In vitro model to simulate multiple drugs with distinct elimination half-lives.

OBJECTIVE: The prevalence of drug resistance in pathogens such as HIV and selected bacteria has been steadily rising, resulting in an increased need for using multiple agents concurrently. Agents used in these combination therapies may have different elimination half-lives in humans. There is an unmet need for in vitro models to evaluate the efficacy of these combinations to guide early drug development. In order to realistically reflect in vivo conditions, useful in vitro model systems must be capable of simulating multiple pharmacokinetic profiles with distinct elimination half-lives. The goal of this study was to experimentally simulate four pharmacokinetic profiles with distinct elimination half-lives in an in vitro hollow-fibre system. METHODS: For illustrative purposes, fluctuating exposures of ceftriaxone were simulated with distinct half-lives of 1, 2.5, 8, and 12 hours. A parallel experimental setup was used to independently connect four supplemental reservoirs to a central reservoir. Target maximum concentration was achieved by direct drug dosing into the central reservoir; supplemental reservoirs were also dosed to offset the rapid drug elimination rate from the central reservoir. Serial pharmacokinetic samples were obtained from the central reservoir, assayed by a spectrophotometric method, and characterized by a one-compartment model. RESULTS: The observed maximum concentrations and elimination half-lives were in agreement with the expected values obtained from the mathematical predictions. CONCLUSIONS: This in vitro experimental system can be used to evaluate the efficacy of up to four-drug combinations against multidrug-resistant bacteria or HIV-infected mammalian cells. The established framework represents an adaptable tool to advance the field of combination therapy.

Rapid In Vitro Assessment of Antimicrobial Drug Effect Bridging Clinically Relevant Pharmacokinetics: A Comprehensive Methodology.

Rapid in vitro assessment of antimicrobial drug efficacy under clinically relevant pharmacokinetic conditions is an essential element of both drug development and clinical use. Here, we present a comprehensive overview of a recently developed novel integrated methodology for rapid assessment of such efficacy, particularly against the emergence of resistant bacterial strains, as jointly researched by the authors in recent years. This methodology enables rapid in vitro assessment of the antimicrobial efficacy of single or multiple drugs in combination, following clinically relevant pharmacokinetics. The proposed methodology entails (a) the automated collection of longitudinal time-kill data in an optical-density instrument; (b) the processing of collected time-kill data with the aid of a mathematical model to determine optimal dosing regimens under clinically relevant pharmacokinetics for single or multiple drugs; and (c) in vitro validation of promising dosing regimens in a hollow fiber system. Proof-of-concept of this methodology through a number of in vitro studies is discussed. Future directions for the refinement of optimal data collection and processing are discussed.

Systematic design of pulse dosing to eradicate persister bacteria.

A small fraction of infectious bacteria use persistence as a strategy to survive exposure to antibiotics. Periodic pulse dosing of antibiotics has long been considered a potentially effective strategy towards eradication of persisters. Recent studies have demonstrated through in vitro experiments that it is indeed feasible to achieve such effectiveness. However, systematic design of periodic pulse dosing regimens to treat persisters is currently lacking. Here we rigorously develop a methodology for the systematic design of optimal periodic pulse dosing strategies for rapid eradication of persisters. A key outcome of the theoretical analysis, on which the proposed methodology is based, is that bactericidal effectiveness of periodic pulse dosing depends mainly on the ratio of durations of the corresponding on and off parts of the pulse. Simple formulas for critical and optimal values of this ratio are derived. The proposed methodology is supported by computer simulations and in vitro experiments.

Deciphering longitudinal optical-density measurements to guide clinical dosing regimen design: A model-based approach.

