Predicting in vitro antibacterial efficacy across experimental designs with a semimechanistic pharmacokinetic-pharmacodynamic model

Pharmacokinetic/pharmacodynamic model-based optimization of temocillin dosing strategies for the treatment of systemic infections

BACKGROUND

Temocillin is increasingly considered as an alternative to carbapenems. However, there is no consensus on optimal dosing strategies and limited data on temocillin efficacy in systemic infections.

OBJECTIVES

We compared temocillin dosing strategies using pharmacokinetic/pharmacodynamic (PK/PD) modelling and simulation based on plasma exposure and in vitro time-kill data.

METHODS

Temocillin effects on four Escherichia coli strains were evaluated using static time-kill experiments and the hollow-fibre infection model, in which unbound plasma concentrations following intermittent and continuous infusion regimens of 4 and 6 g daily were replicated over 72 h. A PK/PD model was developed to describe the time-kill data. The PK/PD model was coupled to a population PK model of temocillin in critically ill patients to predict bacterial killing and resistance development following various dosing regimens.

RESULTS

Amplification of resistant subpopulations was observed within 24 h for all strains. The PK/PD model described the observed bacterial kill kinetics and resistance development from both experimental systems well. Simulations indicated dose-dependent bacterial killing within and beyond the currently used daily dose range, and a superiority of continuous compared with intermittent infusions. However, regrowth of resistant subpopulations was frequently observed. For two strains, bacteriostasis over 72 h was predicted only with doses that are higher than those currently licensed.

CONCLUSIONS

Continuous infusions and 6 g daily doses of temocillin kill E. coli more effectively than 4 g daily doses and intermittent infusions, and may increase efficacy in the treatment of systemic infections. However, higher daily doses may be required to suppress resistance development.

Dose regimen optimization of cephalothin for surgical prophylaxis against Staphylococcus aureus and coagulase negative staphylococci in dogs by pharmacokinetic/pharmacodynamic modeling

First generation cephalosporins such cephalothin of cefazolin are indicated for antimicrobial prophylaxis for clean and clean contaminated surgical procedures because its antimicrobial spectrum, relative low toxicity and cost. Anesthesia and surgery could alter the pharmacokinetic behavior of different drugs administered perioperative by many mechanisms that affect distribution, metabolism or excretion processes. Intravenous administration of the antimicrobial within 30 and 60 min before incision is recommended in order to reach therapeutic serum and tissue concentrations and redosing is recommended if the duration of the procedure exceeds two half-life of the antimicrobial. To the author's knowledge there are no pharmacokinetic studies of cephalothin in dogs under anesthesia/surgery conditions. The aim of this study was (1) to evaluate the pharmacokinetics of cephalothin in anesthetized dogs undergoing ovariohysterectomy by a nonlinear mixed-effects model and to determine the effect of anesthesia/surgery and other individual covariates on its pharmacokinetic behavior; (2) to determine the MIC and conduct a pharmacodynamic modeling of time kill curves assay of cephalothin against isolates of Staphylococcus spp. isolated from the skin of dogs; (3) to conduct a PK/PD analysis by integration of the obtained nonlinear mixed-effects models in order to evaluate the antimicrobial effect of changing concentrations on simulated bacterial count; and (4) to determine the PK/PD endpoints and PK/PDco values in order to predict the optimal dose regimen of cephalothin for antimicrobial prophylaxis in dogs. Anesthesia/surgery significantly reduced cephalothin clearance by 18.78%. Based on the results of this study, a cephalothin dose regimen of 25 mg/kg q6h by intravenous administration showed to be effective against Staphylococcus spp. isolates with MIC values ≤2 μg/mL and could be recommended for antimicrobial prophylaxis for clean surgery in healthy dogs.

Model-based learn and confirm: designing effective treatment regimens against multidrug resistant Gram-negative pathogens

Over the last decade, there has been a growing appreciation for the use of in vitro and in vivo infection models to generate robust and informative nonclinical PK/PD data to accelerate the clinical translation of treatment regimens. The objective of this study was to develop a model-based "learn and confirm" approach to help with the design of combination regimens using in vitro infection models to optimise the clinical utility of existing antibiotics. Static concentration time-kill studies were used to evaluate the PD activity of polymyxin B (PMB) and meropenem against two carbapenem-resistant Klebsiella pneumoniae (CRKP) isolates; BAA2146 (PMB-susceptible) and BRKP67 (PMB-resistant). A mechanism-based model (MBM) was developed to quantify the joint activity of PMB and meropenem. In silico simulations were used to predict the time-course of bacterial killing using clinically-relevant PK exposure profiles. The predictive accuracy of the model was further evaluated by validating the model predictions using a one-compartment PK/PD in vitro dynamic infection model (IVDIM). The MBM captured the reduction in bacterial burden and regrowth well in both the BAA2146 and BRKP67 isolate (R2 = 0.900 and 0.940, respectively). The bacterial killing and regrowth predicted by the MBM were consistent with observations in the IVDIM: sustained activity against BAA2146 and complete regrowth of the BRKP67 isolate. Differences observed in PD activity suggest that additional dose optimisation might be beneficial in PMB-resistant isolates. The model-based approach presented here demonstrates the utility of the MBM as a translational tool from static to dynamic in vitro systems to effectively perform model-informed drug optimisation.

Synergy of polymyxin B and minocycline against KPC-3- and OXA-48-producing Klebsiella pneumoniae in dynamic time-kill experiments: agreement with in silico predictions

OBJECTIVES

Combination therapy is often used for carbapenem-resistant Gram-negative bacteria. We previously demonstrated synergy of polymyxin B and minocycline against carbapenem-resistant Klebsiella pneumoniae in static time-kill experiments and developed an in silico pharmacokinetic/pharmacodynamic (PK/PD) model. The present study assessed the synergistic potential of this antibiotic combination in dynamic experiments.

