Dr Pierre Sicard
email: pierre.sicard@inserm.fr

Timothée Jouitteau

Thales Andrade-Martins

Abdallah Massad

Glaucy Rodrigues De Araujo

Hélène David

Lucile Miquerol

Pascal Colson

Sylvain Richard

Right coronary artery ligation in mice: A novel method to investigate right ventricular dysfunction and biventricular interaction

Keywords: Right ventricular infarction model, diastolic dysfunction, cardiomyocytes Classifications: Pathophysiology; Heart failure

Right ventricular (RV) dysfunction can lead to complications following acute inferior myocardial infarction (MI). However, it is unclear how RV failure after MI contributes to leftsided dysfunction is unclear. The aim of this study was to investigate the consequences of right coronary artery (RCA) ligation in mice. RCA ligation was performed in C57BL/6JRj mice (n=38). The cardiac phenotypes were characterized using high-resolution echocardiography performed up to 4 weeks post-RCA ligation. Infarct size was measured using 2,3,5-triphenyltetrazolium chloride (TTC)-staining 24h post-RCA ligation and the extent of the fibrotic area was determined 4 weeks after MI. RV dysfunction was confirmed 24h post RCA ligation by a decrease in the tricuspid annular plane systolic excursion (p<0.001) and RV longitudinal strain analysis (p<0.001). Infarct size measured ex-vivo represented 45.1±9.1% of RV free wall. RCA permanent ligation increased RV/LV area ratio (p<0.01). Septum hypertrophy (p<0.01) was associated with diastolic septal flattening. During the 4 weeks post-RCA ligation, the LV ejection fraction was preserved, yet it was associated with impaired LV diastolic parameters (E/e', global strain rate during early diastole). Histological staining after 4 weeks confirmed the remodelling process with a thin and fibrotic RV. This study validates that RCA ligation in mice is feasible and induces right ventricular heart failure associated with development of LV diastolic dysfunction. Our model offers a new opportunity to study mechanisms and treatments of RV/LV dysfunction after MI. NEW & NOTEWORTHY: RV dysfunction frequently causes complications after acute inferior MI. How RV failure contributes to left-sided dysfunction is elusive because of the lack of models to study molecular mechanisms. Here, we created a new model of MI by tying permanently the RCA H-00573-2018R1 3 in mice. This model offers a new opportunity to unravel mechanisms underlying RV/LV dysfunction and evaluate drug therapy.

Introduction

Long considered a simple pipe feeding the pulmonary arteries, the right ventricle (RV) is now acknowledged as a main actor of the heart. Despite an increasing interest for its role in pulmonary artery hypertension, injuries following RV infarction have been neglected. RV myocardial infarction (MI) is a specific event, which rarely occurs on its own. RV MI complicates 30 to 50% of inferior left ventricular (LV) infarction and is recognized in this situation as a major prognostic factor [START_REF] Gorter | Right Ventricular Function After Acute Myocardial Infarction Treated With Primary Percutaneous Coronary Intervention (from the Glycometabolic Intervention as Adjunct to Primary Percutaneous Coronary Intervention in ST-Segment Elevation Myocardial Infarction III Trial)[END_REF][START_REF] Horan | Right Ventricular Infarction: Specific Requirements of Management -American Family Physician[END_REF][START_REF] Ondrus | Right ventricular myocardial infarction: From pathophysiology to prognosis[END_REF].

RV infraction is associated with a higher incidence of conduction disturbance, ventricular arrhythmias, cardiogenic shock and short-term death [START_REF] Jacobs | Cardiogenic shock caused by right ventricular infarction: a report from the SHOCK registry[END_REF]. Despite the fact that the RV MI patient presents a better recovery than LV MI [START_REF] Albulushi | Acute right ventricular myocardial infarction[END_REF][START_REF] Popescu | GISSI-3 Echo Substudy Investigators. Right ventricular functional recovery after acute myocardial infarction: relation with left ventricular function and interventricular septum motion. GISSI-3 echo substudy[END_REF], the mechanisms of RV dysfunction and remodelling remain unclear [START_REF] Reddy | Molecular Mechanisms of Right Ventricular Failure[END_REF].

Recent studies have shown that diastolic and systolic ventricular interactions are negatively influenced by the RV regional inhomogeneity and prolongation of contraction. This right-to-left ventricular interaction, integrated into the concept of biventricular interdependence [START_REF] Bernheim | De l'asystolie veineuse dans l'hypertrophie du coeur gauche par stenose concomitante du ventricule droit[END_REF], is notably linked to septal wall sharing, RV architecture participation in LV work and reduction of LV preload by RV inefficiency [START_REF] Harjola | Contemporary management of acute right ventricular failure: a statement from the Heart Failure Association and the Working Group on Pulmonary Circulation and Right Ventricular Function of the European Society of Cardiology[END_REF]. In addition, RV ischemia could directly impair left ventricular contractility [START_REF] Brookes | Acute right ventricular dilatation in response to ischemia significantly impairs left ventricular systolic performance[END_REF].

However, the mechanisms that determine whether RV failure contributes to left-sided dysfunction are not well defined. Tantalizingly, small animal models of RV infarction induced by RCA ligation are currently unavailable, as the most common rodent model used by researchers to address MI remodelling is the permanent occlusion of the left descending coronary artery. In contrast to large animal models, [START_REF] Haraldsen | A porcine model for acute ischaemic right ventricular dysfunction[END_REF][START_REF] Laster | Effects of reperfusion on ischemic right ventricular dysfunction. Disparate mechanisms of benefit related to duration of ischemia[END_REF][START_REF] Malinowski | Large animal model of acute right ventricular failure with functional tricuspid regurgitation[END_REF] a mouse model of RV infarction should be more effective to study molecular mechanisms of RV dysfunction and remodeling after MI. The aim of this study was to develop and validate a mouse model of RV infarction through right coronary artery (RCA) ligation and investigate its consequences on LV function.

Methods

In vivo right ventricular ischemia mice model

Seventy-seven male C57BL/6JRj mice were anesthetized by 2% isofluorane inhalation with analgesia (buprenorphine 0.1 mg/kg s.c), and ventilated by orotracheal intubation (minivent, Harvard apparatus, USA). A specific procedure was designed in order to minimize the size of the thoracotomy and to limit bleeding during RCA ligation, especially during the delicate maneuver of revealing the RCA by maintaining the right atrium. A small incision (2 cm) was made through the skin over the right chest (Figure 1 A). After dissection, cauterization and retraction of the pectoral major and minor muscle, the fourth intercostal space was exposed (Figure 2B). An incision was made at the fourth intercostal space with a cauterization tool to open the pleural membrane (Figure 1C). The right side of the heart was exposed and a sterile compress was used to maintain the right atrium (Figure 1D-E). The RCA was sutured, and ligated at a site ≈3-5 mm from its origin using a 9-0 nylon suture (Figure1 F-H) (n=43).

