A Mathematical Model of the Inflammatory Response to Pathogen Challenge

A mechanistic modelling approach of the host-microbiota interactions to investigate beneficial symbiotic resilience in the human gut

The health and well-being of a host are deeply influenced by the interactions with its gut microbiota. Contrasted environmental conditions, such as diseases or dietary habits, play a pivotal role in modulating these interactions, impacting microbiota composition and functionality. Such conditions can also lead to transitions from beneficial to detrimental symbiosis, viewed as alternative stable states of the host-microbiota dialogue. This article introduces a novel mathematical model exploring host-microbiota interactions, integrating dynamics of the colonic epithelial crypt, microbial metabolic functions, inflammation sensitivity and colon flows in a transverse section. The model considers metabolic shifts in epithelial cells based on butyrate and hydrogen sulfide concentrations, innate immune pattern recognition receptor activation, microbial oxygen tolerance and the impact of antimicrobial peptides on the microbiota. Using the model, we demonstrated that a high-protein, low-fibre diet exacerbates detrimental interactions and compromises beneficial symbiotic resilience, underscoring a destabilizing effect towards an unhealthy state. Moreover, the proposed model provides essential insights into oxygen levels, fibre and protein breakdown, and basic mechanisms of innate immunity in the colon and offers a crucial understanding of factors influencing the colon environment.

Propagation of an idealized infection in an airway tree, consequences of the inflammation on the oxygen transfer to blood

A mathematical model of infection, inflammation and immune response in an idealized bronchial tree is developed. This work is based on a model from the literature that is extended to account for the propagation dynamics of an infection between the airways. The inflammation affects the size of the airways, the air flows distribution in the airway tree, and, consequently, the oxygen transfers to blood. We test different infections outcomes and propagation speed. In the hypotheses of our model, the inflammation can reduce notably and sometimes drastically the oxygen flow to blood. Our model predicts how the air flows and oxygen exchanges reorganize in the tree during an infection. Our results highlight the links between the localization of the infection and the amplitude of the loss of oxygen flow to blood. We show that a compensation phenomena due to the reorganization of the flow exists, but that it remains marginal unless the power produced the ventilation muscles is increased. Our model forms a first step towards a better understanding of the dynamics of bronchial infections.

A data-driven model of the role of energy in sepsis

Exposure to pathogens elicits a complex immune response involving multiple interdependent pathways. This response may mitigate detrimental effects and restore health but, if imbalanced, can lead to negative outcomes including sepsis. This complexity and need for balance pose a challenge for clinicians and have attracted attention from modelers seeking to apply computational tools to guide therapeutic approaches. In this work, we address a shortcoming of such past efforts by incorporating the dynamics of energy production and consumption into a computational model of the acute immune response. With this addition, we performed fits of model dynamics to data obtained from non-human primates exposed to Escherichia coli. Our analysis identifies parameters that may be crucial in determining survival outcomes and also highlights energy-related factors that modulate the immune response across baseline and altered glucose conditions.

A Mathematical Model of the Dynamics of Cytokine Expression and Human Immune Cell Activation in Response to the Pathogen Staphylococcus aureus

Cell-based mathematical models have previously been developed to simulate the immune system in response to pathogens. Mathematical modeling papers which study the human immune response to pathogens have predicted concentrations of a variety of cells, including activated and resting macrophages, plasma cells, and antibodies. This study aims to create a comprehensive mathematical model that can predict cytokine levels in response to a gram-positive bacterium, S. aureus by coupling previous models. To accomplish this, the cytokines Tumor Necrosis Factor Alpha (TNF-α), Interleukin 6 (IL-6), Interleukin 8 (IL-8), and Interleukin 10 (IL-10) are included to quantify the relationship between cytokine release from macrophages and the concentration of the pathogen, S. aureus, ex vivo. Partial differential equations (PDEs) are used to model cellular response and ordinary differential equations (ODEs) are used to model cytokine response, and interactions between both components produce a more robust and more complete systems-level understanding of immune activation. In the coupled cellular and cytokine model outlined in this paper, a low concentration of S. aureus is used to stimulate the measured cellular response and cytokine expression. Results show that our cellular activation and cytokine expression model characterizing septic conditions can predict ex vivo mechanisms in response to gram-negative and gram-positive bacteria. Our simulations provide new insights into how the human immune system responds to infections from different pathogens. Novel applications of these insights help in the development of more powerful tools and protocols in infection biology.

In silico deceased donor intervention research: A potential accelerant for progress

Progress in deceased donor intervention research has been limited. Development of an in silico model of deceased donor physiology may elucidate potential therapeutic targets and provide an efficient mechanism for testing proposed deceased donor interventions. In this study, we report a preliminary in silico model of deceased kidney donor injury built, calibrated, and validated based on data from published animal and human studies. We demonstrate that the in silico model behaves like animal studies of brain death pathophysiology with respect to upstream markers of renal injury including hemodynamics, oxygenation, cytokines expression, and inflammation. Therapeutic hypothermia, a deceased donor intervention studied in human trials, is performed to demonstrate the model's ability to mimic an established clinical trial. Finally, future directions for developing this concept into a functional, clinically applicable model are discussed.

A Whole-Body Mathematical Model of Sepsis Progression and Treatment Designed in the BioGears Physiology Engine

Sepsis is a debilitating condition associated with a high mortality rate that greatly strains hospital resources. Though advances have been made in improving sepsis diagnosis and treatment, our understanding of the disease is far from complete. Mathematical modeling of sepsis has the potential to explore underlying biological mechanisms and patient phenotypes that contribute to variability in septic patient outcomes. We developed a comprehensive, whole-body mathematical model of sepsis pathophysiology using the BioGears Engine, a robust open-source virtual human modeling project. We describe the development of a sepsis model and the physiologic response within the BioGears framework. We then define and simulate scenarios that compare sepsis treatment regimens. As such, we demonstrate the utility of this model as a tool to augment sepsis research and as a training platform to educate medical staff.