METHODS

Two clinical K. pneumoniae isolates producing KPC-3 and OXA-48 (polymyxin B MICs 0.5 and 8 mg/L, and minocycline MICs 1 and 8 mg/L, respectively) were included. Activities of the single drugs and the combination were assessed in 72 h dynamic time-kill experiments mimicking patient pharmacokinetics. Population analysis was performed every 12 h using plates containing antibiotics at 4× and 8× MIC. WGS was applied to reveal resistance genes and mutations.

RESULTS

The combination showed synergistic and bactericidal effects against the KPC-3-producing strain from 12 h onwards. Subpopulations with decreased susceptibility to polymyxin B were frequently detected after single-drug exposures but not with the combination. Against the OXA-48-producing strain, synergy was observed between 4 and 8 h and was followed by regrowth. Subpopulations with decreased susceptibility to polymyxin B and minocycline were detected throughout experiments. For both strains, the observed antibacterial activities showed overall agreement with the in silico predictions.

CONCLUSIONS

Polymyxin B and minocycline in combination showed synergistic effects, mainly against the KPC-3-producing K. pneumoniae. The agreement between the experimental results and in silico predictions supports the use of PK/PD models based on static time-kill data to predict the activity of antibiotic combinations at dynamic drug concentrations.

Pharmacokinetic/pharmacodynamic analysis of ceftazidime/avibactam and fosfomycin combinations in an in vitro hollow fiber infection model against multidrug-resistant Escherichia coli

IMPORTANCE

Mechanistic understanding of pharmacodynamic interactions is key for the development of rational antibiotic combination therapies to increase efficacy and suppress the development of resistances. Potent tools to provide those insights into pharmacodynamic drug interactions are semi-mechanistic modeling and simulation techniques. This study uses those techniques to provide a detailed understanding with regard to the direction and strength of the synergy of ceftazidime-avibactam and ceftazidime-fosfomycin in a clinical Escherichia coli isolate expressing extended spectrum beta-lactamase (CTX-M-15 and TEM-4) and carbapenemase (OXA-244) genes. Enhanced killing effects in combination were identified as a driver of the synergy and were translated from static time-kill experiments into the dynamic hollow fiber infection model. These findings in combination with a suppression of the emergence of resistance in combination emphasize a potential clinical benefit with regard to increased efficacy or to allow for dose reductions with maintained effect sizes to avoid toxicity.

Pharmacokinetic-pharmacodynamic models for time courses of antibiotic effects: VSI: Antimicrobial Pharmacometrics

Pharmacokinetic-pharmacodynamic (PKPD) models have emerged as valuable tools for the characterisation and translation of antibiotic effects, and consequently for drug development and therapy. In contrast to traditional PKPD concepts for antibiotics like MIC and PKPD indices, PKPD models enable to describe the continuous, often species- or population-dependent time course of antimicrobial effects, commonly considering mechanistic pathogen- and drug-related knowledge. This review presents a comprehensive overview of previously published PKPD models describing repeated measurements of antibiotic effects. We conducted a literature review to identify PKPD models based on (i) antibiotic compounds, (ii) Gram-positive or Gram-negative pathogens, and (iii) in vitro or in vivo longitudinal colony forming unit data. We identified 132 publications released between 1963 and 2021, including models based on exposure with single antibiotics (n=92) and drug combinations (n=40), as well as different experimental settings (e.g., static/traditional dynamic/hollow-fibre/animal time-kill models, n=90/27/32/11). An interactive, fully searchable table summarises the details of each model, i.e. variants and mechanistic elements of PKPD submodels capturing observed bacterial growth, regrowth, drug effects, and interactions. Furthermore, the review highlights main purposes of PKPD model development, including the translation of preclinical PKPD to clinical settings and the assessment of varied dosing regimens and patient characteristics for their impact on clinical antibiotic effects. In summary, this comprehensive overview of PKPD models shall assist in identifying PKPD modelling strategies to describe growth, killing, regrowth and interaction patterns for pathogen-antibiotic combinations over time and ultimately facilitate model-informed antibiotic translation, dosing and drug development.

Application of Semi-Mechanistic Pharmacokinetic and Pharmacodynamic Model in Antimicrobial Resistance

Antimicrobial resistance is a major public health issue. The pharmacokinetic/pharmacodynamic (PK/PD) model is an essential tool to optimize dosage regimens and alleviate the emergence of resistance. The semi-mechanistic PK/PD model is a mathematical quantitative tool to capture the relationship between dose, exposure, and response, in terms of the mechanism. Understanding the different resistant mechanisms of bacteria to various antibacterials and presenting this as mathematical equations, the semi-mechanistic PK/PD model can capture and simulate the progress of bacterial growth and the variation in susceptibility. In this review, we outline the bacterial growth model and antibacterial effect model, including different resistant mechanisms, such as persisting resistance, adaptive resistance, and pre-existing resistance, of antibacterials against bacteria. The application of the semi-mechanistic PK/PD model, such as the determination of PK/PD breakpoints, combination therapy, and dosage optimization, are also summarized. Additionally, it is important to integrate the PD effect, such as the inoculum effect and host response, in order to develop a comprehensive mechanism model. In conclusion, with the semi-mechanistic PK/PD model, the dosage regimen can be reasonably determined, which can suppress bacterial growth and resistance development.

Predicting Antimicrobial Activity at the Target Site: Pharmacokinetic/Pharmacodynamic Indices versus Time-Kill Approaches

Antibiotic dosing strategies are generally based on systemic drug concentrations. However, drug concentrations at the infection site drive antimicrobial effect, and efficacy predictions and dosing strategies should be based on these concentrations. We set out to review different translational pharmacokinetic-pharmacodynamic (PK/PD) approaches from a target site perspective. The most common approach involves calculating the probability of attaining animal-derived PK/PD index targets, which link PK parameters to antimicrobial susceptibility measures. This approach is time efficient but ignores some aspects of the shape of the PK profile and inter-species differences in drug clearance and distribution, and provides no information on the PD time-course. Time–kill curves, in contrast, depict bacterial response over time. In vitro dynamic time–kill setups allow for the evaluation of bacterial response to clinical PK profiles, but are not representative of the infection site environment. The translational value of in vivo time–kill experiments, conversely, is limited from a PK perspective. Computational PK/PD models, especially when developed using both in vitro and in vivo data and coupled to target site PK models, can bridge translational gaps in both PK and PD. Ultimately, clinical PK and experimental and computational tools should be combined to tailor antibiotic treatment strategies to the site of infection.