Ischemia was verified by the sudden regional paleness of the myocardium and ST elevation (Figure 1 I). The thoracotomy site was closed while increasing positive end expiratory pressure. Only RCA ligation was omitted in the sham procedure (n=34). A movie of this new method of MI available in the Online Data Supplement.

The Animal Care and Use Committees of the University of Montpellier (CEEA-LR-1435-13129) approved all animal experiments. Mice were housed in a pathogen-free facility and handled in accordance with the principles and procedures outlined in the ARRIVE guidelines [START_REF] Kilkenny | Improving bioscience research reporting: the ARRIVE guidelines for reporting animal research[END_REF] and in the American Journal of Physiology guidelines for experimental models of myocardial ischemia and infarction [START_REF] Lindsey | Guidelines for experimental models of myocardial ischemia and infarction[END_REF]. In order to minimize the number of animals used per experiment in our study, we used only male mice. Moreover, this investigation conformed to the guidelines for ethical care of experimental animals of the European Union (2010/63/EU).

Echocardiography and speckle tracking analysis

High-resolution echocardiography (VisualSonics/Fujifilm, Canada with a MS550D ultrasound probe 40 MHz) was performed under anaesthesia by 2% isofluorane inhalation at 37°C, ECG and respiratory rate were monitored. The mitral valve leaflet was visualized and mitral flow (Mitral valve (MV) flow and MV tissular Doppler) was assessed at long axis b-mode view by placing the transducer on the left lateral chest wall were recorded using pulse wave Doppler. Wall thicknesses, end-systolic and end-diastolic LV dimensions were measured according the American Physiological Society guidelines as applied to mice [START_REF] Lindsey | Guidelines for measuring cardiac physiology in mice[END_REF]. LV wall thickness was measured at the level of intraventricular septum and posterior wall.

H-00573-2018R1

6

LV volume was calculated from Simpson's method of disks and ejection fraction determined from the formula (LV end-diastolic-end-systolic volume)/(LV end-diastolic volume). Longitudinal strain analysis was performed under long axis view, whereas circumferential strain analysis was performed under short axis view.

A four-chamber view was used to characterize the RV function with the Tricuspid annular plane systolic excursion (TAPSE) measurement. Speckle tracking analysis was used to study global and regional RV strain modification. We specifically used left atrium area, Isovolumic Relaxation Time (IVRT), peak early filling (E wave) and late diastolic filling (A wave) ratio (E/A), early filling (E) to early diastolic mitral annular velocity (E') (E/E' ratio), E wave and end diastolic strain rate ratio (E/SRe) to determine diastolic function index [START_REF] Rouhana | Early calcium handling imbalance in pressure overload-induced heart failure with nearly normal left ventricular ejection fraction[END_REF][START_REF] Schnelle | Echocardiographic evaluation of diastolic function in mouse models of heart disease[END_REF][START_REF] Valero-Muñoz | Murine Models of Heart Failure with Preserved Ejection Fraction: a "Fishing Expedition[END_REF]. Offline image analyses were performed using dedicated VisualSonics Vevolab 3.1.0 software.

Infarct size

Triphenyltetrazolium chloride (TTC) staining was realized 24 hours post-MI. Five mice per group were euthanized with pentobarbital (300 mg/kg) and heparin (150 U) intraperitoneally and the heart was quickly excised, sliced into four 1.0-mm-thick sections perpendicular to the long axis of the heart.

The sections were then incubated with 1% TTC at 37°C for 10 min and then scanned. The infarct area was measured using ImageJ software and myocardial infarct sizes were expressed as a percentage of the right ventricle area (n=7 /group).

Histology

Four weeks after permanent RCA ligation, hearts were dissected, fixed for four hours in 4% paraformaldehyde (vol/vol) in PBS, washed in sucrose gradient, then embedded in OCT and cryosectioned. Hearts were observed under a Zeiss Apotome microscope. Fibrotic area was determined with wheat germ agglutinin-Cy3 (WGA-Cy3 from Sigma-Aldrich) as described previously [START_REF] Choquet | Deletion of Nkx2-5 in trabecular myocardium reveals the developmental origins of pathological heterogeneity associated with ventricular non-compaction cardiomyopathy[END_REF][START_REF] Lucas | Gadd45γ regulates cardiomyocyte death and post-myocardial infarction left ventricular remodelling[END_REF]. To measure interventricular wall septum thickness, three sections from each heart were analyzed with ImageJ software. For each section, six different measurements were taken along the septum, and results were represented as average of heart wall thickness of IVS (n=7 /group).

Single-cell contractility

Four weeks after surgery, single RV, LV and septal myocytes were isolated by enzymatic digestion from sham and RCA ligation heart. Hearts were rapidly excised after euthanasia (cervical dislocation) and submitted to enzymatic action (liberase) using a Langendorff perfusion system in order to disperse single rod-shaped left ventricular (LV) myocytes [START_REF] Fazal | Multifunctional mitochondrial epac1 controls myocardial cell death[END_REF][START_REF] Lucas | Gadd45γ regulates cardiomyocyte death and post-myocardial infarction left ventricular remodelling[END_REF]. Only cardiomyocytes with clear edges and quiescent were used within 1-4 h of isolation for experiments. Unloaded cell shortening was measured (Sarcomere length, SL; IonOptix system, Hilton, USA) during field stimulation (1-ms current pulses at 0.5 Hz, room temperature 22 °C ±2 °C, 1.8 mM external Ca 2+ ). Data were analyzed using Ionwizard Software.

Statistical analysis

Results are expressed as mean ± SEM. Kaplan-Meier survival curves plot of the Sham (n = 24) and RCA ligation mice (n=33), where the outcome is time until 4 weeks (Log-rank Mantel-Cox test).

Experimental groups were compared using the Mann-Whitney test for independent samples. A value of p<0.05 was considered significant. Analyses were performed using the GraphPad Prism 6 software.

Results

Surgical procedure and survival analysis

A total of 57 mice were used in the MI survival study. The average procedure time was 30.4±1.5 min for sham and 31.2±2.1 minutes for RCA ligation. Surgical approach differed from classical LCA ligation firstly in the right thoracic access, and especially in the delicate maneuver of revealing the RCA by maintaining the right atrium as shown in Figure 1 D-E and supplemental video 1.

During the peri-surgical period (from the beginning of surgery to 6 hours after), three mice died (12.5%) in the sham group and five mice died (15.1%) in the RCA ligation group (Figure 1 J).

H-00573-2018R1 8
Causes of death were bleeding (6 mice) and pneumothorax (2 mice). After the peri-surgical period, no mice died in the sham group and 2 mice (7.7%) died in the RCA ligation group (Figure 1 K). The reason for those deaths was not identified, yet we assume that this can be attributed to either cardiac arrhythmia or sudden cardiac arrest because autopsy of these mice showed no blood in the thoracic cavity. The overall survival rates (excluding surgical-related death) were 100% in sham group and 74% if peri-surgical death was not included (p=0.133).

