Dr Catherine Droitcourt
email: catherine.droitcourt@chu-rennes.fr

I Vittrup

A Dupuy

A Egeberg

J P Thyssen

The risk of systemic infections requiring hospitalisation in children with atopic dermatitis: a Danish retrospective nationwide cohort study Running head: Risk of hospitalised systemic infections in Danish children with atopic dermatitis

The risk of systemic infections requiring hospitalisation

in children with atopic dermatitis: a Danish retrospective nationwide cohort study

Introduction

Atopic dermatitis (AD) is a highly prevalent chronic inflammatory skin disease of childhood that affect up to 20%. [START_REF] Langan | Atopic dermatitis[END_REF][START_REF] Odhiambo | ISAAC Phase Three Study Group. Global variations in prevalence of eczema symptoms in children from ISAAC Phase Three[END_REF] Children with AD have a severity-dependent increased risk of skin infections due to colonization with bacteria (e.g. Staphylococcus aureus) or viral activity (herpes simplex, eczema herpeticum), in part due to skin barrier impairment that increases pH, but also an altered cellular immunity. [START_REF] Langan | Atopic dermatitis[END_REF][START_REF] Ong | Bacterial and viral infections in atopic dermatitis: a comprehensive review[END_REF][START_REF] Meylan | Skin Colonization by Staphylococcus aureus Precedes the Clinical Diagnosis of Atopic Dermatitis in Infancy[END_REF][START_REF] Beck | Phenotype of atopic dermatitis subjects with a history of eczema herpeticum[END_REF][START_REF] Hsu | Epidemiology of Eczema Herpeticum in Hospitalized U.S. Children: Analysis of a Nationwide Cohort[END_REF] An association between AD and systemic infections has also been suggested. [START_REF] Serrano | Association between atopic dermatitis and extracutaneous bacterial and mycobacterial infections: A systematic review and meta-analysis[END_REF] This may be due to dysregulation of the innate and adaptative immunity, [START_REF] Paternoster | Multi-ancestry genome-wide association study of 21,000 cases and 95,000 controls identifies new risk loci for atopic dermatitis[END_REF] comorbid atopic respiratory disorders, and use of systemic immunosuppressive treatments. The few studies finding an association between childhood AD and systemic infections are based on patient self-report or focused on infections that were managed outside of a hospital setting. [START_REF] Silverberg | Association between severe eczema in children and multiple comorbid conditions and increased health care utilization[END_REF][START_REF] Silverberg | Childhood atopic dermatitis and warts are associated with increased risk of infection: a US population-based study[END_REF][START_REF] Langan | Increased Risk of Cutaneous and Systemic Infections in Atopic Dermatitis-A Cohort Study[END_REF] There are very limited data concerning risk of physician-confirmed infections and infections requiring hospitalisation in patients with AD. [START_REF] Narla | Association between childhood atopic dermatitis, cutaneous, extracutaneous and systemic infections[END_REF] We examined whether children with a hospital diagnosis of AD have an increased risk of developing systemic infections requiring hospitalisation compared to a population of children without hospital diagnosed AD.

Methods

Study design and data sources

We performed a population-based cohort study. The source was the Danish registries covering the entire Danish population (approximatively 5.5 millions of individuals) and linked together through a unique ten-digit personal number given to each Danish resident (number CPR, Civil Personal Register) at birth or immigration. [START_REF] Schmidt | The Danish Civil Registration System as a tool in epidemiology[END_REF] The registries contain anonymized, individual-level data, including demographic data (gender, dates of birth and death); [START_REF] Schmidt | The Danish Civil Registration System as a tool in epidemiology[END_REF][START_REF] Pedersen | The Danish Civil Registration System[END_REF] inpatient, outpatient, and emergency room visits including the diagnoses, from all public and a number of private hospitals in the Danish National Patient Register (DNPR); [START_REF] Andersen | The Danish national hospital register. A valuable source of data for mod-ern health sciences[END_REF][START_REF] Andersen | The Danish National Health Service Register[END_REF][START_REF] Lynge | The Danish National Patient Register[END_REF][START_REF] Schmidt | The Danish National Patient Registry: a review of content, data quality, and research potential[END_REF] all drug dispensations from Danish pharmacies (according to the Anatomical Therapeutic Chemical classification, ATC) with their date of dispensations and the prescriber in the Danish National Prescription Register (DNPrR); [START_REF] Kildemoes | The Danish National Prescription Registry[END_REF] all hospital procedures (including hospital-based pharmacological treatment) in the DNPR; the household and personal income data in the Income Statistic Register (ISR). [START_REF] Baadsgaard | Danish Registers on Personal Income and Transfer Payments[END_REF]

Study population and exposure

Accepted Article

All children born in Denmark between January 1, 1995 and December 31, 2016 recorded in the nationwide Danish registries (source population, 1,439,718 children) were eligible for inclusion in the cohort study.

Definition of exposed cohort:

The exposed cohort included all children (under 18 years) with a hospital diagnosis (in-or outpatient) of AD in childhood (before the age of 18 years) recorded in the DNPR, between

Exclusion criteria

Children with comorbidities with a high-risk infectious profile were excluded before index date to focus on children without particularly affected immune responses. Patients with any ICD-10 diagnostic code of HIV (B20-B24), primary immunodeficiency (D70.0, D70.4, D71, 72.0, D76.1, D80-D84, E70.3, G11.3), leukemia and lymphoma (C77, C81-C96), cancers (C30-C39, C40-C41, C43, C45-C49, C51-58, C60, C62-63, C64-C68, C69-C72, C73-C75, C97), diabetes (E10-E14), organ transplant recipients (Z94, T86), chronic renal failure (N18) and cystic fibrosis (E84) were excluded from the source population.

Children with history of prior infections before the index date were not excluded independently of AD status.

Follow-up

Follow-up for children with AD began at the date of exposure i.e. recorded AD diagnosis (index date). Follow-up for reference children began at the date of matching with child with AD (the index date for the corresponding AD child). Follow-up ended at the time of outcome or study end

Accepted Article

date (December 31, 2017), or their 18th birthday or emigration, or date of death, whichever occurred first. The minimum follow-up was at least one year except in case of censoring (18th birthday or emigration, or death).

Systemic infections leading to hospitalisation

Systemic infections were infections, regardless of the pathogen, which lead to hospitalisation for more than 24 hours. These were identified by a hospital primary diagnosis through the hospital discharge ICD-10 codes in the DNPR (see Supplementary Table S1). Fungal and parasitic infections were not considered given that these are very rare in Denmark. Systemic infections were grouped as follows: upper respiratory tract, lower respiratory tract, gastrointestinal tract, musculoskeletal tract, urinary tract, heart, central nervous system infections and sepsis.

Covariates

We used a directed acyclic graph to identify potential confounders of the association between AD and systemic infections leading to hospitalization (see Supplementary Figure S1). The atopic comorbidity status was assessed and defined as follows: definition of asthma based on the ICD-10 code J45-J46 and/or at least two dispensations of a drug for obstructive airway diseases for children over 5 years according to the ATC code R03, recorded in the DNPR and/or the DNPrR), definition of hay fever (definition based on the ICD-10 code J30 and/or at least two dispensations of an antiallergic or corticosteroids nasal spray according to the ATC code R01AC/R01AD, recorded in the DNPR and/or the DNPrR).

The severity of AD was modeled as a time-dependent variable. Four categories (mild, mild-tomoderate, moderate-to-severe and severe) were defined according to dispensations of treatments (topical and systemic immunosuppressants) used in Denmark for AD between index date and censoring for each included individual according to the below list. An individual categorized to a lower category could be re-categorized into any higher category, whereas no re-categorization to a lower category was allowed. The categories were as follows: mild: baseline until entering a higher severity; mild-to-moderate: at the first dispensation of a moderately potent topical corticosteroid (TCS) e.g. hydrocortisone 17-butyrate or first dispensation of topical tacrolimus 0.03%; moderateto-severe: at the first dispensation of a potent TCS e.g. betamethasone or mometasone furoate or first dispensation of topical tacrolimus 0.1%; severe: at the first dispensation of a very potent TCS e.g. clobetasol propionate or first dispensation for systemic immunosuppressants e.g. methotrexate, azathioprine, cyclosporine or mycophenolate mofetil).

Accepted Article

The ATC codes used for topical and systemic immunosuppressants for AD and identified through the DNPrR and the DNPR are given in the Supplementary Table 2.

The use of systemic corticosteroids (ATC codes H02A and H02B) was studied separately because they are not recommended as systemic treatments for AD and is used exceptionally for AD for a short term period; it was defined by at least one dispensation identified through the DNPrR and the DNPR during the follow-up, the ATC codes are given in the supplementary Table S2.

The socioeconomic status was assessed by the average family income (father and mother) within the five years before the index date and was divided into quintiles.

Statistical analysis

Descriptive statistics were expressed as means and standard deviations for normally distributed continuous variables or median and interquartile ranges for non-normally distributed continuous variables, and frequencies for categorical variables. Incidence rates (IRs) per 10,000 person-years and 95% confidence interval (CI) were calculated by identifying the number of infections and the number of person-years of follow-up for children with AD and reference children separately. To estimate the population impact of pediatric AD on infection risk, we calculated the absolute risk difference with 95% CI for each systemic infection as the difference between AD cohort's IRs and reference cohort's IRs. We used Cox regression with calendar time as the underlying timescale to estimate hazard ratios (HRs) with 95% confidence intervals (95% CI) of the association between systemic infections requiring hospitalisation and AD in childhood (the unadjusted model), with general population without AD as the reference group. We used the log-log graphic method to assess the proportional hazards assumption. Adjustments for gender, age, socioeconomic status (at the entry in the cohort), atopic comorbidities (asthma and/or hay fever, time-updated variable) and systemic immunosuppressant treatment for AD (time-updated variable) was performed (the adjusted model). We also subgrouped analyses by category of AD severity modeled as a timeupdated variable.

