Modelling inflammatory biomarker dynamics in a human lipopolysaccharide (LPS) challenge study using delay differential equations.

ABSTRACT

Clinical studies in healthy volunteers challenged with lipopolysaccharide (LPS), a constituent of the cell wall of Gram-negative bacteria, represent a key model to characterize the Toll-like receptor 4 (TLR4)-mediated inflammatory response. Here, we developed a mathematical modelling framework to quantitatively characterize the dynamics and inter-individual variability of multiple inflammatory biomarkers in healthy volunteer LPS challenge studies. Data from previously reported LPS challenge studies were used, which included individual-level time-course data for tumour necrosis factor α (TNF-α), interleukin 6 (IL-6), interleukin 8 (IL-8) and C-reactive protein (CRP). A one-compartment model with first-order elimination was used to capture the LPS kinetics. The relationships between LPS and inflammatory markers was characterized using indirect response (IDR) models. Delay differential equations were applied to quantify the delays in biomarker response profiles. For LPS kinetics, our estimates of clearance and volume of distribution were 35.7 L h-1 and 6.35 L, respectively. Our model adequately captured the dynamics of multiple inflammatory biomarkers. The time delay for the secretion of TNF-α, IL-6 and IL-8 were estimated to be 0.924, 1.46 and 1.48 h, respectively. A second IDR model was used to describe the induced changes of CRP in relation to IL-6, with a delayed time of 4.2 h. The quantitative models developed in this study can be used to inform design of clinical LPS challenge studies and may help to translate preclinical LPS challenge studies to humans.