SERMENT D'HIPPOCRATE

"Au moment d'être admis à exercer la médecine, je promets et je jure d'être fidèle aux lois de l'honneur et de la probité.

TABLE DES MATIERES

LISTE DES TABLEAUX

LISTE DES FIGURES

INTRODUCTION

Injuries to the deep flexor of the fingers are common and should be managed as an emergency. The repair is demanding and complex and will impact the clinical outcome as much as the associated lesions and postoperative rehabilitation. Today, there is no consensus on the ideal repair technique [START_REF] Bigorre | Primary flexor tendons repair in zone 2: Current trends with GEMMSOR survey results[END_REF].

In Zone 2, excessive exposure of the flexor tendon and sheath by the standard Bruner or midlateral incisions increases scarring in the skin and adhesion formation at the repair site [START_REF] Wong | Minimizing trauma over 'no man's land' with flexor tendon retrieval[END_REF]. It is therefore desirable to avoid skin incisions over this region and use a minimally invasive approach (3) (4).

Mantero et al.( 5) described a pull-out suture for the repair of the flexor digitorum profundus (FDP) tendon in the distal part of the finger as an alternative method of treatment of Zone 1 and distal Zone 2 tendon divisions with less surgical exposure of the Zone 1 sheath and less suture material in this restricted space. This technique was based on an earlier publication of Brunelli [START_REF] Brunelli | La suture tendineuse avec lancet de nylon appuye sans pull out[END_REF] and has been well described by Spingardi et al. [START_REF] Spingardi | Mantero's technique for tendon repair[END_REF]. Dargai and Kassir (8) modified the technique of Mantero for repair of FDP divisions in Zones 2B and 2C by using a distal cannula with a lasso through the pulp and distal FDP tendon rather than two cannulas. The procedure is performed through minimal incisions, limiting adhesion formation and with a suture strong enough for early mobilization.

The aim of this retrospective study was to investigate the outcomes of the modified Mantero technique for repair of FDP lacerations in Zone 2.

MATERIEL AND METHODES

Patient selection (Table 1)

From January 2010 to January 2017, 84 complete FDP divisions in Zone 2B and 2C were treated using the modified Mantero technique Flexor tendon injuries were classified into subzones based on the classification of Tang [START_REF] Tang | Flexor Tendon Repair in Zone 2C[END_REF]. Two patients did not complete the rehabilitation programme and were lost to followup and one patient was unavailable for the long-term assessment. Therefore, the outcomes are based on the 81 patients who completed the study. There were 63 men and 18 women with a mean age of 36 years (range 15-70). The patients were re-examined at a mean of 62 months (range 30-96) after operation. Fiftyone patients also had injuries to the neurovascular bundle that required repair. Flexor tendon injuries with associated fractures, major skin loss or disruption of the superficial flexor tendon were excluded.

Technique

Surgeons with expertise Level 3 according to the criteria of Tang and Giddins [START_REF] Tang | Why and how to report surgeons' levels of expertise[END_REF] carried out the procedures, with assistance from other junior surgeons.

We have adopted the 'wide awake surgery' technique, under local anaesthesia with epinephrine and without a tourniquet, and this allows full flexion and extension of repairs to be checked [START_REF] Lalonde | Wide-Awake Flexor Tendon Repair[END_REF].

If the proximal end of the tendon is not visible, we immediately make a proximal transverse incision from the level of the A1 pulley. A size 10 drain catheter is then passed into the sheath. Once the drain catheter is pushed down the sheath, it can be seen and withdrawn at the proximal incision. A core suture using the 2-strand Kessler A 20-gauge cannula is passed through the tip of the finger pulp, through the distal tendon stump to the level of the laceration site. Unlike the original Mantero technique, we use a single cannula instead of two cannulas and we pass a 3-0 PDS II suture through this cannula as a loop, which is retrieved at the site of the injury. The distal core suture is placed in the loop and slipped through the cannula and externalized at the fingertip (Figure 1(c)).

The cannula is removed, tendon stumps are apposed and the pull-out suture is tied over a piece of drain catheter. A continuous epitendinous suture of 6-0 polypropylene is inserted in the usual way, followed by skin closure (Figure 1(d)).

When the distal end of the tendon and the area of skin injury are not at the same level, the cannula is removed leaving the lasso in place. Finger flexion brings the distal tendon stump into the area of the laceration, with the lasso strands emerging from the distal tendon stump. The core suture ends are then placed within the lasso and brought to the finger pulp (Figure 2). The injured and adjacent pulleys (the A2 pulley and adjacent C1 pulley) are opened to expose the cut tendon for a mean length of 4 mm according to the site of flexor profundus laceration. In Zone 2B part of C1 and the distal part of the A2 pulley are opened and in Zone 2C the A2 pulley is opened proximal to the laceration.

All nerve and vessel damage is repaired under the microscope.

Postoperative management

The repairs are protected in a dorsal blocking splint from 6-8 cm above the wrist to the tip of the fingers with the wrist in 20°-30° of flexion, the metacarpophalangeal joints in 30°-50° of flexion and the interphalangeal joints fully extended. Active flexion without resistance is begun on the first postoperative day. A combined passive-active motion protocol is used. The patient is instructed to carry out these exercises several times a day and supervised by a physiotherapist three times a week. The patient is asked to actively fully extend the interphalangeal joints within the splint. The patient then actively flexes all fingers about two-thirds of the arc of flexion. Finally, the patient uses the contralateral hand to complete the flexion arc passively. The splint is removed at 4 weeks and active flexion and extension of all joints of the hand are allowed against no resistance. At 6 weeks, exercises against resistance are started. The splint and the Mantero suture are removed 6 weeks after surgery. Full tendon load is allowed 12 weeks after surgery regardless of the patient's occupation.

When there is a fixed flexion deformity of the proximal interphalangeal a dynamic splinting programme using either a Capener or low-profile outrigger splint is used. The splint applies a 0.25 kg force to the distal end of the middle phalanx. Each patient is instructed to wear the splint for 8 to 12 hours per 24 hours for 8 weeks, followed by a 2-to 3-week weaning period. This protocol is also used in patients with neurovascular lesions. The pull-out sites are cleaned daily with normal saline and a new dressing applied.

Functional outcome assessment

The range of motion (ROM) of the proximal interphalangeal joints (PIPJs) and distal interphalangeal joints (DIPJs) were measured using a goniometer. The sum of the ROM of PIPJs and DIPJs was recorded for the injured digits. Functional outcomes were assessed using the original Strickland and Glogovac ( 12) criteria (Table 1) and by using DIPJ ROM alone as proposed by Moiemen and Elliot [START_REF] Moiemen | Primary Flexor Tendon Repair in Zone 1[END_REF]. Using the latter assessment, DIP joint ROM after flexor tendon repair between 85% and 100% of the average (77°-91°) is considered excellent, between 70% and 84% (64°-76°) is considered as good and results between 50% and 69% (46°-63°) as fair. Results between 0% and 49% (0°-45°) are regarded as poor. Patients requiring secondary surgery due to complications arising from the tendon repairs were also noted.

Grip strengths were measured using a Jamar hand-held dynamometer (Sammons Preston, Bolingbrook, IL, USA) and compared with the contralateral normal hand.

Statistical analysise

Normality was tested using the Shapiro-Wilk test. The distribution of data was not normal, therefore the Wilcoxon and Mann-Whitney non-parametric tests were used and the results were expressed as medians with interquartile ranges (IQR). A p-value of ≤0.05 was considered to indicate a significant difference.

RESULTS

The results are presented in Table 2.

Table 2 : Comparisons of ranges of motion, distal interphalangeal joint (DIPJ) flexion and QuickDASH scores of fingers between different groups by demographics and injury characteristics. Median values with interquartile ranges.

Functional outcome and complications

The overall median grip strength was, respectively, 38 kg (IQR 34-50) and 45 kg (IQR 40-56) for the injury side and the contralateral uninjured hand respectively (p = 0.007).

Assessment of the ROM showed overall 54 excellent results, 22 good results and five fair results using the original Strickland and Glogovac criteria and 22 excellent results, 27 good results, 15 fair results and 16 poor results using the measurement of DIPJ motion alone.

There were no patients who had a repair for tendon rupture. There was no skin necrosis at the fingertip or other complications. One healthy 20-year-old gardener developed a deep abscess that was treated surgically and had a fair outcome. This infection was at the site of the injury that was contaminated with soil-borne organisms.

The other case was a superficial infection also at the site of injury, which healed with local care without antibiotics.

Three patients required secondary tenolysis. One of these (Zone 2B injury) was not compliant with rehabilitation. We have no explanation for the stiffness of the fingers of the other two patients (Zone 2C injuries), but one had undergone delayed primary repair. These three patients were in the group with fair results using the Strickland and Glogovac criteria.

DISCUSSION

Methods of primary repair and rehabilitation of the digital flexor tendon, developed over the past two decades, include strong repair techniques and early postoperative active motion (1) (14) (15) (16) [START_REF] Tang | Strong Digital Flexor Tendon Repair, Extension-Flexion Test, and Early Active Flexion[END_REF]. The key developments in Zone 2 repairs reported by these authors are the use of 4-or 6-strand repairs.

The current study reports another technique for flexor tendon repair in Zone 2. The results were good and excellent in 91% of treated fingers with no ruptures. Similar or even better results have been observed using other high-strength multi-strand repairs.

For example, Osada et al. ( 18) treated 27 fingers with a 6-strand repair and obtained 96% good or excellent results and no ruptures. Al Qattan [START_REF] Mm | Isolated flexor digitorum profundus tendon injuries in zones IIA and IIB repaired with figure of eight sutures[END_REF] published a series of 36 fingers with isolated FDP injuries in Zones 2A and 2B, repaired with three 'figure of eight' sutures. The outcome was excellent and good in 100%, with no ruptures.

In our series, only three patients (3.7%) required secondary tenolysis. In recent reports, the incidence of tenolysis is typically 5%-10% (4). Dy et al. [START_REF] Dy | The Epidemiology of Reoperation After Flexor Tendon Repair[END_REF] showed that further surgery for rupture or adhesions is required in around 6% of cases of flexor tendon repairs. The explanation for the lower rate of tenolysis in our series is that there is less invasion of the Zone 2 sheath and less suture material in this restricted area compared with the standard techniques and as the load is transferred from the suture site to the fingertip, the modified Mantero technique permits immediate active exercises postoperatively without resistance.

