Wim ; Reybroeck
email: wim.reybroeck@ilvo.vlaanderen.be

T&v Ilvo

Sigrid ; Ooghe

Hubert ; De Brabander

Hubert F De Brabander

Els Daeseleire

Validation of the βeta-s.t.a.r. 1+1 for rapid screening of residues of β-lactam antibiotics in milk

Keywords: drug residues -antibiotics method validation, screening assay, residues, veterinary drug residues -antibiotics, animal products -milk, milk

The test was very selective for the group of β-lactam compounds: the only interference found was by clavulanic acid at 2500 µg kg -1 and above. The modified protocol (βeta-s.t.a.r. 1+1) detected all βlactams with a maximum residue limit (MRL) in milk, but not all these compounds were detected at their respective MRL. Especially the detection of cefalexin (detection capability = 6000 µg kg -1 ; MRL = 100 µg kg -1 ) and penethamate (detection capability = 80 µg kg -1 ; MRL = 4 µg kg -1 ) was poor and also ceftiofur was only detected from 500 µg kg -1 (MRL = 100 µg kg -1 ). The repeatability of the reader and of the test was very good. The test was very robust: test results were not significantly influenced by small changes in the test protocol, by the milk composition or by the type of milk. The test was also suitable to test milk of animal species other than the cow. Favourable results were obtained in testing monitoring samples, in two national ring trials and in an international proficiency test. The βeta-s.t.a.r. 1+1 is a very fast, simple and reliable test that could be used at the farm level to prevent tanker milk contamination by β-lactams.

Introduction

Penicillins and cefalosporins belong to the group of β-lactam antibiotics due to their common β-lactam ring structure. Penicillins remain very important in human and veterinary medicine. In 1997, 225 metric tonnes of penicillins were administered to animals in the European Union (Anonymous 1998).

Mastitis is the most expensive disease affecting dairy cattle worldwide and, therefore, the single largest cause of antibiotic usage in dairy herds. Bacteria from the genera Staphylococcus and Streptococcus, both Gram-positive, are the most common causal agents of mastitis [START_REF] Pyörälä | The bovine udder and mastitis[END_REF]. β-lactam antibiotics are the most frequently administered drugs in parenteral and intramammary therapy.

The drug of choice in many countries is still penicillin, since the minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC) values for the most common mastitis pathogens are very low. When mastitis pathogens show penicillin-resistance, a combination of penicillins and clavulanic acid or isoxazolyl penicillins resistant to penicillinase are often used as alternative treatment [START_REF] Pyörälä | The bovine udder and mastitis[END_REF].

Penicillins all have the same ring structure and are monobasic acids that readily form salts and esters. The penicillin nucleus, 6-aminopenicillanic acid, consists of a fused thiazolidine ring and a β-lactam ring with an amino group at the 6position. The cefalosporins are semisynthetic antibacterials derived from cephalosporin C, a natural antibiotic. The active nucleus is very closely related to the penicillin nucleus and consists of a β-lactam ring fused with a six-membered dihydrothiazine ring and having an acetoxymethyl group at position 7. Penicillins and cefalosporins are bactericidal and act by inhibiting synthesis of the bacterial cell wall (Anonymous 2005). Testing for antimicrobial drug residues (i.e., the drug itself or a metabolite) in milk is therefore necessary for ethical, health and technological reasons [START_REF] Honkanen-Buzalski | Monograph on residues and contaminants in milk and milk products[END_REF]. The presence of β-lactam residues in milk can have several drawbacks: inhibition of dairy starter cultures used in the production of cheese and yoghurt [START_REF] Grunwald | Untersuchungen zur Analytik und zum Einfluss technologischer Prozesse auf Penicillinrückstände in Milch[END_REF]Suhren 1996), possible hypersensitivity reaction by the consumer and contribution to the development of antibiotic resistance.

In the EU, maximum residue limits (MRLs) were fixed in bovine milk for 16 βlactam compounds, ranging from 4 to 125 µg kg -1 (Anonymous 1990(Anonymous & 2009)), and in many countries inhibitory substances are screened in routine in farm milk samples as part of the regulatory quality programme. In 2008, of the 1,456,990 farm milk samples in Belgium analyzed, 1194 or 0.08% were found to be positive by the milk control stations. In most cases, residues of β-lactam substances were the main reason for bulk tank milk failure. In an identification study performed at Technology and Food Science Unit of the Institute for Agricultural and Fisheries Research (T&V-ILVO) on all positive Flemish farm milk samples leading to penalization in the months May and June of 2003, 79% of the samples contained non-synthetic penicillins, 8% synthetic penicillins and 4% a combination of βlactam and non-β-lactam residues. In total, therefore, 91% of the samples contained β-lactams [START_REF] Reybroeck | Invloed bewaring op antibioticaresiduen in melk. Heranalyse positieve stalen en identificatie van remstoffen verantwoordelijk voor een ongunstige resultaat bij de officiële kwaliteitsbepaling van melk[END_REF]. As given in the year report of 2005 of Comité du Lait (Walloon region) the percentage of penalizations due to β-lactams was 94.5% in 2003, 90.0% in 2004and 83.9% in 2005(Anonymous 2006). In Germany, β-lactams could, in 95% of cases, be identified in inhibitor-positive milk samples [START_REF] Kress | Experiences with an identification and quantification program for inhibitor-positive milk samples[END_REF]. Penicillin G was still the predominant antibiotic detected (74.6%) during regulatory control, followed by ceftiofur (11%), ampicillin/amoxicillin (6.3%) and isoxazolyl penicillins (3.2%).

It is worth noting that in routine testing mostly microbial inhibitor tests are used, often with Geobacillus stearothermophilus var. calidolactis as the test organism, chosen for its high sensitivity for penicillins [START_REF] Reybroeck | Résidus d'antibiotiques dans le lait. Utilisation des kits de dépistage des inhibiteurs[END_REF]Suhren and Heeschen 1996). The consequence of this is that milk is rigorously screened for the presence of β-lactams, while residues of other antibacterial groups are not always detected at their respective MRL. The percentage of β-lactams in the data above is, therefore, an overestimation.

One of the potential issues for an assay for β-lactams in milk is their stability.

Internal standard samples, consisting of, respectively, penicillin G and cloxacillin spiked in raw milk and stored for 2 months below -18 °C did not demonstrate any problems with stability. Storing raw milk in the refrigerator (2-8 °C), however, can result in stability problems with β-lactams due to the possible formation of penicillinase by certain milk bacteria [START_REF] Guay | Decrease of penicillin G residue incidence in milk: A fact or an artefact?[END_REF].

Since the result of the routine testing of farm milk on antimicrobials by the milk control stations is only known after the milk is processed, in some European countries milk must be checked for the presence of β-lactam residues on entry to the dairy plant or before production. This control is to ensure the technological safety of the milk for the production of fermented dairy products and also protect the consumer, and several rapid screening tests are on the market for this purpose (Anonymous 2002b;[START_REF] Kroll | Zur Eignung von Schnelltestverfahren zum Rückstandsnachweis von Beta-laktam-Antibiotika in Milch[END_REF][START_REF] Kroll | Evaluation of commercial rapid tests for β-lactam antibiotics in raw milk[END_REF][START_REF] Neaves | Monitoring antibiotics in milk -the changing world of test methods[END_REF][START_REF] Quandt | Identifizierung von antimikrobiellen Rückständen in Milch mittels Schnelltestsystemen[END_REF][START_REF] Reybroeck | Résidus d'antibiotiques dans le lait. Utilisation des kits de dépistage des inhibiteurs[END_REF][START_REF] Reybroeck | The use of microbiological, immunological and receptor tests for monitoring of residues of antimicrobials in milk: the Belgian approach[END_REF][START_REF] Reybroeck | Rapid screening for residues of antibiotics in milk at the factory[END_REF]Žvirdauskiené and Šalomskiené 2007). Further, non-commercial tests or biosensor and immunosensor-based tests are used in some food laboratories [START_REF] Cacciatore | Development of an optical biosensor test for residues of β-lactam antibiotics in milk using the penicillin-binding protein PBP 2×[END_REF][START_REF] Gustavsson | Biosensor analysis of penicillin G in milk based on the inhibition of carboxypeptidase activity[END_REF][START_REF] Knecht | Automated microarray system for the simultaneous detection of antibiotics in milk[END_REF][START_REF] Lamar | Development of a receptor-based microplate assay for the detection of beta-lactam antibiotics in different food matrices[END_REF]. Results of the testing can be obtained in less than 10 min.

In some countries rejected milk needs to be destroyed due to very strict legislation, resulting in large costs being incurred in transport, incineration and for the milk itself. The dairy industry is therefore interested in testing at the farm before collection of the milk, hence placing more responsibility on the farmer.

Materials and methods

Reagents and standards

Penicillin G (PENNA), amoxicillin (A8523), oxacillin (O10002), cloxacillin (C9393), dicloxacillin (D9016), nafcillin (N3269), cefazolin (C 5020), cephapirin (C8270), and cefoperazone (C4292) were all from Sigma-Aldrich (Bornem, Belgium). Ampicillin (9930212) was from the WHO Collaborating Centre for Chemical Reference Substances (Kungens Kurva, Sweden). Ceftiofur (34001) and cefalexin (33989) were from Riedel-de Haën (Bornem, Belgium). Penethamate 2006) were used for the evaluation study. For some parts, e.g. the study of batch to batch differences and the stability of the reagents, lot 060409 (Exp. September 4, 2007) and lot 070331 (Exp. March 31, 2008) were also used. The reagents were stored in a cool room at 4 ±2 °C.

