Lara Leclerc
email: lara.leclerc@univ-st-etienne.fr

Jérémie Pourchez

Gérald Aubert

Sandrine Leguellec

Laurent Vecellio

Michèle Cottier

Marc Durand

Impact of airborne particle size, acoustic airflow and breathing pattern on delivery of nebulized antibiotic into the maxillary sinuses using a realistic human nasal replica

Purpose

Improvement of clinical outcome in patients with sinuses disorders involves targeting delivery of nebulized drug into the maxillary sinuses. We investigated the impact of nebulization conditions (with and without 100 Hz acoustic airflow), particle size (9.9 µm, 2.8 µm, 550 nm and 230 nm) and breathing pattern (nasal vs. no nasal breathing) on enhancement of aerosol delivery into the sinuses using a realistic nasal replica developed by our team.

Methods

After segmentation of the airways by means of high-resolution computed tomography scans, a well-characterized nasal replica was created using a rapid prototyping technology.

A total of 168 intrasinus aerosol depositions were performed with changes of aerosol particle size and breathing patterns under different nebulization conditions using gentamicin as a marker.

Results

The results demonstrate that the fraction of aerosol deposited in the maxillary sinuses is enhanced by use of submicrometric aerosols, e.g. 8.155 ± 1.476 mg/L of gentamicin in the left maxillary sinus for the 2.8 µm particles vs. 2.056 ± 0.0474 for the 550 nm particles.

Utilization of 100-Hz acoustic airflow nebulization also produced a 2-to 3-fold increase in drug deposition in the maxillary sinuses (e.g. 8.155 ± 1.476 vs. 3.990 ± 1.690 for the 2.8 µm particles).

Conclusion

Our study clearly shows that optimum deposition was achieved using submicrometric particles and 100-Hz acoustic airflow nebulization with no nasal breathing. It is hoped that our new respiratory nasal replica will greatly facilitate the development of more effective delivery systems in the future.

KEY WORDS

Aerosol therapy, drug deposition, nasal replica, maxillary sinuses

INTRODUCTION

Health problems caused by rhinosinusitis constitute a considerable financial burden on society [START_REF] Fokkens | European Position Paper on Rhinosinusitis and Nasal Polyps 2012[END_REF][START_REF] Bhattacharyya | Recurrent Acute Rhinosinusitis: Epidemiology and Health Care Cost Burden[END_REF]. Blockage of sinus drainage through infection of the nasal mucosa or impaired mucociliary clearance produces a favorable environment for sinusitis in which pathogens may proliferate. Better targeting of delivery of nebulized antibiotics to the maxillary sinuses could improve clinical outcomes in patients with chronic rhinosinusitis disorders. However, such targeting is complex due to the anatomical features of the maxillary sinuses. These cavities are poorly ventilated and only communicate with the nasal fossa via the maxillary ostium, a narrow duct (about 1-5 mm in diameter; 10-15 mm in length) [START_REF] Tarhan | Acoustic rhinometry in humans: accuracy of nasal passage area estimates, and ability to quantify paranasal sinus volume and ostium size[END_REF]. Drug aerosolization is a common therapeutic approach in the treatment of sinuses disorders such as rhinosinusitis since it is painless and safe and offers a number of advantages over systemic therapy [START_REF] Deshpande | Nasal drug delivery-a review[END_REF][START_REF] Djupesland | Nasal drug delivery devices: characteristics and performance in a clinical perspective-a review[END_REF].

Several studies have demonstrated clinical benefits [START_REF] Vaughan | Use of Nebulized Antibiotics for Acute Infections in Chronic Sinusitis[END_REF], although the question has not been extensively clinically investigated.

In this context, it is clearly of interest to achieve a better understanding of any nebulization features allowing specific targeting of the maxillary sinuses while avoiding pulmonary deposition, since the latter involves a risk of side effects. However, the nebulization conditions required to enhance aerosol deposition in the sinuses are not well established [START_REF] Vecellio | Deposition of aerosols delivered by nasal route with jet and mesh nebulizers[END_REF].

For example, particles larger than 10 µm inhaled nasally are known to be deposited in the nasal cavities (FDA guidance, 2002) but no international consensus or guidelines exist regarding the relationship between aerosol characteristics and precise deposition site within the nasal cavities such as the sinuses.

Human intranasal deposition studies are restricted by the risks associated with exposure and by ethical considerations. As an alternative, anatomical models have been proposed, such as cadaver heads [START_REF] Valentine | A prospective controlled trial of pulsed nasal nebulizer in maximally dissected cadavers[END_REF][START_REF] Durand | Impact of acoustic airflow nebulization on intrasinus drug deposition of a human plastinated nasal cast: new insights into the mechanisms involved[END_REF], nasal cavity replicas [START_REF] Möller | Ventilation and drug delivery to the paranasal sinuses: studies in a nasal cast using pulsating airflow[END_REF][START_REF] Kundoor | Assessment of nasal spray deposition pattern in a silicone human nose model using a color-based method[END_REF] and nasal casts using recent prototyping techniques [fused deposition modeling (FDM) and stereolithography (e.g. the SLA, Viper or SAINT models)] [START_REF] Kelly | Detailed flow patterns in the nasal cavity[END_REF][START_REF] Janssens | The Sophia Anatomical Infant Nose-Throat (Saint) model: a valuable tool to study aerosol deposition in infants[END_REF]. While in vitro studies have shown that nebulized particles may be deposited in the paranasal sinuses, this is always at low concentrations due to ostium morphology as well as aerosol characteristics such as size, pressure and flow rate [START_REF] Hyo | Particle deposition efficiency of therapeutic aerosols in the human maxillary sinus[END_REF][START_REF] Saijo | Particle deposition of therapeutic aerosols in the nose and paranasal sinuses after transnasal sinus surgery: a cast model study[END_REF][START_REF] Hilton | Differential deposition of aerosols in the maxillary sinus of human cadavers by particle size[END_REF][START_REF] Durand | Preliminary study of the deposition of aerosol in the maxillary sinuses using a plastinated model[END_REF][START_REF] Croce | In vitro experiments and numerical simulations of airflow in realistic nasal airway geometry[END_REF].

Moreover, in a recent study we demonstrated a significant increase in intrasinus drug deposition using acoustic airflow nebulization (100 Hz) of micrometric airborne particles [START_REF] Durand | Impact of acoustic airflow nebulization on intrasinus drug deposition of a human plastinated nasal cast: new insights into the mechanisms involved[END_REF].

The aim of this study is to provide a better understanding of the parameters that enable specific drug targeting of the maxillary sinuses. To that end, we assessed and quantified the deposition of gentamicin (aminoglycoside antibiotic, used as a marker) as a function of variations in three nebulization parameters: airborne particle size within the micron and submicron range (230 nm to 9.9 µm), 100 Hz acoustic airflow, and nasal or non-nasal breathing.

The experiments were performed on a realistic nasal replica built using a stereolithography technique.

MATERIALS AND METHODS

Nasal replica

Plastination allows anatomical specimens to be preserved in a physical state approaching that of live physiological conditions with numerous advantages [START_REF] Hagens | Impregnation of soft biological specimens with thermosetting resins and elastomers[END_REF]. In particular, in plastinated head specimens, anatomical and aerodynamic behavior closely resembles patterns seen in vivo. Moreover, such models have a specific lateral-paramedian section providing easy access to the maxillary sinuses. Such plastinated human specimens were previously characterized anatomically, geometrically and aerodynamically [START_REF] Durand | Plastinated nasal model: a new concept of anatomically realistic cast[END_REF] and then used for aerosol deposition studies [START_REF] Durand | Impact of acoustic airflow nebulization on intrasinus drug deposition of a human plastinated nasal cast: new insights into the mechanisms involved[END_REF]. However, the main limitations of previous specimens of this type were the complexity of the washing steps involved, especially the long drying time (around 2 days) and the time required to obtain specimens (6 months). To overcome these drawbacks, a nasal replica of the human plastinated specimen was created for this study using a stereolithography technique.

First, a precise CT-scan of the plastinated model was obtained (LightSpeed VCT scanner, GE Healthcare, Milwaukee, Illinois, US). 226 DICOM scan images of the CT-scan, corresponding to the entire nasal cavities, were processed using HYCAD software to delimit the outlines of the cavities of interest, namely the frontal, ethmoidal and maxillary sinuses and the nasal fossae. Special care was taken in delineating the ostia, which constitute a critical ventilation pathway. The 226 segmented images were then converted and imported into the SolidWorks® software, a mechanical 3D computer-aided design program. The model was reconstructed step by step in 3D, as shown in Figure 1, and the replica was then manufactured in transparent, water-resistant, non-porous resin.

Endoscopy and CT scans were performed on the replica in order to assess the anatomical reproducibility of the known human plastinated model. Precise measurements were compared for the critical anatomical regions of the ostia and maxillary sinuses.

Nebulization systems and aerosol characterization

Micrometric, submicrometric and nanometric aerosols were generated using the following medical jet nebulizers: an Atomisor NL20 (DTF Medical, France) and an Atomisor NL11 (DTF Medical, France), a modified SideStream (Philips Respironics, Ref 12NEB400, England), and a Nanoneb (DTF Medical, France). Aerosol particle sizes were expressed as mass median aerodynamic diameter (MMAD) using an electrical low-pressure impactor (ELPI, Dekati Ltd., Finland), as described in a previous study [START_REF] Durand | Impact of acoustic airflow nebulization on intrasinus drug deposition of a human plastinated nasal cast: new insights into the mechanisms involved[END_REF].

Aerosol characterization was performed using a chemical tracer, sodium fluoride (NaF; 2.5 wt%; 4 mL), as recommended in a European standard (NF EN 13544-1). Operating at an airflow of 10 L.min -1 , the ELPI allowed nebulized particles to be sorted into 12 size groups (7 nm to 10 nm). The nebulizer was connected to the ELPI via a metal United States Pharmacopeia (USP) like artificial throat (height 112 mm; width 42 mm; internal diameter 19 mm). NaF was aerosolized by the nebulizer for 10 min, after which the various elements (USP throat and each stage) were rinsed with 5 mL of deionized water. The NaF concentration of samples was assayed by electrochemical means (PerfectION TM combined with a SevenGo pro TM F-electrode, Mettler Toledo, France). Finally, the MMAD and the geometric standard deviation (GSD) of the nebulized particles were calculated using the electrochemical NaF measurements.

Emitted aerosol fraction (output)

The quantity of aerosol produced by the nebulizer over a 10-minute period was measured using a residual gravimetric method [START_REF] Vecellio None | Residual gravimetric method to measure nebulizer output[END_REF]. The mass of gentamicin was measured on a filter before and after nebulization. The results were expressed as the percentage and as the actual mass of gentamicin collected.