RCA permanent occlusion induced RV dysfunction

We used high-resolution ultrasound as a non-invasive method to measure RV function 24h hour, 1 week and 4 weeks after permanent RCA occlusion. As shown in Figure 2 A, the RCA ligation group exhibited severely impaired and akinetic RV motion compared to sham mice (RV global longitudinal strain (-12.7±0.8 vs. -8.8±0.9, p<0.001) especially in the mid base part of free RV wall (Figure 2 B, p<0.003) while the apex longitudinal strain was progressively restored 4 weeks post-MI. In addition, the TAPSE was decreased (Figure 2 C) during the follow up. RV and RA were clearly dilated 24h post-surgery and even more after 28 days post-MI (Figure 2 D-E, Figure 4 E). Heart rates were similar among all of the groups (503.4 ± 52.1 vs. 487.6 ± 12.9 bpm, p=0.367). Overall, we observed an acute and global deterioration of RV function parameters after ligation of its main artery. We investigated single cell shortening, measured as a variation of SL (Figure 2 F-J). At rest, SL was unchanged (Panel F). However, a decreased in cell peak shortening (p<0.0001) (Panel G) and late acceleration (p<0.0001) (Panel H) and deceleration (p<0.0001) (Panel I) were observed, reflecting impaired single cell contraction (Panel J). Consistent with the echocardiographic observations, histologic analysis with TTC staining confirmed systematic RV infarction in RCA-L group, which was absent in sham mice.

Infarct size was homogeneous between RCA-L mice and represented less than 50% of the RV (Figure 2 K). We performed histological assessment of RV infarction at 4 weeks post-MI as shown in Figure 2 L. RCA-L group presented a thinner fibrotic RV free wall in nearly half of the RV (Figure 2 L-M). We did not identify major interstitial fibrosis in the septum or LV compared to Sham mice.

Segmental behaviour in the LV: hypertrophy and hyperkinesia of the septum

Between the left and the right ventricle, the septum appears as the keystone of bi-ventricular interaction [START_REF] Saleh | The septal motor of biventricular function[END_REF]. In our model, RV dysfunction and dilation caused leftward deviation of the interventricular septum (a D-shaped septum is shown in Figure 3 A) especially during diastole and respiratory phase (supplemental videos 2 and 4 for sham, compared to supplemental video 3 and 5 for RCA ligation mice). In addition, the septal wall was thickened by nearly 20% (Figure 2 N and Figure 3 B) and septal contractility, estimated by circumferential strain (Figure 3 C) and strain rate (Figure 3 D), was improved 4 weeks after RCA ligation compared to Sham mice. The peak of early diastolic strain rate was measured for septal segment (figure 3 E) and revealed a better septal relaxation index after RCA ligation compared to Sham mice (p<0.05). We next decided to isolate septal ventricular cardiomyocytes and study their contractility (Figure 3 F-J). Septal cardiomyocytes from RCA Ligation mice exhibited higher peak rate of cell shortening compared to Sham cardiomyocytes (p<0.0004) (Panel G, J). In addition, velocity of shortening was improved (p<0.017) (Panel I, J).

RCA ligation induced left ventricular diastolic dysfunction

It is well known that RV failure and septal D-shaped is associated with LV dysfunction [START_REF] Calderon | D-Shaped Left Ventricle, Anatomic, and Physiologic Implications[END_REF]. We assessed, through echocardiography, the LV systolic and diastolic functions. LV ejection fraction and global longitudinal strain (systolic function) were preserved (Figure 4 A,B) over time despite RCA ligation. However, cardiac output decreased 4 weeks after RCA ligation (Figure 4 C), and was associated with a reduction of Left Ventricular Internal Size (LVID) in both systole and diastole in the RCA ligation group (Figure 4 D). Heart rate (503.4 ± 52.1 vs. 487.6 ± 12.9 bpm, p=0.367), thickness of left anterior wall (LVAW) and Left Ventricular Posterior Wall (LVPW) were similar between both groups (LVAWd: 0.91 ± 0.02 mm Sham vs 0.96 ± 0.02 mm RCA lig, p=0.115; LVPWd: 0.82 ± 0.03 mm Sham vs. 0.87 ± 0.04 mm RCA lig; p=0.07).

Mice from the RCA Ligation group presented several characteristics for LV diastolic dysfunction, with an increased left and right atrium area (Figure 4 E), a prolonged IVRT (Figure 4 F), a reduction of E/A ratio (Figure 4G). The E/E' (Figure 4 H) and E/SRE ratios (Figure 4I) were both increased.

Discussion

To our knowledge, this is the first description of a murine model of RCA ligation. The surgery provoked an important RV infarction without LV ischemic injuries. Mice presented RV systolic function breakdown and morphological alterations, with RV dilatation and inversion of RV/LV area ratio. In contrast to the LAD ligation procedure in mice [START_REF] Lindsey | Guidelines for experimental models of myocardial ischemia and infarction[END_REF][START_REF] Lucas | Gadd45γ regulates cardiomyocyte death and post-myocardial infarction left ventricular remodelling[END_REF], the RCA is more difficult to access.

The method to properly ligate properly the RCA is challenging because of the thickness of the RV wall and the proximity of the right atrium, which makes the surgical gesture critical. Despite necessary surgical training, the protocol is reliable with systematic infarction, reproductive, as well as safe with a low mortality. Mice can survive several weeks after ligation permitting longitudinal follow-up. RV infarction was associated with an echocardiographic pattern of RV failure. In our hands, achievement of RV infarct size (approximately 50% of the RV free wall) was consistent and comparable to ex-vivo model of global ischemia on isolated heart rats (2).

After 4 weeks follow-up, RCA ligation mice still displayed an impaired RV systolic function with reduced TAPSE and longitudinal strain, although these parameters were improved compared to their early assessment. This corroborates medical data concerning RV improvement after infarction [START_REF] Hoogslag | Determinants of right ventricular remodeling following ST-segment elevation myocardial infarction[END_REF].

Within the RV, areas presented a distinct profile. Apex longitudinal strain recovered progressively while free wall longitudinal strain remained low. RV/LV area ratio was still increasing, but the dispersion of data evokes various remodelling profiles or status after infarction, or/and different infarction seriousness. Partial normalization of RV systolic parameters seen after 4 weeks follow-up corroborates observations about RV recovery following infarction in human and supports clinical relevance of this model [START_REF] Hoogslag | Determinants of right ventricular remodeling following ST-segment elevation myocardial infarction[END_REF]. Compared to LV infarction, the improvement of the RV function may be caused by lower afterload, better left to right collateral flow and systolo-diastolic perfusion. It is interesting to note that the RV is more resilient against ischemia than the LV. The right ventricle needs lower myocardial oxygen demand and a better oxygen supply and coronary perfusion throughout the cardiac cycle [START_REF] Rallidis | Right ventricular involvement in coronary artery disease: role of echocardiography for diagnosis and prognosis[END_REF]. The RV, unlike the LV, has an oxygen extraction reserve, which works as an additional defence mechanism against myocardial ischemia [START_REF] Crystal | Right ventricular perfusion: physiology and clinical implications[END_REF].