The Delvotest SP-NT 5-PACK kits were from DSM-Food Specialties (Delft, The Netherlands). A mixture of raw milk, aseptically collected from four individual cows was used as blank milk. The cows in mid lactation were selected on the basis of not being created with veterinary drugs during the last months and giving milk with a low number of somatic cells (< 2 × 10 5 mL -1 ). The blank milk was always tested before use with a Delvotest NT 5-PACK.

Material

For the incubation of the glass vials a dry-block heater Type BS25-230D (Aerne Analytic, Pfaffenhofen, Germany) was used. For the reading of the dipsticks a reader system (Dipstick Reader, 77 Elektronika Kft, Budapest, Hungary) was used. The reader system was checked daily with a blank calibration strip.

Test procedure and interpretation of the results

For raw milk no sample pre-treatment was required, while milk powder was reconstituted with distilled water. Two hundred microlitres of the milk sample was added to the β-lactam receptor in the glass vial and the mixture was gently swirled after reclosing the glass vial. The homogenous mixture was then incubated for one minute at 47.5 ±1 °C in the block-heater. β-lactam antibiotics in the milk form a stable non-active complex with the selective β-lactam receptor.

The dipstick of immune-chromatographic medium was placed into the glass vial and incubated at 47.5 ±1°C for a further min, during which incubation the liquid flowed vertically on the dipstick and passed through the capture zone. The test line captured remaining active receptor for β-lactams; the upper line or control line captured excess reagents. The intensity of the colour that consequently develops at the selective test line and the control line was inversely proportional to the amount of β-lactam residues and could be interpreted both visually and instrumentally.

For instrumental reading the Dipstick Reader was used, which calculates the ratio of colour, based on either the area or the amplitude, at test line and control line. During measurement the control line acts as a reference line. Milk with a ratio > 1.00 is free of β-lactams ('negative'); milk with a ratio ≤ 1.00 is contaminated ('positive').

Due to the very short incubation periods, it is possible that the control line is very weak or virtually absent directly after finishing the test, and where a clear red test line is already present the test can be interpreted as negative even before the control line is fully developed. However, if the control and the test line are both weak, no correct interpretation can be done until proper line development has occurred. In the case where the control line was completely missing, the instrument indicated 'invalid reading'. This happened a few times during the evaluation period, but the problem was resolved by waiting until the control line

Test and reader repeatability

To calculate the repeatability of the Dipstick Reader, negative and positive strips were measured twice. However, in the situation where the colour formation on the dipsticks after the second incubation step was not fully finished, not exactly the same situation was measured twice. Dipsticks were therefore also allowed to become dry and stable, then these dry dipsticks were measured 10 times and the standard deviation calculated.

The repeatability of the test was calculated at different ratio levels by analyzing and measuring blank and positive milk samples in duplicate.

Test selectivity

The selectivity of the βeta-s.t.a.r. with the classic 5-min protocol test was previously investigated by spiking blank milk with a relatively high concentration (10 × MRL in milk) of a substance belonging to other groups of antibiotics or chemotherapeutics [START_REF] Reybroeck | Evaluation of the βeta star for the detection of β-lactam antibiotics[END_REF][START_REF] Reybroeck | Rapid screening for residues of antibiotics in milk at the factory[END_REF]) and testing in duplicate. One substance was chosen from each of the most important groups: oxytetracycline (tetracyclines), sulfadiazine (sulfonamides), enrofloxacin (quinolones), neomycin (aminoglycosides), erythromycin (macrolides), lincomycin (lincosamides), clavulanic acid (β-lactamase inhibitors), colistin (polymyxins) and trimethoprim (diamino pyrimidine derivatives). The forbidden compounds chloramphenicol and dapsone, spiked at 3 µg kg -1 and 50 µg kg -1 , respectively, were also tested. With the compounds not belonging to the group of β-lactam antibiotics, no interference was observed except in the case of clavulanic acid [START_REF] Reybroeck | Evaluation of the βeta star for the detection of β-lactam antibiotics[END_REF][START_REF] Reybroeck | Rapid screening for residues of antibiotics in milk at the factory[END_REF].

In this study we tested 100 blank milk samples free of antibiotics and the minimal concentration of clavulanic acid in milk causing positive results for the βeta-s.t.a.r.

Detection capability

The most important validation parameter is the detection capability (CCβ). This parameter was determined for all β-lactams mentioned in the list of MRLs in milk (Anonymous, 1990). Therefore, starting from the detection capability concentrations of the classic βeta-s.t.a.r., blank milk was spiked with the βlactams investigated at different concentrations in various ranges in different increments: in the range 1-10 µg kg -1 in 1 µg kg -1 increments; in the range 10-20 µg kg -1 in 2 µg kg -1 increments; in the range 20-50 µg kg -1 in 5 µg kg -1 increments; in the range 50-100 µg kg -1 in 10 µg kg -1 increments; in the range 100-250 µg kg -1 in 25 µg kg -1 increments; in the range 250-500 µg kg -1 in 50 µg kg -1 increments; in the range 500-1000 µg kg -1 in 100 µg kg -1 increments; in the range > 1000-5000 µg kg -1 in 500 µg kg -1 increments. The spiked samples were blind coded before analysis. The analysis was performed within 4 hours after spiking. Each concentration was tested 20 times, in a time period of at least three days. Each day a different blank milk was used. For each β-lactam investigated, the CC β or the lowest concentration giving 19 (low) positive test results on 20 test results was determined, interpreting both visually and with the Dipstick Reader.

Test robustness

Length of incubation

Since incubation time could possibly make the test less robust, other incubation times were tested. The first incubation step was modified to be 45 or 75 s while keeping the second step at 1 min, the second incubation step was modified to be 45 or 75 s while keeping the first step at 1 min, and both incubation steps were modified (45 s each, 75 s each and the combinations of 45 and 75 s). Each situation was tested with four blank milk samples and with four milk samples spiked with one of three β-lactams: penicillin G (4 µg kg -1 ), ampicillin (6 µg kg -1 ) or cloxacillin (12 µg kg -1 ).

Influence of waiting time on reader results

Blank milk samples and samples spiked with one of three β-lactams (penicillin G, 4 µg kg -1 ; ampicillin, 6 µg kg -1 ; cloxacillin, 12 µg kg -1 ) were analysed and the strips were read with the Dipstick Reader directly after the incubation and after 0.5, 1, 3 and 10 min.

Milk influences -Milk quality and composition

The impact of the milk quality (somatic cell count, total bacterial count) and composition (fat and protein content, pH) was tested by comparing the test performance of the βeta-s.t.a.r. 1+1 protocol for 10 different blank milks with either high somatic cell count ((>10 6 mL -1 , 34 samples) or high total bacterial count (> 5 10 5 cfu mL -1 , 31 samples) and 10 different spiked milk samples with a normal and an abnormal composition. Milk of normal and abnormal composition was analysed with and without spiking with one of three β-lactams (penicillin G, 4 µg kg -1 ; ampicillin, 6 µg kg -1 ; cloxacillin, 12 µg kg -1 ). For each different milk type the average, the highest and the lowest ratio value was calculated.

Milk samples with a high number of somatic cells were selected at the milk control station based on Fossomatic 5000 (Foss, Hillerød, Denmark) measurements. Milk samples with a high total bacterial count were obtained by keeping normal milk samples for 4-6 h at room temperature. The final bacterial count was determined by performing a spiral plate count (Eddy Jet, IUL sa, Barcelona, Spain) on plate count agar plates after 3 days incubation at 30 °C.

Milk samples with a low fat content were obtained by removal of the fat layer by centrifugation (3050 × g, 10 min, at 5°C). Milk samples with a high fat content were obtained by addition of cream (50% fat, 6 g) to milk (60 mL). The final fat content was measured by infra-red with a MilcoScan 4000 (FOSS, Hillerød, DK).

Milk samples with a low (< 2.5 g 100 mL -1 ) and a high protein content (> 4 g 100 g -1 ) were natural milk samples with extreme protein content that were selected at the milk control station based on infra-red spectroscopic results (MilcoScan 4000). To gain samples with an abnormal pH, normal milk was initially adjusted to pH 6.0 and pH 7.5 with 1 M HCl or 1 M NaOH, respectively, then the pH was further adjusted with the addition of either 0.1 M HCl or 0.1 M NaOH.

-Type of milk and animal species UHT milk, sterilized milk, reconstituted milk powder, thawed milk, goats' milk, ewes' milk and mares' milk were also tested to determine if the βeta-s.t.a.r. 1+1 was a suitable test for these types of milk. Ten different samples of each milk type were tested, with the exception that a higher number of blank samples were tested for goats' milk (29 samples), ewes' milk (31 samples) and mares' milk (30 samples).

