Thibault Couture

MD Julien Gaudric
email: julien.gaudric@aphp.fr

Sophie Tezenas

Du Montcel

Jérémie Jayet

Dorian Verscheure

Jean Michel Davaine

Mohamed Jarraya

Laurent Chiche

Fabien Koskas

Dorian Versheure

Abdominal Aortic Allografts Used as a Substitute for Infected Prosthetic Grafts in 200 Patients

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

Introduction

The incidence of aortic graft infections (AGI) is low (0.5-6%) [START_REF] Berger | Cumulative incidence of graft infection after primary prosthetic aortic reconstruction in the endovascular era[END_REF][START_REF] Vogel | The incidence and factors associated with graft infection after aortic aneurysm repair[END_REF][START_REF] Harlander-Locke | The use of cryopreserved aortoiliac allograft for aortic reconstruction in the United States[END_REF] but is associated with high morbidity and mortality rates of 10-50% [START_REF] Harlander-Locke | The use of cryopreserved aortoiliac allograft for aortic reconstruction in the United States[END_REF][START_REF] Bisdas | Eight-year experience with cryopreserved arterial homografts for the in situ reconstruction of abdominal aortic infections[END_REF][START_REF] Brown | Arterial reconstruction with cryopreserved human allografts in the setting of infection: A single-center experience with midterm follow-up[END_REF][START_REF] Garot | Intra-abdominal aortic graft infection: prognostic factors associated with in-hospital mortality[END_REF][START_REF] Touma | In situ reconstruction in native and prosthetic aortic infections using cryopreserved arterial allografts[END_REF] . Standard treatment remains controversial ranging from radical surgery with complete excision of the graft and infected tissues and iterative vascular repair, to conservative strategies. Some substitutes with infection-resistant properties are available, including femoral veins, antibiotic-or silver-coated grafts. However, the substitute showing the best resistance to infection and the best long-term results remains a matter of debate.

Radical surgery using cryopreserved arterial allografts (CAAs) for the iterative repair is our preferred strategy since the 1980s because several experimental and clinical studies have shown the resistance of CAAs to colonization by most microorganisms involved in vascular infections [START_REF] Knosalla | Treatment of vascular graft infection by in situ replacement with cryopreserved aortic allografts: an experimental study[END_REF][START_REF] Koskas | Arteries from human beings are less infectible by Staphylococcus aureus than polytetrafluoroethylene in an aortic dog model[END_REF][START_REF] Litzler | Bacterial resistance of refrigerated and cryopreserved aortic allografts in an experimental virulent infection model[END_REF][START_REF] Kieffer | Allograft replacement for infrarenal aortic graft infection: early and late results in 179 patients[END_REF] . Moreover, CAA is considered a safe [START_REF] Kieffer | Allograft replacement for infrarenal aortic graft infection: early and late results in 179 patients[END_REF] and even mechanically ideal material for arterial repair, at least in the short term, with good outcomes [START_REF] Antonopoulos | Editor's Choice -Cryopreserved Allografts for Arterial Reconstruction after Aorto-Iliac Infection: A Systematic Review and Meta-Analysis[END_REF] . However, the benefit of such a strategy remains to be demonstrated in the long term and in large series. Despite the recent recommendations provided by the European Society of Vascular and Endovascular Surgery [START_REF] Chakfe | Editor's Choice -European Society for Vascular Surgery (ESVS) 2020 Clinical Practice Guidelines on the Management of Vascular Graft and Endograft Infections[END_REF] , there is a lack of evidence due to the heterogeneity and small sample sizes of the published series.

This study provided a large database from which solid conclusions could be drawn. Its aim was to investigate the early and late outcomes of patients with arterial graft infection treated with complete excision of the infected graft and iterative arterial repair using a CAA starting from the infrarenal aorta.

Patients and methods.

Patients

All consecutive patients treated with CAA for infrarenal aortic repair in prosthetic arterial infections in our vascular department between January 1997 and December 2013 with a follow-up until January 2016 were included in a monocentric study. Data were recorded in a prospectively maintained database and were analyzed retrospectively [START_REF] Teebken | Recommendations for reporting treatment of aortic graft infections[END_REF] .

Demographics, cardiovascular risk factors, comorbidities and techniques including the CAA features were recorded.

When a diagnosis of graft infection was suspected a Computed Tomography (CT)-scan was systematically performed to identify a periprosthetic abscess, graft-enteric fistula or pseudoaneurysm (PA).

Bacteriological diagnosis

The microorganisms responsible for infection were identified in bacteriological samples collected preoperatively by drainage or CT-guided puncture of perigraft pus drainage or in blood cultures or were directly collected intraoperatively. The analyzed intraoperative samples included intraprosthetic and PA thrombus, perigraft collection or the graft itself. Our institutional algorithm recommended to systematically perform bacteriological samples before initiating antibacterial treatment.

The diagnosis of AGI was ascertained using the MAGIC classification [START_REF] Chakfe | Editor's Choice -European Society for Vascular Surgery (ESVS) 2020 Clinical Practice Guidelines on the Management of Vascular Graft and Endograft Infections[END_REF] if one major criterion or at least two minor clinical, radiological or biological criteria were present. Infection was defined as early if it occurred after <4 months and late if it occurred after >4 months [START_REF] Chakfe | Editor's Choice -European Society for Vascular Surgery (ESVS) 2020 Clinical Practice Guidelines on the Management of Vascular Graft and Endograft Infections[END_REF] .

Then, broad-spectrum antibiotics were initiated before secondary targeted antibiotics after identification of the microorganism by infectious disease specialists.

All survivors underwent CT and/or duplex ultrasound examinations before discharge and were followed with a clinical examination and a new imaging at one and six months and yearly thereafter.

Cryopreservation protocol.

All CAAs were provided by the tissue bank of our institution (Banque de Tissus de l'Assistance Publique Hôpitaux de Paris, Hôpital Saint-Louis, Paris, France). Allografts were obtained from brain-dead multiorgan donors and transported at a temperature between +3 and +10°C to the bank in 500 mL of gelatin (Plasmion) solution containing antibiotics (160 mg of gentamicin, 250 mg of vancomycin, 300 mg of Clindamycin or Lincomycin). After 36 hours in this solution, they were placed in a cryopreservation solution composed of 50 mL of dimethyl sulfoxide (DMSO) and 350 mL of tissue preservation fluid (Solution de Conservation des Organes et Tissus, SCOT 30, Macopharma, Mouvaux, France). Allografts were then frozen in a controlled-rate nitrogen vapor freezing chamber at a rate ranging between -1°C and -2°C/minute up to -40°C and of -5°C/minute from -40°C to -150°C. CAAs were then stored in a nitrogen vapor container (-150°C) until their use.

Surgical technique.

Exhaustive excision of all synthetic material whether or not macroscopically infected, was performed in all cases. Aggressive debridement of the surrounding periprosthetic infected tissues was performed to obtain a macroscopically normal surgical field. Arterial repair was then performed using one or more CAAs. The allograft was systematically separated from the bowels using a retroperitoneal tissue or bovine pericardial patch (Edwards Lifesciences, Irvine, CA, USA) or by omentoplasty.

In all cases with graft-to-enteric fistula, the digestive part of the procedure was performed by a gastrointestinal surgeon as previously described [START_REF] Schoell | Surgery for secondary aorto-enteric fistula or erosion (SAEFE) complicating aortic graft replacement: a retrospective analysis of 32 patients with particular focus on digestive management[END_REF] . The digestive procedure ranged from a simple suture of the bowel to resection and anastomosis with the third portion of the duodenum depending on the tissue loss and fistula location.

Peroperative surgical data and CAA features were collected (intervention duration, blood loss, number of allografts used, clamping level, need for vasoactive drugs, surgical procedure).

Postoperative parameters

Postoperative (at 30 day and in-hospital) mortality and systemic morbidities were recorded.

In-hospital complications requiring revision surgery were also collected. During the follow-up, the need for allograft-related revision surgery, aneurysmal degeneration and thrombosis, reinfection, survival and limb salvage were recorded. Ruptures were considered a reinfection if no mechanical factors were found after reviewing the operative reports.

Outcomes

The primary outcome was the allograft-related revision surgery rate. Secondary outcomes were the rates of 30-day mortality, survival, primary patency, limb salvage and infection recurrence.

Statistical analysis.

Data are presented as a frequency (percentage) for qualitative variables and a mean ± standard deviation for quantitative variables. Statistical analysis was performed using SAS software (version 9.4, SAS Institute, Cary, NC).

The analysis of the long-term mortality, primary patency, and graft-related complication-free survival was performed using the Kaplan-Meier method. Potential risk factors for early mortality were identified using univariate and multivariate logistic regression analysis.

Univariate factors associated with a p-value <.20 were included in the multivariate analysis using a stepwise selection. Odds ratios (OR) with their respective 95% confidence intervals (CI) were computed. Risk factors for short-term septic complications and long-term complications were analyzed using a Cox model according to the method of Fine and Gray.

For the long-term risk factors, patients who died, were lost to follow-up or underwent allograft explantation before 6 months were excluded from the analysis. For both analyses, hazard ratios (HR) with their 95% CI were computed. A p-value <.050 was considered significant. The conduct of this study was approved by our institutional review board under the number 20190906192459.

Results

Patient demographics and clinical presentation

Over the study period, 200 patients with a mean age of 64.2 ± 9.4 years were included (Table 1). The indication for primary surgery was a non-infected aneurysmal or occlusive disease in 65 and 135 cases, respectively. The mean time between initial surgery and the diagnosis of infection was 58 ± 65 months. In 51 cases (25.5%), infection occurred less than 4 months after initial surgery.

The diagnosis of infection was made based on major clinical or radiological criteria in 167 cases (83.5%) (prostheto-digestive fistula, periprosthetic abscess, cutaneous fistula). In case of minor criteria (PA or graft thrombosis), the diagnosis was confirmed by collecting microorganisms from the explanted grafts or intra-operative specimen or inflammatory syndrome according to the MAGIC classification [START_REF] Chakfe | Editor's Choice -European Society for Vascular Surgery (ESVS) 2020 Clinical Practice Guidelines on the Management of Vascular Graft and Endograft Infections[END_REF] . Among the patients with major criteria, 14 also had a PA.

Bacteriology

Microbiological findings are reported in Table 2.

