# Population pharmacokinetic modelling of oxytetracycline in rainbow trout (Oncorhynchus mykiss): Effects of route of administration, temperature and ploidy

Alexis Viel, Florine Bachelet, Annaëlle Chailleux, Céline David, Lionel Pineau, Ségolène Calvez, Antoine Rostang

► To cite this version:

Alexis Viel, Florine Bachelet, Annaëlle Chailleux, Céline David, Lionel Pineau, et al.. Popula-
tion pharmacokinetic modelling of oxytetracycline in rainbow trout (Oncorhynchus mykiss): Ef-
fects of route of administration, temperature and ploidy. Aquaculture, 2026, 610, pp.742917.
10.1016/j.aquaculture.2025.742917. hal-05141538

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# Population pharmacokinetic modelling of oxytetracycline in rainbow trout (Oncorhynchus mykiss): Effects of route of administration, temperature and ploidy

Alexis Viel<sup>a,*</sup>, Florine Bachelet<sup>b</sup>, Annaëlle Chailleux<sup>a</sup>, Céline David<sup>b</sup>, Lionel Pineau<sup>b</sup>, Ségolène Calvez<sup>b</sup>, Antoine Rostang<sup>b</sup>

## ARTICLE INFO

**Keywords:**

Oxytetracycline

Population pharmacokinetics

Rainbow trout

Ploidy

Bioavailability

## ABSTRACT

The aim of this study was to perform a pharmacokinetic (PK) study of oxytetracycline (OTC) in rainbow trout using different routes of administration and different doses, and to investigate the influence of the bodyweight, the ploidy status (diploid *versus* triploid) and the water temperature (10 °C *versus* 16 °C).

A cross-over design was used with 361 trout (median bodyweight: 389 g), each fish receiving OTC intravenously (8–30 mg/kg) and orally (50–150 mg/kg), by gavage or by spontaneous intake *via* a coating of OTC on the feed to mimic farming practice. Each fish, for each modality, was sampled 3–4 times over a period of 11 days, to establish its individual PK profile. Coated feed and plasma samples were assayed using a sensitive HPLC-MS/MS method. A population PK modelling approach was used to analyse plasma data and estimate key PK parameters and their variability.

A bi-compartmental PK model best described the plasma data. The absolute oral bioavailability appeared to be very low (around 3 %) and the elimination of OTC was slow and strongly influenced by temperature (elimination half-life approximately 79 h at 16 °C *versus* 113 h at 10 °C). A comparison of spontaneous intake and gavage showed a significant loss of antibiotic due to leaching (about 30 %). Bodyweight and water temperature were the most influential covariates affecting the PK of OTC compared to the effect of ploidy. Pharmacodynamic (PD) studies with OTC against the major trout pathogens are now required to allow a more robust assessment of the expected efficacy thanks to a PK/PD approach.

## 1. Introduction

Aquaculture has become an increasingly important source of fish for human consumption. Among these, the salmonid family is one of the most sought after by consumers, resulting in ever-increasing production volumes. This is particularly true for rainbow trout (*Oncorhynchus mykiss*), the most widespread freshwater salmonid, for which the European Economic Area is the main production area (Commission et al., 2023). This species is fast growing, has a wide range of environmental tolerances (temperature, salinity), a well-controlled reproductive cycle, and a well-managed diet. However, trout production has changed with longer rearing (2 or 3 years) to obtain larger trout, mainly for smoked trout. Furthermore, to facilitate the breeding of large trout, triploidy

method is often used to obtain sterile trout. Triploid trout now account for a significant proportion of European production: for instance in France, they represent more than half the trout farmed in the country (Carabin, 2022). However, how this genetic modification affects the pharmacokinetics of drugs, particularly antibiotics, has never really been studied. Overall, this prolonged rearing period exposes farms to significant economic losses in the event of disease outbreaks that requires a re-evaluation of practices, particularly with regard to the use of drugs. Finally, global warming is a source of concern for trout farming, both because of reduced access to surface water and because of the emergence of new diseases.

Although increased biosecurity measures and vaccination have reduced the prevalence of bacterial diseases in trout farms, antibiotics

<footnote><sup>a</sup> ANSES, French Agency for Food, Environmental and Occupational Health & Safety, Experimentation, Modelling and Data Analysis Unit, Fougères Laboratory, 35306 Fougères CEDEX, France</footnote>

<footnote><sup>b</sup> Oniris, INRAE, BIOEPAR, 44300 Nantes, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: alexis.viel@anses.fr (A. Viel).</footnote>
are still needed in some situations like for other animal productions.

Among them, tetracyclines remain one of the most widely used classes of antibiotics in aquaculture (Leal et al., 2018). Oxytetracycline (OTC) is usually used as a first-line antibiotic in fish farming, for many reasons. First, this molecule has a very broad spectrum of activity, including Gram-positive bacteria (such as the bacterium responsible for the emerging disease lactococcosis), Gram-negative bacteria (such as *Aeromonas salmonicida* subsp. salmonicida the cause of furunculosis, *Yersinia ruckeri*, responsible for enteric redmouth disease, *Flavobacterium psychrophilum*, responsible for cold water bacterial disease, or *Vibrio* spp., responsible for vibriosis) and alpha-proteobacteria (the strawberry disease, thought to be caused by a member of the rickettsial family, is treated with tetracyclines) (Lloyd et al., 2011; Reimschuessel et al., 2013; Verner-Jeffreys and Taylor, 2015). In addition, its low price is compatible with the profitability of fish farms. The OTC is also very well tolerated in trout (Leal et al., 2018; Reimschuessel et al., 2013). Finally, this compound is classified by AMEG (AntiMicrobial Expert Group) in category D, the preferred category for first-line treatment in veterinary medicine according to the European Medicines Agency (EMA, 2019).

Unfortunately, the recommended OTC dosage regimen for trout is based on rather old and limited data. They have been determined on the basis of an average of pharmacokinetic variables, without taking into account certain specific characteristics of trout (variability within the population, influence of water temperature, ploidy or fish behaviour, etc.), which was the classical approach in the past (Lees et al., 2021). As a result, the dose recommended by the marketing authorisation in France, established more than 30 years ago, is 55 mg/kg/day for 7 to 10 days (SPC, n.d.). However, the doses recommended in the literature are much more variable, ranging from 10 to 150 mg/kg/day and from 1 to 15 days of treatment (Leal et al., 2018; Reimschuessel et al., 2013). The use of inappropriate doses of antibiotics for curative or metaphylactic treatment poses several risks (i) to the fish industry itself, through the selection of antibiotic-resistant pathogenic bacteria that could endanger fish farms; (ii) to public health, through the spread of antibiotic-resistant genes to humans (food or environmental contamination). A population PK/PD approach is needed to re-evaluate the dosing regimen of this antibiotic in trout, as this is the only approach that can guarantee both maximum bacteriological cure and limited development of resistance (Toutain et al., 2002). With regard to the pharmacokinetics of OTC in trout, the data available in the literature are highly variable and relate to a variety of experimental conditions (test temperature, animal weight, ploidy, etc.). Overall, there is a significant half-life of about 10 days at temperatures below 10 °C and about 3 to 5 days at temperatures between 10 and 16 °C, although there is considerable variation between studies (Reimschuessel et al., 2005). Antibiotics are mainly administered to fish orally via medicated feed. For this route of administration, the bioavailability in trout appears to be fairly low, with values of 2.6 % at 7 °C (Rogstad et al., 1991), 2.8 % at 9 °C (Corum et al., 2023), 5.6 % at 16 °C (Bjorklund and Bylund, 1991) and 30 % at 11 °C (Abedini et al., 1998).

The objective of this study is to conduct a population pharmacokinetic (PopPK) study in rainbow trout to better characterise the behaviour of this molecule in fish, as a first step in re-evaluating the dosing regimen. This study used repeated sampling of fish in a cross-over design. This longitudinal monitoring and the use of a population modelling approach allowed better characterisation of inter-individual variability (Bon et al., 2018), which is rarely used in fish due to the difficulty of repeated sampling. All fish were dosed intravenously for the determination of absolute PK parameters. Oral administration through two different procedures (gavage and spontaneous feeding) allows characterisation of bioavailability and leaching, since in this study, as in most European fish farms, the antibiotic was coated on the feed. Finally, PopPK modelling allows to study the effect of covariates such as body weight, temperature or ploidy.

