PK/PD integration for intramuscular dose determination of intramuscular sodium cloxacillin for infections caused by Staphylococcus spp in goat

This study aims to determine therapeutic protocols of intramuscular sodium cloxacillin (IM) in goats with potential antibacterial effects against Staphylococcus spp. We constructed a pharmacokinetic (PK) model of IM, followed by a pharmacokinetic/pharmacodynamic integration (PK/PD). Simulations of different therapeutic protocols were then performed, with the doses ranging from 30 to100 mg/kg every 8, 12, or 24 hours. We calculated the probability to target attainment (PTA) of reach protocol's therapeutic according to the minimum inhibitory concentration (MIC) range of 0.06 to 4 μg/mL. The PK/PD index (PDT) used was "time above the MIC for 40% of the time" (T>MIC ≥40%). Protocols with single administration per day were incapable of achieving PTA ≥ 90% for any of the estimated MICs. However, by decreasing the administration interval, the PTA was increased. Thus, from the dose of 50 mg/kg every 12 hours, a PTA≥ 90% for MICs ≤ 0.5 μg/mL was achieved, while the 30 mg/kg dose every 8 hours was able to achieve a PTA≥ 90% for MICs of 2 μg/mL. The results suggest using 30 mg/kg dose every 8 hours in clinical studies of agents with MICs ≤ 2μg/mL; Nevertheless, the practitioner should adjust the dose in severe patients.


INTRODUCTION
Staphylococcus spp. is a common Gram-positive bacterium of the skin and mucosal microbiota; Nevertheless, it is responsible for several opportunistic infections in humans and animals (Piva et al., 2021).In immunosuppressed animals or a critical care state, the agent can cause skin, soft tissue, bone, and joint infections and, in systemic cases, sepsis (Tong et al., 2015;Balasubramanian et al., 2017).Poorly treated sepsis can induce an inflammatory response, organ dysfunction syndrome, and shock, followed by death (Pollitt et al., 2018).
In this context, cloxacillin, an isoxazolyl penicillin belonging to the beta-lactam group with action against Gram-positive bacteria and excellent activity against Staphylococcus spp.(methicillin-sensitive) makes itself an excellent option in both veterinary and human medicine (Burdet et al., 2018;Courjon et al., 2020;Aldman et al., 2022).Beta-lactams have a bactericidal effect by acting on the bacterial cell wall, which decreases their toxicity.Thus, they are the antibiotics of choice for critically ill patients (Marsot, 2020).
Due to the increase in antimicrobial resistance, researchers have proposed several strategies to contain the emergence of new resistant strains.In 2019, the World Health Organization (WHO) released a list of the antibiotics of critical use in human medicine, which should guide the choice of antibiotic therapy used in veterinary medicine.According to this list, cloxacillin is very important, being the drug of choice in the face of other classes of antibiotics, such as 3rdgeneration cephalosporins, carbapenems, quinolones, and penicillin (aminopenicillins and aminopenicillins with a beta-lactamase inhibitor), which are of maximum and high priority for human medicine (Global…, 2015).
In addition, WHO has directed the optimization of antibiotic therapy based on pharmacokinetic/ pharmacodynamic integration (PK/PD) as a strategy of the Global Action Plan on Antimicrobial Resistance to decrease the emergence of antimicrobial resistance (Global…, 2015;Guardabassi et al., 2018;Toutain et al., 2021).This approach has already been used in veterinary medicine, as demonstrated in several studies, such as oxytetracycline dose optimization for Mannheimia haemolytica and Pasteurella multocida in calves (Lees et al., 2018) and for marbofloxacin against Mycoplasma agalactiae in goats (Fernández-Varón et al., 2021).This approach gathers PK/PD data in an in-silico model that predicts the plasma concentration of a drug, followed by the simulation of different therapeutic protocols to achieve the clinical probability of success (Guideline…, 2016).In human medicine, researchers and doctors are using this methodology to determine the dose regimen of cloxacillin and dicloxacillin for the systemic treatment of infections against pathogens such as Staphylococcus aureus (Yu et al., 2017;Courjon et al., 2020).
This study aims to estimate therapeutic protocols of sodium cloxacillin by intramuscular route in goats with potential antibacterial effect against Staphylococcus spp.by Monte Carlo simulation.