In several biomechanical studies, the pull-out suture technique is reported as being stronger than 4-strand or 6-strand core sutures. However, these data were obtained from cadaver or in vitro studies and the values are much lower than those obtained in vivo. The gap formation forces in 4-strand or 6-strand core suture are measured as between 44 N and 64.2 N (21) (22) (23) [START_REF] Viinikainen | The Strength of the 6-Strand Modified Kessler Repair Performed With Triple-Stranded or Triple-Stranded Bound Suture in a Porcine Extensor Tendon Model: An Ex Vivo Study[END_REF]. In a recent publication, the measurement of the gap formation force was 98 N in the Brunelli technique associated with a modified Kessler suture [START_REF] Başar | Modified Brunelli pull-out suture technique in zone II flexor tendon rupture: a fresh human cadaver study[END_REF]. Rigo and Røkkum (26) found most functional problems with injuries located between the A4 and A2 pulleys (subzones 1C to 2C), as in our series. Subzone 2C, which is the narrowest part of the sheath, is considered the most problematic (Tang and Shi, ( 27)) as movement of both the repaired flexor digitorum superficialis (FDS) and FDP tendons within the rigid A2 pulley is more difficult. The flexor tendons under the A2 pulley tend to adhere to one another, and the FDP tendon gliding is consequently restricted by the excursion of the repaired FDS tendon.

Our results were better when the pulley was vented but we have never needed to open the A2 pulley more than a fifth of its length, namely about 4 mm. As in other techniques, the peripheral sutures serve to tidy up the repair site and prevent gapping. But this suture in the modified Mantero procedure is less bulky than in other techniques, allowing a full passive ROM of the repair, without the need for venting of the pulleys excessively.

The major problems encountered with pull-out techniques are patient tolerance and potential infections owing to the external material that is subject to displacement during motion (Marin-Braun et al., [START_REF] Braun | Repair of the flexor digitorum profundus and the flexor pollicis longus by the "rope down" technique. Results in a series of 77 cases[END_REF]). However, like Wülle (29), Guinard et al. [START_REF] Guinard | The Mantero Flexor Tendon Repair in Zone 1[END_REF] and Baer et al. [START_REF] Baer | The Mantero technique for flexor tendon repair -an alternative?[END_REF] we did not encounter such complications. Both the infections in the series were localized at the site of the injury but not at the pull-out material. All patients were strongly advised to observe strict hygiene.

One of the questions is the technical difficulty of the procedure. It is important to position the cannula and the lasso in the middle of the distal tendon stump section and then ensure that the tendon slides easily during the finger flexion-extension test to ensure that there is no sheath snagging, once the cannula has been removed, leaving the lasso in place. This lasso trick avoids an enlargement of the scar when the skin wound and tendon division are at different levels (Figure 2). We did not record the operating-room time, but it was often less than 45 minutes in our experience.

The advantages of the wide awake local anaesthesia no tourniquet (WALANT) technique here are undeniable in allowing accurate preoperative assessment of the adequacy of repair, gapping or triggering of the tendon during active flexion and extension of the finger (32); [START_REF] Lalonde | Epinephrine in Local Anesthesia in Finger and Hand Surgery: The Case for Wide-awake Anesthesia[END_REF]; [START_REF] Moriya | Incidence of tenolysis and features of adhesions in the digital flexor tendons after multi-strand repair and early active motion[END_REF].

We acknowledge that this study is limited by its retrospective nature. The strengths of this study are the simplification of the original Mantero technique for FDP tendon injuries in Zone 2 with a fairly large number of patients. The procedure is done through minimal incisions, limiting adhesion formation and with a low tenolysis rate. Limiting the length of incision also decreases gliding resistance to the tendon and postoperative oedema (4). The good results and absence of ruptures suggest that the tendon healing and strength of repair are adequate for immediate postoperative motion. Unlike Mantero, who considers that the two-tunnel technique better distributed the forces across the repair site [START_REF] Spingardi | Mantero's technique for tendon repair[END_REF], we think that the forces are transferred to the pulp by the pull-out suture, and a single-tunnel repair technique is sufficient. The use of a single cannula is technically simpler, reducing the risk of placement error and impingement on the pulley or sheath by cannula or suture. We believe that the modified Mantero repair can be recommended as an alternative for the repair of tendon divisions in Zone 2.

CONCLUSION

Suturing the deep flexor is still considered one of the most demanding procedures in hand trauma, where the expertise of the hand surgeon is of real benefit to the patient and his functional prognosis. Zone 2 repair brings together the difficulties related to the flexor but also the digital canal. In contrast to the current concept of "bulky surgical repairs", this work reveals that suturing the deep flexor tendon in zone 2 using a modified montero technique gives encouraging clinical results, proposing a minimally invasive strategy that could be similar to percutaneous repair and could be integrated as a surgical option in the therapeutic arsenal.

Modification de la technique de Mantero pour la réparation des lésions du fléchisseur profond des doigts en zone 2 Résumé

Introduction : Dans la zone 2, l'exposition excessive du tendon fléchisseur et de la gaine par des incisions standard de Bruner ou médio-latérales augmente le risque de formation d'adhérences. Il est donc souhaitable d'éviter les incisions cutanées dans cette région et d'utiliser une approche peu invasive. [START_REF] Mantero | Il pull-out in 'no man's land' e al canale digitale nelle lesioni dei flessori (metodo personale)[END_REF] ont décrit une suture pull-out pour la réparation du tendon du flexor digitorum profundus (FDP) dans la partie distale du doigt comme une méthode alternative de traitement des section du tendon en zone 1 et de la zone 2 distale avec abord chirurgicale moindre de la gaine et moins de matériel de suture dans cet espace restreint. [START_REF] Dargai | Modified Mantero technique for flexor digitorum profundus laceration repair in Zone 2[END_REF] ont modifié la technique de Mantero pour la réparation des divisions du FDP dans les zones 2B et 2C en utilisant une canule distale avec un lasso à travers la pulpe et le tendon distal du FDP plutôt que deux canules. La procédure est réalisée par des incisions minimales, limitant la formation d'adhérences et avec une suture suffisamment solide pour une mobilisation précoce. L'objectif de cette étude rétrospective était d'examiner les résultats de la technique de Mantero modifiée pour la réparation des lacérations du FDP dans la zone 2.

Méthode : De janvier 2010 à janvier 2017, 81 ruptures complètes du tendon du flechisseur profonde des doigts dans les zones 2B et 2C ont été traitées par la technique de Mantero modifiée. Les patients ont été réexaminés en moyenne 62 mois (intervalle 30-96) après l'opération. Nous avons analysé les résultats en fonction de l'âge, du sexe, de l'intégrité de la poulie, des blessures associées et de la durée du suivi. L'amplitude des mouvements (ROM) des articulations interphalangiennes proximales et distales a été mesurée à l'aide d'un goniomètre. La somme des ROM des PIPJ et DIPJ a été enregistrée pour les doigts blessés.

Résultats : La force de préhension médiane globale était, respectivement, de 38 kg (IQR 34-50) et de 45 kg (IQR 40-56) pour le côté blessé et la main contralatérale indemne (p=0,007). L'évaluation de la ROM a montré globalement 54 excellents résultats, 22 bons résultats et cinq résultats passables en utilisant les critères originaux de Strickland et Glogovac. Il n'y a pas eu de nécrose cutanée à l'extrémité du doigt ni d'autres complications. Un jardinier de 20 ans en bonne santé a développé un abcès profond qui a été traité chirurgicalement et a eu un résultat moyen. Trois patients ont dû subir une ténolyse secondaire. Ces trois patients faisaient partie du groupe dont les résultats étaient satisfaisants selon les critères de Strickland et de Glogovac.

Conclusion : La réparation de Mantero modifiée est recommandée comme alternative dans la réparation des ruptures de tendon dans la zone 2B-2C. Les bons résultats et l'absence de ruptures suggèrent que la cicatrisation du tendon et la force de la réparation sont adéquates pour un mouvement postopératoire immédiat. Un problème est la difficulté technique de la procédure. Il est important de positionner la canule et le lasso au milieu de la section distale du moignon du tendon, puis de s'assurer que le tendon glisse facilement lors du test de flexion-extension des doigts, une fois la canule retirée, en laissant le lasso en place.

Discipline : Chirurgie orthopédique et traumatologique, chirurgie de la main

Mots-Clés : Technique de Mantero ; réparation primaire du tendon ; mobilisation active précoce ; résultats ; libération de la poulie.

Flexor digitorum profundus tendon injuries in Zone 2 repaired with a modified Mantero technique

Abstract

Background : Mantero et al. (1973) described a pull-out suture for the repair of the flexor digitorum profundus (FDP) tendon in the distal part of the finger as an alternative method of treatment of Zone 1 and distal Zone 2 tendon divisions with less surgical exposure of the Zone 1 sheath and less suture material in this restricted space. Dargai and Kassir (2019) modified the technique of Mantero for repair of FDP divisions in Zones 2B and 2C by using a distal cannula with a lasso through the pulp and distal FDP tendon rather than two cannulas. The procedure is performed through minimal incisions, limiting adhesion formation and with a suture strong enough for early mobilization. The aim of this retrospective study was to investigate the outcomes of the modified Mantero technique for repair of FDP lacerations in Zone 2.

Method : From January 2010 to January 2017, 81 complete flexor digitorum profundus tendon disruptions in Zones 2B and 2C were treated using the modified Mantero technique. The patients were re-examined at a mean of 62 months (range 30-96) after operation. We analysed outcomes against ages, gender, pulley integrity, associated injuries and follow-up times. The range of motion (ROM) of the proximal interphalangeal joints and distal interphalangeal joints were measured using a goniometer. The sum of the ROM of PIPJs and DIPJs was recorded for the injured digits.

Results : The overall median grip strength was, respectively, 38kg (IQR 34-50) and 45kg (IQR 40-56) for the injury side and the contralateral uninjured hand respectively (p=0.007). Assessment of the ROM showed overall 54 excellent results, 22 good results and five fair results using the original Strickland and Glogovac criteria. There was no skin necrosis at the fingertip or other complications. One healthy 20-year-old gardener developed a deep abscess that was treated surgically and had a fair outcome. Three patients required secondary tenolysis. These three patients were in the group with fair results using the Strickland and Glogovac criteria Conclusion : The modified Mantero repair is recommended as an alternative in the repair of tendon disruptions in Zone 2B-2C. The good results and absence of ruptures suggest that the tendon healing and strength of repair are adequate for immediate postoperative motion. One issue is the technical difficulty of the procedure. It is important to position the cannula and lasso in the middle of the distal tendon stump section and then ensure that the tendon slides easily during the finger flexion-extension test, once the cannula is removed, leaving the lasso in place.