## 2. Material and methods

### 2.1. Animals and environmental conditions

Rainbow trout (*Oncorhynchus mykiss*) were purchased from the Monts d'Arrée Experimental Fish Farm (PEIMA) of the National Research Institute for Agriculture, Food and the Environment (INRAE) in Brittany (France). Two hundred and sixteen trout (162 triploid and 54 diploid) were included in the experimental protocol. Eighty-four additional trout from the same batch were acclimatised in parallel as a precaution for potential fish replacement. These were either triploid female trout, as these are the batches mainly reared in trout farms, or diploid trout, mixed males and females, as it is not always possible to distinguish between them at this age. No significant effect of sex on the PK of oxytetracycline is expected. At this weight (300 g), the animals are considered to be physiologically close to animals of a higher weight (excluding the period of gametogenesis).

The experiment took place at the Oniris Aquaculture Experimental Station, approved for the use of animals for scientific purposes under number E44272. The aquaculture station operates a recirculated water system. Dedicated probes were used to continuously monitor water parameters such as temperature (±1 °C), $O_2$ (90–100 %) and flow rate (2 m³/h). Water quality (pH, nitrite and nitrate levels) was checked every week. Competent and trained staff observed animals at least daily. Several thresholds linked to animal welfare were defined in terms of the environmental parameters of the farm (temperature, oxygen, water quality) and the health of fish (observation of apathetic or anorexic animals, animals with erratic swimming, skin lesions larger than 1 cm², abnormal response to stimulation or severe bilateral exophthalmos). When these thresholds were reached, a compassionate euthanasia was carried-out by overdosing with an anaesthetic (benzocaine 80 mg/L (Sigma-Aldrich, 38297 Saint Quentin Fallavier, France)). This study was approved by the Ministry of Higher Education, Research and Innovation in France and registered under the reference APAFIS #37991-2022071317028847 v4.

On arrival, the fish were acclimatised for 3 weeks at 16 °C (±1 °C) in three 1000-itre fibreglass tanks. Fish were separated following their genetic profiles (diploids vs triploid). Then, they were randomly allocated in groups of 9 and placed into twenty-four different 200-litre fibreglass tanks. Each fish was identified by a microchip and an additional period of 2 weeks of acclimatisation was done before the start of the study. In these tanks, the density varied between 15 (at the beginning) and 25 (at the end) kg/m³ due to weight gain. Environmental enrichment was provided with permanent tubes to allow the fish to hide. The average weight of the animals at the time of allocation was 310 g (CV = 12 %). Fish received standard 4 mm semi-floating NEO 19 CDC pellets (Le Gouessant, Lamballe, France), once a day at a rate of 1 % of biomass at 16 °C. One day a week, the fish were not fed. During the second washout period which lasted 5 weeks (see 2.2), the water temperature was gradually reduced from 16 °C to 10 °C over a period of about 3 weeks. The fish were then allowed to acclimatise to the new temperature for two weeks. At the same time, the rationing rate was reduced to 0.7 %. The average weight of trout per tank over the course of the study is shown in Table S1.

### 2.2. In vivo experiment

#### 2.2.1. Experimental design

The experimental study was carried-out at two successive water temperatures, 16 °C and 10 °C (±1 °C). Each tank of 9 fish was involved in 3 different PK experiment with OTC (PK1 to PK3), each separated by a wash-out period of 5 weeks (cross-over design) – see Fig. 1. Different route of administration were used: intravenous (IV), oral by spontaneous intake (ORsp), oral by gavage (ORgav). In triploid fish, to assess dose linearity, different doses were tested by IV administration: 8 mg/kg (dose G), 15 mg/kg (dose A), 30 mg/kg (dose B) and 60 mg/kg (dose C),
<figure><img src="image_3.png" /><figcaption>Fig. 1. Experimental design of the trial with the 3 successive PK phases held at different water temperatures. BS: blood sample.</figcaption></figure>

and oral administration: 50 mg/kg (dose D), 90 mg/kg (dose E) and 150 mg/kg (dose F). For diploid fish, only the median doses were tested (30 mg/kg by intravenous route, 90 mg/kg by oral route) – see Table 1. We considered that the linearity of the pharmacokinetics was not affected by ploidy. This allowed us to limit the number of fish used in this study. Table 1 gives a breakdown of the procedures tested per tank.

Due to unexpected mortality after PK1, mainly in fish treated intra-
venously at the highest dose, 65 trout were used (51 triploids and 14
diploids) to replace the dead animals between PK1 and PK2. Similarly,
12 trout were euthanised but not replaced between PK2 and PK3, due to
a lack of additional triploid fish. In order to ensure a homogeneous
distribution of modalities, the experimental procedures were allocated
to the different tanks for PK3 taking into account the number of sur-
viving fish. This meant that for most of the fish, blood samples had been
collected for the 3 successive PK experiments, but for a minority of
animals, kinetics only included PK1 + PK2 or PK2 + PK3.

2.2.2. OTC administration

For oral administration, in-house medicated feed was prepared as
follows: an oxytetracycline hydrochloride powder (TETRAVETO, BIOVE
Laboratory, 62510 Arques, France, Lot N°0211919) was coated onto the
feed before administration to the animals. Briefly, diet and OTC powder
were mixed using a tilting head stand mixer with a flat paddle at low
speed for 10 min until a visually homogeneous mixture was obtained.
Cod liver oil (Huile de foie de morue Cooper, Cooperation Pharmaceu-
tique Française, 77020 Melun, France) was then gradually added at a
rate of 20 mL/kg of feed and distributed throughout the bowl and the
mixture was again mixed at low speed for 15 min. The whole mixture
was placed in a dark place at room temperature for about 12 h to ensure
better adsorption to the diet. Medicated feed preparations were made
3-4 days before administration to the fish and stored at +4 °C. Four to
five samples were randomly taken from each preparation to assess the
homogeneity of the mixture and determine the actual amount of anti-
biotic distributed to the animals (see 2.4). Depending on the dosing
group, (theoretical) coated concentrations of antibiotic ranged from
5000 to 22,500 µg/kg of feed.

Regardless of the route of administration, animals were systemati-
cally fasted for 24 h prior to antibiotic administration. Medicated feed
was administered orally in two different ways. For spontaneous intake,
the medicated feed was distributed directly into the tanks similarly to a
classical distribution of feed in farm. This intake was timed and moni-
tored, with any refusals weighed (there were no refusals). Spontaneous
feeding lasted only a few minutes.

For tube feeding (gavage), the coated feed is administered under
general anaesthesia. To achieve this, the fish are immersed in a tricaine
methanesulfonate bath at 80 mg/L for 5–10 min until stage 4 anaes-
thesia is achieved (Carter et al., 2011). This concentration is obtained by
diluting tricaine powder from Sigma-Aldrich (Saint Quentin Fallavier,
France) directly in water. Then, 3 g (±0.2 g) is placed directly into the
stomach of the fish using a cannula, i.e. a syringe designed for the
administration of Doliprane drinkable suspension (Opella Healthcare,
Neuilly sur Seine, France), the end of which has been cut off. The syringe
is gently withdrawn, massaging the lower stomach in the direction of the

feed voucher. The fish is then placed alone in a 5-L bucket to monitor its
awakening and to count each pellet expelled. If any pellets have been
expelled, they are counted but not replaced. When the fish is fully
awake, it is returned to its group tank.

The intravenous dose was administered under general anaesthesia (following the same protocol as for tube feeding). The injectable solution was prepared from oxytetracycline powder (Sigma-Aldrich, 38297 Saint Quentin Fallavier, France, Lot N°0000111843) diluted in ppi water. The solution was slowly injected into the tail vein with a puncture along the ventral midline behind the anal fin. However, different procedures were used for PK1 and for PK2 and PK3, because the fish were less tolerant to intravenous administration of oxytetracycline than expected (see *Results*). Thus, only 0.1 mL was injected into each fish for PK1, whereas more diluted solutions were preferred for PK2 and PK3, with an injected volume of 0.2 mL. Similarly, the highest dose (dose C at 60 mg/kg) was not used for PK2 and PK3, but a lower dose of 8 mg/kg (dose G) was preferred. Finally, the injectable solution for PK1 was prepared in advance and stored at +4 °C until administration, whereas for PK2 and PK3 it was prepared within 15 min of administration and stored at room temperature. All these measures significantly improved the fluidity of the injectable solution and the tolerance of the fish to this route of administration.