A new PKPD model to characterize the inoculum effect of Acinetobacter baumannii on polymyxin B in vitro

The inoculum effect (i.e., reduction in antimicrobial activity at large starting inoculum) is a phenomenon described for various pathogens. Since limited data exist regarding inoculum effect of Acinetobacter baumannii, we evaluated killing of A. baumannii by polymyxin B, a last-resort antibiotic, at several starting inocula and developed a PKPD model to capture this phenomenon. In vitro static time-kill experiments were performed using polymyxin B at concentrations ranging from 0.125 to 128 mg/L against a clinical A. baumannii isolate at four starting inocula from 10⁵ to 10⁸ CFU/mL. Samples were collected up to 30 h to quantify the viable bacterial burden and were simultaneously modeled in the NONMEM software program. The expression of polymyxin B resistance genes (lpxACD, pmrCAB and wzc), and genetic modifications were studied by RT-qPCR and DNA sequencing experiments, respectively. The PKPD model included a single homogeneous bacterial population with adaptive resistance. Polymyxin B effect was modelled as a sigmoidal E_max model and the inoculum effect as an increase of polymyxin B EC₅₀ with increasing starting inoculum using a power function. Polymyxin B displayed a reduced activity as the starting inoculum increased: a 20-fold increase of polymyxin B EC₅₀ was observed between the lowest and the highest inoculum. No effects of polymyxin B and inoculum size were observed on the studied genes. The proposed PKPD model successfully described and predicted the pronounced in vitro inoculum effect of A. baumannii on polymyxin B activity. These results should be further validated using other bacteria/antibiotic combinations and in vivo models.

Live-imaging rate-of-kill compound profiling for Chagas disease drug discovery with a new automated high-content assay

Chagas disease, caused by the protozoan intracellular parasite Trypanosoma cruzi, is a highly neglected tropical disease, causing significant morbidity and mortality in central and south America. Current treatments are inadequate, and recent clinical trials of drugs inhibiting CYP51 have failed, exposing a lack of understanding of how to translate laboratory findings to the clinic. Following these failures many new model systems have been developed, both in vitro and in vivo, that provide improved understanding of the causes for clinical trial failures. Amongst these are in vitro rate-of-kill (RoK) assays that reveal how fast compounds kill intracellular parasites. Such assays have shown clear distinctions between the compounds that failed in clinical trials and the standard of care. However, the published RoK assays have some key drawbacks, including low time-resolution and inability to track the same cell population over time. Here, we present a new, live-imaging RoK assay for intracellular T. cruzi that overcomes these issues. We show that the assay is highly reproducible and report high time-resolution RoK data for key clinical compounds as well as new chemical entities. The data generated by this assay allow fast acting compounds to be prioritised for progression, the fate of individual parasites to be tracked, shifts of mode-of-action within series to be monitored, better PKPD modelling and selection of suitable partners for combination therapy.

Chagas disease is caused by the single cell protozoan parasite Trypanosoma cruzi. Millions of people suffer from this disease in central and south America, which frequently causes heart disease and can result in death. Chagas disease is classified as a neglected tropical disease due to the lack of investment in development of new medicines. The currently available medicines are inadequate as they require long treatments, often with severe side-effects. To develop new medicines, it is critical to build laboratory assays and tools that help predict the ability of new compounds to cure patients. Rate-of-kill assays measure how quickly compounds can kill parasites, providing a route to differentiate promising compounds from poor ones. Here, we describe development of an advanced rate-of-kill assay that, unlike existing assays, can monitor the same cell population over the duration of compound treatment. Using live-cell microscopy, parasite-infected host cells and their response to compound treatment can be continuously monitored. This enables better defined rate-of-kill profiles to be produced, in turn allowing better informed decisions on subsequent compound progression. Here, we report the live-imaging rate-of-kill profiles for several key compounds, including current drugs and compounds in clinical development.

Cellular Growth Arrest and Efflux Pumps Are Associated With Antibiotic Persisters in Streptococcus pyogenes Induced in Biofilm-Like Environments

Streptococcus pyogenes (group A Streptococcus-GAS) is an important pathogen for humans. GAS has been associated with severe and invasive diseases. Despite the fact that these bacteria remain universally susceptible to penicillin, therapeutic failures have been reported in some GAS infections. Many hypotheses have been proposed to explain these antibiotic-unresponsive infections; however, none of them have fully elucidated this phenomenon. In this study, we show that GAS strains have the ability to form antimicrobial persisters when inoculated on abiotic surfaces to form a film of bacterial agglomerates (biofilm-like environment). Our data suggest that efflux pumps were possibly involved in this phenomenon. In fact, gene expression assays by real-time qRT-PCR showed upregulation of some genes associated with efflux pumps in persisters arising in the presence of penicillin. Phenotypic reversion assay and whole-genome sequencing indicated that this event was due to non-inherited resistance mechanisms. The persister cells showed downregulation of genes associated with protein biosynthesis and cell growth, as demonstrated by gene expression assays. Moreover, the proteomic analysis revealed that susceptible cells express higher levels of ribosome proteins. It is remarkable that previous studies have reported the recovery of S. pyogenes viable cells from tissue biopsies of patients presented with GAS invasive infections and submitted to therapy with antibiotics. The persistence phenomenon described herein brings new insights into the origin of therapeutic failures in S. pyogenes infections. Multifactorial mechanisms involving protein synthesis inhibition, cell growth impairment and efflux pumps seem to play roles in the formation of antimicrobial persisters in S. pyogenes.