Aerosol inhalation

The experimental set-up is described on Figure 2 and comprised a nebulizer linked to nasal replica nostrils by a nasal plug (C28, medium size, DTF Medical, France) of a type used in clinical practice. The trachea of the nasal replica was connected to a respiratory pump (Pari, Compas II) allowing reproduction of various sinusoidal breathing patterns. A system of valves was used with the respiratory pump and the nasal cast to simulate different breathing patterns.

A filter was connected to the trachea of the nasal cast to measure the amount of aerosol penetrating into the lung model (Inhalation Filter Pad, Pari GmbH, Germany).

An aminoglycoside antibiotic (gentamicin) was used as the marker (Gentamicin Panpharma, 80 mg/mL, CIP: 3400935120540, Exp: 03/2014, Batch 10267). In each experiment, 4 mL of gentamicin at a concentration of 80 mg/mL was nebulized for 10 minutes.

The nebulization systems were used with an AOLH® air source compressor (Diffusion Technique Française, DTF Medical, Saint-Etienne, France). This compressor can produce a "sonic aerosol" by adding a 100Hz acoustic airflow during aerosol production as described previously [START_REF] Durand | Impact of acoustic airflow nebulization on intrasinus drug deposition of a human plastinated nasal cast: new insights into the mechanisms involved[END_REF]. Each experiment was performed both with and without 100Hz acoustic airflow.

Breathing patterns

-Normal nasal breathing: a cycle was defined as 15 breaths per minute, with a tidal volume (Vt) of 500 mL, extrathoracic dead space of 21 ml, tracheal diameter of 1 cm, principal bronchial diameter of 0.8 cm and inspiratory-to-expiratory time ratio (I:E) of 40/60. Under these conditions, inhalation time was set at 1.6 seconds and exhalation time was set at 2.4 seconds. These breathing parameters correspond to the reference physiological parameters for male adults [START_REF] Criée | Body plethysmography -Its principles and clinical use[END_REF][START_REF] Booker | Interpretation and evaluation of pulmonary function tests[END_REF][START_REF] Flesch | Lung volumes: Measurement, clinical use, and coding[END_REF].

-Slow nasal breathing: a cycle was defined as a breathing rate of 10 breaths per minute and a Vt of 750 mL. Under these conditions, inhalation time was set at 2.4 seconds and exhalation time at 3.6 seconds. Vt values were increased to avoid simulated hypoventilation.

For normal and slow nasal breathing, the set-up simulated inhalation through the nose and expiration through the mouth during operation of the respiratory pump.

-No nasal breathing: we compared nebulization without nasal breathing. The same experimental set-up was used but without any cycles. This experimental condition mimics inhalation and exhalation by the mouth.

Drug deposition in the maxillary sinuses

After nebulization, gentamicin was collected from each maxillary sinus by flushing 3 times with the same saline solution using a 1 mL syringe as previously described [START_REF] Durand | Impact of acoustic airflow nebulization on intrasinus drug deposition of a human plastinated nasal cast: new insights into the mechanisms involved[END_REF]. Gentamicin concentrations in samples were quantified by fluorescence polymerization immunoassay (FPIA) with a TDxFLx® analyzer (Abbott Diagnostics Division, USA), which has a lower detection limit of 0.2 mg/L. After recovery, the nasal replica was washed copiously with tap water and dried with pulsed air. Control nebulizations were performed with saline solution.

Statistical analysis

Analysis was performed and graphs plotted using Prism 5.0 software (GraphPad, San Diego, CA). Significance (***) was established by ANOVA test (p < 0.05).

RESULTS

Anatomical features of the nasal replica

Nasofibroscopy showed that the nasal replica obtained by stereolithography was similar to the original plastinated human specimen. Endoscopic observations demonstrated good preservation of nasal airway anatomy in the nasal replica. Moreover, physical measurements of the replica confirmed exact reproduction of the plastinated model with a mean error of less than 0.3 mm. For example, between the distance between the right and left sinuses for the plastinated model was 90.88 mm vs. 90.51 mm for the nasal replica, and 8.35 mm for the septum in the plastinated nasal septum vs. 8.90 mm for the nasal replica. All dimensions were well-respected, especially in such critical anatomical regions as the ostia of the maxillary sinuses.

Imaging data from CT scans confirmed high preservation of anatomy, particularly regarding the nasal airway and turbinate mucosa, which were as close as possible to actual physiological conditions. Figure 3 compares images of the left and right ostia in the plastinated specimen and the nasal replica where the measurements of the structures in the images were identical between the two models. Like the plastinated specimen [START_REF] Durand | Impact of acoustic airflow nebulization on intrasinus drug deposition of a human plastinated nasal cast: new insights into the mechanisms involved[END_REF][START_REF] Durand | Plastinated nasal model: a new concept of anatomically realistic cast[END_REF], the plastic nasal replica exhibits differences in the dimensions of the individual maxillary ostia: 6 mm long with a diameter of 2 mm for the right maxillary sinus ostium (normal anatomical form: long and narrow) and 2 mm long with a diameter of 5 mm for the left maxillary ostium (abnormally short and broad). These CT and endoscopy results confirm the good preservation of the anatomical and geometrical details in the model, enabling comparison to be made in this study between two different types of ostia morphology.

We earlier determined the reliability of airway geometry (using acoustic rhinometry) and airflow resistance (measured by rhinomanometry) in the plastinated model used as the basis for the stereolithographic nasal replica [START_REF] Durand | Plastinated nasal model: a new concept of anatomically realistic cast[END_REF]. Taking into account all of these elements, the nasal replica manufactured by stereolithography appeared anatomically, geometrically and aerodynamically similar to the original human plastinated specimen, which is a well-validated model of a healthy subject without nasal congestion.

Aerosol particle size and emitted aerosol fraction

The results are shown in Table I.

Each type of nebulizer had its own specific aerosol MMAD: 9.9 µm for the Atomisor NL20 (GSD of 2), 2.8 µm for the Atomisor NL11 (GSD of 3.2), 550 nm for the Sidestream (GSD of 2.1) and 230 nm for the Nanoneb (GSD of 1.6).

The emitted aerosol fraction was different for each type of nebulizer: 6.84±0.29% for the Atomisor NL20, 9.96±1.72% for the Atomisor NL11, 2.06±0.46% for the Sidestream and 0.26±0.04% for the Nanoneb.

Drug deposition in the maxillary sinuses

All results for gentamicin collected in the maxillary sinuses (mg/L and percentage of the emitted dose) under each test condition (particle size, 100 Hz acoustic effect and breathing pattern) are summarized in two tables in the Supplementary Data section.

Impact of anatomy

Aerosols penetrate the maxillary sinuses with different gentamicin deposition profiles due to the anatomical features of the maxillary ostium (Figure 4 A andB). The amount of nebulized active substance collected in the left sinus of the nasal replica was consistently significantly higher for each type of nebulizer in accordance with the morphological differences of the ostia explained in the previous paragraph. These results are perfectly consistent with our previous study [START_REF] Durand | Impact of acoustic airflow nebulization on intrasinus drug deposition of a human plastinated nasal cast: new insights into the mechanisms involved[END_REF], and we again confirmed that the airflow resistance associated with the endonasal anatomy has a huge impact on drug deposition in the maxillary sinuses.

Impact of nebulized particle size

The impact of airborne particle size (different MMAD values) is clearly discernible in Figure 4. Data obtained for the 230 nm size are not exposed on the graphic because values are very close from the detection limit. Since the impact of particle size in aerosols is closely linked to the emitted aerosol fraction, the results shown in Figure 4A are expressed as percentage of emitted aerosol. We clearly demonstrated that deposition in the maxillary sinuses is enhanced for the smallest particle sizes for a normalized emitted aerosol fraction. Under these conditions, optimal results were obtained with the 230-nm nebulizer, particularly in the left maxillary sinus.

Figure 4B expresses the results in terms of the amount of gentamicin collected in the maxillary sinuses in mg/L. The Nanoneb nebulizer generated particles of around 230 nm and the gentamicin collected in the maxillary sinuses was between 0.2 and 0.4 mg/L, which is very close to the control values (around 0.2 mg/L). The SideStream nebulizer generated particles of around 550 nm and the maximum mean quantity of gentamicin deposited was close to 2 mg/L. Use of larger particles appeared to enhance drug deposition in the maxillary sinuses, with the amount of gentamicin collected for the NL11 nebulizer reaching a mean maximum of 10 mg/L. Finally, the largest particles generated by the NL20 nebulizer (9.9 µm) were deposited to a lesser extent than the 2.8-µm particles (maximum of 2 mg/L in the left maxillary sinus). Under these conditions, using current nebulization technologies, the particles most efficiently deposited in the maxillary sinuses in terms of mass are those measuring 2.8 µm.

Impact of breathing patterns

Figure 5 shows the results for the SideStream and the NL11 nebulizers under normal nasal breathing and non-nasal breathing conditions. No significant differences were noted between normal and slow nasal breathing for the various types of nebulizers (data not shown). By contrast, intrasinus deposition with non-nasal breathing was at least twice as high as with nasal breathing (e.g. in the left sinus: 2 mg/L vs. 1 mg/L for the SideStream and 3 mg/L vs.

8 mg/L for the NL11).

Impact of 100-Hz sonic aerosols

The results concerning the impact of acoustic airflow are shown on Figure 6. The data shown are for the SideStream and the NL11 nebulizers with and without 100-Hz acoustic airflow. No significant differences were noted for the NL20 and Nanoneb nebulizers (data not shown).

Graphs A and B show that acoustic airflow significantly enhanced gentamicin deposition in both the left and right maxillary sinuses for the SideStream and the NL11 nebulizers with non-nasal breathing. With normal or slow nasal breathing, acoustic airflow had no significant effect for any of the four types of nebulizer.

DISCUSSION

This study assessed the deposition of a nebulized antibiotic in the maxillary sinuses of a nasal replica while varying three following parameters: particle size, 100 Hz acoustic effect and breathing patterns.

The 3D nasal replica manufactured for this study was highly consistent with a plastinated anatomical model that closely resembles a healthy subject without nasal congestion [START_REF] Durand | Plastinated nasal model: a new concept of anatomically realistic cast[END_REF].