Reagent influence (batch differences)

To study the differences of different batches of reagents, blank and spiked milk samples were analysed at the same time with 2 different batches of βeta-s.t.a.r. (Exp. February 5, 2008). Besides spiking with penicillin G (4 µg kg -1 ), ampicillin (6 µg kg -1 ) or cloxacillin (12 µg kg -1 ), 20 milk samples were also spiked with 28 µg kg -1 cephapirin to obtain ratios close to the cut-off value of 1.00.

In the area around the cut-off, any change in intensity of the test line can be quickly noted.

The stability of reagents during shelf life was also checked. Blank and spiked milk samples were tested with reagents of Lot 70405 shortly after the production date and just one week before the expiry date.

Inter-laboratory testing

Twice a year T&V-ILVO organizes a national ring trial for the Belgian dairy industry regarding the detection of residues of antibiotics in milk by microbiological and rapid tests. In the two ring trials of 2007 the βeta-s.t.a.r. 1+1 procedure was included.

T&V-ILVO participated with the βeta-s.t.a.r. 1+1 in the international proficiency study for the analysis of β-lactam residues in raw milk, organised in 2007 by AFFSA Fougères, Community reference laboratory for antimicrobial residues in food of animal origin.

Daily control samples

During the study, blank and control samples spiked separately with penicillin G (4 µg kg -1 ), ampicillin (6 µg kg -1 ) and cloxacillin (12 µg kg -1 ) were analyzed daily.

Results and discussion

Test and reader repeatability

All repeatability results are shown in Table 1. The repeatability of the Dipstick Reader was very good; very low standard deviations of repeatability (s r ) values were obtained. The more positive were the samples, the better was the repeatability. It is worth noting that, in general, with wet dipsticks a slightly lower The repeatability of the test was also very good, very low s r values were again obtained. It is noteworthy that the same s r values for the test repeatability and reader repeatability were obtained: this indicates that the test is very robust and that for replicates of a sample the same binding, flow and colour formation is essentially obtained. The repeatability for positive samples is also better than that for blank samples and is not influenced by the ratio level.

Test selectivity

All 100 blank milk samples tested negative. To test the minimum concentration of clavulanic acid in milk that could cause positive results for the βeta-s.t.a.r. 1+1, milk spiked with clavulanic acid at different concentrations was tested, and interference by clavulanic acid was only obtained at 2500 µg kg -1 and above.

Therefore, the βeta-s.t.a.r. 1+1 is very selective for the detection of β-lactams.

Inference by the β-lactamase inhibitor clavulanic acid in the βeta-s.t.a.r. 1+1 protocol could be expected since this molecule has a β-lactam structure resembling that of the penicillin nucleus, except that the fused thiazolidine ring of the penicillins is replaced by an oxazolidine ring (Anonymous, 2005).

Within the β-lactam group the test is not specific for any particular β-lactam, but non-synthetic penicillins and the group of synthetic penicillins and cefalosporins could be differentiated after pre-treatment of the milk with penase (data not shown).

Detection capability

A summary of the detection capabilities of the βeta-s.t.a.r. 1+1 is given in Table 2. Not all the β-lactam compounds were detected at their respective MRL. The detection of cefalexin and penethamate was poor and also ceftiofur was only detected from 500 µg kg -1 . It should be noted, however, that from a practical ) is of no significance since penethamate is not stable in milk and is rapidly and completely hydrolysed to penicillin G and diethylaminoethanol. At 37 °C and at pH 7.3 (reflecting the physiological conditions of cows) the half-life of penethamate in aqueous solution is 23 min. In tissue homogenates at 32 °C, 50% of the penethamate has been shown to be hydrolysed within 2 h and 100% by 20 h (Anonymous 2000).

Since the analysis was performed not just immediately but within 4 hours after spiking, a negative influence of the protein binding effect on the test capabilities could not be excluded. When performing the βeta-s.t.a.r. 1+1 protocol instead of the classic 3+2 min protocol [START_REF] Reybroeck | Rapid screening for residues of antibiotics in milk at the factory[END_REF], the test generally lost some capability resulting in a reduced number of compounds detectable at MRL level.

Test robustness

Length of incubation

Performing the βeta-s.t.a.r. 1+1 protocol with the different incubation times tested had no significant impact on the ratios obtained for blank milk (data not shown).

With a longer first incubation period slightly lower ratio values were obtained with positive milk samples, while a shorter first incubation step resulted in slightly higher ratio values (data not shown). The effect was limited for milk spiked with penicillin G (4 µg kg -1 ) and cloxacillin (12 µg kg -1 ) but more visible for ampicillin (6 µg kg -1 ). This indicated that the time needed for a quantitative binding of the receptor to ampicillin is longer in comparison to binding to penicillin G or cloxacillin. The data indicated that for the first incubation a minimum of 1 minute is needed to be respected. Even when the second incubation period differed from the standard protocol, correct and acceptable results were obtained, proving that, within the limits tested, strict adherence to timing for the second incubation was not a critical point.

Influence of waiting time on reader results

If the reading of the dipsticks after incubation was delayed, the ratio values decreased giving a tendency to more positive results. Nevertheless all blank milk samples remained clearly negative with 2.25 as the lowest ratio obtained for a delay of 10 min after incubation before reading. Therefore, delaying the reading does not cause incorrect results but does improve the detection capability.

Milk influences -Milk quality and composition

With respect to testing the impact of the milk quality and composition (somatic cell count, total bacterial count, fat and protein content and pH), the mean, the highest ratio and the lowest ratio value for each milk type is given in Figures 1,2 and 3.

The milk quality and composition had no influence on the performance of the βeta-s.t.a.r. 1+1 when testing blank milk: all blank milk samples were clearly negative with ratio values all above 2.5, except for milk with a high pH for which the lowest ratio was 1.98. With positive milk samples spiked with penicillin G or cloxacillin, only small effects with abnormal milk quality or composition were noticed. In all spiked samples the detection of the β-lactam was never completely hampered. In milk with a low pH (6.0), sensitivity of the test was decreased, and was most pronounced for milk with 6 µg kg -1 ampicillin. Further, the detection capability of the test was slightly diminished when testing milk with a high bacterial load, which could be explained by the possible production of penicillinase by certain bacteria. In such a case Penicillin G and ampicillin would be expected to be more quickly cleaved than cloxacillin.

It should be noted that the best detection was obtained in milk with low protein content, which could be the result of decreased binding of the antibiotics to protein material. However, in large volumes of co-mingled milk such extreme values of composition will not occur; for instance while a high pH milk can occur mastitis, it is unlikely that an entire bulk collection of milk will be affected. Further, it must also be recognised that the test is qualitative rather than quantitative and is used only to discriminate between β-lactam residue-free milk and milk containing such residues. In general, the test is very robust and not severely influenced by the milk composition.

-Type of milk and animal species

The results of the testing of UHT milk, sterilized milk, reconstituted milk powder, thawed milk, goats' milk, ewes' milk and mares' milk are presented in Figures 4, 5 and6. No significant differences were noticed in testing different types of milk.

All blank milk samples tested negative (all ratios > 1.0), although for 1 out of 29 blank goats' milk and for 1 out of 31 blank ewes' milk samples a ratio below 2.0 was obtained. This may have been caused by an abnormal flow of the milk on the dipstick.

Cloxacillin (12 µg kg -1 ) and penicillin G (4 µg kg -1 ) were always detected in quite a uniform way in the different milk types and in the milk from animal species different from the cow. The detection of 6 µg kg -1 ampicillin gives a higher variation in detection and ratio values. The level of detection of ampicillin in sterilized milk, in reconstituted milk powder, in goats' milk and for a lesser extent in ewes' milk would be higher than 7 µg kg -1 as determined in cows' milk (Table 2). It is worth noting that the thawed milk samples were tested with reagents of Lot 70405, while the other milk types were tested with Lot 70213. Lot 70405 was more sensitive, and the difference in detection capability for ampicillin is especially notable. The biggest variation in ratio values was noticed for the detection of ampicillin in goats' milk. Of all milk types spiked with ampicillin and tested with reagents of Lot 70213, the best detection was obtained for mares' milk. The difference in detection for different milk types is smaller than the difference in test capability by the use of different batches of reagents. The βeta-s.t.a.r. 1+1 is therefore not only valid as a raw cows' milk test, but can also be used to test UHT milk, sterilized milk, reconstituted milk powder or thawed milk, and milks of non-bovine species (goat, ewe, mare). However, for UHT milk, sterilized milk, reconstituted milk powder or thawed milk the use of the classic 3+2 version with better detection capabilities for some compounds is recommended.

Test for false positive/false negative results

No false positive or false negative results were obtained when testing farm milk, truck milk, consumption milk samples and milk powders as part of a monitoring programme. For testing the rate of false negative results, incurred milk samples originating from individual cows treated with a veterinary drug, containing penicillin G and neomycin, were analysed with the βeta-s.t.a.r. 1+1. All 59 milk samples with a penicillin G content ≤2.4 µg kg -1 ) tested negative on βeta-s.t.a.r.

1+1; all 23 incurred milk samples with a penicillin G content ≥ 2.5 µg kg -1 were testing positive, except for the sample containing 2.7 µg kg -1 penicillin G. These data confirm that the detection capability for penicillin G in spiked milk (3 µg kg -1 , Table 2) is also valid for the detection of penicillin G in incurred milk samples.

