A set of differential equations was derived in this study to model acute neuroinflammatory phenomena following severe TBI, intended to represent dynamic time-dependent interactions within and to generate hypotheses about the complex communication network between resident microglia and neuronal tissue via circulating cytokines. Microglia are potent effector cells in post-TBI neuroinflammation; however, there is limited early clinical information collected regarding their activation, polarization, and functional plasticity. Therefore, we leveraged cytokine dynamics in our model to generate predictions on the state of neuroinflammation, microglia phenotype distributions, and tissue integrity in the acute injury recovery phase (day 0–5). This mechanistic model was generated on a foundation of a priori information regarding core cytokine interactions established empirically in the field of TBI.
Neuroinflammation, although a main contributor to secondary damage post-TBI, is an inherent set of host defense mechanisms aimed to protect and restore tissue integrity [
2,
39,
40]. While studies aim to label particular aspects of this response neurotoxic or neuroprotective, this is ultimately a context-dependent consideration. The spatial and temporal regulation of select neuroinflammatory mechanisms may potentially preserve positive physiological function and endogenous tissue homeostatic efforts [
3]. Modulating the coordinated balance of pro- and anti-inflammatory cytokines, timely activation of M1 and M2 microglia, and appropriate feedback signaling may provide an adequate amount of pro-inflammation with relatively less secondary tissue damage ensuing [
41,
42]. Our ODE modeling techniques provide a platform that recapitulates the relative levels of evolving inflammatory mediators observed with TBI patient data and projects time courses of microglia activation and tissue damage that are mechanistically consistent with these data, thereby predicting the extent to which secondary TBI pathologies may be arising in these clinically observed scenarios.
In this study, we stratified patient subgroups based on long-term neurological outcome from patients that exhibited distinct day 0–3 neuroinflammatory profiles [
18]. Leveraging this methodology allowed model fits to be generated for each patient cluster and respective outcome, providing insight on potential differences in their acute neuroinflammatory programs that may contribute to disparate 6-month outcomes.
Assessing neuroinflammatory status via cytokine trajectories
Initial statistical work by our group applied principal component and cluster analysis to identify variability in acute neuroinflammatory biomarkers among individuals following TBI [
18]. These analyses suggested sets of cytokines that demonstrate similar acute expression patterns and may contribute to similar courses of inflammation and tissue recovery, helping to justify the inclusion of a small number of specific cytokines in our current modeling work. In this study, we sought to utilize cytokine dynamics to infer the neuroinflammatory state and subsequent microglial activation profile of each patient cluster.
This methodology is a progressive direction in the TBI field in that relative concentrations of cytokines can be tracked and used to inform hypotheses regarding early injury severity patterns and patient prognosis. While studies have shown that absolute levels of acute anti-inflammatory mediators are predictive measures of initial brain damage and complications, such as intracranial pressure [
43], our model illustrates the relative relationships and time courses of mediators to provide a more comprehensive view of neuroinflammation post-TBI. The model was designed on the premise that cytokines are expressed simultaneously following injury, collectively contribute to microglial polarization profiles, and may serve as useful biomarkers patterns to gauge the level of neuroprotection or neurotoxicity in the local microenvironment [
3,
41,
44].
Novelty of modeling TBI-induced neuroinflammation mathematically
In extension to cytokine measurement studies that characterize neuroinflammation post-TBI, this modeling framework is a novel method of investigating (1) temporal dynamics of inflammatory mediators, (2) interdependent cytokine pathways and feedback interactions, and (3) cytokine influences on differential microglia expression and tissue damage responses. Differential equations are well suited for representing post-TBI neuroinflammation because the relative concentration changes of inflammatory mediators can be modeled with respect to time. This initial report serves as a proof-of-concept that implementing mechanistic modeling can further our understanding of inflammatory network dynamics, kinetics, and phenotypic polarization.