Bacterial growth dynamics and pharmacokinetic-pharmacodynamic relationships of rifampicin and bedaquiline in BALB/c mice

BACKGROUND AND PURPOSE

Translational efforts in the evaluation of novel anti-tubercular drugs demand better integration of pharmacokinetic-pharmacodynamic data arising from preclinical protocols. However, parametric approaches that discriminate drug effect from the underlying bacterial growth dynamics have not been fully explored, making it difficult to translate and/or extrapolate preclinical findings to humans. This analysis aims to develop a drug-disease model that allows distinction between drug- and system-specific properties.

EXPERIMENTAL APPROACH

Given their clinical relevance, rifampicin and bedaquiline were used as test compounds. A two-state model was used to describe bacterial growth dynamics. The approach assumes the existence of fast- and slow-growing bacterial populations. Drug effect on the growth dynamics of each subpopulation was characterised in terms of potency (EC₅₀ -F and EC₅₀ -S) and maximum killing rate.

KEY RESULTS

The doubling time of the fast- and slow-growing population was estimated to be 25 h and 42 days, respectively. Rifampicin was more potent against the fast-growing (EC₅₀ -F = 4.8 mg·L^-1 ), as compared with the slow-growing population (EC₅₀ -S = 60.2 mg·L^-1 ). Bedaquiline showed higher potency than rifampicin (EC₅₀ -F = 0.19 mg·L^-1 ; EC₅₀ -S = 3.04 mg·L^-1 ). External validation procedures revealed an effect of infection route on the apparent potency of rifampicin.

CONCLUSION AND IMPLICATIONS

Model parameter estimates suggest that nearly maximum killing rate is achieved against fast-growing, but not against slow-growing populations at the tested doses. Evidence of differences in drug potency for each subpopulation may facilitate the translation of preclinical findings and improve the dose rationale for anti-tubercular drugs in humans.

Model-Informed Drug Development for Anti-Infectives: State of the Art and Future

Model-informed drug development (MIDD) has a long and rich history in infectious diseases. This review describes foundational principles of translational anti-infective pharmacology, including choice of appropriate measures of exposure and pharmacodynamic (PD) measures, patient subpopulations, and drug-drug interactions. Examples are presented for state-of-the-art, empiric, mechanistic, interdisciplinary, and real-world evidence MIDD applications in the development of antibacterials (review of minimum inhibitory concentration-based models, mechanism-based pharmacokinetic/PD (PK/PD) models, PK/PD models of resistance, and immune response), antifungals, antivirals, drugs for the treatment of global health infectious diseases, and medical countermeasures. The degree of adoption of MIDD practices across the infectious diseases field is also summarized. The future application of MIDD in infectious diseases will progress along two planes; "depth" and "breadth" of MIDD methods. "MIDD depth" refers to deeper incorporation of the specific pathogen biology and intrinsic and acquired-resistance mechanisms; host factors, such as immunologic response and infection site, to enable deeper interrogation of pharmacological impact on pathogen clearance; clinical outcome and emergence of resistance from a pathogen; and patient and population perspective. In particular, improved early assessment of the emergence of resistance potential will become a greater focus in MIDD, as this is poorly mitigated by current development approaches. "MIDD breadth" refers to greater adoption of model-centered approaches to anti-infective development. Specifically, this means how various MIDD approaches and translational tools can be integrated or connected in a systematic way that supports decision making by key stakeholders (sponsors, regulators, and payers) across the entire development pathway.

The pharmacokinetic/pharmacodynamic paradigm for antimicrobial drugs in veterinary medicine: Recent advances and critical appraisal

Pharmacokinetic/pharmacodynamic (PK/PD) modelling is the initial step in the semi-mechanistic approach for optimizing dosage regimens for systemically acting antimicrobial drugs (AMDs). Numerical values of PK/PD indices are used to predict dose and dosing interval on a rational basis followed by confirmation in clinical trials. The value of PK/PD indices lies in their universal applicability amongst animal species. Two PK/PD indices are routinely used in veterinary medicine, the ratio of the area under the curve of the free drug plasma concentration to the minimum inhibitory concentration (MIC) (fAUC/MIC) and the time that free plasma concentration exceeds the MIC over the dosing interval (fT > MIC). The basic concepts of PK/PD modelling of AMDs were established some 20 years ago. Earlier studies have been reviewed previously and are not reconsidered in this review. This review describes and provides a critical appraisal of more recent, advanced PK/PD approaches, with particular reference to their application in veterinary medicine. Also discussed are some hypotheses and new areas for future developments.First, a brief overview of PK/PD principles is presented as the basis for then reviewing more advanced mechanistic considerations on the precise nature of selected indices. Then, several new approaches to selecting PK/PD indices and establishing their numerical values are reviewed, including (a) the modelling of time-kill curves and (b) the use of population PK investigations. PK/PD indices can be used for dose determination, and they are required to establish clinical breakpoints for antimicrobial susceptibility testing. A particular consideration is given to the precise nature of MIC, because it is pivotal in establishing PK/PD indices, explaining that it is not a "pharmacodynamic parameter" in the usual sense of this term.

