Dynamical Modeling of the Immune System in Case of Septicemia

Homeostasis is the ability of a living system to maintain a healthy equilibrium using pro-inflammatory and anti-inflammatory mechanisms. Septicemia is the body’s response to a generalized infection of the blood by a pathogen and the living system can lose its ability to maintain healthy equilibrium, possibly leading to death. Sepsis has been recognized as a major public health problem [1].

A study “Sepsis 48h” included twenty-eight patients in septic shock and admitted in two ICUs of a university hospital has been performed. Details are given in [2]. A blood sample was taken every 6 hours for 48 hour, and after 6 days for some patients.

In the literature, the modeling of the immune system is quickly limited by the complexity of the systems. The more common models are based on closed and uniform systems and don’t take into account thermodynamics or transport phenomena between cells and blood [3].

Our approach considers the environment and the different subsystems. The immune system is the blood, the subsystems are leukocyte cells and cytokines. The interactions between blood cells and the environment are described via mass balances. The transport phenomena between cells and blood and thermodynamic equilibrium are considered. The quantities of pro and anti-cytokines are combined to give the inflammatory state of the patient. The proposed dynamic model is strongly nonlinear. Several equilibria and limit cycles can be reproduced after septic shock.

From "Sepsis 48h”, cytokines (IL1 and IL10) and associated receptors have been chosen. Simulation and experimental data of cytokines and receptors evolution have been compared and discussed.

[1] Global Sepsis Alliance. WHA Adopts Resolution on Sepsis. https://www.global-sepsis-alliance.org/news/2017/5/26/wha-adopts-resolution-on-sepsis. Accessed 15 Feb 2018.

[2] Cazalis, M.A. et al. Intensive Care Medecine Experimental 2-20, DOI:10.1186/s40635-014-0020-3 (2014)

[3] Androulakis, I.P. et al., Journal of Critical Care (27), 3 (2012): 314.e1–314.e11.