (i) an equal-order stabilisation method preserving consistency even for lowest-order discretisations, (ii) robust extrapolation of velocities in the time-dependent case to decouple the rheological law from the overall system, (iii) adaptive time step selection and (iv) a fast physics-based preconditioned Krylov subspace solver, to tackle the relevant range of discretisation parameters including highly varying viscosity. Selected numerical experiments are provided demonstrating the potential of our approach in terms of robustness, accuracy and efficiency for problems of practical interest

Efficient split-step schemes for fluid–structure interaction involving incompressible generalised Newtonian flows

Blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states which, in turn, affect the engineering design process. Therefore, any reliable model of such physical processes must consider the coupling of fluids and solids. However, complexity increases for non-Newtonian fluid models, as used, e.g., for blood or polymer flows. In these fluids, subtle differences in the local shear rate can have a drastic impact on the flow and hence on the coupled problem. There, existing (semi-) implicit solution strategies based on split-step or projection schemes for Newtonian fluids are not applicable, while extensions to non-Newtonian fluids can lead to substantial numerical overhead depending on the chosen fluid solver. To address these shortcomings, we present here a higher-order accurate, added-mass-stable fluid–structure interaction scheme centered around a split-step fluid solver. We compare several implicit and semi-implicit variants of the algorithm and verify convergence in space and time. Numerical examples show good performance in both benchmarks and an idealised setting of blood flow through an abdominal aortic aneurysm considering physiological parameters

A global residual‐based stabilization for equal‐order finite element approximations of incompressible flows

Due to simplicity in implementation and data structure, elements with equal-order interpolation of velocity and pressure are very popular in finite-element-based flow simulations. Although such pairs are inf-sup unstable, various stabilization techniques exist to circumvent that and yield accurate approximations. The most popular one is the pressure-stabilized Petrov–Galerkin (PSPG) method, which consists of relaxing the incompressibility constraint with a weighted residual of the momentum equation. Yet, PSPG can perform poorly for low-order elements in diffusion-dominated flows, since first-order polynomial spaces are unable to approximate the second-order derivatives required for evaluating the viscous part of the stabilization term. Alternative techniques normally require additional projections or unconventional data structures. In this context, we present a novel technique that rewrites the second-order viscous term as a first-order boundary term, thereby allowing the complete computation of the residual even for lowest-order elements. Our method has a similar structure to standard residual-based formulations, but the stabilization term is computed globally instead of only in element interiors. This results in a scheme that does not relax incompressibility, thereby leading to improved approximations. The new method is simple to implement and accurate for a wide range of stabilization parameters, which is confirmed by various numerical examples

Semi-implicit fluid–structure interaction in biomedical applications

Fluid–structure interaction (FSI) incorporates effects of fluid flows on deformable solids and vice versa. Complex biomedical problems in clinical applications continue to challenge numerical algorithms, as incorporating the underlying mathematical methods can impair the solvers’ performance drastically. In this regard, we extend a semi-implicit, pressure Poisson-based FSI scheme for non-Newtonian fluids to incorporate several models crucial for biomechanical applications. We consider Windkessel outlets to account for neglected downstream flow regions, realistic material fibre orientation and stressed reference geometries reconstructed from medical image data. Additionally, we incorporate vital numerical aspects, namely, stabilisations to counteract dominant convective effects and instabilities triggered by re-entrant flow, while a major contribution of this work is combining interface quasi-Newton methods with Robin coupling conditions to accelerate the partitioned (semi-)implicit coupling scheme. The numerical examples presented herein aim to finally bridge the gap to real-world applications, considering state-of-the-art modelling aspects and physiological parameters. FSI simulations of blood flow in an iliac bifurcation derived from medical images and vocal folds deforming in the process of human phonation demonstrate the versatility of the framework

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements

Mortality and pulmonary complications in patients undergoing surgery with perioperative SARS-CoV-2 infection: an international cohort study

