domain: spi phys

text:
Caroline Nore

W Herreman

Loic Cappanera

Jean-Luc Guermond

Tom Weier

Are experiments of Metal Pad Roll Instability feasible at Room Temperature?

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Are experiments of Metal Pad Roll Instability feasible at Room

Temperature? Caroline Nore a , Wietze Herreman a , Loic Cappanera b , Jean-Luc Guermond c and Tom Weier d Aluminium Hall-Héroult reduction cells can be the place of the metal pad roll instability (MPR), ie the growth of gravity waves at the interface between the mixture of cryolite and alumina on top and the liquid aluminium on bottom when a weak ambient magnetic field is present [1]. Combining theoretical arguments and numerical simulations, we demonstrate that this MPR instability can occur in a centimeter-scale setup with reasonable values of the magnetic field and electrical current and with metal pairs that are liquid at room temperature (see Figure 1). We investigate two fluid pairs: gallium with mercury (immiscible pair) and gallium with GaInSn eutectic alloy (miscible pair). We propose an experimental setup and discuss a list of difficulties that can be overcome.

a

  Université Paris-Saclay, CNRS, LISN, 91400 Orsay, France b Dep. Mathematics, University of Houston, Houston, Texas 77204-3008, USA c Dep. Mathematics, Texas A&M University, 3368 TAMU, College Station, Texas 77843-3368, USA d Helmholtz-Zentrum Dresden -Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany 1 Sele, Metall. Mater. Trans. B 8, 613 (1977). 2 Nore et al., Phys. Rev. Lett. 126, 184501 (2021).

Figure 1 :

 1 Figure 1: (left) Sketch of the cylindrical setup: a layer of gallium floats on a layer of mercury or eutectic GaInSn alloy, a current J passes through the cell which is subjected to an external vertical magnetic field B e . (right) Interface between the immiscible Ga and Hg setup and turbulent structures in a vertical plane.


Guillaume De Romemont

Simon Rozenkranz

Anne Sergent

Yann Fraigneau

Yann Fraigneau Turbulent

Turbulent plumes in asymmetric rough Rayleigh-Bénard cell

teaching and research institutions in France or abroad, or from public or private research centers.

Turbulent plumes in asymmetric rough Rayleigh-Bénard cell G. de Romemont a , S. Rosenkranz a , Y. Fraigneau a and A. Sergent a,b In a real thermal system, the underlying surfaces involve specific topographies or smallscale roughness which have a significant impact on the heat transfer. Particularly, in the case of turbulent convection, the addition of wall roughness results in a global heat transfer enhancement and even in an increase of the exponent of the heat transfer scaling law [1,2]. It is commonly admitted that the heat transfer enhancement originates from an intensification of the thermal plume emission. In the present study, we consider convection over a regularly roughened plate in a Rayleigh-Bénard cell. The objective of this work is to identify how roughness changes the plume features and their dynamics, depending on the regime. Three-dimensional direct numerical simulations have been performed for Rayleigh numbers covering five decades up to Ra=10 10 and for two roughness sizes. As expected, the three heat transfer regimes have been obtained [3]. Taking advantage of the cavity asymmetry, we conduct a comparative study of the plume dynamics near the rough and smooth horizontal plates within the same set-up. Based on thermal and velocity fluctuations, thermal plumes are extracted from the turbulent background. Temporal and spatial statistical properties of the plumes are analysed in the mixing layer of both cavity sides in terms of fluctuations or energy content. Interactions between roughness, plumes, large scale circulation and turbulent background are also investigated.

a

  Université Paris-Saclay, CNRS, Laboratoire Interdisciplinaire des Sciences du Numérique (LISN), F-91405 Orsay, France b Sorbonne Université, Faculté des Sciences et Ingénierie, UFR Ingénierie, F-75005 Paris, France 1 Xie and Xia. J. Fluid Mech. 825, 573 (2017). 2 Rusaouën et al., J. Fluid Mech. 837, 443 (2018). 3 Belkadi et al. J. Fluid Mech. 923, A6 (2021).

Figure 1 :

 1 Figure 1: Thermal plumes in a water-filled cell at Ra=10 10 with several hundred blocks roughened on the bottom plate.


Didier Lucor

Atul Agrawal

Anne Sergent

PHYSICS/DNS-INFORMED DNN SURROGATES OF TURBULENT THERMAL CONVECTION

1 LIMSI, CNRS, Université Paris-Saclay, didier.lucor@limsi.fr, https://perso.limsi.fr/lucor/ 2 Technical University Munich, atul.agrawal@tum.de 3 LIMSI, CNRS, Sorbonne Université, anne.sergent@limsi.fr, https://perso.limsi.fr/sergent/ Key Words: physics-informed machine learning, deep neural network, turbulent convection The motivation of this work stems from the limited understanding of the physical mechanisms responsible for the heat transfer enhancement in turbulent convection over rough geometry. Indeed, in natural convection, strong dynamic interactions between a large spatial/time scale range from mean wind to small-scale plumes remain difficult to investigate based on partial data acquisition from expensive direct numerical simulations (DNS) [START_REF] Castillo-Castellanos | Cessation and reversals of large-scale structures in square Rayleigh-Bénard cells[END_REF] or the spatially limited measurements of experimental set-ups. Moreover, the development of data-driven surrogate models for the prediction and compression of such complex fluid phenomena, in place of more standard numerical simulations may help when many query and/or real-time simulations are required, for instance in order to perform signal processing and analysis, uncertainty quantification, data assimilation or control [START_REF] Kutz | Deep learning in fluid dynamics[END_REF]. In this study, we make the choice to rely on deep neural networks (DNN). The approach retained is the one of training a DNN by leveraging some underlying physical laws (PDE) of the system. A natural approach is to incorporate (some of) the governing partial differential equations of the physical model (e.g. mass/momentum/energy conservation) at the core of the DNN, i.e. in the loss/likelihood functions, [START_REF] Raissi | Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[END_REF][START_REF] Zhu | Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data[END_REF]. We propose to investigate how this additional information effectively regularizes the minimization procedure in the training of DNN, and allows the recovery of various hidden flow variables when the training is performed with partial data. More specifically, we will report on the influence of the choice of the training domain for data acquisition as well as for the enforcement of the PDE, in relation to the problem geometry and initial/boundary conditions. Finally, we will put in perspective the future use of experimental data in place of DNS data.

14th

  World Congress on Computational Mechanics (WCCM) ECCOMAS Congress 2020 19-24 July 2020, Paris, France PHYSICS/DNS-INFORMED DNN SURROGATES OF TURBULENT THERMAL CONVECTION D. Lucor 1, * , A. Agrawal 2 and A. Sergent 3


Valentin Femenia

Victor Pommier

Helena Huguet

Xavier Iriart

Marie-Christine Picot

Charlene Bredy

Laura Lorca

Gregoire De

La Villeon

Sophie Guillaumont

Jean Luc Pasquié

Marie- Christine Picot

Jean-Luc Pasquie

Stefan Matecki

Francçois Roubertie

Bertrand Leobon

Jean-Benoît Thambo

Zakaria Jalal

Julie Thomas

Jean- Baptiste Mouton

Martina Avesani

Pascal Amedro
email: pascal.amedro@chu-bordeaux.fr

Correlation between three-dimensional echocardiography and cardiopulmonary fitness in patients with univentricular heart: A cross-sectional multicentre prospective study

Keywords:

a b s t r a c t Background:

The prognosis of patients with a functional single ventricle has improved, with better cardiopulmonary fitness, health-related quality of life and survival. Conventional echocardiography remains the first-line technique in single ventricle follow-up. Threedimensional (3D) echocardiography has shown recent value in congenital cardiology, but its ability to predict functional status in patients with a single ventricle remains unknown.

Aim:

To evaluate, in patients with a single ventricle, the association between 3D echocardiography variables and functional status determined by cardiopulmonary fitness.

Methods:

Children and adults with a functional single ventricle were prospectively enrolled in this multicentre study. Cardiopulmonary fitness was assessed by cardiopulmonary exercise test, with measures of maximum oxygen uptake (VO2max) and ventilatory efficiency (VE/VCO 2 slope). 3D echocardiography was performed with off-line reproducibility analyses, using Tom Tec Arena TM software. Health-related quality of life was assessed using the SF-36 questionnaire.

Results:

A total of 33 patients were screened, and 3D echocardiography analyses were feasible in 22 sub-jects (mean age 28 ± 9 years). 3D echocardiography ejection fraction correlated with percent-predictedVO 2max (r = 0.64, P < 0.01), VE/VCO 2 slope (r = -0.41, P = 0.05), twodimensional echocardiography ejection fraction (r = 0.55, P < 0.01) and health-related quality of life physical functioning dimension (r = 0.56, P = 0.04). 3D echocardiography indexed endsystolic volume correlated with percent-predicted VO2max(r = -0.45, P = 0.03) and VE/VCO 2 slope (r = 0.65, P < 0.01). 3D echocardiography reproducibility was good.

Conclusions:

Single ventricle ejection fraction and volumes measured by 3D echocardiography correlated with cardiopulmonary fitness, as determined by two main prognostic cardiopulmonary exercise test variables: VO2maxand VE/VCO 2 slope. Despite good reproducibility, 3D echocardiography feasibility remained limited. 3D echocardiography may be of value in single ventricle follow-up, provided that the technique and analysis software are improved.

Background

Significant advances in prenatal diagnosis, surgical techniques and postoperative care have led to increasing survival rates among patients with single ventricle (SV) physiology [START_REF] Jaquiss | Single ventricle physiology: surgical options, indications and outcomes[END_REF]. However, these patients still have high morbidity and mortality, requiring lifelong follow-up, as well as repeated invasive procedures and prolonged hospitalizations [START_REF] Tabtabai | National trends in hospitalizations for patients with single-ventricle anatomy[END_REF].

Among the different non-invasive examinations used during follow-up of patients with SV physiology, the prognostic role of the cardiopulmonary exercise test (CPET) has been demonstrate [START_REF] Baumgartner | ESC Guidelines for the management of adult congenital heart disease[END_REF][START_REF] Marcadet | FrenchSociety of Cardiology guidelines on exercise tests (part 1): methods and interpretation[END_REF][START_REF] Marcadet | French Soci-ety of Cardiology guidelines on exercise tests (part 2): indications for exercise tests in cardiac diseases[END_REF]. Indeed, two main CPET variablesmaximum oxygen uptake(VO 2max ) and ventilatory efficiency (VE/VCO 2 slope)correlated with functional status, quality of life and mortality in SV [START_REF] Gavotto | The˙Ve/˙Vco(2) slope: a useful tool to evaluate the physiological status of children with congenital heart disease[END_REF][START_REF] Mezzani | Hemodynamic, not ventilatory, inefficiency is associated with high VE/VCO 2 slope in repaired, noncyanotic congenital heart disease[END_REF][START_REF] Myers | A cardiopulmonary exercise testing score for predicting outcomes in patients with heart failure[END_REF][START_REF] Paolillo | Heart failure prognosis over time: how the prognostic role of oxygen consumption and ventilatory efficiency during exercise has changed in the last 20 years[END_REF].The VE/VCO2slope has been validated more recently as a surrogate marker for morbidity and mortality in adult heart failure [START_REF] Myers | A cardiopulmonary exercise testing score for predicting outcomes in patients with heart failure[END_REF][START_REF] Paolillo | Heart failure prognosis over time: how the prognostic role of oxygen consumption and ventilatory efficiency during exercise has changed in the last 20 years[END_REF],and in patients with congenital heart disease [START_REF] Gavotto | The˙Ve/˙Vco(2) slope: a useful tool to evaluate the physiological status of children with congenital heart disease[END_REF][START_REF] Mezzani | Hemodynamic, not ventilatory, inefficiency is associated with high VE/VCO 2 slope in repaired, noncyanotic congenital heart disease[END_REF]. This variable is of particular interest in patients with complex congenital heart disease, especially SV, as it does not require maximal exercise.

