A mathematical model of neuroinflammation in severe clinical traumatic brain injury

Abstract

Background: Understanding the interdependencies among inflammatory mediators of tissue damage following traumatic brain injury (TBI) is essential in providing effective, patient-specific care. Activated microglia and elevated concentrations of inflammatory signaling molecules reflect the complex cascades associated with acute neuroinflammation and are predictive of recovery after TBI. However, clinical TBI studies to date have not focused on modeling the dynamic temporal patterns of simultaneously evolving inflammatory mediators, which has potential in guiding the design of future immunomodulation intervention studies.

Methods: We derived a mathematical model consisting of ordinary differential equations (ODE) to represent interactions between pro- and anti-inflammatory cytokines, M1- and M2-like microglia, and central nervous system (CNS) tissue damage. We incorporated variables for several cytokines, interleukin (IL)-1β, IL-4, IL-10, and IL-12, known to have roles in microglial activation and phenotype differentiation. The model was fit to cerebrospinal fluid (CSF) cytokine data, collected during the first 5 days post-injury in n = 89 adults with severe TBI. Ensembles of model fits were produced for three patient subgroups: (1) a favorable outcome group (GOS = 4,5) and (2) an unfavorable outcome group (GOS = 1,2,3) both with lower pro-inflammatory load, and (3) an unfavorable outcome group (GOS = 1,2,3) with higher pro-inflammatory load. Differences in parameter distributions between subgroups were ranked using Bhattacharyya metrics to identify mechanistic differences underlying the neuroinflammatory patterns of patient groups with different TBI outcomes.

Results: Optimal model fits to data showed different microglial and damage responses by patient subgroup. Upon comparison of model parameter distributions, unfavorable outcome groups were characterized by either a prolonged, pathophysiological or a transient, sub-physiological course of neuroinflammation.

Conclusion: By developing a mathematical characterization of inflammatory processes informed by clinical data, we have created a system for exploring links between acute neuroinflammatory components and patient outcome in severe TBI.

Keywords: Biomarker; Cerebrospinal fluid; Cytokines; Glasgow outcome scale; Inflammation; Mathematical modeling; Microglia; Patient outcome; Traumatic brain injury.

Fig. 1

TBI acute neuroinflammation network schematic. Model variables include resting microglia (mr), M1-like microglia (M1), M2-like microglia (M2), interleukin(IL)-1 (IL1), IL-12 (IL12), IL-4 (IL4), IL-10 (IL10), tissue damage (D), and type 2 T-helper cells (Th2). Model components appearing next to pathways stimulate (+) or inhibit (−) the correspoding reaction

Fig. 2

Cluster 1 ensemble of model trajectories for days 0–5 post-TBI. Dots represent moving-average data (see “Parameter optimization” section) collected from patients, while bars represent standard error of the mean

Fig. 3

Cluster 2A ensemble of model trajectories for days 0–5 post-TBI. Dots represent moving-average data (see “Parameter optimization” section) collected from patients, while bars represent standard error of the mean

Fig. 4

Cluster 2B ensemble of model trajectories for days 0–5 post-TBI. Dots represent moving-average data (see “Parameter optimization” section) collected from patients, while bars represent standard error of the mean

Fig. 5

Disparate parameter distributions between patient clusters. Box and whisker plots depict the distributions of the most dissimilar parameter values between clusters 1, 2A, and 2B. Dots represent the parameter value averages by cluster. A star represents statistical significance for pairwise cluster comparisons