BACKGROUND: Model-based analysis of longitudinal optical density measurements from a bacterial suspension exposed to antibiotics has been proposed as a potentially efficient and effective method for extracting useful information to improve the individualized design of treatments for bacterial infections. To that end, the authors developed in previous work a mathematical modeling framework that can use such measurements for design of effective dosing regimens. OBJECTIVES: Here we further explore ways to extract information from longitudinal optical density measurements to predict bactericidal efficacy of clinically relevant antibiotic exposures. METHODS: Longitudinal optical density measurements were collected in an automated instrument where Acinetobacter baumannii, ATCC BAA747, was exposed to ceftazidime concentrations of 1, 4, 16, 64, and 256 mg/L and to ceftazidime/amikacin concentrations of 1/0.5, 4/2, 16/8, 64/32, and 256/128 (mg/L)/(mg/L) over 20 h. Calibrated conversion of measurements produced total (both live and dead) bacterial cell concentration data (CFU/mL equivalent) over time. Model-based data analysis predicted the bactericidal efficacy of ceftazidime and of ceftazidime/amikacin (at ratio 2:1) for periodic injection every 8 h and subsequent exponential decline with half-life of 2.5 h. Predictions were experimentally tested in an in vitro hollow-fiber infection model, using peak concentrations of 60 and 150 mg/L for injected ceftazidime and of 40/20 (mg/L)/(mg/L) for injected ceftazidime/amikacin. RESULTS: Model-based analysis predicted low (<62%) confidence in clinically relevant suppression of the bacterial population by periodic injections of ceftazidime alone, even at high peak concentrations. Conversely, analysis predicted high (>95%) confidence in bacterial suppression by periodic injections of ceftazidime/amikacin combinations at a wide range of peak concentrations ratioed at 2:1. Both predictions were experimentally confirmed in an in vitro hollow fiber infection model, where ceftazidime was periodically injected at peak concentrations 60 and 150 mg/L (with predicted suppression confidence 38% and 59%, respectively) and a combination of ceftazidime/amikacin was periodically injected at peak concentrations 40/20 (mg/L)/(mg/L) (with predicted suppression confidence 98%). CONCLUSIONS: The paper highlights the potential of clinicians using the proposed mathematical framework to determine the utility of different antibiotics to suppress a patient-specific isolate. Additional studies will be needed to consolidate and expand the utility of the proposed method.

Revisiting the standard for modeling the spread of infectious diseases.

The COVID-19 epidemic brought to the forefront the value of mathematical modelling for infectious diseases as a guide to help manage a formidable challenge for human health. A standard dynamic model widely used for a spreading epidemic separates a population into compartments-each comprising individuals at a similar stage before, during, or after infection-and keeps track of the population fraction in each compartment over time, by balancing compartment loading, discharge, and accumulation rates. The standard model provides valuable insight into when an epidemic spreads or what fraction of a population will have been infected by the epidemic's end. A subtle issue, however, with that model, is that it may misrepresent the peak of the infectious fraction of a population, the time to reach that peak, or the rate at which an epidemic spreads. This may compromise the model's usability for tasks such as "Flattening the Curve" or other interventions for epidemic management. Here we develop an extension of the standard model's structure, which retains the simplicity and insights of the standard model while avoiding the misrepresentation issues mentioned above. The proposed model relies on replacing a module of the standard model by a module resulting from Padé approximation in the Laplace domain. The Padé-approximation module would also be suitable for incorporation in the wide array of standard model variants used in epidemiology. This warrants a re-examination of the subject and could potentially impact model-based management of epidemics, development of software tools for practicing epidemiologists, and related educational resources.

Discerning in vitro pharmacodynamics from OD measurements: A model-based approach.

Time-kill experiments can discern the pharmacodynamics of infectious bacteria exposed to antibiotics in vitro, and thus help guide the design of effective therapies for challenging clinical infections. This task is resource-limited, therefore typically bypassed in favor of empirical shortcuts. The resource limitation could be addressed by continuously assessing the size of a bacterial population under antibiotic exposure using optical density measurements. However, such measurements count both live and dead cells and are therefore unsuitable for declining populations of live cells. To fill this void, we develop here a model-based method that infers the count of live cells in a bacterial population exposed to antibiotics from continuous optical-density measurements of both live and dead cells combined. The method makes no assumptions about the underlying mechanisms that confer resistance and is widely applicable. Use of the method is demonstrated by an experimental study on Acinetobacter baumannii exposed to levofloxacin.

Ziegler and Nichols meet Kermack and McKendrick: Parsimony in dynamic models for epidemiology.