METHODOLOGY
We obtained cloxacillin's minimum inhibitory concentration (MIC) values against Staphylococcus spp.strains from previous studies published in the literature.Virdis et al. (2010) determined the MIC of cloxacillin against Staphylococcus aureus (n=25) and coagulasenegative Staphylococcus (n=75) strains isolated in milk from goats with subclinical mastitis, which showed minimum inhibitory concentrations which growth was inhibited in 90% of isolates (MIC 90 ) of 0.5 and 1.0µg/mL, respectively.In the study of Bolte et al. (2020), the isolates from goats with clinical mastitis, the MIC 90 for Staphylococcus aureus (n=85) was 1.0µg/mL and 2.0µg/mL for the Non-Staphylococcus aureus (n=88) (Table 1).(2019).Data extraction was performed using the WebPlotDigitizer version 4.1.In the study of Khargharia et al. (2013), six goats (three males and three females) of the Black Bengal breed weighing between 12 and 14 kg and aged between 1 to 1.5 years received a dose of 10 mg/kg of cloxacillin intravenously.In the study of Kaleshwari et al. (2019), four non-lactating female sheep aged 2 to 2.5 years and 35±5kg received a 10 mg/kg dose by intramuscular route.
We performed cloxacillin's pharmacokinetic modeling in Monolix 2021R2 software (Lixoft SAS, a Simulations Plus company) from the data obtained from both studies.The intravenous pharmacokinetic model of sodium cloxacillin in goats was constructed from the model of Khargharia et al. (2013).In contrast, the intramuscular pharmacokinetic model of sodium cloxacillin in sheep was constructed from the model of Kaleshwari et al. (2019).We tested various models with extravascular, bolus route, with or without delay, first-order or zero-order absorption, one, two, or three compartments, and linear or Michaelis-Menten elimination.The two structural models were selected based on graphical analyses of observed and predicted (Individual fits graphs) (Traynard et al., 2020).
From a translational approach, we integrated the parameters of the two models to obtain pharmacokinetic parameters for a PK model of sodium cloxacillin by intramuscular route in goats.Thus, the absorption constant (Ka) obtained from the intramuscular sheep model was integrated with the volume of distribution (Vd) and clearance (Cl) parameters obtained from the intravenous goat model.
We performed the simulation in Simulx 2021R2 software (Lixoft SAS, a Simulations Plus Company).A theoretical variability (omega) was added based on models published in the literature (Supplementary Material S1).Therapeutic protocols simulations were performed with different doses ranging from 30 to 100mg/kg, administered once, twice, or three times a day.
To calculate the probability of target attainment (PTA), we performed 1000 Monte Carlo simulations of 50 subjects each (Supplementary Material S2).Then, we determined the PTA for each protocol at a MIC distribution ranging from 0.06 to 4 μg/mL.Dosing regimens with a PTA≥90% were potentially effective (Guideline…, 2016).

