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A Unified Computational Model for the Human Response to Lipopolysaccharide-Induced Inflammation

Part of the Mathematics Online First Collections book series

Abstract

This chapter develops a unified model predicting the whole-body response to endotoxin. We simulate dynamics using differential equations examining the response to a lipopolysaccharide (LPS) injection. The model tracks pro- and anti-inflammatory cytokines (TNF-α, IL-6, IL-10), concentrations of corticotropin-releasing hormone (CRH), adrenocorticotropic hormone (ACTH), and cortisol in the hypothalamic–pituitary–adrenal (HPA) axis. Daily hormonal variations are integrated into the model by including circadian oscillations when tracking CRH. Additionally, the model tracks heart rate, blood pressure, body temperature, and pain perception. Studied quantities function on timescales ranging from minutes to days. To understand how endotoxin impacts the body over this vast span of timescales, we examine the response to variations in LPS administration methods (single dose, repeated dose, and continuous dose) as well as the timing of the administration and the amount of endotoxin released into the system. We calibrate the model to literature data for a 2 ng/kg LPS bolus injection. Results show that LPS administration during early morning or late evening generates a more pronounced hormonal response. Most of the LPS effects are eliminated from the body 24 hours after administration, the main impact of inflammation remains in the system for 48 hours, and repeated dose simulations show that residual effects remain more than 10 days after the initial injection. We also show that if the LPS administration is recurrent or total dosage is increased, the system response is amplified, posing a greater risk of hypotension and pyrexia.

Keywords

  • Inflammation
  • Computational model
  • Ordinary differential equations
  • Lipopolysaccharide (LPS)
  • Endotoxin response
  • Systems model
  • Time scales
  • Dosing strategies

Mathematics Subject Classifications (MSC2020)

  • Primary: 92-10, 92C30, 92C50
  • Secondary: 92C42, 92B25

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Kristen A. Windoloski & Mette S. Olufsen

  2. Technical University of Denmark, Lyngby, Denmark

    Elisabeth O. Bangsgaard

  3. Department of Mathematics, Augusta University, Augusta, GA, USA

    Atanaska Dobreva

  4. Centre for Mathematical Modeling—Human Health and Disease, Roskilde University, Roskilde, Denmark

    Johnny T. Ottesen

Authors
  1. Kristen A. Windoloski
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  2. Elisabeth O. Bangsgaard
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  3. Atanaska Dobreva
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  4. Johnny T. Ottesen
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  5. Mette S. Olufsen
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Correspondence to Mette S. Olufsen .

Appendix

Appendix

See Table 1.

Table 1 Model parameters and initial conditions. Parameters with reference ∼ were scaled from their values reported in Bangsgaard et al. [2017] and Dobreva et al. [2021] to match the appropriate variable concentration in the model, parameters with a * indicate that the parameter was manually adjusted, and parameters with ∼* were both scaled and manually adjusted
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Table 1 (continued)
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Windoloski, K.A., Bangsgaard, E.O., Dobreva, A., Ottesen, J.T., Olufsen, M.S. (2023). A Unified Computational Model for the Human Response to Lipopolysaccharide-Induced Inflammation. In: Mathematics Online First Collections. Springer, Cham. https://doi.org/10.1007/16618_2022_39

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