PK-PD modeling of β-lactam antibiotics: in vitro or in vivo models?

An integrative and translational PK/PD modelling approach to explore the combined effect of polymyxin B and minocycline against Klebsiella pneumoniae

OBJECTIVES

To expand a translational pharmacokinetic-pharmacodynamic (PK/PD) modelling approach for assessing the combined effect of polymyxin B and minocycline against Klebsiella pneumoniae.

METHODS

A PK/PD model developed based on in vitro static time-kill experiments of one strain (ARU613) was first translated to characterize that of a more susceptible strain (ARU705), and thereafter to dynamic time-kill experiments (both strains) and to a murine thigh infection model (ARU705 only). The PK/PD model was updated stepwise using accumulated data. Predictions of bacterial killing in humans were performed.

RESULTS

The same model structure could be used in each translational step, with parameters being re-estimated. Dynamic data were well predicted by static-data-based models. The in vitro/in vivo differences were primarily quantified as a change in polymyxin B effect: a lower killing rate constant in vivo compared with in vitro (concentration of 3 mg/L corresponds to 0.05/h and 57/h, respectively), and a slower adaptive resistance rate (the constant in vivo was 2.5% of that in vitro). There was no significant difference in polymyxin B-minocycline interaction functions. Predictions based on both in vitro and in vivo parameters indicated that the combination has a greater-than-monotherapy antibacterial effect in humans, forecasting a reduction of approximately 5 and 2 log10 colony-forming units/mL at 24 h, respectively, under combined therapy, while the maximum bacterial load was reached in monotherapy.

CONCLUSIONS

This study demonstrated the utility of the PK/PD modelling approach to understand translation of antibiotic effects across experimental systems, and showed a promising antibacterial effect of polymyxin B and minocycline in combination against K. pneumoniae.

Impact of nutritional factors on in vitro PK/PD modelling of polymyxin B against various strains of Acinetobacter baumannii

The main objective of this study was to assess the effect of rich artificial cation-adjusted Mueller-Hinton broth (CAMHB) on the growth of three strains of Acinetobacter baumannii (ATCC 19606 and two clinical strains), either susceptible or resistant to polymyxin B (PMB), and on PMB bactericidal activity. A pharmacokinetic (PK)/pharmacodynamic (PD) modelling approach was used to characterize the effect of PMB in various conditions. Time-kill experiments were performed using undiluted CAMHB or CAMHB diluted to 50%, 25% and 10%, with or without Ca2+ and Mg2+ compensation (known to affect PMB activity), and with PMB concentrations ranging from 0.25 to 256 mg/L based on the strain's MIC. For each strain, time-kill replicates were modelled using NONMEM. Unexpectedly, dilution of CAMHB by up to 10-fold did not affect the growth rate of any of the three strains in the absence of PMB. However, the bactericidal activity of PMB increased with medium dilution, resulting in a reduction in the apparent bacterial regrowth of the various strains observed after a few hours. Data for each strain were well characterized by a PK/PD model, with two bacterial subpopulations with different susceptibility to PMB (more susceptible and less susceptible). The impact of medium dilution and cation compensation showed relatively high, unexplained between-strain variability. Further studies are needed to characterize the mechanism underlying the medium dilution effect.

Translational PK/PD for the Development of Novel Antibiotics-A Drug Developer's Perspective

Antibiotic development traditionally involved large Phase 3 programs, preceded by Phase 2 studies. Recognizing the high unmet medical need for new antibiotics and, in some cases, challenges to conducting large clinical trials, regulators created a streamlined clinical development pathway in which a lean clinical efficacy dataset is complemented by nonclinical data as supportive evidence of efficacy. In this context, translational Pharmacokinetic/Pharmacodynamic (PK/PD) plays a key role and is a major contributor to a "robust" nonclinical package. The classical PK/PD index approach, proven successful for established classes of antibiotics, is at the core of recent antibiotic approvals and the current antibacterial PK/PD guidelines by regulators. Nevertheless, in the case of novel antibiotics with a novel Mechanism of Action (MoA), there is no prior experience with the PK/PD index approach as the basis for translating nonclinical efficacy to clinical outcome, and additional nonclinical studies and PK/PD analyses might be considered to increase confidence. In this review, we discuss the value and limitations of the classical PK/PD approach and present potential risk mitigation activities, including the introduction of a semi-mechanism-based PK/PD modeling approach. We propose a general nonclinical PK/PD package from which drug developers might choose the studies most relevant for each individual candidate in order to build up a "robust" nonclinical PK/PD understanding.