In our model, classical LV systolic parameters remained unchanged over time. This suggests there is no major ischemic remodelling process affecting LV systolic parameters. Our late segmental analysis reports a hyperkinetic and hypertrophic septum wall, contrary to the lateral wall. This could be part of the adaptive hypertrophic mechanism in reaction to RV failure. Diastolic dysfunction presents a complex pattern. First, there is a pattern of impaired relaxation, as described in models of diastolic dysfunction in mice, specifically those involving hypertrophy and pressure overload [START_REF] Schnelle | Echocardiographic evaluation of diastolic function in mouse models of heart disease[END_REF]. Secondly, moderate increase of E/E' and E/SRE evokes an elevation of LV filling pressure, which is explained by two mechanisms: septal hypertrophy associated with fibrosis and dilatation of the RV within the restricted intra-pericardial space impairing LV filling. Acute and chronic RV dysfunction influence LV function because the two ventricles work in series but are anatomically arranged in parallel, sharing a common ventricular septum [START_REF] Friedberg | Imaging Right-Left Ventricular Interactions[END_REF][START_REF] Saleh | The septal motor of biventricular function[END_REF]. Under these conditions, during the end-diastolic phase, there is a leftward displacement of the interventricular septum producing distortion of the short-axis profile of the LV. It is worth to note that RV systolic dysfunction is present in 15% of human myocardial infarction (MI), mostly for patients with pluri-troncular coronary lesions. Moreover, RCA is the culprit coronary artery in one-third of MI (4). Interestingly, women have RV MI more frequently than men [START_REF] Obradovic | Women have right ventricular infarction more frequently than men[END_REF]. Gender plays a major role in cardiovascular disease evolution, especially for HF with preserved ejection fraction that affects more women than men [START_REF] Duca | Gender-related differences in heart failure with preserved ejection fraction[END_REF]. This aspect warrants further investigation.

Overall, this study provides interesting and novel data about chronic remodelling after isolated RV infarction. There was a deficit of knowledge because isolated RV ischemia rarely occurs in human [START_REF] Goldstein | Pathophysiology and management of right heart ischemia[END_REF]. We also unravelled development of LV diastolic dysfunction after RCA permanent ligation.

Among the few studies in large animal models of chronic RV failure after RCA occlusion (5, 14, 16, H-00573-2018R1 12 [START_REF] Laster | Effects of reperfusion on ischemic right ventricular dysfunction. Disparate mechanisms of benefit related to duration of ischemia[END_REF][START_REF] Laster | Determinants of the recovery of right ventricular performance following experimental chronic right coronary artery occlusion[END_REF][START_REF] Malinowski | Large animal model of acute right ventricular failure with functional tricuspid regurgitation[END_REF][START_REF] Ratliff | A model for the production of right ventricular infarction[END_REF] only one reported that RV failure induces LV systolic dysfunction [START_REF] Brookes | Acute right ventricular dilatation in response to ischemia significantly impairs left ventricular systolic performance[END_REF]. We assumed that different perfusion networks between animals and fewer collateral perfusion are responsible for that differences. Large mammalian models (dogs, sheep, pigs) share many cardiovascular characteristics with human, but have a high cost of housing and maintenance. In comparison, mice are easy to handle and housing. In addition, murine models can be easily genetically modified (e.g. Knock out, Knock in mice) allowing for the study of remodelling molecular mechanisms during RV failure.

In conclusion, we developed a new model of selective RV infarction, which allows the investigation of RV adaptation during and after ischemia. This approach could provide valuable information for preclinical mechanistic studies and drug therapy evaluation. Results are expressed as mean ± SEM. Experimental groups were compared using the Mann-Whitney test for independent samples.

  cardiomyocytes from the RCA ligation group showed no major modification compared to that of cardiomyocytes isolated from Sham animals (Figure4 J-N). Only a slight increase in the contraction time for maximal amplitude was evidenced between the two groups (Panel L and N).Taken together, our results demonstrate that this model of MI achieved by RCA ligation in mice is feasible, inducing right ventricular dysfunction associated with septal adaptation and a flawed LV diastolic function.

Figures PanelFigure 1 :

 1 Figures Panel

Figure 2 :

 2 Figure 2: RCA permanent occlusion induces subsequent RV Cardiac Dysfunction Panel A: RV global longitudinal strain (n=8/group) variation between Sham (black circle) and RCA ligation (red triangle) mice during 4 weeks follow-up. Panel B: RV segmental longitudinal strain (n=8/group) in the mid base free wall and RV apex variation between Sham (black circle) and RCA ligation (red triangle) mice 4 weeks post-MI. Panel C: Tricuspid annular plane systolic excursion (TAPSE) measurement between Sham (black circle n=16) and RCA ligation (red triangle n=22) mice during 4 weeks follow-up. Panel D: RV/LV area ratio measurement, by echocardiography during diastole, 24h post-surgery (n=16 sham, n=22 RCA ligation) and after 4 weeks between Sham (black circle n=16) and RCA ligation (red triangle n=22). Panel E: Representative B-mode four chambers view 4 weeks after RCA ligation. Panel F: Diastolic sarcomere length (SL) of cardiomyocytes isolated from RV (n=16-35 cells/group). Panel G: Maximal amplitude of SL shortening during contraction of cardiomyocytes. Panel H: Contraction velocity. Panel I: Relaxation velocity. Panel J: Contraction evoked by electrical field stimulation at 0.5 Hz as measured from SL shortening of single intact RV cardiomyocytes 28 days after surgery in Sham (black line) and RCA ligation (red line) ( 1 Peak amplitude (µm), p<0.0001; 2 Velocity of shortening (µm/sec), p<0.0001; 3 Velocity of lengthening (µm/sec), p<0.0022) (n=16-35 cells/group). Panel K: Representative images and quantification showing cardiac infarct size measured after 24h post RCA ligation. Panel L:Representative images of WGA-Cy3 staining in mid-axis section from sham and RCA ligation hearts.

Figure 3 :

 3 Figure 3: Segmental behaviour in the LV : Hypertrophy and hyperkinesia of the septum Panel A: Representative short axis view in Sham group (Top and supplementary video 4) and in RCA ligation group with a D-shaped septum (bottom and supplementary video 5). Panel B: Septum thickness measured by B-Mode short axis view during diastole (n=20-26/groups) 28 days after surgery in Sham (black circle) and RCA ligation (red triangle) mice. Panel C: Septum circumferential strain (n=21-26/group) 28 days after surgery in Sham (black circle) and RCA ligation (red triangle) mice. Panel D: Septum circumferential strain rate (n=21-26/group) 28 days after surgery in Sham (black circle) and RCA ligation (red triangle) mice. Panel E: Early diastole strain circumferential rate (n=15/groups) 28 days after surgery in Sham (black circle) and RCA ligation (red triangle) mice. Panel F: Diastolic sarcomere length (SL) of cardiomyocytes isolated from the septum (n=25-40 cells/group). Panel G: Maximal amplitude of SL shortening during contraction of cardiomyocytes. Panel H: Contraction velocity. Panel I: Relaxation velocity.Panel J: Contraction evoked by electrical field stimulation at 0.5 Hz as measured from SL shortening of single septal cardiomyocytes 28 days after surgery in Sham (black line) and RCA ligation (red line) ( 4 Peak amplitude (µm), p<0.0004; 5 Velocity of lengthening (µm/sec), p<0.017) (n=25-40 cells/group).