Cardiac imaging is the main diagnostic tool for evaluating cardiac function. However, the accurate evaluation of SV functional status using conventional two-dimensional (2D) echocardiography remains limited, and multimodality cardiac imaging, involving echocardiography, cardiac magnetic resonance imaging and cardiac computed tomography, is recommended [START_REF] Baumgartner | ESC Guidelines for the management of adult congenital heart disease[END_REF][START_REF] Stout | AHA/ACC guideline for the management of adults with congenital heart disease: a report of the American College of Cardiology/American Heart Association Task Force on Clinical Practice Guidelines[END_REF]. Nevertheless, the identification of non-invasive cardiac imaging variables with prognostic value, such as ventricular volume and function, remains challenging, given the physiological and anatomical heterogeneity in SV [START_REF] Kutty | Role of imaging in the evaluation of single ventricle with the Fontan palliation[END_REF].

Three-dimensional (3D) echocardiography has shown recent potential in patients with congenital heart disease [START_REF] Salvo | Imaging the adult with congenital heart disease: a multimodality imaging approach-position paper from the EACVI[END_REF][START_REF] Simpson | Three-dimensional echocardiography in congenital heart disease[END_REF], as it can provide fast and reproducible assessment of SV volumes and ejection fraction, with acquisition of full-volume data sets within a few seconds [START_REF] Bharucha | Recent advances in pediatric echocardiography[END_REF], and fair-to-good accuracy compared with cardiac magnetic resonance imaging [START_REF] Bell | Assessment of right ventricular volumes in hypoplastic left heart syndrome by real-time three-dimensional echocardiography: comparison with cardiac magnetic resonance imaging[END_REF][START_REF] Soriano | Matrix-array 3-dimensional echocardiographic assessment of volumes, mass, and ejection fraction in young pediatric patients with a functional single ventricle: a comparison study with cardiac magnetic resonance[END_REF][START_REF] Zhong | Evaluation of left ventricular volumes and function by real time three-dimensional echocardiography in children with functional single left ventricle: a comparison between QLAB and Tom[END_REF][START_REF] Zhong | Ventricular function and dyssynchrony in children with a functional single right ventricle using real time threedimensional echocardiography after font an operation[END_REF]. Therefore, volume assessment by 3D echocardiography could become a valuable technique for serial routine follow-up in patients with SV [START_REF] Bell | Assessment of right ventricular volumes in hypoplastic left heart syndrome by real-time three-dimensional echocardiography: comparison with cardiac magnetic resonance imaging[END_REF][START_REF] Zhong | Evaluation of left ventricular volumes and function by real time three-dimensional echocardiography in children with functional single left ventricle: a comparison between QLAB and Tom[END_REF][START_REF] Kutty | Serial assessment of right ventricular volume and function in surgically palliated hypoplastic left heart syndrome using real-time transthoracic three-dimensional echocardiography[END_REF]. Nevertheless, 3D echocardiography remains controversial in SV, and its prognostic value has not yet been established.

In this study, we aimed to evaluate, in patients with SV, the association between 3D echocardiography variables and functional status determined by cardiopulmonary fitness .3. Methods

Study design and population

This prospective multicentre cross-sectional study was carried out from November 2021 to June 2022 in three tertiary care congenital heart disease centres in France: Bordeaux University Hospital; Saint-Pierre Institute; and Montpellier University Hospital.

All paediatric and adult patients with an SV, as defined by the American College of Cardiology congenital heart disease classification [START_REF] Houyel | Population-based evaluation of a suggested anatomic and clinical classification of congenital heart defects based on the International Paediatric and Congenital Cardiac Code[END_REF], and aged ≥ 7 years, were consecutively recruited during their routine follow-up.

Clinical and paraclinical variables

All patients enrolled in the study underwent the following examinations: physical examination; electrocardiogram; transthoracic echocardiography; biological sample test (Nterminal prohormone of brain natriuretic peptide, haemoglobinaemia, haematocrit, creatinine, bilirubin, albuminaemia); and CPET. Adult patients were also asked to complete the 36-item Short Form Health Survey (SF-36) questionnaire, a validated generic instrument evaluating the main dimensions of health-related quality of life (physical functioning, energy, emotional well-being, social functioning and general health) [START_REF] Ware | Health survey: manual and interpretation guide[END_REF].

The following clinical variables were collected: sex; age; weight; height; New York Heart Association (NYHA) functional class; and SV anatomy. Depending on the ventricle's predominant morphology, subjects were classified as functional left or right SV.

Echocardiography variables

To determine feasibility and reproduce real-life practice, all eligible patients were consecutively enrolled, regardless of echogenicity; no contrast agent was used, and an ultrasound examination was performed by the patient's usual congenital cardiologist. Echocardiography examinations were performed on different ultrasound systems: EPIQ CVx (Philips, Andover, MA, USA); Affiniti 70 (Philips, Andover, MA, USA); and Vivid E95(General Electric, New York, NY, USA). Image acquisitions were performed using the following matrix transducers: X5-1 and X7-2 probes for Philips systems; and the M5S probe for General Electric systems. According to the international recommendations, electrocardiogram-gated 3D full volume sweeps were acquired from the apical view, with breath-holding during the four-beat acquisition phase [START_REF] Lang | Recommendations for chamber quantification[END_REF].

Echocardiography recordings were prospectively stored in DICOM format, and offline analyses were performed by a single investigator (V.F., congenital cardiology fellow) who was blinded to clinical and CPET data. A second analysis was performed on all recordings, by the same investigator (V.F., congenital cardiology fellow), to assess intra observer reproducibility, and by a second investigator (V.P., congenital cardiology resident), to assess inter-observer reproducibility, with no access to the results of the first analysis. Echocardiography analyses were performed using Tom Tec Arena TM software, version 40 (Tom Tec Imaging Systems GmbH, Unterschleissheim, Germany), a vendor-independent program that can measure all echocardiographic images stored in DICOM format.

Conventional 2D echocardiographic variables for the SV were collected: ejection fraction and volumes using the biplane Simpson method; 2D global longitudinal strain; atrioventricular valve Doppler variables; annular plane systolic excursion; and valve stenosis or regurgitation [START_REF] Buber | Echocardiographic evaluation of univentricular physiology and cavopulmonary shunts[END_REF]. As adult and paediatric patients were eligible for the study, all volume variables were indexed to body surface area. Left and right SV volumes were analysed using, respectively, 4D left ventricle and 4D right ventricle dedicated Tom Tec Arena TM software. Postprocessing included the setting of the position of the tricuspid valve, the mitral valve and the cardiac apex, to determine the orientation of the heart. The best possible views containing a full volume set were chosen for the analysis. The "four"-chamber, coronal and sagittal sections of the ventricle were semi-automatically bordered at end-diastole and end-systole (Fig. 1). A manual correction was performed when necessary. The endocardial tracking included papillary muscles, whereas trabeculae were mostly excluded from the volume because of poor differentiation between trabeculae and myocardium [START_REF] Seguela | Feasibility of three-dimensional transthoracic echocardiography to evaluate right ventricular volumes in children and comparison to left ventricular values[END_REF]. Then, the software generated a 3D volume of the SV throughout the cardiac cycle, with calculation of volumes and ejection fraction. In case there were two functional ventricles with a large septal defect (as in atrioventricular septal defect), the endocardial tracking included both ventricles, using the software adapted to the predominant ventricle.

CPET variables

The main prognosis outcome selected in this study was cardiopulmonary fitness, evaluated by CPET, and represented by two major variables: VO 2max and VE/VCO 2 slope [START_REF] Gavotto | The˙Ve/˙Vco(2) slope: a useful tool to evaluate the physiological status of children with congenital heart disease[END_REF][START_REF] Fernandes | Exercise testing identifies patients at increased risk for morbidity and mortality following Fontan surgery[END_REF][START_REF] Ohuchi | Prognostic value of exercise variables in 335 patients after the Fontan operation: a 23-year single-center experience of cardiopulmonary exercise testing[END_REF].

As in our previous studies using CPET procedures, all centres used a similar cycle ergometer triangular protocol to obtain a homogeneous incremental overall duration of between 10 and15 minutes: a 1-minute rest; a 3-minute warm-up (10 to 20 Watts )in increments of 10, 15 or 20 Watts each minute; a pedalling rate of 60 to 80 revolutions per minute; a 3-minute active recovery (20Watts); and a 2-minute rest [START_REF] Amedro | Impact of a centre and home-based cardiac rehabilitation program on the quality of life of teenagers and young adults with congenital heart dis-ease: the QUALI-REHAB study rationale, design and methods[END_REF][START_REF] Amedro | Correlation between cardio-pulmonary exercise test variables and health related quality of life among children with congenital heart diseases[END_REF]. The exercise test was considered as maximal when three out of the four following criteria were reached: respiratory exchange ratio (VCO 2 /VO 2 ) ≥ 1.1; maximum heart rate > 85% of maximal age-predicted heart rate; limit of the patient's tolerance despite verbal encouragement; plateau of VO 2 (VO 2max ) despite increasing exercise intensity. When oxygen uptake did not reach a plateau, which is very common in patients with SV, the peak VO 2 was recorded. VO 2max values were normalized as a percentage of the predicted VO 2max , using reference values for cycle ergometer test in the general population (named as percent-predicted VO2max) [START_REF] Guazzi | EACPR/AHA Scientific Statement. Clinical recommendations for cardiopulmonary exercise testing data assessment in specific patient populations[END_REF][START_REF] Jones | Normal standards for an incremental progressive cycle ergometer test[END_REF].

The VE/VCO 2 slope corresponds to the ventilation increase in response to CO 2 production, and thus reflects increased ventilatory drive (increased values corresponding to impaired ventilatory efficiency) [START_REF] Weatherald | Ventilatory response to exercise in cardiopulmonary disease: the role of chemo-sensitivity and dead space[END_REF]. The VE/VCO 2 slope was calculated from breath-by-breath data and determined using linear regression of minute ventilation (VE) and CO 2 production (VCO2) obtained during incremental exercise. The VE/VCO2slope value was measured from the beginning of incremental exercise (after the warm-up period) to maximum exercise [START_REF] Gavotto | The˙Ve/˙Vco(2) slope: a useful tool to evaluate the physiological status of children with congenital heart disease[END_REF][START_REF] Paolillo | Heart failure prognosis over time: how the prognostic role of oxygen consumption and ventilatory efficiency during exercise has changed in the last 20 years[END_REF].

Other CPET variables were collected, as previously detailed [START_REF] Amedro | Impact of a centre and home-based cardiac rehabilitation program on the quality of life of teenagers and young adults with congenital heart dis-ease: the QUALI-REHAB study rationale, design and methods[END_REF][START_REF] Amedro | Correlation between cardio-pulmonary exercise test variables and health related quality of life among children with congenital heart diseases[END_REF]: maximum workload; maximum heart rate; heart rate reserve; oxygen pulse increase during exercise; and ventilatory anaerobic threshold.

Formal aspects

The study was conducted in compliance with the Good Clinical Practices protocol and Declaration of Helsinki principles. Our institutional review board approved the study protocol, and the study was registered on ClinicalTrials.gov (NCT05118152). Informed consent to participate in the study was obtained from all patients, including parents or legal guardians of children.