Pharmacokinetic/Pharmacodynamic Modeling and Application in Antibacterial and Antifungal Pharmacotherapy: A Narrative Review

Pharmacokinetics and pharmacodynamics are areas in pharmacology related to different themes in the pharmaceutical sciences, including therapeutic drug monitoring and different stages of drug development. Although the knowledge of these disciplines is essential, they have historically been treated separately. While pharmacokinetics was limited to describing the time course of plasma concentrations after administering a drug-dose, pharmacodynamics describes the intensity of the response to these concentrations. In the last decades, the concept of pharmacokinetic/pharmacodynamic modeling (PK/PD) emerged, which seeks to establish mathematical models to describe the complete time course of the dose-response relationship. The integration of these two fields has had applications in optimizing dose regimens in treating antibacterial and antifungals. The anti-infective PK/PD models predict the relationship between different dosing regimens and their pharmacological activity. The reviewed studies show that PK/PD modeling is an essential and efficient tool for a better understanding of the pharmacological activity of antibacterial and antifungal agents.

Design and Measurement of Drug Tissue Concentration Asymmetry and Tissue Exposure-Effect (Tissue PK-PD) Evaluation

The "free drug hypothesis" assumes that, in the absence of transporters, the steady state free plasma concentrations equal to that at the site of action that elicit pharmacologic effects. While it is important to utilize the free drug hypothesis, exceptions exist that the free plasma exposures, either at C_max, C_trough, and C_average, or at other time points, cannot represent the corresponding free tissue concentrations. This "drug concentration asymmetry" in both total and free form can influence drug disposition and pharmacological effects. In this review, we first discuss options to assess total and free drug concentrations in tissues. Then various drug design strategies to achieve concentration asymmetry are presented. Last, the utilities of tissue concentrations in understanding exposure-effect relationships and translational projections to humans are discussed for several therapeutic areas and modalities. A thorough understanding in plasma and tissue exposures correlation with pharmacologic effects can provide insightful guidance to aid drug discovery.

Optimizing Antimicrobial Therapy by Integrating Multi-Omics With Pharmacokinetic/Pharmacodynamic Models and Precision Dosing

In the era of “Bad Bugs, No Drugs,” optimizing antibiotic therapy against multi-drug resistant (MDR) pathogens is crucial. Mathematical modelling has been employed to further optimize dosing regimens. These models include mechanism-based PK/PD models, systems-based models, quantitative systems pharmacology (QSP) and population PK models. Quantitative systems pharmacology has significant potential in precision antimicrobial chemotherapy in the clinic. Population PK models have been employed in model-informed precision dosing (MIPD). Several antibiotics require close monitoring and dose adjustments in order to ensure optimal outcomes in patients with infectious diseases. Success or failure of antibiotic therapy is dependent on the patient, antibiotic and bacterium. For some drugs, treatment responses vary greatly between individuals due to genotype and disease characteristics. Thus, for these drugs, tailored dosing is required for successful therapy. With antibiotics, inappropriate dosing such as insufficient dosing may put patients at risk of therapeutic failure which could lead to mortality. Conversely, doses that are too high could lead to toxicities. Hence, precision dosing which customizes doses to individual patients is crucial for antibiotics especially those with a narrow therapeutic index. In this review, we discuss the various strategies in optimizing antimicrobial therapy to address the challenges in the management of infectious diseases and delivering personalized therapy.

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.

PKPD Modeling of the Inoculum Effect of Acinetobacter baumannii on Polymyxin B in vivo

The reduction in antimicrobial activity at high bacterial counts is a microbiological phenomenon known as the inoculum effect (IE). In a previous in vitro study, a significant IE was observed for polymyxin B (PMB) against a clinical isolate of Acinetobacter baumannii, and well described by a new pharmacokinetic-pharmacodynamic model. Few in vivo studies have investigated the impact of inoculum size on survival or antibiotic efficacy. Therefore, our objective was to confirm the influence of inoculum size of this A. baumannii clinical isolate on PMB in vivo effect over time. Pharmacokinetics and pharmacodynamics of PMB after a single subcutaneous administration (1, 15 and 40 mg/kg) were studied in a neutropenic murine thigh infection model. The impact of A. baumannii inoculum size (10⁵, 10⁶ and 10⁷ CFU/thigh) on PMB efficacy was also evaluated. In vivo PMB PK was well described by a two-compartment model including saturable absorption from the subcutaneous injection site and linear elimination. The previous in vitro PD model was modified to adequately describe the decrease of PMB efficacy with increased inoculum size in infected mice. The IE was modeled as a decrease of 32% in the in vivo PMB bactericidal effect when the starting inoculum increases from 10⁵ to 10⁷ CFU/thigh. Although not as important as previously characterized in vitro an IE was confirmed in vivo.

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.