Background: The impact of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) on postoperative recovery needs to be understood to inform clinical decision making during and after the COVID-19 pandemic. This study reports 30-day mortality and pulmonary complication rates in patients with perioperative SARS-CoV-2 infection. Methods: This international, multicentre, cohort study at 235 hospitals in 24 countries included all patients undergoing surgery who had SARS-CoV-2 infection confirmed within 7 days before or 30 days after surgery. The primary outcome measure was 30-day postoperative mortality and was assessed in all enrolled patients. The main secondary outcome measure was pulmonary complications, defined as pneumonia, acute respiratory distress syndrome, or unexpected postoperative ventilation. Findings: This analysis includes 1128 patients who had surgery between Jan 1 and March 31, 2020, of whom 835 (74·0%) had emergency surgery and 280 (24·8%) had elective surgery. SARS-CoV-2 infection was confirmed preoperatively in 294 (26·1%) patients. 30-day mortality was 23·8% (268 of 1128). Pulmonary complications occurred in 577 (51·2%) of 1128 patients; 30-day mortality in these patients was 38·0% (219 of 577), accounting for 81·7% (219 of 268) of all deaths. In adjusted analyses, 30-day mortality was associated with male sex (odds ratio 1·75 [95% CI 1·28–2·40], p\textless0·0001), age 70 years or older versus younger than 70 years (2·30 [1·65–3·22], p\textless0·0001), American Society of Anesthesiologists grades 3–5 versus grades 1–2 (2·35 [1·57–3·53], p\textless0·0001), malignant versus benign or obstetric diagnosis (1·55 [1·01–2·39], p=0·046), emergency versus elective surgery (1·67 [1·06–2·63], p=0·026), and major versus minor surgery (1·52 [1·01–2·31], p=0·047). Interpretation: Postoperative pulmonary complications occur in half of patients with perioperative SARS-CoV-2 infection and are associated with high mortality. Thresholds for surgery during the COVID-19 pandemic should be higher than during normal practice, particularly in men aged 70 years and older. Consideration should be given for postponing non-urgent procedures and promoting non-operative treatment to delay or avoid the need for surgery. Funding: National Institute for Health Research (NIHR), Association of Coloproctology of Great Britain and Ireland, Bowel and Cancer Research, Bowel Disease Research Foundation, Association of Upper Gastrointestinal Surgeons, British Association of Surgical Oncology, British Gynaecological Cancer Society, European Society of Coloproctology, NIHR Academy, Sarcoma UK, Vascular Society for Great Britain and Ireland, and Yorkshire Cancer Research

The Genome of Anopheles darlingi, the main neotropical malaria vector

Anopheles darlingi is the principal neotropical malaria vector, responsible for more than a million cases of malaria per year on the American continent. Anopheles darlingi diverged from the African and Asian malaria vectors ∼100 million years ago (mya) and successfully adapted to the New World environment. Here we present an annotated reference A. darlingi genome, sequenced from a wild population of males and females collected in the Brazilian Amazon. A total of 10 481 predicted protein-coding genes were annotated, 72% of which have their closest counterpart in Anopheles gambiae and 21% have highest similarity with other mosquito species. In spite of a long period of divergent evolution, conserved gene synteny was observed between A. darlingi and A. gambiae. More than 10 million single nucleotide polymorphisms and short indels with potential use as genetic markers were identified. Transposable elements correspond to 2.3% of the A. darlingi genome. Genes associated with hematophagy, immunity and insecticide resistance, directly involved in vectorhuman and vectorparasite interactions, were identified and discussed. This study represents the first effort to sequence the genome of a neotropical malaria vector, and opens a new window through which we can contemplate the evolutionary history of anopheline mosquitoes. It also provides valuable information that may lead to novel strategies to reduce malaria transmission on the South American continent. The A. darlingi genome is accessible at www.labinfo.lncc.br/index.php/anopheles- darlingi. © 2013 The Author(s)