Three main families of human nasal casts exist for the study of aerosol deposition: human cadaver models [START_REF] Hilton | Differential deposition of aerosols in the maxillary sinus of human cadavers by particle size[END_REF], plastic replicas [START_REF] Kelly | Detailed flow patterns in the nasal cavity[END_REF][START_REF] Schreck | Correlations between flow resistance and geometry in a model of the human nose[END_REF] and pipe models [START_REF] Möller | Ventilation and drug delivery to the paranasal sinuses: studies in a nasal cast using pulsating airflow[END_REF][START_REF] Maniscalco | Sounding airflow enhances aerosol delivery into the paranasal sinuses[END_REF][START_REF] Cakmak | Effects of paranasal sinus ostia and volume on acoustic rhinometry measurements: a model study[END_REF]. However, these casts have several disadvantages such as biosafety and stability over time for cadaver models and lack of fine detail such as maxillary ostium morphology for plastic replicas and pipe models. The replica of the human plastinated model manufactured for this study appears very useful for in vitro characterization of drug deposition in the maxillary sinuses. This model exhibits many desirable technical characteristics such as anatomical features very closely resembling those of in vivo human nasal cavities, coupled with ease of access to the maxillary sinuses, stability over several years, ease of washing, ease of handling and transport, absence of odors and biological safety.

We demonstrated that sonic aerosols using a variety of acoustic airflow (w/wo 100 Hz), breathing patterns (nasal vs. non-nasal breathing) and particle size (MMAD in the 230 nm-9.9 µm range) lead to disparate intra-sinus drug deposition. These results clearly demonstrate the ability of gentamicin aerosol to penetrate and the maxillary sinuses. We also confirmed the great efficacy of a 100-Hz acoustic airflow in enhancing drug deposition in the maxillary sinuses. These results confirm the conclusions previously described for a single particle size (2.8 µm; NL11) using the human plastinated specimen [START_REF] Durand | Impact of acoustic airflow nebulization on intrasinus drug deposition of a human plastinated nasal cast: new insights into the mechanisms involved[END_REF].

Aerosol deposition within the maxillary sinuses appears to be inversely related to aerosol particle size in the 230 nm -2.8 µm size range (i.e. all except the largest 9.9 µm particles with the NL20 nebulizer). Maximum deposition was achieved with 2.8-µm particles using the NL11 nebulizer. We clearly demonstrated non-significant deposition of the smallest particles generated by the Nanoneb device and weak deposition of the 550-nm and 9.9-µm particles generated by the SideStream and NL20 devices respectively. The clear impact of nebulized particle size on the quantity of drug deposited in the maxillary sinuses was observed under non-nasal breathing conditions. In this case, maximum deposition was observed for the 2.8µm particles (NL11 nebulizer) with an acoustic frequency of 100Hz. It must be noted that for a normalized emitted aerosol fraction, gentamicin deposition of nanometric particles in the maxillary sinuses is enhanced. It suggested the best performance in relation to emitted dose but most of the 230 nm depositions data were very close to the detection limit and therefore should not be over-interpreted. These results are of great interest for the development of new nano-aerosol devices with improved emitted aerosol fractions. For the moment, the NL11 nebulizer seems to be the best compromise for intrasinus targeting.

Interestingly a recent study also presents data of maxillary sinuses deposition in the percentage range of emitted dose [START_REF] Möller | Topical Drug Delivery in Chronic Rhinosinusitis Patients before and after Sinus Surgery Using Pulsating Aerosols[END_REF]. Sinus deposition data are obtained in vivo by means of a radiolabelled aerosol study in patients. Results are approximately 10 times higher than gentamicin deposition obtained in our medication study using a realistic nasal cast. It is however difficult to reach a conclusion because three major parameters change between these studies. 1) Anatomical models are different (in vivo vs. realistic nasal cast). The sinus anatomic features appear to be crucial in predicting the maxillary sinuses deposition even if good consistency has been noticed using realistic nasal cast [START_REF] Durand | Sonic aerosol therapy to target maxillary sinuses[END_REF][START_REF] Guellec | Validation of Anatomical Models to Study Aerosol Deposition in Human Nasal Cavities[END_REF] No differences were observed between normal and slow nasal breathing, even with different particle sizes. By contrast, intrasinus drug deposition was significantly enhanced under nonnasal breathing conditions compared to nasal breathing. These results suggest that the increase in aerosol velocity due to nasal breathing leads to significantly decreased intrasinus drug deposition, underlining the potential value of advocating non-nasal breathing to patients for therapeutic ends.

Our approach is based on the fact that in patients with chronic rhinosinusitis, the ostium of the maxillary sinus is obstructed. Thus, the quantity of antibiotic measured within the maxillary sinus is in fact found at the ostium, which constitutes the "crossroads" of sinus disease (since all gentamicin deposited in the maxillary sinus in our model of a non-congested healthy subject clearly entered the maxillary sinus via the ostium). In addition, for subjects undergoing sinus surgery, meatotomy may enable greater quantities of antibiotic to be deposited in the maxillary sinus than those measured in our model. In either case (operated and unoperated subjects), our results, although obtained in a model of a healthy noncongested subject, are encouraging as regards the potential efficacy of nebulized antibiotics in the treatment of chronic rhinosinusitis, and they demonstrate the relevance of clinical trials on this subject, which should begin in the near future.

While delivery of effective doses of drug continues to be limited by nebulizer technology, micrometric nebulizers such as the NL11 jet appear to offer the best currently available solution for improved drug delivery in sinus patients. In this conditions addition of a 100 Hz acoustic airflow is also recommended.

CONCLUSION

We demonstrated that optimal gentamicin deposition in the maxillary sinuses was obtained with the NL11 nebulizer (MMAD: 2.8 µm) using 100-Hz acoustic airflow and non-nasal breathing. This finding indicates that a specific aerosol pattern should be selected in order to fully enhance intrasinus deposition. Providing patients with specific recommendations concerning the nebulization procedure could thus significantly improve the efficacy of antibiotic treatment.

MMAD (nm

  [START_REF] Durand | Sonic aerosol therapy to target maxillary sinuses[END_REF], Le Guellec 2013). Comparison between results of maxillary sinuses deposition obtained using different anatomical model remains difficult. 2) The maxillary sinuses deposition assessment was evaluated by a 2D radiolabelled methodology vs. in situ dosage of intrasinusal lavage. 2D radiolabelled quantification is very useful for comparing devices but seems to significantly over-estimate deposition in comparison to other methodologies such as 3D SPECT-CT and intrasinusal lavage (31)(Leclerc et al, in press) and a comparison remains difficult. 3) The nebulization devices are also different and should probably have a strong influence on the deposition (DTF vs. PARI Pharma GmbH).

Figure 1 :

 1 Figure 1: Plastic replica made from the plastinated model. A) Plastinated human specimen -

Figure 2 :

 2 Figure 2: Experimental design for aerosol deposition.

Figure 3 :

 3 Figure 3: CT scans performed on the plastinated specimen (A and B) and on the plastic nasal

Figure 4 :

 4 Figure 4: Impact of nebulized particle size (MMAD) and anatomical features such as right vs.

Figure 5 :

 5 Figure 5: Impact of breathing patterns on nebulized gentamicin collected in the maxillary

Figure 6 :

 6 Figure 6: Impact of 100 Hz acoustic airflow on nebulized gentamicin collected in the

Table 1 :

 1 Aerosol characteristics after 10 min of nebulization: mass median aerodynamic diameter (MMAD) evaluated using ELPI. Results are also expressed as a percentage of the emitted aerosol fraction and gentamicin output mass (mg).

		)	GSD	Emitted aerosol fraction (%)	Gentamicin output mass (mg)
	NL20	9900	2	6.84 ± 0.29	21.88
	NL11	2800	3.2	9.96 ± 1.72	31.89
	SideStream	550	2.1	2.06 ± 0.46	6.6
	Nanoneb	230	1.6	0.26 ± 0.04	0.83

ACKNOWLEDGEMENTS

The authors are grateful to the engineering department of Diffusion Technique Française (DTF Medical, Saint-Etienne, France) for their assistance with SolidWorks®.

The authors wish to thank Dr Jean-François Pouget of the Clinique Mutualiste of Saint-Etienne for carrying out the CT scans.

The authors would like to acknowledge the financial support of the Regional French Association for Aid to Chronic Respiratory Failure Patients (ARAIR), Saint-Etienne Métropole and the Conseil Général de la Loire.

CONFLICT OF INTEREST

Marc Durand is a scientific consultant for DTF. Laurent Vecellio and Sandrine Le Guellec are employees of DTF. I: Summary table of nebulized gentamicin collected in the maxillary sinus (MS) in mg/L. Physiological saline solution was nebulized as the control (n=7 for each data set, mean ± SEM, p < 0.05). Significant differences between "100 Hz acoustic airflow" and "Without pressure waves" (***) are highlighted in bold in the table (ANOVA test).

Supplementary Table

Supplementary Table II: Summary table of nebulized gentamicin collected in the maxillary

sinus (MS). Results are expressed in percentage of the emitted dose (NC = Not Calculated).

Physiological saline solution was nebulized as the control (n=7 for each data set, mean ± SEM, p < 0.05).


Henri Gouin
email: henri.gouin@univ-amu.fr

Vesicle model with bending energy revisited

Keywords: Vesicles, surface energy, differential geometry of surfaces, shape equation PACS 45.20.dg, 68.03.Cd, 68.35.Gy, 02.30.Xx Mathematics Subject Classification (2000) 74K15, 76Z99, 92C37

The equations governing the conditions of mechanical equilibrium in fluid membranes subject to bending are revisited thanks to the principle of virtual work. The note proposes systematic tools to obtain the shape equation and the line condition instead of Christoffel symbols and the complex calculations they entail. The method seems adequate to investigate all problems involving surface energies.

Introduction

Lipid molecules dissolved in water spontaneously form bilayer membranes, with properties very similar to those of biological membranes and vesicles [START_REF] Alberts | Molecular biology of the cell, 4th edn[END_REF]. The knowledge of the mechanics of vesicles started more than thirty years ago when both experimental and theoretical studies of amphiphilic bilayers engaged the attention of physicists and the interest of mathematicians [START_REF]Structure and dynamics of membranes[END_REF]. In a viscous fluid, vesicles are drops a few tens of micrometers wide, bounded by impermeable lipid membranes a few nanometers thick. The membranes are homogeneous down to molecular dimensions; consequently, it is possible to represent the vesicle as a two-dimensional smooth surface in three-dimensional Euclidean space. Depending on the cases, the bilayers may be considered as liquid or solid.