The COVID-19 crisis popularized the importance of mathematical modeling for managing epidemics. A celebrated pertinent model was developed by Kermack and McKendrick about a century ago. A simplified version of that model has long been used and became widely popular recently, even though it has limitations that its originators had clearly articulated and warned against. A basic limitation is that it unrealistically assumes zero time to recovery for most infected individuals, thus underpredicting the peak of infectious individuals in an epidemic by a factor of as much as about 2. One could avoid this limitation by returning to the original comprehensive model, at the cost of higher complexity. To remedy that, we blend Ziegler-Nichols modeling ideas, developed for automatic controller tuning, with Kermack-McKendrick ideas to develop novel model structures that predict infectious peaks accurately yet retain simplicity. We illustrate these model structures with computer simulations on real epidemiological data.

SIMULTANEOUS IN VITRO SIMULATION OF MULTIPLE ANTIMICROBIAL AGENTS WITH DIFFERENT ELIMINATION HALF-LIVES IN A PRE-CLINICAL INFECTION MODEL.

Combination therapy for treatment of multi-drug resistant bacterial infections is becoming common. In vitro testing of drug combinations under realistic pharmacokinetic conditions is needed before a corresponding combination is eventually put into clinical use. The current standard for design of such in vitro simulations for drugs with different half-lives is heuristic and limited to two drugs. To address that void, we develop a rigorous design method suitable for an arbitrary number of N drugs with different half-lives. The method developed offers substantial flexibility and produces novel designs even for two drugs. Explicit design equations are rigorously developed and are suitable for immediate use by experimenters. These equations were used in experimental verification using a combination of three antibiotics with distinctly different half-lives. In addition to antibiotics, the method is applicable to any anti-infective or anti-cancer drugs with distinct elimination pharmacokinetics.

Experimental Validation of a Mathematical Framework to Simulate Antibiotics with Distinct Half-Lives Concurrently in an In Vitro Model.

Antimicrobial resistance has been steadily increasing in prevalence, and combination therapy is commonly used to treat infections due to multidrug resistant bacteria. Under certain circumstances, combination therapy of three or more drugs may be necessary, which makes it necessary to simulate the pharmacokinetic profiles of more than two drugs concurrently in vitro. Recently, a general theoretical framework was developed to simulate three drugs with distinctly different half-lives. The objective of the study was to experimentally validate the theoretical model. Clinically relevant exposures of meropenem, ceftazidime, and ceftriaxone were simulated concurrently in a hollow-fiber infection model, with the corresponding half-lives of 1, 2.5, and 8 h, respectively. Serial samples were obtained over 24 h and drug concentrations were assayed using validated LC-MS/MS methods. A one-compartment model with zero-order input was used to characterize the observed concentration-time profiles. The experimentally observed half-lives corresponding to exponential decline of all three drugs were in good agreement with the respective values anticipated at the experiment design stage. These results were reproducible when the experiment was repeated on a different day. The validated benchtop setup can be used as a more flexible preclinical tool to explore the effectiveness of various drug combinations against multidrug resistant bacteria.

The Lambert Function Should Be in the Engineering Mathematical Toolbox.

Discovered well over two centuries ago and little used for long, the Lambert function has emerged in an increasing number of science and engineering applications in the last couple of decades. Here we present case studies relevant to the diverse interests of chemical engineers. We show how the Lambert function can be used for both analysis and computation. While some of these studies expound on prior literature results, the rest are new. We conjecture that if this tool becomes more widely known, many more instances of application will appear. Therefore, given its simplicity and usefulness, we would reasonably argue that the Lambert function should be included in the standard mathematical toolbox of chemical engineers.

Optimizing pharmacokinetics/pharmacodynamics of ß-lactam/ß-lactamase inhibitor combinations against high inocula of ESBL-producing bacteria.