All patients received antibiotics postoperatively and 172 (86%) preoperatively. The mean duration of antibiotherapy was 57.3 ± 91 days.

The bacteriological samples were negative in 35 patients. Among them, 30 had received an empirical antibiotherapy prior to bacteriological sampling. In these 35 patients, the diagnosis of graft infection was based on the presence of a periprosthetic abscess (n=13), a cutaneous fistula (n=9), a prostheto-digestive fistula (n=5), a PA and an inflammatory syndrome (n=7), a periprosthetic urinoma and an inflammatory syndrome (n=1).

Operative Data

Per-operative data concerning the surgical technique is reported in Table 3.

Regarding patients who underwent a 2-stage surgery: all cases of bleeding were treated with local repair (direct suture or a short graft interposition). In case of severe sepsis upon presentation, an abscess drainage was performed before graft explantation. In case of acute ischemia secondary to septic thrombosis, embolectomy was systematically performed.

A mean number of 8.6 ± 7 blood units were transfused, corresponding to a mean blood loss of 3.7 ± 3.7 L per patient.

A mean number of 2 CAAs were used per patient. The cryopreserved arterial segments used were the descending thoracic aorta, the aortic bifurcation and one iliofemoral artery in 40.0, 43.5 and 50.5% of patients, respectively. One or more calcifications were present in 44.7% of CAAs. The mean age of donors was 39 ± 13.3 years. These factors were not predictive of long-term degeneration of the allograft.

Postoperative Outcomes

The 30-day mortality rate was 11% (n=22). The overall mortality rate was 14% (n=28) before discharge (the causes of death are listed in table 4). This rate was even much higher in patients with aorto-enteric fistulas (21%). Early reinfections (<1 month) were associated with a significantly higher rate of in-hospital mortality compared to late reinfections (>1 month), with mortality rates of 27.6% and 11.7%, respectively (OR=0.35 [0.13-1.04], p=.030).

The in-hospital morbidity rate was 57.5% (the postoperative complications are listed in Table 4). In-hospital revision surgery was needed in 59 patients (29.5%) (detailed in Table 5) of whom 14 died. Among the 59 cases of revision surgery, 15 were related to the allograft (7.5%) and led to the death of 3 patients (Table 6).

The predictive factors for post-operative death identified in the multivariate analysis were: the age (OR = 2.9 p<.001) (Table 7).

Among the 172 patients who survived during the early postoperative period, the mean followup was 4.1±3.9 years (median = 2.9 years, IQR 4.8 years). Fifty-three patients (26.5%) were lost to follow-up, of whom 38 during the first 3 years. Fifteen were still alive at 3 years but were lost to follow-up thereafter.

The 1-, 3-and 5-year survival rates were respectively 76%, 66% and 56% (Figure 1).

During the follow-up, 59 other patients died after the early postoperative period. The most common causes were cancer (n=16), extravascular infectious disease (n=11), heart disease (n=6). Six allograft-related deaths due to a rupture were reported (Table 6).

Allograft-related events

Seven late major amputations were reported during the follow-up, 2 were related to the allograft.

The 1-, 3-and 5-year primary patency rates were respectively 92%, 84% and 80% (Figure 1).

The 5-year limb salvage rate was 90% (Figure 1).

The rates of patients free from allograft-related revision surgery were 85%, 77% and 70% at 1, 3 and 5 years, respectively (Figure 1) and the 30-day rate of allograft revision surgery was 6%.

The rate of allograft-related mortality was 3% (n=6 deaths).

All allograft-related complications are reported in Table 6.

Each allograft-related complication was reviewed: 27 patients required revision surgery during the first 6 months (Table 6). Seventeen patients experienced a complete or partial (PA) rupture of the allograft and 3 experienced an anastomotic tear or collateral bleeding. Among these 17 patients, 5 died (including 2 before revision surgery) and 4 experienced successive ruptures. The bacteriological samples collected during revision surgery were positive or multiple ruptures occurred in all cases except one. A total of 22 interventions were performed.

Redo surgery consisted in a partial replacement with a new segment of allograft (n=13), saphenous vein (n=3), in situ rifampicin-bounded prosthesis (n=3), stent-graft (n=1), resection-anastomosis (n=1) and total resection + axillo-bifemoral prosthetic bypass (n=1).

All in situ prostheses except one were secondarily infected and explantation was needed. The first revision surgery was performed after less than 6 weeks in 13 out of the 17 patients.

In the multivariate analysis, diabetes (HR = 4.18 [1.74-10.01], p = .001) and pseudoaneurysm upon presentation (HR = 2.92 [1.18-7.23], p = .020) were the only predictive factors for allograft rupture before 6 months. The type of microorganisms and bowel fistulas were not associated with an increased risk of rupture (Supplementary Table 1).

After 6 months, 25 patients (18%, n=25/139) experienced an allograft-related complication (Table 6). Two ruptures were consecutive to two late allograft-related enteric fistulas (at 12 and 20 months) responsible for 1 death. PA occurred later in 6 patients (1 at 7 months, 2 at 3 years, 3 at 10 years). The PA that occurred at 7 months was a recurrence of a previous PA that occurred after less than 6 months.

The 1-, 3-and 5-year CAA reinfection rates were 10, 12 and 12%, respectively.

Discussion

This series of patients allowed quantifying the complication rate of surgery for abdominal aortic graft infection, in particular allograft-related complications from a homogenous cohort of patients. Despite the acceptable results achieved with allografts used as a substitute for infected aortic prostheses, a significant rate of early failures was observed, leading to an increased risk of mortality.

The early mortality rate found in this study was acceptable (11%) compared to that reported by Antonopoulos [START_REF] Antonopoulos | Editor's Choice -Cryopreserved Allografts for Arterial Reconstruction after Aorto-Iliac Infection: A Systematic Review and Meta-Analysis[END_REF] (14.9%) although the rate of enteric fistulas upon presentation was higher.

Enteric fistulas were not associated with a significantly increased mortality rate contrary to what has been reported in other studies [START_REF] Garot | Intra-abdominal aortic graft infection: prognostic factors associated with in-hospital mortality[END_REF][START_REF] Kieffer | Allograft replacement for infrarenal aortic graft infection: early and late results in 179 patients[END_REF][START_REF] Gabriel | Cryopreserved arterial allografts in the treatment of prosthetic graft infections[END_REF][START_REF] Verhelst | Use of cryopreserved arterial homografts for management of infected prosthetic grafts: a multicentric study[END_REF] , probably because of our aggressive intervention at the bowel defect that prevented fistula recurrence [START_REF] Schoell | Surgery for secondary aorto-enteric fistula or erosion (SAEFE) complicating aortic graft replacement: a retrospective analysis of 32 patients with particular focus on digestive management[END_REF] .

The most common risk factors for early death from aortic sepsis treated with in situ allografts reported in the literature are the age of the patient [START_REF] Garot | Intra-abdominal aortic graft infection: prognostic factors associated with in-hospital mortality[END_REF][START_REF] Touma | In situ reconstruction in native and prosthetic aortic infections using cryopreserved arterial allografts[END_REF][START_REF] Legout | Characteristics and prognosis in patients with prosthetic vascular graft infection: a prospective observational cohort study[END_REF] , the need for emergent surgery [START_REF] Touma | In situ reconstruction in native and prosthetic aortic infections using cryopreserved arterial allografts[END_REF][START_REF] Kieffer | Allograft replacement for infrarenal aortic graft infection: early and late results in 179 patients[END_REF][START_REF] Verhelst | Use of cryopreserved arterial homografts for management of infected prosthetic grafts: a multicentric study[END_REF] , and enterobacteria and Candida infections [START_REF] Harlander-Locke | The use of cryopreserved aortoiliac allograft for aortic reconstruction in the United States[END_REF][START_REF] Ali | Long-term results of the treatment of aortic graft infection by in situ replacement with femoral popliteal vein grafts[END_REF] . However, the only significant independent predictors for death identified in our multivariate analysis were the age of the patient, the presence of post-operative acute renal failure, and the number of transfused blood units reflecting the invasiveness of such a surgery.

Our results confirmed that AGI remains a huge surgical challenge with a high morbidity rate (57%) falling within the range of values reported in Antonopoulos meta-analysis [START_REF] Antonopoulos | Editor's Choice -Cryopreserved Allografts for Arterial Reconstruction after Aorto-Iliac Infection: A Systematic Review and Meta-Analysis[END_REF] . The septic and hemorrhagic context of AGI, the physiological consequences of the surgical procedure, and frequent age-related comorbidities could explain such a high complication rate. That is why a high-volume center with a specialized intensive care unit is crucial for the management of such patients.

Short-term Allograft-Related Complications

Our rate of allograft-related revision surgery during the first 6 post-operative months was 13.5% (n=27). Among these cases, 3 were due to collateral bleeding and 7 to early thrombosis or stenosis. However, the most worrisome causes of allograft-related revision surgery were ruptures (n=17, 8.5%) since they were responsible for 5 deaths (2.5%).

Similarly, the resistance to infection and technical safety have been questioned due to a relatively high rate of early ruptures of 5.9% in a recent meta-analysis [START_REF] Antonopoulos | Editor's Choice -Cryopreserved Allografts for Arterial Reconstruction after Aorto-Iliac Infection: A Systematic Review and Meta-Analysis[END_REF] . Subadventitial rupture can occur as a result of a default in the freezing/thawing process, leading to microcracks in CAA structure as shown in some historical reports when the process was still immature [START_REF] Muller-Schweinitzer | Cryopreservation of vascular tissues[END_REF][START_REF] Pukacki | The mechanical properties of fresh and cryopreserved arterial homografts[END_REF] .

However, after reviewing all cases of postoperative rupture or PA, we observed that among the 17 patients for whom redo surgery was needed, all except one had positive bacterial samples or multiple ruptures, supporting CAA infection rather than mechanical rupture induced by cryopreservation.

