MD Norbert Heinrich

MD; PhD Andreas Mueller

MD Peter Bartmann

Professor; Arne Simon

MD, PhD Gabriele Bierbaum

Professor; Steffen Engelhart

Successful Management of an MRSA Outbreak in a Neonatal Intensive Care Unit

Keywords: Methicillin-resistant Staphylococcus aureus, MRSA, outbreak management, neonates, NICU, gastrointestinal colonization

We report an MRSA outbreak in our 25 bed tertiary neonatal intensive care unit (NICU), which was successfully contained. Patients and Methods: retrospective review of patient files, microbiology records and meeting protocols. Results: During the seven months of outbreak, 27 patients and 7 health care workers (HCWs) had positive cultures for MRSA. The outbreak was caused by the epidemic Rhine-Hessen strain, cultured isolates were monoclonal. After a sharp increase of the number of new MRSA-cases the installation of an outbreak management team (OMT) and implementation of comprehensive measures (extensive screening and decolonization strategy including orally applied vancomycin, isolation wards, intensive disinfection regimen) successfully terminated the outbreak within one month. Ten (53%) of 19 patients with completed follow up and all of the HCWs were decolonized successfully. Gastrointestinal colonization was present in 15 of 27 (56%) neonates, and was associated with poor decolonization success (30% vs. 78% in absence of gastrointestinal colonization); Conclusion: A comprehensive outbreak management can terminate an outbreak in a NICU setting within a short time. Thorough screening of nares, throat and especially stool is necessary for correct cohorting. Gastrointestinal decolonization in neonates seems difficult.

INTRODUCTION

The immaturity of the immune system, use of broad spectrum antibiotics, surgical procedures, invasive devices and mechanical ventilation expose neonatal intensive care patients to an increased risk of colonization and infection with multidrug-resistant pathogens [START_REF] Chuang | Methicillin-resistant Staphylococcus aureus bacteraemia in neonatal intensive care units: an analysis of 90 episodes[END_REF][START_REF] Adams-Chapman | Prevention of nosocomial infections in the neonatal intensive care unit[END_REF].

Among these, outbreaks caused by Methicillin-resistant Staphylococcus aureus (MRSA) are increasingly reported, causing significant morbidity and mortality in neonatal intensive care units (NICUs) [START_REF] Reboli | Epidemic methicillingentamicin-resistant Staphylococcus aureus in a neonatal intensive care unit[END_REF] In 2006, Gerber et al. published a consensus paper from the Chicago-Area Neonatal MRSA Working Group on containment and prevention measures, stating that hospitals took substantially different approaches for MRSA control [START_REF] Gerber | Management of outbreaks of methicillinresistant Staphylococcus aureus infection in the neonatal intensive care unit: a consensus statement[END_REF].Prospectively randomized trials comparing different methods of screening and decolonization treatment are lacking in this high risk neonatal population [START_REF] Singh | Microbiologic surveillance using nasal cultures alone is sufficient for detection of methicillin-resistant Staphylococcus aureus isolates in neonates[END_REF][START_REF] Hitomi | Control of a methicillin-resistant Staphylococcus aureus outbreak in a neonatal intensive care unit by unselective use of nasal mupirocin ointment[END_REF].

This article discusses our experiences and conclusions related to the successful containment of an MRSA outbreak involving 27 neonates and

MATERIALS AND METHODS

Setting and study population

The Decontamination cycles were counted, as well as treatment cycles with oral vancomycin and intravenous linezolid. All patients with at least one MRSA-positive stool sample were classified as gastrointestinal carriers ("GI-positive"), whereas children with at least two negative stool samples were classified as "GI negative".

Cohorting, Isolation, and specific Disinfection Measures

The outbreak was divided into an "endemic" phase from February to The sharp increase in case number in November prompted more intensive measures. An outbreak management team (OMT) was installed in order to implement a detailed concept for screening, hygiene, decontamination and cohorting. The NIMC ward was exclusively used to cohort all patients with known MRSA colonization ("isolation ward"). All non-colonized children were transferred to the NICU, in which all surfaces had been thoroughly disinfected using the spray-fogging technique with terminal wiping of surfaces. After release of MRSA patients from the NIMC ward, rooms were disinfected in the same fashion. Patients newly admitted to the NICU were isolated in a single room, until their MRSA carrier state was determined.

In addition to hand disinfection, staff and family members were instructed to wear gloves, gowns, and a surgical face mask during any contact to an MRSA-colonized patient or to any potential fomites in the patient"s vicinity.

MRSA Screening of Neonates

Before the outbreak, routine MRSA screening was not practised. Once installed, the OMT implemented screening of nasal, pharyngeal, and rectal swabs and stool specimens sampled 24h after admission, and then once weekly.

Three days after the completion of each cycle of decolonization treatment, swabs were taken from the nares, throat, axilla, anus, groins, and stool three times on consecutive days to assess decolonization success.

MRSA screening of Health Care Workers

Health care workers were screened by nasal and pharyngeal swabs, mandatory screening was introduced during the epidemic phase.

Microbiology

Microbiological analysis of swabs was performed using MRSASelect agar (Bio-Rad Laboratories, Marnes-la-Coquette, France), a chromogenic medium, which delivers rapid differentiation based on the activity of mecA gene product.

Pulsed field gel electrophoresis (PFGE)

Chromosomal DNA for the smaI (Roche, Germany) restriction digests was purified as described previously (Goering and Winters, 1992).

Pulsed-field gel electrophoresis (PFGE) was performed on the Chef DRIII system (Bio-Rad, Germany) using Pulsed Field Certified Agarose (1%) (Bio-Rad), 6 V/cm, a field angle of 120°, a switch time of 5-15s for 7

h and 15-60 s for a further 19 h. Staphylococcus aureus NCTC 8325 served as a standard.

Phage typing

Phage typing was performed with the international phage typing set (IPS) Phage types were determined by the strong reactions according to the international rules. Two type strains of the Rhine-Hessen strain (S.

(
aureus 3391/02 and 2981/04) were received from the German National Reference Center for staphylococci, Wernigerode.

Decolonization Regimen for Patients and HCWs

Total body washing of colonized neonates with diluted polyhexanide (Sanalind , Fresenius KABI, Bad Homburg, Germany) was done once

Statistical analysis

Data were analysed using Epi Info (version 6; CDC, Atlanta, GA) and rates were compared using the chi-square test or Fisher´s exact test as appropriate.

RESULTS

The Intravenous treatment with Linezolid resulted in negative culture results 4 days later. Surveillance cultures remained negative for three weeks;

afterwards MRSA was again cultivated from her nares. In the following course, swabs and ascites cultures remained negative until the patient died from her underlying disease at day 309 of her hospitalization.

In the other colonized patients, no symptoms attributable to MRSA were detected, apart from mild conjunctivitis in one patient.

Neonatal Screening Results and Sampling Site

MRSA was most frequently detected in nasal swabs followed by specimens from throat and stool.

Swabs from skin (axilla, groins, anus) did not contribute to detection of persistent colonization. Screening of stool, nares and throat would have detected all 25 episodes of persistent colonization. Screening of nares and throat only would have missed five episodes (19%) of persistent colonization.

To assess the possibility of taking less than three swabs or samples per site for detection of persistent colonisation, the number of swabs positive for MRSA out of three was counted. From 21 episodes with three swabs taken on successive days per sampling site, 1 of 3 swabs was positive in 11 episodes, 2 of three in 4 episodes, and 3 of 3 in 6 episodes.