OBJECTIVES: Reduced in vitro ß-lactam activity against a dense bacterial population is well recognized. It is commonly attributed to the presence of ß-lactamase(s) and it is unknown whether the inoculum effect could be diminished by a ß-lactamase inhibitor. We evaluated different ß-lactam/ß-lactamase inhibitor combinations in suppressing a high inoculum of ESBL-producing bacteria. METHODS: Three clinical isolates expressing representative ESBLs (CTX-M-15 and SHV-12) were examined. The impact of escalating ß-lactamase inhibitor (tazobactam or avibactam) concentrations on ß-lactam (piperacillin or ceftazidime) MIC reduction was characterized by an inhibitory sigmoid Emax model. The effect of various dosing regimens of ß-lactam/ß-lactamase inhibitor combinations was predicted using %T>MICi and selected exposures were experimentally validated in a hollow-fibre infection model over 120 h. The threshold exposure to suppress bacterial regrowth was identified using recursive partitioning. RESULTS: A concentration-dependent reduction in ß-lactam MIC was observed (r2 ≥0.93). Regrowth could be suppressed in all six experiments using %T>MICi ≥73.6%, but only one out of six experiments below the threshold (P = 0.015). The exposures to suppress regrowth might be attained using the clinical dose of avibactam, but a much higher dose than the standard dose would be needed for tazobactam. CONCLUSIONS: A dense population of ESBL-producing bacteria could be suppressed by an optimized dosing regimen of selected ß-lactam/ß-lactamase inhibitor combinations. The reversibility of enzyme inhibition could play an important role in diminishing the inoculum effect. In vivo investigations to validate these findings are warranted.

Azasteroid Alkylators as Dual Inhibitors of AKT and ERK Signaling for the Treatment of Ovarian Carcinoma.

(1) Background: Previous findings show that lactam steroidal alkylating esters display improved therapeutic efficacy with reduced toxicity. The aim of this study was to evaluate the anticancer activity of two newly synthesized aza-steroid alkylators (ENGA-L06E and ENGA-L08E) against human ovarian carcinoma cells, and consequently, the dual inhibition of RAS/PI3K/AKT and RAS/RAF/MEK/ERK signaling pathways, both of which are closely associated with ovarian cancer; (2) Methods: The in vitro cytostatic and cytotoxic effects of ENGA-L06E and ENGA-L08E were evaluated in a panel of five human ovarian cancer cell lines, as well as in in vivo studies. ENGA-L06E and ENGA-L08E, in addition to another two aniline-mustard alkylators, POPAM and melphalan (L-PAM), were utilized in order to determine the acute toxicity and antitumor efficacy on two human ovarian xenograft models. Also, in silico studies were performed in order to investigate the dual inhibition of ENGA-L06E and ENGA-L08E on RAS/PI3K/AKT and RAS/RAF/MEK/ERK signaling pathways; (3) Results: Both, in vitro and in vivo studies demonstrated that ENGA-L06E and ENGA-L08E were significantly more effective with a lower toxicity profile in comparison to POPAM and L-PAM alkylators. Moreover, in silico studies demonstrated that the two new aza-steroid alkylators could act as efficient inhibitors of the phosphorylation of AKT and ERK1/2 molecules; and (4) Conclusions: Both ENGA-L06E and ENGA-L08E demonstrated high anticancer activity through the inhibition of the PI3K-AKT and KRAS-ERK signaling pathways against human ovarian carcinoma, and thus constituting strong evidence towards further clinical development.

Modeling Heterogeneous Bacterial Populations Exposed to Antibiotics: The Logistic-Dynamics Case.

In typical in vitro tests for clinical use or development of antibiotics, samples from a bacterial population are exposed to an antibiotic at various concentrations. The resulting data can then be used to build a mathematical model suitable for dosing regimen design or for further development. For bacterial populations that include resistant subpopulations-an issue that has reached alarming proportions-building such a model is challenging. In prior work, we developed a related modeling framework for such heterogeneous bacterial populations following linear dynamics when exposed to an antibiotic. We extend this framework to the case of logistic dynamics, common among strongly resistant bacterial strains. Explicit formulas are developed that can be easily used in parameter estimation and subsequent dosing regimen design under realistic pharmacokinetic conditions. A case study using experimental data from the effect of an antibiotic on a gram-negative bacterial population exemplifies the usefulness of the proposed approach.

Mathematical model to quantify the effects of risk factors on carbapenem-resistant Acinetobacter baumannii.