CAAs have shown their resistance to colonization by the microorganisms involved in AGI in in vitro [START_REF] Camiade | Optimization of the resistance of arterial allografts to infection: comparative study with synthetic prostheses[END_REF] , in vivo [START_REF] Knosalla | Treatment of vascular graft infection by in situ replacement with cryopreserved aortic allografts: an experimental study[END_REF][START_REF] Koskas | Arteries from human beings are less infectible by Staphylococcus aureus than polytetrafluoroethylene in an aortic dog model[END_REF][START_REF] Litzler | Bacterial resistance of refrigerated and cryopreserved aortic allografts in an experimental virulent infection model[END_REF][START_REF] Moore | The use of fresh tissue arterial substitutes in infected fields[END_REF] and clinical [START_REF] Antonopoulos | Editor's Choice -Cryopreserved Allografts for Arterial Reconstruction after Aorto-Iliac Infection: A Systematic Review and Meta-Analysis[END_REF] studies. But CAA ruptures secondary to persistent infection are poorly defined in the literature.

We did not identify any pathogen that could be more prone to induce rupture, unlike some studies that have identified P. aeruginosa or Candida spp as necrotizing organisms [START_REF] Chakfe | Editor's Choice -European Society for Vascular Surgery (ESVS) 2020 Clinical Practice Guidelines on the Management of Vascular Graft and Endograft Infections[END_REF] . But we showed that infections leading to PA of the native artery, regardless of the microorganism involved, appeared to be associated with a higher risk of early allograft rupture. The systematic collection of data on bacterial phenotypes involved in AGI is a promising field of investigation since some of them could be more likely to induce a disruption of the aortic wall, but unfortunately it was not included in our protocol. From this perspective, a proteomic analysis could be proposed in the future to compare bacterial strains responsible for rupture.

In addition, 8 other patients experienced a rupture or a PA of the CAA, but they occurred 3-10 years after CAA implantation, supporting a degenerating process rather than the consequence of persistent infection. In summary, a recurrence of CAA rupture mainly occurred within six months of surgery and was related to infection recurrence and was found in about 8.5% of our patients. Special care should be taken in case of PA upon presentation, for which a close imaging monitoring is needed during the first 6 months. A duplex ultrasound examination should be performed weekly for the first 6 weeks and then monthly thereafter to early detect a CAA rupture. In case of successive ruptures, allograft explantation combined with prosthetic extra-anatomic bypass should be considered.

The recommended duration of targeted postoperative antibiotherapy varies from 2 weeks to 6 months or even lifelong [START_REF] Chakfe | Editor's Choice -European Society for Vascular Surgery (ESVS) 2020 Clinical Practice Guidelines on the Management of Vascular Graft and Endograft Infections[END_REF] . However, most authors, including us, recommend a 6-week duration [START_REF] Revest | Medical treatment of prosthetic vascular graft infections: Review of the literature and proposals of a Working Group[END_REF] , especially since most (13/17) CAA ruptures occurred during this period.

Harlander-Locke et al. [START_REF] Harlander-Locke | The use of cryopreserved aortoiliac allograft for aortic reconstruction in the United States[END_REF] have found that the partial excision of the infected graft was a significant predictor for failure, confirming our doctrine consisting in systematically resecting all synthetic material and tissues, grossly infected or not, before allografting as recommended [START_REF] Chakfe | Editor's Choice -European Society for Vascular Surgery (ESVS) 2020 Clinical Practice Guidelines on the Management of Vascular Graft and Endograft Infections[END_REF] .

Although the lack of bacteriological confirmation has not been associated with a pejorative predictive factor, effort should be made to avoid it, in order to provide appropriate antibiotherapy [START_REF] Chakfe | Editor's Choice -European Society for Vascular Surgery (ESVS) 2020 Clinical Practice Guidelines on the Management of Vascular Graft and Endograft Infections[END_REF] . In this case, our institutional protocol recommends the use of antibiotics targeting Gram-negative bacillus for 5 days and Gram-positive cocci for 12 days after graft removal. This protocol is based on the bacteriological spectrum we identified.

Mid-term Allograft-Related Complications

Allografts are known to degenerate over time. In our experience as in that of others, late occlusive degeneration is nowadays much more frequent than aneurysmal degeneration (0-11.1% and 0-4.9%, respectively) [START_REF] Harlander-Locke | The use of cryopreserved aortoiliac allograft for aortic reconstruction in the United States[END_REF][START_REF] Bisdas | Eight-year experience with cryopreserved arterial homografts for the in situ reconstruction of abdominal aortic infections[END_REF][START_REF] Brown | Arterial reconstruction with cryopreserved human allografts in the setting of infection: A single-center experience with midterm follow-up[END_REF][START_REF] Touma | In situ reconstruction in native and prosthetic aortic infections using cryopreserved arterial allografts[END_REF][START_REF] Antonopoulos | Editor's Choice -Cryopreserved Allografts for Arterial Reconstruction after Aorto-Iliac Infection: A Systematic Review and Meta-Analysis[END_REF][START_REF] Ahmed | Cryopreserved arterial allografts for in situ reconstruction of abdominal aortic native or secondary graft infection[END_REF] . Our conclusion was that the continuous improvement of the methods for obtaining and preserving CAAs will probably eradicate late aneurysmal degeneration. Even if an occlusive disease is easily treated using endovascular techniques [START_REF] Touma | In situ reconstruction in native and prosthetic aortic infections using cryopreserved arterial allografts[END_REF] , such a high rate remains a concern. Because of the limited life expectancy of patients and the small size of series, the rate of late occlusive degeneration remains imprecise.

In our subgroup of patients still alive at five years, the rate of late occlusive degeneration requiring revision after 6 months was 18% and involved the iliofemoral segment of the CAA in 61.5% of cases. The etiology of late CAA degeneration remains controversial with several theories, including a chronic immune rejection as reported in the arteries of transplanted organs [START_REF] Merola | Recent advances in allograft vasculopathy[END_REF] or a lower resilience to mechanical stress than native tissues as suggested for the mechanisms of late calcification of valvular allografts [START_REF] Schoen | Pathological considerations in replacement cardiac valves[END_REF] . Thus, CAA do not appear as an ideal arterial substitute if their late complications are taken into account.

Nevertheless, in the published studies with the longest follow-up, the 5-year survival rate ranges between 50% and 64% [START_REF] Harlander-Locke | The use of cryopreserved aortoiliac allograft for aortic reconstruction in the United States[END_REF][START_REF] Bisdas | Eight-year experience with cryopreserved arterial homografts for the in situ reconstruction of abdominal aortic infections[END_REF][START_REF] Kieffer | Allograft replacement for infrarenal aortic graft infection: early and late results in 179 patients[END_REF][START_REF] Ahmed | Cryopreserved arterial allografts for in situ reconstruction of abdominal aortic native or secondary graft infection[END_REF][START_REF] Lejay | Cryopreserved Cadaveric Arterial Allograft for Arterial Reconstruction in Patients with Prosthetic Infection[END_REF] . In our study, with a mean survival of 7.6 years, this rate was 57%. Thus, it could be assumed that the sustainability of CAAs is in line with such a survival. Cryopreservation definitely did not prevent the need for late revision surgery, with a rate of 25% at 5 years in our study and of 20% in the study by Harlander-Locke et al. [START_REF] Harlander-Locke | The use of cryopreserved aortoiliac allograft for aortic reconstruction in the United States[END_REF] in 220 patients. The quality of the CAA was also investigated: we concluded that the age of the donor, but also the presence of calcifications were not predictive factors for long-term complications. This result could support an extension of the criteria for artery harvesting in order to compensate the low availability of CAA. However, late revision surgery consists generally in limited "house-keeping" interventions associated with fairly low mortality and morbidity rates.

The limitations of our study include its retrospective design and the inherent inaccuracy that it implies, in particular with regard to antibiotic treatments: as a matter of fact, treatment duration and the precise time between the detection of a microorganism and the initiation of targeted antibiotics were poorly documented. Also, the lack of bacteriological confirmation in 35 patients could have led to an analysis bias due to the inability to administer an adapted antibiotic. In addition, data from patients who were not candidates for surgery were not collected in this study. But non-eligibility criteria were based on patient age and general condition regardless of the septic event, as for any standard aortic surgery. Moreover, the number of patients lost to follow-up could also have induced a bias for the long-term results of CAA.

Conclusion

CAAs provide acceptable results to treat aortic graft infection despite early graft-related reinfections. For that reason, it is recommended to bacteriologically confirm infection before initiating antibiotherapy and to perform a rigorous imaging follow-up. This study showed that this type of surgery is associated with a high morbidity due to patients' comorbidities and surgery invasiveness and a high-volume center is thus needed to performed it. Mid-term allograft-related complications were quite common but associated with low mortality and amputation rates.

Figure Legends

Figure 1 Cumulative Kaplan-Meier estimates with 95% confidence intervals of (A) survival, (B) primary patency, (C) freedom from allograft reintervention, (D) limb salvage after use of cryopreserved abdominal aortic allografts as a substitute for infected prosthetic grafts in 200 patients.

  [1.5-5.5] for 10 years, p=.001), the presence of postoperative acute renal failure (OR = 3.8 [1.3-11.2], p=.014) and the number of transfused blood units (OR = 4.2 [1.8-9.8],

Table 1 :

 1 Preoperative characteristics of 200 patients with aortic graft infection. Data are presented as n (%) or mean ± standard deviation. COPD = Chronic Obstructive

	Pulmonary Disease; PAD= Peripheral Arterial Disease, ASA= American Society of
	Anesthesiologists; PA=Pseudo-aneurysm VGI = Vascular Graft Infection; EVAR =
	endovascular aneurysm repair.

Table 2 :

 2 Microorganisms responsible for infection, identified in local samples (periprosthetic abscess or graft) or blood cultures in 200 patients with aortic graft infection.

	Data are presented as n (%). Sp. = Species.
	*4 with missing data
	† 23 Methicillin-resistant Staphylococcus Aureus

Table 3 :

 3 Peroperative features according to the surgical technique in 200 patients with aortic graft infection. Data are presented as n (%).