Statistical analysis

The study population was described with means ± standard deviations or medians (interquartile ranges) for quantitative variables, and with frequencies for qualitative variables. Continuous variables distributions were tested using the Shapiro-Wilk test.

Correlations between echocardiography results and other variables were evaluated with Pearson or Spearman correlation coefficients.

Inter-and intra-observer reproducibilities of 3D echocardiography readings were assessed by calculating intraclass correlation coefficients (ICCs) of type (2, 1). As defined by Koo et al., values less than 0.5, between 0.5 and 0.75, between 0.75 and 0.9 and greater than 0.90 were indicative of poor, moderate, good and excellent reliability, respectively [START_REF] Koo | A guideline of selecting and reporting intraclass correlation coefficients for reliability research[END_REF].

Statistical significance was set at 0.05, and analyses were per-formed using Statistical Analysis Systems Enterprise Guide, version4.3 (SAS Institute, Cary, NC, USA).

Results

Patients' characteristics

During the study period, a total of 33 patients with SV were screened and were eligible for the study, but only 22 of them (13male subjects) were finally analysed, including three children and19 adults aged 10 to 43 years (mean age 28 ± 9 years) (Table 1).The SV morphology was left for 15 subjects, and 20 patients had undergone total cavopulmonary anastomosis surgical repair at the time of the study (two patients with SV and pulmonary stenosis had undergone Glenn surgery). Most patients were in NYHA functional class I or II (n = 21).

Overall, the SV systolic function assessed by echocardiography was preserved, with median ejection fraction values of 55.8% (interquartile range 50.0-60.0%) using 2D measures, and 59.2%(interquartile range 43.9-63.2%) using 3D measures. However, cardiopulmonary fitness was impaired, with a meanVO2maxraw value of 21.1 ± 8.8 mL/kg/min, and a mean percent-predicted VO2maxvalue of 56.8 ± 18.8%. Ventilatory efficiency was altered overall, with a median VE/VCO 2 slope increase to 37.7(interquartile range 32.9-42.6).

Correlation between 3D echocardiography and cardiopulmonary fitness

The SV ejection fraction measured by 3D echocardiography correlated with both CPET variables: the percent-predicted VO2max(r = 0.64, P < 0.01) and the VE/VCO 2 slope (r = -0.41, P = 0.05) (Fig. 2).

The SV volumes measured by 3D echocardiography correlated with percent-predicted VO2max(r = -0.45, P = 0.03 for indexed end-systolic volume [ESVi]) and VE/VCO 2 slope (r = 0.52, P = 0.01 for indexed end-diastolic volume [EDVi]; r = 0.65, P < 0.01 for ESVi).

Correlations between 3D echocardiography and secondary outcomes

The ejection fraction measured by 3D echocardiography correlated with 2D biplane Simpson measures (r = 0.55, P < 0.01), 2D global longitudinal strain (r = -0.58, P < 0.01) and the SF-36 physical functioning dimension of health-related quality of life (r = 0.56,P = 0.04).No significant association was found between 3D echocardiography variables and biological markers, or between SV 3D volumes and any of the secondary outcomes (Fig. 2, Table 2).The ejection fraction measured by 3D echocardiography correlated with 2D global longitudinal strain (r = -0.58, P < 0.01)(Fig. 2). 2D global longitudinal strain also correlated with percentpredicted VO2max(r = -0.57, P < 0.01) (Table 3).

Feasibility and reproducibility

Assessment of SV function using 3D echocardiography was not possible in one third of the eligible population (n = 11 out of the 33screened patients), as the Tom Tec Arena TM software was unable to analyse 3D data because of image acquisition artefacts. Indeed, in some cases, insufficient resolution occurred because of a poor acoustic window (n = 5) or insufficient breath-holding capacity (n = 1). Also, in extremely dilated SV (n = 5), a portion of the ventricle protruded from the acoustic window, so we missed volume in the data set and endocardial tracking was incomplete.

In patients for whom SV function assessment using 3Dechocardiography was possible (n = 22 out of the 33 screened patients), intra observer reproducibility was good for ejection fraction (ICC = 0.78, 95% confidence interval [CI]: 0.56-0.90) and volumes (ICC = 0.74, 95% CI: 0.49-0.88 for EDVi; ICC = 0.69, 95% CI:0.39-0.85 for ESVi). Inter observer reproducibility was excellent for volumes (ICC = 0.82, 95% CI: 0.62-0.92 for EDVi; ICC = 0.86, 95% CI:0.71-0.94 for ESVi), and moderate for ejection fraction (ICC = 0.62,95% CI: 0.29-0.82) (Table 4).

Discussion

In this prospective multicentre study, we found that SV ejection fraction and volumes measured by 3D echocardiography were significantly associated with cardiopulmonary fitness and health-related quality of life, with good reproducibility, but limited feasibility.

The correlation found in this study between SV ejection fraction and volumes, using 3D echocardiography and the two main cardiopulmonary fitness variables, is of clinical interest, as VO 2max and VE/VCO 2 slope are two major prognostic predictors in SV [START_REF] Gavotto | The˙Ve/˙Vco(2) slope: a useful tool to evaluate the physiological status of children with congenital heart disease[END_REF][START_REF] Fernandes | Exercise testing identifies patients at increased risk for morbidity and mortality following Fontan surgery[END_REF][START_REF] Ohuchi | Prognostic value of exercise variables in 335 patients after the Fontan operation: a 23-year single-center experience of cardiopulmonary exercise testing[END_REF].Indeed, a decline in percent-predicted VO2maxabove 3% per year has been found to be an independent risk factor for morbidity and mortality in adults with SV [START_REF] Egbe | Cardiopulmonary exercise test in adults with prior Fontan operation: the prognostic value of serial testing[END_REF]. Moreover, impaired ventilatory efficiency, marked by an increased VE/VCO 2 slope above 31.5,has been reported to be an independent risk factor for morbidity and mortality in children and adult patients with SV [START_REF] Fernandes | Exercise testing identifies patients at increased risk for morbidity and mortality following Fontan surgery[END_REF]. Similar results were reported by one paediatric cardiac magnetic resonance imaging study, where systolic SV function correlated with cardiopulmonary fitness [START_REF] Klimes | Exercise capacity reflects ventricular function in patients having th eFontan circulation[END_REF]. However, cardiac magnetic resonance imaging is not widely available, may be time consuming and expen-sive, and usually requires sedation in the paediatric population [START_REF] Schulte-Uentrop | Anaesthesia or sedation for MRI in children[END_REF].Hence, the application of 3D echocardiography is attractive because of its availability, non-invasive nature, favourable costs and absence of sedation. The value of 3D echocardiography has been discussed in patients with heart failure, as well as in other types of congenital heart disease [START_REF] Lu | Two-dimensional and three-dimensional transthoracic echocardiography as predictive and prognostic indicators of all-cause mortality in heart failure with reduced ejection fraction in patients with ischemic heart disease[END_REF][START_REF] Mancuso | Prognostic value of real-time three-dimensional echocardiography compared to two-dimensional echocardiography in patients with systolic heart failure[END_REF][START_REF] Simpson | Three-dimensional echocardiography in congenital heart disease: an expert consensus document from the European Association of Cardiovascular Imaging and the American Society of Echocardiography[END_REF], but it is essential to know how robust this technique is, and how it can help to assess functional status and morbidity in patients with complex congenital heart disease, such as SV. Indeed, the wide spectrum of SV includes various complex anatomical features, multiple surgical procedures and different haemodynamic conditions [START_REF] Houyel | Population-based evaluation of a suggested anatomic and clinical classification of congenital heart defects based on the International Paediatric and Congenital Cardiac Code[END_REF], which, altogether, make 3Dechocardiography analysis difficult. In fact, in our study, 3D echocardiography analysis was not feasible in one third of the eligible population. This may reflect real-life routine practice, but there is surely room for technical and medical improvements. A better overall gain adaptation could result in better endocardial border visualization, and specific training is advisable for physicians and sonographers dedicated to cardiac imaging in congenital heart dis-ease. Therefore, cardiac magnetic resonance imaging should be used as a priority in patients with SV for whom 3D echocardiography analysis is not possible.

Nevertheless, good-to-moderate intra observer and inter observer reproducibilities for the assessment of SV volumes and function using 3D echocardiography were found in this study. Data analyses with Tom Tec Arena TM vendor-independent software seems appropriate in close-to-real-life use, as echocardiograms are usually performed on different ultrasound machines by different sonographers. Moreover, we observed a good correlation between3D and 2D echocardiography assessment of ejection fraction, suggesting potential value for 3D echocardiography in the followup of patients with SV physiologies. Indeed, analyses of SV volumes and function using 2D echocardiography are based on geometrical assumptions [START_REF] Klaeboe | Echocardiographic assessment of left ventricular sys-tolic function[END_REF]. Furthermore, in this study, ejection fraction measured by 3D echocardiography correlated with 2D strain (a marker of global systolic ventricular function). Similar results have been reported in adult patients with heart failure [START_REF] Palmieri | Novel wall motion scorebased method for estimating global left ventricular ejection fraction: validation by real-time 3D echocardiography and global longitudinal strain[END_REF]. Zaidi et al. found a correlation between 2D strain and some biomarkers in patients with SV [START_REF] Zaidi | Correlation of serum biomarkers in adults with single ventricles with strain and strain rate using 2D speckle tracking[END_REF]. However, the prognostic value of 2D strain in patients with SV remains undetermined.

Interestingly, ejection fraction measured by 3D echocardiography was associated with the physical functioning dimension of health-related quality of life, which further reinforces the relevance of using 3D echocardiography in the follow-up of patients with SV. Indeed, patientreported outcomes have been increasingly used in clinical research in congenital cardiology [START_REF] Amedro | Quality of life of children with congenital heart diseases: a multicenter con-trolled cross-sectional study[END_REF], and the physical dimension of health-related quality of life is classically associated with the major prognostic factors in congenital heart disease, such as NYHA functional class [START_REF] Amedro | Health-related quality of life of patients with pulmonary arterial hypertension associated with CHD: the multicentre cross-sectional ACHILLE study[END_REF], VO 2max [START_REF] Amedro | Correlation between cardio-pulmonary exercise test variables and health related quality of life among children with congenital heart diseases[END_REF] or ventricle ejection fraction [START_REF] Lu | Relation of right ventricular dilation, age of repair, and restrictive right ventricular physiology with patient-reported quality of life in adolescents and adults with repaired tetralogy of fallot[END_REF]. Unsurprisingly, impaired exercise performance alters the quality of life of patients with SV [START_REF] Atz | Longitudinal outcomes of patients with single ventricle after the Fontan procedure[END_REF]; therefore, the use of 3Dechocardiography could be of interest in future research on cardiac rehabilitation using patient-reported outcomes in patients with SV [START_REF] Amedro | Impact of a centre and home-based cardiac rehabilitation program on the quality of life of teenagers and young adults with congenital heart dis-ease: the QUALI-REHAB study rationale, design and methods[END_REF].