When liquid, the lipid molecules form a two-dimensional lattice and the membranes are described with an effective energy that does not penalize tangential displacements. Their mechanical properties permit a continuous mechanical description; such a deformable object is characterized by a flexion-governed membrane rigidity resulting from the curvature energy. The general theory accounts for surface strain, director extension, and director tilt associated with the misalignment of the surface normal. Galilean invariance is tantamount to the invariance of the energy under arbitrary two-dimensional orthogonal transformations and regarded as a function of a symmetric two-dimensional tensor. In this respect, the Helfrich Hamiltonian, which is quadratic in the curvature eigenvalues, provides a good description of lipid membranes and associates bending with an energy penalty [START_REF] Helfrich | Elastic properties of lipid bilayers: theory and possible experiments[END_REF][START_REF] Zhong Can | Bending energy of vesicle membranes: General expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders[END_REF][START_REF] Seifert | Configurations of fluid membranes and vesicles[END_REF]. Equilibrium configurations of the membrane satisfy a single normal 'shape' equation corresponding to the extrema of the Hamiltonian. Fournier used a variational method to study fluid membranes [START_REF] Fournier | On the stress and torque tensors in fluid membranes[END_REF]. Contrary wise, in this note, we revisit the mechanical behaviour of vesicle membranes by using the principle of virtual work [START_REF] Germain | The method of the virtual power in continuum mechanics -Part 2 : microstructure[END_REF][START_REF] Daher | The method of virtual power in continuum mechanics: application to media presenting singular surfaces and interfaces[END_REF][START_REF] Gouin | The d'Alembert-Lagrange principle for gradient theories and boundary conditions[END_REF] together with lemmas from the intrinsic differential geometry of surfaces; consequently, we do not need to use coordinate lines and Christoffel symbols associated with the membrane metric are useless here. For the Helfrich model, we established the equilibrium equation and the boundary conditions -which even apply to compressible media and extensible membranes on cell surfaces -as well as the condition on a surface/vesicle contact line [START_REF] Steigmann | Energy minimizing states of capillary systems with bulk, surface and line phases[END_REF][START_REF] Capovilla | Stresses in lipid membranes[END_REF][START_REF] Biscari | Impermeability effects in three-dimensional vesicles[END_REF][START_REF] Napoli | Equilibrium of nematics vesicles[END_REF][START_REF] Tu | Geometry of membranes[END_REF]. For example, in the case of bending energy, we obtain the equilibrium equation of the vesicle, the conditions on surfaces and line when the vesicle is in contact with a solid boundary; the condition on the vesicle membrane yields the 'shape' equation and a modified Young-Dupré equation on the line.

The note is organized as follows:

In Section 2, we recall the principle of virtual work. Section 3 introduces universal geometrical tools associated with the notion of virtual displacements introduced in Section 2.1 and the Stokes formula for volumes, surfaces and lines. The variations of tensorial quantities and differential forms on surfaces and lines are proposed in an intrinsic form, with no representation in coordinate lines. Section 4 describes the vesicles' main background and the consequence it has on the variation of the vesicle's energy. A conclusion focusing on the advantage of the intrinsic geometrical method ends the note.

The principle of virtual work applied to continuous media

In continuum mechanics, the equilibrium of a medium can be studied with either the Newton model of forces or the Lagrange model of work of forces. At equilibrium, a minimization of the energy associated with a one-parameter family corresponds with the zero value of a linear functional of virtual displacements. The linear functional expressing the forces' work is related to the theory of distributions; a decomposition, associated with displacements considered as test functions whose supports are compact manifolds, uniquely determines a separated form respecting both the test functions and their transverse derivatives [START_REF] Schwartz | Théorie des distributions[END_REF]. Then, the equilibrium equation and the boundary conditions are straightforwardly deduced from the principle of virtual work.

The notion of virtual displacement

The position of a continuous medium is classically represented by a transformation ϕ of a three-dimensional reference domain D 0 into the physical set D. In order to describe ϕ analytically, the variables X = (X 1 , X 2 , X 3 ) which single out individual particles in D 0 correspond to Lagrange's variables; the variables x = (x 1 , x 2 , x 3 ) in D correspond to Euler's variables. Transformation ϕ thus represents the position of a continuous medium,

x = ϕ (X) or x i = ϕ i (X 1 , X 2 , X 3 ) , i ∈ {1, 2, 3} ,
and possesses inverse and continuous derivatives up to the second order except on singular surfaces, curves or points. To formulate the principle of virtual work in continuum mechanics, we recall the notion of virtual displacements [START_REF] Serrin | Mathematical principles of classical fluid mechanics[END_REF]: A one-parameter family of varied positions possessing continuous partial derivatives up to the second order and analytically expressed by the transformation x = Φ (X, η)

with η ∈ O,
where O is an open real set containing 0, and is such that Φ (X,0) = ϕ (X). The derivative, with respect to η at η = 0, is noted δ and is named variation [START_REF] Serrin | Mathematical principles of classical fluid mechanics[END_REF] . In the physical space, the virtual displacement ζ of a particle at x is such that ζ = δx when we assume δX = 0 and δη = 1 at η = 0; the virtual displacement ζ belongs to T x (D), a tangent vector bundle to D at x,

x ∈ D -→ ζ = ψ(x) ≡ ∂Φ ∂η | η=0 ∈ T x (D).

The background underlying the principle of virtual work

The virtual work of forces δτ is a linear functional value of the virtual displacement δϕ determined by the variation of each particle and defined by

δτ =< ℑ, δϕ > (1)
where < , > denotes an inner product. In Relation (1), δϕ is submitted to covector ℑ denoting all forces and stresses. Let us simply note that in case of motion, we must add the inertial forces, corresponding to the accelerations of masses, to the volume forces, and eventually add the viscous stresses to the conservative stress tensor. The virtual displacements are naturally submitted to the constraints resulting from constitutive equations such as mass conservation for compressible media. In this case, the constraints are not necessarily expressed by Lagrange multipliers but are directly taken into account by virtual displacements submitted to the variations of the constitutive equations. Conversely, when geometrical assumptions are assumed, the Lagrange multipliers associated with geometrical conditions constrain the virtual displacements, which in all cases are named virtual displacements compatible with the constraints. The principle of virtual work is expressed in the form : For all virtual displacements compatible with the constraints, the virtual work of forces is null.

If the distribution ( 1) is in a separated form [START_REF] Schwartz | Théorie des distributions[END_REF], the principle of virtual work yields the equilibrium (or motion) equation and the boundary conditions [START_REF] Gouin | The d'Alembert-Lagrange principle for gradient theories and boundary conditions[END_REF].

Intrinsic geometrical tools for the energy of surfaces and lines

We assume that D has a differential boundary S, except on its edge C. We respectively note S 0 and C 0 the images of S and C in D 0 ; D and D 0 are Euclidian sets. The unit vector n and its image n 0 are the oriented normal vectors to S and S 0 ; c m ≡ (R m ) -1 is the mean curvature of S; the vector t is the oriented unit vector to C and n ′ = t × n is the unit binormal vector [START_REF] Aris | Vectors, tensors, and the basic equations of fluid mechanics[END_REF][START_REF] Kobayashi | Foundations of differential geometry[END_REF]. The tensor F ≡ ∂x/∂X denotes the Jacobian transformation of ϕ; symbols div, rot, tr and superscript T refer to the divergence, rotational, trace operators and the transposition, respectively; 1 denotes the identity tensor.

Lemma 1 : we have the following relations

δ det F = det F div ζ , (2)
δ F -1 n = -F -1 ∂ζ ∂x n + F -1 δn. (3)

Proof of Rel. (2):

The Jacobi identity written in the form δ(det F ) = det F tr F -1 δF and

δF = δ ∂x ∂X = ∂ζ ∂X , imply, tr F -1 δF = tr ∂X ∂x ∂ζ ∂X = tr ∂ζ ∂X ∂X ∂x = tr ∂ζ ∂x = div ζ.
For an incompressible medium, det F = 1 and

ζ verifies div ζ = 0. ( 4
)
Proof of Rel. (3):

δ F -1 n = δ F -1 n + F -1 δn and F -1 F = 1 =⇒ δ F -1 F + F -1 δF = 0, imply δ F -1 = -F -1 ∂ζ ∂X F -1 = -F -1 ∂ζ ∂x . (5)
Lemma 2 : The variation of E = S σ ds is given by the relation

δE = S δσ - 2σ R m n T + grad T σ 1 -nn T ζ ds + C σ n ′ T ζ dl. ( 6
)
where σ is a scalar field defined on S and ds, dl are the surface and the line measures.

Proof of Rel. ( 6):

The normal vector field is locally extended in the vicinity of S by the relation n(x) = grad d(x), where d is the distance of point x to S; for any vector field w,

rot(n × w) = n div w -w div n + ∂n ∂x w - ∂w ∂x n.
From n T ∂n ∂x = 0 and div n = -2 R m , we deduce on S,

n T rot(n × w) = div w + 2 R m n T w -n T ∂w ∂x n. (7)
Due to E = S σ det (n, d 1 x, d 2 x) where d 1 x and d 2 x are two coordinate lines of S, we get,

E = S0 σ det F det(F -1 n, d 1 X, d 2 X), with d 1 x = F d 1 X, d 2 x = F d 2 X. Then, δE = S0 δσ det F det (F -1 n, d 1 X, d 2 X) + S0 σ δ det F det (F -1 n, d 1 X, d 2 X) .
Due to Lemma 1, n T ∂n ∂x = 0 and to n T δn = 0,

S0 σ δ det F det (F -1 n, d 1 X, d 2 X) = S σ div ζ det(n, d 1 x, d 2 x) + σ det (δn, d 1 x, d 2 x) -σ det ∂ζ ∂x n, d 1 x, d 2 x ds = S div(σ ζ) -(grad T σ) ζ -σn T ∂ζ ∂x n ds. Relation (7) yields div (σ ζ) + 2σ R m n T ζ -n T ∂(σ ζ) ∂x n = n T rot (σ n × ζ). Then, S0 σ δ det F det (F -1 n, d 1 X, d 2 X) = S - 2σ R m n T + grad T σ (nn T -1) ζ ds + S n T rot (σ n × ζ) ds,
where grad T σ (1nn T ) ≡ grad T tg σ belongs to the cotangent plane to S and

S n T rot (σ n × ζ) ds = C (t, σ n, ζ) dl = C σ n ′ T ζ dl.
Then, we obtain relation [START_REF] Fournier | On the stress and torque tensors in fluid membranes[END_REF].

Lemma 3 : The variation of the internal energy is

δ D ρ α dv = D (grad p) T ζ dv - S p n T ζ ds. ( 8
)
where ρ is the mass density, α(ρ) is the fluid specific energy, p = ρ 2 ∂α ∂ρ is the thermodynamical pressure [START_REF] Rocard | Thermodynamique[END_REF] and dv is the measure of volume.