2.2.3. Blood sampling

For each fish included in the study, 3 individual blood samples were taken over a period of 11 days, for each PK phase, in order to get an individual kinetic profile. In the final experiment (PK3), a fourth individual blood sample was taken from several fish just before being euthanised. In the same tank, fish were sampled at different times (unbalanced sparse sampling) to get the whole pharmacokinetic profile. A washout period of at least 4 weeks after the end of the sampling period (2 weeks) was applied between each sampling series, mainly to ensure that the fish had regained a normal haematocrit, as complete washout is not required for population PK modelling (Viel et al., 2021).

For each sample, each fish was captured 1/2 h before blood sampling and placed in a holding tank for general anaesthesia (following the same protocol as for tube feeding and IV administration). A 0.4 mL blood sample was then collected from the caudal venous sinus at the intersection of the lateral line (1 mm below) and the virtual line connecting the posterior base of the dorsal fin to the anus. The syringe and needle used for sampling were heparinised beforehand with Heparine Choay 5000 IU/mL (Cheplapharm France, 92300 Levallois-Perret, FRANCE). The fish was then placed in a 5-litre recovery tank and observed until fully awake. It was then returned to its initial tank. Each blood sample was centrifuged at 2000g for 10 min at room temperature, and plasma was collected and stored at -20 °C before assay.

A minimum of 3 fish per dose group were sampled at each sampling
time that were for IV administration: 0.5 h, 1 h, 2 h, 4 h, 6 h, 12 h, 18 h,
24 h, 48 h, 4d, 7d, 9d, 11d; and for oral administration: 1 h, 2 h, 3 h, 4 h,
6 h, 8 h, 12 h, 18 h, 24 h, 48 h, 3d, 4d, 6d, 7d, 8d, 9d, 10d, 11d. For PK3,
additional samples were collected at the time of euthanasia, between 16
and 17 days after dosing, depending on the animal. All blood samples
were individual and not mixed. Synchronised chronometers placed in
<caption>**Table 1**</caption>

Overview of the experimental design for the 3 PK experiments, with the different doses, routes of administration, sampling times (d, day) and water temperature for each batch. Each tank contained 9 fish.

<table><thead><tr><th rowspan="3">Batch number</th><th rowspan="3">Triploids</th><th colspan="3">PK phase & temperature</th></tr><tr><th>PK 1</th><th>PK 2</th><th>PK 3</th></tr><tr><th colspan="2">16 °C</th><th>10 °C</th></tr></thead><tbody><tr><td></td><td>Tank 1</td><td>IV - dose A</td><td>ORgav - dose D</td><td>IV - dose A</td></tr><tr><td></td><td>Tank 2</td><td>IV - dose A</td><td>ORgav - dose D</td><td>ORgav - dose D</td></tr><tr><td></td><td>Tank 3</td><td>ORgav - dose D</td><td>IV - dose A</td><td>ORgav - dose E</td></tr><tr><td></td><td>Tank 4</td><td>IV - dose B</td><td>ORgav - dose E</td><td>IV - dose B</td></tr><tr><td></td><td>Tank 5</td><td>IV - dose B</td><td>ORgav - dose E</td><td>ORgav - dose D</td></tr><tr><td></td><td>Tank 6</td><td>ORgav - dose E</td><td>IV - dose B</td><td>ORsp - dose D</td></tr><tr><td></td><td>Tank 7</td><td>IV - dose C</td><td>ORgav - dose F</td><td>IV - dose G</td></tr><tr><td></td><td>Tank 8</td><td>IV - dose C</td><td>ORgav - dose F</td><td>ORgav - dose E</td></tr><tr><td></td><td>Tank 9</td><td>ORgav - dose F</td><td>IV - dose G</td><td>ORgav - dose F</td></tr><tr><td></td><td>Tank 10</td><td>IV - dose A</td><td>ORsp - dose D</td><td>IV - dose A</td></tr><tr><td></td><td>Tank 11</td><td>IV - dose A</td><td>ORsp - dose D</td><td>ORgav - dose F</td></tr><tr><td></td><td>Tank 12</td><td>ORsp - dose D</td><td>IV - dose A</td><td>ORsp - dose D</td></tr><tr><td></td><td>Tank 13</td><td>IV - dose B</td><td>ORsp - dose E</td><td>IV - dose B</td></tr><tr><td></td><td>Tank 14</td><td>IV - dose B</td><td>ORsp - dose E</td><td>ORsp - dose E</td></tr><tr><td></td><td>Tank 15</td><td>ORsp - dose E</td><td>IV - dose B</td><td>ORsp - dose F</td></tr><tr><td></td><td>Tank 16</td><td>IV - dose C</td><td>ORsp - dose F</td><td>IV - dose G</td></tr><tr><td></td><td>Tank 17</td><td>IV - dose C</td><td>ORsp - dose F</td><td>ORsp - dose E</td></tr><tr><td></td><td>Tank 18</td><td>ORsp - dose F</td><td>IV - dose G</td><td>ORsp - dose F</td></tr><tr><td rowspan="7">Diploids</td><td>Tank 19</td><td>IV - dose B</td><td>ORgav - dose E</td><td>ORgav - dose E</td></tr><tr><td>Tank 20</td><td>IV - dose B</td><td>ORgav - dose E</td><td>IV - dose B</td></tr><tr><td>Tank 21</td><td>ORgav - dose E</td><td>IV - dose B</td><td>ORgav - dose E</td></tr><tr><td>Tank 22</td><td>IV - dose B</td><td>ORsp - dose E</td><td>ORsp - dose E</td></tr><tr><td>Tank 23</td><td>IV - dose B</td><td>ORsp - dose E</td><td>IV - dose B</td></tr><tr><td>Tank 24</td><td>ORsp - dose E</td><td>IV - dose B</td><td>ORsp - dose E</td></tr><tr><td>Time of individual blood sampling (at least 3 fish per dose group per time)</td><td></td><td colspan="2">IV: 0.5 h, 1 h, 2 h, 4 h, 6 h, 12 h, 18 h, 24 h, 48 h, 4d, 7d, 9d, 11d.<br>Oral: 1 h, 2 h, 3 h, 4 h, 6 h, 8 h, 12 h, 18 h, 24 h, 48 h, 3d, 4d, 6d, 7d, 8d, 9d, 10d, 11d</td><td colspan="2">Same sampling times + 16 or 17d</td></tr></tbody></table>

IV: intravenous; ORsp: spontaneous intake; ORgav: gavage.

various key areas of the aquaculture station allowed injection and sampling times to be recorded to the minute for each series of samples taken over 15 days.

## 2.3. Protein binding of oxytetracycline in plasma

The ultrafiltration method was used to determine the unbound fraction (fu) of OTC in plasma, based on a method previously validated (Vegas Cúmitre et al., 2021). Briefly, frozen plasma samples from five different untreated trout were thawed, and each was supplemented with oxytetracycline (Sigma-Aldrich, Saint Quentin Fallavier, France) at concentrations of 0.1, 0.5, 5, 50 and 200 µg/mL. 100 µL of these supplemented plasma samples were transferred into a Pall Nanosep Omega 10 K ultrafiltration device. Then, 10 µl of potassium phosphate (1 M) buffer, at pH 7.5, was added. The samples were centrifuged (4000 rpm, 40 min, 16 °C) in an ultracentrifuge with a fixed-angle rotor. The ultrafiltrate was then stored at -20 °C until assay.

All experiments were performed in duplicate (technical replicates) for each of the five individual trout plasma samples.

## 2.4. Analytical method

### 2.4.1. Chemicals and reagents

Analytical or HPLC grade methanol, acetonitrile, ethyl-enediaminetetraacetic acid disodium dehydrate (Na₂EDTA) were purchased from Fisher Scientific (Loughborough, UK). Formic acid and isooctane were purchased from Merck (Darmstadt, Germany), and DMSO from Carlo Erba Reagents (Val de Reuil, France). Ultrapure water was obtained after purification through a Milli-Q IQ 7000 Ultra-Pure Water System (Merck, Molsheim, France).

Solutions of Na₂EDTA 20 and 100 were prepared with ultrapure water for plasma and medicated feed liquid-liquid extractions.

### 2.4.2. Oxytetracycline assay

Analysis was performed on an LC-MS/MS system composed of a Thermo Scientific Ultimate 3000 HPLC and UPLC system coupled to a TSQ Vantage triple quadrupole mass spectrometer (Villebon-sur-Yvette, France). Data were acquired and processed on the Xcalibur software (Version 2.2).