Study limitations

In this pilot study, data from cardiac magnetic resonance imaging were not prospectively available for all patients. In the rare studies evaluating 3D echocardiography in patients with SV, SV volumes were systematically compared with cardiac magnetic resonance imaging, with controversial results [START_REF] Bell | Assessment of right ventricular volumes in hypoplastic left heart syndrome by real-time three-dimensional echocardiography: comparison with cardiac magnetic resonance imaging[END_REF][START_REF] Soriano | Matrix-array 3-dimensional echocardiographic assessment of volumes, mass, and ejection fraction in young pediatric patients with a functional single ventricle: a comparison study with cardiac magnetic resonance[END_REF][START_REF] Zhong | Evaluation of left ventricular volumes and function by real time three-dimensional echocardiography in children with functional single left ventricle: a comparison between QLAB and Tom[END_REF][START_REF] Zhong | Ventricular function and dyssynchrony in children with a functional single right ventricle using real time threedimensional echocardiography after font an operation[END_REF].

The number of subjects analysed in the study was limited, basing our results on univariate analyses, but was roughly equivalent to similar studies [15 ,19]. Finally, the Tom Tec Arena TM software used in this study for right and left SV analyses was only validated for structurally normal right or left ventricles, respectively, and normal systemic and pulmonary outflow tracts. Therefore, the abnormal morphology and atypical location of the outflow tracts in SV required several manual tracking corrections. Technical refinements in the current version of the software are clearly necessary to make it more robust for univentricular anatomy .

Conclusions

In this multicentre study, SV ejection fraction and volumes measured by 3D echocardiography correlated with cardiopulmonary fitness, as determined by two major prognostic CPET variables:VO 2max and VE/VCO 2 slope. Moreover, 3D echocardiography variables were associated with conventional 2D echocardiography variables, as well as with the physical dimension of health-related quality of life. Despite good reproducibility, the feasibility of 3D echocardiography in patients with SV remained limited, as the software was unable to perform the analysis in one third of the eligible population. These results suggest a potential value of 3Dechocardiography in the follow-up of patients with SV physiologies, provided that the technique and analysis software are improved.

Sources of funding

Dr. Avesani was supported by an EACVI training grant(App000088435).

Acknowledgments

We sincerely thank the families for their generous participation.

Disclosure of interest

The authors declare that they have no competing interest.


Yanshu Wang

Anne Sergent

Gilles Bernard-Michel

Patrick Le Quéré

Dns

DNS modelling of hydrogen turbulent buoyant jet in a two-opening air-filled cavity

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

14th World Congress in Computational Mechanics (WCCM) ECCOMAS Congress 2020 19 -24 July 2020, Paris, France

DNS MODELLING OF HYDROGEN TURBULENT BUOYANT JET IN A TWO-OPENING AIR-FILLED CAVITY

Y. Wang 1 , A. Sergent 2,* , G. Bernard-Michel 3 and P. Le Quéré 4

1 DEN/DANS/DM2S/STMF/LIEFT, Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Saclay, France, yanshu.wang@cea.fr 2 LIMSI, CNRS, Sorbonne Université, Paris, France, anne.sergent@limsi.fr, https://perso.limsi.fr/sergent/ 3 DEN/DANS/DM2S/STMF/LIEFT, Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Saclay, France, gilles.bernard-michel@cea.fr 4 LIMSI, CNRS, Université Paris-Saclay, Orsay, France, patrick.le-quere@limsi.fr

Key Words: DNS, semi-open flow, binary mixture, buoyant jet, turbulence, hydrogen safety

We present numerical results from direct numerical simulations (DNS) of an air-hydrogen turbulent buoyant jet in a two-vented cavity, configuration dedicated to analysis of hydrogen distribution in accidental situations for highly confined environments (garage, containment building …). In the retained configuration, the injection of the light fluid in the floor center leads to the development of a buoyant jet flowing up across a tri-layer concentration structuration, with accumulation of a homogeneous light mixture at the top of the cavity. Most of the studies of literature use helium as injected fluid instead of hydrogen, when experiments are involved for security reason.

This study aims at determining how the nature of the injected fluid modifies the flow structure, and its turbulent mixing properties which are crucial for the species distribution within the cavity. Indeed, despite a similar Schmidt number, the density of hydrogen is more than twice as light as that of helium. Two main numerical difficulties are identified: the large density ratio between the injected and the ambient fluids, the numerical modelling of the two vents where the mass flow rate and the mixture properties are not prescribed [START_REF] Saikali | Highly resolved large eddy simulations of a binary mixture flow in a cavity with two vents: Influence of the computational domain[END_REF]. The code TrioCFD in the platform TRUST, developed by CEA [START_REF]CEA TRUST-TrioCFD code[END_REF] is used to carry out parallel computations on several hundred processors. By comparing results obtained with air, helium and hydrogen as injected fluid, we investigate how the turbulent flow properties are altered by the change of the buoyant flux at the injection source, and in particular the buoyancy production term of turbulence. Macroscopic quantities are derived from DNS results and used to confront existing different 1D models describing the light gas distribution inside the cavity, such as [START_REF] Linden | The fluid mechanics of natural ventilation[END_REF]. Shortcomings are identified, and a new model accounting for large density differences in an inhomogeneous environment is proposed.


Cédric Ribeiro

Dr Michele Cariello

Aurélie Malfait

Dr Marc Bria

Prof David Fournier

Dr Joël Lyskawa

Gaëlle Le Fer

Jonathan Potier

Richard Hoogenboom
email: richard.hoogenboom@ugent.be

Graeme Cooke
email: graeme.cooke@glasgow.ac.uk

Patrice Woisel
email: patrice.woisel@centralelille.fr

Dr G Le Fer

Prof P Woisel

Prof G Cooke

Dr V R De La Rosa

Prof R Hoogenboom

Synergistic topological and supramolecular control of Diels-Alder reactivity based on a tunable self-complexing host-guest molecular switch

Keywords: chemical reactivity, Diels-Alder reaction, topological chemistry, supramolecular chemistry, host-guest chemistry

Compartmentalization and

binding-triggered conformational change regulate many metabolic processes in living matter. Here, we have synergistically combined these two biorelevant processes to tune the Diels-Alder (DA) reactivity of a synthetic self-complexing host-guest molecular switch CBPQT 4+ -Fu, consisting of an electron-rich furan unit covalently attached to the electron-deficient cyclobis(paraquat-p-phenylene) tetrachloride (CBPQT 4+ , 4Cl-) host. This design allows CBPQT 4+ -Fu to efficiently compartmentalize the furan ring inside its host cavity in water, thereby protecting it from the DA reaction with maleimide. Remarkably, the self-complexed CBPQT 4+ -Fu can undergo a conformational change through intramolecular decomplexation upon the addition of a stronger binding molecular naphthalene derivative as a competitive guest, triggering the DA reaction upon addition of a chemical regulator. Remarkably, connecting the guest to a thermoresponsive lower critical solution temperature (LCST) copolymer regulator controls the DA reaction on command upon heating and cooling the reaction media beyond and below the cloud point temperature of the copolymer, representing a rare example of decreased reactivity upon increasing temperature. Altogether, this work opens up new avenues towards combined topological and supramolecular control over reactivity in synthetic constructs, enabling control over reactivity through molecular regulators or even mild temperature variations.

Introduction

The compartmentalization of (bio)chemical functions is a central feature of living matter. [1,2] Biological systems can physically and spatially confine molecular constituents and functions in delimited compartments through thermodynamic and/or kinetic barriers while enabling molecular communication and energy exchange with their external environments to regulate vital biochemical processes. [3,4] One typical example is the compartmentalized nucleus of eukaryotic cells that acts as a biological host to store the genetic material and regulate the DNA transcription by guiding the chromosome folding in the nuclear space through spatial interactions. [START_REF] Alberts | Molecular Biology of the Cell[END_REF][START_REF] Pan | [END_REF][7] Other fascinating compartmentalized natural hosts are viral capsids composed of several self-assembled oligomeric proteins that package and protect genomic material, infect other host organisms, and quickly open up to release the genome after replication. [8,9] Over the years, inspired by such biological systems, many scientists have designed synthetic host structures that mimic the functionality achieved by compartmentalized natural systems. Hence, various synthetic capsules have been reported to efficiently sequester guests (i.e., with high affinity and selectivity) and modulate their reactivity. [10,[START_REF] Hof | Proc. Natl. Acad. Sci[END_REF] According to the design of host-guest systems, the reactivity of guests can be exacerbated with potentially an enhancement of selectivity, or conversely, capsule cavities can act as protective vessels from external environments or events, allowing the stabilization of short-lived guests or metastable intermediates. [12- 17] In this context, the Diels-Alder (DA) cycloaddition reaction, [18] which counts as one of the most popular transformations in Organic Chemistry, has often been used as a model reaction to illustrate the ability of synthetic host systems to drive the course of a chemical reaction in terms of kinetics and selectivity of adducts when carried out in water with suitable supramolecular receptors. In this vein, Fujita and co-workers have engineered self-assembled coordinated cages [19,20] and porous networks [21,22] that can trap DA substrates (dienes and dienophiles) through intermolecular interactions and mediate DA reactions of unreactive dienes and/or cycloadditions with enhanced reactivity and controlled regioselectivity. Furthermore, computational methods were undertaken for the de novo design of an enzyme that catalyzes the DA reaction with high stereoselectivity and substrate specificity. [23] Scherman and co-workers also reported the use of the Cucurbit [7]uril host (CB [7]) as a supramolecular artificial enzyme to perform intramolecular DA cycloaddition reactions of unreactive N-allyl-2-furfurylamine derivatives in an aqueous environment. [24] Upon complexation with CB [7], a rearrangement of substrates occurs within the host cavity, leading to a highly reactive conformation resulting in asymmetric cycloadditions. Recently, Nitschke and co-workers also showed that iron-based coordinated cages could encapsulate furan and serve as protecting environment, impeding its reaction with maleimide in water. [25] The entrapped furan could be released upon adding a competing guest as a regulator to switch on the DA reaction. Besides compartmentalization capability, biological systems are also intrinsically dynamic, and this peculiar characteristic significantly affects their function. For instance, proteins can feature significant ligand-induced conformational changes. [26][27][START_REF] Daniels | Proc. Natl. Acad. Sci[END_REF] These conformational changes can have topological effects that result in the release or the blocking of reactive sites of the protein and thus regulation of the biological function, including catalysis, [START_REF] Bordelon | [END_REF]30] signaling, [31] and self-assembly of biomacromolecules into complex architectures [START_REF] Devarakonda | Proc. Natl. Acad. Sci[END_REF] for therapeutic applications. [START_REF] Boehr | [END_REF]34] Here, we combined the two concepts, i.e., compartmentalization and regulator-induced conformational change, to control the Diels-Alder reactivity between a furan moiety and maleimide in water. In particular, we have designed a furan functionalized cyclobis(paraquat-p-phenylene) tetrachloride (CBPQT 4+ ,4Cl -) CBPQT 4+ -Fu derivative where the electron-rich cyclic diene unit formed a stable self-complexed conformation with the CBPQT 4+ moiety in water as shown in Figure 1. This closed intramolecularly complexed topology compartmentalizes the furan sub-unit inside the host cavity, thereby preventing its reaction towards maleimide in water. Nevertheless, upon adding naphthalene derivatives (Napht-1 and Napht-2) as regulators with a higher binding affinity towards the CBPQT 4+ host compared to the furan unit, the CBPQT 4+ -Fu will adopt a new open conformation where the furan unit is located outside the protective host cavity, enabling the DA reaction with maleimide, resulting in the initiation of the DA process. Increasing the temperature of an organic reaction generally speeds up its rate. Here, conversely, we demonstrate that the combined topological and supramolecular control enables us to switch off the DA at high temperature, while it is enabled by lowering the temperature. This has been achieved by using a thermoresponsive naphthalene end-functionalized copolymer Napht-2 displaying a cloud point (Tcp) in water as thermoresponsive regulator for the DA reactivity [35] . The thermoresponsive copolymer regulator could be easily removed from the reaction after the DA transformation, leading to the uncomplexed cycloadducts of CBPQT 4+ -Fu and maleimide. The designed molecular system and regulators are shown in Figure 1.

