Mathematical modeling the effect of antimicrobials on heterogeneous bacterial populations



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This dissertation comprises of six chapters with chapters 2-4 being individual case studies, each case study corresponding to a project involving use of mathematical modeling to characterize the effect of antimicrobials on bacterial populations.
In the second chapter a novel mathematical modeling framework to characterize the inoculum effect is proposed. In our approach the inoculum effect was solely attributed to reduced effective drug exposure. Accordingly, a simplified model pharmacodynamic model was developed where the reduced effective drug exposure was expressed as a function of initial bacterial burden. A case of Escherichia coli against a combination of piperacillin and tazobactum was used to characterize the model and validate the model assumptions. In the third chapter, a pharmacodynamic model was used to characterize the biphasic killing profiles observed for the effect of flouroquinolones against both gram-positive and gram-negative bacteria. Time-kill experiment data for the Escherichia coli against moxifloxacin and Staphyloccocus aureus against levofloxacin was used to characterize the model. Further, the model was used to make predictions regarding the design of the optimal dosing strategy which was selectively validated in the Hollow Fiber Infection Model. In chapter four, the issue of fluctuating bacterial susceptibilities in the presence of a combination antibiotic and inhibitor was addressed using a novel modeling approach. Instantaneous Minimum Inhibitory Concentration (MICi) was defined to capture fluctuating susceptibilities. A theoretical concept capturing fluctuating susceptibility over time was used to define a novel pharmacodynamic index (Time above instantaneous MIC [T > MICi]). The approach was illustrated using a novel beta-lactamase inhibitor MK-7655 in combination with imipenem against a clinical isolate of Klesiella pneumonia Klebseilla pneumoniae. Finally in the fourth chapter mathematical modeling was used to characterize immune-response (granulocyte clearance) against bacterial infections. The semi-mechanistic immune response model was then integrated with a drug effect model to characterize bacterial dynamics in the presence of both immune and drug pressure. The immune-response model was used to characterize bacterial time-kill dynamics for naïve and neutropenic mice. The immune-drug integrated model was later used to model the invivo time-kill data for naïve and neutropenic mice infected with Klebsiella pneumoniae (KP-1470) treated with PF-05081090.



Mathematical modeling, Antimicrobials, Bacteria, Heterogeneity