Stock standard solutions were prepared at 1 mg/mL for Oxytetracycline (OTC) and at 0.5 mg/mL for Tetracycline (TC) in methanol. All stock standard solutions were stored at -18 °C. For plasma samples, chromatographic standards were prepared by dilution of the OTC stock standard solution to obtain a range of concentration from 0.04 µg/mL to 250 µg/mL. For medicated feed samples, only one chromatographic standard was prepared at 200 µg/mL. For all these matrices, an internal standard solution of TC was prepared at 5 µg/mL. Chromatographic standards solutions were stored at 4 °C. Plasma extraction was carried-out following the method described previously (Santos-Santórum Suárez et al., 2022b) but was slightly modified due to the smaller amount of volume sample available (70 µL) and the larger range of concentration targeted. Briefly, 100 µL of Na₂EDTA 20 mmol/L were added to 70 µL of sample, which has been already spiked with 30 µL of internal standard and 70 µL of ultrapure water. After 10 min, 1 mL of HPLC acetonitrile was added before stirring for 10 min in a rotatory stirrer at 100 rpm. The sample was then centrifuged at 20,000 g for 5 min at 4 °C. The totality of the supernatant was transferred in another tube containing 50 µL of DMSO (to avoid complete evaporation and degradation of compound) and evaporated under nitrogen at 50 °C. The residue was resuspended with 250 µL of ultrapure water and vortexed to finally be filtrated through 0.45 µm filters and transferred in autosampler vials.

For medicated feed samples, the published method from Gaugain et al. (Gaugain et al., 2020) was used. Around 35 g of sample was first homogenized and ground to obtain a fine powder. Then, 1 ± 0.02 g of ground feed was weighed and 2 mL of ultrapure water and 200 µL of internal standard were added. After 10 min, 1 mL of Na₂EDTA 100
mmol/L was added. Then after 10 min, 10 mL of acetonitrile were added and the sample was stirred 10 min in a rotatory stirrer at 100 rpm before being centrifuged 5 min at 17,000 g at 4 °C. One milliliter of the supernatant was transferred into another tube and 10 mL of water were added. After being vortexed, 3 mL of isooctane were added and the tube was slowly agitated. After another centrifugation (5 min, 3500 rpm), 400 µL of the lower phase were filtered (0.45 µm) and transferred into autosampler vials.

LC-MS/MS conditions were the same for both type of samples. The separation was performed with a Kinetex Biphenyl column (100 × 2.1 mm, 2.6 µm, Phenomenex) protected by a C18 guard column (4 × 2 mm, Phenomenex). A gradient elution of two mobile phases (A: 0.2 % formic acid in water; B: 0.2 % formic acid in methanol) was used with initial conditions of 90 % of mobile phase A for 1 min which changes to 2 % from minute 1 to minute 3, and then goes back to 90 % after minute 3.1 until the end of the run at 7 min. The column was maintained at 28 °C and the flow rate was fixed at 0.350 mL/min.

The analytical method performances (trueness, precision) were assessed using an approach based on total error (accuracy profile) (Santos-Santórum Suárez et al., 2022a; Tardiveau et al., 2021). The e-
noval software (version 4.1, Arlenda, Liège, Belgium) was used to
perform this assessment. The validation protocol and analytical method
performances are detailed in the supplementary materials. Briefly, for
all matrices, a quadratic regression (1/X) model was selected as cali-
bration curve. The β tolerance interval established at 80 % was inside the
acceptance limits and consequently the method was validated for both
matrix. Limit of quantification (LOQ) were determined at 0.039 µg/mL
in plasma and at 20 µg/kg in medicated feed.

2.5. Data analysis

2.5.1. Population PK model development

All individual plasma data were analysed using a non-linear mixed effect (NLME) approach with Monolix (Monolix 2024R1, Lixoft SAS, Simulations Plus) in order to get a population PK model with estimations of primary PK parameters and their associated variabilities, as performed previously with another antibiotic on rainbow trout (Viel et al., 2021). Data below the LOQ but above the LOD were kept in the dataset and treated as censored data thanks to the M4 method (Ahn et al., 2008).

In the dataset, the individual amount of OTC administered to each
fish was determined as follows: (i) for the IV route, the injected volume
was converted to an amount of OTC; (ii) for the oral administrations, the
measured concentrations in feed (see Results - 3.1) were used to correct
the theoretical dose; (iii) additionally, for the spontaneous feeding, the
expected amount of pellets ingested by each fish (and therefore the
amount of OTC) was calculated based on individual bodyweight and
feeding rate (1 % of the bodyweight at 16 °C, and 0.7 % at 10 °C).

First, only data obtained after IV administrations were analysed in order to select the best structural model (number of compartments) and to obtain good initial estimates of the main PK parameters (clearance and volumes). The best structural model was chosen thanks to several diagnostic plots (observed value vs predicted value, scatter plots of residuals, NPDE). The selection between different structural models was based on a decrease of the corrected Bayesian Information Criteria (cBIC). Different error models were tested (additive, proportional and combined).

All data (both after IV and oral administrations) were then combined into a unified dataset and analysed simultaneously. The structural model was modified to account for oral absorption of OTC (rate constants and bioavailability parameters). All parameters were estimated based on the final structural model, including those that were previously estimated with the IV data.

A log-normal distribution was assumed for all parameters except
those related to bioavailability (logit-normal distribution). Wherever
possible, inter-individual variability (IIV) and inter-occasion variability
(IOV) were estimated for each parameter, corresponding respectively to

between-subject variability and within-subject variability. In our
experimental model, an occasion is defined as the period of time
following a new administration of the drug; therefore, each individual
fish had a maximum of 3 successive occasions (PK1, PK2 or PK3 - see
2.2.2 for the experimental design). Individual parameters may thus vary
from occasion to occasion.

The COSSAC method (Ayal et al., 2021) implemented in Monolix was used to find the relevant parameter-covariate relationships that could explain part of the IIV or IOV. Ploidy (diploid vs triploid) was the only discrete covariate. Bodyweight, drug amount and water temperature were continuous covariates and were scaled to the median value of each of them, i.e. 389 g, 37 mg/kg and 13 °C respectively. The full model for a parameter following a log-normal or logit-normal distribution is described in Eqs. (1) and (2), respectively:

$$
\begin{equation}
\begin{split}
\log(X_{ik}) = \log(X_{pop}) &+ \beta_{X_{\text{ploidy-D}}} + \beta_{X_{\text{TEMP}}} \times \log\left(\frac{\text{Temp}_i}{13}\right) \\
& + \beta_{X_{\text{AMOUNT}}} \times \log\left(\frac{\text{Amount}_i}{37}\right) + \beta_{X_{\text{BW}}} \times \log\left(\frac{\text{BW}_i}{389}\right) + \eta i + \Upsilon_{ik}
\end{split}
\tag{1}
\end{equation}
$$

$$
\begin{equation}
\begin{split}
\log\left(\frac{Xik}{1 - Xik}\right) ={}& \log\left(\frac{Xpop}{1 - Xpop}\right) + \beta_{X_{\text{ploidy-D}}} + \beta_{X_{\text{TEMP}}} \times \log\left(\frac{\text{Temp}_i}{13}\right) \\
& + \beta_{X_{\text{AMOUNT}}} \times \log\left(\frac{\text{Amount}_i}{37}\right) + \beta_{X_{\text{BW}}} \times \log\left(\frac{\text{BW}_i}{389}\right) + \eta i + \Upsilon_{ik}
\end{split}
\tag{2}
\end{equation}
$$

where Xik is the value of parameter X of individual i for occasion k; Xpop is the population value of parameter X; βXploidy-D is the value associated to the categorical covariate diploidy; βXTEMP, βXAMOUNT and βXBW are the values associated to the scaled covariate temperature (Temp), drug amount (Amount) and bodyweight (BW) for individual i; ηi the random effect (IIV) for individual i and Yik the random effect of individual i for occasion k (IOV).

When any β value was significantly different from zero, the
parameter-covariate relationships was kept in the model.

The covariate relationship with drug amount was only tested for parameters related to clearance and bioavailability (see Results, 3.3).

Several secondary parameters were computed based on the Empirical Bayes Estimates (EBE) given by the model, such as the terminal half-life (based on the equation given in (Toutain and Bousquet-Melou, 2004b)) and the area under the curve from 0 to infinity (AUC₀ Inf).