Results and Discussion

CBPQT 4+ -Fu was synthesized from the dipyridinum salt 1 [36] and the dibromobenzyl derivative 2 [37] through the template-directed clipping methodology, using an electron-rich naphthalene based template (Figure 2A; experimental details are provided in the Supporting Information). After the reaction, the template was removed by liquid-liquid extraction (CHCl3/H2O) and the pure CBPQT 4+ -Fu was obtained as a deep yellow solid in 30 % yield following silica column chromatography. The optical absorption of the complex in the visible light region arises from the formation of a donor-acceptor charge-transfer (CT) interaction between the electron-rich furan moiety and the electron-deficient CBPQT 4+ cavity, and was confirmed by the absorption band centered at 380 nm in the UV-Vis spectrum of CBPQT 4+ -Fu in water (Figure 2B). 1 H NMR spectroscopy (Figure 2C) provided further evidence for the furan moiety being accommodated inside the host cavity. A clear deshielding (+0.2 ppm<<+0.4 ppm) for H and HPh protons on the CBPQT 4+ macrocycle was also observed, whereas all protons belonging to the guest moiety experienced shielding (Ha= -2.8 ppm, Hb= -1.8 ppm, Hc= -4.3 ppm) compared with those for the free Fu. The large magnitude of these upfield shifts of the furan protons during the complexation indicates that they are engaged in addition to - interactions with the bipyridinium segments, and strong edge-to-face C-H- interactions with the p-phenylene linkers in the ring, which is consistent with previously reported Naphthalene:CBPQT 4+ based complexes. [38] This proximity of the protons mentioned above in the complex was confirmed in the 2D NOESY spectrum (Supporting Information, Figure S15), which revealed notably strong cross-correlations between the Ha, Hb, Hc protons of the furan moiety and the H, Hb and HPh protons of the cyclophane part, and between the Hb and the methylene protons Hd, He of the linker of CBPQT 4+ -Fu, suggesting that the furan moiety adopts a near central and deep position inside the cavity.

Concentration dependence (studied concentration ranges up to 50 mM) was not observed in the proton resonances in the NMR spectra, and furthermore, the diffusion coefficient (D) of protons belonging to CBPQT 4+ -Fu, and the heat exchange from isothermal titration calorimetry (ITC) experiments (Supporting Information, Figure S16 and S17), [39] provided evidence for an intramolecular self-included conformation for CBPQT 4+ -Fu. ITC titration experiments between CBPQT 4+ -Fu and a strong binding naphthalene guest (Napht-1) [40] were also undertaken to evaluate the equilibrium constant Kin (Figure 3), [41] defined as the concentration ratio [CBPQT 4+ -Fu-in]/ [CBPQT 4+ -Fu-out], and the apparent association constant Kapp related to CBPQT 4+ -Fu-in/ CBPQT 4+ -Fu-out:Napht-1 complexes (Supporting Information, Table S1 and Figure S18). Thermodynamic data exhibited no significant difference in association strength between Napht-1 and both CBPQT 4+ (Ka=8.6 ×10 5 M -1 ) and preformed CBPQT 4+ :Fu complex (Ka=9.5 ×10 5 M -1 ), which was in line with the relatively low binding affinity of Fu toward CBPQT 4+ (Ka =10 2 M -1 ) determined by UV-Vis titration (Supporting Information, Figure S20). Remarkably, the Napht-1 guest displayed a thousand times lower association constant with CBPQT 4+ -Fu (Kapp = 6.2 x 10 2 M - 1 ) than CBPQT 4+ . Kin could be estimated to be ~1×10 3 from these binding experiments, confirming the significant prevalence of the CBPQT 4+ -Fu-in form for CBPQT 4+ -Fu in solution. UV-vis spectroscopy next confirmed the thermal stability of CBPQT 4+ -Fuin as spectra recorded at different temperatures (Supporting Information Figure S19) showed no significant decrease in the charge transfer absorption band centred at 380 nm at least up to 85°C. Further confirmation of the prevalent self-included conformation CBPQT 4+ -Fu-in was also given through density functional theory (DFT) calculations (Figure 3, details are provided in Supporting Information). [42] Geometry-optimized structures in water revealed less twisted pyridinium rings and a smaller inter-planar distance (d) in CBPQT 4+ -Fu-in (d = 3,2 Å) than in CBPQT 4+ -Fu-out (d = 3,4 Å), suggesting the possible formation of π-π stacking interactions between the furan and the two viologens surrounding it for CBPQT 4+ -Fu-in. This was confirmed by the electrostatic potential (ESP) maps showing a clear contrast between the more positive (blue) area inside the cavity and the more negative (red) furan unit for CBPQT 4+ -Fu-out, whereas the electrostatic difference was more muted in CBPQT 4+ -Fu-in, indicating that charge-transfer takes place between the guest and the host. Also in line with the experimental results is the further stabilization of the furan in CBPQT 4+ -Fu-in through the formation of non-covalent CH- interactions between the p-xylyl rings and Ha (2.6 Å) and Hc (3.2 Å). The conformational locking of the furan unit linked to the ring through CH- interactions and the CT complex could also explain the higher stability of CBPQT 4+ -Fu-in, which was found experimentally to be the prevalent conformer. A difference in total energy (sum of the zero point and electronic contribution) of 6.69 kcal/mol was found between the two conformations. After confirming that CBPQT 4+ -Fu formed a stable self-inclusion complex, we next examined the chemical reactivity of its furan moiety with maleimide at 25°C in water. Therefore, we monitored the formation of DA cycloadducts (exo and endo isomers) in the presence of an excess of maleimide (16-fold excess, i.e., under pseudo-first-order kinetic conditions) by in situ 1 H NMR spectroscopy (Supporting Information, Figure S27). As control experiments, the kinetics of DA reactions were also recorded for Fu and the intramolecular CBPQT 4+ :Fu complex in similar conditions with an excess of maleimide (Supporting Information, Figure S23 and S25). The progress of the DA reactions of Fu, CBPQT 4+ :Fu, and CBPQT 4+ -Fu with maleimide, shown in Figure 4A, shows similar trends for both cycloadditions with a complete conversion reached after 1200 minutes and comparable pseudofirst-order reaction rate constants (k1, k2) of ~3×10 -3 min -1 (Figure 4B). This observation agrees with the relatively low association constant and the dynamic nature of the CBPQT 4+ :Fu complex as determined by UV-Vis and NMR spectroscopy, respectively (Supporting Information, Figure S21). The pseudo-first-order rate constants (k1, k2, k3) were obtained from the slopes of the pseudo-first kinetic plots.

Remarkably, the kinetic study relating to the DA reaction of CBPQT 4+ -Fu with maleimide revealed a negligible conversion of its furan moiety into corresponding cycloadducts with the studied time-frame, and an extremely low pseudo-first-order reaction rate constant (k3), that is 100 times lower compared to the model reactions, thereby univocally demonstrating that the synergistic topological and supramolecular effects suppress the DA reactivity

CBPQT 4+ -Fu-out CBPQT 4+ -Fu-in
of the furan-moiety of CBPQT 4+ -Fu. DFT investigations provided theoretical insights into the molecular reactivity of CBPQT 4+ -Fuin towards a DA reaction with a dienophile (e.g., maleimide) (Supporting information Figure S22). These calculations indicated i) that the highest occupied molecular orbital (HOMO) was localised on the furan, whereas the lowest unoccupied molecular orbital (LUMO) was delocalized over the viologen units, and ii) the proximity of furan and viologen in CBPQT 4+ -Fu-in induced the overlap of the frontier molecular orbital and the formation of the intra-molecular CT complex, thus preventing the spatial overlap between the HOMO of the furan and the LUMO of the dienophile. Hence, the lack of the reactivity of CBPQT 4+ -Fu-in would have a dual origin: the steric hindrance conferred by the tetracationic macrocycle and the electronic deactivation of the furan moiety towards undertaking DA reaction.

We have previously shown that Napht-1 can bind CBPQT 4+ -Fu through ITC experiments. To probe whether the intermolecular Napht-1:CBPQT 4+ -Fu complex formation could result in a conformational change of CBPQT 4+ -Fu (from CBPQT 4+ -Fu-in to CBPQT 4+ -Fu-out), UV-vis and 1 H NMR spectroscopic titrations were carried out. Upon addition of aliquots of Napht-1 to a CBPQT 4+ -Fu solution, UV-visible spectra (Supporting Information Figure S37) showed the disappearance of the absorption band of the self-complexed CBPQT 4+ -Fu (at =380 nm) and the simultaneous emergence of an absorption at = 520 nm due to the intramolecular Napht-1 :CBPQT 4+ -Fu complex. [43] The 1 H NMR spectra (Supporting Information Figure S38) exhibited new signals for the complexed naphthalene unit (H2/6 ~ 6.5 ppm, H3/7~ 6.3 ppm, and H4/8 ~ 2.9 ppm) and uncomplexed furan moiety (Ha ~ 7.4 ppm, Hb ~ 6.2 ppm and Hc ~ 6.1 ppm), respectively, accompanied by the disappearance of resonance of Hb and Hc protons in its complexed form. Thus, these results confirmed the ousting of the furan from the cyclophane ring upon the addition of Napht-1. Hence, Napht-1 acts as a topological regulator by inducing the release of the furan moiety.

We then investigated whether this conformational change of CBPQT 4+ -Fu, when exposed to Napht-1, could initiate the DA reaction between the non-complexed Fu and the maleimide. Indeed, the DA kinetics confirmed that the addition of Napht-1 as a regulator released the reactivity of the furan moiety, which showed similar conversion (Figure 5A) and kinetic rate (Figure 5B) for the DA reaction with maleimide as the model system (i.e., DA between Fu and maleimide). Previously, we reported the switch on/off regulation of the recognition properties of CBPQT 4+ in aqueous media through the coil-to-globule transition (LCST) of thermosensitive (co)polymers featuring complementary naphthalene guest modules. [35,44] In such systems, a full disassembly of the complexes was observed upon heating the solutions above their Tcp, leading to the precipitation of Naphthalene functionalized co(polymers) and the liberation of free host CBPQT 4+ into the solution. Here, we hypothesized that this thermally controlled phase of Napht-2, showing a Tcp of 27°C (for details regarding its synthesis and characterizations, see Supporting Information), could be used to turn on and off the DA reaction between CBPQT 4+ -Fu and maleimide at low (T<Tcp) and high (T>Tcp) temperature, respectively. As a control experiment, we first investigated the influence of temperature on the progress of the DA reaction between the Napht-1/CBPQT 4+ -Fuout complex and maleimide. As reported for other DA reactions [45] , the conversion was in line with the Arrhenius equation and proceeded more quickly when the temperature raised from 25 to 45°C (see Supporting Information Figure S39 andS40).