	501
		Morbidity -	Deaths -n
		n
	Cardiac	36 (18)
	Myocardial infarction	17	(8.5)
	Cardiac arrhythmia	10	(5)
	Acute pulmonary edema	4	(2)
	Cardiac arrest	3	(1.5)
	Cardiogenic shock	2	(1)
	Pulmonary	45	(22.5)
	Pneumopathy	34	(17)
	Atelectasis	10	(5)
	ARDS	1	(0.5)
	Pulmonary embolism	1	(0.5)
	Digestive	30	(15)
	Ischemic colitis	14	(7)
	Digestive bleeding	5	(2.5)
	Bowel occlusion	4	(2)
	Pancreatitis	4	(2)
	Cholecystitis	3	(1.5)
	Renal	63	(31.5)
	Acute renal failure	49	(24.5)
	Acute renal failure with dialysis	14	(7)
	Septic shock	21	(10.5)
	Hemorrhagic shock	10	(5)
	Multiorgan failure	5	(2.5)
	502

Table 4 :

 4 Morbidity and causes of death during the postoperative in hospital period in 200

	503
	504	patients with aortic graft infection.
	505
	506
	507	Data are presented as n (%). ARDS: Acute Respiratory Distress Syndrome.
	508
	509
	510
	511
	512
	513
	514
	515
	516
	517

Table 5 :

 5 Inpatient complications requiring revision surgery during the postoperative hospital stay after allograft implantation for aortic graft infection in 200 patients. A given patient could experience several complications. Data are presented as n (%).

	Parameters	Univariate analysis		Multivariate analysis
		OR (95% CI)	p value	OR (95% CI)	p value
	No bacteria in samples	*	.006
	Pseudomonas Aeruginosa	2.02 (0.73-5.58)	.22
	MRSA	2.01 (0.68-5.98)	.20
	Candida	3.32 (1.22-9.02)	.023
	Anaerobia	1.33 (0.28-6.46)	.66
	Enterobacteria	2.33 (1.01-5.38)	.043
	Age	2.58 (1.15-5.82)	.019	2.90 (1.53-5.50)	.001
	ASA score	0.03 (0.42-2.07)	.86
	Preoperative antibiotics	0.72 (0.23-2.23)	.56
	Antibiotics		.95
	-Non selective vs	1.19 (0.45-3.13)
	selective
	-No antibiotics vs	0.82 (0.27-2.45)
	selective
	Hypertension	0.85 (0.37-1.95)	.70
	Diabetes	0.67 (0.19-2.39)	.78
	CKD	1.46 (0.54-3.95)	.42
	COPD	1.14 (0.45-2.87)	.78
	Coronaropathy	0.70 (0.27-1.84)	.47
	Emergency surgery	5.4 (1.86-15.7)	.004
	Digestive fistula	2.12 (0.93-4.81)	.070
	Preoperative hemorragy	1.43 (0.44-4.57)	.52
	Clamping level		<.001
	-Infra renal	1
	-Inter renal	0.59 (0.16-2.23)
	-Supra renal	5.10 (1.98-13.10)
	-Coeliac	2.23 (0.42-11.83)
	Intraoperative shock	6.05 (2.5-14.64)	<.001
	Postoperative ARF	3.87 (1.67-8.94)	<.001	3.84 (1.32-11.20)	.014
	Postoperative dialysis	4.12 (1.26-13.4)	.027
	Amputation	1.81 (0.36-9.21)	.62
	Major medical complication	4.56 (1.64-12.7)	<.001
	Preoperative septic shock	4.33 (0.69-27.18)	.14
	Hypogastric reimplantation	2.17 (0.55-8.58)	.38
	Number of transfused blood	4.4 (2.2-8.7)	<.001	4.23 (1.83-9.78)	<.001
	units
	Early revision surgery	3.43 (1.41-8.30)	.011

Table 7 .

 7 Uni-and multivariate analysis of early mortality in 200 patients treated with cryopreserved abdominal aortic allograft for aortic graft infection.

Conflict of Interest/Funding: None Copy editors: please note that only the critical style editing has been made to these tables.

Full copy editing is still needed. I have used green background color to highlight the edits that should be repeated in the following rows in the same column. After having moved the percentages from the last column to the previous column, please delete the last column. Please note that the hierarchy for the first column should be created by italics and indenting, not by bolding the texts.


Gillian Barratt
email: gillian.barratt@cep.u-psud

Philippe Legrand

Comparison of the efficacy and pharmacology of formulations of amphotericin B used in treatment of leishmaniasis

Keywords: Amphotericin B, HIV, leishmaniasis, lipid formulation, resistance Abbreviations: AmB -Amphotericin B, GFP -green fluorescent protein, GM-CSF -

Purpose of the Review

Several lipid-based formulations of the anti-fungal and anti-parasitic drug Amphotericin B are now available on the market. The purpose of this review is to assess their efficacy against leishmaniasis in both experimental and clinical settings, and to point out new developments in the formulation of this antibiotic.

Recent Findings

The development of resistance to pentavalent antimony compounds has shifted the emphasis to amphotericin B for the treatment of visceral leishmaniasis in India. Lipid formulations show good efficacy but are expensive. However, the treatment period with lipid formulations is shorter, which reduces hospitalization costs. As a result, in developed countries where these costs are an important proportion of the treatment, lipid formulations are preferred, whereas they remain largely inaccessible in developing countries. Lipid-associated amphotericin B has been found to be effective for secondary prophylaxis in HIV-positive patients, in studies carried out in European countries bordering the Mediterranean.

Summary

The reduced toxicity of lipid-based formulations of amphotericin B is no longer in doubt. In India, their efficacy against visceral leishmaniasis and shorter treatment periods compared with the conventional formulation with deoxycholate has to be counter-balanced against the very high cost. On the other hand, in developed countries around the Mediterranean, where leishmaniasis occurs mainly in immunocompromised subjects, lipid formulations have become the treatment of choice for visceral disease. On the other hand, the efficacy against cutaneous lesions is variable and in some reports oral miltefosine was active after failure of treatment with amphotericin B.

Introduction

The profile of infection with Leishmania species is changing. Although the disease, in the visceral form known as kala azar, is endemic in India where it represents a major public health problem, it is also becoming increasingly prevalent as an opportunistic infection in Western countries, among individuals who are infected with the HIV virus or are immunocompromised for other reasons (1, 2**). In the latter group, cutaneous and mucocutaneous manifestations are often found. This dichotomy is reflected in the literature which has been published recently.

Immunological Factors

The outcome of Leishmaniasis infection is closely linked to the immunological status of the patient. A mechanistic study by Murray (3*) in various mouse strains lacking different components of the immune system demonstrated the importance of functional T cells (either CD8 + or CD4 + ) in preventing recrudescence in animals in which 90-95% of the parasites had been eliminated by treatment with amphotericin B (as a conventional formulation). Despite the particular immunomodulatory properties of AmB (4), the authors suggest that these observations can be transposed to other forms of antileishmanial chemotherapy.

Taking into account the importance of immunological status, recent clinical results will be discussed according to whether the patients were immunocompromised or not.

Immunocompetent Patients

Recent studies from India have concentrated on pin-pointing the most effective therapeutic regime in the immuno-competent population suffering from kala-azar. A review by Singh and Sivakumar (2**) shows that with the development of resistance to pentavalent antimony compounds the emphasis has shifted to AmB, as reported by two recent trials (5*, 6). The ability of lipid-based formulations of AmB to reduce the substantial toxicity of the conventional form containing deoxycholate is no longer in doubt [START_REF] Aguado | Assessment of nephrotoxicity in patients receiving amphotericin B lipid complex: a pharmacosurveillance study in Spain[END_REF], but the prohibitive cost of these new formulations, combined with the fact that it is not clear that they are as effective as the conventional formulation in curing visceral leishmaniasis, although higher doses can be given. This question of conventional versus lipid formulations of AmB was addressed in a recent study by Sundar et al., (8**) on patients from Bihar state, India. Both a liposomal formulation (AmBisome ® ) and a lipid complex (Abelcet ® ) were tested. The cure rates were essentially similar and the lipid formulations provoked less infusion-related toxicity; however, their extremely high cost was only partly offset by the reduced hospitalisation necessary -5 days at 2mg/kg as opposed to 30 days at 1 mg/kg for the conventional formulation. Several recent review articles underline the lack of toxicity and short treatment cycles of lipid formulations of AmB, while commenting on the cost (9-11**, [START_REF] Murray | Progress in the treatment of a neglected infectious disease: visceral leishmaniasis[END_REF][START_REF] Berman | Recent developments in leishmaniasis: epidemiology, diagnosis, and treatment[END_REF][START_REF] Dupouy-Camet | New drugs for the treatment of human parasitic protozoa[END_REF]. In a European situation, when cost is not such a preponderant issue, lipid-associated amphotericin B has become the treatment of choice, for example in Italy [START_REF] Gradoni | Change in human visceral leishmaniasis treatment in Italy: retrospective study of 630 patients[END_REF].

In developed countries, Leishmaniasis in adults is generally linked to an immunocompromised state. However, a few reports have described cases, both visceral and mucocutaneous in immunocompetent individuals [START_REF] Paradisi | Atypical multifocal cutaneous leishmaniasis in animmunocompetent patient treated by liposomal amphotericin B[END_REF][START_REF] Markle | Cutaneous leishmaniasis: recognition and treatment[END_REF][START_REF] Virgilio | A case of mucocutaneous leishmaniasis[END_REF][START_REF] Ju | Visceral leishmaniasis: a trip to the Greek Islands is not always idyllic[END_REF]. This emphasizes the importance of awareness by general practitioners of this disease as a possible diagnosis in patients who travel for work or leisure, and the necessity for new diagnostic tools (see below).

A recent review has covered the neglected subject of treatment of visceral leishmaniasis in pregnancy [START_REF] Figueiro-Filho | Visceral leishmaniasis (kala-azar) and pregnancy[END_REF]. AmB is recommended as the first choice drug because of lower side-effects. In particular, lipid-associated AmB has been shown to have no adverse effects on the foetus [START_REF] Pagliano | Visceral leishmaniasis in pregnancy: a case series and a systematic review of the literature[END_REF].