While early delivery of anti-inflammatory agents has been an intuitive strategy for containing post-TBI neuroinflammation, the lack of consistent success suggests there is more to consider for this approach. Suppressing a single neuroinflammatory mechanism does not facilitate healthy tissue recovery due to complex interdependencies of neuroinflammation [
3,
39]. There has been a shift of perspective in the TBI field that acknowledges not only the dual role of neuroinflammation post-TBI, but also the dichotomy of roles such as perpetuating damage and maintaining homeostasis by individual mediators, including cytokines and microglia phenotypes [
9,
45]. The utility of ODE modeling in this context is to elucidate the benefit or detriment of particular mediators relative to time-post-injury and expression of other local mediators.
Model simulations performed on patient-specific data from different outcome groups produced quantitative projections of cytokine dynamics and qualitative predictions of microglia and tissue damage dynamics. The ensembles of parameters, which were tuned to generate optimal fits for each patient cluster, were statistically compared to generate hypotheses regarding differences in the neuroinflammatory regimes of each cluster. These analyses are a contribution to ongoing attempts to characterize the functional roles and heterogeneous effects of microglia and related cytokines in acute TBI neuroinflammation [
9,
46]. This report presents the first computational model in the field that aims to model the temporal evolution and M1/M2 phenotypic balance of microglia. In the following sections, we discuss the inflammatory trends, unique parameter differences, and additional clinical considerations for each respective patient cluster and long-term outcome.
Unfavorable outcome groups (clusters 1 and 2B)—maladaptive features of neuroinflammation
R.G. Kumar et al. had identified a group of individuals (cluster 1) with relatively high day 0–3 CSF inflammatory loads, almost all of which experienced poor long-term outcomes [
18]. After subgrouping cluster 2 individuals by 6-month GOS score, we identified another poor outcome group yet with a relatively lower acute inflammatory load (cluster 2B). We hypothesized that the disparity in acute neuroinflammatory profiles could drive differential, yet both detrimental, courses of inflammation post-TBI that hinder recovery.
Cluster 1—evidence of prolonged inflammation
Elevated inflammation and highly activated microglia were apparent through several model parameter differences that emerged when comparing across clusters. In comparison to cluster 2B, cluster 1 model parameters were significantly lower for microglial (both M1 and M2 types) and IL-10 decay rates; higher for IL-1β and IL-12 release rates; and higher for sensitivity to pro-inflammatory cytokine and damage signals. This combination of parameter differences is potentially reflective of the failure of acute neuroinflammation and microglia activity to resolve appropriately.
The self-perpetuating cycle of inflammation displayed in cluster 1 trajectories has been shown to be detrimental to recovery for various reasons. While initial upregulation of pro-inflammatory processes is intrinsically a host defense response essential for the phagocytosis of cellular debris and activation of immune system [
6,
46], extended activation may hinder neurogenesis and contribute to additional neuronal loss and unselective clearance of healthy tissue [
8,
41]. In cluster 1 microglia trajectories, the M2 response appears to persist along with M1 activity but is not elevated enough to keep M1-induced secondary damage suppressed via compensatory pro-health mechanisms.
Of note, the mean age of cluster 1 individuals (46.09 ± 3.26 year) was significantly higher than both cluster 2A and 2B indicating that there may be age-related dysfunctions in microglia involved after TBI. With increasing age, microglia morphology changes and functional impairments are observed. Microglia are found in less ramified form with altered cytokine receptor patterns which may hinder their ability to respond appropriately to inflammatory stimuli [
33,
40,
44]. In addition to an already elevated baseline inflammatory state in aged individuals, surveying microglia cells lean toward a “primed” phenotype characterized by activation at a lower threshold, tendency to adopt an exaggerated pro-inflammatory phenotype, and resistance to regulatory anti-inflammatory cues [
6,
40]. In cerebral ischemia injury models, stress has similarly been shown to contribute to microglial priming which may exacerbate inflammatory dynamics following brain injury [
47]. Stress-related implications likely arise in cluster 1, as acute CSF cortisol levels are significantly elevated compared to the other clusters. These findings are in line with previous work showing that exaggerated inflammatory responses, especially among aged individuals, are associated with elevated acute CSF cortisol levels and TBI mortality [
19,
38].
