Abstract
In recent years, there has been an increasing interest in the mathematical and computational modeling of the human immune system (HIS). Computational models of HIS dynamics may contribute to a better understanding of the relationship between complex phenomena and immune response; in addition, computational models will support the development of new drugs and therapies for different diseases. However, modeling the HIS is an extremely difficult task that demands a huge amount of work to be performed by multidisciplinary teams. In this study, our objective is to model the spatio-temporal dynamics of representative cells and molecules of the HIS during an immune response after the injection of lipopolysaccharide (LPS) into a section of tissue. LPS constitutes the cellular wall of Gram-negative bacteria, and it is a highly immunogenic molecule, which means that it has a remarkable capacity to elicit strong immune responses. We present a descriptive, mechanistic and deterministic model that is based on partial differential equations (PDE). Therefore, this model enables the understanding of how the different complex phenomena interact with structures and elements during an immune response. In addition, the model's parameters reflect physiological features of the system, which makes the model appropriate for general use.
Highlights
The human immune system (HIS) consists of a wide and complex network of cells, tissues and organs
Our model allows each point of the tissue to be irrigated by arterioles and vessels, so that cells in the blood stream can enter into the tissue at any point. This is equivalent to a two-domain model, in which one domain represents the concentration of immune cells in the vascular system (in our case, neutrophils, N max(x, t), and macrophages, Mmax(x, t)) and the other domain represents the different cells and molecules present in the tissue (our model considers lipopolysaccharide (LPS), neutrophils (N), apoptotic neutrophils (ND), pro-inflammatory cytokines (CH), anti-inflammatory cytokines (AC), protein granules (G), resting (RM) and hyperactivated (AM) macrophages)
We have proposed a mathematical model that incorporates the main interactions occurring between LPS and some cells and molecules of the innate immune system
Summary
The human immune system (HIS) consists of a wide and complex network of cells, tissues and organs. Case 4: incorporates protein granules into the model, which are produced by neutrophils and contribute to an increase in the endothelium’s permeability, allowing more monocytes to enter into the tissues and differentiate in resting macrophages.
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