Reagent influence (batch differences)

A summary of the results of the testing of spiked milk samples with two different batches of βeta-s.t.a.r. reagents is given in Table 3. Differences in test capability were found between batch Lot 70405 and Lots 70213 and 70205, the former giving lower ratios for the spiked milk samples than Lots 70213 and 70205. The difference was most pronounced for the milk samples spiked with 6 µg kg -1 ampicillin and 28 µg kg -1 cephapirin. Note that the detection capability of ampicillin and cephapirin is respectively 7 and 28 µg kg -1 (Table 2). Blank milk gave the same ratio values with all the different batch lots tested.

The stability of reagents during shelf life was also checked. Blank and spiked standards were tested with reagents of Lot 70405 shortly after the production date and one week before the expiry date. In general comparable results were (the mean values were: blank, 3.23; penicillin G at 4 µg kg -1 , 0.03; ampicillin at 6 µg kg -1 , 0.27; cloxacillin at 12 µg kg -1 , 0.32).

Interlaboratory testing

Twice a year T&V-ILVO organizes a national ring trial for the Belgian dairy industry regarding the detection of residues of antibiotics in milk by microbiological and rapid tests. In the two ring trials of 2007 the βeta-s.t.a.r. 1+1 was also included as a rapid test.

The results for the βeta-s.t.a.r. 1+1 in both ring trials were excellent: no falsepositive results were obtained and the spiked milk samples gave the expected positive results with the exception that the sample spiked with penicillin at 3 µg kg -1 tested negative (ratio = 1.281; test capability = 3 µg kg -1 ). The sample spiked with penicillin at 4 µg kg -1 gave a clear positive (ratio = 0.033). Of all the samples that tested positive with the classic (3min + 2 min) βeta-s.t.a.r. 3+2 protocol, only three samples tested negative with the rapid βeta-s.t.a.r. 1+1 protocol, i.e., samples spiked with 4 µg kg -1 ampicillin (test capability = 7 µg kg -1 ), 20 µg kg -1 cefquinome (test capability = 28 µg kg -1 ) and 3 µg kg -1 penicillin G (test capability = 3 µg kg -1 ). Details of the results are given in separate reports (Ooghe and Reybroeck 2007a & b).

In the international proficiency study organised by AFSSA Fougères 6 blind coded milk samples were distributed among the participating laboratories. The blank milk and the 5 spiked milk samples, respectively containing cefquinome at 50 µg kg-1, cloxacillin at 40 µg kg-1, cefalonium at 20 µg kg-1 and penicillin G at 6 µg kg-1 (in duplicate), were all correctly analyzed by βeta-s.t.a.r. 1+1 at T&V-ILVO (Anonymous 2008).

Daily control samples

During the study, blank and control samples spiked with 4 µg kg -1 penicillin G, 6 µg kg -1 ampicillin or 12 µg kg -1 cloxacillin were analyzed daily. The results are while from day 27 onwards Lot 70405, which was significantly better at detecting ampicillin, was used. For the entire period, following average ratio values were obtained: blank milk, 3.38 ± 0.34; milk spiked with 4 µg kg -1 penicillin G, 0.17 ± 0.08; milk spiked with 6 µg kg -1 ampicillin, 0.14 ± 0.31; milk spiked with 12 µg kg -1 cloxacillin, 0.40 ± 0.10. Since most of the time the 6 µg kg -1 ampicillin control sample was giving negative results its value for quality control could be discussed. However, small differences in test capability of the reagents can be detected by the use of milk samples spiked with ampicillin. This compound is therefore used by Neogen Corporation in their quality control for product release.

Conclusions

With a total test time of 2 min the βeta-s.t.a.r. 1+1 is, presently, the fastest single test on the market for the detection of β-lactam residues in milk meeting the criteria required by Commission Decision (EC) N° 2002/657. The short test time and the very easy test protocol and the possibility of visual interpretation of the test, enables the use of the test at the farm before collection. Shortening of the test protocol from 5 min to 2 min influences the test capability for some β-lactam compounds, but does not challenging test robustness. Further, the use of βetas.t.a.r. 1+1 at the farm level instead of using the classic 5 min βeta-s.t.a.r. test at the entrance of the dairy plant would resolve the issue of dilution "disguising" contaminated milk (since milk is bulked from an average of 10 farms) and would lead to stronger on-farm practices. On-farm checking would also reduce costs for the destruction of large volumes of β-lactam-contaminated milk, since again it would be at the individual farm level, rather than bulked milk from several farms.

On the other side testing at the farm means a larger number of determinations, higher costs for reagents and more work for the truck driver. It's the task of the responsible for the milk collection to make a balance of pros and cons and to calculate the price differences between the two strategies. If time is not the crucial factor (dairy entrance control) or no further dilution of the milk is expected, The horizontal line at a ratio of 1.00 gives the cut off between a negative and a positive result. The horizontal line at a ratio of 1.00 gives the cut off between a negative and a positive result. Note: a Except for cephapirin, which was tested using Lot 70205.

3

  All antimicrobial drugs administered to cows enter the milk to some degree.

  such a strategy, a short test time is very important due to the number of tests involved. The βeta-s.t.a.r. (Neogen Corporation, Lansing, MI, USA) is a dipstick receptor assay, using a selective receptor linked to gold particles for the detection of βlactams in milk (Reybroeck 2000; Reybroeck and Ooghe 2006) that originally involved a 5 minute protocol. The βeta-s.t.a.r. 1+1 is a faster version of the 5 minute βeta-s.t.a.r. protocol using identical reagents, but with 2 incubation steps of 1 minute each giving, overall, a 2 minute protocol. In this study, we describe how a validation of the βeta-s.t.a.r. 1+1 was performed at T&V-ILVO according to Commission Decision 2002/657/EC (Anonymous 2002a). The specificity, detection capability and test ruggedness of the assay were demonstrated as meeting the criteria required by the EU Commission Decision. Some of the results of this evaluation study were presented in 2008 at the EuroResidue VI Conference on Residues of Veterinary Drugs in Food (Egmond aan Zee, The Netherlands; Reybroeck and Ooghe 2008).

(

  PE-0708004) was from Deltapharma s.a. (Barcelona, Spain), cefquinome (Batch 01-01) from Intervet International GmbH (Unterschleiβheim, Germany), cefacetrile (22020D000) from Novartis Animal Health Inc. (Basel, Switzerland), cefalonium (2629) from Schering-Plough (Levallois-Perret, France) and clavulanic acid from DSM Anti-Infectives (Delft, The Netherlands).

6

  Comparisons were made for cefazolin (Cat 1097 603) with reference material from United States Pharmacopeia (Rockville, Maryland, USA) and for penicillin G (9930226) and cloxacillin (9930261) from the WHO Collaborating Centre for Chemical Reference Substances (Kungens Kurva, Sweden). The antibiotic standards were dissolved in water except for ceftiofur, cefalonium and for cefazolin (acetonitrile/water, 1:1, v/v). The acetonitrile (01207802) was from Biosolve B.V. (Valkenswaard, The Netherlands). Standard stock solutions of the antibiotic standards of 100 mg L -1 were made in water and kept below 4 °C for maximum 7 days. Dilutions of 1 and 0.1 mg L -1 were freshly prepared on a daily basis. The βeta-s.t.a.r.-250 kits were from Neogen Corporation. In general, lots TH00616-042405/4 (Exp. November 23, 2005) and lot 051607/2 (Exp. July 16,

  after appearance of the control line could a correct interpretation be performed.

  this study milk spiked with clavulanic acid at different concentrations was tested.

  Test for false positive/false negative results 117 Farm milk samples, 65 truck milk samples, 32 consumer milk samples and 18 milk powders were analysed with βeta-s.t.a.r. 1+1 as part of a monitoring programme. The same samples were also tested by Delvotest SP-NT (DSM Food Specialties, Delft, NL), Bacillus cereus-test (Suhren and Heeschen 1993), Escherichia coli-test (Suhren 1997) and Charm MRL-Lactam Test (Charm Sciences Inc., Lawrence, MA). For testing the rate of false negative results, 82 incurred milk samples originating from 27 individual cows treated with a veterinary drug containing penicillin G and neomycin were analysed with the βeta-s.t.a.r. 1+1 and with other microbiological and β-lactam receptor screening tests. Sampling started at the end of the withholding period. The exact concentration of penicillin G present in the milk samples was determined by LC/MS-MS in an external lab.

  reagents(Lot 70405, Exp. April 5, 2008 and Lot 70213, Exp. February 13, 2008)

  for the second reading due to further colour formation on the strips as they dried.

  detection capability of 80 µg kg -1 for penethamate in relation to the MRL (4 µg kg -1

  milk due to damage of the blood/milk barrier by sub-clinical

  the stability of the reagents over the recommended shelf life

  7. Over 29 working days the control samples gave very constant ratio values. It should be noted that tests for days 1 to 26 used reagent Lot 70213,

  min βeta-s.t.a.r. protocol could still be preferred to get the best test sensitivity. The βeta-s.t.a.r. 1+1 protocol is not only suitable for raw cows' milk, but could also be used to test milk of species other than the cow (goat, ewe, mare).