We performed a secondary analysis exploring the definition of infections by including all infections which lead to hospital management (outpatient: visit to emergency unit or outpatient visit hospital or outpatient hospital day stay and inpatient: hospitalisation) and also included subgrouping by AD severity.

Sensitivity analyses

We performed a sensitivity analysis with adjustment for the use of systemic corticosteroid treatment. Sensitivity analysis also included subgrouping by AD severity.

Accepted Article

Due to the numbers of comparisons and subsequent risk of type I errors, Bonferroni correction was used and p-values <0.00069 were considered statistically significant.

Authorizations

Approval from an ethics committee is not required for register studies in Denmark (Danish law: Lov om videnskabsetisk behandling af sundhedsvidenskabelige forskningsprojekter, § 14, stk. 2).

This study was approved by the Danish Data Protection Agency (number VD-2018-286).

Results

We included 19,415 children with AD and 194,150 reference children, with a median follow-up time of 7.4 (IQR=3.3-13.3) and 7.7 (IQR=3.6-13.5) years, respectively (Figure 1). At entry cohort, half of them were under 2 years and 56% were boys; asthma and/or allergic rhinitis were more prevalent in children with AD compared with reference children (13.7% vs 4.7%, p<0.0001) (Table 1). Over the follow-up period, 89% of children with AD had received at least one dispensation of TCS, 16.2% a topical calcineurin inhibitor, and 1.6% a systemic immunosuppressant (Table 1); children with AD treated with a systemic immunosuppressant were older and had more atopic comorbidities compared with children without treatment with systemic immunosuppressant (mean (standard deviation, SD) 6.0 years (5.0) vs 3.6 years (3.8); 63.4% vs 48.4%, respectively)). Compared with reference children, incidence rates for all categories of systemic infections were increased in children with AD (Table 2). The absolute risk difference per 10,000 person-years was 26.4 (CI95% 23.0-29.8) for lower respiratory, 3.1 (CI95% 1.6-4.7) for upper respiratory, 3.6 (CI95% 1.8-5.4) for urinary tract, 0.9 (CI95% 0.2-2.0) for musculoskeletal and 8.7 (CI95% 5.7-11.7) for gastrointestinal infections. The absolute risk difference for all categories of systemic infection requiring hospitalisation is given in the supplementary material (Table S3). We observed an association between AD and risk of upper and lower respiratory, gastrointestinal, urinary tract and musculoskeletal infections (Table 2, Figure 2). The strongest associations were for lower and upper respiratory tract infections (respectively, aHR (adjusted HR)=1.79, CI95%1.65-1.94 and aHR=1.59, CI95%1.34-1.88) and urinary tract infections (aHR=1.34 CI95%1.16-1.54) (Table 2, Figure 2).

The association with systemic infections did not vary with the severity of AD (Figure 3).

In the secondary analysis extending the definition of systemic infections to infections which leads to a hospital management, we found similar findings. The adjusted HRs were 1.39 (CI95% 1.26-1.53) for upper respiratory tract, 1.77 (CI95% 1.65-1.90) for lower respiratory tract, 1.44 (CI95% 1.21-1.72) for musculoskeletal, 1.30 (CI95% 1.21-1.35) for gastrointestinal tract and 1.21 (CI95%

Accepted Article

1.09-1.35) for urinary tract infections (Table 3, Figure 4, Figure 5 and supplementary Table S4).

In the sensitivity analysis adjusting for the use of systemic corticosteroids, the results were very close to the main analysis (Supplementary Table S5).

Discussion

Analysis of Danish nationwide registries over a 20-year period showed that children with AD managed in a hospital in-or outpatient setting had a higher occurrence of infections that required hospitalisation, including upper and lower respiratory tract, gastrointestinal tract, urinary tract and musculoskeletal infections. Two previous cross-sectional studies investigated the association between childhood AD and extra-cutaneous infections and observed higher prevalence of strep throat, head or chest cold, influenza/pneumonia, sinus infections, recurrent ear infections, chickenpox, and urinary tract infections. [START_REF] Silverberg | Association between severe eczema in children and multiple comorbid conditions and increased health care utilization[END_REF][START_REF] Silverberg | Childhood atopic dermatitis and warts are associated with increased risk of infection: a US population-based study[END_REF] The association did not vary with AD severity. [START_REF] Silverberg | Association between severe eczema in children and multiple comorbid conditions and increased health care utilization[END_REF] In both studies, 9,10 AD and infection diagnoses as well as AD severity [START_REF] Silverberg | Association between severe eczema in children and multiple comorbid conditions and increased health care utilization[END_REF] were based on self-report. We confirm the increased risk of systemic infections, and further show that these demanded hospitalisation, hence indicating severe disease. A cross-sectional study using the hospital discharge data of a 20% sample of US hospitalisations found higher prevalence of different systemic infections leading to hospitalisation including respiratory infections, encephalitis, endocarditis and arthritis, among adults with AD. [START_REF] Narla | Association between childhood atopic dermatitis, cutaneous, extracutaneous and systemic infections[END_REF] In our study we found no association with central nervous system and heart infections maybe due to an overall low number of cases. This difference may also in part be explained by the inability in the previous study [START_REF] Narla | Association between childhood atopic dermatitis, cutaneous, extracutaneous and systemic infections[END_REF] to adjust for the use of immunosuppressant treatment, which could play a critical role in the pathway between AD and serious infections. [START_REF] Fleming | Risk of infection in patients with atopic dermatitis treated with dupilumab: A meta-analysis of randomized controlled trials[END_REF] Here, we adjusted for these potential important risk factors, hence allowing us to study the specific contribution from AD.

Moreover, unlike the study by Narla et al., [START_REF] Narla | Association between childhood atopic dermatitis, cutaneous, extracutaneous and systemic infections[END_REF] we have investigated the temporality of the association between AD and systemic infections requiring hospitalization, and to our knowledge, this is the first cohort study focusing strictly on infections requiring hospitalisation among children with AD.

The association with systemic infections did not clearly vary with the severity of AD despite a slight trend towards increased risk from the mild category to the moderate-to-severe category. Surprisingly, we did not observe a higher risk in the category of severe AD. Some hypotheses could explain this result. First, children treated with immunosuppressant treatment have a thorough assessment focusing among other on infection risk before these medications are prescribed, and they also undergo repeated monitoring. These efforts likely minimize the risk

Accepted Article

children with AD who are immunosuppressed, and even prevents it use in those who have higher baseline risk of severe infection. Second, systemic treatments for AD could reduce infection risk by improving the skin barrier function and hence the risk of first cutaneous and later systemic infection driven by Staphylococcus aureus. Indeed, a recent meta-analysis of randomized controlled trials of dupilumab for AD concluded that dupilumab treated adult AD patients had a lower incidence of skin infections and eczema herpeticum. [START_REF] Fleming | Risk of infection in patients with atopic dermatitis treated with dupilumab: A meta-analysis of randomized controlled trials[END_REF] Third, the severity of AD was defined by proxy measures (dispensations of AD treatments) without any information on AD control and with a potential misclassification bias.

Although the cause of the association between AD and systemic infections remains unclear, our results might suggest causal mechanisms partly linked to AD itself and not only atopic disease. Indeed, the estimation of the associations with systemic infections remained significant even after adjusting for important atopic comorbidities. For respiratory tract infections, some respiratory symptoms encoded as infections could be actually the first symptoms of undiagnosed asthma, therefore some misclassifications may have occurred. This hypothesis is more plausible in infants (less than 2 years of age) for whom the diagnosis of asthma is defined by at least three or more recurrent wheezing regardless the cause (infectious or not). [START_REF] Tabachnik | Postgraduate course presentation. Infantile bronchial asthma[END_REF] Diagnoses of asthma is also more likely to be made in the AD cohort than diagnoses of upper respiratory tract infections; this nondifferential misclassification would bias the effect estimate toward the null, that means that our estimates may be cautious estimates of the association between atopic dermatitis and upper respiratory infections.

Regarding the association between childhood AD and urinary tract infections, two prior studies have found higher prevalence of urinary tract infections among children with AD, a survey-based study including 9,417 children 10 and a study of 57 infants with a dermatologist-confirmed AD diagnosis and 57 controls including systematic urine samples. [START_REF] Farajzadeh | The Relationship Between Infantile Atopic Dermatitis and Urinary Tract Infection[END_REF] Some hypotheses might be considered: systemic immune dysfunction linked to AD, [START_REF] Yang | Skin Barrier Abnormalities and Immune Dysfunction in Atopic Dermatitis[END_REF] scratching in genital area which could be a portal of entry for bacteria or a random finding.

The exhaustiveness of infections requiring hospitalisation at nationwide level, a follow-up period over 20 years and physician-confirmed diagnoses both for AD and infectious diseases are among the strengths of our study, as is the quality of the information enabling in theory no loss of followup and no attrition bias. Some potential limitations should be discussed. First, the population was all children with a hospital diagnosis with AD and the results could not be generalized to the AD population of

Accepted Article

children seen in primary care. We nevertheless had access to all dermatologist records, from hospitals and some private clinics giving it relevance to AD patients seen by dermatologists in general. Moreover, AD diagnosed outside hospital may have occurred in the reference group but this would tend to underestimate difference. Second, we did not have clinical details outside the hospital discharge codes notably on the disease flares and the effect of AD treatment on AD control, the question is here "when" rather than "who" and our design could not address this question. Third, we have studied the association with systemic infections regardless of the pathogen. Fourth, we did not study the early antibiotic exposure before the diagnosis of AD and the vaccination status which could play a role in the development of AD and severe infectious diseases. [START_REF] Tsakok | Does early life exposure to antibiotics increase the risk of eczema? A systematic review[END_REF][START_REF] Tamburini | Descriptive characteristics of the non-exposed cohort (reference children) and the exposed cohort (children with atopic dermatitis) at the index date and during the follow-up Reference children N=194,150 AD a children N=19,415[END_REF] Obesity could also be a potential confounding or intermediate factor in the study of the association between childhood AD and infections, but we did not have the possibility to take into account the body mass index because unavailable in the registries. Fifth, our findings that children with AD have an increased risk of developing systemic infections requiring hospital care could be due to surveillance bias. Nevertheless, this bias is less likely for infections requiring hospitalisation and the adjustment on the number of hospital visits neither confirm nor invalidate the evidence of surveillance bias (data not shown). At last, the absolute risk difference between children with AD and reference children was small; for example, if we followed 5,000 children with AD for 2 years, we might expect 3 excess upper respiratory infections due to their AD.