As far as infantile visceral leishmaniasis is concerned, epidemiological features studied over a 5 year-period in a Brazilian endemic area showed this infection is mainly associated with underprivileged people with a tendency towards urban areas [START_REF] Queiroz | Visceral leishmaniasis: clinical and epidemiological features of children in an endemic area[END_REF]. In this region Glucantime is used in 98% of the cases. On the other hand, in the Mediterranean area (Greece, Italy and France) all the long-term studies have revealed that amphotericin B lipid formulations are safe and effective and improve the comfort of patients by reducing hospitalisation without increasing of the overall cost of treatment (22**, [START_REF] Cascio | A 6 day course of liposomal amphotericin B in the treatment of infantile visceral leishmaniasis: the Italian experience[END_REF][START_REF] Minodier | First-line liposomal amphotericin B for pediatric visceral leishmaniasis in southern France[END_REF]. In Greece 4 mg/kg/day for 5 days, 4 mg/kg/day on day 1-5 and 9, 5 mg/kg/day for 4 days or 10mg/kg/day for 2 days with liposomal AmB are as effective as pentavalent antimony in all infants and are preferable to antimonate (20 mg/kg/day for 21 days) (22**). In Italy and in France six doses of 3mg/kg of liposomal AmB on days 1-5 and 10 have been the first-line treatments of infantile visceral leishmaniasis for 10 years. A two-day regimen with 10 mg/kg or even 20 mg/kg would have been be preferable, although allergic reactions to the infusion forced the patients to be hospitalized for 7 days. These allergic reactions seem to be caused by the lipid. AmB lipid complexes have higher AmB/lipid ratios than AmB liposomes. It therefore might be worthwhile testing AmB lipid complexes at higher doses, to see whether cures can be achieved quickly without allergic reactions.

Immunocompromised Patients

The diagnosis and management of Leishmania/HIV co-infection is a major concern [START_REF] Sinha | Diagnosis and management of leishmania/HIV co-infection[END_REF]. In these immunocompromised patients, visceral disease may relapse as cutaneous manifestations [START_REF] Calza | Disseminated cutaneous leishmaniasis after visceral disease in a patient with AIDS[END_REF]. Recent results obtained with lipid-associated AmB in cases of co-infection have been variable.

In India, responses to AmB, in conventional or lipid formulations, as to antimony compounds, have been limited [START_REF] Sinha | Diagnosis and management of leishmania/HIV co-infection[END_REF]. On the other hand, treatment with oral miltefosine was promising. However, a case study [START_REF] Pandey | Nexus of infection with human immunodeficiency virus, pulmonary tuberculosis and visceral leishmaniasis: a case report from Bihar, India[END_REF] reported that AmB was effective in a triple infection with HIV, pulmonary tuberculosis and visceral leishmaniasis.

A case of cutaneous leishmaniasis in an African migrant infected with HIV did not respond to AmB in either the conventional or liposomal form, but was cured by oral miltefosine [START_REF] Schraner | Successful treatment with miltefosine of disseminated cutaneous leishmaniasis in a severely immunocompromised patient infected with HIV-1[END_REF]. On the other hand, a patient from Italy who developed cutaneous lesions after an initial visceral disease was cured by liposomal AmB [START_REF] Calza | Disseminated cutaneous leishmaniasis after visceral disease in a patient with AIDS[END_REF]. A report from Brazil has also shown the efficacy of lipid formulations of AmB in cutaneous disease [START_REF] Amato | Successful treatment of cutaneous leishmaniasis with lipid formulations of amphotericin B in two immunocompromised patients[END_REF]. An HIV-positive patient was treated with Amphocil, while another who had undergone a kidney transplant was treated with AmBisome ® . The combination of liposomal AmB with GM-CSF to boost the immune system has been found beneficial in one study [START_REF] Mastroianni | Liposomal Amphotericin B and rHuGMCSF for treatment of visceral leishmaniasis in AIDS[END_REF].

Two recent studies have investigated the use of lipid formulations of AmB for secondary prophylaxis in HIV-infected patients. A multicentre study in Spain and Portugal compared treatment with AmB lipid complex (Abelcet ® , 3 mg/kg every 3 weeks for 51 weeks) with no treatment in HIV-positive patients who had previously experienced at least one episode of leishmaniasis but were currently parasite-free. They concluded that the treatment with lipidassociated AmB was effective in preventing recurrence of visceral leishmaniasis and was well tolerated (31**). Another study, from Marseille, France, has investigated the use of liposomal AmB for prevent relapse of visceral leishmaniasis in HIV-infected patients [START_REF] Montana | Liposomal amphotericin B in secondary prophylaxis of visceral leishmaniasis in HIV-infected patients: report of five clinical cases[END_REF]. Although the number of evaluable patients was low, they concluded that a successful outcome depended on using a high initial dose (cumulative doses ranging from 60 to 86 mg/kg at day 30), higher than those recommended by the manufacturers, to avoid therapeutic escape.

As referred to above, kidney transplant patients are also at risk of developing leishmaniasis, which poses a diagnostic and therapeutic challenge to the clinician [START_REF] Maggi | Leishmaniasis in patients with chronic renal failure: a diagnostic and therapeutic challenge for the clinician[END_REF]. In this category, liposomal AmB was found to be both better tolerated and more effective than AmB lipid complex. Visceral leishmaniasis has also been described as an opportunistic infection in bonemarrow-transplant patients [START_REF] Sirvent-Von Bueltzingsloewen | Visceral leishmaniasis: a new opportunistic infection in hematopoietic stem-cell-transplanted patients[END_REF] and in connective tissue disease [START_REF] Castellino | Visceral leishmaniasis complicating a connective tissue disease: three case reports from Italy[END_REF].

Drug Resistance

The possibility of developing drug resistance to AmB is discussed by Ouellette et al, (36**) citing in-vitro work by Mbongo et al. (37). For this reason, it is recommended that dogs carrying Leishmania parasites in the Mediterranean area should not be treated systematically with AmB [START_REF] Oliva | Canine leishmaniasis: evolution of the chemotherapeutic protocols[END_REF].

A recent study has looked at the drug sensitivity of Indian kala-azar field isolates in experimental models (mouse macrophages infected in vitro and hamsters, 39*). The sensitivity to pentavalent antimonials was retained after repeated passages in vitro and in vivo, showing that the unresponsive strains showed true resistance. These strains were sensitive to both AmB (used as the conventional formulation) and miltefosine.

New Perspectives

Maesabalide III, an oleane triterpene saponin isolated from the Vietnamese plant Maesa balansae with antileishmanial activity has been evaluated in vivo against Leishmania donovani (MHOM/ET/67/L82)-infected golden hamsters after one single subcutaneous dose as compared with liposomal AmB as a reference (40*). Prophylactic and curative administration at 0.2 mg/kg and 0.8 mg/kg respectively were as efficient as AmBisome in reduction of liver amastigotes burdens. Multiple dose treatments should now be tested to determine whether a better clinical protection can be obtained with this interesting new drug.

In the search for new delivery systems for AmB, hydrophilic albumin microspheres of AmB were also evaluated in Leishmania infantum infected hamsters (41, 42). These formulations did not show any signs of toxicity for single injected doses up to 40mg/kg. They led to higher drug levels in spleen and liver as compared with free AmB and a greater reduction of the parasite burdens in these organs at both early and later stages of infection. These new delivery systems would be economical alternative to liposomes for the treatment of visceral leishmaniasis if they demonstrate their efficacy and their tolerance as compared with liposomal amphotericin B.

An article from the same group demonstrates how the physical state of AmB can influence toxicity and activity [START_REF] Sanchez-Brunete | Amphotericin B molecular organization as an essential factor to improve activity/toxicity ratio in the treatment of visceral leishmaniasis[END_REF]. A formulation which organized AmB as large aggregates (detected by spectrophotometric techniques) was less toxic than AmB complexed with cyclodextrin in a monomolecular form, which released the drug rapidly. The multi-aggregate form was also slightly more effective against Leishmaniasis than the conventional formulation; however, no comparison was made with lipid formulations.

LicTXNPx, a recombinant protein conserved among different Leishmania species, was identified as a possible new marker for diagnosis and for monitoring the efficacy of treatment. In fact the results of a Portuguese study [START_REF] Santarem | Antibodies against a Leishmania infantum peroxiredoxin as a possible marker for diagnosis of visceral leishmaniasis and for monitoring the efficacy of treatment[END_REF] showed that this protein presented the highest immunoreactivity and the evolution of the production of antibodies against LicTXNPx followed the evolution of the number of parasites even during the treatment with AmB or antimoniate. It is now necessary to determine whether these results, which were obtained with a group of 36 children, can be extended to a wider population.

Dube et al. (39*) have developed an interesting technique for the in-vitro evaluation of drug sensitivity. Leishmania parasites were transfected with the GFP gene. The green fluorescent labelling allowed their survival as amastigotes within mouse macrophages to be monitored easily. In general, the amastigote form of the parasite living within macrophages is considered to be a more relevant disease model for drug screening that the free-living promastigote form.

Conclusion

The use of lipid formulations of AmB to treat leishmaniasis is now more a question of economics than efficacy. There is still room for the development of new formulations which could reduce the cost of treatment. Apart from one report in 2003 [START_REF] Kayser | Formulation of amphotericin B as nanosuspension for oral administration[END_REF], there have been no recent studies of formulations which could increase the efficacy of AmB by the oral route, although such a formulation would be a considerable breakthrough in treatment.


Ravi Pathak
email: ravipathak51189@gmail.com

U Dadwal

A K Kapoor

Maxim Vallet

Alain Claverie

R Singh

Study of surface exfoliation induced by hydrogen implantation and annealing in GaSb (100) substrates

Keywords: Hydrogen, Implantation, GaSb, Strain, Exfoliation

We investigate the surface blistering/exfoliation in H-implanted GaSb (100) substrates.

Samples were implanted by 50 keV hydrogen ions with fluence of 5 × 10 16 and 1 × 10 17 ions/cm 2 at room temperature. Post-implantation annealing studies were carried out up to 300 ºC to observe surface blistering. For the samples implanted with fluence 5 × 10 16 ions/cm 2 , annealing showed no sign of surface blistering. However, post-implantation annealing at 200 ºC for 2 min resulted in surface blistering for the samples implanted with fluence 1 × 10 17 ions/cm 2 . Exfoliation of the surface in the form of craters was observed for 1 × 10 17 ions/cm 2 implantation case which was quantified using various parameters. Interestingly, surface exfoliation over large area was observed for both fluences after post-implantation annealing.

High resolution X-ray diffraction studies of the H-implanted samples showed the existence of damage-induced strain and its dependence on the hydrogen fluence. Microstructural investigations of the damage region have been carried out using cross-sectional transmission electron microscopy. The width of the damage region and the formation of microstructures were found to depend on the fluence of hydrogen ions which eventually guides the surface blistering/exfoliation.