The dose-linearity was assessed by fitting a power model between the administered dose and the AUC₀ₗ, split by water temperature. The slope (β1) and its associated 90 % confidence interval (CI) were compared to the reference interval as proposed in (Smith et al., 2000), with a ratio of maximal to minimal dose called r, and lower and upper acceptance limits equals to 0.8 and 1.25, respectively.

2.5.2. Population PK model internal validation

An internal validation of the final model was done first based on classical goodness of fit (GOF) plots: observations (OBS) versus predictions (at the individual (IPRED) and population (PRED) level), individual weighted residuals (IWRES) versus time or versus IPRED, normalized prediction distribution errors (NPDE) versus time or versus PRED. Finally, prediction-corrected visual predictive checks (pcVPC) were generated (Bergstrand et al., 2011). Briefly, n = 500 simulations were carried out from the initial dataset, and the 10th and 90th percentiles (with their respective 90th confidence intervals) were plotted against the (corrected) observed data. The uncertainty of the parameter values was refined using a parametric bootstrap method (as implemented in Monolix) with 100 replicates, to get the 95 % confidence interval for each estimated parameter.

2.5.3. Population PK model external validation

To test the predictive ability of the model, simulations from the model were compared with independent (external) PK data of OTC in
rainbow trout that were not used during model development. For that purpose, data were extracted from the literature from two previous studies: (i) data from Miller et al., with fish raised at 12 °C with a mean BW of 172 ± 44 g that were administered orally (gavage) with medicated feed at a dose of 75 mg/kg/d for 10 days (Miller et al., 2012). Mean (and sd – standard deviation) concentration values were extracted thanks to WebplotDigitizer (Rohatgi, 2018); (ii) data from Corum et al., with fish raised at 9±0.8 °C with a mean BW of 155 ± 15 g that were administered orally (gavage) with medicated feed at a dose of 60 mg/kg/d for 7 days (Corum et al., 2023). Concentration values were directly accessible within the manuscript. Due to lack of information, fish were considered as being diploids for both studies.

Based on the final pop PK model, Monte Carlo simulations were performed using Simulx (Simulx 2024R1, Lixoft SAS, Simulations Plus) taking into account the experimental design of each study as described above as well as the uncertainty of parameters after the bootstrap analysis. For each scenario, 100 replicates (one replicate corresponds to a random sampling of parameter values within their uncertainty distribution) of 1000 concentration curves (representing a virtual population of 1000 different fish) were generated (therefore a total of n = 100,000 individual curves). Then, the 90th prediction interval of all these simulations was plotted against the extracted data for visual comparison.

# 3. Results

## 3.1. Medicated feed analysis

The measured concentrations in the medicated feed varied from 42 % to 73 % of the expected concentration. The higher the theoretical concentration, the greater the difference with the measured concentration (Fig. 2).

The measured values were used to correct for the actual amount of OTC administered per individual in the PK modelling dataset. Therefore, taking into account these corrected values, the individual BW and the feeding rate, the actual oral dose ranges (min-max) were 25–45 mg/kg, 37–75 mg/kg and 50–110 mg/kg for the theoretical oral dose groups of 50, 90 and 150 mg/kg, respectively.

## 3.2. Protein binding

Results from the protein binding experiments are presented in Fig. 3. There was no significant difference of the free fraction (fu) value for the total concentrations ranging from 0.1 to 50 µg/mL. However, at the

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Measured OTC concentrations vs theoretical OTC concentrations in feed. Each blue point represents the mean (and the associated sd) of 4 to 5 different samples from the same batch of medicated feed (n = 11 batches). The blue line is the regression line with the R² coefficient. The dashed black represents the line of identity. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

highest concentration of 200 µg/mL, there was a significant decrease in the free fraction (p < 0.05, one-way ANOVA including Holm correction for post-hoc analysis). Excluding this highest concentrations (with no *in vivo* relevance), the average value of the free fraction was 47.7 % (equivalent to 52.3 % of protein binding).

## 3.3. *In vivo* study and popPK modelling

All dosing regimens were well tolerated by the fish except the highest dose (dose C) following intravenous injection (see 2.2.2). The IV solution prepared for PK1 was probably too concentrated and lacked sufficient fluidity, resulting in increased inflammation around the injected area, close to the spine, which caused high mortality. As a result, some fish failed to emerge from anaesthesia, others showed severe general impairment requiring euthanasia (erratic swimming, poor buoyancy management, loss of balance) and still others, weakened by the procedure, fell victim to an opportunistic fungus (*Saprolegnia* spp.) in the days following administration. The mortality rate for this first administration was very high, reaching almost 24 % of the fish. Only animals that were given intravenous injections were affected, with up to 47 % of animals at the highest dose. The measures taken for PK2 and PK3 (see Section 2.2) reduced this mortality to only 4 % of the animals.

There was no refusal or slowing of food intake during spontaneous intake at any of the proposed OTC concentrations, highlighting no difficulties related to the palatability of the drugs. After gavage, very few fish regurgitated pellets, usually in very small quantities (<3 pellets). The doses administered were corrected for these regurgitated pellets.

A total of 1663 plasma data were analysed after removing 91 results due to irrelevant values considered as outliers. In this dataset, 3 % (51 samples) were below the LOQ following oral administration, most of them after spontaneous feeding with medicated feed (Fig. 4). After IV administration, OTC was quantifiable at all doses up to the last collection time point (400 h p.a.). After oral administration, an early peak was observed within 3 h after administration, but at different levels depending on whether administration was by gavage or spontaneous administration (see Fig. S1). A secondary peak was observed for both types of administration around 24 h–48 h after dosing.

Based on the shape of the IV data, a two-compartment and a three-compartment model were tested; the bi-compartmental one gave a better fit and was kept as the final structure (see Fig. 5). For the oral route, two absorption phases were required to describe the early peak: a first fraction of the dose was absorbed with a rapid rate constant (*ka1*), and the remaining fraction was absorbed with a delay (*Tlag*) and a slower rate constant (*ka2*). The absolute bioavailability of OTC (*Foral*) after oral administration could be estimated by comparison with the IV data. An additional correcting factor for the actual amount ingested was also estimated for spontaneous intake *via* medicated feed (Fsp, Fig. 5). This parameter took into account the potential loss of OTC (i.e. leaching into the water) and the potential competition for food access between fish, which could lead to deviations from the expected amount of OTC ingested.

All model parameters with their estimated values including IIV and IOV are summarized in Table 2. All parameters were well estimated (narrow 95 % confidence intervals after bootstrap analysis, slightly larger for beta parameters and random effects), but the early absorption rate (*ka1*) had to be fixed to an arbitrary high value due to convergence problem. Variability at the individual level (IIV) and/or occasion level (IOV) could be estimated for all estimated structural parameters except *ka1*.

Fig. 6 represents the pcVPC plots for the different routes (IV, gavage and spontaneous intake). These plots supported the choice of a bi-compartmental model and the two successive absorption phases with no major misspecifications between observed and simulated data. This was also confirmed with the other GOF plots (see Figs. S2–S3).

The value of body clearance for a typical individual of this study (triploid, BW = 389 g, water temperature = 16 °C) was estimated at
<figure><img src="image_5.png" /><figcaption>Fig. 3. Free fraction (fu) of OTC) for different levels of OTC concentrations represented as the mean (±sd) values from 5 different individual trout plasma.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. Raw data of OTC plasma concentrations after IV or oral (gavage and spontaneous) administrations. Each colour represents a different (theoretical) dosing regimen. The dashed line is the LOQ and all data below this line have been assigned to the LOQ value (red dot) for graphical purpose. IV: intravenous, GV: gavage, SP: spontaneous intake. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Final structural PK model.
All parameters are described in Table 2. IV: intra-venous.</figcaption></figure>

20.8 mL/h/kg (Table 2). The bodyweight had an effect on clearance: an increase of 10 g compared to the median bodyweight (389 g) increased the clearance value of 3.5 % (and vice versa for a decrease in body-weight). As expected, the decrease in water temperature from 16 to 10 °C induced a decrease of the clearance of about 32 % (14.1 mL/kg/h). Diploidy also had an impact on clearance but to a lesser extent with a decrease of about 12 % (see Table 2). The relationship between clearance, BW, ploidy and temperature as given by our popPK model is illustrated in Fig. S4. The bodyweight had also a significant impact on the peripheral volume, with a positive correlation.