Conclusion

We found that children with AD have an increased risk of developing systemic infections that lead to hospitalisation for respiratory tract, gastrointestinal, urinary tract and musculoskeletal infections. Associations were not explained by other atopic comorbidity or use of immunosuppressive treatment. While the risk for these infectious diseases was elevated among children with AD, the absolute risk was low.

Accepted Article

Accepted Article

Figure 2: Association between atopic dermatitis and serious infections (only infections requiring hospitalisation) (Main Analysis)

Adjusted on age, gender, socioeconomic level (at the index date), systemic immunosuppressant treatment for AD (time-updated variable) and atopic comorbidities (asthma and/or hay fever, time-updated variable)

bjd_19825_f2.docx bjd_19825_f3.docx

Accepted Article

Accepted Article

Figure 4: Association between atopic dermatitis and serious infections (infections with hospital health contact) (Secondary Analysis)

Adjusted on age, gender, socioeconomic level (at the index date), systemic immunosuppressant treatment for AD (time-updated variable) and atopic comorbidities (asthma and/or hay fever, time-updated variable)

bjd_19825_f4.docx

Accepted Article

January 1 ,

 1 1995 and December 31, 2016. The diagnosis of AD was defined as the first diagnostic code of AD (L20.x, primary or associated diagnosis, according the International Classification of Diseases, 10th version, (ICD-10)) recorded and made by a hospital physician, before the age of 18 years. The positive predictive value of an AD diagnosis in childhood in the Danish registries is 98%. 21 Definition of matched unexposed cohort: Each child with a hospital diagnosis of AD was randomly matched to ten reference children from the source population on birth date and gender at the date of AD diagnosis for the corresponding child with AD, identified through the Danish National Patient Register (reference population). The index date was the date of AD diagnosis for both exposed (children with AD) and matched nonexposed children (matched reference children). The reference children had no in-or outpatient hospital diagnosis of AD made by a physician in the study inclusion period.

a

  Atopic dermatitis made by a hospital physician during childhood, using the diagnostic J20 code of the International Classification of Diseases 10th revision b Asthma (based on the ICD-10 code J45-J46 and/or at least two dispensations of a drug for obstructive airway diseases for children over 5 years according to the ATC code R03, recorded in the DNPR and/or the RMPS), hay fever (based on the ICD-10 code J30 and/or at least two dispensations of a antiallergic or corticosteroids nasal spray according to the ATC code R01AC/R01AD, recorded in the DNPR and/or the RMPS) c based on family income at index date; study population divided into quintiles Accepted Article

Figure 3 :

 3 Figure 3: Association between atopic dermatitis and serious infections (only infections requiring hospitalisation) according to AD severity (Main analysis, adjusted model)

Figure 5 :

 5 Figure 5: Association between atopic dermatitis and serious infections (infections with hospital health contact) according to AD severity (Secondary analysis, adjusted model)

Over the follow-up period Asthma and/or hay fever b

	Cyclosporine	11 (0.01)	52 (0.27)
	Systemic corticosteroids (at least one dispensation), n (%) Long-term systemic corticosteroids (more than six weeks), n (%) Oral immunosuppressant treatment for AD, n (%) Methotrexate Azathioprine Accepted Article Mycophenolate mofetil	30,935 (15.93) 2,339 (1.20) 258 (0.13) 138 (0.07) 113 (0.06) 3 (0.00)	9,440 (48.62) 897 (4.62) 77 (0.40) 179 (0.92) 146 (0.75) 11 (0.06)

Abbreviations: N, number of adult patients; IQR, interquartile range; SD, standard deviation.

Table 2 : Association between atopic dermatitis and serious infections (only infections requiring hospitalisation) (Main Analysis)

 2 Adjusted on age, gender, socioeconomic level (at the index date), systemic immunosuppressant treatment for AD (time-updated variable) and atopic comorbidities (asthma and/or hay fever, time-updated variable) c Categories of infection defined using the diagnostic codes of the International Classification of Diseases 10th revision listed in TableS1, in the

	Crude Model	Adjusted b Model

b *

Accepted Article

Table 3 : Association between atopic dermatitis and serious infections (infections with hospital health contact) (Secondary Analysis)

 3 Adjusted on age, gender, socioeconomic level (at the index date), systemic immunosuppressant treatment (time-updated variable) and atopic comorbidities (asthma and/or hay fever, time-updated variable) c Categories of infection defined using the diagnostic codes of the International Classification of Diseases 10 th revision listed in TableS1in the Supplementary Material.Significance after Bonferroni correction is marked by *

	Crude Model	Adusted b Model

b

Adjusted on age, gender, socioeconomic level (at the index date) and atopic comorbidities (asthma and/or hay fever) as a time-updated variable)bjd_19825_f5.docxAccepted Article

Acknowledgments

The authors are grateful to the Fondation de la Dermatite Atopique, the Collège des Enseignements en Dermatologie (CEDEF) and the International Society of Atopic Dermatitis for their support.

Accepted Article

The study was supported by a research grant from the International Society of Atopic Dermatitis (ISAD) Catherine Droitcourt has received Honoria from Sanofi-Genzyme. Ida Vittrup has received salary from a research grant from Regeneron Pharmaceuticals. Alain Dupuy: has attended advisory boards for Sanofi-Genzyme. Alexander Egeberg has received research funding from Pfizer, Eli Lilly, the Danish National Psoriasis Foundation, and the Kgl Hofbundtmager Aage Bang Foundation, and honoraria as consultant and/or speaker from AbbVie, Almirall, Leo Pharma, Samsung Thyssen has attended advisory boards for Sanofi-Genzyme, Regeneron, LEO Pharma, and Eli Lilly & Co, and received speaker honorarium from LEO Pharma, Regeneron, Abbvie and Sanofi-Genzyme, and been an investigator for Sanofi-Genzyme,


Emmanuel Moulay
email: emmanuel.moulay@irccyn.ec-nantes.fr

Michel Dambrine
email: michel.dambrine@univ-valenciennes.fr

Nima Yeganefar
email: nima.yeganefar@ec-lille.fr

Wilfrid Perruquetti
email: wilfrid.perruquetti@ec-lille.fr

Finite-time stability and stabilization of time-delay systems

Keywords: Finite-time stability, Finite-time stabilization, Time-delay systems

Finite-time stability and stabilization of retarded type functional differential equations is developed. First, a theoretical result on finite-time stability inspired by the theory of differential equations, using Lyapunov functionals, is given. As it is not usable in practice, we show how to obtain finite-time stabilization of linear systems with delays in the input by using an extension of the Artstein's model reduction to nonlinear feedback. With this approach, we give an explicit finite-time controller for scalar linear systems and for the chain of integrators with delays in the input.

Introduction

In the framework of ordinary differential equations, several studies have shown the possibility of stabilizing a system in finite-time -and not merely asymptotically -using continuous, time-invariant feedbacks. Several aspects of finite-time stability have been considered in the literature, both from a theoretical point of view with precise definitions, Lyapunov and converse Lyapunov results, regularity properties of the settling-time function [START_REF] Bhat | Finite time stability of continuous autonomous systems[END_REF][START_REF] Haimo | Finite time controllers[END_REF][START_REF] Moulay | Finite time stability and stabilization of a class of continuous systems[END_REF], and from a practical point of view with applications in robotics [START_REF] Hong | Finite-time control for robot manipulators[END_REF] and from the fact that such control laws exhibit good properties of robustness and disturbance rejections [START_REF] Bhat | Continuous finite-time stabilization of the translational and rotational double integrator[END_REF]. Recently, finite-time stabilization for triangular control systems described by retarded functional differential equations has been studied in [START_REF] Karafyllis | Finite-time global stabilization using time-varying distributed delay feedback[END_REF] by using the back-stepping technique.

First, in this paper, we show how to obtain a theoretical sufficient condition of finite-time stability for general retarded functional differential equations by using the method of Lyapunov-Krasovskii functionals. This result is inspired by the results on finite-time stability of ordinary differential equations (see [START_REF] Bhat | Finite time stability of continuous autonomous systems[END_REF][START_REF] Haimo | Finite time controllers[END_REF][START_REF] Moulay | Finite time stability and stabilization of a class of continuous systems[END_REF]) and can be easily extended to the neutral-type cases. Unfortunately, this theoretical result is not so usable in practice for studying the finitetime stabilization problem. This is due to the fact that it is really difficult to find a Lyapunov functional satisfying the assumptions of our theoretical result. Only a simple example is given; the reader may understand that this result is a only theoretical one. This is the reason why we develop a more practical method. So, we will demonstrate how an extension of the theory of the Artstein's reducing transformations defined in [START_REF] Artstein | Linear systems with delayed controls: A reduction[END_REF] can be used to solve the finite-time stabilization problem of linear delayed control systems. This kind of models are generally used to describe systems with delay on the transmission lines as in the teleoperation or remote systems. The presented method is then used to give a finite-time feedback control for scalar linear systems and for the chain of integrator with delays in the input.

The paper is organized as follows. In section 2, we will provide some notations and definitions useful all along the paper. A sufficient condition for finite-time stability of retarded functional differential equations will be addressed in section 3. In section 4, an extension of the Artstein models reduction will be given. The reduction enables us to employ the literature on ordinary systems, and to analyze the finite-time stabilization of linear systems with delays on the input variables with an example. Finally, the conclusions of the paper are given in section 5.