Figure 4 :Supplemental video 1 : 18 Supplemental video 3 :Supplemental video 4 :Supplemental video 5 :

 4118345 Figure 4: RCA ligation induced left ventricular diastolic dysfunction Panel A: Ejection fraction (n=21-26/group) between Sham (black circle) and RCA ligation (red triangle) mice 4 weeks after RV MI. Panel B: LV global longitudinal strain (n=16/group) variation between Sham (black circle) and RCA ligation (red triangle) mice 4 weeks after RV MI. Panel C: Cardiac output measurement in Sham (black circle) and RCA ligation (red triangle) mice 4 weeks after RV MI (n=16/group). Panel D: left ventricle internal dimension during systole (LVIDs) and during diastole (LVIDd) measurement in Sham (black circle) and RCA ligation (red triangle) mice 4 weeks after RV MI (n=21-26/group). Panel E: left and right atrium area measurement during diastole in Sham (black circle) and RCA ligation (red triangle) mice 4 weeks after RV MI (n=9-17/group). Panel F: Isovolumic relaxation time (IVRT) measurement in Sham (black circle) and RCA ligation (red triangle) mice 4 weeks after RV MI (n=21-25/group). Panel G: E/A ratio measurement in Sham (black circle) and RCA ligation (red triangle) mice 4 weeks after RV MI (n=21-25/group). Panel H: E/E' ratio measurement in Sham (black circle) and RCA ligation (red triangle) mice 4 weeks after RV MI (n=16/group). Panel I: E/SRE ratio measurement in Sham (black circle) and RCA ligation (red triangle) mice 4 weeks after RV MI (n=16-26/group). Panel J: Diastolic sarcomere length (SL) of cardiomyocytes isolated from LV (n=22-28 cells/group). Panel K: Maximal amplitude of SL shortening during contraction of cardiomyocytes. Panel L: Contraction velocity. Panel M: Relaxation velocity. Panel N: Contraction evoked by electrical field stimulation at 0.5 Hz as measured from SL shortening of single intact LV 28 days after surgery in Sham (black line) and RCA ligation (red line) ( 6 Velocity of shortening (µm/sec), p<0.001) (n=22-28 cells/group).Results are expressed as mean ± SEM. Experimental groups were compared using the Mann-Whitney test for independent samples.

Acknowledgments

We gratefully thank Patrice BIDEAUX and the staff for animal housing (PhyMedExp). We thank Imagerie du Petit Animal de Montpellier (IPAM) for the access to high resolution ultrasound.

Funding

This work was supported by grants from INSERM, CNRS, Université de Montpellier, a Bilateral Research Collaborative program CAPES-COFECUB between Brazil and France (n°768/13 to SR; PhD grant to TM, post-doctoral grant to GRdA) and by grant from the Fondation Leducq (RETP).

Conflict of interest

The authors have declared that no competing interests exist.


Karl Doerner

Richard Eglese

Richard F Hartl

Jakob Puchinger

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

Preface: Special Issue on the VeRoLog 2015 Conference

VeRoLog is the annual conference sponsored by the EURO Working Group on Vehicle Routing and Logistics Optimization within EURO, the Association of the European Operational Research Societies. It brings together the large community of researchers and practitioners interested in vehicle routing optimization and its relations with logistics. The conference is open to high-quality methodological contributions as well as relevant real-world applications and case studies from the industry and service sectors. VeRoLog 2015, which forms the basis of the current special issue, was organized in Vienna. The former conferences were located in Bologna (2012), Southampton (2013), andOslo (2014).

Researchers in the field of Vehicle Routing and Logistics from many parts of Europe and beyond met at the University of Vienna from June 8th to June 10th, 2015. There were 181 participants from 29 countries (Algeria, Argentina, Australia, Austria, Belgium, Brazil, Canada, Chile, China, Colombia, Denmark, France, Germany, Greece, India, Israel, Italy, Netherlands, Norway, Poland, Portugal, Serbia, Slovenia, South Korea, Spain, Switzerland, Turkey, United Kingdom, USA). The conference was organized into two plenaries (given by Martin Savelsbergh and Tolga Bektas) and 37 sessions including 123 presentations. A strong focus was on rich and real-world routing, especially in the field of green and electric vehicle routing problems, city logistics and bike sharing, and safe and secure routing. In total 28 presentations focused on one of these topics. VeRoLog now also has a solver challenge on rich vehicle routing. The paper of the winner is also included in the special issue.

The following seven papers are a selection of the best papers presented during the conference.

The paper by Belloso, Juan, Faulin, and Martinez, entitled "A Biased-Randomized Metaheuristic for the Vehicle Routing Problem with Clustered and Mixed Backhauls," analyzes the Vehicle Routing Problem with Backhauls, where delivery and pickup customers are served from a central depot. Initially, it focusses on the version with clustered backhauls (VRPCB), where all delivery customers on a route have to be served before the first pickup customer can be visited. This is motivated by the fact that vehicles are often rear loaded. The paper presents a relatively simple to implement yet efficient metaheuristic algorithm that employs a biased randomized version of the popular savings heuristic within a metaheuristic framework. A skewed probability distribution is used to induce a biased (oriented) randomization effect on the savings list of routing edges, and the sequencing constraints are considered via penalty costs. On some classical benchmark instances for the VRPCB, competitive results are obtained and a new best-known solution is found. In order to show the robustness of the proposed approach, it is also applied-after a minor adaptation-to the Vehicle Routing Problem with Mixed Backhauls, where line-haul and backhaul customers might appear in any order during a route.

The second paper, entitled "An Adaptive and Diversified Vehicle Routing Approach to Reducing the Security Risk of Cash-in-Transit Operations" and authored by Bozkaya, Salman, and Telciler, considers the new problem class of inconsistent vehicle routing problems. The authors consider the transportation of valuables (e.g., cash). Due to the highrisk nature of this operation (e.g., robberies), they consider a bi-objective function where they attempt to minimize the total transportation cost and the security risk of transporting valuables along the designed routes. For risk minimization, they propose a composite risk measure that is a weighted sum of two risk components: (i) following the same or very similar routes, and (ii) visiting neighborhoods with low socio-economic status along the routes. They also consider vehicle capacities in terms of monetary value carried as per insurance regulations. As the solution technique, an Adaptive Randomized Bi-Objective Path Selection Algorithm is used.