Screening Results in Health Care Workers and Environment

During the endemic phase, no MRSA was isolated from 60 HCW screenings. From 118 environmental samples taken, MRSA was isolated twice from a stethoscope. During the epidemic phase, no MRSA was isolated from 42 environmental samples; 142 HCWs were screened, nine persons (6.3%, five nurses, three nursing students and one ward assistant responsible for environmental cleaning and disinfection procedures in the NICU) were identified as nasal and/or throat MRSA carriers. However, only seven isolates (4.9%) were related to the outbreak isolate. All staff members were successfully decolonized. Two nurses had to undergo a second cycle of mupirocin, one nurse suffering from atopic dermatitis was successfully decolonized after three cycles.

Due to underlying bronchial asthma, disinfection-related coughing and throat colonization with MRSA, the ward assistant was assigned to a workplace outside of neonatology department.

Phage Typing, PFGE and in vitro Antibiotic Sensitivity

All of the 27 neonatal and seven of the nine HCW-related outbreak isolates showed strong reactions in phage group III (47, 54, 75, 77, 83)

and group M (81) of the IPS, with the additional regional phages (D11, 16, 192) and the MRSA phage set (MR8, MR12 and M3). This pattern characterized the isolates as epidemic Rhine-Hessen clone of hospitalacquired MRSA. All isolates tested showed a pattern characteristic to the epidemic Rhine-Hessen clone MRSA.

All strains were resistant to ß-lactams, erythromycin, clindamycin and ciprofloxacin in vitro, in accordance with the usual phenotype of hospitalacquired MRSA.

Decolonization Success in Neonates

Of the 27 neonates with positive MRSA cultures, 8 patients were discharged or transferred to other units as "MRSA positive" before completion of decolonization. Of the 19 remaining patients with available results after decolonization, 9 (47%) showed persistent colonization and 10 (53%) were decolonized successfully.

One standard cycle of mupirocin and polyhexanide bathing was sufficient to decolonize seven children, one of whom received additional oral vancomycin. Two patients were decolonized after two cycles. More than two cycles were applied to three children, but without success.

Gastrointestinal colonization was detected in 15 of 27 (56%) neonates.

Sufficient follow-up data after decolonisation was available for 10, 3 of whom were decolonised successfully (i.e., 30% vs. 78% in absence of gastrointestinal colonization; RR = 0,39 [95% Confidence interval: 0.14-

1.06]).

Vancomycin was applied orally to seven patients with GI-positive cultures. In only one of these, a successful decolonization was confirmed by cultures.

DISCUSSION

The hospital-acquired MRSA outbreak in our NICU was caused by a single clone, confirmed by phage and PFGE-typing. We assume a combination of indirect patient-to-patient transmission and spread through the colonization of health care workers as previously described [START_REF] Bertin | Outbreak of methicillin-resistant Staphylococcus aureus colonization and infection in a neonatal intensive care unit epidemiologically linked to a healthcare worker with chronic otitis[END_REF], which may have been supported by insufficient adherence to standard hygiene procedures and the ability of MRSA to persist for long periods on contaminated surfaces [START_REF] Hota | Contamination, disinfection, and cross-colonization: are hospital surfaces reservoirs for nosocomial infection?[END_REF][START_REF] Dancer | Importance of the environment in meticillin-resistant Staphylococcus aureus acquisition: the case for hospital cleaning[END_REF]. Fortunately, no patient other than the index case suffered a serious infection due to MRSA. During an initial endemic phase (February to October) with a mean of 1.7 (0 -4)

new MRSA-cases/month, standard preventive measures were taken.

The installation of an outbreak management team (OMT), prompted by a sharp increase in incidence, including the decision-makers of the unit helped to implement measures successfully. We assume that our comprehensive approach targeting patients, staff and environment as possible reservoirs for MRSA (cohorting on isolation wards, comprehensive disinfection measures, extensive screening and decontamination strategy) was important for the successful termination of the outbreak.

Since December 2005, one month after installation of the OMT, no single new MRSA-case was registered for more than a year.

In contrast to other authors, who declared nasal swabs as the "one and only" screening site [START_REF] Singh | Microbiologic surveillance using nasal cultures alone is sufficient for detection of methicillin-resistant Staphylococcus aureus isolates in neonates[END_REF], our data show a higher sensitivity of stool cultures, in particular in the detection of persisting carriage, and suggest screening of nares, thorat and stool. The gastrointestinal tract has been identified as an important reservoir of MRSA in persistent carriers in adult patients [START_REF] Donskey | The role of the intestinal tract as a reservoir and source for transmission of nosocomial pathogens[END_REF][START_REF] Klotz | Possible risk for re-colonization with methicillin-resistant Staphylococcus aureus (MRSA) by faecal transmission[END_REF][START_REF] Boyce | Frequency and possible infection control implications of gastrointestinal colonization with methicillin-resistant Staphylococcus aureus[END_REF][START_REF] Boyce | Widespread environmental contamination associated with patients with diarrhea and methicillin-resistant Staphylococcus aureus colonization of the gastrointestinal tract[END_REF][START_REF] Acton | Intestinal carriage of Staphylococcus aureus: how does its frequency compare with that of nasal carriage and what is its clinical impact?[END_REF], and in a pediatric intensive care unit [START_REF] Thorburn | Use of surveillance cultures and enteral vancomycin to control methicillin-resistant Staphylococcus aureus in a paediatric intensive care unit[END_REF]. Contrary to the data reviewed by Acton et al, rectal swabs were clearly inferior to stool samples in detecting persistent colonization [START_REF] Acton | Intestinal carriage of Staphylococcus aureus: how does its frequency compare with that of nasal carriage and what is its clinical impact?[END_REF].

We assume that gastrointestinal colonization in neonates contributes significantly to the overall risk of environmental contamination, particularly if standard hygiene procedures and routine surface disinfection are not strictly followed [START_REF] Hota | Contamination, disinfection, and cross-colonization: are hospital surfaces reservoirs for nosocomial infection?[END_REF][START_REF] Dancer | Importance of the environment in meticillin-resistant Staphylococcus aureus acquisition: the case for hospital cleaning[END_REF]. The approach to administer vancomycin to GI-positive patients [START_REF] Thorburn | Use of surveillance cultures and enteral vancomycin to control methicillin-resistant Staphylococcus aureus in a paediatric intensive care unit[END_REF] has been disappointing in our patients.

In screening for persistent colonisation, we advise against using less than three swabs per site, since in the majority of episodes only one swab out of three yielded MRSA. Although health care workers (HCW) have been involved in outbreaks [START_REF] Bertin | Outbreak of methicillin-resistant Staphylococcus aureus colonization and infection in a neonatal intensive care unit epidemiologically linked to a healthcare worker with chronic otitis[END_REF], the role of routine HCW-screening and the question how to handle a positive result in a HCW is still a matter of debate. However, screening and decolonization of HCWs and exclusion from direct patient care may play an important role. The detection of MRSA colonization in a woman (presenting with bronchial asthma, throat MRSA colonization, and disinfection-associated coughing) responsible for surface cleaning and disinfection efforts in our unit underlines the necessity to include not only nurses and physicians into the screening population.

In summary, we conclude that a comprehensive outbreak management including the decision-makers can successfully terminate an outbreak in a NICU setting within short time. Thorough screening of nares, throat and stool for MRSA, repeated three times, is necessary for correct cohorting of patients. However, gastrointestinal decolonization in neonates seems difficult.