Proof of Rel. ( 8):

δ D ρ α dv = D ρ δα dv where δα = (∂α/∂ρ) δρ. Due to mass conserva- tion, ρ det F = ρ 0 (X), (9)
where ρ 0 is defined on D 0 . The differentiation of Eq. ( 9) yields δρ det F + ρ δ(det F ) = 0, and from Lemma 1, we get

δ ρ = -ρ div ζ.
Consequently, div (p ζ) = p div ζ + (grad p) T ζ and we deduce relation [START_REF] Daher | The method of virtual power in continuum mechanics: application to media presenting singular surfaces and interfaces[END_REF].

In the same way, Lemma 4 : For any scalar field p defined on D,

δ D p div ζ dv = - D (grad p) T ζ dv + S p n T ζ ds. ( 10
)
Lemma 5 : The variation of the external unit vector normal to S is

δn = nn T -1 ∂ζ ∂x T n. ( 11
)
Proof of Rel. [START_REF] Capovilla | Stresses in lipid membranes[END_REF]:

The property n T dx = 0 =⇒ n T F dX = 0 implies that vector F T n is normal to S 0 and consequently, n T 0 n 0 = 1 yields

n 0 = F T n (n T F F T n) , n = F -1T n 0 (n T 0 F -1 F -1T n 0 )
.

Then, δn 0 = 0 on the reference surface S 0 implies,

δn = δF -1T n 0 n T 0 F -1 F -1T n 0 - 1 2 F -1 n 0 δ n T 0 F -1 F -1T n 0 n T 0 F -1 F -1T n 0 3 2
.

From Eq. ( 5), δF -1T = -∂ζ ∂x T F -1T and consequently,

δn = - ∂ζ ∂x T n + 1 2 n n T ∂ζ ∂x n + n T ∂ζ ∂x T n .
Then, n T ∂ζ ∂x n = n T ∂ζ ∂x T n implies relation [START_REF] Capovilla | Stresses in lipid membranes[END_REF].

Lemma 6 : The variation of the mean curvature of S is

δc m = ∂c m ∂x ζ + 1 2 ∆ tg (n T ζ), (12)
where ∆ tg is the tangential Beltrami-Laplace operator on surface S.

Proof of Rel. (12):

The variation of a derivative is given by

δ ∂n ∂x = ∂δn ∂x - ∂n ∂x ∂ζ ∂x . (13)
From 2 c m = -div n = -tr ∂n ∂x and Eq. ( 13) we get,

2 δc m = -tr ∂δn ∂x + tr ∂n ∂x ∂ζ ∂x = -div δn + div ∂n ∂x ζ -2 ∂(div n) ∂x ζ.
But, ∂(div n) ∂x = -2 ∂c m ∂x and by using Eq. ( 11) we get,

-div δn + div ∂n ∂x ζ = div   1 -nn T ∂ n T ζ ∂x T   = div grad tg (n T ζ),
and from div grad tg (n

T ζ) = ∆ tg (n T ζ) ( 1 )
, we deduce relation [START_REF] Biscari | Impermeability effects in three-dimensional vesicles[END_REF].

1 For all vector fields x ∈ D → v(x), divtgv = divv-n T (∂v/∂x) n. Then, divtgv = divvtr nn T (∂v/∂x) . But div nn T v = div nn T v + tr nn T (∂v/∂x) and div nn T = 4 Description of a vesicle membrane in contact with a solid surface

Membranes' bending energy

Vesicles consist in a three-dimensional domain bounded by a liquid bilayer. Vesicle interfaces are represented by material surfaces endowed with a bending surface energy. In our representation, a vesicle fills set D and lies on the surface of a solid; the vesicle is also surrounded by a fluid (see Fig. 1). All the interfaces between vesicle, solid and liquid are assumed to be regular. We note To obtain the equilibrium equation and the boundary conditions, it is neces-

div (n) n T + n T (∂n/∂x) T . From (∂n/∂x) n = 0 and divn = -2/Rm , we get divtgv = div (1 -nn T ) v -2 n T v/Rm . From divtgvtg = divvtg where vtg = (1 -nn T )v, we get div gradtg(n T ζ) = divtg gradtg (n T ζ) = ∆tg(n T ζ).
2 Our aim is not to consider the thermodynamics of interfaces. Consequently σ i , i ∈ {1, 2, 3} are not taken into account as a function of variables like temperature or entropy.

sary to propose a constitutive behaviour for the membrane's energy density σ 2 . As proved in the literature, the surface energy density on S 2 must be a function of the curvature tensor along the surface. To be intrinsic, σ 2 must be a function of the two curvature tensor invariants. If we note c 1 = 1/R 1 and c 2 = 1/R 2 the eigenvalues of the curvature tensor, the mean curvature and the Gauss curvature of S 2 are respectively noted,

H = c 1 + c 2 2 = 1 R m , K = c 1 c 2 = 1 R 1 R 2 .
The external normal n 2 to S 2 can be locally extended in the vicinity of S 2 by the relation n 2 (x) = grad d 2 (x), where d 2 is the distance of point x to S 2 (see Section 3, Lemma 2). Then,

2H = -div n 2 ≡ -tr ∂n 2 ∂x , ∂n 2 ∂x = ∂n 2 ∂x T , n 2 T ∂n 2 ∂x = 0, (14)
2K = tr ∂n 2 ∂x 2 -tr ∂n 2 ∂x 2 .
The surface's energy density σ 2 is assumed to be a regular function of H and K, but in the Helfrich model, the vesicle's surface energy is linear in K.

The Gauss-Bonnet theorem ensures that the integration term corresponding to K is constant for closed surfaces, otherwise, the geodesic curvature of the boundary plays a role; this means, as established in [START_REF] Fournier | On the stress and torque tensors in fluid membranes[END_REF], that the Gaussian curvature affects the boundary line actions. Nonetheless, experimental and theoretical studies have shown that the energy mainly stems from the bending [START_REF]Structure and dynamics of membranes[END_REF]; consequently, in the Helfrich model, the surface energy density on S 2 is taken as a form without term in K:

σ 2 = σ o + κ 2 [2H -c o ] 2 , ( 15
)
where κ is the bending rigidity, c o is the spontaneous curvature and σ o is the superficial energy of capillarity. The main interest being the membrane's bending energy and its behaviour, we assume that the values of σ o , σ 1 and σ 3 are constant. This special case can be easily extended, as done in [START_REF] Gouin | Interfaces endowed with non-constant surface energies revisited with the d'Alembert-Lagrange principle[END_REF] for an other problem of capillarity.

Lemma 7 : The variation of the bending energy

E 2 = S2 σ 2 ds of a mem- brane is δE 2 = S2 dσ 2 dn 2 -2H σ 2 + 1 2 ∆ tg ∂σ 2 ∂H n T 2 ζ ds + C n ′T 2 (σ 2 ζ + w) dl, ( 16
)
where w = 1 2

∂σ 2 ∂H grad tg (n T 2 ζ) -n T 2 ζ grad tg ∂σ 2 ∂H and d dn 2 ≡ ∂ ∂x n 2
is the normal derivative in the direction n 2 .

Proof of Rel. ( 16):

From Eq. ( 6), σ 2 = σ 2 (H) and Eq. ( 12), we obtain,

δE 2 = S2 ∂σ 2 ∂H ∂H ∂x ζ + 1 2 ∂σ 2 ∂H div grad tg (n T 2 ζ) -2 σ 2 Hn T 2 ζ -grad σ 2 1 -n 2 n T 2 ζ ds + C σ 2 n ′T 2 ζ dl But, grad σ 2 = ∂σ 2 ∂H ∂H ∂x ; then, δE 2 = S2 1 2 ∂σ 2 ∂H div grad tg (n T 2 ζ) + dσ 2 dn 2 -2 H σ 2 n T 2 ζ ds+ C σ 2 n ′T 2 ζ dl,
and from 1 2

∂σ 2 ∂H div grad tg (n T 2 ζ) = 1 2 ∆ tg ∂σ 2 ∂H n T 2 ζ + div w,
we deduce relation [START_REF] Serrin | Mathematical principles of classical fluid mechanics[END_REF].

Expression of the virtual work of forces

For the Helfrich model, the total energy of the vesicle writes

Ξ = D ρ α(ρ) dv + S1 σ 1 ds + S2 σ 2 ds.
The virtual work of volume force ρ f defined on D writes D ρ f T ζ dv. The virtual work of surface force T exerted on S is S T T ζ ds. Due to Eq. ( 6), -C σ 3 n ′ T 1 ζ dl corresponds to the action of S 3 on edge C. Finally, the virtual work of forces writes

δτ = -δΞ + D ρ f T ζ dv + S T T ζ ds - C σ 3 n ′ T 1 ζ dl. (17)
From Eqs. ( 6), ( 8), ( 16) and [START_REF] Aris | Vectors, tensors, and the basic equations of fluid mechanics[END_REF], we obtain

δτ = D ρ f T -grad T p ζ dv + S1 p + 2 σ 1 R m1 n T 1 + T T 1 ζ ds + S2 p - dσ 2 dn 2 + 2H σ 2 - 1 2 ∆ tg ∂σ 2 ∂H n T 2 + T T 2 ζ ds + C (σ 1 -σ 3 ) n ′ T 1 -σ 2 n ′ T 2 ζ -n ′ T 2 w dl, (18)
where 2/R m1 is the mean curvature of S 1 , and T 1 and T 2 correspond to the surface forces exerted on S 1 and S 2 , respectively.

Equations governing equilibrium and boundary conditions

The fundamental lemma of variational calculus applied to each integral of Eq. ( 18) yields the equilibrium equation associated with domain D, the conditions on surfaces S 1 and S 2 and the condition on contact line C.

Equilibrium equation in D

grad p = ρ f . This is the classical condition for equilibrium.

Condition on surface

S 1 p + 2 σ 1 R m1 n 1 + T 1 = 0.
Then T 1 = -p 1 n 1 is a normal stress vector to surface S 1 and we obtain the classical Laplace condition,

p 1 -p = 2 σ 1 R m1 . Condition on membrane surface S 2 p - dσ 2 dn 2 + 2H σ 2 - 1 2 ∆ tg ∂σ 2 ∂H n 2 + T 2 = 0. ( 19
)
Then, the stress vector must be normal to S 2 . In fact T 2 = -p 2 n 2 corresponds to the action of the external fluid on the membrane. From σ 2 = σ 2 (H), and taking Eq. ( 14 Finally, Eq. ( 19) yields,

p -p 2 -(2 H 2 -K) ∂σ 2 ∂H + 2H σ 2 - 1 2 ∆ tg ∂σ 2 ∂H = 0. (20)
In the case of the Helfrich model ( 15), we obtain from Eq. ( 20) the 'shape' equation ( 3):

p -p 2 + κ (2 H -c o ) 2K -2H 2 -c o H + 2 H σ o -2κ∆ tg H = 0. ( 21
)
Condition on line C .