Notations and definitions

The upper right Dini derivative of a function f :

[a, b] → R is the function D + f : [a, b] → R defined by D + f (x) = lim sup h→0 + f (x + h) -f (x) h .
Let a > 0, a continuous function g : [0, a] → [0, +∞[ belongs to class K if it is strictly increasing and g(0) = 0. Let A be a matrix, x ∈ R n and f a real function, |||A||| denotes a matrix norm,

f ∞ = sup x≥0 |f (x)|
the infinity norm and x n the Euclidean norm in R n . The spectrum of a matrix A is denoted by σ (A). Throughout this paper, we use the following notations: C h n is the space of continuous functions φ : [-h, 0] → R n with h ≥ 0, and

C ǫ = φ ∈ C h n : φ C h n < ǫ with φ C h n = sup -h≤s≤0 φ(s) n .
We are interested by retarded functional differential equations of the form

ẋ(t) = f (x t ), t ≥ 0, (1)
where x t : [-h, 0] → R n is given by x t (s) = x(t + s) and ẋt (s) = ẋ(t + s) for every s ∈ [-h, 0]. ẋ(t) denotes the right hand derivative of x(t), f : C h n → R n is a continuous functional such that f (0) = 0. In the following, we suppose that the system (1) possesses uniqueness of solutions in forward time.

As usual, x(t) is called a solution of the system (1) with initial condition φ at the origin if

x(t) is defined on [-h, b) with b ∈ R such that: (i) x 0 ≡ φ, (ii) x(t) is continuous on [0, b), (iii) x(t) satisfies the equation (1) for all t ∈ [0, b).
x(t) is denoted by x(t, φ) and x t by x t (φ).

The system (1) is said to be: (i) stable if for any ǫ > 0 there exists δ(ǫ) > 0, such that φ ∈ C δ(ǫ) implies that (a) x(t, φ) is defined for all t ≥ 0, (b) x(t, φ) n < ǫ for all t ≥ 0, (ii) asymptotically stable if it is stable and there exists δ such that φ ∈ C δ implies lim t→+∞ x(t, φ) = 0.

Definition 1

The system (1) is finite-time stable if:

(i) the system (1) is stable for the system (1), (ii) there exists δ > 0 such that, for any φ ∈ C δ , there exists 0 ≤ T (φ) < +∞ for which x(t, φ) = 0 for all t ≥ T (φ).

T 0 (φ) = inf {T (φ) ≥ 0 : x(t, φ) = 0 ∀t ≥ T (φ)}
is a functional called the settling time of the system (1). Remark 2 The finite-time stability implies that the system (1) cannot be Lipschitz at the origin. Indeed, if the system (1) is finite-time stable, there is no uniqueness of solutions in backward time at the origin due to the fact that all solutions reach the origin. This motivates the assumption on the continuity of the system (1) with uniqueness of solutions in forward time. It implies the existence of a global semi-flow and the continuous dependence on the initial data (see [8, Chapitre 2]).

Preliminary results on finite-time stability

The first lemma is called the Comparison Lemma. Its proof and more general versions can be found in [9, Section 5.2] and [10, Section 4].

Lemma 3 (Comparison Lemma) Let J be a segment of R, if the scalar differential equation ẋ = f (x),
x ∈ J has the global semi-flow Φ : R ≥0 × J → R, where f : J → R is continuous, and if g : [a, b) → J (b could be infinity) is a continuous function such that

D + g(t) ≤ f (g(t)), t ∈ [a, b) , then g(t) ≤ Φ(t, g(a)) for all t ∈ [a, b).
We denote by

V (x t ) = lim sup h→0 + V (x t+h ) -V (x t ) h = D + V (x t ) .
Proposition 4 Consider the system (1) with uniqueness of solutions in forward time. If there exists δ > 0 and a continuous functional

V : C δ → R ≥0 , ǫ > 0, two functions α, r of class K such that ż = r(z) has a flow and for all φ ∈ C δ , (i) α( φ (0) n ) ≤ V (φ), (ii) V (φ) ≤ -r(V (φ)) with ǫ 0 dz r (z)
< +∞, then the system (1) is finite-time stable with a settling time satisfying the inequality

T 0 (φ) ≤ V(φ) 0 dz r(z) .
Proof. Let V : C δ → R ≥0 be a Lyapunov functional for the system (1). The Lyapunov-Krasovskii theorem (see [8, § 5.3]) ensures that the system (1) is asymptotically stable. Let x(t, φ) be a solution of (1) which tends to the origin with the settling time 0 ≤ T 0 (φ) ≤ +∞. It remains to prove that T 0 (φ) < +∞. Let us consider the system ẏ = -r(y), y ≥ 0, with the flow Φ(t, y) for y ≥ 0. For all t ≥ 0 and all φ ∈ C δ ,

V (x t (φ)) ≤ -r(V(x t (φ))).
Now, if we apply the Comparison Lemma 3, we could deduce that

V (x t (φ)) ≤ Φ(t, V(φ)), t ≥ 0, φ ∈ C δ .
From [START_REF] Haimo | Finite time controllers[END_REF], we know that

Φ(t, V(φ)) = 0 for t ≥ V(φ) 0 dz r(z) .
With the positive definiteness of V, we could conclude that, for all t ≥ 0 and all φ ∈ C δ ,

x(t, φ) = 0 for t ≥ V(φ) 0 dz r(z) .
Thus, the system (1) is finite-time stable with the settling time

T 0 (φ) ≤ V(φ) 0 dz r(z) < +∞.
Thus the system (1) is finite-time stable. It is worth noticing that T 0 is actually continuous at the origin.

Let us consider a simple example of a finite-time stable retarded system. Example 5 Let 0 < α < 1 and consider the delayed system

ẋ (t) = -|x (t)| α sgn (x (t)) 1 + x (t -h) 2 .
The solutions of such a system depend continuously on the initial data. Indeed, the functional is Lipschitz everywhere in x (th) and Lipschitz outside the origin and continuous everywhere in x (t). We know that the Lipschitz property of the right hand side of the system implies the uniqueness solutions. As the only solution starting from the origin of the system is the zero solution x (t) ≡ 0, the system possesses uniqueness of solutions in forward time. Let

V (x t ) = x (t) 2 2 we have V (x t ) = -|x (t)| 1+α 1 + x (t -h) 2 ≤ -|x (t)| 1+α = -2 1+α 2 V (x t ) 1+α 2
.

So the system is finite-time stable under the settling time

T 0 (x t ) ≤ |x (t)| 1-α 1 -α .
Figure 1 shows the evolution of x(t) for α = h = 0.5 and x 0 ≡ 0. Remark 6 Let us consider the system

ẋ (t) = f (x (t) , x (t -h 1 ) , . . . , x (t -h k )) (2)
where h 1 , . . . , h k are positive numbers and a non zero continuous function such that the origin is the only point of the domain of f satisfying f (0, . . . , 0) = 0. Then the system can not be finite-time stable. Indeed, suppose that the system is finite-time stable. Let x (t) be a solution satisfying x (t) = 0 for all t ≥ T . It implies that ẋ (t) = 0 for all t ≥ T . With the assumption on f , we deduce that x (t) = 0 for all t ≥ T -max (h 1 , . . . , h k ).

f : R n × . . . × R n → R n
Step by step, we conclude that x (t) = 0 for all t ≥ 0, then x (t) ≡ 0 and f ≡ 0. This leads to a contradiction.

The previous remark implies that there is no way to solve the finite-time stabilization problem for the class of discrete delayed systems whose closed-loop system is defined by [START_REF] Haimo | Finite time controllers[END_REF]. In particular, the use of a discrete delayed feedback control is inadequate to solve the finite-time stabilization problem. In order to give a constructive method for the problem of finite-time stabilization of a class of linear systems, we will use the Artstein's reduction-type scheme which leads to the use of a feedback control with distributed-delays.

Extension of the Artstein's transformation: application to the finite-time stabilization problem

Let us consider the system

ẋ(t) = Ax(t) + k i=0 B i u(t -h i ), t ≥ 0 (3)
where

x(t) ∈ R n , u(t) ∈ R m , A is a n × n matrix,
(i) u (0) = 0, (ii) the closed-loop system ẋ(t) = Ax(t) + k i=0 B i u(t -h i ), x ∈ R n .
is a finite-time stable. In order to simplify the notation, we denote u (t) the feedback control even if it is state dependant, in order to easily calculate u(th i ). Such kind of systems are generally used to represent the time delay introduced by transmission lines as, for example, in teleoperation or network controlled systems (see [START_REF] Bushnell | Networks and control[END_REF]). By using the Leibniz's formula for differentiating integrals depending on parameters, we deduce that if

y (t) = x (t) + k i=0 L hi (A,Bi) u t
where u t : [-h, 0] → R m is given by u t (s) = u (t + s) for every s ∈ [-h, 0] and

L h (A,Bi) f = 0 -h e A(-h-s) B i f (s) ds then ẏ (t) = Ay (t) + Bu (t) (4)
with

B = k i=0 e -Ahi B i .
Now, we may give an extension of the Artstein's model reduction given in [7, Theorem 6.1] and [START_REF] Kwon | Feedback stabilization of linear systems with delayed control[END_REF] to nonlinear feedback.