Introduction

Hydrogen (H) implantation in semiconductor materials has various applications in the microelectronic industry. One such application is the passivation of defects and the fine tuning of their electrical properties [START_REF] Pankove | Hydrogen in semiconductors[END_REF]. Hydrogen implantation is also used in the ion-cut process to transfer thin crystalline layers from a H-implanted substrate onto another host material [START_REF] Bruel | Silicon on insulator material technology[END_REF][START_REF] Tong | Wafer Bonding and Layer Splitting for Microsystems[END_REF][START_REF] Christiansen | Wafer Direct Bonding: From Advanced Substrate Engineering to Future Applications in Micro/Nanoelectronics[END_REF].

In principle, it could be used for the heterogeneous integration of compound III-V semiconductors on a silicon platform for opto-electronic applications [START_REF] Singh | Investigation of helium implantation induced blistering in InP[END_REF][START_REF] Dadwal | Blistering study of H-implanted InGaAs for potential heterointegration applications[END_REF]. In this context, gallium antimonide (GaSb) is interesting because many compound semiconductors whose bandgap lies between 0.3 and 1.58 eV can be easily matched on its crystalline lattice [START_REF] Dutta | The physics and technology of gallium antimonide: An emerging optoelectronic material[END_REF]. Such GaSb/SiO2/Si based substrates would be perfect for fabricating high frequency devices, laser diodes and infrared detectors [START_REF] Akahane | Heteroepitaxial growth of GaSb on Si(0 0 1) substrates[END_REF][START_REF] Aifer | W-structured type-II superlattice long-wave infrared photodiodes with high quantum efficiency[END_REF][START_REF] Longenbach | Molecular beam epitaxy of GaSb[END_REF]. Up to now, most of such structures are grown on semiinsulating gallium arsenide (GaAs) substrates [START_REF] Brar | Spiral growth of GaSb on (001) GaAs using molecular beam epitaxy[END_REF][START_REF] Graham | Growth of GaSb on GaAs substrates[END_REF]. The large lattice mismatch of ~7% between GaSb and GaAs inevitably results in high dislocation densities at the GaSb/GaAs interface [START_REF] Brar | Spiral growth of GaSb on (001) GaAs using molecular beam epitaxy[END_REF][START_REF] Graham | Growth of GaSb on GaAs substrates[END_REF]. To overcome the lattice mismatch problem, several attempts have been made including the use of low temperature buffer layers [START_REF] Ivanov | Molecular beam epitaxy growth and characterization of thin (<2 mu m) GaSb layers on GaAs (100) substrates[END_REF][START_REF] Chidley | Photoluminescence of GaSb grown by metal-organic vapour phase epitaxy[END_REF]. The ion-cut process could be an alternative approach to solve the issue by directly transferring high quality GaSb layers with controlled thickness onto silicon wafers.

Today, the ion-cut process is being used to fabricate most of the silicon-on-insulator (SOI) wafers sold on the planet [START_REF] Bruel | Silicon on insulator material technology[END_REF][START_REF] Tong | Wafer Bonding and Layer Splitting for Microsystems[END_REF][START_REF] Christiansen | Wafer Direct Bonding: From Advanced Substrate Engineering to Future Applications in Micro/Nanoelectronics[END_REF]. Thus, the mechanism leading to the fracture of the material is well understood in silicon [START_REF] Höchbauer | Physical mechanisms behind the ion-cut in hydrogen implanted silicon[END_REF][START_REF] Nastasi | Nucleation and growth of platelets in hydrogen-ion-implanted silicon[END_REF][START_REF] Huang | Onset of blistering in hydrogen-implanted silicon[END_REF][START_REF] Grisolia | A transmission electron microscopy quantitative study of the growth kinetics of H platelets in Si[END_REF]. Hydrogen ions are implanted with doses and energies so that the hydrogen concentration reaches a few percent at the projected range of the ions. The hydrogen ions induce damage in the crystal lattice, initially as vacancies and interstitials which recombine during and following implantation at room temperature until stable complexes are formed [START_REF] Nastasi | Nucleation and growth of platelets in hydrogen-ion-implanted silicon[END_REF][START_REF] Grisolia | A transmission electron microscopy quantitative study of the growth kinetics of H platelets in Si[END_REF]. During post-implantation annealing, these complexes transform and precipitate in the form of nanometer-size platelets which further grow in size by Ostwald ripening and finally coalesce to form highly hydrogen pressurized micrometer-size cracks parallel to the wafer surface [START_REF] Huang | Onset of blistering in hydrogen-implanted silicon[END_REF][START_REF] Weldon | On the mechanism of the hydrogen-induced exfoliation of silicon[END_REF]. If the implantation depth is not too large, the surface can elastically relax the stress exerted by the hydrogen pressure inside the cavities. This gives rise to the appearance of blisters on the surface [START_REF] Huang | Onset of blistering in hydrogen-implanted silicon[END_REF]. If the surface cannot relax this stress, because of its too large amplitude or because the cavities are too deep below the surface, cracks propagate parallel to the surface, eventually lifting off the top surface and leaving craters on the surface [START_REF] Reboh | Localized exfoliation versus delamination in H and He coimplanted (001) Si[END_REF]. This is called layer exfoliation. The possibility to form blisters and exfoliate the material is admitted to be a prerequisite condition for the successful application of the ioncut process of some material [START_REF] Lee | Effects of hydrogen implantation temperature on ion-cut of silicon[END_REF][START_REF] Moutanabbir | Narrow fluence window and giant isotope effect in low-energy hydrogen ion blistering of silicon[END_REF]. Indeed, in this process a "handle" wafer is bonded onto the implanted surface before annealing. Acting as a stiffener, it prevents the implanted material to elastically relax the stress generated by the cavities and favors crack formation and propagation until fracture of the whole wafer occurs [START_REF] Tong | Wafer Bonding and Layer Splitting for Microsystems[END_REF][START_REF] Christiansen | Wafer Direct Bonding: From Advanced Substrate Engineering to Future Applications in Micro/Nanoelectronics[END_REF]. This is why most research aimed at investigating the possibility of transferring new materials using the ion-cut process starts with the study of blistering/exfoliation phenomena. This work focuses on the study of hydrogen implantation and annealing induced surface exfoliation for the GaSb single crystalline substrate.

The conditions required for the transfer of high quality GaSb layers using the ion-cut process have not been much explored so far. Hobart and Kub showed that thin films of GaSb could be transferred onto insulating substrates using H-implantation in combination with direct wafer bonding [START_REF] Hobart | Transfer of GaSb thin film to insulating substrate via separation by hydrogen implantation[END_REF]. Subsequently, Zheng et al. also performed H implantation-induced blistering/splitting studies in GaSb. The implantation involved 150 keV H + ions at a fluence of 5.5 × 10 16 cm -2 [START_REF] Zheng | Transfer of n-type GaSb onto GaAs substrate by hydrogen implantation and wafer bonding[END_REF]. In our preliminary work, we reported on surface blistering and exfoliation over regions of few micrometers in diameter in H-implanted GaSb [START_REF] Pathak | Study of hydrogen implantation-induced blistering in GaSb for potential layer transfer applications[END_REF]. Post-implantation annealing temperature and duration of annealing was varied from 200 to 500 °C and 1 minute to 80 minutes, respectively. This resulted in surface blisters of sizes 10 -20 µm along with exfoliation extended over tens of micrometer area [START_REF] Hobart | Transfer of GaSb thin film to insulating substrate via separation by hydrogen implantation[END_REF][START_REF] Zheng | Transfer of n-type GaSb onto GaAs substrate by hydrogen implantation and wafer bonding[END_REF][START_REF] Pathak | Study of hydrogen implantation-induced blistering in GaSb for potential layer transfer applications[END_REF]. However, large surface area exfoliation, which is one of the favorable requirements for layer transfer, has not been reported so far. Also, there is no report available in the literature on different characteristics of the GaSb implanted layers which determine the efficiency and quality of the process. Thus, in the present work, we report on the influence of the implanted fluence onto the strain, onto the nature of microstructural damage resulting from ion implantation and annealing and finally, on blistering/exfoliation phenomena in GaSb.

Experimental 2-inch in diameter p-type Si doped (100) GaSb wafers were purchased from Wafer World, Inc.

USA. They were diced to quarter size samples and implanted with 50 keV hydrogen ions at fluences of 5 × 10 16 or 1 × 10 17 ions/cm 2 . H-implantation was carried out at room temperature (RT) with a current density of 10 µA cm -2 . The sample surface normal was set ~7° off the hydrogen ion beam to minimize ion channeling [START_REF] Plummer | Silicon VLSI Technology[END_REF]. Post-implantation annealing was carried out in air using a box type furnace in the 200-400 °C range and for times ranging from 1 to 30 min [START_REF] Zheng | Transfer of n-type GaSb onto GaAs substrate by hydrogen implantation and wafer bonding[END_REF][START_REF] Pathak | Study of hydrogen implantation-induced blistering in GaSb for potential layer transfer applications[END_REF]. The surface topography of the samples was investigated using an optical microscope (Nikon ECLIPSE LV100D) in Nomarski contrast mode and an atomic force microscope (AFM) from Bruker (Dimension Icon) in contact mode. The physical dimensions of the blisters were measured using a stylus surface profilometer (KLA-Tencor). The depth profile of the implanted hydrogen ions was measured by secondary ion mass spectroscopy (SIMS) using a CAMECA IMS 4F. The strain in the as-implanted sample was measured using high resolution X-ray diffraction (HRXRD). For that, triple-axis diffraction (TAD) 2θ/ω was carried out around the (004) Bragg peak using a Philips X'Pert PRO diffractometer.

Microstructural investigations were carried by cross-sectional transmission electron microscopy (XTEM) using an aberration-corrected FEI TECNAIF20, equipped with an FEG source. Samples were prepared by focused ion beam (FIB) techniques using a FEI Helios Nanolab 600 dual-beam FIB and SEM.

