Mathematical modeling of pulmonary tuberculosis therapy: development of a first prototype model with rifampin
S. Goutelle (1,2), L. Bourguignon (1,2), R.W. Jelliffe (3), J.E. Conte Jr (4,5), P. Maire (1,2)
(1) University of Lyon 1, UMR CNRS 5558, Lyon, France; (2) University Hospitals of Lyon, Geriatric Hospital Group, Department of Pharmacy and ADCAPT, Francheville, France; (3) Laboratory of Applied Pharmacokinetics, USC Keck School of Medicine, Los Angeles, USA ; (4) Department of Epidemiology & Biostatistics, University of California, San Francisco, San Francisco, USA; (5) American Health Sciences, San Francisco, USA
Objectives: There is a critical need for a shorter tuberculosis (TB) treatment to improve TB control. Current experimental models of TB, while still valuable, are poor predictors of the antibacterial effect of drugs in vivo. Mathematical models may be helpful to understand current problems associated with TB therapy and to suggest innovations. The objective of this study was to set up a prototype mathematical model of TB treatment by rifampin (RIF), based on pharmacokinetic (PK), pharmacodynamic (PD), and physiological submodels.
Methods: A pulmonary diffusion model of RIF was used as the PK model . The PD model was a Hill equation-based model with parameter values derived from experimental data [2,3]. Those two submodels were assembled with the Kirschner's model which describes the dynamics of bacteria, cytokines and cells in the lungs during TB infection . The full model implemented in Matlab software featured 21 differential equations. PK variability was introduced in the model by using the parameter values of 34 subjects estimated in the population study . Therapeutic simulations were performed with the full model to study the antibacterial effect of various dosage regimens of RIF in lungs. The log-reductions of extracellular bacteria (BE) over the first days of therapy simulated by the model were compared with published values of early bactericidal activity (EBA). In addition, simple PK/PD models derived from the full model were analysed to study the consequences of model reductions on the simulated antibacterial effect.
Results: The full model can simulate the time-course of the bacterial population in lungs from the first day of infection to the last day of therapy. The bactericidal activities (mean ± SD log10 BE/ml/day) predicted by the model over the first 2 days in 34 subjects were 0.102 ± 0.090 and 0.277 ± 0.229 for a 300 mg and a 600 mg daily dose, respectively. Those results were in agreement with published values of EBA . The kill curves simulated by the model showed a typical biphasic decline in the number of bacteria consistent with observations in TB patients. Simulations performed with simple PK/PD models indicated a possible role of a protected intracellular bacterial compartment in such biphasic decline.
Conclusions: This work is a very preliminary effort towards a complete mathematical description of TB therapy. However, this first prototype model suggests a new hypothesis for the bacterial persistence during TB treatment.
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