Figure 6 shows the progress of the Diels-Alder reaction in the presence of Napht-2 at different temperatures. At 25°C (below Tcp), the sample was purple due to complex formation between Napht-2 and CBPQT 4+ -Fu, and the DA reaction proceeded as the furan moiety was outside the CBPQT 4+ cavity. At a temperature above Tcp, the sample lost its purple color (indicating the decomplexation of the Napht-2:CBPQT 4+ -Fu complex) and became turbid (due to the collapse of the Napht-2). A UV-vis spectrum recorded on Napht-2/ CBPQT 4+ -Fuout at 45°C confirmed its dissociation above the Tcp, and the concomitant reformation of the self-included BB-Fin conformation by the disappearance of the characteristic absorption band at 520 nm and the re-emergence of an absorption at 380 nm, respectively (see Supporting Information Figure S42). Importantly, in contrast to the DA reaction between carried out lower temperatures, the DA reaction stopped at elevated temperature, and no conversion of the furan sub-unit was observed, confirming the LCST-induced control over the DA reaction between CBPQT 4+ -Fu and maleimide. Furthermore, no retro-DA reactions were observed at 45°C, indicating the thermal stability of cycloadducts in conditions used for kinetic investigations (see Supporting Information Figure S44). Finally, upon re-cooling the sample below the Tcp, the DA reaction restarted due to the re-solubilization of the copolymer and its subsequent complexation with CBPQT 4+ -Fu to finally reach 100% conversion. Furthermore, once fully converted, cycloadducts can be isolated from Napht-2 by a simple workup, including a filtration step at T>Tcp (see details in Supporting Information).

Conclusion

In summary, we have successfully demonstrated the synergistic control over furan DA reactivity through supramolecular association and topological effects by coupling the furan to CBPQT 4+ . Within this system, the cyclic diene subunit was efficiently compartmentalized inside the host moiety, masking its reactivity towards a DA reaction with maleimide. Adding more strongly binding naphthalene guest molecules as topological supramolecular regulators resulted in the release of the furan guest subunit from the protective host vessel, thereby triggering the DA reaction between furan and maleimide. This molecularly controlled regulation of furan reactivity was subsequently transformed into a temperature-induced control of the DA reactivity through the coil-to-globule transition (LCST) of a thermosensitive naphthalene end-functionalized (co)polymer. As such, the reactivity of the furan moiety could be switched on at lower temperatures (below the Tcp) while it was switched off at elevated temperatures (above Tcp), representing a rare example of lower reactivity at raised temperature. This work provides thus essential insight into synergistically controlling chemical reactivity through supramolecular topological chemistry, combined with different regulators (molecular and thermal), providing an important step towards synthetic molecular reaction networks.

Experimental Section

Materials

Unless otherwise stated, commercially available materials were used without purification. N-Isopropylacrylamide (NIPAm, ≥ 98 %, Aldrich) was recrystallized from n-hexane and 2,2′-azobis(isobutyronitrile) (AIBN, ≥ 98 %, Aldrich) was recrystallized from methanol. N,N-Dimethylacrylamide (99 %, Aldrich) was passed through basic aluminum oxide column to remove the inhibitor before use. All organic solvents were analytical grade and water was purified with a Millipore system combining inverse osmosis membrane (Milli RO) and ion exchange resins (Milli Q) for purification.

NMR spectroscopy

1 H, 13 C, COSY 1 H-1 H and HSQC 1 H- 13 C NMR spectra were recorded on a Bruker 300 MHz AVANCE III HD spectrometer using a standard 5mm BBFO Probe at 25 °C. Deuterated acetonitrile (CD3CN) and deuterated water (D2O) were used as solvents and all chemical shifts (δ) were expressed in ppm relative to the residual solvent protons. Coupling constants (J) are reported in Hz and relative intensities are reported. Twodimensional diffusion-ordered 1 H NMR spectroscopy (DOSY) experiments were performed at 25 °C on a Bruker AVANCE NEO spectrometer operating at 400 MHz (9.4 T) using a 5 mm TBI Probe and equipped with a Bruker multinuclear z-gradient inverse probe head capable of producing gradients in the z direction with strength of 5.35 G.mm -1 . The DOSY spectra were acquired with the ledbpgp2s pulse program from Bruker Topspin software. All spectra were recorded with 16,384 time-domain data points in t2 dimension and 16 t1 increments. The gradient strength was logarithmically incremented in 16 steps from 2 % up to 95 % of the maximum gradient strength. All analyses were performed with a compromise diffusion delay Δ of 0.06 s in order to keep the relaxation contribution to the signal attenuation constant for all samples. The gradient pulse length δ was 2100 µs in order to ensure full signal attenuation. The D1 value was 10 s. The diffusion dimension of the 2D DOSY spectra was operating by DOSY treatment software Bruker Topspin 4.1.4 and Dynamics center version 2.8.0.1. 2D NMR nuclear Overhauser enhancement spectroscopy (NOESY) were performed at 25 °C and acquired at 400 MHz, using a 650 ms mixing time and a 10 μs 1 H 90° pulse width. The experiments were done with 256 numbers of experiments (TD F1), 4 numbers of scan (NS) and 10.773 W power level for pulse (PlW1).

For the kinetic investigation of the Diels-Alder reactions, 1 H NMR spectra were recorded on a Bruker AVANCE NEO spectrometer at 400 MHz and at 25 °C with the following experimental conditions: 128 scans, 2 s relaxation delay and 6.5 µs pre-scan delay. Concerning the kinetic monitoring of the Diels-Alder reaction in presence of Napht-2 copolymer, 1 H NMR spectra were recorded on a Bruker AVANCE NEO spectrometer at 400 MHz at 45 °C (precipitated state) and at 25 °C (soluble state) with the following experimental conditions: 128 scans, 2 s relaxation delay and 6.5 µs pre-scan delay.

Fourier transform infrared (FTIR) spectroscopy

FTIR spectra were registered on a Perkin Elmer Spectrum Two equipped with an attenuated total reflection (ATR) accessory. The spectra were recorded in a range of 450-4000 cm -1 , a resolution of 4 cm -1 and 16 scans were performed for each specimen.

UV-vis spectroscopy

An Agilent Cary 3500 Scan UV-Visible spectrophotometer equipped with a multicell Peltier temperature controller was used. For the variabletemperature investigations, a solution of CBPQT 4+ -Fu was prepared at 1.5 mM and placed in a 10 mm path length quartz cell. For all titration experiments, UV-Visible spectra were recorded at 20 °C. A 12 mM solution of Napht-2 copolymer was prepared and placed in a 10 mm path length quartz cell. Turbidimetry curves were built by collecting the absorbance at 700 nm with a scanning rate of 1 °C.min -1 . The cloud point temperatures were determined during the heating ramp at 50 % transmittance.

Elemental analysis method description

The compounds (CHNS) were determined using the thermo scientific FlashSmart automated analyzer. For CHNS determination, the samples were weighted in tin containers and introduced into the combustion reactor. The reactor is filled with copper oxide followed by wire reduced nickel and maintained at 950°C and operates with dynamic flash combustion of the sample. The N, C, H and S were detected as N2, CO2, H2O and SO2 respectively. The resulted gases were separated on a packed column heated at 65°C in an oven and detected by a TCD (thermal conductivity detector). For each sample, 3 replicates were done

Isothermal Titration Calorimetry (ITC)

The affinity constant of CBPQT 4+ -Fu:Napht-1 complex was measured at 20 °C using a nano-ITC titration calorimeter from TA Instruments following standard procedures. Compounds were dissolved in Milli-Q water and the solutions were degassed gently under vacuum before use. The sample cell (⁓1 mL) was initially filled with Napht-1 or Milli-Q water for dilution measurements, while CBPQT 4+ -Fu solution was introduced into a 250 µL injection syringe. Each titration comprised an initial 2 µL pre-injection followed by 24 × 10 µL of CBPQT 4+ -Fu solution into the sample cell under continuous stirring (400 rpm). A similar procedure was used at 20 °C for the titration of CBPQT 4+ and CBPQT 4+ :Fu with Napht-1. Control experiments with identical injections of CBPQT 4+ -Fu, CBPQT 4+ and CBPQT 4+ :Fu into Milli-Q water were used to correct the titration baseline. The enthalpy of complexation (ΔH) was obtained after subtraction of the dilution curve from the titration one. The association constant (Ka), as well as other thermodynamic parameters including free energy (ΔG) and entropy (ΔS), were obtained after data fitting using the independent fitting model.

Size exclusion chromatography (SEC)

Size exclusion chromatography (SEC) analysis was carried out at 35 °C in DMF as mobile phase at a flow rate of 0.7 mL.min -1 using toluene as a flow marker. Napht-2 copolymer solution was prepared at a concentration of 5 mg.mL -1 and filtered through a 0.45 µm PTFE membrane. SEC measurements were performed on a Agilent system equipped with three columns (PLgel 100A, PLgel 500A, PLgel 10E4A) placed in series and coupled with a differential refractive index (RI) detector from Wyatt (Optilab). The relative number-average molar mass (𝑀 𝑛 ̅̅̅̅ ), relative weight-average molar mass (𝑀 𝑤 ̅̅̅̅ ) and the dispersity (Ɖ = (𝑀 𝑤 ̅̅̅̅ /𝑀 𝑛 ̅̅̅̅ )) were calculated from a calibration curve based on narrow poly(methyl methacrylate) (PMMA) standards.

Computations

DFT calculations were run to better understand the chemical reactivity of CBPQT 4+ -Fu towards the Diels-Alder reaction. Two configurations of the tetracationic molecule, with the furan inside (CBPQT 4+ -Fuin) or outside (CBPQT 4+ -Fuout), were geometrically optimized, using the RM062X functional with a 6311**G (d,p) basis set. A first optimization was run in vacuum, followed by a second one in water (IEFPCM). The absence of negative frequencies was verified through frequency calculations at the same level of accuracy. No imaginary frequencies were detected. Total energy were obtained as the sum zero point and electronic energies. The coordinates of the geometrically optimized molecules in water are reported in Table S2 (Supporting Information).

Synthesis

2-Hydroxymethyl furan (Fu) (98 %, Aldrich) was purified by distillation before use. Compounds Napht-1, [46] , CBPQT 4+ [47] ,1 [49] and the naphthalene based template [50] were synthesized following literature procedures.

