Mathematical modeling of septic shock: an innovative tool for assessing therapeutic hypotheses

Mathematical models of cystic fibrosis as a systemic disease

Cystic fibrosis (CF) is widely known as a disease of the lung, even though it is in truth a systemic disease, whose symptoms typically manifest in gastrointestinal dysfunction first. CF ultimately impairs not only the pancreas and intestine but also the lungs, gonads, liver, kidneys, bones, and the cardiovascular system. It is caused by one of several mutations in the gene of the epithelial ion channel protein CFTR. Intense research and improved antimicrobial treatments during the past eight decades have steadily increased the predicted life expectancy of a person with CF (pwCF) from a few weeks to over 50 years. Moreover, several drugs ameliorating the sequelae of the disease have become available in recent years, and notable treatments of the root cause of the disease have recently generated substantial improvements in health for some but not all pwCF. Yet, numerous fundamental questions remain unanswered. Complicating CF, for instance in the lung, is the fact that the associated insufficient chloride secretion typically perturbs the electrochemical balance across epithelia and, in the airways, leads to the accumulation of thick, viscous mucus and mucus plaques that cannot be cleared effectively and provide a rich breeding ground for a spectrum of bacterial and fungal communities. The subsequent infections often become chronic and respond poorly to antibiotic treatments, with outcomes sometimes only weakly correlated with the drug susceptibility of the target pathogen. Furthermore, in contrast to rapidly resolved acute infections with a single target pathogen, chronic infections commonly involve multi-species bacterial communities, called "infection microbiomes," that develop their own ecological and evolutionary dynamics. It is presently impossible to devise mathematical models of CF in its entirety, but it is feasible to design models for many of the distinct drivers of the disease. Building upon these growing yet isolated modeling efforts, we discuss in the following the feasibility of a multi-scale modeling framework, known as template-and-anchor modeling, that allows the gradual integration of refined sub-models with different granularity. The article first reviews the most important biomedical aspects of CF and subsequently describes mathematical modeling approaches that already exist or have the potential to deepen our understanding of the multitude aspects of the disease and their interrelationships. The conceptual ideas behind the approaches proposed here do not only pertain to CF but are translatable to other systemic diseases. This article is categorized under: Congenital Diseases > Computational Models.

Dynamical modeling of pro- and anti-inflammatory cytokines in the early stage of septic shock

A dynamical model of the pathophysiological behaviors of IL18 and IL10 cytokines with their receptors is tested against data for the case of early sepsis. The proposed approach considers the surroundings (organs and bone marrow) and the different subsystems (cells and cyctokines). The interactions between blood cells, cytokines and the surroundings are described via mass balances. Cytokines are adsorbed onto associated receptors at the cell surface. The adsorption is described by the Langmuir model and gives rise to the production of more cytokines and associated receptors inside the cell. The quantities of pro and anti-inflammatory cytokines present in the body are combined to give global information via an inflammation level function which describes the patient’s state. Data for parameter estimation comes from the Sepsis 48 H database. Comparisons between patient data and simulations are presented and are in good agreement. For the IL18/IL10 cytokine pair, 5 key parameters have been found. They are linked to pro-inflammatory IL18 cytokine and show that the early sepsis is driven by components of inflammatory character.