Additionally, mean IL-10 levels in cluster 1 were significantly higher than both cluster 2A and 2B (57.54 vs. 8.08 and 11.54 pg/mL, respectively) over the first 5 days post-TBI. Despite increased anti-inflammatory presence, pro-inflammatory production levels and microglia activity persisted perhaps due to reduced sensitivity of microglia to anti-inflammatory mediation [
40] and insensitivity of cytokine release to anti-inflammation (elevated
a∞2 in our model). Our findings for cluster 1 are consistent with previous studies that found associations between CSF IL-10 levels, age, and mortality rates [
48,
49].
Cluster 2B—evidence of transient inflammation
In contrast to cluster 1, both M1 and M2 microglia and IL-10 levels decrease early and rapidly in cluster 2B. Pro-inflammatory mediator levels remain elevated but plateau, providing little to no re-initiation of microglial activation and polarization once the levels fall to baseline. There is a late rise in IL-1β that appears over day 3, possibly due to secondary tissue damage release, but the model could not capture an elevation of such low magnitude. This rise in IL-1β does, however, fit nicely to the late IL-12 rise. The consistent pro-inflammatory expression through day 5, coupled with the rapid decreases of IL-4 and IL-10 and greater sensitivity to IL-10 inhibition of further cytokine, leads to the elevated tissue damage in cluster 2B model ensembles.
The most elevated levels of the tissue damage term are observed for cluster 2B. This qualitative evidence from our modeling efforts supports the concept that the complete suppression of the neuroinflammatory response and microglial activity, of either phenotype, is potentially detrimental to tissue recovery post-TBI [
5,
6]. In the absence of adequate microglia activity over the first 5 days, damage from the initial injury may not be addressed, leading to further damage and perpetuating other secondary injury cascades.
By PCA and cluster analysis [
18], cluster 2A and 2B were indistinguishable when considering day 0–3 neuroinflammatory profiles. However, when considering CSF hormone data, we found that cluster 2B individuals were characterized by significantly higher cortisol levels than cluster 2A over the first 3 days post-TBI, consistent with differences in cortisol trajectories group membership found between patient groups in previous work [
38]. Elevated cortisol immediately following injury potentially contributes to the premature immunosuppression observed with cluster 2B, leading to a sub-physiological microglial response.
Favorable outcome group (cluster 2A)—neuroprotective features of neuroinflammation
Cluster 2A model ensembles best demonstrate a beneficial physiological response to TBI. Microglial activity was present for a length of time that was neither permissive nor indiscriminate in pro-inflammatory mediated damage (as in cluster 1), or sub-physiological in minimizing tissue damage associated with other forms of secondary injury (as in cluster 2B). This observation is reflected in significant parameter differences regarding the decay of microglia and IL-10, as well as release rates of the pro-inflammatory cytokines. Although we observe a gradual increase in the damage expression, it is lower in magnitude than both unfavorable outcome clusters and appears to be well contained as it plateaus near day 5. Particularly of note, the relative ratio of M2:M1 microglia in cluster 2A was approximately 1:1 after the initial injury, becoming larger than 1 as the microglial response progressed. Conversely, M2:M1 ratios in clusters 1 and 2B were nearly 1:4 initially and became even smaller over time. These findings may support the physiological importance of microglia, even perhaps of the stereotypically neurotoxic M1-like phenotype, in the acute injury phase post-TBI.
Challenges and limitations of modeling microglial physiology
There is considerable need in the TBI field to characterize neuroinflammation, particularly with respect to the contributions of microglial functionality, in order to assess acute injury progression and tailor intervention strategies to enhance neuroprotection for particular patient subgroups. In this study, we implemented CSF cytokine time courses as proxies to indicate the state of neuroinflammation post-TBI and inform microglia activation and polarization dynamics. However, the consistent collection of informative neuroinflammatory data is not always clinically feasible. The refinement of cerebral microdialysis (CMD) and CSF cytokine measurement methodology will contribute to ongoing efforts to centrally monitor TBI-induced neuroinflammation [
50].