The absolute bioavailability after oral administration was dose-
dependent (negative correlation): indeed, the lowest dose (25 mg/kg)
and the highest dose (110 mg/kg) in this study correspond to a typical
bioavailability of 3.5 % and 2.2 %, respectively. Overall, the oral
bioavailability was very low (3.1 %), with individual values ranging
from 1.4 % to 6.7 %. Regarding the spontaneous intake of medicated
feed compared to gavage, it was estimated that only 70.5 % (median
value) of the initial dose coated on the feed was actually accessible to the
fish after ingestion (Fsp), which most likely corresponds to a loss due to
leaching (see Discussion). This parameter Fsp was however very variable
with individual values ranging from 35 % to 112 % (half of the fish with
values between 60 and 73 %). The fraction of the dose (Frac1) given by
gavage that was early absorbed with the (fixed) high rate constant ka1
was also dose-dependent (positive correlation): typical values ranged
from 18 % to 35 % for the lowest and highest dose, respectively; with the
same doses, this fraction was greatly reduced to 4–9 % when OTC was
absorbed spontaneously. The remaining dose fraction was absorbed
following a much slower process (ka2 = 0.038 h⁻¹) and after a delay
(Tlag) of about 9 h at 16 °C and about 11 h at 10 °C.

The linearity of OTC PK was only assessed after IV administration, because non-linearity (or dose-dependency) was already observed after oral administration as described above. The average maximal to minimal dose ratio (r) was equal to 3.59 and 4.02 for the experiments at 10 °C and 16 °C, respectively. Over this dose range, after fitting with the power model, a dose-proportionality could not be rejected for 10 °C (β1 = 1.08, 90 % CI = [1.06; 1.09], Suppl Fig. 5) but the result was inconclusive for 16 °C (β1 = 1.15, 90 % CI = [1.12; 1.19], Suppl Fig. 5). Indeed, for the latter case, although being very close, the confidence interval was not completely included within the reference interval. However, during the popPK model development, no significant relationship between the covariate “dose amount” and the clearance could be found, meaning that linear elimination best fitted the data.

Finally, an external validation of the popPK model was carried-out
against independent published data obtained after repeated oral

dosing with OTC (Fig. S6). Data from Corum et al. (Corum et al., 2023) were slightly under-predicted during the absorption phase but were overall well included within the prediction interval (Fig. S6-A) whereas data from Miller et al. (Miller et al., 2012) were clearly over-predicted by the model (Fig. S6-B). The terminal slopes of these PK data after repeated administrations were rather well predicted by the model, strengthening the hypothesis of a linear clearance, i.e. not dose-dependent.

4. Discussion

This study is the first to use a population PK modelling approach to
describe the pharmacokinetics of OTC in rainbow trout. This allowed a
detailed description of the influence of the different routes of adminis-
tration, in particular one that mimics fish farming practice, i.e. sponta-
neous ingestion of feed coated with an antibiotic. It also quantified the
effect of major covariates such as water temperature or ploidy status
despite the fact that the data were sparse (at the individual level) and
unbalanced (Toutain, 2024). For the following discussion about PK
analysis, results are given for a typical individual of this study (triploid
fish of 389 g reared in a water at 16 °C), unless otherwise stated.

The intravenous administration was necessary to estimate the ab-
solute bioavailability for the oral routes of administration and to obtain
primary PK parameters such as body clearance. The typical values for
clearance at 10 °C and at 16 °C were equal to 14.1 mL/h/kg and 20.8
mL/h/kg, respectively. The oral bioavailability was found to be
extremely low with a range (min–max) of 1.4 %–6.7 %. These values are
in very good agreement with other studies that also conducted IV and
oral administrations of OTC under similar experimental conditions (and
considering the fish as diploids). Indeed, in a recent PK study with OTC
given at 60 mg/kg in rainbow trout (mean BW = 155 g), reared at 9 ±
0.8 °C, the mean values for clearance and bioavailability were 8.09 mL/
h/kg (our popPK model predicts a median value of 9.8 mL/kg/h for this
BW, see Suppl Fig. 4) and 2.80 %, respectively (Corum et al., 2023). In
another study conducted at 16 °C with OTC doses of 20 mg/kg by IV, and
75 mg/kg by oral administration, the average body clearance and
bioavailability of OTC for trout (mean BW = 541 g) were estimated to be
16.2 mL/h/kg (our model predicts a median value of 20.2 mL/kg/h for
this BW, see Suppl Fig. 4) and 5.6 %, respectively (Bjorklund and
Bylund, 1991).

Our data were best described by a bi-compartmental model, as out-
lined by the VPC and the satisfactory GOF plots (Fig. 6 and Figs. S2–S3).
Early publications on the PK of OTC in several salmonids (*Oncorhynchus
mykiss*, *Salmo salar*) after systemic administration proposed the same
<table><caption>**Table 2**
Parameters of the popPK model (see Fig. 5).</caption><thead><tr><th>Parameter (unit)</th><th>Symbol (unit)</th><th>Typical value (2.5%; 97.5% CI)</th><th>IIV as CV % (2.5%; 97.5% CI)</th><th>IOV as CV % (2.5%; 97.5% CI)</th></tr></thead><tbody><tr><td>Clearance</td><td>Cl (mL/h)</td><td>8.10<sup>a</sup><br>(7.66;8.56)</td><td>na</td><td>17.0<br>(12; 23)</td></tr><tr><td>Coefficient related to the effect of water temperature on Cl</td><td>beta_CL_TEMP</td><td>0.83<br>(0.71; 1.02)</td><td>–</td><td>–</td></tr><tr><td>Coefficient related to the effect of (scaled) bodyweight on Cl</td><td>beta_CL_logBW</td><td>1.01<br>(1.06; 1.50)</td><td>–</td><td>–</td></tr><tr><td>Coefficient related to the effect of being diploid on Cl</td><td>beta_CL_[ploidy=D]</td><td>-0.12<br>(-0.21; -0.044)</td><td>–</td><td>–</td></tr><tr><td>Central volume</td><td>V1 (mL)</td><td>161<br>(144; 176)</td><td>na</td><td>58<br>(45;69)</td></tr><tr><td>Coefficient related to the effect of bodyweight on V1</td><td>beta_V1_logBW</td><td>0.69<br>(0.168; 1.33)</td><td>–</td><td>–</td></tr><tr><td>Peripheral volume</td><td>V2 (mL)</td><td>650<br>(608; 698)</td><td>na</td><td>27<br>(11;36)</td></tr><tr><td>Coefficient related to the effect of bodyweight on V2</td><td>beta_V2_logBW</td><td>1.56<br>(1.35; 1.87)</td><td>–</td><td>–</td></tr><tr><td>Inter-compartmental clearance</td><td>Q2 (mL/h)</td><td>37.2<br>(33.3; 41.4)</td><td>44<br>(32;65)</td><td>na</td></tr><tr><td>Absolute bioavailability (for both oral administrations)</td><td>Foral (%)</td><td>3.10<br>(2.75; 3.54)</td><td>20<br>(14;28)</td><td>18<br>(12;25)</td></tr><tr><td>Coefficient related to the effect of (scaled) drug amount on Foral</td><td>beta_Foral_amt</td><td>-0.32<br>(-0.55; -0.082)</td><td>–</td><td>–</td></tr><tr><td>Fraction of dose actually available for absorption after spontaneous administration</td><td>Fsp (%)</td><td>70.5<br>(64.9; 79.4)</td><td>16<br>(8;25)</td><td>18<br>(9;29)</td></tr><tr><td>Absorption constant (early absorption)</td><td>ka1 (1/h)</td><td>500<br>(FIX)</td><td>na</td><td>na</td></tr><tr><td>Fraction of dose absorbed following ka1</td><td>Frac1 (%)</td><td>22.4<br>(18.7; 26.3)</td><td>28<br>(10;41)</td><td>41<br>(30;55)</td></tr><tr><td>Coefficient related to the effect of spontaneous administration on Frac1</td><td>beta_Frac1_SP</td><td>-1.62<br>(-1.88; -1.45)</td><td>–</td><td>–</td></tr><tr><td>Coefficient related to the effect of (scaled) drug amount on Frac1</td><td>beta_Frac1_amt</td><td>0.56<br>(0.20; 0.94)</td><td>–</td><td>–</td></tr><tr><td>Secondary absorption constant (delayed absorption)</td><td>ka2 (1/h)</td><td>0.036<br>(0.034; 0.043)</td><td>na</td><td>9<br>(3.6;20)</td></tr><tr><td>Lag-time between early and delayed absorption</td><td>Tlag (h)</td><td>9.2<sup>a</sup><br>(7.93; 10.2)</td><td>na</td><td>26<br>(15;37)</td></tr><tr><td>Coefficient related to the effect of water temperature on Tlag</td><td>beta_Tlag_TEMP</td><td>-0.87<br>(-1.2; -0.293)</td><td>–</td><td>–</td></tr><tr><td>Proportional component for the error model</td><td>b (%)</td><td>23<br>(20;26)</td><td>–</td><td>–</td></tr></tbody></table>