Compound 2. A solution of 3-(2-furyl)propionic acid (1.77 g, 12.65 mmol), 1,3-dicyclohexylcarbodiimide (2.6 g, 12.65 mmol), 4dimethylaminopyridine (0.154 g, 1.265 mmol) and compound 1 (2.86 g, 9.73 mmol) in dry CH2Cl2 (200 mL) was stirred under N2 for 48 h at room temperature. The resulting suspension was filtered and the filtrate was dried under vacuum. The residue was purified using column chromatography (SiO2: CH2Cl2/petroleum ether, 4:6). All fractions containing the product were combined together and concentrated under vacuum to obtain compound 2 as a white solid (3.24 g, 7.78 mmol, 80% yield). 1 H NMR: (300 MHz, CD3CN, 298 K): δ= 7.48-7.37 (m, 3H, Hi), 7.35 (dd, J= 0.8 and 1.9 Hz, 1H, Ha), 6.30 (dd, J= 1.9 and 3 Hz, 1H, Hb), 6.05 (dd, J= 0.9 and 3 Hz, 1H, Hc), 5.23 (s, 2H, Hf), 4.62 (s, 2H, Hh), 4.56 (s, 2H, Hg), 2.95 (t, J= 7.45 Hz, 2H, Hd), 2.72 ppm (t, J= 7.45 Hz, 2H, He). 13 CBPQT 4+ -Fu A solution of compound 2 (1.33 g, 3.21 mmol), compound 3 (2.26 g, 3.21 mmol) and naphthalene template (3.5 g, 9.62 mmol) in dry DMF (100 mL) was stirred under N2 at room temperature for 10 days. The solvent was removed under vacuum and the residue was subjected to liquid-liquid extraction (CHCl3/H2O) to remove the naphthalene template. The aqueous layer was concentrated and the residue was purified using column chromatography (SiO2: NH4Cl(2M)/MeOH/MeNO2, 4:4:2). All fractions containing the product were combined together and concentrated under vacuum. The residue was dissolved in a small amount of hot water and a saturated aqueous NH4PF6 solution was added to obtain CBPQT 4+ -Fu, 4 PF6 -. The precipitate was collected by filtration, washed with water (×5), with CH2Cl2 (×3) and with Et2O (×3) and dried under vacuum at 70 °C. To change the nature of the counterion of CBPQT 4+ -Fu from PF6 -to Cl -, CBPQT 4+ -Fu, 4 PF6 -was dissolved in a small amount of hot nitromethane and a saturated solution of tetraethylammonium chloride in nitromethane was added to obtain CBPQT 4+ -Fu, 4 Cl -. The precipitate was collected by filtration, washed with nitromethane (×5), with CH2Cl2 (×3) and with Et2O (×3) and dried under vacuum at 70 °C to obtain the desired product as a yellow powder (0.784 g, 9.63×10 -1 mmol, 30% yield). 1 H NMR: (D2O, 300 MHz, 298 K): δ= 9.28 (m, 4H, H1, '1), 9.15 (m, 4H, H2, '2), 8.35 (d, J= Napht-2 A solution of a naphthalene functionalized RAFT agent (NaphtOH-CTA) [48] (112 mg, 1.96×10 -1 mmol), AIBN (8 mg, 4.91×10 -2 mmol), NIPAm monomer (2 g, 17.67 mmol) and DMAc monomer (195 mg, 1.96 mmol) in DMF (4 mL) was deoxygenated by bubbling nitrogen for 15 min at room temperature. The reaction flask was placed in an oil bath at 80 °C. The polymerization was allowed to proceed for 1 h under magnetic stirring. Then, the solution was cooled down with an ice bath and the copolymer was isolated by precipitation in n-hexane. The copolymer was isolated as a white powder (1.9 g, 1.61×10 -1 mmol, 87wt% yield) after two successive precipitations from acetone into Et2O and dried under vacuum.

Entry for the Table of Contents

Figure 1 .

 1 Figure 1. Principle of the control over Diels-Alder reactivity based on a tunable self-complexing host-guest molecular switch CBPQT 4+ -Fu. Molecular structures of CBPQT 4+ -Fu (Cl -counterions not included), Napht-1 and Napht-2 guestsMain Text Paragraph.

Figure 2 .

 2 Figure 2. A) Synthetic route for CBPQT 4+ -Fu starting from 1 and 2; B) UVvisible spectra of CBPQT 4+ and CBPQT 4+ -Fu, recorded in water at 25°C; C) 1 H NMR spectra of Fu (top), CBPQT 4+ -Fu (middle) and CBPQT 4+ (down) recorded in D2O at 25°C.

Figure 3 .

 3 Figure 3. Thermodynamic equilibrium between CBPQT 4+ -Fu-out and CBPQT 4+ -Fu-in; DFT geometry optimization and ESP distribution of CBPQT 4+ -Fu-out and CBPQT 4+ -Fu-in.

Figure 4 .

 4 Figure 4. A) Diels-alder reaction kinetics at 25°C in water between maleimide (16 equiv.) and Fu (), CBPQT 4+ :Fu () or CBPQT 4+ -Fu (), B) Plots of the ln(1/(1-)) vs time in the DA reaction of maleimide with Fu (), CBPQT 4+ :Fu (), or CBPQT 4+ -Fu ().  is the conversion for the formation of cycloadducts.

Figure 5 .

 5 Figure 5. A) Diels-alder reaction kinetics at 25°C in water between maleimide (16 equiv.) and CBPQT 4+ :Fu ()or CBPQT 4+ -Fu (), B) Plots of the ln (1/(1-)) vs time in the DA reaction of maleimide with CBPQT 4+ :Fu () or CBPQT 4+ -Fu ().is the conversion for the formation of cycloadducts. The pseudo-firstorder rate constants (k3, k4) were obtained from the slopes of the pseudo-first kinetic plots.

Figure 6 .

 6 Figure 6. Diels-Alder reaction kinetics at 25°C in water between maleimide (16 equiv.) and CBPQT 4+ -Fu () in the presence of the thermoresponsive Napht-2 (3 equivalent) as a guest, under different heating regimes (T=25°C for 800 minutes followed by T=45°C for 300 minutes and finally T=25°C for 1000 minutes). Photographs show changes in color and phase transitions of the

6. 5

 5 Hz, 2H, Hb1), 8.25 (m, 4H, Hb'1, b2), 8.14 (d, J= 6.5 Hz, 2H, Hb'2), 8.0 (m, 2H, HPh2, Ph3), 7.9 (m, 1H, HPh4), 7.8 (m, 4H, HPh1), 6.07 (s, 2H, Hg1), 5.97 (s, 2H, Hg3), 5.93 (s, 2H, Hg4), 5.86 (s, 2H, Hg2), 5.45 (s, 2H, Hf), 4.77 (d, J= 1.2 Hz, 1H, Ha), 4.64 (dd, J = 3.2 Hz and 1.2 Hz, 1H, Hb), 2.14 (d, J= 3.2 Hz, 1H, Hc), 2.08 (t, J = 7.3 Hz, 2H, Hd), 1.89 ppm (m, 2H, He), 13 C NMR: (D2O, 75 MHz, 298 K): δ= 173.81 (C10), 152.75 (C11), 148.56 (C9), 147.77 (C5), 144.72 (C4), 147.34 (C8), 145.75 , 144.96 , 144.93 , 144.73 , 141.18 (Ca), 136.93 (C1), 136.81 (C2), 136.44 (C3), 135.95 (C7), 135.54 (C8), 135.03 (CPh2), 133.61(CPh3), 130.50 (CPh4), 130.26 (CPh1), 126.99 (Cb'1), 126.72 (Cb1), 126.43 (Cb2), 126.17 (Cb'2), 109.25 (Cb), 103.56 (Cc), 65.0 (Cg2), 64.80 (Cg3), 64.77 (Cg4), 63.49 (Cf), 61.88 (Cg1), 32.58 (Ce), 22.06 ppm (Cd). FTIR (ATR, cm -1 ): 3362, 3120, 3042, 1731, 1634, 1561, 1508, 1447, 1359, 1281, 1229, 1160, 861, 786. HRMS: m/z calcd for C44H40Cl4N4O3 + Na + : 837.1723 [M + Na] + ; found: 837.1724

  Combining two biorelevant concepts, i.e., compartmentalization and regulator-induced conformational change allows controlling the Diels-Alder reactivity between a furan moiety and maleimide in water. Using a thermosensitive regulator enables the Diels-Alder reaction to be turned off at elevated temperature, whereas it is activated by lowering the temperature, representing a rare example of reduced reactivity at elevated temperature.

Acknowledgements

host-guest complexes by ITC. PW thanks Joëlle Thuriot for the elemental analysis. This research was supported by the ANR agency (MISMATCH project, ANR-12-BS08-0005). The Chevreul Institute is thanked for its help in the development of this work through the ARCHI-CM project supported by the "Ministère de l'Enseignement Supérieur de la Recherche et de l'Innovation", the region "Hauts-de-France", the ERDF program of the European Union and the "Métropole Européenne de Lille". GC thanks the EPSRC (EP/E036244/1).

Supporting Information

Full experimental details on compounds characterization, kinetic experiments, determination of the equilibrium constant Kin, and computational investigations are provided the Supporting Information.The authors have cited additional references within

The authors have cited an additional reference within the Supporting Information. [51]


A Agrawal

D Lucor

Y Fraigneau

B Podvin

A Sergent

PDE-CONSTRAINED NEURAL NETWORK FOR TURBULENT RAYLEIGH-B ÉNARD CONVECTION

. In particular, a reasonable approach is to incorporate (some of) the governing equations of the physical model (e.g. mass/momentum/energy conservation) at the core of the DNN, i.e. in the loss/likelihood functions. We propose to investigate how this additional information effectively regularizes the minimization procedure in the training of DNN, and enables them to generalize well with fewer training samples. More specifically, we will report on the influence of the choice of the domain of interest for data acquisition as well as subsequent training and predictions, in relation to the problem geometry and initial/boundary conditions. Finally, we will report on the DNNs training attempt on large direct numerical simulations database acquired for turbulent convective flow in rectangular cavity with rough bottom plate.


Atul Agrawal

Anne Sergent
email: anne.sergent@limsi.fr

Yann Fraigneau

Didier Lucor
email: didier.lucor@limsi.fr

Investigation of PDE-constrained deep neural networks for efficient flow field assimilation

Keywords: physics-informed machine learning, deep neural network, data assimilation

The development of data-driven surrogate models for the prediction of complex fluid phenomena, in place of more standard numerical simulations, is an ongoing challenge in various fields and may help when manyquery and/or real-time simulations (e.g. uncertainty quantification, data assimilation, control...) are required. Here, we decide to investigate the potential of integrating deep neural networks (DNN), which are known to be performant in capturing transient and intermittent phenomenon with the possibility of handling translations, rotations and other invariances, in more classical numerical methods for computational fluid mechanics [START_REF] Kutz | Deep learning in fluid dynamics[END_REF]. Inspired by recent works [START_REF] Raissi | Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[END_REF][START_REF] Zhu | Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data[END_REF], the strategy retained in this study is the one of training a DNN by leveraging some underlying physical laws of the system. The idea is to incorporate prior scientific knowledge to be used as a guideline for designing efficient deep learning models. In particular, a natural approach is to incorporate (some of) the governing partial differential equations (PDEs) of the physical model (e.g. mass/momentum/energy conservation) at the core of the DNN, i.e. in the loss/likelihood functions. We propose to investigate how this additional information effectively regularizes the minimization procedure in the training of DNN for fluid flows, and enables them to generalize well with fewer training samples. More specifically, we will report on the influence of the choice and the dimensionality of the domain of interest for data acquisition as well as subsequent training and predictions, in relation to the problem geometry, initial/boundary conditions and flow regimes. Finally, we will report on the DNNs training attempt on large direct numerical simulations database acquired for turbulent convective flow in rectangular cavity with rough bottom plate. [u,v,p] (t,x,y) , are correctly learned and predicted through the implicit encoding of the underlying PDEs.

Figs. ( 1 - 2 )

 12 Figs.[START_REF] Kutz | Deep learning in fluid dynamics[END_REF][START_REF] Raissi | Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[END_REF] present some preliminary results for an incompressible, laminar, time-dependent 2D flow past a stationary cylinder with an imposed fixed wall temperature (Reynolds and Peclet numbers: Re=100 and Pec=71). Only the simulated temperature field within the domain depicted by the [2, 10] × [-3, 3] yellow rectangle, cf. Fig.[START_REF] Kutz | Deep learning in fluid dynamics[END_REF], is collected for several shedding cycles and used for the DNN training. In addition, numerical constraints corresponding to the advection-diffusion temperature transport equation, conservation of mass and momentum equations of the fluid are imposed to the DNN-predicted quantities during the training. Results presented at a particular instant of the time-window, cf. Fig.[START_REF] Raissi | Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[END_REF], show that hidden quantities, here, [u, v, p] (t,x,y) , are correctly learned and predicted through the implicit encoding of the underlying PDEs.

Figure 1 :

 1 Figure 1: System considered: DNS-simulated two-dimensional flow past a heated cylinder. The simulated temperature field within the domain depicted by a [2, 10] × [-3, 3] yellow rectangle is collected for several shedding cycles and used for the DNN training.

