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.

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.

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.

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 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.