  . Proficiency study for the analysis of beta-lactam residues in raw milk. November 2007 -March 2008. Final report. Fougères, France: Community Reference Laboratory for Antimicrobial Residues in Food from Animal Origin, AFSSA Fougères. Anonymous. (2009). Council Regulation (EC) No 470/2009 of the European Parliament and of the Council of 6 May 2009 laying down Community procedures for the establishment of residue limits of pharmacologically active substances in foodstuffs of animal origin, repealing Council 1997. Microbiologischer Hemmstofftest mit Escherichia coli zum nachweis von Chinolon-Rückständen in Milch. Paper presented at: 38. Arbeitstagung des Deutsches veterinairmedizinische Gesellschaft Lebensmittelhygiene, 29 September -2 October 1997; Garmisch Partenkirchen, Germany.Suhren G., Heeschen W. 1993. Detection of tetracyclines in milk by a Bacillus cereus microtitre test with indicator. Milchwissenschaft 48:259-263. Suhren G., Heeschen W. 1996. Detection of inhibitors in milk by microbial tests. A review. Food/Nahrung. 40: 1-7. Žvirdauskiené R., Šalomskiené J. 2007. An evaluation of different microbial and rapid tests for determining inhibitors in milk. Food Control. 18: 541-547.

Figure 1 .

 1 Figure captions

Figure 2 .

 2 Figure 2. Ratios for normal and abnormal milks containing 6 µg kg -1 ampicillin ( , mean; , lowest; , highest). Milks were of normal composition (1) or with; (2) high somatic cell count; (3) high bacterial count; (4) low fat content; (5) high fat content; (6) low protein content; (7) high protein content; (8) low pH; (9) high pH.The horizontal line at a ratio of 1.00 gives the cut off between a negative and a positive result.

Figure 3 .

 3 Figure 3. Ratios for normal and abnormal milks containing 4 µg kg -1 penicillin ( , mean; , lowest; , highest). Milks were of normal composition (1) or with: (2) high somatic cell count; (3) high bacterial count; (4) low fat content; (5) high fat content; (6) low protein content; (7) high protein content; (8) low pH; (9) high pH.The horizontal line at a ratio of 1.00 gives the cut off between a negative and a positive result.

Figure 4 .

 4 Figure 4. Ratios for blank milk( , mean; , lowest; , highest) and different milks containing 12 µg kg -1 cloxacillin ( , mean; , lowest; , highest). Raw cows' milk (1) compared with: (2) UHT milk; (3) sterilized milk; (4) reconstituted milk powder; (5) thawed milk; (6) goats' milk; (7) ewes' milk; (8) mares' milk. The horizontal line at a ratio of 1.00 gives the cut off between a negative and a positive result.

Figure 5 .

 5 Figure5. Ratios for different milks containing 6 µg kg -1 ampicillin ( , mean; , lowest; , highest). Raw cows' milk (1) compared with: (2) UHT milk; (3) sterilized milk; (4) reconstituted milk powder; (5) thawed milk; (6) goats' milk; (7) ewes' milk; (8) mares' milk. The horizontal line at a ratio of 1.00 gives the cut off between a negative and a positive result.

Figure 6 .

 6 Figure6. Ratios for different milks containing 4 µg kg -1 penicillin ( , mean; , lowest; , highest). Raw cows' milk (1) compared with: (2) UHT milk; (3) sterilized milk; (4) reconstituted milk powder; (5) thawed milk; (6) goats' milk; (7) ewes' milk; (8) mares' milk. The horizontal line at a ratio of 1.00 gives the cut off between a negative and a positive result.

Figure 7 .FoodFoodFoodFoodFoodFoodFood

 7 Figure7. Ratios obtained for 29 dairy control samples with blank milk ( ) and milks containing ( ) 4 µg kg -1 penicillin G, ( ), 6 µg kg -1 ampicillin or ( ) 12 µg kg -1 cloxacillin. The horizontal line at a ratio of 1.00 gives the cut off between a negative and a positive result.

Table 1 .

 1 Repeatability of the reader (dry and wet dipsticks) and repeatability of the βeta-s.t.a.r. 1+1 test at different ratios.

	Milk	Compound and	Number	Mean	s r a	CV% b	Formatted
		concentration	of	ratio
			samples
	Reader repeatability -wet dipsticks
	Blank milk Positive milk Penicillin G; 4 µg kg -1 Ampicillin; 6 µg kg -1 Cloxacillin; 12 µg kg -1	30 30 30 30	4.08 0.12 0.33 0.05	0.30 0.04 0.04 0.02	0.52 0.13 0.13 0.04
	Reader repeatability -dry dipsticks
	Blank milk Positive milk Penicillin G; 1 µg kg -1 Penicillin G; 2 µg kg -1 Penicillin G; 2.5 µg kg -1 Penicillin G; 3 µg kg -1 Penicillin G; 4 µg kg -1	10 10 10 10 10 10	2.40 1.89 1.94 0.85 0.35 0.17	0.02 0.10 0.06 0.03 0.03 0.01	0.06 0.09 0.05 0.03 0.03 0.01
	Test repeatability
	Blank milk Positive milk Penicillin G; 4 µg kg -1 Ampicillin; 6 µg kg -1 Cloxacillin; 12 µg kg -1	20 20 20 20	4.35 0.10 0.34 0.05	0.33 0.05 0.09 0.03	0.55 0.09 0.14 0.04
	Note: a s r , standard deviation of repeatability					Formatted

b CV%: relative standard deviation

Table 2 .

 2 Detection capabilities in raw cows' milk of the βeta-s.t.a.r. 1+1 instrumental reading with a cut-off ratio of 1.00 a in comparison to the βeta-s.t.a.r.. Notes: a Detection capability defined as the lowest concentration tested giving a minimum of 19 positive results out of 20.

	Group	Compound	MRL b (µg kg -1 )	Detection capability βeta-s.t.a.r. 1+1 βeta-s.t.a.r. c,d
				protocol
	Penicillins	Penicillin G	4	3	3
		Ampicillin	4	7	4
		Amoxicillin	4	8	4
		Oxacillin	30	11	6
		Cloxacillin	30	9	6
		Dicloxacillin	30	8	5
		Nafcillin Penethamate	30 4	36 80	14 nd e
	Cefalosporins Ceftiofur	100	500	110
		Cefquinome	20	28	10
		Cefazolin	50	175	60
		Cephapirin	60	28	12
		Cefacetrile	125	100	40
		Cefoperazone	50	7	6
		Cefalexin	100	6000	>1000
		Cefalonium	20	4	4

b MRL, maximum residue limit (Council Regulation (EC) No 470/2009 and Commission Regulation (EU) No 37/2010) . c 3+2 classic protocol d Reybroeck, & Ooghe (2004) and unpublished data. e nd, no data available.

Table 3 .

 3 Ratios obtained when testing the same positive (Pos) and negative (Neg) milk samples with βeta-s.t.a.r. reagents from different batches.

	Tested			Lot 70405					Lot 70213 a
			Ratio		Number		Ratio		Number
		Mean	Min	Max	Pos	Neg	Mean	Min	Max	Pos	Neg
	Blank Penicillin G at 4 µg kg -1 Ampicillin at 6 µg kg -1 Cloxacillin at 12 µg kg -1 Cephapirin at 28 µg kg -1	3.67 0.04 0.24 0.15 0.80	3.20 0.00 0.01 0.10 0.41	4.04 0.15 0.42 0.25 1.06	0 20 20 20 19	20 0 0 0 1	3.06 0.09 0.96 0.35 1.03	2.63 0.00 0.79 0.29 0.77	3.70 0.19 1.36 0.42 1.44	0 20 14 20 11	20 0 6 0 9

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Acknowledgements

The authors appreciate the valuable work performed by Veroniek De Paepe (T&V-ILVO) and Jorien Lambrecht (KaHo Sint-Lieven, Sint-Niklaas, BE) and thank Neogen Corporation for kindly providing βeta-s.t.a.r. test reagents, Tim Coolbear (Fronterra Cooperative Group Limited, Palmerston North, NZ) for correction of the manuscript, MelkControleCentrum Vlaanderen for providing part of the raw cow's milk samples with a special composition or quality and for the MilcoScan 4000 and Fossomatic 5000 measurements, Siegrid De Baere (UGent) for the incurred milk samples used for testing of false negative results and for the determination of penicillin G content of these incurred samples.

was validated at the Technology and Food Science Unit of the Institute for Agricultural and Fisheries Research according


Wendie Liliane Claeys
email: wendie.claeys@favv.be

Katleen Baert

Frédéric Mestdagh

Jan Vercammen

Paul Daenens

Bruno De Meulenaer

Guy Maghuin-Rogister

André Huyghebaert

Wendie ; Claeys

Policy Control Baert Katleen ; Fasfc

Policy Control Mestdagh Frédéric ; Fasfc

Wendie Claeys

Assessment of the acrylamide intake of the Belgian population and the effect of mitigation strategies

Keywords: Risk assessment, Exposure assessment, Probabalistic modelling, Chromatography -LC/MS Additives/Contaminants: Process contaminants -acrylamide Food Types: Processed foods acrylamide, risk assessment, exposure, food, mitigation, probabilistic 37 38

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

of Very High Concern (ECHA 2009). Under the ECHA proposal, AA has been listed as a gingerbread, almond or sweet spiced biscuits, chocolate, popcorn, breakfast cereals and cereal 125 bars. The classification is based on the AA levels in different foodstuffs and is in line with the 126 grouping applied in other studies (Mestdagh et al. 2007;[START_REF] Boon | 352 Calculations of dietary exposure to acrylamide[END_REF][START_REF] Matthys | Risk assessment of 429 dietary acrylamide intake in Flemish adolescents[END_REF].