  DES ABRÉVIATIONS ....................................................................................................................... LISTE DES TABLEAUX ............................................................................................................................... LISTE DES FIGURES ................................................................................................................................... INTRODUCTION ............................................................................................................................................ MATERIEL AND METHODES ...................................................................................................................... PATIENT SELECTION (TABLE 1) ......................................................................................................................... TECHNIQUE ........................................................................................................................................................ FUNCTIONAL OUTCOME ASSESSMENT ............................................................................................................. RESULTS ..................................................................................................................................................... FUNCTIONAL OUTCOME AND COMPLICATIONS ................................................................................................ DISCUSSION ............................................................................................................................................... CONCLUSION ............................................................................................................................................. REFERENCES BIBLIOGRAPHIQUES ..................................................................................................... LISTE DES ABRÉVIATIONS FDP : Flexor digitorum profundus. PDS : Polydioxanone. ROM : Range of Motion. PIPJs : Proximal Interphalangeal Joints. DIPJs : Distal Interphalangeal Joints. IQR : Interquartile Ranges.

Figure 1 : 8 Figure 2 :

 182 Figure 1 : Zone 2C FDP tendon laceration caused by broken glass in the ring finger of a 36-year-old man. (a) The steps in retrieving the flexor tendons using a drain catheter. (b) The proximal tendon stump was sutured. (c) A 20-gauge cannula with a lasso was passed through the distal FDP tendon and the suture was pulled out of the fingertip. (d) Completion of surgery. ........................................................................... 8

  technique with a 3-0 polydioxanone monofilament suture (PDS II; Ethicon, Somerville, NJ, USA) is placed in the proximal end of the FDP tendon. No knot is tied. Both ends of the core suture are passed into the drain catheter (Figure 1(a)). The tendon can be delivered distally by pulling the suture, with gentle flexion and extension of the digit (Figure 1(b)).

Figure 1 :

 1 Figure 1 : Zone 2C FDP tendon laceration caused by broken glass in the ring finger of a 36-year-old man. (a) The steps in retrieving the flexor tendons using a drain catheter. (b) The proximal tendon stump was sutured. (c) A 20-gauge cannula with a lasso was passed through the distal FDP tendon and the suture was pulled out of the fingertip. (d) Completion of surgery.

Figure 2 :

 2 Figure2: Lasso trick used when the distal tendon end and the skin wound are not in the same area. The cannula is removed but the lasso is left in place. Finger flexion delivers the distal tendon stump to the laceration site with the strands of the lasso emerging from the substance of the distal tendon stump.

  Discipline : Orthopaedic and trauma surgery, hand surgery Keywords : Mantero technique; Primary tendon repair; early active mobilization; outcomes; pulley release.

Table 1 :

 1 Patient demographics and injury characteristics .......................................... 7

Table 2 :

 2 Comparisons of ranges of motion, distal interphalangeal joint (DIPJ) flexion and QuickDASH scores of fingers between different groups by demographics and injury characteristics. Median values with interquartile ranges. ................................ 12

Table 1 :

 1 Patient demographics and injury characteristics

Mon premier souci sera de rétablir, de préserver ou de promouvoir la santé dans tous ses éléments, physiques et mentaux, individuels et sociaux.

Je respecterai toutes les personnes, leur autonomie et leur volonté, sans aucune discrimination selon leur état ou leurs convictions.

J'interviendrai pour les protéger si elles sont affaiblies, vulnérables ou menacées dans leur intégrité ou leur dignité.

Même sous la contrainte, je ne ferai pas usage de mes connaissances contre les lois de l'humanité.

J'informerai les patients des décisions envisagées, de leurs raisons et de leurs conséquences.

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Je donnerai mes soins à l'indigent et à quiconque me les demandera.

Je ne me laisserai pas influencer par la soif du gain ou la recherche de la gloire.

Admis dans l'intimité des personnes, je tairai les secrets qui me seront confiés.

Reçu à l'intérieur des maisons, je respecterai les secrets des foyers et ma conduite ne servira pas à corrompre les moeurs.

Je ferai tout pour soulager les souffrances. Je ne prolongerai pas abusivement les agonies. Je ne provoquerai jamais la mort délibérément.

Je préserverai l'indépendance nécessaire à l'accomplissement de ma mission.

Je n'entreprendrai rien qui dépasse mes compétences. Je les entretiendrai et les perfectionnerai pour assurer au mieux les services qui me seront demandés.

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Que les hommes et mes confrères m'accordent leur estime si je suis fidèle à mes promesses : que je sois déshonoré et méprisé si j'y manque."


Gottdenker

Recommendation

Zoonotic pathogens, those transmitted from animals to humans, constitute a major public health risk with high associated global economic costs. Diseases associated with these pathogens represent more than 60% of emerging infectious diseases and predominantly originate in wildlife (1). Over the last decades, the emergence and re-emergence of zoonotic pathogens have led to an increasing number of epidemics, as illustrated by the current Covid-19 pandemic. There is ample evidence that human impact on native ecosystems such as deforestation, agricultural development, and urbanization, is linked to spillover of pathogens from animals to humans (2). However, research and calls to action have mainly focused on the importance of surveillance and prevention of zoonotic emergences along landscape interfaces, with special emphasis on tropical forests and agroecosystems, and studies and reviews pointing out the zoonotic risk associated with cities are scarce. Additionally, cities are sometimes wrongly seen as one homogeneous ecosystem, almost exclusively human, with a Northern hemisphere-biased perception of what a city is, which fails to take into account the ecological and socio-economic diversities that can constitute an urban area.

Here, Dobigny and Morand (3) aim to draw attention to the importance of urban ecosystems in zoonotic risk and advocate that further attention should be paid to urban, peri-urban and suburban areas. In this well-organized and welldocumented review, the authors show, using updated literature, that cities are places where massive contacts occur between wildlife, domestic animals, and human inhabitants (thus constituting spillover opportunities), and that it is even likely that human and wildlife contact in urban centers is more prevalent than in wild areas, perhaps contrary to intuition. Indeed, cities currently constitute the most important environment of human life and are places for millions of close

interactions between humans and animals, including pets and domestic animals, wild animals through the intrusion of wild urban-adapted species (e.g., some bat, rodent, or bird species among others), manipulation and consumption of wildlife meat, and the existence of wildlife meat markets, which all constitute a major risk for zoonotic spillover. In cities, lab escapees of zoonotic pathogens also exist, and trends of adaptation to urban ecological conditions of many vectors of primary health importance is also a concern. The authors further argue that cities are predominant places for both epidemic amplification of human-human transmitted pathogens, because they are places with high human densities and population growth, and for dissemination of reservoirs, vectors and pathogens, as they are transport hubs. Dobigny & Morand further predict, likely correctly, that cities may be important places for pathogen evolution. Finally, they propose actions and recommendations to limit the risk of zoonotic spillover events from urban ecosystems and future directions for research aiming at assessing this risk.

The reviewers found the manuscript well-organized and presented, timely, and bringing novel contributions to the field of zoonotic emergence. I strongly recommend this article, which should benefit a large audience, particularly in the context of the current Covid-19 pandemics and the ongoing One Health initiatives aiming at preventing future zoonotic disease emergence (4). by three independent reviewers which found the manuscript relevant, but suggested some improvements. Therefore, I invite you to submit a revised version of the manuscript that addresses the points raised during the review process. If you agree, please revise your manuscript accordingly and explain the changes carefully (or your reasons for not having followed the comments) in your rebuttal letter. Reviewer's comments can be found below.

Reviewed by Eric Dumonteil, 25 May 2022

This is a nice review, well organized and presented, with clear recommendations for future directions of discussions and research. My only concern is the heavy focus on viruses and to a leseer extent bacteria. Although this is understandable, given their rapid evolutionay time scale that can favor their rapid emergence, it would be important to better include parasites in this discussion as urban habitats can also favor their evolution as well, even though this may be a slower process. It is also surprising that the section on arthropod vectors does not extend more on vectors that are already well adapted to urban environments and responsible for major disease burden (dengue, Zika, Chagas disease, etc...).

Reviewed by anonymous reviewer, 13 May 2022

This review aims to draw readers' attention to the importance of urban ecosystems on disease emergence from wildlife I found this paper very timely. The recent Covid outbreak attracted the attention on wildlife-human new interfaces due to overexploitation of agro systems in many tropical countries, but it is true that cities (including peri-urban areas) and their specific conditions were overlooked as potential important places of zoonotic emergence. Yet, the plague outbreak in middle-age in Europe was amplified in cities.

I have a number of comments, but I have to say that none of them jeopardizes the publication of this paper, which seems important to me.

1-

The paper is about emergence of diseases in humans. I think that this should be emphasizes in the general introduction, because there are also potentials for cities to be important places for emergence and spread of diseases staying in the animal compartment (e.g. avian influenza) 2-P. 4, L. 5 and others references to figures. Figures 1 and2 are of poor quality in this version. Is it possible to improve this quality? Else, P. 12, there is a reference to Figure 3, but there is no figure 3 in the version I have access to.

3-P. 9 L. 20. I would add a sentence of general conclusion for summarizing this important chapter (high animal densities + high prevalence + frequent contacts with humans = high probability of spillover) 4-P. 10 L. 17-20. At least, even if not the source, the market here played a role in the amplification of epidemics. 5-P. 12, L. 8. To hammer the nail, I would begin the sentence by something like "Importantly, even before human contamination"… 6-P. 12 or somewhere else. Maybe it would be worth adding a paragraph on cities as ideal socioecosystems for emergence of diseases carrying resistance to antibiotics (which would add a problem to the problem). Antibiotic resistance is noted in the "evolutionary consequences" (P. 13 after L. 23), with the possibility for recombination between microbe strains, but I think that cities, because to high level of pollution and overconsumption of antibiotics may also provide direct strong selective pressures for resistance selection, e.g. 7-P. 15, L. 13. About the heterogeneity of urban socio-environment. Well, opposing urban vs. nonurban also suppose that non-urban is also homogeneous, which is obviously not the case! 8-P. 15, L. 26 and after. Are these proposals specific to urban areas? 9-P. 17, L. 6-17. Perhaps it would be interesting to compare these recommendations with those for invasive species, in order to draw inspiration from them.