A data-based mathematical modelling study to quantify the effects of ciprofloxacin and ampicillin on the within-host dynamics of Salmonella enterica during treatment and relapse

Antibiotic therapy has drastically reduced the mortality and sequelae of bacterial infections. From naturally occurring to chemically synthesized, different classes of antibiotics have been successfully used without detailed knowledge of how they affect bacterial dynamics in vivo. However, a proportion of patients receiving antimicrobial therapy develop recrudescent infections post-treatment. Relapsing infections are attributable to incomplete clearance of bacterial populations following antibiotic administration; the metabolic profile of this antibiotic-recalcitrant bacterial subpopulation, the spatio-temporal context of its emergence and the variance of antibiotic-bacterial interactions in vivo remain unclear. Here, we develop and apply a mechanistic mathematical model to data from a study comparing the effects of ciprofloxacin and ampicillin on the within-host dynamics of Salmonella enterica serovar Typhimurium in murine infections. Using the inferential capacity of our model, we show that the antibiotic-recalcitrant bacteria following ampicillin, but not ciprofloxacin, treatment belong to a non-replicating phenotype. Aligning with previous studies, we independently estimate that the lymphoid tissues and spleen are important reservoirs of non-replicating bacteria. Finally, we predict that post-treatment, the progenitors of the non-growing and growing bacterial populations replicate and die at different rates. Ultimately, the liver, spleen and mesenteric lymph nodes are all repopulated by progenitors of the previously non-growing phenotype in ampicillin-treated mice.

Theoretical investigation of stochastic clearance of bacteria: first-passage analysis

Understanding mechanisms of bacterial eradication is critically important for overcoming failures of antibiotic treatments. Current studies suggest that the clearance of large bacterial populations proceeds deterministically, while for smaller populations, the stochastic effects become more relevant. Here, we develop a theoretical approach to investigate the bacterial population dynamics under the effect of antibiotic drugs using a method of first-passage processes. It allows us to explicitly evaluate the most important characteristics of bacterial clearance dynamics such as extinction probabilities and extinction times. The new meaning of minimal inhibitory concentrations for stochastic clearance of bacterial populations is also discussed. In addition, we investigate the effect of fluctuations in population growth rates on the dynamics of bacterial eradication. It is found that extinction probabilities and extinction times generally do not correlate with each other when random fluctuations in the growth rates are taking place. Unexpectedly, for a significant range of parameters, the extinction times increase due to these fluctuations, indicating a slowing in the bacterial clearance dynamics. It is argued that this might be one of the initial steps in the pathway for the development of antibiotic resistance. Furthermore, it is suggested that extinction times is a convenient measure of bacterial tolerance.

Combination of polymyxin B and minocycline against multidrug-resistant Klebsiella pneumoniae: interaction quantified by pharmacokinetic/pharmacodynamic modelling from in vitro data

Lack of effective treatment for multidrug-resistant Klebsiella pneumoniae (MDR-Kp) necessitates finding and optimising combination therapies of old antibiotics. The aims of this study were to quantify the combined effect of polymyxin B and minocycline by building an in silico semi-mechanistic pharmacokinetic/pharmacodynamic (PKPD) model and to predict bacterial kinetics when exposed to the drugs alone and in combination at clinically achievable unbound drug concentration-time profiles. A clinical K. pneumoniae strain resistant to polymyxin B [minimum inhibitory concentration (MIC) = 16 mg/L] and minocycline (MIC = 16 mg/L) was selected for extensive in vitro static time-kill experiments. The strain was exposed to concentrations of 0.0625-48 × MIC, with seven samples taken per experiment for viable counts during 0-28 h. These observations allowed the development of the PKPD model. The final PKPD model included drug-induced adaptive resistance for both drugs. Both the minocycline-induced bacterial killing and resistance onset rate constants were increased when polymyxin B was co-administered, whereas polymyxin B parameters were unaffected. Predictions at clinically used dosages from the developed PKPD model showed no or limited antibacterial effect with monotherapy, whilst combination therapy kept bacteria below the starting inoculum for >20 h at high dosages [polymyxin B 2.5 mg/kg + 1.5 mg/kg every 12 h (q12h); minocycline 400 mg + 200 mg q12h, loading + maintenance doses]. This study suggests that polymyxin B and minocycline in combination may be of clinical benefit in the treatment of infections by MDR-Kp and for isolates that are non-susceptible to either drug alone.

Translational Model-Informed Approach for Selection of Tuberculosis Drug Combination Regimens in Early Clinical Development

The development of optimal treatment regimens in tuberculosis (TB) remains challenging due to the need of combination therapy and possibility of pharmacodynamic (PD) interactions. Preclinical information about PD interactions needs to be used more optimally when designing early bactericidal activity (EBA) studies. In this work, we developed a translational approach which can allow for forward translation to predict efficacy of drug combination in EBA studies using the Multistate Tuberculosis Pharmacometric (MTP) and the General Pharmacodynamic Interaction (GPDI) models informed by in vitro static time-kill data. These models were linked with translational factors to account for differences between the in vitro system and humans. Our translational MTP-GPDI model approach was able to predict the EBA_{0-2 days} , EBA_{0-5 days} , and EBA_{0-14 days} from different EBA studies of rifampicin and isoniazid in monotherapy and combination. Our translational model approach can contribute to an optimal dose selection of drug combinations in early TB clinical trials.

Urinary piperacillin/tazobactam pharmacokinetics in vitro to determine the pharmacodynamic breakpoint for resistant Enterobacteriaceae

Urinary tract infections caused by multidrug-resistant Enterobacteriaceae are a growing burden worldwide. Recent studies of urinary pharmacokinetics described high piperacillin/tazobactam (TZP) concentrations in urine, but it is unknown whether this results in treatment efficacy. This study investigated the pharmacodynamics of TZP in a static in vitro model for Enterobacteriaceae to determine the concentration-effect relationship and ultimately the required free (unbound) time above the minimum inhibitory concentration (fT_>MIC) required for bacterial killing. The static simulation model investigated TZP fT_>MIC between 0% and 100%. Resistant Escherichia coli and Klebsiella pneumoniae isolates with piperacillin/tazobactam MICs of 4096/512, 1024/128 and 128/16 mg/L were investigated; two of the three organisms were carbapenemase-producers. Clinical efficacy was determined as a 3-log reduction over the dosing interval by comparing interval growth with controls. TZP was observed to exhibit time dependence for all organisms. The fT_>MIC was determined to be 37.5%, 37.5% and 50% for MICs of 4096/512, 1024/128 and 128/16 mg/L, respectively. Linear regression identified the overall target to be 49.85 ± 16.9% fT_>MIC. In conclusion, bactericidal activity against TZP-resistant Enterobacteriaceae occurred at 49.85 ± 16.9% fT_>MIC. This suggests that highly resistant urinary organisms, including carbapenemase-producers, with MICs up to 4096/512 mg/L could be treated with TZP. Further investigations are required to elucidate urinary breakpoints and to explore the impact of different resistance mechanisms.