The third paper, authored by Kloimüllner and Raidl, is entitled "Full-Load Route Planning for Balancing Bike Sharing Systems by Logic-Based Benders Decomposition." Public Bike Sharing Systems require some kind of rebalancing in order to avoid rental stations running empty or entirely full, which would make the system ineffective and annoy customers. Usually a fleet of vehicles with trailers is used for moving bikes between stations. A rarely studied real-world aspect of the problem is that in large efficient bike sharing systems, drivers almost never pick up or deliver only a few bikes, but normally work with full vehicle loads. Many stations even require several visits with full loads. In this paper, the authors investigate such a simplified model, in which only full vehicle loads are moved between the rental stations. They formulate the rebalancing problem as a selective unit-capacity pickup and delivery problem with time budgets on a bipartite graph and present a compact mixed integer linear programming model, a logic-based Benders decomposition, and a variant named Branch-and-Check for it. The solution approach is applied to instances derived from realworld data provided by Citybike Wien, which is based in Vienna.

The fourth paper by Lum, Cerrone, Golden, and Wasil, entitled "Partitioning a Street Network into Compact, Balanced, and Visually Appealing Routes" deals with a problem of practical relevance by looking at the aesthetic quality of a set of routes. In real-world applications, the visual appeal of a proposed set of routes can have a strong influence on the willingness of a client to accept or reject a specific routing plan. Hence, the routes should not only be short, but also as compact as possible, and overlap minimally. They consider the Min-Max K-Windy Rural Postman Problem (MMKWRPP), in which a homogeneous fleet of K vehicles is routed such that the cost of the longest route is minimized. An algorithmically simple heuristic is developed, which produces competitive solutions, and performs well with respect to metrics measuring compactness and separation. The heuristic uses a partitioning scheme in which the weight of a vertex includes contributions from both incident streets requiring service and the distance needed to travel to a vertex. Computational results are presented for a set of instances generated from real-world street networks and for a set of artificial instances.

The fifth paper, entitled "Iterated Local Search for the Capacitated Vehicle Routing Problem with Sequence-Based Pallet Loading and Axle Weight Constraints," is authored by Pollaris, Braekers, Caris, Janssens, and Limbourg. The authors present an Iterated Local Search (ILS) algorithm for the capacitated vehicle routing problem with sequence-based pallet loading and axle weight constraints. The challenge of axle loading constraints is becoming increasingly important in the transportation industry and has been addressed only by a few authors. The problem considered in this paper has been introduced by the authors in a previous article, where a mathematical formulation of the problem has been presented. The proposed algorithm is based on a variable neighborhood descent approach embedded in an ILS procedure. The results of the proposed metaheuristic compare well with the ones obtained using CPLEX. In addition, the effect of introducing axle weight constraints in a CVRP on total routing cost is analyzed. Results show that integrating axle weight constraints does not lead to a large cost increase. However, not including axle weight constraints in the planning process may induce major axle weight violations.

The sixth paper, entitled "An Iterated Beam Search Algorithm for the Green Vehicle Routing Problem" by Yavuz proposes an iterated beam search algorithm for solving a variant of the green vehicle routing problem. The vehicles considered in this research are "alternative fueled vehicles" (AFVs) that need to be recharged/refueled at internal (customer nodes) and external (additional nodes) service stations. At internal service stations, refueling is performed during the service time at the customer node, whereas the vehicles are fully refueled/recharged at external service stations. The proposed algorithm can employ different lower and upper bounding strategies, and can work as an exact or a heuristic algorithm. A dominance strategy is also presented improving the efficiency of the algorithm. Computational experiments on various-sized test instances show that the algorithm's performance is competitive with existing approaches. The author compares the results of the proposed algorithm to results obtained using a standard optimization package (CPLEX) as well as to best known solutions from the literature.

Last, but not least, the paper by Geiger from the solver challenge, entitled "On an Effective Approach for the Coach Trip with Shuttle Service Problem of the VeRoLog Solver Challenge 2015," describes the solution approach of the winning algorithm. It provides a solution approach for the coach trip with shuttle service problem (CTSSP), a passenger transportation problem. The algorithm is based on variable neighborhood search and iterated local search. Efficient tree data structures are used for the representation of feasible solutions. The source code of the algorithm presented in this article is available online.

ACKNOWLEDGMENTS

Editing a focused issue of Networks would not have been possible without the most valuable input of a large number of people. First of all, we wish to thank all the authors for their contributions. Furthermore, we greatly appreciate the valuable help from the large number of referees. Last but not least we are grateful to the Editor-in-Chief Professor Bruce Golden for his support and assistance. We especially acknowledge the support and advice received from Daniele Vigo, founder and coordinator of the Verolog working group.

Guest Editors

Karl F. Doerner, Richard Eglese, Richard F. Hartl, and Jakob Puchinger


Werlé-Legendre Separation in a Hydraulic Machine Draft Tube

The three-dimensional turbulent flow in a compact hydraulic machine elbow draft tube is numerically investigated for several operating conditions, covering an extended range around the best efficiency point. Comparisons with the experimental data are presented as validation. The interest is focused on the experimentally observed pressure recovery drop occurring near the best efficiency point. The flow is first analyzed locally by means of a topological analysis, then globally with an energetic approach. The study provides evi-dence for the role played by a Werlé-Legendre separation originating in the bend. The separation is due to the contrasting flow angles imposed by the blades, and the angle resulting from the secondary flow.

Introduction

Draft tubes are components which act to convert a maximum of dynamic pressure into static pressure. A measure of the efficiency of these devices is the static pressure recovery obtained. A large number of hydraulic turbomachinery installations are ageing. Thus, there is potential during refurbishment to implement changes in the design for improved efficiency and associated power output as well as greater operating stability. Usually the runner and guide vanes are focused upon in the refurbishment process. Due to capital construction costs the spiral casing and the draft tube are seldom modified. Unfavorable flow behavior occurs when the runner and the draft tube are unsuitably matched. This can sacrifice flow stability and reduce the optimal operating range of the machine. Typically a sudden drop of the pressure recovery in the draft tube is observed near the best efficiency operating condition. The comprehension of this unexplained phenomenon is the objective of the present study. For this aim an extended range of operating conditions is numerically investigated. After the description of the model, a grid convergence study is presented, then comparisons with experimental data are briefly shown as validation. The flow is first analyzed globally with an energetic approach, then locally by means of a topological analysis. The framework introduced by Tobak and Peake ͓1͔ is adopted to describe the topological evolution of the flow in the draft tube as the flow rate is varied. A debate on the terminology can be found in Hornung and Perry ͓2͔ and other references cited therein.

Case

Experimental studies are carried out on a vertical axis reduced scale model ͑1:10͒ of an existing water turbine at the test rig facilities of the EPFL-Laboratory for Hydraulic Machines. A high specific speed Francis runner supplies the symmetrical draft tube with a single pier ͑Fig. 1͒. The numerical flow analysis is carried out at a constant head for 14 flow rates ranging from 90% to 110% of the best efficiency discharge. The Reynolds number based on the inlet mean velocity and diameter is Re D ϳ1.5 10 6 . The inlet conditions are experimentally investigated on the symmetry axis diameter at six operating points by means of the local density approximation ͑LDA͒ technique. The three components of the velocity and the turbulent kinetic energy profile ͑Fig. 2͒ are obtained through two positions of a two-dimensional ͑2D͒ laser probe, ͓4͔. The measurement uncertainties are estimated to be less than 3%. The other conditions are linearly interpolated from the measurements.