Reviewed by Nicole L. Gottdenker, 20 Jun 2022

This is a review-concept paper of zoonotic disease emergence in urban systems there are many of these kind of reviews in the literature, but this one has some additional novel contributions. The review overlooks some recent synthetic reviews discussiong socioecological factors related to urbanization and zoonotic disease emergence (Combs et al. 2021. https://doi.org/10.1111/gcb.16033). The review is among many that discuss urbanization and zoonotic disease. Comments regarding some details and larger issues in the paper are as follows:

Please note that there are many English/syntax errors and I am not reading the paper to capture and correct all of these-Actually, the paper seems very 'rushed' the way it has been written and merits some significant editing-will put some of the corrections below. I think that an overall diagraom summarizing the papers key points would be useful for the reader and a good synthesis of the material. I suggest adding one (a diagram or illustration that serves as a synthesis and summmary of article's key points). abstract: line 18-19 Delete '(e.g., better description of extended urban socio-ecosystems in urban health ecology studies; truly evaluated interventional researches') not necessary line 19-I would use another term instead of 'slum' even if the UN and other agencies use it-it is a loaded term and has a heavy bias associated with it (see Gilbert, A., 2007. "The return of the slum: does language matter?".International Journal of Urban and Regional Research, 31(4), pp.697-713.) First paragraph of the first paragraph of the introduction. lines 23-24 (and also the end of the first paragraph of the it there are studies on per-urba, urban and suburban areas on zoonotic diseases (see studies on rabies in Canada, leptospirosis and other diseases in New Orleans, leptospirosis in Rio de Janeiro, urban Chagas in Venezuela). introduction line 16-change 'many researches' to 'much research' p. 4 line 20, delete -'Thus, whatever this is good news or not' p. 5-change 'apprehension' to 'comprehension'

The section in page 5 'Cities as places for millions of close animal-human interactions ' makes a very good point about some cities being close to a lot of biodiversity or zoonoses and merits a bit more development of some specific examples of this point you are making (examples of some emergent diseases and these biodiverse urban locations. section on pets and domestic animalsagain, p. 5 line 28-please use another word other than 'slums' p. 5 line 29-change 'owner' to 'owners'

In addition to the section on 'pets and domestic animals', I suggest adding a paragraph about stray animals in urban areas (dogs and cats), some suggestions include feral cats and urbanization and disease in Soeul 'Hwang et al. 2018, PeerJ, 6, e4988. https://doi.org/10.7717/peerj.4988', urban rabies in peru-De la Puente-León, M., Levy, M. Z., Toledo, A. M., Recuenco, S., Shinnick, J., & Castillo-Neyra, R. (2020). Spatial Inequality Hides the Burden of Dog Bites and the Risk of Dog-Mediated Human Rabies. The American journal of tropical medicine and hygiene, 103(3), 1247-1257.). p. 6 line 3, change 'death occur' to 'deaths occur' p. 6 line 8, omit 'were recently demonstrated to' p. 6 line 16 the sentence that urban wildlife ' shelter an overall higher pathogen richness than their non-urban counterparts' is not always/universally true, but this can be context-dependent. p. 6 lines 22-23-the section of this sentence needs to be rephrased for clarity: ' Many testimonies (e.g., Barkham, 2017) demonstrate that 22 peri-urban zones, when not core cities are now regularly visited by sometimes large and unexpected 23 animals: ' p. 7 line 6 ' very large size' change to 'large population sizes' also in the section on wild animals perhaps mentioning urban rabies and raccons would add to this discussion-again please use another word for slums throughout the manuscript. p. 9-the discussion on laboratory escape is very interesting-perhaps mentioning that one of the SARS cov-2 unproven hypothesis includes lab escape. Regardless, this section should be its own subsection separate from selling animals in marketplaces. in Section 3.3, please do not use the term 'bush meat' or 'wet market' perhaps just change the terms 'wildlife meat commerce'. Can you change 'wet market' to 'animal meat market' ?= Wet market came from a direct mandarin translation, so perhaps just usuing the term 'animal meat/product market' is better.

The last section on cities as incubators for 'evolutionary novelties' I think brings up some interesting points but needs some cohesion with evolutionary theory or processes (perhaps organizing paragraphs in this section in terms of evolutionary processes (See Gluckman The 'call for some actions' section is a bit 'rambling' perhaps shortening or significantly editing this section would increase the paper's clarity-it is a very broad paper. I am not sure how much the Fiuure 2 reprint is useful for this study and maybe couldb be replaced by thte larger more synthetic diagram that I suggested.

  Rilstone, V; Vignale, L; (...); Champagne, P. The role of antibiotics and heavy metals on the development, promotion, and dissemination of antimicrobial resistance in drinking water biofilms. CHEMOSPHERE 282, DOI 10.1016/j.chemosphere.2021.131048 Buelow, E; Ploy, MC and Dagot, C Role of pollution on the selection of antibiotic resistance and bacterial pathogens in the environment. CURRENT OPINION IN MICROBIOLOGY 64 , pp.117-124, DOI: 10.1016/j.mib.2021.10.005

  E.g. (among many others) Reaser, JK ; Burgiel, SW (…) ; Burgos-Rodriguez, J The early detection of and rapid response (EDRR) to invasive species: a conceptual framework and federal capacities assessment. BIOLOGICAL INVASIONS, Volume22, Issue1, Page1-19 DOI10.1007/s10530-019-02156-w Miralles, L ; Ibabe, A (…);Borrell, YJ "If You Know the Enemy and Know Yourself": Addressing the Problem of Biological Invasions in Ports Through a New NIS Invasion Threat Score, Routine Monitoring, and Preventive Action Plans. FRONTIERS IN MARINE SCIENCE, Volume 8, Article Number 633118, DOI10.3389/fmars.2021.633118 10-P. 18, L. 16. This also implies sharing the knowledge rapidly, without any political ulterior motive… (Utopia, I'm afraid)

  et al. 2011-Evol Appl. 2011 Mar; 4(2): 249-263.). p. 13-This page has a couple of paragraphs that don't fit under the evolutionary novelties heading and should have their own subsection, perhaps something like 'Cities as transportation hubs for pathogen movement and exchange' and then the next paragraph have another subsection 'Impact of urbanization on microbial interactions' p. 14 line 12-change 'repeated animal-human transmission' to 'iteration of animal-human humananimal transmission events p. 14 line 24-change' researches are' to 'research is' p. 14 line 32-change 'researches' to 'research' Cane you define briefly'riposte' as used on p. 15 and 16? p. 18-change-'trans sectorial-to 'trans disciplinary' p. 18-do you know of any examples of centers of excellence in ecology and health research and training?'

Conflict of interest:

The recommender in charge of the evaluation of the article and the reviewers declared that they have no conflict of interest (as defined in the code of conduct of PCI) with the authors or with the content of the article.


Teodor Burghelea
email: teodor.burghelea@univ-nantes.fr

Chaotic mixing of yield stress materials

Keywords: yield stress materials, laminar chaotic advection, mixing, Finite Time Lyapunov exponents

Pasty materials academically referred to as "yield stress" materials are ubiquitous in daily life whether we think of food products (e. g. mayonnaise, mustard, ketchup etc.), beauty products (e.g. hand creams, hair gels, shower gels etc.), construction materials (cement, mud) or we try to understand the geophysical scale dynamics of volcanic magmas and land-slides. A key issue that has been little (or not at all) addressed so far is rather basic and may be shortly phrased as "'How do we mix such materials?" which sets up the global aim of the present contribution. To address this issue, I will first reveal a catastrophic failure of the mixing by the laminar chaotic advection induced by the presence of the yield stress. Next, I will dwell deeper into the physical reasons underlying this fact in terms of both a systematic Eulerian frame and a systematic Lagrangian frame analysis. As a key finding, I will show a clear departure of the spectra of fluctuations of the passive scalar from the analytical prediction proposed by G. K. Batchelor for a temporarily random and spatially smooth flow in terms of the emergence of a spectral peak that blocks the passive scalar cascade. The additional space scale related to the position of the spectral peak is related to the characteristic size of unyielded materials. Finally, I will discuss two simple solutions able to alleviate to some extent the loss of mixing without paying a hefty energetic price.

Figures and tables

J o u r n a l P r e -p r o o f

coefficient D eff /D } v R u R ] ] v R ] ] v ] ˙ } ( R ]
o ] v ( U P ˙min computed for regular mesh (black squares) obtained from the data sets presented in the top three sub-panels of Fig. 2 and the adaptive mesh (red circle) obtained from the data set presented in the bottom panel of Fig. 2.

CRediT author statement

N/A

1 .

 1 Figure 1. Schematic representation of the channel equipped with three rotating arc-walls (in scale). J o u r n a l P r e -p r o o f

Figure 2 .

 2 Figure 2. Transverse profiles of the passive scalar concentration C at the exit of the mixer} ] v ( } ] } o } ( R u o o u R ] P ˙ u ] v ] v ]ated in the top inserts. The case illustrated in the bottom panel refers to the adaptive meshing technique -see text for description. The full lines in each panel are nonlinear fitting functions according to the analytical solution.

Figure 3 .

 3 Figure 3. Dependence of the effective diffusion coefficient normalized by the molecular diffusioncoefficient D eff /D } v R u R ] ] v R ] ] v ] ˙ } ( R ]o ] v ( U P ˙min computed for regular mesh (black squares) obtained from the data sets presented in the top three sub-panels of Fig.2and the adaptive mesh (red circle) obtained from the data set presented in the bottom panel of Fig.2.

Figure 4 .

 4 Figure 4. Illustration of the adaptive grid during a simulation of the mixing process at large bulk Bingham number, Bn bulk = 26.5. The dense grid points coloured in yellow mark the interface of the passive scalar while those marked in red mark the yield surface (see text for description). The dense black grid points have resulted from the vorticity based dynamic mesh adaptivity.

Figure 5 .

 5 Figure 5. Mixing patterns for the Newtonian case (Bn bulk = 0, N = 1) at several time instants indicated in the top inserts. J o u r n a l P r e -p r o o f

Figure 6 .

 6 Figure 6. Space time plots obtained for the Newtonian case (Bn bulk = 0, N = 1) at the centre of the mixer (top panel) and at the exit of the mixer (bottom panel).

Figure 7 .

 7 Figure 7. Time series of the mixing indicator C std obtained for the Newtonian case (Bn bulk = 0, N = 1) at the centre of the mixer (circle) and at the exit of the mixer (square). The full line is an exponential fitting function.

Figure 9 .