  Department of Neonatology of the University of Bonn is a tertiary neonatal care unit, providing 25 beds in a level III NICU and a neonatal intermediate care unit (NIMC), which are situated at a distance of about 8 km. Approximately 400 infants are admitted per year. All neonates admitted to the NICU during the outbreak period were included into this retrospective analysis. Basic clinical patient data of MRSA-colonized infants were extracted from patients" files. Microbiological results were obtained from the database of the hospital laboratory (Institute of Medical Microbiology, Immunology and Parasitology, University of Bonn). All patients with at least one culture positive for MRSA were included.

  daily. Mupirocin cream (Turixin ,GlaxoSmithKline, Munich, Germany) was applied to the nares three times per day for five days. In selected patients with persistent gastrointestinal colonization, vancomycin was given orally (30 mg/kg/d in three single doses) for 10 days, together with Lactobazillus GG capsules. Decolonization of HCWs included nasal mupirocin, throat and skin application of polihexanide and/or octenidine, daily change and washing (>60°C) of clothes and bedding, instruction in hand disinfection techniques, and daily disinfection of hand-contact surfaces (working and home setting).

  outbreak lasted for 11 months (Feb 2005-Jan 2006) and involved 27 patients. During the following year, no MRSA was detected in any patient in the NICU. Of 358 admissions during the outbreak period, 27 (7.5%) patients had at least one culture positive for MRSA. None of these patients were transferred in from an external hospital. The 27 MRSApositive patients had a median birth weight of 1,550g (interquartile range, IQR, 1,073-1,765g); the median gestational age at birth was 31 weeks (IQR, 29-34 weeks). The median duration of hospitalization was 51 days (IQR, 25,5-83 days). In none of these patients, the length of stay in hospital was prolonged as a result of MRSA colonization or infection. The index patient was born at 34+0 weeks of gestation. She suffered from congenital generalized lymphangiectasia, and required long-term mechanical ventilation. MRSA was first detected in ascites and pleural effusion during a systemic infection after retransfer from surgery.

ACKNOWLEDGEMENT

The authors thank the nursing staff of the Department of Neonatology, the company medical officer, and the clinical staff of the Department of Hospital Hygiene for their contribution to control this outbreak. Financial support: No financial support Potential conflict of interest: All authors no conflict


S Dazert

A Minovi

  L'archive ouverte pluridisciplinaire

Introduction Antimicrobial peptides (AMP)

Generally speaking surfaces like the skin or the oral mucosa are protected by several factors including the adaptive and innate immune systems against invading bacteria and fungi. The antimicrobial mucosal shield of the human airways has been subject of several studies and is well investigated [START_REF] Cole | Innate antimicrobial activity of nasal secretions[END_REF][START_REF] Hiemstra | The role of epithelial beta-defensins and cathelicidins in host defense of the lung[END_REF][START_REF] Beisswenger | Antimicrobial peptides in lung inflammation[END_REF]. A growing number of different human antimicrobial peptides (AMP) have been described which are produced e. g. by surface epithelial cells or by neutrophil granulocytes. The AMPs have a broad, but not identical spectrum of antimicrobial activity against bacteria, virus or fungi. A synergistic and additive effect of different AMPs has been reported [START_REF] Shai | Host defense peptides and lipopeptides: modes of action and potential candidates for the treatment of bacterial and fungal infections[END_REF]. In addition to their antimicrobial charactics, AMPs play a major part in inflammation, immune activation, and wound healing [START_REF] Koczulla | Antimicrobial peptides: current status and therapeutic potential[END_REF][START_REF] Yang | Multiple roles of antimicrobial defensins, cathelicidins, and eosinophil-derived neurotoxin in host defense[END_REF][START_REF] Yang | Mammalian defensins in immunity: more than just microbicidal[END_REF]. Some of the well described AMPs are subject to this study and therefore will be further described.

The human ß-Defensins (hBD)

The family of human ß-Defensins (hBD) is named after their beta-sheet structure which is stabilised by intramolecular disulfide bonds. Human ß-Defensin 1 (hBD1) was first isolated from hemofiltrate [START_REF] Bensch | hBD-1: a novel ß-defensin from human plasma[END_REF] and is expressed in epithelial cells of the urinary, respiratory tract and in keratinocytes [START_REF] Sørensen | Wound Healing and Expression of Antimicrobial Peptides/Polypeptides in Human Keratinocytes, a Consequence of Common Growth Factors[END_REF][START_REF] Goldman | Human bdefensin-1 is a salt-sensitive antibiotic in lung that is inactivated in cystic fibrosis[END_REF]. It has a strong antimicrobial effect on Gram-negative bacteria [START_REF] Krisanaprakornkit | Expression of the peptide antibiotic human b-defensin 1 in cultured gingival epithelial cells and gingival tissue[END_REF][START_REF] Schneider | Human defensins[END_REF]. Human ß-Defensin 2 (hBD2) is an inducible (by Escherichia coli, Pseudomonas aeruginosa, Helicobacter pylori, Lipoprotienacid, Candida albicans, Tumor-Necrosis-Factor-α, Interleucine1-ß) peptide [START_REF] Schröder | Human beta-defensin-2[END_REF][START_REF] Sørensen | Differential Regulation of -Defensin Expression in Human Skin by Microbial Stimuli[END_REF][START_REF] Uehara | Human betadefensin-2 induction in Helicobacter pylori-infected gastric mucosal tissues: antimicrobial effect of overexpression[END_REF] with a strong antimicrobial effect on Escherichia coli, Pseudomonas aeruginosa and Candida albicans, and a relatively weak effect on Staphylococcus aureus [START_REF] Schröder | Human beta-defensin-2[END_REF]. The human ß-Defensin 3 (hBD3) can be induced by tumor necrosis factor α and contact with Pseudmonas aeruginosa or Staphalyococcus aureus e. g. in keratinocytes [START_REF] Harder | Isolation and Characterization of Human ß-Defensin-3, a Novel Human Inducible Peptide Antibiotic[END_REF]. HBD3 has antimicrobial activity against Staphylococcus aureus, including Methicillin restistant Staphylococcus aureus (MRSA), Streptococcus pyogenes, Pseudomonas aeruginosa, Escherichia coli, Vancomycin-resistant Enterococcus faecium, Candida albicans and Haemophilus influenza [9; 12; 17].

Human LL-37 (LL-37)

LL-37 is the 37-amino acid long C-terminus and the antimicrobial active component of the human Cathelicidin antimicrobial peptide . It is expressed in leukocytes (monocytes, neutrophiles, T-cells, B-cells), epithelial cells (skin, gastrointestinal and respiratory tract) and secreted into wound and airway surface fluid [START_REF] Bals | The peptide antibiotic LL-37/hCAP-18 is expressed in epithelia of the human lung whereit has broad antimicrobial activity at the airway surface[END_REF][START_REF] Agerberth | The human antimicrobial and chemotactic peptides LL-37 and alphadefensins are expressed by specific lymphocyte and monocyte populations[END_REF][START_REF] Wang | Antibacterial activities of the cathelicidins prophenin (residues 62 to 79) and LL-37 in the presence of a lung surfactant preparation[END_REF][START_REF] Nilsson | The Human Cationic Antimicrobial Protein (hCAP18), a Peptide Antibiotic, Is Widely Expressed in Human Squamous Epithelia and Colocalizes with Interleukin-6[END_REF]. LL-37 alone and in combination with other AMPs is bactericidal against a broad spectrum of Gram-positive and Gram-negative bacteria [18; 21-23]. Apart from the antimicrobial activity LL-37 plays a role in angiogenesis, cancer development, neutralisation of bacterial lipopolysaccharide and is chemotactic for human monocytes, neutrophils and CD 4 T-lymphocytes [24-26.].

Human Secretory Leucoprotease Inhibitor (hSLPI)

hSLPI is a 11.7-kDa heavy protein which is expressed in macrophages, neutrophils and epithelial cells [27-28.].

The antimicrobial activity against Gram-negative and Gram-positive bacteria lays in the N-terminal domain of the protein [START_REF] Hiemstra | Antibacterial activity of antileukoprotease[END_REF]. hSLPI inhibits human immunodeficiency virus (HIV) infections by blocking the viral DNA synthesis [START_REF] Wahl | Secretory leukocyte protease inhibitor (SLPI) in mucosal fluids inhibits HIV-I[END_REF].