Parameters in bold font are related to the structural model whereas parameters in italic font described the significant parameter-covariate relationships. IIV: inter-individual variability. IOV: inter-occasion variability; CI: confidence interval; –: not concerned; na: not identifiable.

structural model, albeit giving different estimations of PK parameters (Bjorklund and Bylund, 1991; Dagoglu et al., 2004; Elema et al., 1996; Türel et al., 2003; Uno et al., 1997). Other authors fitted a tri-compartmental model to their PK data (Abedini et al., 1998; Grondel et al., 1989). A third phase could be hidden due to a limited number of sampling times either at the very beginning (early phase) or at the end (late terminal phase) of the PK, as well as due to an analytical method with a low sensitivity (high LOQ) (Toutain and Bousquet-Melou, 2004b). The high sensitivity of the analytical procedure used in the present study (LOQ = 40 ng/mL) and the abundance of data over a long period after OTC administration (11 to 15 days) give us great confidence in the relevance of the pharmacokinetic profiles obtained in the present study, and thus the choice of the bicompartmental model.

For most parameters, it was only possible to estimate either IOV or IOV but not both (except for Frac1, see Table 2). For parameters with only IOV, this variability actually includes both a between-subject and an inter-occasion variability, which was not easily distinguishable due to the sparse sampling design of this study (even if the total number of data was consequent).

Based on our final PK model, the terminal half-life for the typical individual was equal to 113 h at 10 °C, and 79 h at 16 °C, i.e. a decrease of ~30 %. This is in very good agreement with a previous study of OTC in rainbow trout reared at the same temperatures, where the decrease in half-life was about 22 % (Björklund and Bylund, 1990). As trout are

poikilothermic animals, the higher the temperature, the higher the clearance value, and thus the lower the half-life. The strength of the population PK approach is the ability to measure the magnitude of this (covariate) effect. Comparatively, the influence of ploidy, although significant, was much less important on clearance than the impact of temperature (see Table 2). This is similar to our previous population PK study with enrofloxacin in rainbow trout (Viel et al., 2021); however, the underlying reasons for the influence of genetic factors remain to be elucidated.

After gavage, an early peak was observed, followed by a delayed secondary peak (Fig. 4 and Fig. S1). This first absorption phase is important as it represents an estimated (median) dose fraction (Frac1) of 22.4 % (min-max of 10–45 %). When OTC was administered by spontaneous ingestion, this fraction decreased to about 6 % (min-max of 2–19 %) and could be negligible for most individuals from a therapeutic point of view. In terms of modelling, this double-peak profile was well described by two successive absorption processes (see pcVPCs in Fig. 6). However, the first rate constant ka1 had to be fixed to an (arbitrary) high value due to an estimation problem, probably due to the limited number of sampling times immediately after oral administration. An early peak has already been observed after oral administration with OTC in salmonids (Oncorhynchus mykiss, Salmo salar) (Pye-MacSwain, 1992; Uno et al., 1992) or in other fish species such as tilapia (Oreochromis spp.) (Sidhu et al., 2018). Entero-hepatic recycling is often proposed as a

<footnote>a Values corresponding to a water temperature of 16 °C.</footnote>
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Prediction-corrected visual predictive check plot for the final model, stratified by route of administration. Blue points represent the observed data, red dots represent the censored data at their simulated value. The dashed lines and the solid lines are the 10th, 50th (median) and 90th percentiles of the simulated values (predicted percentiles) and of the observed data (empirical percentiles), respectively. The area represents the 90 % confidence intervals around the 10th (blue), 90th (blue) and 50th (red) percentiles of the simulated values. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

possible explanation for this double (or multi) peak disposition for tet-
racyclines in fish, such as OTC (Ingebrigtsen et al., 1985; Sidhu et al.,
2018) or doxycycline in carp (Ctenopharyngodon idella) (Xu et al., 2019).
Modelling an enterohepatic recycling is complex and requires rich in-
dividual data (Okour and Brundage, 2017), which is often not possible
for fish such as trout. Furthermore, in our study, no double-peak profile
was observed after intravenous administration, which would preclude
the use of such a model (Davies et al., 2010). Finally, the first peak re-
mains very moderate after spontaneous ingestion, even though the OTC
coated feed was produced with the same protocol as the medicated feed
used for gavage. Although we cannot exclude the possibility of hepatic
recycling of OTC, this double peak should be due to differences in the
protocols used for gavage and spontaneous ingestion, particularly
related to anaesthesia and leaching of the drug. In fact, when using oil-
coated medicated feed, a significant proportion of OTC could easily
leach out of the pellets. This is reinforced by the fact that this fraction of
dose absorbed early (Frac1) was found to be dose-dependent (positive
beta parameter, Table 2), with a higher fraction when the dose increases.
Thus, immediately after gavage, this leaching of OTC occurs in the
stomach, and an early absorption process begins rapidly, which may be
exacerbated by the slowing down of the food bolus during and after

anaesthesia, explaining this first peak. Conversely, although sponta-
neous feed intake in trout is very rapid (a few minutes after the coated
feed has been distributed in the tank), leaching of OTC into the water
can occur, and this fraction of the dose (Frac1) is then largely lost before
being available for absorption by the fish. This would also explain the
difference in bioavailability observed between oral force-feeding and
spontaneous oral intake, with the estimated 27 % to 40 % of drug loss
(100 – Fsp, see Table 2) in the latter case. Rigos et al. have already shown
that for OTC, up to 42 % of the initial dose could be lost after only a few
minutes of contact with water at 16 °C (Rigos et al., 1999). The
remaining OTC fraction would then be absorbed more slowly in the
intestines, following the dissolution process, explaining the delayed
secondary peak. However, in previous PK studies using force feeding of
OTC to trout, this early peak was not observed (Bjorklund and Bylund,
1991; Corum et al., 2023). This difference could be due to either the first
sampling time being quite late after administration and/or the use of
OTC powder mixed into the feed, i.e. not coated on the surface of the
feed. The decision to use an antibiotic-coated feed in this study was
made to reflect the practices encountered in trout farming in some
countries of Europe.

According to our model, the bioavailability of OTC is dose-
dependent, with a decrease in its value as the dose increases (Table 2, negative beta parameter for Foral). Saturation of the absorption process (Michaelis-Menten equation) was tested, but this increased the complexity of the model (more parameters to estimate) without a better fit than the actual covariate relationship with the dose. For the recommended doses, such as 55 mg/kg (France) or 75 mg/kg (USA), this gives typical Foral values of 2.7 % and 2.5 %, respectively, thus with minimal impact on the PK profiles. However, the variability in oral bioavailability was high, with a range (min-max) of 1.4–6.7 %, meaning that the fish exposure (AUC) to OTC could vary by more than 4-fold, even though overall bioavailability remains very low. This is classically encountered with drugs having poor bioavailability, leading to under- or over-exposure of individuals, and challenging the choice of an optimal dose (Toutain and Bousquet-Melou, 2004a).

Moreover, despite the inconclusive result for the IV route at 16 °C (see Fig. S5), the dose-proportionality assessment, in conjunction with the selection of a structurally appropriate model, led to the conclusion that the elimination of OTC is linear over the wide range of doses and concentrations tested in this study. Corum et al. found a longer terminal t1/2 (about twice) for OTC in rainbow trout after an oral multiple-dose administration compared to an oral single-dose administration, a result they suggested was due to saturation of the elimination pathways (Corum et al., 2023). However, they also observed no difference in t1/2 after a single IV dose and a single oral dose (both 60 mg/kg), although plasma concentrations were about 10 to 100-fold higher in the IV study, contradicting this hypothesis of saturation. Actually, t1/2 is a hybrid parameter that depends on clearance and volume of distribution (Toutain and Bousquet-Melou, 2004b). A longer t1/2 may rather be due to an increase in volume of distribution caused by many factors, such as the growth of the animal (increase in the volume of the peripheral compartment such as adipose tissue) or a change in binding affinity to the tissue (hence a change in the unbound fraction in the tissues) (Toutain and Bousquet-Melou, 2004c). The best way to conclude about the linearity of OTC PK would be to get PK profiles at steady-state (ss), since the AUCss over a dosing interval should be equal to the AUC₀ₗₐₗ after a single administration (Yousef et al., 2024). However, steady-state is expected to be achieved after 4 to 5 times the half-life (Toutain and Bousquet-Melou, 2004b), and due to the very long terminal half-life for OTC in trout, this would mean (with our typical values) at least 13 days (312 h at 16 °C) or 18.5 days (448 h at 10 °C) of treatment.