To get the line condition, we must consider a virtual displacement tangent to the fixed surface S 1 and consequently ζ = α t + β t × n 1 , where α and β are two scalar fields defined on C. From the last integral of Eq. ( 18), we get immediately: For any scalar field

x ∈ C -→ β (x) ∈ ℜ, C (σ 1 -σ 3 ) n ′ T 1 -σ 2 n ′ T 2 ζ -n ′ T 2 w dl = 0, Due to the fact that n T 2 ζ = β n T 2 (t × n 1 ) = β t T (n 1 × n 2 ) = β sin θ, where θ = ( n 1 , n 2 )
is the Young angle, and the term β sin θ is uniquely function of arc length l, we get n ′ T 2 grad tg (β sin θ) = 0. Consequently, from Lemma 7,

n ′ T 2 w = - 1 2 n T 2 ζ n ′ T 2 grad tg ∂σ 2 ∂H = - 1 2 β sin θ σ ′′ 2 (H) dH dn ′ 2 ,
where dH dn ′ 2 is the value of the derivative of H along the line orthogonal to C

on S 2 . Consequently, ∀ {l -→ β(l) ∈ ℜ}, C β (σ 1 -σ 3 ) n ′ T 1 (t × n 1 ) -σ 2 n ′ T 2 (t × n 1 ) + σ ′′ 2 (H) 2 dH dn ′ 2 sin θ dl = 0. Then, C -β (σ 1 -σ 3 ) + σ 2 n T 2 n 1 - σ ′′ 2 (H) 2 dH dn ′ 2 sin θ dl = 0,
and we obtain the line condition where the scalar λ 0 is a constant Lagrange multiplier and p is a distributed Lagrange multiplier. Due to Eq. ( 10), the 'shape' equation that they deduced is identical to Eq. (21).

(σ 1 -σ 3 ) + σ 2 cos θ - σ ′′ 2 (H) 2 dH dn ′ 2 sin θ = 0. ( 22

Conclusion and remarks

In this note, we propose simple systematic tools coming from surface geometry and from the principle of virtual work to obtain the boundary conditions on surfaces and lines for three-dimensional domains where the surfaces are endowed with surface energy densities. The tools are based on the Helfrich model with bending energy which is usually proposed to study the mechanics of biological membranes. The model does not take line energy into account, but the calculations will be similar to obtain the conditions at the boundaries of three-dimensional domains. Relation ( 6) is the key point of the model and highlights the extreme importance of knowing the variation of δσ and consequently the behaviour of the surface energy σ. For example, in [START_REF] Gouin | Interfaces endowed with non-constant surface energies revisited with the d'Alembert-Lagrange principle[END_REF] we obtained a case where the capillary surface energy depended on the composition of the surface layer. The obtained results do not need to assume vesicle incompressibility and constant area of the membrane. We notice that the calculations proposed in the literature use the Christoffel symbols associated with coordinate curves on the surfaces, but the Christoffel symbols do not appear in the resulting expressions of the boundary conditions. This is an important reason for the straightforwardness of our method.

Fig. 1 A

 1 Fig. 1 A drop-shaped vesicle lies on a solid surface. The vesicle is bordered by a fluid (liquid) and a solid; S 1 is the boundary between liquid/solid; S 2 is the interface between vesicle/fluid (membrane of the vesicle); S 3 is the boundary between fluid/solid; n 1 and n 2 are the unit normal vectors to S 1 and S 2 , external to the domain of the vesicle; contact line C is shared by S 1 and S 2 and t is the unit tangent vector to C relative to n 1 ; n ′ 1 = n 1 × t and n ′ 2 = t × n 2 are the binormals to C relative to S 1 and S 2 , respectively.

)

  In the Helfrich model[START_REF] Schwartz | Théorie des distributions[END_REF] the condition (22) yields(σ 1 -σ 3 ) + σ 2 cos θ -2 κ dH dn ′ 2 sin θ = 0. (23) Condition (23) replaces the classical Young-Dupré condition by taking additive term -2 κ dH dn ′ 2 sin θ into account.total constant area S 0 and introduce the constraint S ds = S 0 . Then, the virtual work is expressed asδτ = D ρ f T ζ dv + S T T ζ ds -δ S σ ds + λ 0 δ S ds + δ D p div ζ dv,

Let us note that Helfrich et al[START_REF] Helfrich | Elastic properties of lipid bilayers: theory and possible experiments[END_REF][START_REF] Zhong Can | Bending energy of vesicle membranes: General expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders[END_REF][START_REF] Seifert | Configurations of fluid membranes and vesicles[END_REF] consider the vesicle as incompressible and the virtual displacement verifies div ζ = 0 (see Eq. (4)). They assume that the lipid bilayer S has a


Lara Leclerc
email: lara.leclerc@univ-st-etienne.fr

Jean-Philippe Klein

Valérie Forest

Delphine Boudard

Matteo Martini

Jérémie Pourchez

Marie-Geneviève Blanchin

Michèle Cottier

Testicular Biodistribution of Silica-Gold Nanoparticles after Intramuscular Injection in Mice

Keywords: Nanoparticles, mice, testes, intramuscular injection, reproductive toxicity

Background

With the continuing development of nanomaterials, the assessment of their potential impact on human health, and especially human reproductive toxicity, is a major issue. The testicular biodistribution of nanoparticles remains poorly studied. This study investigated whether goldsilica nanoparticles could be detected in mouse testes after intramuscular injection, with a particular focus on their ability to cross the blood-testis barrier. To that purpose, wellcharacterized 70-nm gold core-silica shell nanoparticles were used to ensure sensitive detection using high-resolution techniques.

Results

Testes were collected at different time points corresponding to spermatogenesis stages in mice. Transmission electron microscopy and confocal microscopy were used for nanoparticle detection, and nanoparticle quantification was performed by atomic emission spectroscopy.

All these techniques showed that no particles were able to reach the testes. Results accorded with the normal histological appearance of testes even at 45 days post sacrifice.

Conclusion

High-resolution techniques did not detect 70-nm silica-gold nanoparticles in mouse testes after intramuscular injection. These results are reassuring about the safety of nanoparticles with regard to male human reproduction, especially in the context of nanomedicine.

INTRODUCTION

During the last 20 years, nanotechnology has drastically evolved, leading to increasing population-level exposure to engineered nanoparticles and nanomaterials. A wide variety of fields, such as the textile industry, computer sciences, cosmetics, and medicine, have taken advantage of nanostructured compounds. Their intrinsic small size and high surface reactivity (Oberdörster et al. 1994), which could allow specific interactions with biological structures, raise concerns in the scientific community about potential environmental or human health toxicity (Peralta-Videa et al. 2011). Concomitantly, declining sperm counts have been documented in most Western countries (Lackner et al. 2005;[START_REF] Rolland | [END_REF]. Thus, concerns have been raised about the ability of nanoparticles to impair human reproduction, especially male fertility (Ema et al. 2010;Lan and Yang 2012). Two types of studies have focused on this topic: (1) testicular biodistribution and biopersistence studies and (2) testicular biotoxicity studies.

With regard to biodistribution, all studies performed in mice or rats have concluded that very limited amounts of nanoparticles can reach the testes regardless of the exposure routes (inhalation, intravenous, oral) and the physico-chemical properties of nanoparticles, including carbon nanotubes and gold, cerium oxide, silica and silver nanoparticles measuring between 10 and 5000 nm (Bai et al. 2010;Balasubramanian et al. 2010;Geraets et al. 2012;De Jong et al. 2008;Lankveld et al. 2010;Lan and Yang 2012;Morishita et al. 2012;Park et al. 2010;van der Zande et al. 2012). Most studies agree that the testes is a minor target for distribution of nanoparticles compared with other organs (Geraets et al. 2012;De Jong et al. 2008;Lankveld et al. 2010). However, the studies are not entirely consistent. Nanoparticle size variation may explain some of these discrepancies (De Jong et al. 2008;Morishita et al. 2012;Park et al. 2010), and exposure route and particles agglomeration may also contribute to the differences. Testicular biopersistence of nanoparticles seems to depend on exposure route; for instance, biopersistence of silver nanoparticles was less than 2 weeks following intravenous exposure (Lankveld et al. 2010), but more than 4 months after oral exposure (Lee et al. 2013;van der Zande et al. 2012). Furthermore, some authors have suggested that nanoparticles could cross the blood-testis barrier, but only Moroshita et al. (2012) have provided evidence.

Their study in mice demonstrated the presence of nanoparticles in spermatocytes after an intravenous injection of 70-nm silica nanoparticles.

Regarding testicular biotoxicity, three concerns have been raised: reduction in daily sperm production (Gromadzka-Ostrowska et al. 2012;[START_REF] Xu | [END_REF]Yoshida et al. 2009), although this outcome is not reported by all authors (Bai et al. 2010); increase in testosterone synthesis (Li et al. 2009;Ramdhan et al. 2009;Tassinari et al. 2014;Yoshida et al. 2009); and the appearance of histological abnormalities. Histological analysis of mice testes after multiple intravenous injections of carbon nanotubes showed damage to seminiferous tubules, particularly reductions in the thickness of the germinative layer and the number of germ stem cells; however, the abnormalities resolved after 60 days (Bai et al. 2010). Gromadzka-Ostrowska et al. (2012) showed that intravenous injection of 200-nm silver nanoparticles in rats induced enlargement of intercellular spaces and vacuolization of the germinal epithelium, while 20-nm silver nanoparticles did not have the same effects. In another study, inhalation of carbon black nanoparticles of 14-95 nm in mice led to the degeneration of some seminiferous tubules compared to the control group (Yoshida et al. 2009).

In contrast, Morishita et al. (2012) revealed that although intravenously injected 70 nm silica particles reached the testes, they did not trigger any histological abnormalities in mice.

Similarly, Chen et al. (2013) found no testicular histological abnormalities after intraperitoneal injection of pegylated gold nanoparticles in mice, (Chen et al. 2013) and [START_REF] Xu | [END_REF] did not find any histological changes in mice testes after 13 days of intravenous exposure to silica nanoparticles, apart from reversible ultrastructural changes in mitochondria.

Finally, no study has found any impact of nanoparticles on testis weight.