RESULTS
The pharmacokinetic model that best fit the data from the in vivo experiment was extravascular administration, no delay, first-order absorption, one-compartment distribution, and linear elimination (Fig. 1).
In a microbiological study of neonatal foals, 83% of the bacteria isolated were Gram-positive, most notably Staphylococcus spp., which represents 24% of the isolates (Toombs-Ruane et al., 2016).In addition, bacteremia and sepsis can occur from nosocomial infections due to surgical wound exposure, contaminated material, valve transplants, and orthopedic equipment (Tong et al., 2015).Early treatment of bacteremia and sepsis is critical, and it is necessary to establish effective antibiotic therapies against Staphylococcus spp.(Campos et al., 2022).Therefore, for this study, the MIC was based on studies from other countries, such as Germany (Bolte et al., 2020) and Italy (Virdis et al., 2010).We selected data from Staphylococcus spp.mastitis in goats, in which the MIC 90 ranged from 0.5 to 2.0 µg/mL.From the Monte Carlo simulation, we calculated the PTA of different therapeutic protocols of sodium cloxacillin according to probable MICs of Staphylococcus spp.
Based on Monte Carlo simulations, the PTA of different therapeutic protocols of cloxacillin sodium were calculated according to probable MICs.Observing Figure 3, the protocol with an interval between administrations every 24 hours does not reach the PTA of 90% in any of the simulated MICs.In short half-life antibiotics, such as cloxacillin, it can be hard to maintain the plasma concentration above the MIC for a large percentage of the time; however, this can be optimized by increasing the dose or decreasing the interval between administrations (Papich, 2014).Therefore, we performed regimens with shorter administration intervals (8 and 12 hours).Reducing the interval between administrations made it possible to achieve a PTA ≥90% for several MICs.
The protocols of 30 and 50mg/kg every 8 hours showed PTA of 91% and 93%, respectively, for MIC of 2.0 µg/mL.This value was the highest among all simulated protocols.For protocols with two daily administrations (every 12 hours), increasing the dose did not increase the PTA≥90% for the MICs of 1.0 µg/mL and 2.0 µg/mL (Table 2).Protocols with shorter intervals (8 hours) may not be attractive due to the difficulty of handling the animals, especially for livestock.The simulated protocols target patients in critical care with infections requiring systemic therapy, with sepsis, or at high risk of developing sepsis.Therefore, in this case, the animals are expected to be in a hospital environment.
From Table 2, it is possible to determine the best protocol for each MIC of the isolated agent, so it is at the veterinarian's discretion which therapeutic regimen to use.From the point of view of a higher PTA, the protocol of 50 mg/kg every 8 hours presents a greater chance of therapeutic success, even for bacteria with a MIC of 2 µg/mL.One can obtain similar results with 30 mg/kg dose every 8 hours.At this dose, the PTA is within the recommended limit (PTA≥90%), besides reducing the amount of the drug by 40% (approximately 2000 mg).For bacteria with a MIC of 0.5 µg/mL, more protocol options are available, such as the protocol of 50 mg/kg every 12 hours, which would make management easier since there are only two daily applications.Another option is the protocol of 30 mg/kg every 8 hours; despite increasing one application, the daily drug amount would be lower, therefore, better for the patient and the environment.
One must keep in mind that critically ill patients present physiological alterations, especially those related to hemodynamics, renal and hepatic function, and decreased muscle and intestinal perfusion, which result in changes in pharmacokinetics (Veiga and Paiva, 2018;Gyssens et al., 2020).In these cases, it is possible to observe an increased volume of distribution and clearance, so these patients generally have suboptimal exposure to antibiotics when used at usual doses (Abdul-Aziz et al., 2020;Heffernan et al., 2021).Thus, it is ideal for personalizing therapy according to the severity of the case, such as doctors perform in human medicine (O'Jeanson et al., 2021;Roggeveen et al., 2022).
Thus, in cases of critically ill patients, an alternative to avoid underdose is the adoption of continuous rate infusion (CRI) in the first 24 hours to keep the cloxacillin concentration above the MIC of the infecting microorganism (Magdesian, 2017;Courjon et al., 2020).In this case, it is necessary to research to determine cloxacillin CRI protocols in goats.
In the present study, the simulated protocols present a daily dose that varies from 3150 to 7000 mg, similar to the study carried out by Courjon et al. (2020) for a new cloxacillin protocol in humans infected by Staphylococcus aureus, which ranged from 2000 to 12000 mg/24 hours.The proposed values are consistent with the medical clinic.This form of daily drug quantification is essential to assess the degree of exposure in the animal to estimate the risk of adverse effects and the degree of toxicity, besides assessing the exposure to the surrounding environment, which is of utmost importance since the use of antimicrobials influences the ecosystem.As a result of microbiome sharing and environmental exposure, microorganisms can share resistance genes between different strains, which corroborates the emergence of new antimicrobial-resistant (Trinh et al., 2018).
Beta-lactams have low toxic potential due to their mechanism of action and can be administered in higher doses, when necessary, without causing severe adverse effects.A safety study of cloxacillin demonstrated a lethal dose 50 (LD 50 ) of 1117 mg/kg and 916 mg/kg in mice by intramuscular and intravenous routes, respectively (Cloxacillin…, 2022).The maximum intramuscular dose in adult humans indicated is 500 to 1000 mg, divided between one to four daily administrations (up to 4000 mg/24 hours).If necessary, the doctor can double the dose intravenously, reaching a maximum daily dose of 8000 mg/24 hours.Nevertheless, in severe cases, the maximum dosage can be adjusted and reach 12000 mg/24 hours, in continuous rate infusion (CRI), as in the case of the study by Courjon et al. (2020).
The present study targets bacteria of the genus Staphylococcus spp.; however, it is worth noting that the simulated protocols can be adapted for various species of bacteria with MICs within the simulated range.Furthermore, this study shows that this methodology can be applied to determine protocols for other bacteria and antibiotics of interest in veterinary medicine.

Figure 1 .
Figure 1.Schematic representation of the pharmacokinetic models of sodium cloxacillin.A. Intravenous pharmacokinetic model of sodium cloxacillin in goats was constructed from the model of Khargharia et al. (2013).B. Intramuscular pharmacokinetic model of sodium cloxacillin in sheep was constructed from the model of Kaleshwari et al. (2019).C. Intramuscular pharmacokinetic model (translational) of sodium cloxacillin in goat.IV -Intravenous; Vd -Volume of distribution; Cl -Clearance; Ka -Absorption constant; V1 -Volume of the central compartment (most vascularized organs); V2 -Volume of the peripheral compartment; Q -Transit between compartments; IM -Intramuscular.

Figure 2 .
Figure 2. Simulation of therapeutic protocols of sodium cloxacillin in doses of 30, 50, and 100 mg/kg every 24 hours intramuscularly in goats, using a Monte Carlo simulation (n=1000).
In this scenario, cloxacillin stands out because it has an excellent antistaphylococcal action, traditionally used in mastitis treatment, as the

Table 1 .
Minimum Inhibitory Concentration Values (MIC 50 and MIC 90 ) of cloxacillin against Staphylococcus aureus, coagulase-negative Staphylococci and non-aureus Staphylococci inter-dose interval (Papich, 2014).The mean plasma concentrations of cloxacillin over time were obtained from the publications of Khargharia et al. (2013) and Kaleshwari et al.