We performed an external validation of our popPK model to assess its predictive ability i.e. to test the model's performance in a population sample different from the one used to develop the model (Cheng et al., 2021). This is rarely done, especially in veterinary medicine, whereas a major goal of a popPK model for antibiotics is to predict new scenarios and optimise dosing regimens for a better efficacy in clinical use (Boulanger et al., 2024). Unfortunately, other published PK studies with spontaneous intake of OTC in rainbow trout under field conditions have primarily focused on residue depletion (San Martín et al., 2021) but without any PK plasma data that would enable external validation of our model using field data. We thus selected 2 recent PK studies with repeated oral dosing (by gavage) of OTC in trout (Corum et al., 2023; Miller et al., 2012). The simulations showed that our popPK model accurately predicted the terminal slopes, supporting the choice of the bi-compartmental model. However, we also observed a slight under-prediction of the data from Corum et al., and a clear overprediction of the data from Miller et al. We expected a discrepancy, as these two studies already had discordant results. Indeed, Miller et al. obtained a lower Cmax (~1 µg/mL) compared to the results of Corum et al. (7.82 µg/mL), despite using higher doses (75 vs 60 mg/kg), and a longer duration of administration (10 vs 7 days). The water temperature was also 2 °C higher in Miller's study, but this is unlikely to explain these discrepancies. Overall, the reasons for the observed differences between all these PK studies, including ours, remain uncertain. The use of repeated anaesthesia for the repeated gavages, the difference in OTC formulations, feed composition or preparation of the mixture, the

rearing conditions or the potential non-linear PK for absorption processes are among the numerous factors that could affect the PK profiles. Disentangling the contribution of each is a real challenge. To overcome these limitations in future population modelling approaches, a meta-analysis of existing (individual) PK data with all potential covariates documented should be performed to investigate the main drivers of PK variability in this fish species (Li et al., 2015; Toutain, 2024). To this end, the data should be available and stored in an open repository (open science), as we have done for this study (Doi: 10.57745/4TOPUC).

As only the free concentration of antibiotic drugs is the relevant predictor of the extracellular biophase concentration, where most bacteria are located (Toutain et al., 2021), the unbound fractions of OTC were determined over a wide range of concentrations. An average protein binding of 52 % was found, consistent with previously reported values in rainbow trout (51 %–55 %) (Bjorklund and Bylund, 1991; Uno et al., 1997). However, we discarded the highest OTC concentrations (200 µg/mL) because the protein binding result was higher (~63 %). This increased protein binding seems counterintuitive but atypical protein binding for the tetracycline family has been frequently described (Toutain et al., 2021). Moreover, this high level of OTC plasma concentration will not be encountered in trout farming practice as only the oral route is used. A limitation of the determination of protein binding in this study relies on the use of spiked thawed plasma samples instead of directly assay the collected *in vivo* plasma samples. Indeed, the latter approach is best suited to characterise the inter-individual variability of protein binding, a source of variability that is rarely taken into account (Portugal et al., 2023).

As demonstrated by previous PK studies conducted following repeated oral administration, steady-state is not reached after 7 days (Corum et al., 2023), or even after the typical 10-day duration of OTC administration (Miller et al., 2012). Indeed, due to the long terminal half-life, OTC behaves like a long-acting drug in rainbow trout, and an accumulation over time is observed when given on a daily basis. One solution would be to use a loading dose and then delay the next oral administration (Viel et al., 2021). However, the use of higher doses of OTC in feed is known to cause palatability problems (Rigos et al., 1999; Toften and Jobling, 1997). Moreover, due to the extremely low bioavailability and the associated high variability (see above), an unrealistic loading dose would be required. In addition, the amount of drug that can be coated onto trout feed remains limited, as evidenced by the discrepancy observed between the theoretical coated dose and the actual concentration measured in the feed (Fig. 2). In France, veterinarians usually prescribe feed coated with OTC at 9000 ppm, which corresponds to a dose of 90 mg/kg at a feed rate of 1 %. Increasing the level of antibiotics in medicated feed does not result in a proportional increase in fish exposure: the more the concentration in the feed is increased, the further the actual level in the feed will be from the theoretical level, encouraging under-dosing and therefore inappropriate use of antibiotics.

Overall, the extremely low bioavailability, as already highlighted in previous publications with *Oncorhynchus mykiss* (Bjorklund and Bylund, 1991; Corum et al., 2023; Rogstad et al., 1991), is a major limiting factor to promote the use of OTC in medicated feeds for this fish species. The use of alternative formulations could improve this bioavailability, as has already been shown for OTC administered with a specific lipid vehicle (Serdoz et al., 2010), and more recently with a micro-encapsulation system based on algae (Trincado et al., 2024). However, these new formulations appear to increase bioavailability only moderately, which is likely to result in little, if any, gain in therapeutic efficacy. Moreover, this low bioavailability also indicates that a significant part of OTC remains in the gastrointestinal tract and may impact the microbiota of trout. Indeed, a recent study has shown that an OTC treatment over 1 week resulted in a decline of beneficial bacterial communities accompanied by the expansion of potential opportunistic groups (Payne et al., 2022). The use of other molecules belonging to the tetracyclines family, but with a higher bioavailability, such as doxycycline, may be a better
solution (Altan et al., 2024). However, further pharmacodynamic studies to better assess the activity of these tetracycline drugs, and especially OTC, against major fish pathogens (such as *A. salmonicida*) are still lacking (Rigos and Smith, 2015). Combining these PD data with the current PK data into a PK/PD modelling approach will enable a more robust assessment of the expected efficacy of OTC in clinical situations with the current dosing regimens (Toutain et al., 2021).

## 5. Conclusion

This population PK study allowed to quantify the influence of several covariates on the PK of OTC in rainbow trout such as bodyweight, water temperature and ploidy status. For the first time, the influence of spontaneous intake was investigated, which allowed the loss of OTC due to leaching to be estimated when using oil-coated medicated feed. Overall, we confirmed previous results about the very low oral bioavailability of OTC in rainbow trout, which is a major limitation in proposing optimised dosing regimens and may increase concerns about the risk of antimicrobial resistance in the environment.

### CRediT authorship contribution statement

**Alexis Viel:** Visualization, Project administration, Data curation, Writing – original draft, Funding acquisition, Conceptualization, Writing – review & editing, Resources, Methodology, Formal analysis.
**Florine Bachelet:** Resources, Data curation, Investigation, Methodology.
**Annaëlle Chailleux:** Investigation, Formal analysis, Methodology.
**Céline David:** Resources, Methodology, Data curation, Investigation.
**Lionel Pineau:** Resources, Investigation, Methodology, Data curation.
**Ségolène Calvez:** Project administration, Supervision, Investigation, Writing – review & editing, Funding acquisition.
**Antoine Rostang:** Writing – review & editing, Supervision, Methodology, Data curation, Writing – original draft, Resources, Investigation, Formal analysis, Conceptualization, Visualization, Project administration, Funding acquisition.

### Funding

This study was financed through "MEDIC'EAU", research project supported by FEAMP/EMFF (Fonds européen pour les affaires maritimes et la pêche/European Maritime and Fisheries Fund): project PFEA470020FA1000006.

### Acknowledgements

The authors would like to thank the veterinary company fili@vet for their help in designing a protocol that best reflects the reality of practice in the field: Pierre-Marie Boitard and Matthieu Jamin, and all the following members of BIOEPAR who helped with data collection: Sandie Arnoux, Suzanne Bastian, Nathalie de la Cotte, Philippe Gontier, Emmanuelle Moreau, Guillaume Morgant, Nora Navarro-Gonzalez, Kenny Oberlé. We would also like to thank Professor Pierre-Louis Tou-tain for his help in assessing dose proportionality.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.aquaculture.2025.742917.

### Data availability

All PK data generated in this study and used for the popPK analysis has been published and is available here: Doi: 10.57745/4TOPUC.

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