Human Bactericidal/permeability-increasing protein (BPI)

The human bactericidal / permeability-increasing protein (BPI) is a 55 kD heavy single-chain cationic protein [START_REF] Weiss | Purification and characterization of a potent bactericidal and membrane active protein from the granules of human polymorphonuclear leukocytes[END_REF] which can be divided by proteolysis into two fragments with the antibiotic and endotoxin-neutralizing functions in the N-terminal fragment [START_REF] Ooi | A 25-kDa NH2-terminal fragment carries all the antibacterial activities of the human neutrophil 60-kDa bactericidal/permeability-increasing protein[END_REF]. BPI was mainly found in the granules of neutophiles [START_REF] Weiss | Purification and characterization of a potent bactericidal and membrane active protein from the granules of human polymorphonuclear leukocytes[END_REF] but was also detected in dermal fibroblasts [START_REF] Reichel | Bactericidal/permeability-increasing protein is expressed by human dermal fibroblasts and upregulated by interleukin 4[END_REF], and the excretory lacrimal gland ducts [START_REF] Peuravuori | Bactericidal/permeability-increasing protein in lacrimal gland and in tears of healthy subjects[END_REF]. BPI has a strong antimicrobial potency and selectivity towards Gram-negative bacteria [START_REF] Weiss | Purification and characterization of a potent bactericidal and membrane active protein from the granules of human polymorphonuclear leukocytes[END_REF]. Von der Mohlen et al. could show that BPI has a significant protective effect in meningococcal sepsis [START_REF] Der Mohlen | Inhibition of endotoxin-induced cytokine release and neutrophil activation in humans by use of recombinant bactericidal/permeability-increasing protein[END_REF]. Several phase I and II studies have dealt with the pharmacokinetics and possible indications of a recombinant fragment of bactericidal/permeability increasing protein [START_REF] Demetriades | Bactericidal/permeability-increasing protein (rBPI21) in patients with hemorrhage due to trauma: results of a multicenter phase II clinical trial. rBPI21 Acute Hemorrhagic Trauma Study Group[END_REF][START_REF] Levin | Recombinant bactericidal/permeability-increasing protein (rBPI21) as adjunctive treatment for children with severe meningococcal sepsis: a randomised trial. rBPI21 Meningococcal Sepsis Study Group[END_REF][START_REF] Giroir | Preliminary evaluation of recombinant amino-terminal fragment of human bactericidal/permeability-increasing protein in children with severe meningococcal sepsis[END_REF], but have not yet led to an approved clinical application.

Human Lactoferrin (Lfc)

The human Lactoferrin (Lfc) can be found in tears, saliva, milk, neutrophil granulocytes, salivary glands and nasal mucosa [START_REF] Stenfors | Immuncytochemiacal localization of lysozyme and lactoferrin attached to the surface bacteria of the palatine tonsils during infectious mononuclesosis[END_REF]. Its antimicrobial spectrum includes Streptococcus mutans, Vibrio cholerae, Escherichia coli, Actinobacillus actinomycetemcomitans, Legionella pneumophila, Enterobacteriaceae, Candida albicans and Pseudomonas aeruginosa [START_REF] Yamauchi | Antimicrobial activity of lactoferrin and a pepsin-derived lactoferrin peptide fragment[END_REF][START_REF] Otto | Transferrins and heme-compounds as iron sources for pathogenic bacteria[END_REF].

Human Neutrophil Peptides 1-3 (HNP1-3)

The Human Neutrophil Peptides 1-3 (HNP1-3) belong to the α-Defensin family and were originally isolated from the azurophilic granules of neutrophil granulocytes [START_REF] Ganz | Defensins. Natural peptide antibiotics of human neutrophils[END_REF]. Apart from a broad-spectrum of antimicrobial activity HNP1-3 play a role in the regulation of inflammatory and immunologic processes influencing complement activation, cytotoxicity, chemotaxis of immature dendritic cells, T-cells and monocytes, enhancement of immune response and wound repair [START_REF] Soehnlein | Neutrophil primary granule proteins HBP and HNP1-3 boost bacterial phagocytosis by human and murine macrophages[END_REF][START_REF] Aarbiou | Human neutrophil defensins induce lung epithelial cell proliferation in vitro[END_REF][START_REF] Murphy | Defensins are mitogenic for epithelial cells and fibroblasts[END_REF].

Ear wax (Cerumen)

Cerumen, colloquial known as ear wax, is a waxy substance which is secreted by 1000-2000 sebaceous glands and modified apocrine sweat glands of the external auditory canal (EAC) [START_REF] Alvord | Anatomy and orientation of the human external ear[END_REF]. In general two different kinds of cerumen exist: the wet type can be found in Causasians and Africans and has a brown or dark colour. The dry type is most common in Asians and Native Amaricans and is grey in colour [START_REF] Overfield | Biologic Variation in Health and Illness: Race, Age, and Sex Differences[END_REF]. The reason is a change of a single nucleotide in the "ATP-binding cassette C11" gene [START_REF] Yoshiura | A SNP in the ABCC11 gene is the determinant of human earwax type[END_REF][START_REF] Bass | Cerumen types in Eskimos[END_REF]. This genetically determined difference of ear wax was even used to track human migratory patterns [START_REF] Ibraimov | Cerumen phenotypes in certain populations of Eurasia and Africa[END_REF][51].

Cleaning and lubricating the blind ending EAC and thereby providing mechanical protection from bacteria and fungi are described as the main functions of ear wax [START_REF] Burkhart | Cerumen composition by flash pyrolysis-gas chromatography/mass spectrometry[END_REF]. The high lipid content produced by the sebaceous glands prevents desiccation, itching and burning. These characteristics were utilized in the first lip balm which was based on ear wax [START_REF] Bortz | Composition of cerumen lipids[END_REF]. The lipids consist of squalene (6.4%), cholesterol esters (9.6%), wax esters (9.3%), triacylglycerols (3.0%), fatty acids (22.7%), cholesterol (20.9%), ceramides (18.6%), cholesterol sulfate (2.0%), and several unidentified polar components (7.5%) [START_REF] Okuda | The organic composition of earwax[END_REF]. Apart from this merely chemical analysis of ear wax very little is still known about the proteins within the ear wax.

Material and Methods:

This study was approved by the commission of ethics of the Ruhr-University of Bochum (No.: 2949) and the experiments were conducted in accordance with the Helsinki Declaration of 1975, as revised in 1983. Cerumen was collected with a sterile ear-wax-hook under microscopic control from 20 healthy adults consulting the ENT department of the Ruhr-University of Bochum, Germany. All cerumen belonged to the typical wet form. There was no incidence of infection of the EAC. The samples were kept in a sterile bottle at -80°C until further preparation.

Isolation of proteins:

We performed the isolation of proteins from ear wax according to the already published protocol [START_REF] Roeser | Physiology, pathophysiology, and anthropology/epidemiology of human earcanal secretions[END_REF]. The ear wax was treated as one pool. After weighing the pool of cerumen was divided into similar parts and pulverized using mortal and pestle which were cooled by liquid nitrogen. The pulverized sample was then transferred into a 2 ml sterile tube. As described previously the isolation of proteins was conducted using the Qproteome TM Mammalian Protein Prep Kit by Qiagen (Catalog no. 37901). 11 samples were treated according to the protocol with PBS washing before isolation of proteins. The washing reduced the ear wax to the cellular components within the wax. 9 samples were not treated with PBS washing so that the sample was used as a whole.

Afterwards the total protein concentrations of all 20 samples were measured using the "Pierce ® BCA Protein Assay Kit" by Thermo Scientific (Catalog number: 23225) and the Ultrospec® 2000 UV/visible Spectrophotometer originally supplied by Pharmacia Biotech, now part of GE Healthcare, at 562 nm wave length. The protein concentration of the ear wax samples was determined based on the standard curve. Each sample was than diluted to a concentration of 20 μg/ml.