 9 Figure 9. Space time plots of the passive scalar C obtained for the highest yield stress case (Bn bulk = 26.5, N = 0.75) at the centre of the mixer (top panel) and at the exit of the mixer (bottom panel).

Figure 10 .

 10 Figure 10. Time series of the mixing indicator C std obtained for the highest yield stress case (Bn bulk = 26.5, N = 0.75) at the centre of the mixer (circle) and at the exit of the mixer (square). The full line illustrates a failed attempt to fit exponentially the time series of the mixing indicator at the channel exit.

  Figure 11. Dependence of the mixing efficiency defined as the variance of the passive scalar concentration at the exit of the mixer, C std , on the bulk Bingham number Bn bulk . Both the color v R o ] ] } ( R ˙ u } o u R ( o ] } v w C std of the mixing indicator C std around its dynamical steady state value.

Figure 12 .

 12 Figure 12. LEFT: Time averaged transverse profiles of the axial velocity; RIGHT: Time averaged transverse profiles of the transverse velocity.

Figure 14 .

 14 Figure 14. Exemplification of instantaneous flow patterns for the Newtonian case (left column) and Bn bulk =26.5 (right column). The time instants are indicated in the top inserts of each panel.

Figure 16 .

 16 Figure 16. Dependence of the correlation times of the passive scalar fluctuations computed in the bulk of the flow (blue circles) and within the boundary layers (orange squares) on the bulk Bingham number Bn bulk . J o u r n a l P r e -p r o o f

Figure 18 .

 18 Figure 18. Size statistics of the un-yielded blobs in the active mixing region: left t probability distribution function (pdf), right t dependence of the mean size of the unyielded blobs R av on the bulk Bingham number Bn bulk .

Figure 23 .

 23 Figure 23. Dependence of the spaced averaged Lyapunov exponent averaged over the last five periods of the mixing process on the bulk Bingham number Bn bulk . J o u r n a l P r e -p r o o f

Acknowledgments  Yann Moguen (former postdoc at University of Pau)  Yves Le Guer -University of Pau  Kamal El Omari -University of Pau  Eliane Younes (former PhD candidate in our group)  Cathy Castelain J o u r n a l P r e -p r o o f

Funding: This work was supported by t h e F r e n c h r e s e a r c h P r o g r a m N o .

A N R -1 6 -C E 0 6 -0 0 0 3 (Novel active inline Mixer for Yield Stress fluids, NaiMYS).

Declaration of interests

Please tick the appropriate statement below and declare any financial interests/personal relationships which may affect your work in the box below.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Please declare any financial interests/personal relationships which may be considered as potential competing interests here.

Author Biography

Teodor Burghelea is a researcher with the Centre Nationale de la Recherche Scientifique (CNRS) at the Laboratoire de Thermique et Energie de Nantes, Nantes, France. His research interests are in non-Newtonian fluid mechanics and rheology. In particular he is interested in the fluid mechanics of yield stress materials.

J o u r n a l P r e -p r o o f


Pierre-Emmanuel Peyneau

in single particle ICP-MS time scans †

Statistical properties of spikes

Introduction

Tremendous progress has been made over the last decades in the ability to characterize and quantify nanomaterials, and in particular nanoparticles. Several experimental techniques are employed nowadays, alone or in a hyphenated way [1][2][3] , and new techniques continue to pop up to fill some gaps pertaining to specific challenges.

One notable example is single particle inductively coupled plasma-mass spectrometry [4][5][6][7] (sp-ICP-MS), which has been put forward over the last decade to analyze the presence of nanoparticles in the environment, on a particle per particle basis 8 . This high-throughput, chemically sensitive technique, allows the determination of the particle number concentration and the particle mass distribution of dilute nanoparticle dispersions 9,10 .

Despite being used in an increasing number of environmental studies 8,11 , single particle ICP-MS is not yet fully mature. Until recently, the theory associated with this experimental technique had only been developed and experimentally checked for very dilute nanoparticle dispersions 12,13 . It is linear within this limit, but linearity is alas restricted to the very dilute range 12 .

Extending and consolidating the theoretical underpinnings of sp-ICP-MS thus appears desirable. This process has been freshly engaged with the derivation of the nonlinear mathematical relationship linking the average number of spikes discernible in a a Univ Gustave Eiffel, GERS-LEE, F-44344 Bouguenais, France. E-mail: pierreemmanuel.peyneau@univ-eiffel.fr † Electronic Supplementary Information (ESI) available: [details of any supplementary information available should be included here]. See DOI: 00.0000/00000000. sp-ICP-MS time scan with the nanoparticle flux rate entering the plasma 14 . The difference between the average numbers of particles and spikes, that corresponds to the counting bias inherent to this technique 7,12 , has thus been calculated. It has the fortunate property to be universal, in the sense that the result does not depend on the whole distribution of the duration of the shortlived peak produced by a single particle in the time scan, but only on the average of this duration 14 . This feature is very appealing since this distribution is not known and probably depends on several factors (nanoparticle size, instrument geometry, instrument settings, etc.) 7,10,[15][16][17][18] .

In this article, the statistical properties of the individual spikes themselves are investigated. The average number of particles per spike is calculated and shown to be universal, i.e. it does depend on the average value of the duration of particle events, but not on other details of the unknown probability distribution ruling this duration. The average duration of spikes share the same property and a very good approximate expression for this quantity is derived. The distribution of the number of particles per spike is also almost universal, in the sense that it mostly depends on the average value of the duration of particle events, in the limit where the coefficient of variation of this duration is small enough. All these theoretical results are in superb agreement with computer simulations and fit very well experimental data measured on gold nanoparticles dispersions. These fundamental developments are valid regardless of the value of the particle number concentration of the dispersion.

The article ends with a discussion about some applications of these relationships regarding the average mass of nanoparticles present in a multimodal dispersion of arbitrary particle number concentration and some issues related to data processing consistency.

Theory and Monte Carlo simulations

Single particle ICP-MS relies on the introduction of a nanoparticle dispersion into the instrument. Nanoparticles contained in droplets enter randomly in the plasma with an average flux rate denoted λ . Droplets are vaporized, particles are then atomized and their constituents are ionized in the plasma. If a particle contains a high enough mass of the monitored isotope, a fraction of the cloud of ions generated by this very particle in the plasma produces a detectable short-lived peak in the time scan, lasting typically a few hundredths of microseconds 7,19,20 . In the following, a peak generated by a single particle will be called a particle event.

The time sequence of particle events can be mapped to the points of discontinuity of a homogeneous Poisson process of parameter λ 13 . This feature, which has been predicted theoretically and checked experimentally, has been recently leveraged to study the concentrated regime, where the probability of particle events overlap is not negligible 14 . In this regime, the individual spikes detectable in a time scan -in this work, a spike is defined as a sequence of nonzero readings bounded by zero readings before the first and after the last nonzero values -can be produced by individual particle events or by particle event coincidence generating a single composite spike. Consequently, the number of spikes is smaller than the number of nanoparticles and the higher the nanoparticle flux rate, the greater the difference between these two numbers. It turns out that the average number of spikes N s can be calculated, whatever the value of the nanoparticle flux rate λ entering the plasma and the distribution of the duration of particles events are 14 . The average number of spikes only depends on λ , the average duration τ of particle events, the dwell time τ dw of the measurement and the duration τ obs of the experiment. For the record,

N s = e -2λ τ dw e λ τ dw -1 e -λ τ τ obs /τ dw , (1)
N s = e -2λ τ dw e λ τ dw -1 λ τ dw e -λ τ N p . (2)
The second equation stems from the fact that the average number of particles entering the plasma during τ obs is equal to N p = λ τ obs . Eq. 1 and 2 are universal, in the sense that they are valid for every possible distribution of the duration of particle events, even when it is multimodal 14 . Furthermore, in Eq. 2, the multiplicative factor e -λ τ corresponds to the overlap bias related to possible particle event pile-up, whereas the multiplicative factor R(λ , τ dw ) = e -2λ τ dw e λ τ dw -1 λ τ dw (3) corresponds to the sampling bias associated with the nonzero value of the dwell time.

In the next subsections, the highlights are on the existence of additional universal or almost universal properties in sp-ICP-MS pertaining to the individual spikes that make up the time scan: i) the average number of particles per spike detectable in a sp-ICP-MS time scan, which can be explicitly calculated and is universal; ii) the probability mass function of the number of particles per spike, which is almost universal; iii) the average spike duration that is also universal and can be calculated with a very good level of precision.

For the last two statistical properties, which are the toughest to derive, an approach similar to that taken in Ref. 14 is followed. It relies on a three-step derivation : firstly, it is assumed that the duration of a particle event is constant and equal to τ p and that the time scan is continuously sampled (zero dwell time and constant τ p ); secondly, the constant assumption regarding the duration of a particle event is relaxed and one only assumes that it is a nonnegative random variable (zero dwell time and arbitrary nonnegative random variable τ distributed according to a probability density function (pdf) denoted f ); and thirdly, the case of a nonzero dwell time (nonnegative dwell time and arbitrary nonnegative random variable τ distributed according to a pdf f ) is considered.

Average number of particles per spike

According to Eq. 2, the average number of particles per spike, N p / N s , is expected to be equal to

N = e λ τ R(λ , τ dw ) = e 2λ τ dw λ τ dw e λ τ dw -1 e λ τ , (4)
regardless of the probability distribution of the particle event duration τ. The excellent agreement between this theoretical prediction and Monte Carlo simulations is evidenced in Fig. 1 and in Supplementary Information; Fig. S1 confirms the universal character of N .

Fig. 1 Average number of particles per spike: Monte Carlo simulations (circles) and theoretical average number of particles per spike N given by Eq. 4 (black line). The average duration of particle events was set to τ = 0.9 ms. The dwell time was τ dw = 0.1 ms. Inset: zoom on the λ < 1100 s -1 range; the grey straight line corresponds to the first two terms (linear approximation) of the Taylor series expansion of

N , N = 1 + ( τ + 3 2 τ dw )λ + O(λ 2 ).
In the zero dwell time limit, R(λ , τ dw ) tends toward 1 and ac-cording to Eq. 4, N becomes equal to N DT=0 = e λ τ . Additionally, when the particle event duration is constant valued and equal to τ p , the average number of particles per spike equals e λ τ p . In the very dilute limit classically seeked out to perform sp-ICP-MS experiments, both λ τ dw and λ τ are much smaller than 1, hence N ≈ 1 is a good approximation, entailing that most of the spikes are non-composite in this case. Eq. 4 describes accurately the departure from this limit, with a sharp growth of this average number of particles per spike as λ increases.