In a previous study, we demonstrated the presence of individual 450-nm fluorescent particles in the testes after intramuscular injection in mice (Klein et al. 2013). The intramuscular route was specifically chosen because it is normally used for vaccine delivery, and nanoparticles are increasingly being used and explored as vaccine adjuvants (Gregory et al. 2013;Oyewumi et al. 2010;Peek et al. 2008). However, to our knowledge, no other reports have been published about testicular biodistribution or biotoxicity of nanoparticles used as vaccine adjuvants.

Given that some works have shown that smaller nanoparticles induce better immunogenicity (Fifis et al. 2004) and trigger better cellular immune responses (Oyewumi et al. 2010), we studied the testicular biodistribution of smaller particles (70-nm gold core-silica shell nanoparticles) after intramuscular injection in mice. The hybrid nature of these particles allowed (i) an easy detection by high-resolution transmission electron microscopy (TEM) and inductively coupled plasma-atomic emission spectroscopy (ICP-AES) due to the gold core, and (ii) fluorescence detection due to the FITC dyes encased within the silica shell. The histological morphology of testes was also examined to identify any possible morphological alterations in the blood-testis barrier by the presence of particles; the cellular integrity of the seminiferous epithelium was also verified.

METHOD Nanoparticles synthesis and characterization

All colloidal solutions used for biodistribution assays were provided by the ILM laboratory and consisted of 5-nm gold cores coated with a 65-nm polysiloxane shell (SiOx) doped with fluorescein molecules. The particle surface was functionalized by the addition of -COOH groups to ensure long-term stability for biological assays. Fluorescein dyes covalently entrapped within a silica matrix were chosen for their strong emission luminescence at 518 nm as tracers for epifluorescence microscopy detection (Olympus). Briefly, the colloidal solution was prepared according to a previous method (Martini et al. 2009) based on sol-gel synthesis in a water/oil microemulsion to control the size, dye amount, and homogeneity of the particle population. Thereafter, particles were purified by ultrafiltration using 300 kDa PES membranes (with a purification rate higher than 10 8 ) and then dispersed in aqueous solution (20 g.L -1 ) for further dilutions.

The detailed structural and morphological examination of samples was carried out by transmission electron microscopy (TEM) using a HITACHI H-800 microscope. The samples were prepared by depositing a drop of diluted colloidal solution onto a carbon grid (200 mesh) and allowing the solvent to evaporate at room temperature. Measurements of the hydrodynamic size and the Zeta-potential were performed on a Dynamic Light Scattering apparatus (Zetasizer NanoZS, Malvern).

Animals

Eighteen male C57BL6 mice (Centre d'Elevage René Janvier, France) were housed at the animal experimental platform of the Jean Monnet University (PLEXAN -Plateforme d'EXpérimentation et ANalyses, Agreement number 42-18-0801) and all experiments were performed in compliance with the French laws and institutional guidelines. An authorization approving the experiments was obtained from the French Ministère de l'Enseignement Supérieur et de la Recherche (MESR, field number 00462.02). Experiments were started when the mice were between 6 and 8 weeks of age.

Intramuscular injection of nanoparticles

Particles were diluted in physiological water and a volume of 50 µL was injected in each tibialis anterior muscle of 15 mice, for a total amount of 1.6 × 10 13 particles per mouse. Three mice received an injection containing only physiological water and constituted the negative control group.

Biological samples

The 15 injected mice were divided into five groups and sacrificed by cervical dislocation after 1 h (H1), 4 days (D4), 21 days (D21), 36 days (D36), or 45 days (D45) post injection. These time points coincide with the duration of spermatogenesis in mice. For each series, testes were excised and prepared for characterization (ICP-AES, histological analysis, TEM, and confocal microscopy); mice from the control group were sacrificed after 45 days. To that purpose testes were obtained and then subdivided in several pieces for the various investigations.

Mice were immobilized and their urine was collected in a tube; blood was collected by retroorbital puncture just before sacrifice. The silica-gold nanoparticles' structural stability as well as their capacity to translocate from the site of injection were assessed by TEM in whole blood and by ICP-AES in urine samples, respectively.

Induced Coupled Plasma-Atomic Emission Spectroscopy

At each time point, testes were excised, weighted, mechanically dilacerated, and incubated overnight in a bath of 6 M HCl under agitation. Samples were then dried at 90°C and diluted in 2 M HCl before ICP analyses of the amount of gold using adequate controls (ICP-AES, Horiba Jobin Yvon Activa-S coupled with Jobin Yvon AS 421 autosampler).

The same protocol was used to evaluate the levels of gold in urine samples.

Histological analysis

Freshly excised testes were cut and fixed in Japanese fixator (3% paraformaldehyde, 2% sodium cacodylate, and 0.2% picric acid), then rinsed three times (5 min per wash) in sodium cacodylate, and finally dehydrated in two acetone baths (30 min each). Samples were impregnated overnight at 4°C in glycolmethacrylate (GMA) and then embedded in resin (GMA and aniline/propanol solution) at 4°C until complete polymerization.

Nonadjacent 3-µm-thick sections of resin-fixed testes were prepared using a microtome (Leica RM 2065). The sections were placed on slides (Superfrost Plus, Thermo Scientific), stained with Masson Trichrome stain, dried, and mounted with an appropriate mounting medium (Eukitt®: Sigma, France). Since the mouse testis is a homogenous organ, we considered each section as representative of the whole testis. Observations were performed with an optical microscope (Nikon Eclipse 80i) coupled with a digital-sight Nikon camera and a series of microscope objectives (×10, ×40, ×60). The samples were randomly and blindly observed.

Transmission Electron Microscopy

Freshly excised testes were fixed with a solution of 2% paraformaldehyde, 4% glutaraldehyde, 0.2 M monosodium dipotassium buffer at pH 7.4. Testes samples of about 1 mm 3 were then cut and washed five times in 0.175 M monosodium dipotassium buffer and postfixed in 2% osmium tetroxide. After washing, samples were dehydrated by graded series of ethanol baths (30%, 50%, 70%, 90%, 100%) with a last bath in a transition solvent (propylene oxide) before embedding in EPON 812 resin. Samples were then sliced using an ultramicrotome (Leica, MTXL).

For conventional TEM studies, 65-nm-thick slices were deposited on Formvar MESH Grid and contrasted by means of uranyl acetate and lead citrate. TEM observations, up to magnification ×150,000, were carried out on the samples using a H-800 electron microscope (Hitachi) at 75 kV. Once filtrated and deposited on copper grids, whole blood samples were also analyzed by TEM without the use of contrasting agents.

For elemental gold analysis, slices were deposited onto TEM copper grids covered with carbon film and contrasted only by means of uranyl acetate. High-resolution (HR) TEM studies with electron dispersive X-ray (EDX) analyses were performed using a TOPCON electron microscope capable of a 0.18-nm point to point resolution (EM-002B Ultra High Resolution Analytical Electron Microscope) operated at 120 kV equipped with EDX detector (Thermo Electron Corporation Noran SI X system). For first step HR imaging some slices were deposited onto TEM copper grids covered with carbon film and contrasted only by means of uranyl acetate. For elemental Au analysis, slices deposited on carbon film grids were prepared without coloration: no uranyl acetate nor lead citrate.

Confocal microscopy

A portion of the samples was placed in a cryopreservative solution (Tissue-Tech®: Sakura, Netherlands) and cryoconserved in liquid nitrogen. For confocal analyses, 10-µm slides were cut with a cryostat at -20°C (Leica CM-3000). Sections were then dried, mounted with an appropriate mounting medium (Fluokeep®: Argene, France), and stored at 4°C in the dark.

Analyses were performed using a confocal microscope TCS-SP2 (Leica ® Microsystems, Heidelberg, Germany) coupled to an inverted microscope with oil immersion objective (HCX APO L U-V-I 63 9 1.2 NA), and fitted with acousto-optical beam splitter covering a 350-850 nm wavelength range.

RESULTS

Nanoparticles characterization

Physico-chemical features of the nanoparticles are reported in Figure 1. The monoexponential correlation function obtained allows us to determine the Z-average, polydispersity index, and zeta potential values before the application. The size distribution of nanoparticles (Fig. 1A) assessed by dynamic light scattering showed an average diameter of 70 nm with negligible variation. The good homogeneity of the particle size as well as the absence of particle agglomeration allowed the use of colloidal solutions for biodistribution assays. As expected, the zeta potential at physiological pH (Fig. 1B) was negative and equal to -13 mV, due to the covalently grafted carboxylate surface groups. On TEM images (Fig. 1C) the gold core was highlighted by dark-contrast spot at the center of the particle, this picture also illustrates the good reproducibility of the nanoparticle synthesis. The fluorescent signal of the particles was validated using epi-fluorescent microscopy (Fig. 1D).

The presence of silica-gold nanoparticles in whole blood samples was assessed by TEM and in urine samples by ICP-AES, as shown in Figure 2. A significant amount of gold was detected in urine at H1 and D4 (Fig. 2A) and nanoparticles were observed in blood samples at D4 and D21 (Fig. 2B), indicating that nanoparticles were able to leave the site of injection and maintain their integrity over time in biological media.

ICP quantification

The presence of gold was quantified in the testes using the ICP-AES technique. A dilution series of nanoparticles was performed to assess the detection limit of the technique (1/10, 1/100, 1/500, 1/1000, 1/10,000, 1/100,000). These preliminary data showed that under a 1/100,000 dilution the ICP technique was not able to detect gold in the samples, defining a threshold of 1.6 × 10 8 nanoparticles (data not shown).

Figure 3 summarizes the estimated amount of gold in the testes (expressed in ppm) normalized by the organ weight. A positive control corresponding to the same amount of nanoparticles injected directly into a freshly excised testis was used. Regardless of the time of analysis after exposure, gold amounts were very weak, indicating a negligible testicular presence of the nanoparticles after intramuscular injection. A calibration curve revealed that less than 1 out of 10 5 nanoparticles reached the testis.

Histological observations

After Masson Trichrome staining, tissue sections from control mice and mice injected with the nanoparticles were compared to investigate potential histological alterations (Fig 4).

Regardless of the time of analysis, the testis generally appeared well preserved, without morphological alterations. Even after 45 days of exposure, no tubule necrosis or histological disorganization at the level of germinal cells and spermatozoids were observed, either in the intertubular spaces with blood vessels or in the Leydig cells. Moreover, the Sertoli cells, which form the blood-testis barrier that might be able to internalize nanoparticles, appeared morphologically normal and abundant. The proportion of each cell type seemed normal at each time of exposure (Fig 4 A andB).