Theorem 7 If the system (4) is stabilizable (respectively finite-time stabilizable) by a feedback control

u (t) = k (t) f (y (t))
with k (t) bounded and f : R n → R m continuous such that f (0) = 0 and there exists a function α of class K such that

f (x) m ≤ α ( x n ) ,
then the system (3) is stabilizable (respectively finite-time stabilizable) by the feedback control

u(t) = k(t) f x(t) + k i=0 L hi (A,Bi) u t . (5)
Proof. The fact that the integral equation ( 5) admits a continuous solution is left to the reader. Suppose that the system (4) is stabilizable by a feedback control

u (t) = k (t) f (y (t))
with k (t) bounded and f continuous such that f (0) = 0. First, we notice that

f • y t C h i m = max -hi≤s≤0 f (y (t + s)) m , ≤ max -hi≤s≤0 α ( y (t + s) n ) by assumption, ≤ α max -hi≤s≤0 y (t + s) n since α ∈ K, ≤ α y t C h i n .
So, we have

x (t) ≤ y (t) + k i=0 0 -hi e A(-hi-s) B i u (t + s) ds ≤ y (t) + k i=0 h i e A. C h i n |||B i ||| u t C h i m ≤ y (t) + k i=0 h i e A. C h i n |||B i ||| k ∞ f • y t C h i m ≤ y (t) + k i=0 h i e A. C h i n |||B i ||| k ∞ α( y t C h i n ).
The characterization of the asymptotic stability given for example in [13, Lemma 4.5] leads to the fact that if y (t) tends asymptotically to the origin then x (t) tends also. proof is also true for finite-time stability. Remark 8 The realization-implementation of the feedback control ( 5) is a challenge. To do that, it would be useful to use some results given in [START_REF] Wright | Nonlinear decoupling control in the presence of sensor and actuator deadtimes[END_REF] for the Smith predictor.

Here we want to develop the finite-time stabilization of scalar time delayed systems. Consider the system ẏ = ay + bu, y, u ∈ R

with b = 0. Proposition 9 Let a, b i ∈ R for 0 ≤ i ≤ k, the system

ẋ (t) = ax (t) + k i=0 b i u (t -h i ) , t ∈ R (7)
is finite-time stabilizable under the feedback control

u (t) = -1 b [a y (t) + |(y (t))| α sgn (y (t))]
where 0 < α < 1,

y (t) = x (t) + k i=0 L hi (a,bi) u t and b = k i=0 b i e -ahi .
Moreover, the settling time satisfies

T 0 (x t ) ≤ |y (0)| 1-α 1 -α + max 0≤i≤k h i .
Proof. System ( 6) is finite-time stabilizable by the feedback control u = -ay -|y| α sgn (y) b with 0 < α < 1 and the settling time function is given by

T (y (t)) = |y (0)| 1-α 1 -α (8)
(see [START_REF] Haimo | Finite time controllers[END_REF]). By using Theorem 7 with

b = k i=0 b i e -ahi
we have the first part of the result. Now, we have to prove is that

T 0 (x t ) ≤ |y (0)| 1-α 1 -α + max 0≤i≤k h i .
Equation ( 8) leads to the fact that

y (t) = x (t) + k i=0
L hi (a,bi) u t reaches the origin in a finite amount of time

T (y (t)) = |y (0)| 1-α 1 -α so x (t) = - k i=0 L hi (a,bi) u t for all t ≥ |y(0)| 1-α 1-α . In the same time u (t) = -1 b [ay (t) + |(y (t))| α sgn (y (t))] = 0 for all t ≥ |y(0)| 1-α 1-α . Then, L hi (a,bi) u t = 0 -hi e a(-hi-s) b i u (t + s) ds becomes zero for all t ≥ |y(0)| 1-α 1-α + h i . As it is true for all 0 ≤ i ≤ k, we deduce that T 0 (x t ) ≤ |y (0)| 1-α 1 -α + max 0≤i≤k h i .
Let us give an illustrative example of Proposition 9. Example 10 By using Proposition we know that the system ẋ (t) = x (t) + u (th) is finite-time stabilizable under the feedback control

u (t) = -y (t) -|(y (t))| 1 2 sgn (y (t))
with y (t) = x (t) + L h (1,1) u t . This leads to the simulation on figure 2. Remark 11 We may notice that the feedback controls in Theorem 7 and Proposition 9 involve storing the past control input history and computing an integral at every instant.

As it has been mentioned in the introduction, these feedback controls are with distributed-delays.

Finally, we consider the problem of finite time stabilization of the chain of integrator with delay in the input given by 

              ẋ1 (t) = x 2 (t) . . . ẋn-1 (t) = x n (t) ẋn (t) = u (t -h) (9)
and denoted in short by ẋ (t) = Ȃx (t) + B u (th)

=         0 1 0 • • • 0 . . . . . . . . . . . . . . . . . . . . . 1 . . . 0 • • • • • • 0 0         , B =         0 . . . 0 1         . Proposition 12 Let k = (k 1 , . . . , k n ) ∈ R n such
         α i-1 = α i α i+1 2α i+1 -α i , 2 ≤ i ≤ n α n = α, α n+1 = 1 . ( 11
)
The proof is a direct consequence of Theorem 7 and [15, Proposition 8.1].

Conclusions

Here, we are interested in the finite-time stability of functional differential equations and the finite-time stabilization problem of linear systems with delays in the input. A general theoretical result involving the Lyapunov functional gives a general sufficient condition for the finite-time stability of RFDEs and an example of a finite-time stable delayed system is addressed. Nevertheless, this result is not practical and cannot be used to stabilize in finite time a large class of linear systems. This is the reason why we expand the Artstein's model reduction to nonlinear feedback, in order to use a finite-time controller for a linear system with delays in the input. This lead to the finite-time stabilization of linear scalar systems and of the chain of integrator under a distributed delayed feedback control.

Fig. 1 .

 1 Fig.1. A finite time stable delayed system with h = 0.5

Fig. 2 .

 2 Fig. 2. Simulation with h = 0.2, x (0) = 0 and u (t) = 0 for t < 0 with

  the matrices B i are n × m, h i are positive constants. The control system (3) is finite-time stabilizable if there exists a feedback control law u which is time and state dependent such that:

  that the polynomial s n + k n s n-1 + . . . + k 2 s + k 1 is Hurwitz, there exists ǫ ∈ (0, 1) such that for all α ∈ (1ǫ, 1), the system (9) is globally finite time stabilizable under the continuous feedback control u

α (t) = -k 1 ⌊y 1 (t)⌉ α1 -. . .k n ⌊y n (t)⌉ αn

[START_REF] Yoshizawa | Stability Theory by Liapunov's Second Method[END_REF]

where

⌊x⌉ α = |x| α sgn (x) , x ∈ R y (t) = x (t) + L h ( Ȃ,B) u t , B = e -Ah B

and α 1 , . . . , α n satisfy

Acknowledgment

The authors would like to thank Jean-Pierre Richard and Lotfi Belkoura for many useful conversations on the subject of this paper.


Marine Gaudry
email: marine.gaudry@ap-hm.fr

Alizée Porto

Arnaud Blanchard

Jean-Victor Chazot

Laurence Bal

Mariangela De Masi

Axel Bartoli

Pierre-Antoine Barral

Alexis Jacquier

Vlad Gariboldi

Fréderic Collart

Valérie Deplano
email: valerie.deplano@univ-amu.fr

Philippe Piquet

A 10-Year Aortic Center Experience with Hybrid Repair of Chronic "Residual" Aortic Dissection After Type A Repair

Keywords: A aortic dissection, Chronic residual type B aortic dissection, Hybrid repair, Supra-aortic debranching RAD Residual aortic dissection after type

Purpose Hybrid aortic arch repair in patients with chronic residual aortic dissection (RAD) is a less invasive alternative to conventional surgical treatment. The aim of this study was to describe the short-term and long-term results of hybrid treatment for RAD after type A repair. Methods In this retrospective single-center cohort study, all patients treated for chronic RAD with hybrid aortic arch repair were included. Indications for treatment were rapid aortic growth, aortic diameter > 55 mm, or aortic rupture. Results Between 2009 and 2020, we performed 29 hybrid treatments for chronic RAD. Twenty-four patients were treated for complete supra-aortic debranching in zones 0 and 5 with left subclavian artery debranching alone in zone 2. There was 1 perioperative death (3.4%): The patient was treated for an aortic rupture. There was no spinal cord ischemia and 1 minor stroke (3.4%). After a median follow-up of 25.4 months (range 3-97 months), the long-term mortality was 10.3% (3/29) with no late aortic-related deaths. Twenty-seven patients (93.1%) developed FL thrombosis of the descending thoracic aorta; the rate of aneurysmal progression on thoraco-abdominal aorta was 41.4% (12/29), and the rate of aortic reintervention was 34.5% (10/29). Conclusion In a high-volume aortic center, hybrid repair of RAD is associated with good anatomical results and a low risk of perioperative morbidity and mortality, including that of patients treated in zone 0. A redo replacement of the ascending aortic segment is sometimes necessary to provide a safer proximal landing zone and reduce the risk of type 1 endoleak after TEVAR.

Introduction

The rate of reintervention after type A aortic dissection repair is estimated to be between 10 and 25% and is directly related to residual aortic dissection (RAD) in the arch and distal aorta [START_REF] Concistre | Reoperation after surgical correction of acute type A aortic dissection: risk factor analysis[END_REF][START_REF] Zierer | Aortic enlargement and late reoperation after repair of acute type A aortic dissection[END_REF][START_REF] Tamura | The prognostic impact of distal anastomotic new entry after acute type I aortic dissection repair[END_REF][START_REF] Fattouch | Long-term results after repair of type A acute aortic dissection according to false lumen patency[END_REF][START_REF] Kimura | Reoperation for enlargement of the distal aorta after initial surgery for acute type A aortic dissection[END_REF]. These reinterventions are influenced by the technique used for the initial type A dissection repair. The avoidance of arch treatment during the initial procedure is of great concern, as the aortic arch is the most challenging area to treat, whether at the first procedure or at a later date.