127

The AA data were further expanded with German data from the AA European Monitoring 128 Database, which is compiled by the Institute for Reference Materials and Measurements (IRMM percentile, etc.) can be applied as on the original data set. As such a 'bootstrap' distribution of 143 500 97.5 th , 99.9 th percentiles, etc. is created that characterizes the uncertainty of the original 144 data set (Vose 2006). The model input distributions were randomly sampled by the Latin 145 Hypercube method. Calculations were performed by the software @Risk ® (Palisade 146 Corporation, Version 4.5.5, NY, USA).

147

AA concentrations below the quantification limit (LOQ) were replaced by LOQ/2 ('middle 148 bound scenario'). For the conversion of the AA level of roasted or grounded coffee beans 149 (coffee surrogate) to liquid coffee (coffee surrogate) a conversion factor of 0.046 was applied 150 (van Dooren et al., 1995). Regarding the AA level of chocolate biscuits, chocolate and biscuit 151 were considered separately. Based on chocolate levels mentioned on the package it was 152 assumed that 40% of the biscuit consists of chocolate. Variability in preparation conditions (e.g. deep-frying of chips, toasting of bread, etc.) was not taken into account.

153

F

155

Results and Discussion 156

Dietary exposure of the Belgian consumer to acrylamide 157

Table 1 shows the AA intake per food group and the overall AA intake of the Belgian 158 population. The contribution of the most relevant food groups to the AA intake (contribution > 159 1%) is also shown in Figure 1.

160

The average AA intake was calculated as 0.35 µg/kg bw/day (P50 = 0.2 µg/kg bw/day). For 161 high consumers the intake may be several times higher, amounting to 1.58 µg/kg bw/day for the 162 97.5 th percentile or P97.5. Overall, about 6% of the population has an intake higher or equal to On average, chips contributed the most to the AA intake (23%), followed by coffee (19%), 169 biscuits (13%) and bread (12%) (Figure 1). For the lower intake percentiles, coffee and bread 170 appeared to be most important sources of AA, whereas for the higher percentiles (≥ P85) chips, 171 crisps and biscuits became more important sources. This reflects the difference in dietary 172 pattern according to the AA intake (Dybing et al. 2005;[START_REF] Matthys | Risk assessment of 429 dietary acrylamide intake in Flemish adolescents[END_REF].

173

The AA level, and as such the contribution to the AA intake, of different food groups and of 174 foods within the same food group can vary greatly depending on the formulation of the food, 175 manufacturing conditions, etc. The contribution of a food or food group to the intake is however, The AA intake given in Table 1, corresponds well to the range of values calculated previously 186 for Belgium (restricted target population of adolescents and visitors of a university canteen) 187 (Mestdagh et al. 2007;[START_REF] Matthys | Risk assessment of 429 dietary acrylamide intake in Flemish adolescents[END_REF] and reported for other European countries (Boon et 188 al. 2005;Dybing et al. 2005;Svensson et al. 2003). In general, values between 0.3 to 2.0 µg 189 AA/kg bw/day are reported for the average AA intake of adults. The high intake percentiles (P90 190 to P97.5) range from 0.6 to 3.5 µg/kg bw/day with 5.1 µg/kg bw/day reported for P99. Food that 191 contribute most to the AA intake are in general chips (16-30%), crisps (6-46%), coffee (13-39%),

198

Any exposure assessment is confronted with a number of uncertainties (Kroes et al. 2002).

199

In this study, the long-term intake was predicted based on a two-day consumption survey and 200 consumption data were considered to be independent. The linkage between the analyzed and 201 consumed food items, the categorization into food groups, the conversion factors applied (i.e.

202

for chocolate in chocolate biscuits and for liquid coffee), and the fact that variability in 203 preparation conditions was not accounted for and that values below the LOQ were unknown 204 and replaced by LOQ/2, are additional sources of uncertainty in the estimated AA intake.

205

Risk characterization 206

Given that AA is probably genotoxic and carcinogenic to humans (IARC group 2A) (JECFA

217

depending on the exposure data and toxicological values used (Table 2). The JECFA calculated 218 a MOE of 300 based on an average exposure of 1 µg AA/kg bw/day and a BMDL10 (the lower 219 confidence limit on the benchmark dose associated with 10% response) of 300 µg AA/kg 220 bw/day for the induction of breast tumours in rats. For high consumers with an intake of 4 µg

221

AA/kg bw/day, the MOE was 75 (JECFA 2005). The average (0.2 µg/kg bw/day) and the P97.5

222

(1.6 µg/kg bw/day) intake calculated in this study, would thus correspond to MOE values of 1500

240

Table 3 shows the effect of some of the specific AA mitigation possibilities reported in 241 literature on the dietary exposure. It should be noted however, that the reduction percentages results in a ~10% reduction of the average AA intake, which is of the same order of magnitude 269 as the average reduction of 13% determined by [START_REF] Boon | 352 Calculations of dietary exposure to acrylamide[END_REF] for the Dutch consumer. For 270 a high consumer of fried potato products, the intake can even be reduced with 20%.

271

In addition, [START_REF] Boon | 352 Calculations of dietary exposure to acrylamide[END_REF] calculated that the AA intake decreases on average with about

272

4% when the AA level in gingerbread is reduced with 60%, which can be obtained when sodium 273 bicarbonate is used instead of ammonium carbonate as baking agent (scenario 5). In this study, 274 a similar reduction of the intake was obtained for the higher percentiles. [START_REF] Boon | 352 Calculations of dietary exposure to acrylamide[END_REF] 275 determined also the reduction that would be achieved when the two latter mitigation options are 276 combined (scenario 4 and 5) and obtained an average reduction of 17%. A comparable 277 reduction of 9 to 25% for the higher intake percentiles was calculated in this study.

278

Seal et al. ( 2008) addressed the effect of some mitigation options on the AA intake as well,

279

discussing not only the benefits (reduction of the AA intake) but also the risks (health, quality or

308

of the intake for the higher (≥ P95), but not for the lower intake percentiles. This can partly be 309 explained by the fact that the signal values are P90 values limiting the higher AA concentration measures. Signal values or action limits can be a useful tool for policymakers to encourage the 327 food industry to take action by means of a specific AA value. It is nevertheless the task of the 328 food industry to ensure that the AA content of their products is as low as possible. In literature 329 several possibilities are proposed for reducing the AA level in food. For example, the CIAA 330 (Confederation of the food and drink industries of the EU) developed the "AA Toolbox", which 331 contains a brief description of possible intervention steps evaluated in cooperation with industry 332 for reducing the AA content of food products and has published AA pamphlets for five different 333 sectors (CIAA 2009 a & b). However, also the consumer has to take responsibility for reducing 334 his AA intake. It is estimated that about half of the AA intake results from home-made meals or 335 meals prepared in restaurants (Grob 2007). Even by means of some simple measures such as 336 avoiding excessive browning when frying, baking or roasting potato and cereal products, the AA 337 intake can be significantly reduced. In addition, the recommendations of having a diversified diet 338 including sufficient vegetables and fruit, without exaggerating the consumption of fried food, are 339 still valid and help to reduce the AA intake (Mestdagh et al. 2007).

340

Finally, it must be stressed that awareness of the food industry and the consumer as well as 341 a clear information campaign, are indispensable for dealing with the AA issue.

43 category 2

 2 carcinogen and a category 2 mutagen. The chemical has a large number of industrial 44 applications including the production of polyacrylamides, which are among others used in

  figure of the exposure and the relative contribution of each food group to the exposure may

207 2005 ;

 2005 IARC 1994), it is recommended to keep the AA exposure 'as low as reasonably 208 achievable' (ALARA). Nevertheless, to prioritise risks associated with unavoidable contaminants 209 that are both genotoxic and carcinogenic, the 'margin of exposure' (MOE) concept has been put 210 2005). The MOE is the ratio between a particular point on the dose-response 211 curve leading to tumours in experimental animals and the exposure. The size of the MOE gives 212 an indication about the possible extent of the risk. The higher the MOE, the lower the risk of 213 exposure to the component concerned. The Scientific Committee of the European Food Safety 214 Authority (EFSA) considers the figure of 10,000 or higher as (in general) being of low concern 215 from a public health point of view and might reasonably be considered as a low priority for risk 216 management actions. For AA MOE values between 50 and 2000 have been reported,

  223 and 188 respectively. Such low MOE values imply that additional efforts have to be taken for 224 reducing the AA content in foods and that AA is a process contaminant of high priority. (For 225 comparison: MOE values between 17,900 and 9500 are given for the polycyclic aromatic 226 hydrocarbons (EFSA 2008c)).

  reduce the acrylamide exposure 231Various methods are reported in the literature to reduce the AA content of food, such as the 232 selection of potato, wheat and other plant cultivars with low levels of theAA precursors 2004; Taeymans et al. 2004).