Soup with or without meatballs: Impact of nutritional factors on the MIC, kill-rates and growth-rates

BACKGROUND

The Minimum Inhibitory Concentration (MIC) is a reference value for susceptibility testing of bacteria. However, the MIC is a net result of growth and killing after a certain duration of exposure under standardized favourable in vitro conditions. Killing and growth characteristics of a drug may yield more information on its activity and help to explain discrepancies between efficacy observed in vitro and in vivo.

METHODS

The MIC of meropenem was determined for P. aeruginosa ATCC 27853 both by microdilution and the E-test in dilutions of Mueller Hinton (MH) broth from 100% to 1%. Time-kill curves were obtained for twofold dilutions of meropenem. Growth rates and kill rates at each concentration and dilution were obtained by linear regression. The Hill equation was fit to the kill rates vs concentrations.

RESULTS

Growths rates decreased log linearly from 0.63/h at 100% to 0.29/h at 6% MH. Over the 100-6% MH dilution range, there was a log-linear decrease of the MIC of meropenem of both the E-test and microdilution. The EC50s decreased from 0.29 mg/L to 0.07 mg/L, which is in agreement with the MIC results. There was a log-linear relationship between MIC and EC50 for the various dilutions MH.

CONCLUSIONS

The availability of nutritional factors is related to the MIC, and a lower availability is related to both a lower growth rate and higher kill rate. Since nutritional factors are less abundantly available in vivo as compared to in vitro, this should be taken into account when translating in vitro to in vivo pharmacodynamics.

Antibiotic-induced population fluctuations and stochastic clearance of bacteria

Effective antibiotic use that minimizes treatment failures remains a challenge. A better understanding of how bacterial populations respond to antibiotics is necessary. Previous studies of large bacterial populations established the deterministic framework of pharmacodynamics. Here, characterizing the dynamics of population extinction, we demonstrated the stochastic nature of eradicating bacteria with antibiotics. Antibiotics known to kill bacteria (bactericidal) induced population fluctuations. Thus, at high antibiotic concentrations, the dynamics of bacterial clearance were heterogeneous. At low concentrations, clearance still occurred with a non-zero probability. These striking outcomes of population fluctuations were well captured by our probabilistic model. Our model further suggested a strategy to facilitate eradication by increasing extinction probability. We experimentally tested this prediction for antibiotic-susceptible and clinically-isolated resistant bacteria. This new knowledge exposes fundamental limits in our ability to predict bacterial eradication. Additionally, it demonstrates the potential of using antibiotic concentrations that were previously deemed inefficacious to eradicate bacteria.

A whole-body physiologically based pharmacokinetic (WB-PBPK) model of ciprofloxacin: a step towards predicting bacterial killing at sites of infection

The purpose of this study was to develop a whole-body physiologically based pharmacokinetic (WB-PBPK) model for ciprofloxacin for ICU patients, based on only plasma concentration data. In a next step, tissue and organ concentration time profiles in patients were predicted using the developed model. The WB-PBPK model was built using a non-linear mixed effects approach based on data from 102 adult intensive care unit patients. Tissue to plasma distribution coefficients (Kp) were available from the literature and used as informative priors. The developed WB-PBPK model successfully characterized both the typical trends and variability of the available ciprofloxacin plasma concentration data. The WB-PBPK model was thereafter combined with a pharmacokinetic-pharmacodynamic (PKPD) model, developed based on in vitro time-kill data of ciprofloxacin and Escherichia coli to illustrate the potential of this type of approach to predict the time-course of bacterial killing at different sites of infection. The predicted unbound concentration-time profile in extracellular tissue was driving the bacterial killing in the PKPD model and the rate and extent of take-over of mutant bacteria in different tissues were explored. The bacterial killing was predicted to be most efficient in lung and kidney, which correspond well to ciprofloxacin's indications pneumonia and urinary tract infections. Furthermore, a function based on available information on bacterial killing by the immune system in vivo was incorporated. This work demonstrates the development and application of a WB-PBPK-PD model to compare killing of bacteria with different antibiotic susceptibility, of value for drug development and the optimal use of antibiotics .

Modeling the growth dynamics of multiple Escherichia coli strains in the pig intestine following intramuscular ampicillin treatment

Background

This study evaluated how dosing regimen for intramuscularly-administered ampicillin, composition of Escherichia coli strains with regard to ampicillin susceptibility, and excretion of bacteria from the intestine affected the level of resistance among Escherichia coli strains in the intestine of nursery pigs. It also examined the dynamics of the composition of bacterial strains during and after the treatment. The growth responses of strains to ampicillin concentrations were determined using in vitro growth curves. Using these results as input data, growth predictions were generated using a mathematical model to simulate the competitive growth of E. coli strains in a pig intestine under specified plasma concentration profiles of ampicillin.

Results

In vitro growth results demonstrated that the resistant strains did not carry a fitness cost for their resistance, and that the most susceptible strains were more affected by increasing concentrations of antibiotics that the rest of the strains. The modeling revealed that short treatment duration resulted in lower levels of resistance and that dosing frequency did not substantially influence the growth of resistant strains. Resistance levels were found to be sensitive to the number of competing strains, and this effect was enhanced by longer duration of treatment. High excretion of bacteria from the intestine favored resistant strains over sensitive strains, but at the same time it resulted in a faster return to pre-treatment levels after the treatment ended. When the duration of high excretion was set to be limited to the treatment time (i.e. the treatment was assumed to result in a cure of diarrhea) resistant strains required longer time to reach the previous level.