Conventional open total aortic arch replacement provides durable results, but is a technically demanding redo surgery that requires prolonged cardiopulmonary bypass and circulatory arrest, leading to significant morbidity and mortality rates between 5 and 20% [START_REF] Nakamura | Risk factor analysis for ascending aorta and aortic arch repair using selective cerebral perfusion with open technique: role of open-stent graft placement[END_REF][START_REF] Kazui | Aortic arch replacement using selective cerebral perfusion[END_REF]. Full endovascular techniques with branched or fenestrated endoprostheses are still in development and associated with a neurological risk ranging from 5 to 20%, depending on the type of pathology [START_REF] Haulon | Global experience with an inner branched arch endograft[END_REF]. Hybrid repair (HR), which is associated with thoracic endovascular aortic repair (TEVAR) and open supra-aortic (SA) debranching to provide an adequate proximal landing zone, has been introduced to address these lesions [START_REF] Koullias | State-of-the-art of hybrid procedures for the aortic arch: a meta-analysis[END_REF]. The outcomes of such hybrid aortic arch repair compared to open surgical repair are not well documented in the literature [START_REF] Cao | Systematic review of clinical outcomes in hybrid procedures for aortic arch dissections and other arch diseases[END_REF]. The application of HR in mostly high-risk patients increases adverse outcomes and makes the assessment of those results difficult. Outcomes of this approach seem to be directly correlated with the number of arterial debranching procedures performed as well as the proximal landing zone and the type of pathology treated.

The aim of this study was to analyze the short-term and long-term results of hybrid aortic arch repair for residual distal dissection after type A aortic repair.

Patients and Methods

Study Population

All patients included in this study were clearly informed about the use of their data for clinical research. Additionally, they were aware that their data would be used anonymously for research purposes. The institutional review board approved the project (approval number 2019-48) and waived the requirement of informed consent for the use of the patients' medical data for this study.

In this single-center retrospective cohort study, we included all patients who received hybrid treatment with a proximal landing zone of the stent graft in the aortic arch for chronic RAD. Our center is an aortic center specialized in the treatment of acute aortic syndromes. HR for aortic arch lesions is our first-line option; it is preferred over frozen elephant trunk and branched or fenestrated endoprostheses.

All cases were discussed in a multidisciplinary meeting that included vascular surgeons and cardiac surgeons, as well as an interventional radiologist, a cardiologist, and an anesthesiologist, and individualized treatment strategies were developed.

Indications for treatment were aortic rupture, rapid aortic growth (> 10 mm/year), or a diameter greater than 55 mm.

Patients were included as soon as treatment of the lesion required transposition of at least one SA trunk prior to TEVAR, regardless of whether it was the innominate artery (IA), left common carotid artery (LCCA), or left subclavian artery (LSA). Endovascular treatment during type A repair was an exclusion criterion.

Demographic, anatomic, and intraoperative details were collected. Operative complication rates as well as anatomic response and reinterventions were noted during follow-up.

Initial Surgery for Acute Type A Aortic Dissection

When the entry tear was located in the ascending aorta, we performed the replacement of the ascending aorta or the hemiarch aorta. Hemiarch replacement with open distal anastomosis during moderate hypothermic circulatory arrest (CA) with cardiopulmonary bypass (CPB) and selective antegrade cerebral perfusion (ACP) was preferred when possible (to include repair of the lesser curvature of the arch). Partial arch replacement, which was defined as a replacement between the IA and LSA, was performed in cases of primary entry tear between the IA and LSA. In these cases, the IA was debranched in the proximal part of ascending aortic repair. Total arch replacement was performed when the primary entry tear was located in the distal part of the aortic arch and could not be repaired, and when the distal anastomosis could be performed after the LSA with a frozen elephant trunk. Nevertheless, total arch replacement was seldom used in the initial acute type A repair to better enhance early survival, and partial arch replacement with IA debranching was preferred in most of cases.

Aortic root replacement with a composite prosthesis was performed according to the modified Bentall procedure in patients with dilation of the aortic root or an aortic root damaged by the entry tear.

After systemic heparinization, CPB was established by direct cannulations of the right axillary artery. Retrograde cold blood cardioplegia was infused every 15 min. CA was instituted when the vesical temperature was 25 °C. We preferred moderate hypothermia with ACP for cerebral protection during CA. In all cases, bilateral invasive blood pressure monitoring was performed via radial arteries. Additionally, intraoperative cerebral monitoring was provided by near-infrared s p e c t r o s c o p y ( N I R S ) a n d t r a n s c r a n i a l D o p p l e r ultrasonography.

Hybrid Repair Procedure for Aneurysmal Degeneration of RAD Procedures were performed in two separate interventions: the debranching procedure followed by TEVAR around 1 month later.

Supra-Aortic Debranching

We used the Ishimaru classification to categorize the proximal landing zone of the stent graft.

& Zone 0 (Z0) debranching was performed by a prosthetic bypass between the ascending aortic replacement, IA, LCCA, and LSA through a median sternotomy. The choice of a redo replacement of the ascending aortic segment was made in case of graft angulation (Fig. 1a) or a short previous ascending aortic replacement (Fig. 1b) that did not provide a good proximal landing zone.

In these cases, we performed a partial aortic arch replacement with CPB and CA with ACP to ensure a proximal landing zone > 20 mm without angulation (Fig. 1c-d) to prevent a type I endoleak.

The technique used to redo partial aortic arch replacement was the same as previously described for the type A repair. The choice of the cannulation technique was made preoperatively based on computed tomography (CT) scan, but right axillary artery cannulation was our preferred choice when possible. CA was performed under moderate hypothermia with ACP.

In cases of previous IA debranching (during type A repair), we performed an intra-thoracic debranching without CPB with direct or indirect reimplantation of the LCCA in young patients without comorbidities (Fig. 2a) or an extra-thoracic debranching with a carotid to carotid prosthetic bypass (8 mm prosthesis) in elderly patients with comorbidities (Fig. 2b). & Zone 2 debranching was performed by direct or indirect LSA reimplantation through a left supraclavicular incision in cases of previous total arch replacement or when the RAD did not involve the aortic arch (Fig. 3a-b).

TEVAR

Procedures were performed in a hybrid suite (Discovery IGS 730, GE Healthcare, Chicago, USA) by both a vascular surgeon and a radiologist. Transesophageal ultrasound was used systematically to ensure the correct positioning of the guide in the true lumen. Two different stent grafts were used: C-TAG (WL Gore & Associates Inc. Flagstaff, AZ.) and Zenith TX2 with proximal bare stent (Cook Medical, Bloomington, IN). The decision to extend the proximal landing zone was based on the location of the main residual entry tear (whether at the distal anastomosis of the ascending aortic repair, aortic arch, or the descending thoracic aorta). The distal extension of the stent graft was based on the distal extension of the dissected aortic aneurysm. Since 2017, in addition to TEVAR, we have added a bare stent deployment in the thoraco-abdominal aorta (the Zenith dissection endovascular stent (ZDES), Cook Medical, Bloomington, IN) to induce remodeling of the distal dissected aorta (stent-assisted balloon-induced intimal disruption and relamination in aortic dissection repair-STABILISE technique) [START_REF] Faure | Stent-assisted balloon-induced intimal disruption and relamination of distal remaining aortic dissection after acute DeBakey type I repair[END_REF][START_REF] Faure | Stent-assisted balloon dilatation of chronic aortic dissection[END_REF]. This technique was chosen when anatomical criteria were favorable (maximum aortic diameter less than 42 mm).

The diameter of the stent graft was sized based on the proximal and distal sealing zone with a maximum 20% of oversizing compared with the native aorta or ascending aortic graft.

Cerebrospinal fluid drainage (CSFD) was performed when there was extensive coverage of the thoracic aorta (> 250 mm). Spinal drains were placed preoperatively by anesthesiologists, a small (14-gauge) epidural catheter was placed using anatomic landmarks, with needle placement at L3-L4, and the catheter was advanced 10 cm after entering the dura. Antiplatelets were stopped 5 days earlier. Spinal fluid was drained to obtain a spinal fluid pressure < 10 mmHg before device deployment.

Radiological Analysis

All patients were followed up with a postoperative CT scan before discharge and then at 3 and 6 months and then annually. The preoperative CT scan (after type A repair, before HR for aneurysmal degeneration) and the last CT scan during follow-up were analyzed using three-dimensional imaging software (OSIRIX software, Pixmeo SARL, Geneva, Switzerland). Diameter measurements were performed on the perpendicular axis according to the centerline using a semiautomated centerline algorithm.

Technical success was defined as the exclusion of the lesion, without a type I or III endoleak on perioperative digital subtraction angiography and without perioperative death or surgical conversion.

An unfavorable anatomical outcome was defined as an increase in maximum aortic diameter more than 5 mm, a partial false lumen (FL) thrombosis in the thoracic aorta, a persistent patent FL, or a type I or III endoleak on the postoperative CT scan.

Statistical Analysis

Data are presented as the mean ± standard deviation for continuous variables and as counts (%) for categorical data. The relationship between categorical variables was studied using the chi-square test or Fisher's exact test, when appropriate. The Mann-Whitney U test was used for continuous variables. Normal distribution of the variables was assessed with the Shapiro-Wilk test. All statistical analyses were done using IBM SPSS Statistics 20.0 (IBM Inc., New York, USA).

The probability of survival without distal reinterventions was determined according to the time to last follow-up, including the 95% confidence intervals (CI), and obtained using Kaplan-Meier estimates. All statistical tests were two-sided, and P values <0.05 were considered to indicate statistical significance.

Results

Demographic Data

Between November 2009 and January 2020, 529 patients were treated for a type A aortic dissection in our aortic center. We performed 29 HR for chronic RAD for aneurysmal degeneration of the descending thoracic aorta. Two patients were treated emergently: 1 for aortic rupture and 1 for severe thoracic pain with an aneurysm of 60 mm. The patient's mean age was 59.4 years (range 38 to 78). There were 22 men (75.9%), and the characteristics of the patients and the first surgical procedures are shown in Table 1.

Debranching Procedure (Table 2)

The mean delay between the first intervention (type A aortic dissection repair) and HR was 43.8 months (range .