Carbapenem-resistant Acinetobacter baumannii (CRAB) infections are increasing, and they are associated with an increased risk of mortality in hospitalized patients. Linear regression is commonly used to identify concurrent trends, but it cannot quantify the relationship between risk factors and resistance. We developed a model to quantify the impact of antibiotic consumption on the prevalence of CRAB over time. Data were collected from January 2007 to June 2013 from our institution. Quarterly antibiotic consumption was expressed as defined daily dose/1,000 inpatient days. Six-month prevalence of CRAB was expressed as a percentage of all nonrepeat A. baumannii isolates tested. Individual trends were identified using linear regression. Antibiotic consumption from 2007 to 2011 was input as a step function in a relationship with CRAB. Model fit was evaluated by visual inspection and the residual sum of squares. The final model was validated using the best-fit (95% confidence interval) parameter estimates and antibiotic consumption to predict CRAB prevalence from January 2012 to June 2013. Cefepime, ertapenem, and piperacillin-tazobactam consumption and CRAB prevalence increased significantly over time. CRAB prevalence was best correlated to ertapenem (use sensitive; r2=0.76), and accounting for additional concurrent antibiotic use did not significantly improve model fit. Prospective validation with ertapenem consumption correlated well with CRAB observations, suggesting good predicting ability of the model. Our model provided the quantitative impact of antibiotic consumption on CRAB. We plan to further refine this model to account for multiple risk factors. Interventions should focus on controlling risk factors with the highest impact on resistance.

Novel modeling framework to guide design of optimal dosing strategies for ß-lactamase inhibitors.

The scarcity of new antibiotics against drug-resistant bacteria has led to the development of inhibitors targeting specific resistance mechanisms, which aim to restore the effectiveness of existing agents. However, there are few guidelines for the optimal dosing of inhibitors. Extending the utility of mathematical modeling, which has been used as a decision support tool for antibiotic dosing regimen design, we developed a novel mathematical modeling framework to guide optimal dosing strategies for a beta-lactamase inhibitor. To illustrate our approach, MK-7655 was used in combination with imipenem against a clinical isolate of Klebsiella pneumoniae known to produce KPC-2. A theoretical concept capturing fluctuating susceptibility over time was used to define a novel pharmacodynamic index (time above instantaneous MIC [T>MIC(i)]). The MK-7655 concentration-dependent MIC reduction was characterized by using a modified sigmoid maximum effect (E(max))-type model. Various dosing regimens of MK-7655 were simulated to achieve escalating T>MIC(i) values in the presence of a clinical dose of imipenem (500 mg every 6 h). The effectiveness of these dosing exposures was subsequently validated by using a hollow-fiber infection model (HFIM). An apparent trend in the bacterial response was observed in the HFIM with increasing T>MIC(i) values. In addition, different dosing regimens of MK-7655 achieving a similar T>MIC(i) (69%) resulted in comparable bacterial killing over 48 h. The proposed framework was reasonable in predicting the in vitro activity of a novel beta-lactamase inhibitor, and its utility warrants further investigations.

Predicting bacterial fitness cost associated with drug resistance.

OBJECTIVES: It has been proposed that antimicrobial resistance could be associated with a fitness cost in bacteria, which is often determined by competition experiments between isogenic strains (wild-type and mutant). However, this conventional approach is time consuming and labour intensive. An alternative method was developed to assess the fitness cost in drug-resistant bacteria. METHODS: Time-growth studies were performed with approximately 1 × 10(5) cfu/mL of Acinetobacter baumannii or Pseudomonas aeruginosa at baseline. Serial samples were obtained to quantify the bacterial burden over 24 h. The growth rates (K(g)) of isogenic strains (antibiotic susceptible and resistant) were determined individually and used to predict their relative abundance in a co-culture over an extended period of time. The predicted difference between the two strains was subsequently validated by in vitro growth competition experiments. RESULTS: The growth rates of A. baumannii were not significantly different in different strengths of growth medium. The difference in bacterial burden observed in competition studies was in general agreement with the predicted difference based on K(g) values, suggesting good predicting ability of the mathematical model. CONCLUSIONS: The proposed mathematical model was found to be reasonable in characterizing bacterial growth and predicting the fitness cost of resistance. This simple method appears robust in the assessment of fitness cost associated with drug resistance and warrants further investigations.

Quantitative impact of neutrophils on bacterial clearance in a murine pneumonia model.