ELISA:

ELISA were conducted according to the protocols using "Human Beta Defensin

Statistics:

After checking the results for equality of variances by using the Levene´s test an independent samples t-test was conducted to compare the concentrations of hBD1-3, Lactoferrin, human LL-37, human SLPI, human BPI, HNP1-3 for the preparation with (cellular components of ear wax sample) and without PBS washing (whole ear wax sample).

Results:

For the hBD1 concentration there is a significant difference in the scores for with PBS washing (M=28,17 pg/mg; SD=39,2 pg/mg) and without PBS washing [M=136,6 pg/mg; SD=60,68 pg/mg; t(18)=-4,83; p<0,005; eta square=0,56]. For the hBD2 concentration there is a significant difference in the scores for with PBS washing (M=17,1 pg/mg; SD=23,29 pg/mg) and without PBS washing [M=306,16 pg/mg; SD=287,8 pg/mg; t(8,09)=-3,0; p=0,017; eta square=0,33]. For the hBD3 concentration there is a significant difference in the scores for with PBS washing (M=102,19 pg/mg; SD=64,42 pg/mg) and without PBS washing [M=947,89 pg/mg; SD=751,53 pg/mg; t(8,1)=-3,37; p=0,01; eta square=0,39]. Diagram 1 shows the concentrations of hBD 1-3. For the human LL-37 concentration there is no significant difference in the scores for with PBS washing (M=36, [START_REF] Robinson | Impacted cerumen: a disorder of keratinocyte separation in the superficial external ear canal?[END_REF]

Discussion:

We still lack knowledge on a subject with which the ENT doctor is confronted every day: ear wax. After all obturating ear wax is present in 10% of all children and up to 57% of older patients in nursing homes [START_REF] Roeser | Physiology, pathophysiology, and anthropology/epidemiology of human earcanal secretions[END_REF].

Contradictory reports about the bactericidal activity of cerumen are published. The argumentation against a bactericidal activity are based on the consideration that the rich nutrients of ear wax enable bacteria and fungi to grow [START_REF] Creed | Investigations regarding the function of aural cerumen[END_REF][START_REF] Perry | Studies on the growth of bacteria in the human ear canal[END_REF][START_REF] Singer | Otitis externa: bacteriological and mycological studies[END_REF][START_REF] Campos | Influence of human wet cerumen on the growth of common and pathogenic bacteria of the ear[END_REF][START_REF] Hyslop | Earwax and host defense[END_REF]. On the other hand there are several reports describing an antimicrobial effect of ear wax with an effect against a wide range of bacteria including Haemophilus influenzae, Staphylococcus aureus, Escherichia coli and fungi [START_REF] Hyslop | Earwax and host defense[END_REF][START_REF] Petrakis | Demonstration and implications of lysozyme and immunoglobulins in human earwax[END_REF][START_REF] Chai | Bactericidal activity of cerumen[END_REF][START_REF] Lum | Antibacterial and antifungal properties of human cerumen[END_REF][START_REF] Pata | Has cerumen a protective role in recurrent external otitis?[END_REF][START_REF] Stone | Bactericidal activity of wet cerumen[END_REF]. Stoeckelhuber et al. reported the detection of the antimicrobial proteins ß-defensin-1, ßdefensin-2, cathelicidin, lysozyme, lactoferrin, MUC1 and the secretory component of IgA in the ceruminous glandular cells by histochemical analysis [START_REF] Stoeckelhuber | Human Ceruminous Gland: Ultrastructure and Histochemical Analysis of Antimicrobial and Cytoskeletal Components[END_REF]. It could be shown that not only the glands but also the skin of the EAC produce antimicrobial peptides like human ß-Defensin 1 (hBD1) and human ß-Defensin 2 (hBD2) [START_REF] Meyer | Association between human beta defensin expression and cholesteatoma formation[END_REF][START_REF] Silvola | Human ß-Defensin-1 mRNA is transcribed in tympanic membrane and adjacent auditory canal epithelium[END_REF].

Yoon et al. already isolated hBD1 and hBD2 in human cerumen in 2008 [START_REF] Yoon | Presence of hBD-1 and hBD-2 in human cerumen and external auditory canal skin[END_REF].

Because of the complex chemical composition of ear wax isolation and identification of special proteins was complicated until we developed a protocol for the protein isolation as reported previously [START_REF] Schwaab | Protein isolation from ear wax made easy[END_REF]. This method in combination with well established ELISA-Kits enabled us not only to prove the existence but also determine the concentration of ten well defined human antimicrobial peptides in ear wax. Apart from answering the question about the source of the antimicrobial effect of cerumen these data also demonstrate that some proteins are primarily cell bound and some proteins are not. The proteins hLL-37, hSLPI and hBPI had no significant difference in the protein concentration with and without PBS washing. After washing the samples with PBS at the beginning of the protein isolation the cell bound fraction only was used in 11 samples for further preparation.

Those proteins which were not cell bound were washed away. This indicates that the proteins hLL-37, hSLPI and hBPI are more or less cell bound proteins. Jung et al. reported on the expression of hCAP18 / hLL-37 in the granular and prickle cell layers of the skin of the external ear canal [START_REF] Jung | Expression of a Cathelicidin Antimicrobial Peptide Is Augmented in Cholesteatoma[END_REF] and the expression of SLPI in the stratum granulosum of the skin of the external ear canal [START_REF] Lee | Expression of secretory leukocyte protease inhibitor in middle ear cholesteatoma[END_REF]. This is the first report on the existence of hBPI in the human ear in general and especially in the EAC.

The proteins hBD 1-3, Lactoferrin and HNP 1-3 have a higher concentration in those samples which were not washed with PBS before protein isolation. These 9 samples consist of cells and not cell bound proteins. The sources for hBD1-2 and lactoferrin have been reported to be in the ceruminous glands, the skin of the external canal and the tympanic membrane [START_REF] Stoeckelhuber | Human Ceruminous Gland: Ultrastructure and Histochemical Analysis of Antimicrobial and Cytoskeletal Components[END_REF][START_REF] Meyer | Association between human beta defensin expression and cholesteatoma formation[END_REF][START_REF] Silvola | Human ß-Defensin-1 mRNA is transcribed in tympanic membrane and adjacent auditory canal epithelium[END_REF]. HNP 1-3 are released into the extracellular space by exocytosis from the azurophilic granules of neutrophiles in general [START_REF] Ganz | Defensins. Natural peptide antibiotics of human neutrophils[END_REF] although this is the first report on the existence of HNP 1-3 as well as hBD3 in the human EAC. The difference in the protein concentrations indicates that hBD 1-3, Lactoferrin and HNP 1-3 must be actively secreted into the ear wax because during the protein isolation the not cell bound proteins were not washed away.

Taking into consideration that up to 60% of a cerumen plug consists of cellular components and that some AMPs are cell bound [START_REF] Robinson | Impacted cerumen: a disorder of keratinocyte separation in the superficial external ear canal?[END_REF] may explain why some previous studies have failed to prove the antimicrobial effect of ear wax if they did not include the cellular components within the ceruminal plug.

Several studies have proven that each antimicrobial peptide has an antimicrobial effect itself, but more than that they have an even stronger additive and synergistic effect in combination [START_REF] Singh | Synergistic and additive killing by antimicrobial factors found in human airway surface liquid[END_REF]. Singh et al. could show that combinations of lactoferrin and SLPI were synergistic and the combinations involving the human -defensins, LL-37 and tobramycin had an additive effect [START_REF] Singh | Synergistic and additive killing by antimicrobial factors found in human airway surface liquid[END_REF]. Chen et al. analyzed the individual and synergistic activities of hBD 1-3, LL-37 and lysozyme in different milieus and found that these AMPs exhibited an antibacterial activity against S. aureus and E. coli in a dose-dependent manner in neutral and acidic pH milieus. The antibacterial activity of hBD 1-3 and lysozyme but not LL-37 was even significantly enhanced in acidic milieu (pH 4.6). The synergistic effect of hBDs, LL-37 and lysozyme against S. aureus was significantly enhanced in acidic milieu. The proteins showed to have an additive not synergistic effect on antibacterial activity in acidic milieu against E. coli [START_REF] Chen | Synergistic effect of antibacterial agents human beta-defensins, cathelicidin LL-37 and lysozyme against Staphylococcus aureus and Escherichia coli[END_REF].