Results and discussion

The implantation of hydrogen ions in semiconductors gives rise to various defects and damages the crystal lattice [START_REF] Daghbouj | Effect of the order of He + and H + ion co-implantation on damage generation and thermal evolution of complexes, platelets, and blisters in silicon[END_REF][START_REF] Personnic | Impact of the transient formation of molecular hydrogen on the microcrack nucleation and evolution in H-implanted Si (001)[END_REF]. After post-implantation annealing, these defects rearrange themselves in such a way to cause blistering/exfoliation of the implanted semiconductor wafers. Thus, the study of these defects in the as-implanted state becomes important. To understand the effect of hydrogen implantation in GaSb, the current study has been divided into two parts; (i) as-implanted and (ii) post-implantation annealing study of hydrogen implanted GaSb.

As-implanted study of hydrogen implanted GaSb Fig. 1 shows the depth-distribution of hydrogen obtained by SIMS in the sample implanted with 1 × 10 17 H + /cm -2 . The maximum hydrogen concentration is 3.25 × 10 21 atom/cm 3 at a depth of ~ 410 nm from the sample surface. The area under the SIMS profile, which represents the fluence of hydrogen actually implanted within GaSb, was found to be approximately equal to the hydrogen fluence to which the material was submitted, indicating that there was no fluence loss of hydrogen ions during or after implantation. The energy of the H-implanted ions decides the projected range of ions inside the material. Fig. 2 shows the result of the Monte Carlo simulation of this implantation using the Stopping and Range of Ions in Matter (SRIM) code [START_REF] Ziegler | The Stopping and ranges of Ions in Matter[END_REF]. The simulation predicts about the same concentration of hydrogen but at a slightly larger depth (~ 440 nm) than measured by SIMS. The damage profile, which represents the distribution of point defects initially generated by the implant, has its maximum at a slightly shallower depth ( ~390 nm from the top of the H-implanted surface). the two samples were carried out in the as-implanted state. Fig. 3 shows a set of cross-sectional TEM images of the sample implanted at a fluence of 5 × 10 16 . Fig. 3a is a bright field image taken under dynamical diffraction conditions. Under such conditions, the black regions in the image denote the strain fields generated by the defects resulting from the implantation. A "damage band" containing these defects is found centered at a depth of about 420 nm from the top of the surface and extends over a width of about 115 nm. Fig. 3b is a high magnification image of the same sample but taken under out-of-Bragg, out-of-focus conditions, suitable for the detection of gas-filled objects through the Fresnel contrast they generate in the image [START_REF] Grisolia | A transmission electron microscopy quantitative study of the growth kinetics of H platelets in Si[END_REF].

This image shows alignments of nano-bubbles and the presence of platelets and nano-cracks, 50 to 80 nm in diameter, preferably at the bottom of the damage band (mean depth 460 nm), both aligned parallel to the surface. Fig. 4a is a bright field image of the sample implanted at 1 × 10 17 ions/cm 2 . The damage band has substantially increased in width, now at about 190 nm, but is centered at a shallower depth than it was. In other words, when increasing the fluence, the damage band has extended more on its surface side than on its deep side. Fig. 4b shows that the damage band is filled with platelets and alignments of nano-bubbles. Numerous nanocracks are visible, confined at the very bottom of the damage band. Some of them have visibly coalesced, forming larger cracks more or less parallel to the wafer surface. Still, the material is not fractured as there exist regions between the cracks which are not delaminated.

The implantation of hydrogen ions generates defect complexes that lead to the distortion or strain in the lattice (Modelling of point defect complex formation and its application to H+ ion implanted silicon, N. Cherkashin et al., Acta Materialia 99 (2015) 187-195). HRXRD investigations have been carried out to determine the effect of fluence on the strain and thereby on blistering or exfoliation in H-implanted GaSb. A TAD 2θ/ω scan was carried out around (004) Bragg peak. Fig. 5 shows the XRD profiles we have recorded on these samples around Commenté [c1]: In silicon, it is demonstrated that strain is mostly generated by HnVm complexes. VH4 and V2V6 are the most efficient to generate strain. their (004) Bragg peaks, normal to the wafer surfaces. For the pristine GaSb, a sharp peak is observed at the characteristic angle 𝜃 = 60.72º. For the implanted samples, this peak has shifted toward 𝜃 = 60.32 º and 60.24º, for the samples implanted at 5 × 10 16 and 1 × 10 17 ions/cm 2 , respectively. These negative shifts demonstrate the deformation of the implanted layers, which increases with the fluence. Reboh. et al. [START_REF] Reboh | Orientation of H platelets under local stress in Si[END_REF] and more recently, Cherkashin et al. have discussed in detail this behaviour in H-implanted silicon [START_REF] Cherkashin | Impact of He and H relative depth distributions on the result of sequential He + and H + ion implantation and annealing in silicon[END_REF]. Following implantation, numerous defect complexes are formed. Their overall effect is to put the implanted layer under compression. As in pseudomorphic heterostructures, this stress cannot relax in-plane and the material thus reacts by generating an out-of-plane (perpendicular to the wafer surface) tensile strain, 𝜀 = ∆ , where d is the interplanar spacing between (004) planes and ∆𝑑 is the change in this interplanar spacing due to H-induced damage. From the experimentally observed shifts of the Bragg's peaks, we find 𝜀 ~ 0.65 % and ~ 0.79 % for the samples implanted with 5 × 10 16 and 1 × 10 17 H + /cm 2 , respectively. Assuming the material is isotropic, the in-plane compressive stresses at the origin of these strains can be calculated from the relation, σxx = -2µ ∆ , where µ is the shear modulus of the material [START_REF] Reboh | Orientation of H platelets under local stress in Si[END_REF]. Taking µ = 24.1 GPa for GaSb, we get in-plane compressive stresses of -482 and -578 MPa for the two respective fluence values. Moreover, the full width at half maximum (FWHM) of the damage peak, which is an indication of the width of the damage region, also increases with the fluence, from 0.042 to 0.065 and is in agreement with the TEM observations.

Post-implantation annealing study of hydrogen implanted GaSb

Surface blistering is a complex phenomenon and is required to observe layer splitting in Himplanted semiconductors. H-induced blistering depends on various implantation parameters such as ion fluence and implantation temperature [START_REF] Li | Effect of implantation temperature on exfoliation of H2 + -implanted Si[END_REF][START_REF] Moutanabbir | The fluence effect in hydrogen-ion cleaving of silicon at the sub-100-nm scale[END_REF][START_REF] Dadwal | Effect of implantation temperature on the H-induced microstructural damage in AlN[END_REF]. Post-implantation annealing parameters viz temperature and time also affect the surface blistering [START_REF] Pathak | Study of hydrogen implantation-induced blistering in GaSb for potential layer transfer applications[END_REF][START_REF] Dadwal | Effect of implantation temperature on the H-induced microstructural damage in AlN[END_REF]. Thus, both these post-implantation parameters have been varied to study the surface blistering of GaSb samples. Fig. 6a and6b show optical images of the surfaces of the GaSb samples implanted with 5 × 10 16 H + /cm -2 after annealing at 200 ºC for 2 and 5 min, respectively. Though annealing was expected to result in surface blistering however, we observed large area surface exfoliation as can be seen in fig 6a. Increasing the annealing time to 5 min finally resulted in the total exfoliation of the implanted layer. Fig. 7a, 7b, 7c and7d show the optical images of the GaSb samples implanted with 1 × 10 17 cm -2 after isothermal annealing at 200 ºC for 2, 5, 10 and 30 min, respectively. After 2 min annealing, blisters are seen on the surface with diameters and heights in the 2 to 10 µm and 30 to 90 nm ranges, respectively, as measured by profilometry (Fig. 7a). Moreover, in a few places, craters are also observed with sizes ranging from 10 to 50 µm. These craters are thought to result from the exfoliation of the material due to the coalescence of a group of blisters. When increasing the annealing time, the craters get distributed uniformly over the surface while their density increases (Fig. 7b, 7c and 7d)), visibly at the expense of the surface region.

Fig. 8a is an AFM image obtained in contact mode of the edge of a surface crater (see red circle in Fig. 7a). Fig. 8b is a line-scan extracted from this image. This scan shows that the edge of the crater is somehow curved upward and that the distance between the top edge and the bottom of the crater is of about ~ 474 nm. This compares well with the depth at which the nanocracks have been detected by XTEM in the as implanted sample (see Fig. 4b).

Alternatively, Fig. 9a, 9b, 9c and 9d show the optical images of the GaSb samples after 10 min isochronal annealing at 200, 225, 250 and 300 ºC, respectively. These figures show that the percentage of the surface which is exfoliated increases with the annealing temperature. Thus, exfoliation behavior of the H-implanted GaSb was assessed as a function of annealing temperature. To quantify this aspect, we have defined three characteristic parameters: (i) exfoliation efficiency (𝐴 ); defined as 𝐴 (%) = 𝐴 𝐴 × 100, where 𝐴 is the total exfoliation area obtained by sum of the individual exfoliated areas and 𝐴 is the total area of the image, (ii) mean exfoliation area (𝑆 ); defined as 𝑆 = 𝐴 𝑁 ⁄ , where 𝑁 is the total number of the individual exfoliation areas measured in the image, and (iii) exfoliation density (𝐷 ); defined as 𝐷 = 𝑁 𝐴 ⁄ [START_REF] Woo | Blistering/exfoliation kinetics of GaAs by hydrogen and helium implantations[END_REF]. These parameters were calculated from the images obtained from the Nomarski optical microscopy and the corresponding results are given in Table 1. For each annealing temperature, different regions of the exfoliated areas were selected to calculated these parameters. It was found out that with the increase in the annealing temperature, the exfoliation efficiency A and the mean exfoliation area S increased (see Table 1). However, the exfoliation density D first increases and reaches a value of 0.082 for 225 ºC and then decreases. This could be due to the implanted hydrogen which nucleates the implantation-induced cavities in the damage region. The increase in the exfoliation efficiency A and the mean exfoliation area S with the annealing temperature is related to the concentration of hydrogen atoms within these Hinduced cavities inside the damage region. Reboh et al. reported that with the increase in the annealing temperature, the internal pressure within the cavities increases which results in the coalescence of neighboring cavities [START_REF] Reboh | H-induced subcritical crack propagation and interaction phenomena in (001) Si using He-cracks templates[END_REF]. When the pressure inside cavities is high enough, the exfoliation of the top surface occurs in the form of surface craters. However, for annealing at temperature 300 ºC, large area exfoliation of the top surface was observed (Fig. 9d). Also, the exfoliation of the top surface for the implantation with fluence 5 × 10 16 ions/cm 2 occurs at 200 ºC for 5 min. On the other hand, for the implantation with fluence 1 × 10 17 ions/cm 2 , exfoliation was observed at a higher temperature of 300 ºC for 10 min. This could be due to the formation of the narrow damage band in the case of implantation with fluence 5 × 10 16 ions/cm 2 . Hinduced defects generated are distributed in a narrow damage region and upon postimplantation annealing, hydrogen is released from the H-induced defects complexes and accumulates inside the extended defects (platelets). Consequently, platelets grow to form nanocracks and eventually lead to the formation of large cracks parallel to the H-implanted surface which resulted in surface exfoliation after post-implantation annealing at a lower temperature.