Population Pharmacokinetic Modeling as a Tool To Characterize the Decrease in Ciprofloxacin Free Interstitial Levels Caused by Pseudomonas aeruginosa Biofilm Lung Infection in Wistar Rats

Biofilm formation plays an important role in the persistence of pulmonary infections, for example, in cystic fibrosis patients. So far, little is known about the antimicrobial lung disposition in biofilm-associated pneumonia. This study aimed to evaluate, by microdialysis, ciprofloxacin (CIP) penetration into the lungs of healthy and Pseudomonas aeruginosa biofilm-infected rats and to develop a comprehensive model to describe the CIP disposition under both conditions. P. aeruginosa was immobilized into alginate beads and intratracheally inoculated 14 days before CIP administration (20 mg/kg of body weight). Plasma and microdialysate were sampled from different animal groups, and the observations were evaluated by noncompartmental analysis (NCA) and population pharmacokinetic (popPK) analysis. The final model that successfully described all data consisted of an arterial and a venous central compartment and two peripheral distribution compartments, and the disposition in the lung was modeled as a two-compartment model structure linked to the venous compartment. Plasma clearance was approximately 32% lower in infected animals, leading to a significantly higher level of plasma CIP exposure (area under the concentration-time curve from time zero to infinity, 27.3 ± 12.1 μg · h/ml and 13.3 ± 3.5 μg · h/ml in infected and healthy rats, respectively). Despite the plasma exposure, infected animals showed a four times lower tissue concentration/plasma concentration ratio (lung penetration factor = 0.44 and 1.69 in infected and healthy rats, respectively), and lung clearance (CL_lung) was added to the model for these animals (CL_lung = 0.643 liters/h/kg) to explain the lower tissue concentrations. Our results indicate that P. aeruginosa biofilm infection reduces the CIP free interstitial lung concentrations and increases plasma exposure, suggesting that plasma concentrations alone are not a good surrogate of lung concentrations.

Correlating Drug-Target Kinetics and In vivo Pharmacodynamics: Long Residence Time Inhibitors of the FabI Enoyl-ACP Reductase

Drug-target kinetics enable time-dependent changes in target engagement to be quantified as a function of drug concentration. When coupled to drug pharmacokinetics (PK), drug-target kinetics can thus be used to predict in vivo pharmacodynamics (PD). Previously we described a mechanistic PK/PD model that successfully predicted the antibacterial activity of an LpxC inhibitor in a model of Pseudomonas aeruginosa infection. In the present work we demonstrate that the same approach can be used to predict the in vivo activity of an enoyl-ACP reductase (FabI) inhibitor in a model of methicillin-resistant Staphylococcus aureus (MRSA) infection. This is significant because the LpxC inhibitors are cidal, whereas the FabI inhibitors are static. In addition P. aeruginosa is a Gram-negative organism whereas MRSA is Gram-positive. Thus this study supports the general applicability of our modeling approach across antibacterial space.

Pharmacokinetics/pharmacodynamic correlations of fluconazole in murine model of cryptococcosis

The emergence of fluconazole-resistant Cryptococcus gattii is a global concern, since this azole is the main antifungal used worldwide to treat patients with cryptococcosis. Although pharmacokinetic (PK) and pharmacodynamic (PD) indices are useful predictive factors for therapeutic outcomes, there is a scarcity of data regarding PK/PD analysis of antifungals in cryptococcosis caused by resistant strains. In this study, PK/PD parameters were determined in a murine model of cryptococcosis caused by resistant C. gattii. We developed and validated a suitable liquid chromatography-electrospray ionization tandem mass spectrometry method for PK studies of fluconazole in the serum, lungs, and brain of uninfected mice. Mice were infected with susceptible or resistant C. gattii, and the effects of different doses of fluconazole on the pulmonary and central nervous system fungal burden were determined. The peak levels in the serum, lungs, and brain were achieved within 0.5h. The AUC/MIC index (area under the curve/minimum inhibitory concentration) was associated with the outcome of anti-cryptococcal therapy. Interestingly, the maximum concentration of fluconazole in the brain was lower than the MIC for both strains. In addition, the treatment of mice infected with the resistant strain was ineffective even when high doses of fluconazole were used or when amphotericin B was tested, confirming the cross-resistance between these drugs. Altogether, our novel data provide the correlation of PK/PD parameters with antifungal therapy during cryptococcosis caused by resistant C. gattii.

Response of a clinical Escherichia coli strain to repeated cefquinome exposure in a piglet tissue-cage model

BACKGROUND

In order to provide some basis for effective dosage regimens that optimize efficacy with respect to bacteriological and clinical cures, the in vivo activity of cefquinome against a clinical Escherichia coli (E.coli) strain (the minimum inhibitory concentration value for this strain equals to the MIC90 value of 0.25 μg/ml for 210 E.coli strains isolated from pigs) was investigated by using a piglet tissue-cage infection model. The aim was to elucidate the pharmacokinetic/pharmacodynamics (PK/PD) index associated with cefquinome efficacy, and then to identify the magnitude of the PK/PD parameter required for different degree of efficacy in clinical treatment.