Clinical consequences

In healthy individuals the physiological pH of ear wax is around 5,4 [START_REF] Kim | Change of external auditory canal pH in acute otitis externa[END_REF] and therefore provides optimal conditions for the synergistic and additive effect of AMPs. Kim et al. could show that there is a change of the pH in the EAC in an acute otitis externa with an increase of the pH-value [START_REF] Kim | Change of external auditory canal pH in acute otitis externa[END_REF] leading to a loss of antimicrobial efficiency of the cerumen. Often acidifying agents such as boratic acid are used to treat an infection of the EAC.

These substances help to regain the antimicrobial potency by restoring the physiological pH in the EAC. Another clinical aspect resulting from the knowledge that ear wax has a protective antimicrobial potency is that the fast and often used practice to clean the external ear canal by rinsing the ear with water leads to a complete elimination of cerumen and a change in the physiological pH. This may explain why otitis externa can develop after rinsing the ear with water. In conclusion removing ear wax manually for example with a hook and may be even leaving some ear wax in the ear canal would maintain the physiological antimicrobial potency of the EAC.

Apart from the antimicrobial potency some antimicrobial peptides like HNP1-3 and hLL37 play a role in the regulation of inflammatory and immunologic processes, influencing complement activation, cytotoxicity, chemotaxis, wound repair, angiogenesis or cancer development [43-45; 23-25]. At the moment we are learning to understand the complexity behind the synergistic and additive effects of AMPs. Although Weber et al. could show that no significant antibiotic resistances have developed from the use of ototopical antibiotic treatment [START_REF] Weber | The development of antibiotic resistant organisms with the use of ototopical medications[END_REF] gaining a better understanding of the natural possibilities of the external ear canal could lead to new therapeutic strategies for barely understood diseases like otitis externa or otitis necroticans and thereby help to prevent resistant bacteria in the EAC.

It is essential for a blind ending sac like the EAC to have a good protection against invading bacteria and fungi.

We could identify 10 out of a variety of different human antimicrobial peptides to be part of the local protection of the external ear canal. Further studies are necessary to decode the components of cerumen and determine possible changes during acute or chronic infections. Understanding the antimicrobial potency of the human body in general may lead to new strategies preventing infections without using a chemical treatment. (only cell bound fraction and total sample). For both analysed protein groups there was a significant difference in the scores between both groups. The concentrations were higher in the total samples indicating that the proteins are not only cell bound in the ear wax.

  1 ELISA Kit" (ALPHA DIAGNOSTIC INTERNATIONAL; Cat. No.: 100-240-BD1), "Human Beta Defensin 2 ELISA Kit" (ALPHA DIAGNOSTIC INTERNATIONAL, Catalog No.: 100-250-BD2), "Beta-Defensin 3 (Human) ELISA Kit" (Phoenix Pharmaceutics. Inc. U.S.A., Catalog No.: EK-072-38), "Lactoferrin ELISA Kit" (Calbiochem, Catalog No.: 427275), "Human LL-37 ELISA Test Kit" (Hbt Hycukt biotechnology b.v., Catalog No.: Hbt HK321), "Human SLPI ELISA Test Kit" (Hbt Hycukt biotechnology b.v., Catalog No.: Hbt HK316), "Human BPI ELISA Kit" (Hbt Hycult biotechnology b.v., Catalog No.: Hbt HK314), "HNP1-3 ELISA Kit" (Hbt Hycult biotechnology b.v., Catalog No.: Hbt HK317). The specific protein concentrations in pg were calculated and related to the weight of the cerumen in mg.

Figure 1 Figure 2 Figure 3

 123 Figure1shows the hBD1-3 concentrations in ear wax between the two compared groups (only cell bound fraction and total sample). For all three analyzed human ß-Defensins there was a significant difference in the scores between both groups. The concentrations of hBD 1-3 were higher in the total samples indicating that the proteins are not only cell bound in the ear wax.

Acknowledgement:

Part of these data was reported at the annual meeting of the Association of Ear-Nose-and Throat -Physicians of West Germany in Bochum in March 2010.

We thank Dr med. M. D. Pearson for proofreading this manuscript and making corrections in his mother language.

Conflict of interest:

The authors have declared that no conflict of interest exists. There was no sponsorship or funding arrangements relating to the research.


Sébastien Benzekry

Guillemette Chapuisat

Joseph Ciccolini

Alice Erlinger

Florence Hubert

A new mathematical model for optimizing the combination between antiangiogenic and cytotoxic drugs in oncology

Keywords:

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

A new mathematical model for optimizing the combination between antiangiogenic and cytotoxic drugs in oncology Sébastien Benzekry * -Guillemette Chapuisat ** -Joseph Ciccolini *** -Alice Erlinger * -Florence Hubert * Version française abrégée La découverte du phénomène d'angiogénèse tumorale par J. Folkman [START_REF] Folkman | Tumor angiogenesis: therapeutic implications[END_REF] en 1971 a permis la mise en place de traitements antiangiogéniques des cancers et préfigure l'avènement des thérapies dites ciblées, au début des années 2000. Ces traitements sont généralement administrés en parallèle avec un ou plusieurs agents cytotoxiques classiques. Les agents cytotoxiques inhibent la réplication tumorale en induisant une mort cellulaire, le plus souvent de nature apoptotique. Les antiangiogéniques, en interférant avec les voies de signalisation impactant sur la formation de néo-vaisseaux, diminuent l'apport de nutriments et d'oxygène à la tumeur et limitent ainsi sa crois-sance. En combinant les deux, on peut espérer avoir un effet synergique. Toutefois, en pratique clinique, les associations thérapies ciblées/cytotoxiques reposent, dans leurs modalités d'administration, essentiellement sur des considérations pratiques et logistiques liées au protocole chimiothérapeutique choisi et à la présence effective du patient dans le service. Or, en affectant la vasculature tumorale, il n'est pas impossible qu'un traitement antiangiogénique freine également le bon accès au site d'action des cytotoxiques co-administrés. Dans ce contexte, on peut emmettre l'hypothèse qu'il existe une modalité optimale d'association entre ces deux types de traitements. Nous proposons ici un modèle mathématique qui permet de rendre compte de l'état du réseau vasculaire de la tumeur (influencé par le traitement antiangiogénique) sur l'apport et donc l'efficacité des médicaments. Il est centré sur les équations suivantes :

     dn dt (t) = λn(t) log s(t) n(t) -kq(t)s(t)C(t)n(t) ds dt (t) = χu(t) -τ s(t) du dt (t) = -χu(t) + γn(t) -δn(t)