242

  mentioned are indicative values and that the yield of the proposed mitigation possibilities might 243 be different in practice (for one because there are different types of biscuits, breads, etc. with

  280 nutritional implications). The mitigation scenarios studied by Seal et al. (2008) decreased the 281 exposure by 1 to 14%, which is the same range as observed in this study. Application of all 282 mitigation measures simultaneously resulted in a reduction of 31-39%, depending on the 283 percentile of exposure considered. measure for reducing the AA intake is by establishing signal values (action 288 values). In this respect, Germany introduced in 2002 the 'minimisation concept', which pursuits 289 a gradual reduction of the AA levels in foodstuffs while retaining the product's properties (BVL, 290 2005). In this concept the lowest AA level of 10% of the food with the highest AA concentration 291 (P90) is taken as a signal value, with a ceiling of 1000 µg AA/kg food product. The German P90 292 signal value is revised each year and reduced when necessary. A signal value can be 293 maintained, but never increased. When a signal value is exceeded, it is discussed with the 294 companies involved which actions might be taken to lower the AA level.295

  342 consumption data, and the Scientific Committee of the Belgian Federal Agency for the Safety of 346 the Food Chain (FASFC) for their guidance of this study. Frédéric Mestdagh is post-doctoral 347 researcher funded by the Research Foundation Flanders (FWO Vlaanderen).

Figure 1 .

 1 Figure 1. Contribution of the most important food groups to the estimated dietary exposure to

  163the average intake of 1 µg/kg bw estimated by the Joint FAO/WHO Expert Committee on Food

	164
	165	Additives (JECFA 2005).
	166
	167	[Table 1]
	168

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  Table4shows the effect of the German 2008 signal values on the total AA intake of the296Belgian consumer (see bottom line of the table). Hereto, AA levels above the German signal were replaced by the P90 signal value. It should be noted that there are no German 298 signal values given for chocolate, bread, bread rolls, popcorn and cereal bars. For biscuits the 299 signal value for diet biscuits was applied. For toast the signal value of knäckebröd was 300 considered, but this value turned out to be higher than the levels measured for toast. The effect 301 of applying the P90 signal value concept on the Belgian data (P90 of Belgian AA concentration 302 data as signal value) is also presented in Table4, (i) for each food group separately and (ii) for Application of the German signal values on the Belgian data results in a significant reduction

	303
	304	all food groups together.
	305 306 307	[Table 4]	F o r
			P
			e
			e r
			R
			e
			v i e
			w
			O n l
			y
			12/17

values

  Minimierungskonzept zur Senkung der Acrylamidgehalte in Lebensmitteln[Internet].

	355 384	2009 January 22]. Available from: http://www.efsa.europa.eu/en/datex/datexfooddb.htm. http://www.inchem.org/documents/iarc/vol60/m60-11.html
		Germany: EFSA. 2008c. European Food Safety Authority. Polycyclic aromatic hydrocarbons in food. BVL; [cited 2005 Nov 28]. Available from:
		F o r F o r F o r F o r
		P P P P
		e e e e
		e r e r e r e r
		R R R R
		e e e e
	401 402	v i e w content of semi-finished biscuit on industrial scale. Food Sci. Technol. 39: 724-728. v i e v i e v i e Granvogl M, Koehler P, Latzer L, Schieberle P. 2008. Development of a stable isotope dilution w w w
	403 404 405	O n l assay for the quantitation of glycidamide and its application to foods and model systems. J. Agric. Food Chem. 56: 6087-6092. Grob K. 2007. Options for legal measures to reduce acrylamide contents in the most relevant O n l O n l O n l
	406	foods. Food Addit. Contam. 24: 71-81.	y y y y
		Hills S. 2008 Aug 04. Chips companies settle acrylamide lawsuit. Food USA [Internet].
			15/17 16/17 1/1

Table 1 .

 1 Contribution of the different food groups to the dietary exposure of the Belgian 1 population to acrylamide (µg/kg bw/day; best estimation [95% confidence interval]).

	2

Table 2 .

 2 Comparison of 'Margins of exposure' (MOEs) determined in the present study with

	4
	5	MOE values given in literature for acrylamide
	6
		T25	BMDL 10	Exposure
		(µg/kg	(µg/kg	(µg/kg		MOE	Remarks	Ref.
		bw/day)	bw/day)	bw/day)
					T25	BMDL
		650	310	0.41	1600	760	Mean exposure ♂ (Norway)	(1)
				0.42	1600	740	Mean exposure ♀(Norway)	(1)
				0.43	1500	720	Mean exposure (USA)	(1)
				0.92	710	340	P90 exposure (USA)	(1)
			200 a 2000 a	2.31 1 / 4	280	130 2000 / 500 200 / 50	P90 exposure 2-5 years old (USA) Mean / high exposure	(1) (2)
			300	1 / 4		300 / 75	Mean / high exposure	(2)
			300	0.2 / 1.6		1500 / 188	Mean / P97.5 exposure	Present study
	7
		Notes: (1): O'Brien et al. 2006; (2): JECFA 2005

Table 3 .

 3 Effect of some specific mitigation scenarios on the acrylamide intake of the Belgian 11 population (expressed as % reduction of the intake assuming the % decrease in AA content as 12 stated in the scenario).

	13
	14
	Scenario	Average P50	P75 P90 P95 P97.5 P99 P99.9
	1	bread & bread rolls -60%	9.7	29.6	27.6 15.4	8.0	5.1	3.3	1.7
	2	coffee -30%	5.6	15.2	16.2	8.7	4.7	3.3	2.4	1.9
	3	biscuit -70%	9.1	0.0	0.0	7.4	9.9	10.6 11.2 12.4
	4	chips -35%	7.7	0.0	0.0	9.4	11.0	9.4	8.2	7.9
		crisps -35%	2.7	0.0	0.0	0.0	2.5	3.6	4.3	12.4
		chips & crisps -35%	10.4	0.0	0.0	9.4	13.6 13.0 12.4 20.3
	5	gingerbread -60%	2.2	0.0	0.0	0.0	0.0	3.1	4.2	4.1
	4+5 chips & crisps -35% + gingerbread -60% 12.6	0.0	0.0	9.4	13.6 16.1 16.6 24.5

Table 4 .

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Acknowledgements 344

The authors would like to acknowledge the Belgian Institute of Public Health for access to the


Pierre-Vincent Koseleff

P. -V Koseleff

D Pecker

Every knot is a billiard knot

Keywords: Billiard knots, Lissajous knots, Chebyshev knots, Cylinder knots Mathematics Subject Classification 2000: 14H50, 57M25, 14P99

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

The study of billiard trajectories in a polyhedron was introduced in 1913 by König and Szücs in [KS]. They proved density results for a billiard trajectory in a cube. Their theorem is strongly related to the famous Kronecker density theorem (see [HW]).

More recently, Jones and Przytycki considered the periodic billiard trajectories with no self-intersection as knots. They proved that billiard knots in a cube are isotopic to Lissajous knots, and deduced that not all knots are billiard knots in a cube ( [JP], see also [La, C, BHJS, BDHZ]). They also proved that every torus knot (or link) of type (n, k), where n ≥ 2k + 1 can be realized as a billiard knot in a cylinder (or in a prism with a regular n-gonal floor). Przytycki went deeper into the study of symmetrical billiards in [P].

Lamm and Obermeyer [LO] proved that billiard knots in a cylinder are either periodic or ribbon, hence not all knots are billiard knots in a cylinder. In [KP] we constructed many other examples of billiard knots in convex polyhedrons (in fact irregular truncated cubes). Dehornoy constructed in [D] a billiard which contains all knots, but this billiard is not convex.

In this paper we prove the following conjecture of Jones and Przytycki:

Every knot is a billiard knot in some convex polyhedron.

Our result is more precise: Theorem 8 Every knot (or link) is a billiard knot (or link) in some convex right prism.

Using a theorem of Manturov [M], we first prove that every knot has a diagram which is a star polygon. Then, perturbing this polygon, we obtain an irregular diagram of the same knot. We deduce that it is possible to suppose that 1 and the arc lengths of the crossing points are linearly independent over Q. Then, it is possible to use the classical Kronecker density theorem to prove our result.

2 Every knot has a projection which is a star polygon A toric braid is a braid corresponding to the closed braid obtained by projecting the standardly embedded torus knot into the xy-plane. A toric braid is a braid of the form

τ k,n = σ 1 σ 2 • • • σ k-1 n
, where σ 1 , . . . , σ k-1 are the standard generators of the full braid group B k . A quasitoric braid of type (k, n) is a braid obtained by changing some crossings in the toric braid τ k,n . The quasitoric braids form a subgroup of B k . Consequently there exist trivial quasitoric braids of arbitrarily great length, and any quasitoric braid is equivalent to a quasitoric braid of type (k, n) with n ≥ 2k + 1.

Manturov's theorem tells us that every knot (or link) is realized as the closure of a quasitoric braid ( [M]).

The following definition of polygonal stars will be useful for links.

Definition 1 Let p, q be integers. The polygonal star { p q } ⊂ R 2 is given by its vertices e(k) = e 2kiπ p , and its sides (e(k), e(k + q)), k = 0, . . . , p -1.