Twenty-four patients were treated with a complete SA debranching in zone 0.

Five patients had LSA debranching alone and endoprosthesis implantation in zone 2.

Zone 0 Debranching with CPB and CA Most of the patients had a previous short ascending aortic replacement or a hemiarch replacement with a residual angulation (Fig. 1a-b), which may compromise a good proximal landing zone. CPB with CA and selective ACP was necessary in 13 patients to ensure a good proximal landing zone for the TEVAR (Fig. 1c-d). Central cannulation with cerebral protection was performed with ACP: The right axillary artery was perfused in 9 patients (69.2%), IA in 2 (15.3%), LCCA in 1 (7.7%), and right axillary artery with the LCCA in 1 (7.7%). The durations of CPB, aortic cross clamp time, and CA are reported in Table 2.

Zone 0 Debranching Without CPB and CA Three patients had a partial lateral aortic cross clamp.

In 8 cases of previous IA debranching, we performed intrathoracic debranching without CPB in 4 patients and extrathoracic debranching with an intercarotid prosthetic bypass and LSA reimplantation in 4 (Fig. 2a-b).

Zone 2 Debranching

Among 5 cases of zone 2 debranching, 2 had a total aortic arch replacement during the initial repair. Additionally, in 3 patients, the RAD did not involve the aortic arch. In these 3 cases, patients benefited from a hemiarch replacement during initial type A repair. Moreover, on the postoperative CT scan, there was a RAD beginning after the LSA without RAD on the aortic arch (Fig. 3a-b).

TEVAR

In 25 patients, a staged procedure was chosen, whereas a concomitant TEVAR was performed in 4 patients (1 rupture, 3 elective). The mean delay between the 2 procedures was 52.1 days (0-214 days). The mean proximal landing zone diameter was 32.6 mm (28-40), the mean proximal stent graft diameter was 37.7 mm (32-45 mm), the mean aortic coverage was 239.5 mm (115-340), and the mean oversizing was 15.6% [START_REF] Cao | Systematic review of clinical outcomes in hybrid procedures for aortic arch dissections and other arch diseases[END_REF][START_REF] Faure | Stent-assisted balloon-induced intimal disruption and relamination of distal remaining aortic dissection after acute DeBakey type I repair[END_REF][START_REF] Faure | Stent-assisted balloon dilatation of chronic aortic dissection[END_REF][START_REF] Czerny | Chronic type B "residual" after type A: what I would do?[END_REF][START_REF] Dell'aquila | Early outcomes in re-do operation after acute type A aortic dissection: results from the multicenter REAAD database[END_REF][START_REF] Malvindi | Reoperation after acute type A aortic dissection repair: a series of 104 patients[END_REF][START_REF] Quintana | Open aortic arch reconstruction after previous cardiac surgery: outcomes of 168 consecutive operations[END_REF][START_REF] Bartolomeo | Long-term outcomes of open arch repair after a prior aortic operation: our experience in 154 patients[END_REF][START_REF] Verscheure | Endovascular treatment of post type A chronic aortic arch dissection with a branched endograft: early results from a retrospective international multicenter study[END_REF][START_REF] Papakonstantinou | Aortic arch reconstruction: are hybrid debranching procedures a good choice?[END_REF][START_REF] Shirakawa | The efficacy and short-term results of hybrid thoracic endovascular repair into the ascending aorta for aortic arch pathologies[END_REF][START_REF] Antoniou | Hybrid treatment of complex aortic arch disease with supra-aortic debranching and endovascular stent graft repair[END_REF][START_REF] Canaud | Hybrid aortic repair of dissecting aortic arch aneurysm after surgical treatment of acute type A dissection[END_REF][START_REF] Antoniou | Hybrid repair of the aortic arch in patients with extensive aortic disease[END_REF][START_REF] Vallejo | Hybrid repair of thoracic aortic lesions for zone 0 and 1 in high-risk patients[END_REF][START_REF] Conzelmann | Analysis of risk factors for neurological dysfunction in patients with acute aortic dissection type A: data from the German Registry for Acute Aortic Dissection type A (GERAADA)[END_REF]. Since 2017, we have treated 7 patients with the STABILISE technique when the maximum aortic diameter on the thoraco-abdominal aorta was less than 42 mm. We performed a CFD in 8 cases.

In-Hospital Morbidity and Mortality

Perioperative morbi-mortality is described in Table 3 according to zone 0 or zone 2 debranching.

Technical success was achieved in 96.5% (28/29) of cases: There was one perioperative death (3.4%) in a patient treated for rupture of a chronic RAD. Among patients treated with complete SA debranching, the mortality rate was 4.2% (1/24).

There was no spinal cord ischemia (SCI), 1 minor stroke after TEVAR (3.4%) with complete recovery, 1 myocardial infarct (3.4%), and 6 pulmonary complications (20.7%). Two patients had bleeding complications secondary to spinal drains. One patient had a medullar hematoma with cauda equina syndrome (loss of bowel and bladder function without leg paralysis). Another one had a subdural hematoma with complete recovery after neurosurgical evacuation. These patients were on anticoagulation due to a previous mechanic Bentall intervention. The rate of minor complications was 27.6% (8/29): 4 patients with recurrent laryngeal nerve paralysis (2 patients with complete and 2 patients with partial recovery), 3 patients with bleeding complications, and 1 patient with delayed healing.

Late Outcomes

After a median follow-up of 25.4 months (range 3-97 months), the rate of long-term mortality was 10.3% (3/29) with no late aortic-related death; 1 patient died at 9 months due to massive hemorrhagic stroke, and 1 patient died at 97 months due to pneumonia. Complete FL thrombosis of the descending thoracic aorta developed in 27 patients (93.1%); the rate of aortic reintervention was 34.5% (10/29): One patient (3.4%) developed a type II endoleak from the LSA at 2 months treated successfully by embolization, 8 patients (27.6%) had a reintervention on the thoraco-abdominal aorta, and 1 patient (3.4%) had a proximal reintervention (Bentall intervention) (Table 4). The rate of distal aneurysmal progression was 41.4% (12/29). There were 4 patients (13.7%) with Marfan syndrome, all of whom presented with a distal aortic expansion. In 7 patients treated with STABILISE technique, 6 had a complete aortic remodeling with a thrombosed of the FL on the thoracic aorta and complete reapposition of the FL with relamination of the intimal flap on thoraco-abdominal aorta. The Kaplan Meier estimated freedom for aortic reintervention or death at 2 years and 5 years was 73% and 66.5%, respectively (Fig. 4).

Risk Factors for Distal Aortic Aneurysmal Degeneration and Reinterventions

Risk factors for distal aneurysmal degeneration were delay between acute type A repair and HR (73.1 vs. 28.9 months, P = 0.068), the initial maximal aortic diameter (71.7 vs. 59.1 mm, P < 0.01), and the presence of a distal new entry tear (45.4% (5/11) vs. 11.1% (2/18), P = 0.07). Risk factors for distal aortic reintervention were delay between acute type A repair and HR (82.8 vs. 31.4 months, P = 0.014), the initial maximal aortic diameter (75.1 vs. 59.8, P < 0.01), and the presence of a distal new entry tear (57.1% (4/7) vs. 13.6 % (3/22), P = 0.038) (Table 5).

There was 14.2% (1/7) distal aneurysmal degeneration on thoraco-abdominal aorta in the STABILISE group compared to 45.5% (10/22) in the TEVAR alone group (P = 0.20) and none distal reintervention (P = 0.14). Proximal landing zone management did not influence late outcomes and risk of distal aneurysmal degeneration and reinterventions.

Comment

We report here an observational study with interesting results because it is the largest study on HR in chronic RAD. There are no guidelines regarding the treatment of distal aneurysmal degeneration of chronic RAD. Open surgery with total arch replacement, frozen elephant trunk (FET), hybrid treatment with supra-aortic trunk debranching and TEVAR, or total endovascular solution with fenestrated/branched endoprosthesis are different options [START_REF] Czerny | Chronic type B "residual" after type A: what I would do?[END_REF].

Open aortic arch surgery with prior ascending aortic replacement is challenging and is associated with a high rate of mortality, ranging from 5 to 20% [START_REF] Dell'aquila | Early outcomes in re-do operation after acute type A aortic dissection: results from the multicenter REAAD database[END_REF][START_REF] Malvindi | Reoperation after acute type A aortic dissection repair: a series of 104 patients[END_REF][START_REF] Quintana | Open aortic arch reconstruction after previous cardiac surgery: outcomes of 168 consecutive operations[END_REF][START_REF] Bartolomeo | Long-term outcomes of open arch repair after a prior aortic operation: our experience in 154 patients[END_REF]. In a recent study, Total endovascular aortic arch repair with branched endograft, avoiding open reoperation, may be a good option with a potentially low stroke and death rate (4%), as shown in a recent study published by Verscheure et al. [START_REF] Verscheure | Endovascular treatment of post type A chronic aortic arch dissection with a branched endograft: early results from a retrospective international multicenter study[END_REF]. Currently, these devices and techniques are investigational, limited to a few centers, with results to be duplicated on a larger scale.

Our study reports the results of hybrid arch repair specifically for chronic RAD and confirmed that hybrid treatment could be a safe and effective technique with a low rate of inhospital mortality and morbidity relative to historical controls. The rate of in-hospital mortality after hybrid aortic arch repair varies from 3 to 30% in several studies [START_REF] Papakonstantinou | Aortic arch reconstruction: are hybrid debranching procedures a good choice?[END_REF][START_REF] Shirakawa | The efficacy and short-term results of hybrid thoracic endovascular repair into the ascending aorta for aortic arch pathologies[END_REF][START_REF] Antoniou | Hybrid treatment of complex aortic arch disease with supra-aortic debranching and endovascular stent graft repair[END_REF], correlated with the number of arterial debranching procedures performed, proximal landing zone, and type of pathology treated.