Modeling. Three-dimensional ͑3D͒ steady Reynoldsaveraged Navier-Stokes ͑RANS͒ flow computations with the standard k-⑀ turbulence model and logarithmic wall functions are performed. The flow in the draft tube is simulated using the commercial code CFX-TASCFLOW 2.10. Details on the code are given in Refs. ͓5,6͔. The computation is considered converged to the steady solution when the value of the maximal normalized equation residual is less than 10 Ϫ4 . The fluid properties are set to the values corresponding to the water at atmospheric conditions. The calibration of modeling parameters has been performed in previous studies, see Refs. ͓7,8͔, and is here briefly summarized. The inlet profile is specified at the inlet using a cubic spline. A linear interpolation is applied to the circumference. The radial component is imposed as C r ϭC r tan(r/R). The inclination of the velocity vector in the radial direction is, therefore, determined by the geometry of the cone. This theoretical profile performs better than the profile extrapolated from the relatively few and wiggly measured values. The influence of the radial component is important in spite of its small magnitude. The nearest measurement point is at 0.076 inlet diameter from the wall. The extrapolation of the velocity profile from the last measurement point to the wall has a strong influence on the flow prediction in the draft tube. The influence of the momentum thickness on the efficiency of a diffusor is well known. The velocity components at the wall are set as a factor of the velocity at the nearby interior measurement point. Best results with respect to measurements are achieved with a factor of 0.9. The standard k-⑀ model assumes that ⑀ϭk 3/2 /L ⑀ . For the determination of ⑀ from the measured turbulent kinetic energy, the length scale L ⑀ defining the size of the largest eddies must be specified. This parameter has an important influence on the overall flow. L ⑀ ϭ0.002 D leads to the best results. Several models of the outlet region show a limited influence on the upstream flow. The domain is, therefore, simply prolonged with a downstream channel of length 2 D. At the outlet the flow is considered developed. Several two-equation turbulence models and one second-order closure scheme have been tested. While the twoequation turbulence models perform similarly, the Reynolds-stress model does not increase agreement with the experimental results in spite of the theoretically greater potential. A structured multiblock mesh discretizes the geometry of the draft tube model. A butterfly topology with a C-shaped grid around the pier is used. The y ϩ values of the first grid points lie in the validity range of the model.

Verification. An a posteriori numerical error estimation based on the generalized Richardson extrapolation not requiring any restriction to integer refinement and applicable to solution functionals is carried out. Following Roache ͓10͔ the more conservative Grid Convergence Index is also reported. The flow rate in the left channel obtained with three meshes is compared at *ϭ0.994 in Table 1. The number of nodes corresponds to the effective number of points in the draft tube geometry ͑double nodes at the block interfaces are counted only once, the downstream channel is not considered͒. The grid refinement is reported simply in terms of total number of grid points used in the two meshes as r i j ϭ(N i /N j ) 1/3 . The meshes have the same topology but the grid refinement is not uniform in the space. This may give an inaccu-rate estimation of the accuracy depending on whether the grid refinement occurs in the critical areas or not. Depending on the mesh resolution at the inlet the resulting flow rate will change and must be corrected to retrieve the measured value by multiplying the velocity field by a factor. The slight differences in the inlet boundary conditions introduce an additional inaccuracy. The meshes seem to be in the asymptotic range; the actual asymptotic rate of convergence is indeed pϭ1.98, to be compared with the theoretical order pϭ2. These results are expected to be only partially representative for other operating conditions due to the important flow differences. The results at the points *ϭ0.919-1.108 are compared in Table 2. The mesh with N 3 ϭ328,360 nodes insures a GCI smaller than 7% for all operating points. The results obtained with these meshes show the same flow topology and compare very similar with respect to the measured velocity and pressure profiles on several sections. The coarser mesh is, therefore, adequate for our purposes.

Validation

The comparison with measurements is not emphasized here, the objective being the characterization of the ''numerical flow.'' Only the recovery factor and the velocity field at the draft tube outlet are shown. Several other comparisons on the whole geometry have been performed showing that while the main flow features and trends are correctly captured, locally important differences occur, see, Refs. ͓7-9͔. The recovery factor is compared with the measurements in Fig. 3. The global behavior is fairly well predicted. The pressure recovery drop takes place at the same flow rate observed experimentally, however, the computations overestimate the recovery factor over the whole range, with a maximal difference of 14% of the measured value. Near the best efficiency conditions the maximal difference is 6%. The velocity field at the draft tube outlet is compared for the two extreme operating points in Fig. 4. Static Pressure Recovery. The specific static pressure energy recovery is summarized in Fig. 5 over the whole computed operating range. Most of the recovery occurs in the cone. The efficiency drop taking place in the second half of the bend is clearly visible in the range *ϭ1.021-1.049. This deficiency is partially recovered in the last part. The domain is split into two symmetrical parts allowing a comparison between the left and the right channel, even upstream at the pier's leading edge. The recovery drops on the left side due to a flow acceleration, while on the right channel the pressure recovery is very small in the straight diffuser, indicating an unfavorable flow situation. The flow rate distribution in the channels is shown in Fig. 6. The right channel is clearly blocked in the efficiency drop region.