Only small alterations of tubules were occasionally observed on the slides, irrespective of the time of analysis. Similar alterations were also seen on the control slides, indicating no correlation with the nanoparticle exposure (Fig 4 C,D,E). Some giant germinal cells with large vacuolized cytoplasm as well as desquamation of the germinal cells in the lumen of tubules were observed.

A particular alteration was noticed on one mouse at D4, with empty tubules showing only Sertoli cells without germinal cells (Fig 4F). Although this type of alteration is compatible with a toxic event, in this case it was considered to be an artifact because it was observed very soon after exposure and was observed only for a single mouse.

TEM studies

TEM observations can give information about the inner morphology of testes as well as the spatial distribution of nanoparticles present in the tissues. Analyses were performed on the testes with a multiscale approach to detect whether nanoparticles were present. The mouse testis is a homogenous organ, with repetitions of the morpho-functional unit corresponding to the seminiferous tubule surrounded by the intertubular spaces, which contain the Leydig cells.

Thus, it was assumed that each sliced section was representative of the whole testis. To visualize all the structures at each time point, 40 slices per sample were observed. This reduced any systematic error due to the specific choice of a few slices.

First, conventional (Hitachi microscope) TEM observations (Fig. 5) were performed for the detection of nanoparticles in the samples. All slices were carefully imaged and entirely inspected. Cellular structures such as cytoplasmic vacuoles in Sertoli and germinal cells and the intertubular spaces containing the Leydig cells were studied to find nanoparticles.

Particular care was taken in examining the seminiferous tubules (two to three tubules sections contained in each slice) to determine if nanoparticles can cross the blood-testis barrier. For each time point of the spermatogenesis process, no nanoparticles were identified in any of the regions of interest. One fourth of the sections were selected for HR imaging coupled with EDX analysis using the TOPCON microscope (Fig 6). No contrast metallization of the slices was performed to suppress the background noise from lead and uranyl compounds, and consequently the signal of the copper grid was detected on the spectra. Reference data were recorded from a control sample (Fig 6A) obtained from a section slice covered by a drop of the silica-gold nanoparticle suspension. An area imaged in Fig. 6A displays the characteristic features of the silica-gold nanoparticles, and the EDX spectrum recorded on the corresponding slice region exhibits a well-marked peak resulting from the contributions of the silicon and gold elements in addition to the peaks from copper and osmium. The results from the D45 samples reproduced in Figure 6B are representative of those for all other time points.

Again the slices were carefully inspected by high resolution/high magnification imaging (Fig. 6B) and no indication of the nanoparticles (morphology, size, contrast) could be identified on the images. The corresponding EDX spectra showed only a weak peak, corresponding to the osmium post-fixing agent included in the samples during the preparation, but no silicon-gold peak. Similar spectra were observed for series of samples, revealing the absence of the silicon-gold signal. The problem of the Minimum Detectable Mass (MDM) of a given element in a given matrix has been investigated both theoretically and experimentally [START_REF] Reimer | Transmission Electron Microscopy[END_REF][START_REF] Williams | Practical Analytical Electron Microscopy in Materials Science[END_REF]. For the TEM / EDX system used here and operated in the conditions of the present studies the MDM of a heavy element like Au in a biological thin foil (light elements with a very small concentration of osmium) should be a few 10 -19 g, whereas the mass of one 5 nm gold core is more than 10 -18 g. Thus the cross correlation of HR imaging inspection with corresponding EDX analysis supports the conclusion that there is no gold core nanoparticle in the observed sections.

Confocal observations

To optimize fluorescein emission detection, reflection imaging was used to visualize testes, avoiding tissue autofluorescence as demonstrated in our previous study (Klein et al. 2013).

For all samples, five slices were screened for each time point without being able to distinguish any fluorescent nanoparticles (Fig 7A -7F). Cellular structures appeared fluorescent on the samples, even on the negative control within the intertubular spaces. These areas corresponded to red blood cells, which are known to be autofluorescent.

DISCUSSION

The aim of this study was to assess the testicular biodistribution of 70-nm gold-silica nanoparticles after intramuscular injection in mice and to define their histological reproductive toxicity. As previously mentioned, the use of nanoparticles as a vaccine adjuvant is promising due to their ability to enhance immune response. However, safety has been poorly documented, especially considering the intramuscular exposure route. This study was intended to address this issue. The nanoparticles were designed to be detectable by several complementary methodologies (epi-fluorescence and confocal microscopy, ICP-AES, electron microscopy). All of the physico-chemical properties as well as the morphology and stability of tracers were validated before the nanoparticles were injected into mice. The ability of nanoparticles to enter the circulatory system and their stability in the blood were assessed by observing them in blood samples at D4 and D21 using TEM. It was also shown that significant amounts of particles were excreted through urine at H1 and D4.

Here an original multiscale approach using high-resolution methodologies (confocal microscopy, ICP-AES, TEM, and EDX) was achieved. Regarding qualitative techniques, especially confocal microscopy, though testicular autofluorescence remained a problem despite the use of reflection imaging, the present image features do not seem indicative of the presence of nanoparticles. Testicular autofluorescence is mainly in the visible spectrum, so we are currently developing Cyanine 5.5-doped nanoparticles of the same size (70 nm): their emission is centered in the near infrared region, which will help us to reduce background noise and obtain more reliable results using confocal microscopy. ICP-AES detection threshold for the nanoparticles used in this study was estimated to be 1.6 × 10 8 nanoparticles, which corresponded to 1/100,000 of the injected dose. The use of other measurement techniques such as ICP-MS could improve the sensitivity of nanoparticles detection by reducing this threshold. Despite the limitations of confocal microscopy and ICP-AES techniques their correlation with the conclusive results of present imaging and analysis TEM studies supported the conclusion that nanoparticles were absent in the testes.

Previous biodistribution studies showed that small amounts of sub-micrometric particles reached the testes, depending on experimental conditions. For example, after a single intravenous injection of 5 mg/kg of carbon nanotubes in mice, 151 ng of particles were found in testes 24 h later, corresponding to about 0.1% of the injected particles (Bai et al. 2010). Lankveld et al. (2010) found comparable results after intravenous injection of 20-nm silver nanoparticles for 5 days. Testicular distribution of 80-nm and 110-nm particles was also observed in very low amounts. De Jong et al. (2008) reported that after intravenous injection of 80 µg of 10-nm gold nanoparticles in rats, 55 ng/g was found in the testes, which means 1 out of 100,000 particles. Balasubramanian et al. (2010) observed similar results with a small amount of 20-nm gold nanoparticles (3 µg per rats) injected intravenously. Lee et al. (2013) also showed that about one 10-or 25-nm silver nanoparticle out of 10 6 was able to reach the rat testis after 4 weeks of oral exposure. Our previous results showed that 1 out of 10 7 450-nm particles injected by the intramuscular route was found in the testes (Klein et al. 2013). In the present study, using smaller particles (70 nm), it was observed that less than 1 out of 10 5 nanoparticles was able to reach the testes after intramuscular injection. This result seems in agreement with other quantitative studies about particles larger than 50 nm injected by intravenous route, which tend to be either not distributed in testes or distributed in very small amounts (Morishita et al. 2012). Similarly, De Jong et al. (2008) also demonstrated that 50-, 100-, and 250-nm particles were unable to reach testes (De Jong et al. 2008). Therefore, despite different exposure routes, the results tend to support the same conclusion, suggesting that nanoparticle size could be a key point for differences in testicular biodistribution.

In this study, we also confirmed that no morphological alterations of the testes were apparent as a result of exposure to nanoparticles. This result is in accordance with Morishita et al. (2012) and Chen et al. (2013).

To put the low testicular distribution of nanoparticles observed in this study into perspective with the risk of reproductive toxicity of nanoparticles in real-life situations, in vitro studies are useful. Indeed, these investigations are complementary to in vivo models and provide additional information. The use of cell lines is particularly appropriate for the investigation of the mechanisms or thresholds of toxicity. Asare et al. (2012) showed that after murine testicular cells underwent a 48-h exposure to 10 µg/ml of silver nanoparticles, the metabolic activity measured by MTT assay was reduced and the number of necrotic cells was slightly increased; however, other toxic effects, such as apoptosis and DNA damage, were only observed for higher concentrations (Asare et al. 2012). It was also shown that carbon black nanoparticles at a concentration of 10 µg/ml were able to increased StAR expression in Leydig cells, which could cause an increase in testosterone synthesis. Smaller concentrations of TiO 2 , carbon black, or diesel exhaust particles had no impact on Leydig cells (Komatsu et al. 2008), whereas Bradich-Stolle et al. (2005) showed that silver (Ag, 15 nm), molybdenum (MoO 3 , 30 nm), and aluminum (Al, 30 nm) nanoparticles at a concentration of 5 µg/ml increased leakage of lactate dehydrogenase from germ-line stem cells (Braydich-Stolle et al. 2005). Taken together, these data suggest that studies using different kinds of nanoparticles, different cells types, and so forth yield varying results, making it difficult to draw definitive conclusions. However, a clear trend is emerging: in most of the published papers, toxic effects were observed only for high concentrations of particles (above 5 µg/ml). Thus, considering that our results showed that less than 1 out of 10 5 particle reached the testis after an intramuscular injection, this route can be considered as safe as long as the quantity of nanoparticles injected into mice does not exceed 50 mg. This value appears too high to be clinically relevant or even realistic. Therefore, we may extrapolate that the probability of toxicity on the reproductive system is very low.

CONCLUSIONS

FIGURESFigure 1 :

 1 FIGURES

Figure 2 :

 2 Figure 2: Assessment of nanoparticles detection, morphological stability and ability to reach

Figure 3 :

 3 Figure 3: ICP quantification of gold in the testes. Results are expressed in parts per million

Figure 4 :

 4 Figure 4: Representative images of histological slides of testis. The left part of the figure

Figure 5 :

 5 Figure 5: Representative images of testis samples observed by TEM (H1, D4, D21, D36, and

Figure 6 :

 6 Figure 6: HR imaging studies coupled with EDX analysis in the TOPCON electron

Figure 7 :

 7 Figure 7: Confocal microscopy observations at the different times of sacrifice (A to H

Acknowledgments

The authors would like to acknowledge the financial support of the French Rhône Alpes Region through the ARC3 Environnement Research Program. They are grateful to Dr N.

Blanchard for his help in operating the TOPCON microscope at ILM Institute.

Compliance with Ethical Standards

All experiments were performed in compliance with the French laws and institutional guidelines. An authorization approving the experiments was obtained from the French Ministère de l'Enseignement Supérieur et de la Recherche (MESR, field number 00462.02).

Authors