Figure 2 :

 2 Figure 2: System predicted: reference DNS-simulated (left column) and DNN-predicted (middle column) snapshots of temperature (1st row), streamwise (2nd row) and crossflow (3rd row) velocities and pressure (last row) fields at a particular time instant t 0 . The right column represents the relative error (in percentage) normalized with the maximum value of the simulated field at that time. Only the simulated temperature field data is used to train the DNN, which is capable of reconstructing the hidden fields with satisfactory accuracy.


Gauthier Delvallez

Sokleaph Cheng

Stéphane Marot

Arnold Gervillien

Théophile Malonga

Steve Cocherie

Vincent Wignall

Sophat Calvez

Kem Phal

Anne-Geneviève Vichet

Marcelin

Gervillien Arnold Malonga

Théophile Cocherie

Steve Wignall

Vincent Calvez

Sophat Phal

Kem Vichet

Anne-Geneviève Marcelin

AUTHOR. Dr Aude Jary
email: aude.jary@aphp.fr

Affiliations

Comparative Performance of Anyplex II HPV28 and Cobas 4800 Human Papillomavirus (HPV) Assays for High-Risk HPV Detection in Self-collected Anal Samples

Keywords: Anal lesions, self-sampling, HPV-testing, Anyplex II HPV28, Cobas 4800, HPV16, MSM, TWG, Cambodia

BACKGROUND

Around 30 000 new cases of anal squamous cell carcinoma (ASCC) are diagnosed each year worldwide [START_REF] Martel C De | Global burden of cancer attributable to infections in 2018: a worldwide incidence analysis[END_REF]. Key-population, such as men having sex with men (MSM) and people living with HIV (PLWHIV), have an increased risk of developing ASCC. For instance, HIV-infected MSM has the highest incidence rate of ASCC with 85 new cases per 100 000 person-year [START_REF] Clifford | A meta-analysis of anal cancer incidence by risk group: Toward a unified anal cancer risk scale[END_REF]. Human Papillomavirus (HPV) is involved in roughly 90% of ASCC, of whom 90% are HPV16 positive. ASCC is preceded by precancerous lesions, i.e. anal intraepithelial neoplasia 1, 2 and 3 (AIN1, AIN2 and AIN3), AIN1 being identify as low grade anal lesions (LGAIN), AIN2 and AIN3 as high grade anal lesions (HGAIN). However for now, high-risk HPV testing (hrHPV) is not recommended for the screening of anal precancerous and cancer lesions, while it has been clinically validated with multiple hrHPV tests in cervical cancer screening [START_REF] Meijer | Guidelines for human papillomavirus DNA test requirements for primary cervical cancer screening in women 30 years and older[END_REF][START_REF] Ejegod | Clinical validation of the Cobas 4800 HPV assay using cervical samples in SurePath medium under the VALGENT4 framework[END_REF]. Although anal HPV16 genotyping is not yet a widely accepted molecular marker in anal cancer screening, it is by far the most carcinogenetic type in the anus [START_REF] Wei | Epidemiology of anal human papillomavirus infection and high-grade squamous intraepithelial lesions in 29 900 men according to HIV status, sexuality, and age: a collaborative pooled analysis of 64 studies[END_REF]. Indeed, (i) HPV16 prevalence increases across the anal lesion from normal to precancerous and anal cancer [START_REF] Lin | Human papillomavirus types from infection to cancer in the anus, according to sex and HIV status: a systematic review and meta-analysis[END_REF] and (ii) in a recent prospective study, HGAIN HPV16positive are less likely to clear compared to those with other hrHPV genotypes [START_REF] Poynten | The Natural History of Anal High-grade Squamous Intraepithelial Lesions in Gay and Bisexual Men[END_REF].

In this study, we aim to compare the agreement and performance of the Cobas 4800 HPV-test (Roche®) and the Anyplex TM II HPV28 Detection (Seegene Inc) to detect hrHPV in self-sampling anal swabs from asymptomatic MSM and transgender women (TGW) in Phnom Penh, Cambodia; especially for HPV16 detection which was the most prevalent HPV genotype found in this population [START_REF] Jary | Prevalence and risk factors of anal human papillomavirus infections among men having sex with men and transgender women in Phnom Penh, Cambodia[END_REF].

MATERIALS AND METHODS

Study population

A cross-sectional retrospective study was conducted between October 1 st , 2021 and November 30 th , 2021 in different clinics in Phnom Penh, Cambodia and under the scope of activities of Men's Health Cambodia, a non-governmental and non-profit organization working on men, including men having sex with men (MSM) and transgender women (TGW) issues in Cambodia. During consultation, a questionnaire was used to collect patient data and the anal collection (FLOQSwabs, Copan) was self-performed using anal swabs discharged in Viral Transport Media (VTM). They were then stored at -80°C at the Institut Pasteur du Cambodge (IPC) until further analysis. A comprehensive explanation of eligibility criteria and procedures has been published before [START_REF] Jary | Prevalence and risk factors of anal human papillomavirus infections among men having sex with men and transgender women in Phnom Penh, Cambodia[END_REF]. DNA-extraction (from 200 l of sample to 100 l) was performed with the E-mag device (Biomérieux) and both samples and extracted DNA were stored at -80°C. Then HPV-testing was performed with the Anyplex TM II HPV28 Detection (Seegene Inc) which detects and differentiates 28 distinct HPV-types including the 14 hrHPV detected by the Cobas 4800 HPV-test and 14 others HPV (not analyzed in this paper). Both HPV-testing also detect a human gene as internal control (IC) to assess the quality of the sampling and the efficiency of the PCR amplification. If IC was not amplified, samples were referred as invalid.

HPV-testing and methods' comparison

Statistical analysis was performed with the package rstatix from R software. McNemar and kappa indices were calculated to compare the proportion of positive samples and the degree of agreement between the two methods to detect the 14 hrHPV, respectively. A p-value of < 0.05 in two-tailed were considered significant.

RESULTS

Overall, 162 participants were included with a median age of 28.1 [24. 4 -31.8] years, of whom 56% were MSM and 8% were HIV-infected. None of them received any HPVvaccine.

One hundred and sixty-two anal samples were tested with both the Roche and Seegene methods and HPV-testing failed for 59 (36%) and 41 (25%) samples, respectively. The prevalence of HPV16, HPV18 and others hrHPV types were not significantly different between the two methods: 20% versus 25% (p=0.52), 16% versus 17% (p=0.86) and 50% versus 59% (p=0.18), respectively (Table 1).

Further statistical analyses for method comparison were performed on 97 samples, 65 samples being referred as invalid in one or the two methods. The concordance of the results for HPV16, HPV18 and others hrHPV types detection were 97%, 100% and 88%, respectively (Table2). Fifteen samples were discordant: (i) 3 for HPV16 positivity, of whom 2 HPV16 missed by Roche and 1 missed by Seegene, (ii) 12 for others hrHPV positivity, of whom 8 hrHPV-types missed by Roche and 4 by Seegene (Supplementary Table 1). HPV52 was the most common hrHPV type missed by Roche (6/10 cases), followed by HPV16 and HPV56

(2/10 cases each one). For most of the hrHPV missed by Roche, they were detected tardily by Seegene, after 40 cycles of amplification.

The agreement (Cohen's Kappa test) for HPV16, HPV18 and others hrHPV detection were 0.91 [0.81-1.00], 1.00 [1.00-1.00] and 0.75 [0.62-0.88], respectively. The performance to detect HPV16, HPV18 and others hrHPV positivity were not significantly different between the 2 tests (McNemar test, p>0.05) (Table 2 and Supplementary Table 2). In total, the global performance to detect any of the 14 hrHPV types was not significantly different (McNemar test,p=0.44).

DISCUSSION

To our knowledge, this is the first study conducted in self-collected anal samples which compared the Cobas 4800 HPV-test (Roche®) and the Anyplex TM II HPV28 Detection (Seegene Inc) tests for hrHPV detection.

First, comparing the 2 methods on 97 samples revealed a good agreement between them and comparable worldwide ability to identify any of the 14 hrHPV genotypes currently recommended for the cervical cancer screening. This result was also consistent for HPV16 alone, HPV18 alone and the others hrHPV genotypes detected with the 2 methods. However, compared to the Seegene approach, the Cobas test missed more anal hrHPV infection. In term of hrHPV prevalence in normal cervical tissue, a difference was also identified between the Cobas method and GP5+/6+ PCR testing followed by genotyping with Luminex [START_REF] Ejegod | Clinical validation of the Cobas 4800 HPV assay using cervical samples in SurePath medium under the VALGENT4 framework[END_REF].

However, equal frequency was showed in samples with abnormal cytology. In our work, we dealt with anal samples and we did not assess the association with cytology results, thus these two factors may have an impact on the difference between the 2 procedures.

The prevalence of HPV16 was the highest in our high-risk population as expected and the 2 methods showed high agreement and performance to detect the most oncogenic genotype in anal site. This is of importance as HPV16 testing could be one of the biomarkers used as anal cancer screening in key-population in the near future. For instance in France, new guidelines propose to use HPV16 testing in anal cytology specimen collected by physician as anal cancer screening marker in MSM living with HIV [START_REF]Recommandations pour la Pratique Clinique -LESIONS PRECANCEREUSES ANALES LIEES AUX PAPILLOMAVIRUS HUMAINS : DEPISTAGE ET PRISE EN CHARGE[END_REF]. If positive, a reflex cytology is performed on the same sample and patient is referred to a proctologist.

Similarly to self-collected vaginal swabs for cervical cancer screening [START_REF] Arbyn | Detecting cervical precancer and reaching underscreened women by using HPV testing on self samples: updated meta-analyses[END_REF], self-collected anal samples could be of interest to reach patients outside the healthcare system [START_REF] Heid-Picard | Ambulatory anal self-sampling in MSM living with HIV, an acceptable and reliable screening method[END_REF]. In our work, 41 (25%) and 59 (36%) samples failed to be amplified by the Anyplex TM II HPV28 Detection and Cobas 4800 HPV-test, respectively. Low-cellularity due to inappropriate sampling and misunderstanding of the participants may explain this high rate of invalid results. If implemented in this population, self-collection instructions should be improved.

In conclusion, both the Anyplex TM II HPV28 Detection and the Cobas 4800 HPV-test are suitable to detect the 14 hrHPV genotypes in self-collected anal samples, as well as more specifically the HPV16 genotype.

Authors contributions. Conception and design of the study: AJ, SC and GD; acquisition of the clinical data: SW, SP and KV; execution of the experiments: GAM; analysis of the data: AJ, SM and GD; drafting of significant portion of the manuscript or figures: AJ, VC, AGM and GD. All the authors red, corrected and approved the final version of the manuscript.

Transparency declarations. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

First

  analysis was performed at IPC on 400 l of sample with the Cobas 4800 HPV-test (Roche®) which allows the detection of 14 hrHPV types by PCR and nucleic acid hybridization. This test specifically identifies HPV16, HPV18 and 12 others hrHPV in the same channel including HPV31-33-35-39-45-51-52-56-58-59-66-68. Then, 1ml of frozen VTM was sent to the Virology Department of the Pitié-Salpêtrière hospital, Paris, France.

Funding. This study was funded by the Institut Pasteur du Cambodge and the ANRS MIE (Agence Nationale de recherche sur le SIDA et les hépatites virales -Maladies infectieuses émergentes).

Ethics. Permission for the study was obtained from the National Ethics Committee for Health Research (NECHR) in Cambodia (Approval letter number 189NECHR).