Flow Topology. The main characteristics of the skin friction lines are investigated. Experimentally the flow patterns at the wall can be obtained by means of the oil film method. The power of topological visualization is that, given the singular ͑critical͒ points and their principal tangent curves, an observer can visually infer the shape of other tangent curves and hence the structure of the whole vector field. A representation of the global topology is much more readily visualized than the original data set. The main flow characteristics are summarized in Fig. 7, where the change of the flow direction in the right channel due to the increase of the secondary flow introduced by the bend, and to the change of the rotation direction at the inlet ͑Fig. 2͒, is put in evidence by means of separation lines. These are lines drawn in the flow toward which other trajectories are asymptotic. A universal definition of separation in a three-dimensional flow is still subject of debate. The specification of separation by means of a reverse flow or vanishing wall shear stress is usually inadequate in threedimensional flows. A necessary condition for the occurrence of flow separation is the convergence of skin friction lines onto a separation line. The regions of flow separation are important because of the reduced kinetic energy and the consequent blockage effect that these regions can introduce. The point before the efficiency drop shows local ͑not passing through any critical point͒ separation lines at the surface. After the drop the flow stemming from the cone region situated at the outer side with respect to the bend curvature is forced by the secondary flow to the inner side, while the flow angle imposed by the blade geometry remains constant for all operating points. The collision of these two flow directions leads to the onset on the surface of a focus in company with a saddle point leading to a global Werle ´-Legendre separation ͑see also Fig. 8, showing the wall region where the onset of the critical points occurs͒. In this particular form of separation one leg of the line of separation emanating from the saddle point winds into the focus to form the curve on the surface from which the dividing surface stems. The focus on the wall extends into the fluid as a concentrated vortex filament, while the surface rolls up around the filament. This flow behavior was first hypothesized by Legendre in 1965 and confirmed by the experiments of Werle ͑1962͒. The cooperation between these two scientist is described in Ref. ͓3͔. As the flow rate reaches a critical value the flow bifurcates, breaking the symmetry of the precedent flow and adopting a form of lesser symmetry in which dissipative structures arise to absorb just the amount of excess available energy that the more symmetrical flow no longer was able to absorb. The flow pattern in the inner domain can be seen in Fig. 9, where the vortex core originating from the focus and the tangential streamlines on two cross-sections are shown. There is a practical difficulty to define the separation region delimited by the stream surface originating from the line of separation. A simple separation region extraction algorithm is used to define a volume. Streamlines are started from the zone at the wall where separation occurs. A streamline is then equidistantly divided and from each point the intersection of the corresponding normal plane with all other streamlines is computed. From each group of points the mean point is calculated and used to define a new line and the procedure is repeated until the desired convergence is achieved. From each cloud of points, corresponding to the intersection of the normal plane of this mean line with all streamlines, the best fitting ellipse to the external points of the cloud is computed. The resulting tube with elliptic sections approximates the separation zone. In this case the separation forms a swirling structure. The vortex evolution is shown in Fig. 10. Just prior to the drop the separated region is small and attached to the sidewall. Then the vortex structure is formed and moves toward the center of the section and increases its size and strength until *ϭ1.032, then begins to decay and at *ϭ1.054 the focus disappears ͑Fig. 11͒. The relationship to the flow rate distribution shown in Fig. 6 and to the pressure recovery illustrated in Fig. 5 is evident.

Conclusion

The origin of the static pressure recovery drop can be clearly localized in the bend region by means of an energetic analysis. The study of the skin friction lines in this region shows the onset of a global Werle ´-Legendre separation as the flow rate reaches a critical value. The topological structure of the skin friction field bifurcates with the emergence of a saddle point and a focus in the surface pattern. The evolution of the vortex region originating in the focus is visualized in the inner flow clearly illustrating how the separation blocks the right channel leading to a flow acceleration in the other channel. The static pressure recovery is strongly affected, leading to an important loss in the overall machine efficiency.

Nomenclature

͗ f ͘ Q ϭ(1/Q)
ϫ͐ A f c ជ .n ជ dA ϭ Volume flow weighted surface average

Fig. 1 Fig. 2

 12 Fig. 1 Investigated geometry. Cross area evolution. Sections definition.

Fig. 4 Fig. 6

 46 Fig. 4 Comparison measurements "M…-computation "C… at the draft tube outlet. Normal "C n … and vertical "C v … velocity components, C 0 : mean sectional velocity magnitude. *Ä0.919 and *Ä1.108. The measurements do not cover the whole channels' surface.

Fig. 8

 8 Fig. 8 Computed skin friction lines, onset on the surface of a focus in company with a saddle point. Before the efficiency drop: *Ä0.994, *Ä1.014, after: *Ä1.021, *Ä1.032, *Ä1.038, *Ä1.054.

Fig. 9

 9 Fig. 9 Computed vortex core and separation line, *Ä1.021

Fig. 10

 10 Fig. 10 Predicted vortex evolution. Before the drop: *Ä1.014, after: *Ä1.021, *Ä1.027, *Ä1.032, *Ä1.038. The last picture summarizes the first four operating conditions "lighter core: *Ä1.014, darker core: *Ä1.032….

Fig. 11

 11 Fig. 11 Interpretation of Fig. 8. S: Saddle, F: Focus, N: Node.

Table 1 *

 1 Ä0.994. N

: Number of nodes, l: Flow rate in the left channel †% ‡, E: Estimated fractional error, GCI: grid conver- gence index. Values for E, GCI are reported in †% ‡ using p Ä2 as order of the discretization.

		͑a͒
	l 1 ϭ72.526 E 12 ϭ0.06 GCI 12 ϭ0.17	l 2 ϭ72.544 E 12 ϭ0.08 GCI 12 ϭ0.24 ͑b͒	l 3 ϭ72.576 E 23 ϭ0.12 GCI 23 ϭ0.37
	l 1 ϭ65.094 E 12 ϭ0.93 GCI 12 ϭ2.80	l 2 ϭ65.367 E 12 ϭ1.44 GCI 12 ϭ4.06	l 3 ϭ65.886 E 23 ϭ2.23 GCI 23 ϭ6.71

N 1 ϭ1,107,237 N 2 ϭ633,720 N 3 ϭ328,360 l 1 ϭ63.232 l 2 ϭ63.309 l 3 ϭ63.445 E 12 ϭ0.27 E 12 ϭ0.39 E 23 ϭ0.60 GCI 12 ϭ0.81 GCI 3 ϭ1.17 GCI 23 ϭ1.82 Table 2 "a… *Ä0.919 "b… *Ä1.108. See caption in Table 1.

  A ref ϭ Reference section area C ϭ Velocity field C 0 ϭ Mean local normal velocity Dϭ0.4 ͓m͔ ϭ Runner outlet diameter E k o ϭ͗C 2 /2͘ Q ϭ Inlet mean kinetic specific energy e p i ϭE p i /E k o ϭ Local mean specific static pressure energy coefficient E p i ϭ͗p/͘ Q i ϭ Local mean static pressure specific energy ⑀ ϭ Turbulent disspation rate k ϭ Turbulent kinetic energy L ⑀ ϭ Turbulent eddy length scale Q ϭ Flow rate r ϭ Radius R ϭ Inlet radius Re D ϭC 0 D/v ϭ Reynolds number y ϩ ϭ Nondimensional distance from the wall ϭ((1/)⌬ P dt )/ (0.5(Q/A ref ) 2 ) ϭ Pressure recovery factor ⌬ P dt ϭ Mean wall pressure difference between draft tube inlet and outlet v ϭ Water kinematic viscosity ϭ Flow rate coefficient * ϭ Flow rate coefficient divided by the of the best efficiency point ϭ Water density ϭ Half cone opening angle

J. L. Kueny F. Avellan LMH-Laboratory for Hydraulic Machines, EPFL-Swiss Federal Institute of Technology, Av. Cour 33bis, Lausanne 1007, Switzerland

Acknowledgments

This study is established within the Flindt project ͑Eureka No. 1625͒ whose participants are EPFL, Electricite de France, Alstom Power, General Electric Canada, VA Tech Escher Wyss, and Voith Hydro who are gratefully acknowledged. The project is also supported by the Swiss Federal Commission for Technology and Innovation ͑PSEL͒ and the German Ministry of Science and Technology ͑BMBF͒. The authors wish to thank G. Ciocan and J. Arpe for the experimental data and the staff of the Laboratory for Hydraulic Machines for providing support in the experimental and numerical work.