The present study is one of the larger studies that included only patients with chronic RAD [START_REF] Canaud | Hybrid aortic repair of dissecting aortic arch aneurysm after surgical treatment of acute type A dissection[END_REF], with a mortality rate of 4.2% (1/20) in patients with zone 0 debranching, far below the mortality rates of 20-40% found in other series [START_REF] Antoniou | Hybrid treatment of complex aortic arch disease with supra-aortic debranching and endovascular stent graft repair[END_REF][START_REF] Antoniou | Hybrid repair of the aortic arch in patients with extensive aortic disease[END_REF][START_REF] Vallejo | Hybrid repair of thoracic aortic lesions for zone 0 and 1 in high-risk patients[END_REF].

The rate of neurologic complications can also be very significant in these challenging cases [START_REF] Conzelmann | Analysis of risk factors for neurological dysfunction in patients with acute aortic dissection type A: data from the German Registry for Acute Aortic Dissection type A (GERAADA)[END_REF]. In a case series published in 2016 by Canaud et al., the authors reported 2 strokes and 1 SCI among 7 hybrid arch repairs for chronic RAD [START_REF] Canaud | Hybrid aortic repair of dissecting aortic arch aneurysm after surgical treatment of acute type A dissection[END_REF]. In our cohort, there was only 1 stroke and no paraplegia. We believe that systematic reimplantation of the LSA is protective [START_REF] Cao | Systematic review of clinical outcomes in hybrid procedures for aortic arch dissections and other arch diseases[END_REF][START_REF] Antoniou | Hybrid repair of the aortic arch in patients with extensive aortic disease[END_REF], and CSFD performed when there is extensive coverage of the thoracic aorta (> 250 mm) reduces the rate of spinal cord complications. However, we did observe 2 complications linked to CSFD in patients with therapeutic anticoagulation; CSFD should probably be used with care in these cases.

In 13 cases, we opted for a redo replacement of the ascending aorta, when the previous ascending replacement during type A repair did not provide a good proximal landing zone Fig. 4 Long-term outcomes: Kaplan-Meier event-free survival curve for distal aortic reintervention or death (aortic events) after TEVAR for residual aortic dissection (+: censored data). *SE > 10% (angulation or short replacement) and the residual dissection involved the aortic arch. In our experience, this approach allows for a safer proximal landing zone and significantly reduces the risk of type 1 endoleak after TEVAR. With a technical success rate of 96.4%, the absence of in-hospital mortality in elective patients and the absence of type I endoleak, this study showed encouraging early results that could be explained by a complete and multidisciplinary preoperative evaluation, the use of ACP systematically in case of CA and the vast experience of our aortic center. Moreover, HR provides a less invasive option in this specific setting by limiting the extent of surgical intervention on the aortic arch, reducing the duration of the CA and perioperative mortality [START_REF] Conzelmann | Analysis of risk factors for neurological dysfunction in patients with acute aortic dissection type A: data from the German Registry for Acute Aortic Dissection type A (GERAADA)[END_REF]. However, despite good anatomical results in stabilizing the proximal part of the thoracic aorta, we observed aneurysmal progression of the thoraco-abdominal aorta in about half of the patients, requiring aortic reintervention in most cases. Faure et al. proposed the STABILISE technique to avoid these negative evolutions [START_REF] Faure | Stent-assisted balloon-induced intimal disruption and relamination of distal remaining aortic dissection after acute DeBakey type I repair[END_REF][START_REF] Faure | Mid-term outcomes of stent assisted balloon induced intimal disruption and relamination in aortic dissection repair (STABILISE) in acute type B aortic dissection[END_REF]. In our series, there were no major complications related to this technique, and the STABILISE technique seems to be associated with good anatomical results. We identified a delay between type A aortic dissection and HR as a risk factor of distal aneurysmal degeneration and aortic reinterventions. Indeed, the chronicity of the dissection has relevance with regard to aortic remodeling after endovascular therapy, which is significantly greater in patients with acute or subacute dissection. Endovascular repair of acute or subacute dissection is associated with rapid expansion of the true lumen and collapse of the FL. In contrast, endovascular treatment for chronic dissection can induce FL thrombosis in the treated segment without a change in the aortic diameter in most cases and with a patent FL on thoraco-abdominal aorta [START_REF] Sayer | Aortic morphology following endovascular repair of acute and chronic type B aortic dissection: implications for management[END_REF]. This also links to distal new entry tears identified in the present study as risk factors for distal aneurysmal degeneration and reinterventions. Stent graft-induced new entry is a well-known risk factor for aneurysm development and is more common in chronic aortic dissection and when the distal oversizing of the graft stent is > 20% [START_REF] Canaud | Risk factors for distal stent graft-induced new entry tear after endovascular repair of thoracic aortic dissection[END_REF].

Finally, initial aortic diameter was also significatively associated with an increased risk of aneurysmal degeneration and reintervention. This suggests that aortic dissection is a pathology of the whole aorta. The more severe the disease is at the thoracic level, the more severe it is at the thoraco-abdominal level.

Limitations

The small size and retrospective nature of our study limits the interpretation of the results. Moreover, these results were observed at one aortic center, which can introduce a possible confounding bias. Moreover, the lack of a comparison arm is a limitation of this study, but we cannot provide a comparative study because HR remains our first-line therapy.

Conclusion

HR of RAD in a high-volume center is associated with good anatomical results and an acceptable risk of perioperative morbi-mortality, including for patients treated in zone 0. As a less invasive approach compared to conventional surgery, this treatment provides an alternative. A redo replacement of the ascending aortic segment is necessary when the previous ascending replacement during type A repair does not provide a good proximal landing zone (angulation or short replacement) to reduce the risk of type I endoleak after TEVAR.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1007/s10557-021-07150-w.

Fig. 1 Fig. 2

 12 Fig. 1 Hybrid repair of residual aortic dissection with redo replacement of the ascending aortic segment in cases of zone 0 debranching. a Preoperative CT scan showing graft angulation that did not provide a good proximal landing zone. b Postoperative CT scan showing the proximal landing zone after redo replacement of the ascending segment and after TEVAR. c Preoperative CT scan showing short ascending replacement that did not provide a good proximal landing zone. d Postoperative CT scan showing elongation of ascending graft after redo replacement of the ascending segment and after TEVAR. The white arrow shows graft angulation. The red arrow shows the distal anastomosis of the ascending aortic graft

Fig. 3

 3 Fig. 3 Hybrid repair of residual aortic dissection that did not involve the aortic arch: left subclavian artery (LSA) debranching alone with endoprosthesis implantation in zone 2. a Preoperative CT scan showing that RAD did not involve the aortic arch. b Control CT scan showing LSA debranching and TEVAR in zone 2

Table 2

 2 Distribution of patients according to the proximal landing zone and peroperative data

	Population	n = 29
	Zone 0 debranching with CPB and circulatory arrest, n (%) 13 (44.8)
	Euroscore 2, mean (SD)	10.7 (5.5)
	CPB time (min), mean (SD)	175 (59)
	Aortic cross clamp time (min), mean (SD)	100 (50)
	Circulatory arrest time (min), mean (SD)	40 (17)
	Partial aortic arch replacement, n (%)	13 (55.5 44.8)
	Aortic root management
	Bentall, n (%)	2 (7.4 6.9)
	Supra coronary aortic replacement, n (%)	11 (48.1 37.9)
	Zone 0 debranching without CPB and circulatory arrest, n (%) 11 (37.9)
	Partial lateral aortic cross clamp, n (%)	3 (27.2 10.3)
	Previous IA debranching *
	Intra-thoracic debranching, n (%)	4 (36.4 13.8)
	Extra-thoracic debranching, n (%)	4 (36.4 13.8)
	Zone 2 debranching, n (%)	5 (17.2)
	Extra-thoracic debranching: LCCA and LSA debranching from right
	common carotid artery through bilateral cervicotomy
	CPB cardiopulmonary bypass; IA innominate artery; SD standard
	deviation
	*Intra-thoracic debranching: left common carotid artery (LCCA) and left
	subclavian artery (LSA) debranching from IA through median
	sternotomy

Table 3

 3 Perioperative morbi-mortality according to zone 0 or zone 2 debranching EVAR endovascular aortic repair; TEVAR thoracic endovascular aortic repair; LSA left subclavian artery *Aneurysmal degeneration limited to infrarenal abdominal aorta among 117 reoperations after acute type A aortic dissection repair, Dell'Aquila et al. reported an in-hospital mortality of 19.6%. Furthermore, 31 patients underwent a distal reoperation (61.2% of total arch reoperation and 22.5% of FET), with an in-hospital mortality of 25.8%[START_REF] Dell'aquila | Early outcomes in re-do operation after acute type A aortic dissection: results from the multicenter REAAD database[END_REF].

	Zone 0 debranching

Table 5

 5 Risk factors for distal aneurysmal degeneration and reinterventions

	Aneurysmal degeneration n = 11	No aneurysmal degeneration n = 18	P value

Acknowledgements We would like to thank Professor Michel S. Makaroun (Pittsburgh, PA) for his careful reading and comments.

Author Contribution All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Alizée Porto, Arnaud Blanchard, Jean Victor Chazot, Laurence Bal, Mariangela De Masi, Pierre-Antoine Barral, Alexis Jacquier, Vlad Gariboldi, Frederic Collart, Valerie Deplano, and Marine Gaudry. The first draft of the manuscript was written by Marine Gaudry, Philippe Piquet, and Alizee Porto. Axel Bartoli made all figure revisions needed to improve the manuscript. All authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Availability of Data and Material

All the patients included in this study were clearly informed about the use of their data for clinical research, and the institutional review board approved the project (approval number 2019-48).

Code Availability Not applicable.

Declarations

Ethical Approval All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards.

Informed Consent Informed consent was obtained from all participants included in the study.

Conflict of Interest

The authors declare no competing interests.

Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.