When p and q are coprime integers, this is the usual definition of star polygons. The following picture shows the polygonal stars { 10 3 }, { 10 2 } and { 9 3 }, as projections of billiard torus links T (10, 3), T (10, 2) and T (9, 3). The dotted lines correspond to the parts z < 0 of the link.

Figure 1: The polygonal stars { 10 3 }, { 10 2 } and { 9 3 }, projections of the torus links T (10, 3), T (10, 2) and T (9, 3).

Theorem 2 Every knot (or link) has a projection that is a polygonal star.

Proof. Let our knot be realized as the closure of a quasitoric braid of type (k, n). By our remark, we can suppose n ≥ 2k + 1. Now, we use the result of Jones and Przytycki which says that every torus knot of type (k, n), n ≥ 2k + 1 can be realized as a billiard knot in a cylinder. In their construction, the projection on the xy-plane is the closure of the toric braid τ k,n , which proves our result. Remark 3 It is also possible to use a theorem of Lamm and Obermeyer [LO] to give another proof of theorem 1 in the knot case. A Rosette braid is a braid of the form

σ ε 1 1 • • • σ ε k-1 k-1 n , ε i = ±1
, and a Rosette knot is the closure of a Rosette braid. The theorem of Lamm and Obermeyer tells us that every Rosette knot can be represented by a billiard knot in a cylinder. The knot diagrams obtained in their proof are star polygons isotopic to the closures of some quasitoric braids.

Breaking the symmetry

Since we want to obtain all knots, we need irregular diagrams.

First, let us recall some facts about billiard trajectories. If ABC is a piece of a polygonal line, then the mirror placed at B, is the hyperplane µ(B) which is orthogonal to the internal bisector of B at B. The mirror room at B is the closed half-space containing A, B, C and the mirror at B.

We define a billiard trajectory to be a finite union of polygonal lines, which is contained in all its mirror rooms. A billiard knot (or link) is a polygonal knot (or link) ( [A, C]) which is a billiard trajectory.

The following result allows us to forget about the billiard, and focus our attention on the trajectory. It is valid in every dimension.

Lemma 4 Let Q = (Q 0 , . . . , Q n-1 ), be a billiard trajectory such that Q µ(Q k ) = Q k .
Then, if P = (P 0 , . . . , P n-1 ) is sufficiently close to Q, it is a billiard trajectory in some convex polyhedron.

Proof. Let -→ u k (Q) be the unit vector of the internal bisector of Q k . The hypothesis means that for every k, i, i = k, the scalar product -→

u k (Q) . ---→ Q k Q i is positive. Since -→ u k (Q) and ---→ Q k Q i depend
continuously on Q, this condition remains true for any trajectory P that is sufficiently close to Q.

2

Proposition 5 Let K be a knot. There exists a plane billiard trajectory P which is a projection of a knot isotopic to K, and which satisfies the following irregularity condition: If t i are the arc lengths corresponding to the crossings of P, then the numbers 1, t i are linearly independent over Q.

Proof. Let Q = (Q 0 , . . . , Q n-1 ), Q n = Q 0 be
a star polygon which is a projection of K. Let us suppose that each line (Q k Q k+1 ) has an equation of the form y = α k x + β k . Then, if (a k , b k ) are sufficiently close to (α k , β k ), the lines {y = a k x + b k } determine a nonconvex polygon P = (P 0 , . . . , P n-1 ) close to Q. By our lemma, P is a periodic billiard trajectory in some convex polygon. By Baire's theorem, we can suppose that the numbers a 0 , a 1 , . . . , a n-1 and b 0 , b 1 , . . . , b n-1 are algebraically independent over Q. Let I be the set of integer pairs (i, j), j = i -1, such that the intersection of [P i , P i+1 ] and [P j , P j+1 ] is a point P i,j .

The vertex P i is the point P i-1,i . The abcissa of P i,j is x i,j = b i -b j a j -a i , and the length of

[P i , P i,j ] is |ℓ i,j |, where ℓ i,j = 1 + a 2 i x i,j -x i-1,i .
Let us show that the numbers ℓ i,j and 1 are linearly independent over Q. Suppose that we have a linear relation with rational coefficients (i,j)∈I λ i,j ℓ i,j = λ, with λ, λ i,j ∈ Q.

This is an algebraic relation between the a i and the b i . Since these numbers are algebraically independent over Q, this relation must be an identity.

Let k ≤ n -1 be a fixed non-negative integer, and let us substitute b k = 1 and b i = 0 if i = k in this identity.

We obtain a new identity between the a i .

n-1 j=0 λ k,j 1 + a 2 k 1 a j -a k - 1 a k-1 -a k - n-1 j=0 λ k+1,j 1 + a 2 k+1 a k+1 -a k + n-1 i=0 λ i,k 1 + a 2 i a i -a k = λ (1)
where

λ k,k = λ k,k-1 = λ k+1,k = 0. Substituting a k = √ -1, in this identity, we obtain - n-1 j=0 λ k+1,j 1 + a 2 k+1 a k+1 - √ -1 + n-1 i=0 λ i,k 1 + a 2 i a i - √ -1 = λ.
Let h = k + 1 be an integer, and let

a h → √ -1. From lim z→ √ -1 √ 1 + z 2 z - √ -1 = ∞, we obtain λ h,k = 0.
Since this is true for every h and k, we deduce that λ i,j = 0 for all (i, j) ∈ I.

Finally, since the arc lengths of the points P i,j are given by t

i,j = |ℓ 0,1 | + |ℓ 1,2 | + • • • + |ℓ i-1,i | + |ℓ i,j |, we deduce the result.
2

Proposition 6 Let L be a link. There exists a plane billiard trajectory P which is a projection of a link isotopic to L, and which satisfies the following condition.

If R is a component of P parametrized by arc length, and if t i are the arc lengths corresponding to the crossings, then the numbers 1, t i are linearly independent over Q.

Proof. The proof is almost identical to the preceding one.

There is a link isotopic to L whose plane projection is a union of polygons

P = P (1) ∪ P (2) ∪ • • • ∪ P (d)
whose vertices are (P 0 , P 1 , . . . , P N -1 ). Let R be a component of P, we can suppose that the vertices of R are (P 0 , P 1 , . . . , P n-1 ).

Furthermore, we can suppose that the equations y = a k x + b k of the sides of P are such that the numbers a k and b k , k = 1, . . . , N -1, are algebraically independent over Q.

Here, we consider the set I of integer pairs (i, j), i ∈ {0, . . . , n -1}, j ∈ {0, . . . , N -1}, j = i -1, corresponding bijectively to the arc lengths of the vertices and crossings contained in R.

Then, the rest of the proof is exactly the same as in the case of knots. 2

4 Proof of the theorem

We will use Kronecker's theorem ( [START_REF] Hardy | An Introduction to the Theory of Numbers[END_REF]Theorem 443]):

Theorem 7 (Kronecker ( 1884)) If θ 1 , θ 2 , . . . , θ k , 1 are linearly independent over Q, then the set of points (nθ 1 ), . . . , (nθ k ) is dense in the unit cube. Here (x) denotes the fractional part of x.

Now, we can prove our main theorem.

Theorem 8 Every knot (or link) is a billiard knot (or link) in some convex prism.

Proof. First, we consider knots. By Theorem 2 there exists a knot isotopic to K whose projection on the xy-plane is a periodic billiard trajectory in a convex polygon D. If t i are the arc lengths corresponding to the crossings, we can suppose by Proposition 5 that the numbers t 1 , . . . , t k , 1 are linearly independent over Q. Using a dilatation, we can suppose that the total length of the trajectory is 1.

Consider the polygonal curve defined by (x(t), y(t), z(t)), where z(t) is the sawtooth function z(t) = 2|(nt + ϕ) -1/2| depending on the integer n and on the real number ϕ. If the heights z(P k ) of the vertices are such that z(P k ) = 0, 1, then it is a periodic billiard trajectory in the prism D × [0, 1] (see [JP, La, LO, P, KP]). If we set ϕ = 1/2 + z 0 /2, z 0 ∈]0, 1[, we have z(0) = z 0 . Now, using Kronecker's theorem, there exists an integer n such that the numbers z(t i ) are arbitrarily close to any chosen collection of heights, which implies the result.

The case of links is similar. First, we find a plane billiard diagram of our link, and then we parameterize each component.

2

Remark 9 If the diagram has some regularity, then it is generally impossible to use Kronecker's theorem. This is illustrated by Lissajous knots and cylinder knots. This is also true for more general diagrams. For example, suppose that there are four crossings of arc lengths t 1 , t 2 , t 3 , t 4 such that t 2 -t 1 = t 4 -t 3 . So, if z(t) = 2 (nt+ϕ)-1 2 is the height function, then ε i z i = 2(nt i +ϕ)-1, with ε i = ±1. We deduce that ε 1 z 1 -ε 2 z 2 -ε 3 z 3 + ε 4 z 4 ∈ 2Z. Consequently, we see that z 1 = z 2 = z 3 = 1 implies z 4 = 1. This clearly shows that the heights of the crossings cannot be chosen arbitrarily.

Figure 2 :

 2 Figure 2: Naming the vertices and crossings of a pentagonal trajectory.