Distribution of the number of particles per spike

Zero dwell time and constant particle event duration.

When the duration τ of a particle event is constant, equal to a value denoted τ p , and the time scan is continuously sampled, the number of particles per spike follows a geometric distribution with parameter e -λ τ p . The argument goes likes this. Firstly, each particle event generates a nonzero signal during τ p . Due to the Poissonity of particle events 13,14 , the probability that another particle event starts during this period of time is equal to 1e -λ τ p . Secondly, according to the way a spike is defined in this work, the probability that a given spike stems from k ≥ 1 particles is equal to e -λ τ p (1e -λ τ p ) k-1 , which entails that the number of particles in an individual spike follows a geometric distribution with parameter e -λ τ p . [START_REF] Pitman | Probability[END_REF] The expected value of a geometric distribution being equal to the inverse of its parameter, one recovers the result established at the end of Sec. 2.1, namely that the average number of particles per spike is equal to e λ τ p in the zero dwell time and constant particle event duration case.

Zero dwell time and random particle event duration.

In the random particle event duration case herein considered, the number of particles in an individual spike is not strictly geometrically distributed anymore. Indeed, when the particle event duration is not constant, the stochastic process associated with the spikes is no longer memoryless: the probability that a spike is the outcome of k ≥ 1 particle events depends on the whole history of the process * . The geometric distribution being the only memoryless discrete distribution, it cannot describe exactly the distribution of the number of particles per spike when the particle event duration is random.

For this reason, the geometric distribution cannot be a fully universal feature of sp-ICP-MS. However, it can be deemed as almost universal since computer simulations show that this distribution with parameter e -λ τ † is a good approximation of the exact distribution when the coefficient of variation of τ is much smaller * For instance, a particle event #1 can end after another subsequent particle event #2, having started after #1. An event of this kind is impossible when the particle event duration is constant. † If a geometric distribution can approximate the true underlying distribution of the number of particles per spike in the zero dwell time and random particle event duration case, its parameter is necessarily equal to e -λ τ . Indeed, according to the end of Sec. 2.1, the average number of particles per spike is equal to N DT=0 = e λ τ in this case, hence the parameter of the tentative approximate geometric distribution since the parameter of a geometric distribution is equal to the inverse of the expected value of the distribution.

than one and the nanoparticle flux rate λ is small enough.

Nonnegative dwell time and random particle event duration.

Finally, when τ dw > 0 and for a random particle event duration, the geometric distribution with parameter e -2λ τ dw e λ τ dw -1 λ τ dw e -λ τ = 1/N is a good approximation of the exact distribution governing the number of particles per spike when the coefficient of variation of the particle event duration is much smaller than one. The explanation regarding the value of the parameter is the same as the one given previously, in Sec. 2.2.2. More precisely (details are provided in Supplementary Information, Sec. S4), according to Monte Carlo simulations, the geometric distribution with parameter e -2λ τ dw e λ τ dw -1 λ τ dw e -λ τ can be deemed as acceptable as long as the coefficient of variation of the particle event duration τ is smaller than 0.33. This assessment is based on the Pearson's χ 2 test and a p-value threshold of 0.05 regarding the rejection of the null hypothesis. When the coefficient of variation of τ is greater than 0.67, the geometric distribution is still acceptable from a statistical viewpoint, but only for low enough nanoparticle flux rates (≤ 20 s -1 ). As the coefficient of variation of τ increases, the range of λ where the geometric distribution is a satisfactory approximation of the distribution of the number of particles per spike shrinks.

Monte Carlo simulations thus demonstrate that the geometric distribution with parameter e -2λ τ dw e λ τ dw -1 λ τ dw e -λ τ can be a good or even a very good approximation of the probability mass function governing the number of particles per spike when the coefficient of variation of τ or the nanoparticle flux rate are small enough. For this reason, the geometric distribution can be considered as almost universal.

In the very dilute limit used in practice to conduct sp-ICP-MS experiments, the parameter of the geometric distribution is very close to 1 and the distribution of the number of particles per spike is close to a Dirac mass function. This is no longer the case outside of this limit.

Average spike duration

The average spike duration τ s can be accurately calculated in the zero dwell time and constant particle event duration case, and estimated (tight upper bound) otherwise.

Zero dwell time and constant particle event duration.

In the zero dwell time limit and when τ is constant and equal to τ p , τ s is expected to be equal to

(e λ τ p -1)E(t |t ≤ τ p ) + τ p , (5)
where E(t |t ≤ τ p ) denotes the expected value of t, given that t is smaller than τ p . Indeed, according to Sec. 2.2.1, there are on average e λ τ p -1 gaps between the average number of particles per spike e λ τ p and a duration τ p after the beginning of the last particle event.

As the occurrence of each particle event corresponds to an event of a homogeneous Poisson process 13 , the conditional expectation E(t |t ≤ τ p ) can be easily calculated when the dwell time is zero. Since t is exponentially distributed with parameter λ and the probability that τ is less than or equal to τ p is equal to 1e -λ τ p , 22 E(t |t ≤ τ p ) = (1e -λ τ p ) -1 τ p 0 λte -λt dt, yielding

τ s = (e λ τ p -1) 1 -(1 + λ τ p )e -λ τ p / λ (1 -e -λ τ p ) + τ p . (6)
Eq. 6, obtained thanks to a heuristic argument, can be derived rigorously and Monte Carlo simulations confirm its validity (shown in Supplementary Information, Sec. S5.1).

Zero dwell time and random particle event duration.

Carrying an exact calculation in this case seems out of reach.

However, an upper bound can be obtained for the average spike duration τ s , which will prove to be close to τ s . When the duration of particle events is random, in the zero dwell time limit, a typical spike results from the overlap of e λ τ distinct particle events (see Sec. 2.1). There are at most e λ τ -1 gaps between these particle events. Based on this heuristic reasoning,

τ s ≤ e λ τ -1 E DT=0 + τ , (7)
where E DT=0 denotes the average duration between the starts of two consecutive overlapping particle events. The last term in the previous equation, τ , corresponds to the average duration of the particle event that the spike ends with, which can be -or notthe last to appear.

According to the expression of the average duration between the starts of consecutive overlapping particle events obtained in Sec. 2.3.1, one gets for a random duration of particle events,

E DT=0 = +∞ 0 dτ f (τ) 1 -(1 + λ τ)e -λ τ λ (1 -e -λ τ ) (8)
Combining Eqs. 7 and 8, the following upper bound for the average spike duration is expected,

τ s ≤ e λ τ -1 +∞ 0 dτ f (τ) 1 -(1 + λ τ)e -λ τ λ (1 -e -λ τ ) + τ (9)
.

In addition, the function x →

1-(1+λ x)e -λ x λ (1-e -λ x )
being concave -its second derivative is indeed a nonpositive function, Jensen's inequality leads to

τ s ≤ e λ τ -1 1 -(1 + λ τ )e -λ τ λ (1 -e -λ τ ) + τ . ( 10
)
Computer simulations show that this upper bound is rather tight. From a practical point of view, the '≤' symbol in the previous equation can be considered as a '≈' symbol.

Nonnegative dwell time and random particle event duration.

When τ is an arbitrary nonnegative random variable and τ dw > 0, a reasoning similar to the one followed in Sec. 2.3.2 leads to

τ s ≤ (N -1)E + τ + τ dw . (11)
According to Sec. 2.1, N -1 is the tightest upper bound for the number of gaps between the average number of particles per spike N . E is the conditional expectation of the duration between two consecutive particle events that belong to the same spike. τ is an upper bound for the average duration of the particle event ending the spike and τ dw is the dwell time. The term τ dw is due to the time discretization of a sp-ICP-MS time scan: a spike, whatever its true physical duration, generates at least one nonzero reading in an experimental time scan corresponding to the integration time τ dw of the measurement. Two consecutive particle events belong to the same spike if i) the second particle event starts before the end of the first one; or ii) the second particle event starts after the end of the first one, whilst the first particle event ends and the second one starts during the same dwell time interval, or in two contiguous dwell time intervals. Possibilities i) and ii) are mutually exclusive. Thus, τ+v) .

E = E DT=0 + +∞ 0 dτ f (τ) τ dw 0 du τ dw 2τ dw u dv τ dw (τ + v)λ e -λ (
(12) The double integral in the variables u and v appearing in Eq. 12 can be computed analytically.

One gets E = +∞ 0 dτ f (τ)ε(τ, λ , τ dw ), ε being a function admitting a closed form expression,

ε(τ, λ , τ dw ) = 1 -(1 + λ τ)e -λ τ λ (1 -e -λ τ ) + e -λ (τ+τ dw ) λ 2 τ dw e λ τ dw (λ τ + 2) -λ (τ + τ dw ) -2 - e -λ (τ+2τ dw ) λ λ (τ + τ dw ) + 1 . (13)
Finally, the map τ → ε(τ, λ , τ dw ) can be shown to be concave: thus, according to Jensen's inequality, E ≤ ε τ , λ , τ dw . This leads to the following upper bound for the average spike duration

τ s ≤ N -1 ε( τ , λ , τ dw ) + τ + τ dw , (14)
ε being defined in Eq. 13 and N in Eq. 4.

Monte Carlo simulations show that the right hand side of Eq. 14 is a very good numerical approximation of τ s , whatever the value of λ is (see Fig. 2). This upper bound is thus rather tight, as in the zero dwell time case. Hence, from a practical viewpoint,

τ s ≈ N -1 ε( τ , λ , τ dw ) + τ + τ dw . (15)
Fig. 2 shows that τ s is a non-bounded, increasing function of λ , starting from τ + τ dw and rising sharply afterward. Last but not least, computer simulations also evidence that, as the average number of particles per spike N , τ s is also universal. The numerical data provided in Supplementary Information (Fig. S6) indeed demonstrate that the average spike duration only depends on λ , τ dw and τ , and not on other details of the distribution of particle event durations.