The rapid increase in the prevalence of antibiotic-resistant pathogens is a global problem that has challenged our ability to treat serious infections. Currently, clinical decisions on treatment are often based on in vitro susceptibility data. The role of the immune system in combating bacterial infections is unequivocal, but it is not well captured quantitatively. In this study, the impact of neutrophils on bacterial clearance was quantitatively assessed in a murine pneumonia model. In vitro time-growth studies were performed to determine the growth rate constants of Acinetobacter baumannii ATCC BAA 747 and Pseudomonas aeruginosa PAO1. The absolute neutrophil count in mice resulting from different cyclophosphamide preparatory regimens was determined. The dynamic change of bacterial (A. baumannii BAA 747) burden in mice with graded immunosuppression over 24 h was captured by a mathematical model. The fit to the data was satisfactory (r(2) = 0.945). The best-fit maximal kill rate (K(k)) of the bacterial population by neutrophils was 1.743 h(-1), the number of neutrophils necessary for 50% maximal killing was 190.8/µl, and the maximal population size was 1.8 × 10(9) CFU/g, respectively. Using these model parameter estimates, the model predictions were subsequently validated by the bacterial burden change of P. aeruginosa PAO1 at 24 h. A simple mathematical model was proposed to quantify the contribution of neutrophils to bacterial clearance and predict the bacterial growth/suppression in animals. Our results provide a novel framework to link in vitro and in vivo information and may be used to improve clinical treatment of bacterial infections.

Modelling biphasic killing of fluoroquinolones: guiding optimal dosing regimen design.

OBJECTIVES: Fluoroquinolones are commonly believed to exhibit concentration-dependent killing, but time-kill studies have revealed that fluoroquinolone activity could be a complex combination of concentration-dependent and -independent killing. We had previously developed a mathematical modelling framework to describe the dynamics of bacterial populations under the effect of antimicrobials, which could facilitate the design of optimal dosing regimens. Our objective was to extend the framework to describe the effect of fluoroquinolones on heterogeneous populations of Escherichia coli and Staphylococcus aureus. METHODS: A mathematical model was fitted to time-kill data of moxifloxacin (0-128× MIC; MIC = 0.0625 mg/L) against E. coli MG1655 and levofloxacin (0-64× MIC; MIC = 0.25 mg/L) against S. aureus ATCC 29213 over 24 h. Based on the best-fit model parameters, the likelihood of resistance development associated with various dosing regimens was predicted. Subsequently, in vitro studies with a hollow-fibre infection model were selectively performed to validate the mathematical model predictions, using simulated human half-lives (moxifloxacin = 12 h; levofloxacin = 5-7 h). RESULTS: Bacterial regrowth and resistance development were observed with suboptimal dosing regimens. Parallel time-growth studies substantiated the modelling assumption that there was no significant biofitness cost in resistant mutants. The mechanism of fluoroquinolone resistance was confirmed by PCR. CONCLUSIONS: Our model was found to be reasonable in characterizing biphasic killing of fluoroquinolones and predicting dosing regimens to suppress resistance development. Our work demonstrated improvements resulting from using the proposed mathematical modelling as a decision support tool for guiding the design of dosing regimens.

A novel approach to pharmacodynamic assessment of antimicrobial agents: new insights to dosing regimen design.

Pharmacodynamic modeling has been increasingly used as a decision support tool to guide dosing regimen selection, both in the drug development and clinical settings. Killing by antimicrobial agents has been traditionally classified categorically as concentration-dependent (which would favor less fractionating regimens) or time-dependent (for which more frequent dosing is preferred). While intuitive and useful to explain empiric data, a more informative approach is necessary to provide a robust assessment of pharmacodynamic profiles in situations other than the extremes of the spectrum (e.g., agents which exhibit partial concentration-dependent killing). A quantitative approach to describe the interaction of an antimicrobial agent and a pathogen is proposed to fill this unmet need. A hypothetic antimicrobial agent with linear pharmacokinetics is used for illustrative purposes. A non-linear functional form (sigmoid Emax) of killing consisted of 3 parameters is used. Using different parameter values in conjunction with the relative growth rate of the pathogen and antimicrobial agent concentration ranges, various conventional pharmacodynamic surrogate indices (e.g., AUC/MIC, Cmax/MIC, %T>MIC) could be satisfactorily linked to outcomes. In addition, the dosing intensity represented by the average kill rate of a dosing regimen can be derived, which could be used for quantitative comparison. The relevance of our approach is further supported by experimental data from our previous investigations using a variety of gram-negative bacteria and antimicrobial agents (moxifloxacin, levofloxacin, gentamicin, amikacin and meropenem). The pharmacodynamic profiles of a wide range of antimicrobial agents can be assessed by a more flexible computational tool to support dosing selection.