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.

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.

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.