Conclusion

In

  conclusion, we have investigated the blistering/exfoliation in the H-implanted GaSb as a function of ions fluence. Samples implanted with fluence of 5 × 10 16 ions/cm 2 showed exfoliation of the top surface after post-implantation annealing at 200 ºC for 5 min. However, for the samples implanted with fluence 1 × 10 17 ions/cm 2 , exfoliation of the surface along with craters was observed after post-implantation annealing at 300 ºC for 10 min. The exfoliation behavior of the H-implanted samples with annealing temperature was investigated using three parameters: exfoliation efficiency, mean exfoliation area and exfoliation density. It was observed that the exfoliation efficiency and mean exfoliation area increase with the increase in annealing temperature. HRXRD showed the dependence of H-induced strain on the fluence of implanted ions. Damage-induced strain was found to be more in the case of implantation with fluence 1 × 10 17 ions/cm 2 . Microstructural investigation revealed the formation of damage region decorated with extended defects in the form of platelets of size between 50 and 80 nm for fluence 5 × 10 16 ions/cm 2 and nanocracks formation for fluence 1 × 10 17 ions/cm 2 . The width of the damage region was found to be less in the case of H-implantation for the fluence 5 × 10 16 ions/cm 2 . This resulted in narrow distribution of the defects within the damage region resulting blistering after post-implantation annealing and eventually exfoliation of the top surface.

Fig. 1

 1 Fig. 1 Experimental depth-distribution (SIMS profile) of hydogen after 1 × 10 17 H + /cm 2 , 50 keV ion implantation into GaSb.

Fig. 2

 2 Fig. 2 Monte Carlo simulations of the ion and damage profiles (SRIM code) resulting from 50 keV H + ions in GaSb sample.

Fig. 3

 3 Fig. 3 (a) Cross-sectional TEM image of the GaSb sample implanted with 50 keV H + ions with the fluence of 5 × 10 16 ions/cm 2 . (b) high magnification cross-sectional TEM image of the damage region.

Fig. 4

 4 Fig. 4 (a) Cross-sectional TEM image of GaSb sample implanted with 50 keV H + ions with the fluence of 1 × 10 17 ions/cm 2 . (b) The high magnification cross-sectional TEM image of the damage region.

Fig. 5 20 Fig. 6

 5206 Fig. 5 HRXRD of the pristine GaSb sample and the H-implanted samples with fluence 5 × 10 16 ions/cm 2 and 1 × 10 17 ions/cm 2 , respectively. A triple-axis diffraction (TAD) 2θ/ω scan was carried out around (004) Bragg peak.

Fig. 7 Fig. 8 (Fig. 8

 788 Fig. 7 Nomarski optical images of the GaSb samples after post-implantation annealing at 200 ºC for (a) 2 min, (b) 5 min, (c) 10 min, and (d) 30 min. H-implantation was carried out at room temperature with ions fluence of 1 × 10 17 ions/cm 2 .

Table . 1

 . . Exfoliation efficiency A , mean exfoliation area S and the exfoliation density D for the GaSb samples implanted with 50 keV hydrogen ions for a fluence of 1 × 10 17 cm -2 at room temperature. The samples were annealed at 200, 225, 250 and 300 ºC for 10 min, respectively.

	Annealing Temperature	𝑨 𝐞𝐱	𝑺 𝐞𝐱	𝑫 𝐞𝐱
	(ºC)		(µm 2 )
	200	42%	5.25	0.076
	225	52%	6.10	0.082
	250	58%	8.75	0.069
	300	100%	NA	NA

Acknowledgments

The authors would like to acknowledge the Nanoscale Research Facility (NRF), Indian Institute of Technology Delhi, New Delhi for supporting this work.


Rémy Hosseinkhan Boucher

Amine Saibi

Michele Alessandro Bucci

Onofrio Semeraro

Lionel Mathelin

EXPLORATION STRATEGIES FOR CONTROL OF CHAOTIC DYNAMICAL SYSTEMS USING REINFORCEMENT LEARNING

Numerous research efforts have been devoted to the application of control theory to fluid flows in the last decades. Common approaches consist of reduced order models of the original system, often within the linear limit, for enabling the control design based on standard control theory. However, these approximated representations are often the main limitation of standard applications, as these control techniques usually exhibit poor performance when applied in off-control design conditions; an example is provided by the impact that non-linearities have on the dynamics of the closed-loop when neglected [START_REF] Sipp | Linear Closed-Loop Control of Fluid Instabilities and Noise-Induced Perturbations: A Review of Approaches and Tools[END_REF].

REINFORCEMENT LEARNING

An alternative is represented by fully data-driven methods where a physical model is not employed; Reinforcement Learning (RL) algorithms allow such a strategy while preserving optimality of the control solutions. Indeed, some RL algorithms can be regarded as a fully data-driven counterpart of the discrete-in-time optimal control strategies based on the Bellman equation, where the policy -i.e., the control actionis directly learnt from interactions of the system with the environment without relying on an a-priori physical model [START_REF] Sutton | Reinforcement Learning: An Introduction[END_REF]. The relevance of a control action when the system is in a given state is measured by a reward and the expected cumulative rewards (or Value function) is the objective to be maximized. When neural networks are employed as an approximation format, the framework is referred to as deep RL (DRL). Recent works show the feasibility of the approach for the control of instabilities classically found in fluid mechanics systems [START_REF] Rabault | Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control[END_REF][START_REF] Beintema | Controlling rayleigh-bénard convection via reinforcement learning[END_REF][START_REF] Paris | Robust flow control and optimal sensor placement using deep reinforcement learning[END_REF].

IMPROVING LEARNING BY IMPROVING THE EXPLO-RATION

The methods we consider here are fully data-driven, without prior knowledge of a model. This implies that the modelling step is now replaced by the so-called exploration. Since the dimension of the phase space of the system under consideration is very large with respect to traditional tasks in Reinforcement Learning, the data efficiency of state-of-the-art methods such as Proximal Policy Optimization [START_REF] Schulman | Proximal policy optimization algorithms[END_REF] and Deep Deterministic Policy Gradient [START_REF] Lillicrap | Continuous control with deep reinforcement learning[END_REF] must be improved.

As an illustration in this work, we will consider the system governed by the Kuramoto-Sivashinsky (KS) equations. This system is described by a partial differential equation with initial value and spatial periodicity conditions:

∂u ∂t (t, x) = -u(t, x) ∂u ∂x (t, x) - ∂ 2 u ∂x 2 (t, x) - ∂ 4 u ∂x 4 (t, x), (1)
with an initial condition u(0, x), and periodicity in space u(t, x + M ) = u(t, x) given a length of the domain M ∈ R + . This 1-D dynamical system exhibits a chaotic behavior for a range of values of M and is often used as a convenient proxy of turbulent flow regimes. As such, it has recently been used as a practical tool to evaluate the robustness of machine learning methods. Properties of the KS system as discussed in detail in [START_REF] Cvitanović | On the state space geometry of the kuramotosivashinsky flow in a periodic domain[END_REF]. As an illustration, a controllable trajectory in the chaotic regime is depicted in Fig. 1. In a previous work [START_REF] Bucci | Control of chaotic systems by deep reinforcement learning[END_REF], we have shown that using the Deep Deterministic Policy Gradient (DDPG) algorithm allows to stabilize these chaotic trajectories; Fig. 2 shows an illustration of the method. More precisely, the controller task is to drive the trajectory of the chosen dynamical system to transit from one system equilibrium to an other one by accumulating statistical knowledge of the solution space (environment). The resulting policies were however far from being the optimal ones discussed in [START_REF] Armaou | Feedback control of the kuramoto-sivashinsky equation[END_REF]. In this contribution, we hence intend to understand and identify the multiple factors and their influence on the policy identification, with a quantitative scope, but without relying on physics constraints or prior knowledge. In particular, we develop consistent exploration strategies which allow to carefully sample new observations, based on the previous ones, in order to achieve the knowledge of the system to be controlled. As a result, better control policies -in principle, the optimal ones -could be obtained with a lower amount of interactions with the system. From this perspective, we rely on information theory and optimal design of experiments to quantify the knowledge the controller gathers during the process.

We will compare the control policies achieved with the different strategies, and contrast them with the standard linear solutions. More generally, the final goal is to improve the use of data-driven and statistical learning for computational fluid dynamics, and specifically reinforcement learning. This approach, at the crossing between machine learning and dynamical systems, can also be of help to the streaming learning community to gather insights for explaining and understanding behaviour of data-based modelling. 2: Reinforcement Learning scheme: from an initial state, the control law applies a forcing to the state of the dynamical system. Given this forcing action (or control) and the new state, a reward is obtained. An optimal reinforcement learning policy is a set of control decisions which maximises the asymptotical sum of rewards. In this case, a reward or cost could be the energy of the system. Taken from [START_REF] Bucci | Control of chaotic systems by deep reinforcement learning[END_REF].

Figure 1 :

 1 Figure 1: A sampled chaotic trajectory emanating from the neighbourhood of the equilibrium u = 0 of the Kuramoto-Sivashinsky equation under chaotic regime (M = 22); the visualization is obtained by projecting on the first 3 Fourier modes. The 3 non-trivial equilibria (stationary solutions) are also shown.

Figure

  Figure2: Reinforcement Learning scheme: from an initial state, the control law applies a forcing to the state of the dynamical system. Given this forcing action (or control) and the new state, a reward is obtained. An optimal reinforcement learning policy is a set of control decisions which maximises the asymptotical sum of rewards. In this case, a reward or cost could be the energy of the system. Taken from[START_REF] Bucci | Control of chaotic systems by deep reinforcement learning[END_REF].