Introduction

A cancer is an abnormal cell proliferation within a tissue. This proliferation is generally due to genetic mutations in a single normal cell leading to dysregulation of the cell division and inability to undergo programmed cell-death or apoptosis. The resulting dividing cells can form a tumor localised to the organ (primary tumor) or subsequently disseminate throughout the body (secondary tumor or metastases). Here we will consider the antiproliferative effect of a combined therapy on the growth of a primary tumor only. Conventional treatments consist in blocking cell division and eventually killing cancer cells with cytotoxic agents. Such agents act on all rapidly dividing cells, i.e. most tumor cells as well as bone marrow, intestinal or folicles. Thus, they have numerous and possibly life-threatening side effects which frequently require a decrease in dosing or treatment discontinuation until the patient recovers. Another therapeutic possibility takes advantage of oxygen and nutrient requirements for proper tumor growth. Oxygen and nutrients being supplied by blood, tumors develop new blood vessels to ensure their growth. This process, termed tumor angiogenesis, was discovered in the 1970's by Judah Folkman [START_REF] Folkman | Tumor angiogenesis: therapeutic implications[END_REF]. Without angiogenesis, admittedly the size of most primary tumors would not exceed 2 -3 mm. To promote new vessels formation, cancer cells secrete specific growth factors like VEGF (Vascular Endothelial Growth Factor). These factors bind to receptors on vascular endothelial cells and stimulate their proliferation and migration to the tumor. Several other exocrine factors like PDGF, SDF1, PIGF or FGF2 are now recognized as regulating the neo-angiogenic process in the tumor environment. This discovery led to the new era of antiangiogenic therapies, whose purpose is to inhibit new vessels formation and thus tumor growth ultimately. To date, the humanized monoclonal antibody bevacizumab is the only marketed drug that acts directly as an antiangiogenic agent by targeting circulating VEGF, thus preventing it to reach its receptor and to promote neoangiogenesis. Bevacizumab has been approved for treating breast and colorectal cancers in combination with various cytotoxics, and is currently under clinical investigations in a variety of solid tumors like lung cancer. In this paper, bevacizumab will be used as the paradigm of antiangiogenic drugs. Our aim is to develop a mathematical model describing a combinational therapy using a cytotoxic agent (we have chosen etoposide) and bevacizumab in a localized tumor. The originality of our model is to take into account the interactions between the two drugs, in particular the influence of the quantity and quality of the vasculature on the delivery of the drugs to the tumor.

Model

Our model of combination therapy is based on already well known models. We have chosen to start from the classical model of tumor growth of Gompertz [START_REF] Gompertz | On the nature of the function expressiv of the law of human mortality and on a new mode of determining the value of life contigencies[END_REF] where the number of cancer cells n follows the law

dn dt (t) = λn(t) ln θ n(t) (1)
with θ a constant which we will call carrying capacity. This constant represents the maximal size the tumor could reach. This original model does not take into account the process of angiogenesis. That is why Hahnfeldt et al. [START_REF] Hahnfeldt | Tumor development under angiogenic signaling: A dynamical theory of tumor growth, treatment response, and postvascular dormancy[END_REF] have proposed a modification of the Gompertz model which considers the carrying capacity as a variable linked to the size of the vasculature at the given time and no longer as a constant. Equation ( 1) becomes dn dt

(t) = λn(t) ln θ(t) n(t) . (2)
In Hahnfeldt's model, the dynamics of the carrying capacity is the result of a balance between a term of stimulation of the vasculature by the tumor cells and a term of inhibition. Indeed, without inhibition, the vasculature would become anarchical and inefficient for tumor growth. Thus

dθ dt (t) = bn(t) -dn(t) 2 3 θ(t). (3)
It remains to add the effects of combination of the cytotoxic (CT) and the antiangiogenic (AA) agents. A pharmacokinetic and pharmacodynamic approach as the one developed in [START_REF] Barbolosi | Optimisation de la posologie et des modalités d'administration des agents cytotoxiques à l'aide d'un modèle mathématique[END_REF] is necessary to link the doses of drugs administred to their effective concentrations. We denote C(t) the effective concentration of CT and A(t) the effective concentration of AA.

Since the cytotoxic agent decreases tumor growth rate, the tumor growth equation [START_REF] Barbolosi | Optimisation de la posologie et des modalités d'administration des agents cytotoxiques à l'aide d'un modèle mathématique[END_REF] becomes

dn(t) dt = λn(t) log θ(t)) n(t) -kC(t)n(t). (4)
For its part, the antiangiogenic drug adds an inhibition term in the evolution of the carrying capacity and equation (3) becomes

dθ dt (t) = bn(t) -dn(t) 2 3 θ(t) -eA(t)θ(t). (5)
However, the model ( 4)-( 5) does not allow to assess the interactions between the two treatments and in particular the influence of the vasculature state on the delivery of CT and AA to the tumor. To take into account such interactions, we propose a modification of this model that consists in separating the vasculature into stable (mature) and unstable (immature) vessels.

Variables. We denote in the sequel n the number of cancer cells, s and u variables related respectively to the density of stable and unstable vessels. Let C and A be the effective concentrations of cytotoxic agent and of antiangiogenic agent.

Biological hypotheses. Our model is build from the Hahnfeldt et al. model [START_REF] Barbolosi | Optimisation de la posologie et des modalités d'administration des agents cytotoxiques à l'aide d'un modèle mathématique[END_REF], [START_REF] Barbolosi | Modélisation du rique d'évolution métastatique chez les patients supposés avoir une maladie localisée[END_REF] with the following additional assumptions on the vasculature. Only stable vessels supply nutrients and oxygen, s will thus substitute for the carrying capacity θ of Hahnfeldt's model. Only stable vessels supply pharmacological agents. Only unstable vessels are subjected to stimulatory and inhibitory signals coming from the tumor. Unstable vessels maturate with a constant rate denoted by χ, stable vessels are subject to natural death (apoptosis) with a rate τ .

For the dynamics of the therapy, we assume moreover that the effects of the agents are proportional to their effective concentration but with a constant depending on the density of the vasculature and on the quality of this vasculature. The antiangiogenic agent bevacizumab acts as a vessel disruptive agent only on immature vessels. The quality of the vasculature for distributing the pharmacological agents depends on the proportion of stable vessel in the vasculature. Let us introduce the function q(t) = s(t) s(t)+u(t) , to describe this quality of the vasculature Equations. Starting from these biological hypotheses, the equations of our model are

     dn dt (t) = λn(t)
Parameter values. The parameter values used in the illustrations below are fixed to reproduce the growth of a human tumor in absence of treatment like in [START_REF] Iwata | A dynamical model for the growth and size distribution of multiple metastatic tumors[END_REF]. We set λ = 4.2 × 10 -3 , χ = 7.56 × 10 -3 , τ = 7.5 × 10 -3 , γ = 1 and δ = 5.73 × 10 -8 .

The parameters k and η as well as the effective concentrations C(t) and A(t) depend on the chosen therapy. In the following, we opted for oral etoposide and bevacizumab. The cytotoxic agent etoposide follows a one-compartment pharmacokinetic model as described by Jong et al. [START_REF] Jong | Randomized comparison of etoposide pharmacokinetics after oral etoposide phosphate and oral etoposide[END_REF], the effective concentration C(t) being the concentration in this compartment above a threshold. The antiangiogenic agent follows a two-compartment pharmacokinetic model as described by Bruno et al. [START_REF] Bruno | A population pharmacokinetic model for docetaxel (Taxotere): model building and validation[END_REF], the effective concentration A(t) being the concentration in the second compartment above a threshold. The linear ordinary differential equations obtained with this approach will not be described here (see [START_REF] Barbolosi | Optimisation de la posologie et des modalités d'administration des agents cytotoxiques à l'aide d'un modèle mathématique[END_REF] or [START_REF] Benzekry | Modelling the impact of anticancer agents on metastatic spreading[END_REF] for more details). We arbitrarily fixed k = 1.37 × 10 -9 and η = 6.85 × 10 -11 in order to obtain realistic drug effects.

Illustrations

We investigate in this section the performance of this new model for studying the interactions between etoposide and bevacizumab, depending on the way the drugs are given. To support our hypothesis, we have chosen to simulate the impact of variations in time interval between the administrations of bevacizumab and oral etoposide, a regimen that has been tested recently to treat glioblastomas. In section 3.1, we will illustrate the effect of two distinct protocols on the tumor and its vasculature. In section 3.2, we will further show how our model allows to optimize the administration of the drugs in a given protocol.