Conclusion

No fitness cost was found to be associated with ampicillin resistance in E. coli. Besides dosing factors, epidemiological factors (such as number of competing strains and bacterial excretion) influenced resistance development and need to be considered further in relation to optimal treatment strategies. The modeling approach used in the study is generic, and could be used for prediction of the effect of treatment with other drugs and other administration routes for effect on resistance development in the intestine of pigs.

Electronic supplementary material

The online version of this article (doi:10.1186/s12866-016-0823-3) contains supplementary material, which is available to authorized users.

A pharmacokinetic-pharmacodynamic (PKPD) model based on in vitro time-kill data predicts the in vivo PK/PD index of colistin

OBJECTIVES

For antibiotics, extensive animal PKPD studies are often performed to evaluate the PK/PD driver for subsequent use when recommending dosing regimens. The aim of this work was to evaluate a PKPD model, developed based on in vitro time-kill data for colistin, in predicting the relationships between PK/PD indices and the bacterial killing previously observed in mice.

METHODS

An in silico PKPD model for Pseudomonas aeruginosa exposed to colistin was previously developed based on static in vitro time-kill data. The model was here applied to perform an in silico replication of an in vivo study where the effect of colistin on P. aeruginosa was studied in the thigh infection model. Concentration-time profiles of unbound colistin were predicted and used as input to drive the bacterial killing in the PKPD model. The predicted bacterial count at 24 h was related to each of the PK/PD indices and the results were compared with reported observations in vivo.

RESULTS

The model was found to adequately predict in vivo results from mice; both in terms of which PK/PD index best correlates to effect (fAUC/MIC) as well as the magnitude needed for a 2 log kill. The fAUC/MIC needed to achieve a 2 log reduction in bacterial counts after 24 h was here predicted to be 9 compared with 31 previously reported in vivo.

CONCLUSIONS

This study provides further support that PKPD models based on longitudinal data can be a useful tool to make drug development more efficient within the infectious diseases area.

Distinguishing Antimicrobial Models with Different Resistance Mechanisms via Population Pharmacodynamic Modeling

Semi-mechanistic pharmacokinetic-pharmacodynamic (PK-PD) modeling is increasingly used for antimicrobial drug development and optimization of dosage regimens, but systematic simulation-estimation studies to distinguish between competing PD models are lacking. This study compared the ability of static and dynamic in vitro infection models to distinguish between models with different resistance mechanisms and support accurate and precise parameter estimation. Monte Carlo simulations (MCS) were performed for models with one susceptible bacterial population without (M1) or with a resting stage (M2), a one population model with adaptive resistance (M5), models with pre-existing susceptible and resistant populations without (M3) or with (M4) inter-conversion, and a model with two pre-existing populations with adaptive resistance (M6). For each model, 200 datasets of the total bacterial population were simulated over 24h using static antibiotic concentrations (256-fold concentration range) or over 48h under dynamic conditions (dosing every 12h; elimination half-life: 1h). Twelve-hundred random datasets (each containing 20 curves for static or four curves for dynamic conditions) were generated by bootstrapping. Each dataset was estimated by all six models via population PD modeling to compare bias and precision. For M1 and M3, most parameter estimates were unbiased (<10%) and had good imprecision (<30%). However, parameters for adaptive resistance and inter-conversion for M2, M4, M5 and M6 had poor bias and large imprecision under static and dynamic conditions. For datasets that only contained viable counts of the total population, common statistical criteria and diagnostic plots did not support sound identification of the true resistance mechanism. Therefore, it seems advisable to quantify resistant bacteria and characterize their MICs and resistance mechanisms to support extended simulations and translate from in vitro experiments to animal infection models and ultimately patients.

Mathematical models are increasingly used for analysis and interpretation of in vitro efficacy results of antimicrobial drugs. Various models are employed in the scientific literature and it seems that they are equally able to describe the observed data. The aim of the present study was to compare different models in various experimental designs and with different resistance mechanisms of bacteria. For that purpose we have generated experimental data through Monte-Carlo simulations and then used six different mathematical models to analyze these results. We showed that statistical comparison of models did not allow determining which was the true mechanism of resistance, i.e. the one used for the simulation step. Moreover mathematical parameters for bacterial resistance were estimated with bias and with a low precision except for the simpler cases. This suggests that the choice of the mathematical model for data analysis should be guided by experimental characterization of the bacterial mechanism of resistance.

Pharmacodynamic modelling of in vitro activity of tetracycline against a representative, naturally occurring population of porcine Escherichia coli

Background

The complex relationship between drug concentrations and bacterial growth rates require not only the minimum inhibitory concentration but also other parameters to capture the dynamic nature of the relationship. To analyse this relationship between tetracycline concentration and growth of Escherichia coli representative of those found in the Danish pig population, we compared the growth of 50 randomly selected strains. The observed net growth rates were used to describe the in vitro pharmacodynamic relationship between drug concentration and net growth rate based on E_max model with three parameters: maximum net growth rate (α_max); concentration for a half-maximal response (E_max); and the Hill coefficient (γ).

Results

The net growth rate in the absence of antibiotic did not differ between susceptible and resistant isolates (P = 0.97). The net growth rate decreased with increasing tetracycline concentrations, and this decline was greater in susceptible strains than resistant strains. The lag phase, defined as the time needed for the strain to reach an OD₆₀₀ value of 0.01, increased exponentially with increasing tetracycline concentration. The pharmacodynamic parameters confirmed that the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \alpha_{max} $$\end{document}αmax between susceptible and resistant strains in the absence of a drug was not different. EC₅₀ increased linearly with MIC on a log–log scale, and γ was different between susceptible and resistant strains.

Conclusions

The in vitro model parameters described the inhibition effect of tetracycline on E. coli when strains were exposed to a wide range of tetracycline concentrations. These parameters, along with in vivo pharmacokinetic data, may be useful in mathematical models to predict in vivo competitive growth of many different strains and for development of optimal dosing regimens for preventing selection of resistance.