RESULTS

Tissue-cage infection model was established in piglets, and then the animals received intramuscular injection of cefquinome twice a day for 3 days to create a range of different drug exposures. The tissue-cage fluid was collected at 1, 3, 6, 9 and 12 h after every drug administration for drug concentrationdetermination and bacteria counting. Different cefquinome regimens produced different percentages of time during that drug concentrations exceeded the MIC (%T > MIC), ranging from 0% to 100%. Cefquinome administration at 0.2, 0.4, 0.6, 0.8, 1, 2 and 4 mg/kg reduced the bacterial count (log10 CFU/mL) in tissue-cage fluid by -1.00 ± 0.32, -1.83 ± 0.08, -2.33 ± 0.04, -2.96 ± 0.16, -2.99 ± 0.16, -2.93 ± 0.11, -3.43 ± 0.18, respectively. The correlation coefficient of the PK/PD index with antibacterial effect of the drug was 0.90 for %T > MIC, 0.62 for AUC0-12/MIC, and 0.61 for Cmax/MIC, suggesting the most important PK/PD parameter was %T > MIC. A inhibitory form of sigmoid maximum effect (Emax) model was used to estimate %T > MIC, and the respective values required for continuous 1/6-log drop, 1/3-log drop and 1/2-log drop of the clinical E.coli count during each 12 h treatment period were 3.97%, 17.08% and 52.68%.

CONCLUSIONS

The data derived from this study showed that cefquinome exhibited time-dependent killing profile. And from the results of the present study, it can be assumed that when %T > MIC reached 52.68%, cefquinome could be expected to be effective against a clinical E.coli strain for which the MIC value is below 0.128 μg/ml (3-log drop of bacteria count can be achieved after six successive administrations for 3 days).

The immune response and antibacterial therapy

The host's immune defence mechanisms are indispensable factors in surviving bacterial infections. However, in many circumstances, the immune system alone is inadequate. Since the 1940s, the use of antibacterial therapy has saved millions of lives, improving the span and quality of life of individuals. Unfortunately, we are now facing an era where antibacterial agents are threatened by resistance. In addition to targeting bacteria, some antibacterial agents affect various aspects of the immune response to infection. Since many antibacterial drugs are failing in efficacy due to resistance, it has been strongly suggested that any synergy between these drugs and the immune response be exploited in the treatment of bacterial infections. This review explores the influence of antibacterial therapy on the immune response and new approaches that could exploit this interaction for the treatment of bacterial infections.

Population pharmacokinetic modeling of the unbound levofloxacin concentrations in rat plasma and prostate tissue measured by microdialysis

Levofloxacin is a broad-spectrum fluoroquinolone used in the treatment of both acute and chronic bacterial prostatitis. Currently, the treatment of bacterial prostatitis is still difficult, especially due to the poor distribution of many antimicrobials into the prostate, thus preventing the drug to reach effective interstitial concentrations at the infection site. Newer fluoroquinolones show a greater penetration into the prostate. In the present study, we compared the unbound levofloxacin prostate concentrations measured by microdialysis to those in plasma after a 7-mg/kg intravenous bolus dose to Wistar rats. Plasma and dialysate samples were analyzed using a validated high-pressure liquid chromatography-fluorescence method. Both noncompartmental analysis (NCA) and population-based compartmental modeling (NONMEM 6) were performed. Unbound prostate tissue concentrations represented 78% of unbound plasma levels over a period of 12 h by comparing the extent of exposure (unbound AUC0-∞) of 6.4 and 4.8 h·μg/ml in plasma and tissue, respectively. A three-compartment model with simultaneous passive diffusion and saturable distribution kinetics from the prostate to the central compartment gave the best results in terms of curve fitting, precision of parameter estimates, and model stability. The following parameter values were estimated by the population model: V1 (0.38 liter; where V1 represents the volume of the central compartment), CL (0.22 liter/h), k12 (2.27 h(-1)), k21 (1.44 h(-1)), k13 (0.69 h(-1)), Vmax (7.19 μg/h), kM (0.35 μg/ml), V3/fuprostate (0.05 liter; where fuprostate represents the fraction unbound in the prostate), and k31 (3.67 h(-1)). The interindividual variability values for V1, CL, Vmax, and kM were 21, 37, 42, and 76%, respectively. Our results suggest that levofloxacin is likely to be substrate for efflux transporters in the prostate.

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.