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�Predicting experimental sepsis survival with a mathematical model of acute inflammation��

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Julia Arciero

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Associate Professor

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Department of Mathematical Sciences

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Indiana University – Purdue University Indianapolis

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Understanding sepsis

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  • Problem: The inflammatory response is not always contained locally; if it becomes systemic, organ dysfunction may result

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  • Question: Why does a host mount an overwhelming inflammatory response that leads to sepsis in some cases but not in others?

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  • Goal: To determine methods for identifying septic trajectories early so that interventions can be made accordingly

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Experimental sepsis

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31 rats were injected with increasing levels of E. coli:

Calibrating Data Set

Validating Data Set

    • 1.28e8 bacteria
    • 2.48e8 bacteria
    • 5.05e8 bacteria

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Motivating Questions

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Why does the mortality time of some rats differ dramatically despite nearly identical bacterial doses?

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Is early data on the pathogen and host response sufficient to predict a health or disease outcome?

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Mathematical model of sepsis

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Reynolds et al. 2006

Barber et al. 2021

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Model equations: Bacteria

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Reynolds et al. 2006

Arciero et al. 2010

Barber et al. 2021

k1: pathogen growth rate

Dosing function (exponential)

Bacterial growth

Non-specific, local, innate immune response

Bacterial elimination

k2: local immune response strength

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Model equations: Pro-inflammatory response

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Natural decay

Pro-inflammatory response triggered by immune cells, bacteria, and damage

ν1: pro-inflammatory activation rate

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Model equations: Anti-inflammatory response

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Anti-inflammatory mediators

Natural decay

Anti-inflammatory response activation

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Model equations: Damage

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Damage repair

Generation of damage

 

 

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Results: effect of varying pathogen growth rate (k1)

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k1 = 1.2/h

k1 = 1.2/h

k1 = 1.2/h

k1 = 1.2/h

k1 = 1.3/h

k1 = 1.3/h

k1 = 1.3/h

k1 = 1.3/h

k1 = 1.4/h

k1 = 1.4/h

k1 = 1.4/h

k1 = 1.4/h

Sepsis

Asepsis

Healthy

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Results: accuracy of model predictions

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In the model, tc (time of death) is the model-predicted time at which the value of damage reached a critical level (εcrit)

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Results: comparing time dynamics for varying bacterial loads and mortality data

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Observed mortality time <= 24 h

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Observed mortality time > 24 h

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For Rat 11:

k1 = 1.27/h

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For Rat 20:

k1 = 1.2/h

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Results: compare rats with similar initial bacterial loads

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Results: sensitivity of model outcome to parameters

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Varying pathogen growth rate

Varying local immune response

Varying pro-inflammatory activation rate

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Discussion of theoretical interventions

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  • Modeling showed that variability in outcomes can result from variability in pathogen growth rate, strength of the local immune response, or maximum activation rate of the pro-inflammatory response

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  • Experimental or clinical variability can be explained by very small differences in initial conditions (e.g., due to underlying stressors)

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  • Model predictions implied that the pro-inflammatory, anti-inflammatory, or bacterial levels at early time points (8 h) cannot be used to predict outcomes from a statistical perspective

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  • Mathematical modeling is instrumental in understanding possible mechanisms that explain dichotomies in outcomes

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Acknowledgements

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Funding support

Collaborators

    • Dr. Yoram Vodovotz (University of Pittsburgh)
    • Dr. Rami Namas (University of Pittsburgh)
    • Dr. Jared Barber (IUPUI)
    • REU students: Amy Carpenter, Allison Torsey, Tyler Borgard

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    • NSF DMS-1654019
    • NSF DMS-1852146
    • NSF DMS-1951531
    • NIH U01EB021960
    • NIH R01EY030851