Applications of physiologically based pharmacokinetic modeling for the optimization of anti-infective therapies

INTRODUCTION

The pharmacokinetic properties of anti-infective drugs are a determinant part of treatment success. Pathogen replication is inhibited if adequate drug levels are achieved in target sites, whereas excessive drug concentrations linked to toxicity are to be avoided. Anti-infective distribution can be predicted by integrating in vitro drug properties and mathematical descriptions of human anatomy in physiologically based pharmacokinetic models. This method reduces the need for animal and human studies and is used increasingly in drug development and simulation of clinical scenario such as, for instance, drug-drug interactions, dose optimization, novel formulations and pharmacokinetics in special populations.

AREAS COVERED

We have assessed the relevance of physiologically based pharmacokinetic modeling in the anti-infective research field, giving an overview of mechanisms involved in model design and have suggested strategies for future applications of physiologically based pharmacokinetic models.

EXPERT OPINION

Physiologically based pharmacokinetic modeling provides a powerful tool in anti-infective optimization, and there is now no doubt that both industry and regulatory bodies have recognized the importance of this technology. It should be acknowledged, however, that major challenges remain to be addressed and that information detailing disease group physiology and anti-infective pharmacodynamics is required if a personalized medicine approach is to be achieved.

Pharmacokinetic-pharmacodynamic model to evaluate intramuscular tetracycline treatment protocols to prevent antimicrobial resistance in pigs

High instances of antimicrobial resistance are linked to both routine and excessive antimicrobial use, but excessive or inappropriate use represents an unnecessary risk. The competitive growth advantages of resistant bacteria may be amplified by the strain dynamics; in particular, the extent to which resistant strains outcompete susceptible strains under antimicrobial pressure may depend not only on the antimicrobial treatment strategies but also on the epidemiological parameters, such as the composition of the bacterial strains in a pig. This study evaluated how variation in the dosing protocol for intramuscular administration of tetracycline and the composition of bacterial strains in a pig affect the level of resistance in the intestine of a pig. Predictions were generated by a mathematical model of competitive growth of Escherichia coli strains in pigs under specified plasma concentration profiles of tetracycline. All dosing regimens result in a clear growth advantage for resistant strains. Short treatment duration was found to be preferable, since it allowed less time for resistant strains to outcompete the susceptible ones. Dosing frequency appeared to be ineffective at reducing the resistance levels. The number of competing strains had no apparent effect on the resistance level during treatment, but possession of fewer strains reduced the time to reach equilibrium after the end of treatment. To sum up, epidemiological parameters may have more profound influence on growth dynamics than dosing regimens and should be considered when designing improved treatment protocols.

Pharmacokinetic-pharmacodynamic modeling of antibacterial drugs

Pharmacokinetic-pharmacodynamic (PKPD) modeling and simulation has evolved as an important tool for rational drug development and drug use, where developed models characterize both the typical trends in the data and quantify the variability in relationships between dose, concentration, and desired effects and side effects. In parallel, rapid emergence of antibiotic-resistant bacteria imposes new challenges on modern health care. Models that can characterize bacterial growth, bacterial killing by antibiotics and immune system, and selection of resistance can provide valuable information on the interactions between antibiotics, bacteria, and host. Simulations from developed models allow for outcome predictions of untested scenarios, improved study designs, and optimized dosing regimens. Today, much quantitative information on antibiotic PKPD is thrown away by summarizing data into variables with limited possibilities for extrapolation to different dosing regimens and study populations. In vitro studies allow for flexible study designs and valuable information on time courses of antibiotic drug action. Such experiments have formed the basis for development of a variety of PKPD models that primarily differ in how antibiotic drug exposure induces amplification of resistant bacteria. The models have shown promise for efficacy predictions in patients, but few PKPD models describe time courses of antibiotic drug effects in animals and patients. We promote more extensive use of modeling and simulation to speed up development of new antibiotics and promising antibiotic drug combinations. This review summarizes the value of PKPD modeling and provides an overview of the characteristics of available PKPD models of antibiotics based on in vitro, animal, and patient data.

Pharmacokinetic/pharmacodynamic (PK/PD) indices of antibiotics predicted by a semimechanistic PKPD model: a step toward model-based dose optimization

A pharmacokinetic-pharmacodynamic (PKPD) model that characterizes the full time course of in vitro time-kill curve experiments of antibacterial drugs was here evaluated in its capacity to predict the previously determined PK/PD indices. Six drugs (benzylpenicillin, cefuroxime, erythromycin, gentamicin, moxifloxacin, and vancomycin), representing a broad selection of mechanisms of action and PK and PD characteristics, were investigated. For each drug, a dose fractionation study was simulated, using a wide range of total daily doses given as intermittent doses (dosing intervals of 4, 8, 12, or 24 h) or as a constant drug exposure. The time course of the drug concentration (PK model) as well as the bacterial response to drug exposure (in vitro PKPD model) was predicted. Nonlinear least-squares regression analyses determined the PK/PD index (the maximal unbound drug concentration [fC(max)]/MIC, the area under the unbound drug concentration-time curve [fAUC]/MIC, or the percentage of a 24-h time period that the unbound drug concentration exceeds the MIC [fT(>MIC)]) that was most predictive of the effect. The in silico predictions based on the in vitro PKPD model identified the previously determined PK/PD indices, with fT(>MIC) being the best predictor of the effect for β-lactams and fAUC/MIC being the best predictor for the four remaining evaluated drugs. The selection and magnitude of the PK/PD index were, however, shown to be sensitive to differences in PK in subpopulations, uncertainty in MICs, and investigated dosing intervals. In comparison with the use of the PK/PD indices, a model-based approach, where the full time course of effect can be predicted, has a lower sensitivity to study design and allows for PK differences in subpopulations to be considered directly. This study supports the use of PKPD models built from in vitro time-kill curves in the development of optimal dosing regimens for antibacterial drugs.