Experimental validation

Experiments

Various dispersions of 60 nm diameter gold nanoparticles stabilized with a citrate buffer were analyzed. They were all prepared Fig. 2 Average spike duration calculated by Monte Carlo simulation (circles) and theoretical estimation (black line) given by Eq. 15, for an average duration of particle events τ = 0.9 ms and a dwell time τ dw = 0.1 ms. Inset: zoom on the λ < 2100 s -1 range. The grey straight line corresponds to the first two terms (linear approximation) of the Taylor series expansion of the upper bound of τ s , equal to τ

+ τ dw + 1 4 ( τ + 2τ dw )(2 τ + 3τ dw ) λ + O(λ 2 ).
by dilution of a stock solution purchased from Sigma-Aldrich, whose particle number concentration equals 1.9 × 10 10 mL -1 . The dispersions were introduced at 0.346 mL min -1 in a Agilent 8900 ICP-MS-QQQ mass spectrometer. The plasma RF power was 1550 W and the sampling depth was 7 mm. 197 Au was monitored with a zero settling time and a τ dw = 100 µs dwell time during τ obs = 60 s. Measurements were done with the dilution factors 250000, 7500, 3750, 2500, 1875, 1500, 1250, 1071, 938, 833, 750, 682, 625, 577, 536, 500, 250, and were repeated three times for each dilution factor.

Thirty milliseconds long snapshots of experimental time scans acquired with 60 nm gold nanoparticles for several values of λ , ranging from 18.2 to 9110 s -1 , are displayed in Fig. 3. Visually, the time scans become more and more complex as λ increases: particle events are clearly visible when λ = 18.2 s -1 , but they become less and less apparent as λ increases. At some point, the spikes become overwhelmingly composite; despite this apparent complexity, these experimental results support the theory developed in Sec. 2.

Comparison with theory

The spikes present in the experimental time scans were detected as described in Ref. 14. The cumulative number of counts and the duration of each spike was calculated, and the validity of the theory regarding the average number of particles per spike N (Eq. 4) and the average spike duration τ s (Eq. 15) was checked.

The prediction of Eq. 4 can be compared with experimental data as follows. Measurements were done with pure gold spherical nanoparticles: the average diameter of a nanoparticle is hence expected to be proportional to the average of the cumulative number of counts of the spikes detected in the experimental sp-ICP-MS time scans, divided by N (to get the average cumula- tive number of counts associated with a single nanoparticle) and raised to the one-third power (to account for the fact that for pure metal spherical nanoparticles as the ones used in this study, the mass of a particle is proportional to its diameter raised to the power three). Through this procedure, assuming a reference average diameter of 60 nm for the lowest nanoparticle flux rate, Tab. 1 was obtained. This table shows that the average nanoparticle diameter obtained thanks to this approach is very close to the reference average diameter, with relative variations smaller than 4%, whatever the value of λ , even when the average number of particles per spike is far greater than 1 (up to ≈ 5700), thus validating the theory regarding the average number of particles per spike. For these experiments, τ dw was set to 100 µs, while the values of λ and τ ( τ = 803.4 µs in this case) were those fitted previously 14 . It is worth underlining that Tab. 1 was obtained without any additional adjustment, which illustrates the soundness of the theory. The average spike duration was measured from the experimental time scans for different nanoparticle flux rates λ . Fig. 4 shows the average spike duration and the corresponding fit (Eq. 15). Again, the parameter values obtained previously 14 were employed, for λ and τ , without any additional adjustment. Once more, the agreement between experiments and theory is very good, on three orders of magnitude.

The predictions of the theory regarding the average number of particles per spike N and the average spike duration τ s are thus experimentally validated. I did not manage to find a wise way to check experimentally the prediction regarding the distribution of the number of particles per spike, which is expected to be geometrically distributed in very good approximation, but it has been checked numerically and I am confident of its validity.

Practical implications

Beyond the additional knowledge brought by this study about the fundamentals of sp-ICP-MS, the results obtained regarding the average number of particles per spike and the average duration of spikes can be leveraged in different ways.

Data processing consistency

The mathematical relationship giving an upper bound for the average duration of spikes (Eq. 14) can be used to check the consistency of the data processing algorithm employed to detect the spikes in an experimental time scan. To illustrate this point, the usual algorithm 6,[START_REF] Tuoriniemi | [END_REF] employed to process sp-ICP-MS time scans to the measurements obtained with gold nanoparticle dispersions was applied, for several dilution factors. Readings above the average value plus three times the standard deviation of the entire data set were identified, removed, and the same process was applied to the remaining data set, and so on and so forth. The data obtained at the end of this iterative procedure and the number of spikes obtained with MassHunter, Agilent's proprietary software, are gathered in Tab. 2. Two interesting features are visible on Tab. 2. Except for the most dilute dispersion, the numbers of spikes calculated with the usual algorithm are markedly different from those found with the algorithm used in this study, the latter one being tailored to the very definition of a spike given in Sec. 2 and developed bearing in mind the possibility of a high level of particle coincidence 14 . The difference between the number of spikes given by the two algorithms becomes more pronounced as λ increases. This conclusion also holds regarding the number of spikes obtained with MassHunter. The same discrepancy prevails with the average duration of spikes, which diverges completely between both algorithms as λ increases. With the usual algorithm, this average duration starts to increase and then decreases until it reaches a stationary value for a decreasing dilution factor. By contrast, it increases sharply with the algorithm employed in this study.

For the smallest dilution factors, < 1000, i.e. the most concentrated dispersions, the average spike duration becomes ≈ 0.1 ms. This result is at odds with the theory developed in Sec. 2.3, and in particular with Eq. 15. Indeed, according to this equation, τ s should be greater than τ + τ dw = 0.9 ms with the present experiments. This inconsistency sheds light on the shortcomings of the usual data processing algorithm. If the time scan is affected by many particle coincidences, one gets results that differ significantly from the theory herein presented. In the present study, it shows that the usual data processing strategy provides dubious results for the most concentrated dispersions. This is not a genuine surprise in that case. The usual algorithm makes no real sense in the concentrated range, since it was developed for, and is thus adapted to, very dilute nanoparticle dispersions with a moderate dissolved fraction 6 . In the present case, it yields a dissolved concentration that has no true meaning: gold nanoparticle dispersions are very stable and in the experiments reported here, this nonzero dissolved concentration is an artifact which is due to the huge overlap of particle events in the time scan. The usual algorithm is thus misfitted in the concentrated range, where particle events frequently overlap. This consistency test, based on the average spike duration, can be used to check whether the outcomes of a data processing step are coherent from a theoretical viewpoint. In general, an inconsistency between the number of spikes and the range of average spike durations predicted by the theory should raise the alarm. The easiest way to proceed is as follows: count the number of spikes, use this number divided by the duration of the experiment as a lower bound for the nanoparticle flux rate entering the plasma, calculate the range of theoretically admissible average spike duration with the linear approximation of τ s and compare the theoretical prediction with the experimental value of the average spike duration. If they significantly differ, the experimenter should question his/her results, as it casts some doubt either on the data processing methodology, the presence of detectable nanoparticles in the sample, or the magnitude of the particle number concentration.

Average nanoparticle size

A raw particle size distribution (PSD) can be calculated straightforwardly from sp-ICP-MS data 6,24,25 . It contains both genuine and spurious information. Genuine information correspond to features of the underlying real PSD that are accurately reflected in the raw PSD. Spurious information gather all the artifacts affecting the raw PSD, which are unrelated to the features of the real PSD but depends on the experimental method itself. For instance, particle coincidence within a single spike can be a source of spurious features in the raw PSD.

One very interesting feature that turns out to be genuine is the average mass of nanoparticles in a -possibly multimodal -dispersion, or equivalently the average diameter for spherical nanoparticles having all the same composition. Indeed, according to the law of total expectation [START_REF] Ross | A First Course in Probability[END_REF] , the average cumulative number of counts in spikes, I s , is equal to the average cumulative number of counts in particle events, I p , multiplied by the average number of particles per spike N , I s = N I p . According to this formula, the average mass (or diameter for identical spherical nanoparticles) of nanoparticles in a dispersion, which is directly related to the average cumulative number of counts in particle events, can be readily inferred from the average cumulative number of counts of individual spikes. It was experimentally checked that this is indeed the case with a dispersion containing a 3:1 mixture of 60 and 150 nm nanoparticles, even with a very high level of particle coincidence: the expected average diameter of the nanoparticles was 81.6 nm, whilst experimentally, an average value of 82.4 nm is obtained by measuring I s and dividing by N to get I p , for several nanoparticle flux rates (details are provided in Supplementary Information, Sec. S6). This excellent agreement is consistent with former studies: previous experiments demonstrated that the average sizes stemming from high resolution scanning electron microscopy (HR-SEM), which is a NIST reference method, and from sp-ICP-MS 25 compare well. Mathematically speaking, this concordance merely relies on the fact that I s = N I p .

Conclusion

In this work, the average number of nanoparticles per spike in a single particle ICP-MS time scan was calculated. A tight upper bound for the average duration of spikes was also derived. The nonlinear relationships derived in this work are very robust: the comparison with Monte Carlo simulations and experimental data shows an excellent agreement with the theoretical predictions, for the full spectrum of values of nanoparticle flux rate λ that was tested, which encompassed three orders of magnitude -from λ ≈ 10 to 10 4 s -1 .

The average number of nanoparticles per spike and the average spike duration only depend on three parameters: the nanoparticle flux rate entering the plasma, the dwell time of the instrument and the average duration of a particle event generated by a single nanoparticle in the time scan. They do not depend on the full probability distribution of the duration of particle events, but only on its average, a feature we have referred to as universality, which is intimately connected to the underlying Poisson process governing particle arrivals in the plasma.

When the standard deviation of this duration is small enough compared to its average, the probability mass function ruling the number of nanoparticles per spike is well approximated by a geometric distribution, with a parameter that does not depend on the full distribution of τ, but only on itsaverage. Consequently, the particle mass function ruling the nu r of particles per spike can be considered as almost universal.

All these results increase our understanding of sp-ICP-MS data. Beyond their intrinsic value from a fundamental viewpoint, these theoretical developments have also interesting practical implications. Running sp-ICP-MS experiments in the very dilute limit should of course be privileged as much as possible to extract the maximum amount of information. However, for specific samples, when dilution is not an option, our theory demonstrates that the average mass of nanoparticles could be recovered from experimental sp-ICP-MS time scans, regardless of the level of particle coincidence, even for multimodal dispersions. To make it a tangible option though, one still have to deal with a possible nonzero value of the background signal due to the presence of the monitored element under dissolved form or interferences.

These new insights have also been applied to check the consistency of results obtained thanks to the usual data processing algorithm employed in sp-ICP-MS. A consistency test was designed based on the theoretical developments reported in this work. The usual algorithm fails to pass this test in the concentrated range. It would be very appealing to develop a thorough methodology to treat the experimental data obtained in pulse-overlapped mode, as well as in the dilute limit. Assessing the range of validity of various algorithms, finding when they provide reliable results that can be trusted with eyes closed, and when the user finds herself/himself on a slippery slope, is a worthwhile perspective.