Evolution of tumor size and vessels during a cycle of chemotherapy

Current combinational therapies are administered as successive courses, whom frequency and duration are mostly limited by a Maximal Tolerated Dose (MTD), when it is not by logistic considerations such as availability of the patient in the medical unit. Although dosage and periodicity of the courses (ie, usually from one to three weeks) are supposed to remain the same for a given protocol, frequent changes occur due to appearance of treatment-related toxicities in patients that require delay in the administration of the forthcoming courses, or reduction in dosage. In addition, a same protocol can be administered following a wide range of modalities, thus leading to numerous variations. Overall, it is widely acknowledged now that most anticancer regimen are administered on a rather empirical basis [START_REF] Davies | Treatment of metastatic colorectal cancer[END_REF][START_REF] Sargent | Sound footing or slippery slope? The value of secondary analyses of randomized trials[END_REF]. CT alone: oral etoposide is administered from day 1 to day 5 but no antiangiogenic agent is given. AA alone: bevacizumab is administered on day 1 but no cytotoxic agent is given. AA then CT: bevacizumab is administered on day 1 followed by the administration of oral etoposide from day 8 to day 13. CT then AA: oral etoposide is administered from day 1 to day 5 followed by the administration of bevacizumab on day 8. AA and CT: oral etoposide is administered from day 1 to day 5 and bevacizumab is given on day 1.

With our model, we have simulated the evolution in size of a given tumor over a course of 21-days with different drugs. Our main focus was the impact of the wait between etoposide and bevacizumab administrations on treatment efficacy, rather than the impact of the drug dosage. Thus every time the AA agent is administred, 525 mg of bevacizumab is given as a short infusion. Concerning the CT agent, the patient takes orally 212 mg a day during five consecutive days.

Figure 1 presents the results of our model when no treatment is given, when a single agent (AA or CT) is given, when both agents are given simultaneously and when both agents are given with a delay of one week between the administrations (AA then CT and CT then AA). The posology has obviously a strong influence on the final size of the tumor and even when both drugs are given, the issue of the treatment depends strongly on the order the drugs are given. With this model, the treatment that obtains the best results consists in giving bevacizumab first and etoposide one week later.

These results are consistent with the observations of Jain in [START_REF] Jain | Molecular regulation of vessel maturation[END_REF]. In this paper, Jain assumes that in a first concentration range, bevacizumab could lead to a normalisation of the vasculature, hence to a better delivery of etoposide. In the same paper, he claims also that, in a higher concentration range, bevacizumab could disrupt most of the vasculature and thus impair the delivery of etoposide, we have not tested this fact yet. Figures 1(b) and 1(d) shows that, in the concentration range we have used, bevacizumab significantly increases the quality of the vasculature without disrupting all stable vessels which deliver etoposide. The final purpose of this model is to provide an insight on how both drugs can be best combined to ensure a maximum efficacy. Once the model is set up, in silico simulations can help to predict the various effects on tumor growth reduction, so as to chose the best regimen. In this feasibility study, our data strongly suggest that the best sequence is antiangiogenic followed by the cytotoxic agent.

Optimization of the time interval between the administrations of bevacizumab and of etoposide

We are now interested in optimizing the effect of the combination therapy by adjusting the delay between the administrations of both agents. The agents are given with the same dosage as in the previous section. As suggested by the preceding results, bevacizumab is given first to normalize the vasculature. Figure 2(a) shows the evolution of the tumor during 3 cycles of combination therapy for various delay in the administration of both agents and figure 2(b) shows the minimum size of the tumor over the 3 cycles depending on the delay between the administration of both agents. On this figure, we observe that the best delay is about one week. This optimal delay may depend on the parameter values (specially on k and η which were fixed arbitrarily) but it seems that there always exists a minimum.

Conclusion and perspectives

This work is a novel approach to describe the effects of a combination between cytotoxic and antiangiogenic agents. Its originality is to take into account the nonlinear interlinkings between the two drugs. Our illustrations clearly show that this new model is able to describe a part of these interlinkings and that the consequences of these effects should not be neglected when a protocol of combination therapy is established.

For now, the model, beside the description of the effects of the combination on tumor growth, can be used to optimize and to rationalize the association between antiangiogenic and cytotoxic drugs. But in this preliminary study, we have used a set of parameter values which should be adjusted to each individual patient. A sensitivity study of these parameters will have to be carried out and set against non-clinical data obtained in mice, so as to adjust the model. An interesting feature will be to further extend this approach to the treatment of metastatic cancer as in [START_REF] Barbolosi | Mathematical and numerical analysis for a model of growing metastatic tumors[END_REF][START_REF] Barbolosi | Modélisation du rique d'évolution métastatique chez les patients supposés avoir une maladie localisée[END_REF][START_REF] Benzekry | Mathematical and numerical analysis of a model for antiangiogenic therapy in metastatic cancers[END_REF][START_REF] Benzekry | Modelling the impact of anticancer agents on metastatic spreading[END_REF].

Figure 1 .

 1 Figure1. Evolution of tumor size, quantity of stable and unstable vessels, and quality of vasculature in six different protocols. Without treatment: no drug is administered. CT alone: oral etoposide is administered from day 1 to day 5 but no antiangiogenic agent is given. AA alone: bevacizumab is administered on day 1 but no cytotoxic agent is given. AA then CT: bevacizumab is administered on day 1 followed by the administration of oral etoposide from day 8 to day 13. CT then AA: oral etoposide is administered from day 1 to day 5 followed by the administration of bevacizumab on day 8. AA and CT: oral etoposide is administered from day 1 to day 5 and bevacizumab is given on day 1.

  (a) Evolution of the tumor size (b) Minimum tumor size depending on the delay

Figure 2 .

 2 Figure 2. Optimization of the combination therapy. Bevacizumab is administered on day 1 and etoposide is administered during 5 days after a delay of 0 to 17 days.

u(t) -ηq(t)s(t)A(t)u(t) où n représente le nombre de cellules tumorales, s la quantité de vaisseaux stables, u la quantité de vaisseaux instables, q la qualité de la vasculature, C la concentration effective en agent cytotoxique et A la concentration effective en agent antiangiogénique. Ces équations sont dérivées des modèles de Gompertz[START_REF] Gompertz | On the nature of the function expressiv of the law of human mortality and on a new mode of determining the value of life contigencies[END_REF] et de Hahnfeldt et al.[START_REF] Hahnfeldt | Tumor development under angiogenic signaling: A dynamical theory of tumor growth, treatment response, and postvascular dormancy[END_REF]. Les concentrations effectives sont calculées à l'aide de modèles pharmacocinétiques et pharmacodynamiques[START_REF] Barbolosi | Optimisation de la posologie et des modalités d'administration des agents cytotoxiques à l'aide d'un modèle mathématique[END_REF].En résolvant numériquement ce modèle dans le cas d'une thérapie couplée etoposide oral et bevacizumab, on constate effectivement qu'à dose égale, le délai entre l'administration des différents agents influence fortement l'impact du traitement sur la croissance tumorale (fig.1). Il semble plus intéressant d'administrer l'agent antiangiogénique en premier afin qu'il améliore la qualité de la vasculature avant d'administrer l'agent cytotoxique. En cela, on retrouve les conclusions de Jain[START_REF] Jain | Molecular regulation of vessel maturation[END_REF]. On peut alors chercher numériquement le délai optimal pour minimiser la taille minimale de la tumeur (fig.2). On obtient une durée de 6 à 7 jours correspondant à l'intervalle optimal d'utilisation séquentielle des deux molécules. Certains paramètres du modèle ayant été fixés arbitrairement, les résultats numŕiques présentés ici ne peuvent être directement transférés en clinique mais il apparaît clairement que le calcul de la posologie optimale (doses et temps d'administration) pour ces traitements couplés pourrait grandement impacter l'efficacité de ces thérapies.