Fig. 3

 3 Fig.3Snapshots of experimental time scans obtained with 60 nm gold nanoparticles at several nanoparticle flux rates λ during a 30 ms time interval with τ dw = 100 s (each snapshot thus contains 300 readings). From top to bottom, λ = 18.2, 607, 1215, 1822, 2429, 3037, 3644, 4253, 4856, 5468, 6073, 6679, 7288, 7894, 8498, and 9110 s -1 . The vertical range is twice as large for the last six time traces than for the first ten.

Fig. 4

 4 Fig. 4 Average spike durations measured from experimental sp-ICP-MS time scans (circles). The dashed line corresponds to the numerical adjustment to the model using Eq. 15, with τ = 803.4 µs and τ dw = 100 µs.

Table 1

 1 Average diameter and average number of particles per spike as a function of the nanoparticle flux rate λ . The smallest flux rate was taken as reference.

	Flux rate λ (s -1 )	N	Average diameter (nm)
	18.2	1.0	60.0
	607	1.8	59.9
	1215	3.2	59.2
	1822	5.7	60.1
	2429	10.1	59.6
	3037	18.0	59.5
	3644	32.0	60.2
	4253	57.1	61.5
	4856	101	59.6
	5468	181	58.7
	6073	321	61.2
	6679	570	62.2
	7288	1016	60.6
	7894	1803	59.0
	8498	3193	62.0
	9110	5695	59.7

Table 2

 2 Number of spikes and average spike duration for several dilution factors using the usual sp-ICP-MS data processing algorithm. For comparison, the results given between parenthesis correspond to those obtained with the algorithm employed in this work and detailed in Ref.14. The results given between square brackets were those given by MassHunter version 4.3.

	Dilution factor	Number of spikes	Average spike duration (ms)
	250000	996 (999) [999]	0.9 (0.9)
	7500	10125 (20218) [14227]	1.4 (1.2)
	3750	10450 (23142) [17102]	12.1 (1.7)
	2500	28652 (19164) [34093]	0.2 (2.5)
	1875	20439 (14535) [6695]	0.2 (3.7)
	1500	16444 (10231) [6817]	0.2 (5.5)
	1250	13681 (6736) [6801]	0.2 (8.6)
	1071	11817 (4187) [6769]	0.2 (14.1)
	938	10514 (2873) [6791]	0.1 (20.7)
	833	9290 (1865) [6725]	0.1 (32.2)
	750	7989 (1053) [6719]	0.1 (57.4)
	682	7136 (608) [6624]	0.1 (99.9)
	625	6189 (395) [6615]	0.1 (152.1)
	577	5524 (258) [6715]	0.1 (233.4)
	536	4832 (134) [6566]	0.1 (449.8)
	500	4202 (95) [6619]	0.1 (669.1)
	250	1268 (1) [6068]	0.1 (60000)

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J o u r n a l N a me , [ y e a r ] , [ v o l . ] ,

Acknowledgements

Martin Guillon kindly provided experimental sp-ICP-MS data sets and Émilie Faillard reread the manuscript.

This research was supported by the French National Research Agency (grant no. ANR-17-CE04-010).

Code availability

The Python program written to perform the Monte Carlo simulations is available at https://github.com/peyneau/publicati ons/tree/main/Peyneau_JAnalAtSpectrom_2022.

Conflicts of interest

There are no conflicts to declare.


Huss, H.H., Quality and quality changes in fresh fish, in FAO Fisheries Technical Paper -348, Food and Agriculture Organization, Editor 1995, FAO. p. 195. Gram, L. and Nowadays , the freshness of fish is assessed by numerous physical, sensory or chemical methods.

The aim of this work is to follow the progress of the alteration of trimethylamine-N oxide (TMAO) with a new SPME-GC-MS approach. TMAO is a specific molecule of the flesh of marine fishes.

All of these techniques possess biases (subjectivity of the judges, working only on whole fishes, etc.).  Injection at 210°C, split of 5 and an initial temperature of the column at 60°C displays peaks of TMA with the best significant markers of resolution.  Application of the method to a study of spoilage of fishes.

  H.H. Huss, Microbiological spoilage of fish and fish products. International Journal of Food Microbiology, 1996. 33(1): p. 121-137. Dos Santos, J.-P., et al., Molecular analysis of the trimethylamine N-oxide (TMAO) reductase respiratory system from a Shewanella species. Journal of Molecular Biology, 1998. 284(2): p. 421-433. Duflos, G., et al., Quantitative PCR Method for Evaluating Freshness of Whiting (Merlangius merlangus) and Plaice (Pleuronectes platessa). Journal of Food Protection, 2010. 73(7): p. 1344-1347. Nielsen, M.K. and B.M. Jørgensen, Quantitative relationship between trimethylamine oxide aldolase activity and formaldehyde accumulation in white muscle from gadiform fish during frozen storage. Journal of Agricultural and Food Chemistry, 2004. 52(12): p. 3814-3822. Duflos, G., et al., Freshness characterisation of whiting (Merlangius merlangus) using an SPME/GC/MS method and a statistical multivariate approach. Journal of the Science of Food and Agriculture, 2010. 90(15): p. 2568-2575. Heising, J. K., et al., A non-destructive ammonium detection method as indicator for freshness for packed fish: Application on cod. Journal of Food Engineering, 2012. 110: p. 254-261. When: Conservation at freezing temperatures (0°C to -30 ºC) Cause: Endogenous enzymes in Gadidae Consequences

Figure 1 :

 1 Figure1: Chromatograms obtained with different sample preparations (from 2 minutes to 6 minutes). The sample consists of the flesh of a whiting (Merlangius merlangus) kept several months at -20°C. Red curves correspond to the chromatograms of samples prepared with bidistilled water. Bleu curves correspond to the samples prepared with saturated saline solution (30% NaCl w:w). Darker curves correspond to the samples, where a KOH pellet was added to improve the pH of solution.

  After using total ion chromatogram (TIC) from 33 to 200 m/z a single ion monitoring (SIM) approach was performed. It allows to follow the detection of specific ions markers of TMA (58 & 59 m/z) and DMA (44 & 45 m/z).  Efficient and specific detection of TMA & DMA with the SIM method.  Specific detection of TMA and DMA is now effective with optimised parameters of extraction and separation.  Screening of potential internal standards.  Development of a method of quantification (determination of LOD & LOQ).

Figure 2 :

 2 Figure 2 : Total and single ions chromatograms of a sample prepared from the flesh of a whiting (Merlangius merlangus) kept several months at -20°C with KOH and saturated saline solution. The blue curve corresponds to the total ions chromatogram. The red curves correspond to the specific ions of TMA : 58 m/z (darker) and 59 m/z (lighter). The green curves correspond to the specific ions of DMA : 44 m/z (darker) and 45 m/z (lighter).


Alexandre Dehaut

Graziella Midelet-Bourdin

Jean-Sébastien Py

Benoît Gassilloud

Anne Brisabois

Guillaume Duflos

Anne Bris

Characterizations of H2S positive and negative strains of Shewanella baltica isolated from spoiled whiting (Merlangius merlangus)

Introduction

Materials & Methods

Results

Conclusions

In-depth reading... Isolated from a spoiled whiting (Merlangius merlangus) and selection on tryptone soya agar yeast extract with 1.5 % (w/v) NaCl (TSA-Ye -NaCl). gyrB 16S rRNA Among the numerous Shewanella species described in marine animals and sea water, Shewanella putrefaciens has been described as the spoiling agent for fresh fish stored on melting ice (Gram & Dalgaard, 2002).

Phenotypic and Biochemical approaches

Nonetheless S. putrefaciens is more likely a bacterial group composed of four sub-groups than a single species.

S. putrefaciens group II, reclassified as Shewanella baltica, is a very heterogeneous group recently characterized by MultiLocus Sequence Typing (MLST) in nine clades (Ziemke et al., 1998;Deng et al., 2014).

S. baltica has been described as a potential spoilage organism and the most H 2 S producing bacteria during storage of marine fish (Vogel et al. 2005).

Phenotypic and biochemical approachs failed to accuretly identify the four strains of Shewanellaceae.

Genotypic approach, by sequencing the two genes 16s rRNA and gyrB, allowed to identify the whole isolates as members of S. baltica species. Proteomic approach, using the MALDI-TOF, confirmed the conclusion of the genotypic study and highlits slight differences between strains.

Isolate 14LSABSM1SHW, unable to produce H 2 S, displayed an atypic phenotype that is why it was filed in the collection of the Institut Pasteur with the identifier CIP 110804.

H 2 S production might not be the most appropriate screening parameter for isolation of Shewanella isolates.

The spoiling potential of 14LSABSM1SHW has to be characterized. Overall, isolates display homogeneous MALDI-TOF profiles.

MALDI-TOF study led to good identification scores (≥ 2.3) and low %RSD among the 10 replicates per strain.

Using the Brüker database, isolates were identified as closer to S. baltica OSS 155 MALDI-TOF profile.

More deeply, some differences have been highlighted between the four isolates :

  alexandre.dehaut@anses.fr  The present study describes the phenotypic, genotypic and proteomic characterization of four S. baltica strains isolated from spoiled whiting (Merlangius merlangus).

  a large range of temperature (4-30°C) and are able to grow anaerobically, in presence of TMAO, with the development of the specific fish off-odor. Heterogeneous biochemicals patterns observed. One strain is surprinsigly H 2 S negative, two strains synthetize an ornithine decorboxilase and all the strains, except one, are able to use sucrose and arabinose. All the strains were identified as S. baltica by both 16S rRNA and gyrB partial sequencing. The second gene, gyrB, gave more informations on the diversity of the isolated isolates.



  Ion 3025 m/z differentiate 14LSABSM1SHW & 14LSABSM3SHW from 14LSABSM2SHW & 14LSABSM4SHW.  Ions 3359 m/z, 3767 m/z, & 3780 m/z differentiate 14LSABSM2SHW from 14LSABSM4SHW.  Ions 3767 m/z, 3780 m/z, 7536 m/z & 7562 m/z differentiate 14LSABSM1SHW from 14LSABSM3SHW.

Confirmation of genotypic identification by the MALDI-TOF study. This technology allowed to visualize some slight differences between the proteomic profiles of the strains.

Three approaches

Thanks : Coming from Alexandre Dehaut's Ph.D work co-funded by the Nord-Pas-de-Calais region and Anses