While cytokine data was available from a large patient cohort, more limited samples were available to contribute to each 6-h smoothed mean. Serial sampling and cytokine data at a greater temporal resolution would improve model trajectories to provide more accurate predictions of the progression of neuroinflammation post-TBI. The inflammatory data remained oscillatory in nature despite a smoothing procedure for averaging. Marked changes in inflammatory mediator dynamics were largely absent, with most levels present at consistently low levels. As a result, the fits to cytokine data did not produce noticeable fluctuations between microglia phenotypes.
There is inherent abstraction in mathematically modeling biological processes. In our model, microglia subtypes and tissue damage are qualitatively projected with arbitrary units rather than quantified by cell count or tissue volume. This limits the direct interpretation of these time courses to an estimate of the M1- or M2-like “state” of the brain following injury. Moreover, parameter values cannot be taken as literal rates with established units. Although model parameters were initially guided by existing experimental literature, scaling procedures on cytokine data and confounding factors in experimental situations complicate the direct rate interpretations. Our determination of differences between parameter value distributions should be viewed as a relative test of neuroinflammatory distinctions between clusters, which integrated additional statistical metrics to inform the degree to which the distributions differed. Due to limitations of the statistical methodology, we in fact de-emphasized the value of traditional hypothesis testing alone and considered two Bhattacharyya metrics to inform our comparative parameter analyses. Parameter value differences were ranked by lowest overlap (BC) and highest spread (BD) to highlight the most dissimilar parameter distributions between clusters.
Additionally, as a reduced model, the set of ODEs derived were limited to prototypical markers of microglia activation and acute inflammation to encompass basic regulatory components in the inflammatory network: initiation, propagation, phenotype switching, and inhibition. The model was designed to represent recent findings that IL-4 and IL-10 act as switch-like factors in microglia polarization. However, the self-regulating and immunosuppressive role of these anti-inflammatory mediators may be overemphasized in this model, based on the relatively rapid return of microglia to baseline levels predicted in all clusters. Inclusion of additional mediators may create a more comprehensive and nuanced illustration of the inflammatory network that drives the microglial response to TBI.
In general, the understanding of microglia classification and roles is still evolving in the neurotrauma field. At first, a spectrum of activation states was proposed, ranging from M1 to M2 extremes, with multi-functional subtypes of M2 in between [
46,
51]. Not only are more nuanced views now being considered as alternatives to these rigid phenotype classifications, a layer of complexity has been added as simultaneous expression of M1 and M2 phenotypic markers on the same cell has now been observed in animal models [
9]. This developing research area calls for further classification of molecular profiles and associated functional roles of microglia, particularly advancements that successfully translate in vitro findings to in vivo scenarios. Macrophage research and dynamics have informed our ODEs and have paved the way for much of our understanding of phenotype polarization and functionality; however, it is necessary to investigate these parallels in the brain with microglia in order to extend M1 and M2 characterizations explicitly. A key strength of our work is that the modeling framework that we utilize need not be interpreted in terms of a strict M1/M2 dichotomy. Rather, the framework allows for a flexible interpretation of the M1 and M2 variables as cell counts, states, or even associated microglia functions. The focus is on the relative contribution and effects of the pre-specified cytokines on the model behavior of those variables as well as the physiological processes of pro- and -inflammatory cytokine production, tissue damage, and healing that M1 and M2 represent in our model; as long as these elements are present and interrelated in the biological response to damage, our predictions related to these quantities are not dependent on any specific M1/M2 dichotomy.
More generally, our model encodes physiological interactions among biological quantities thought to contribute to inflammatory response dynamics as well as to tissue damage and healing in the acute phase post-TBI. This framework requires making assumptions about which physiological processes contribute and in what ways. We acknowledge that alternative sets of assumptions could lead to different conclusions, but we have attempted to tailor our modeling choices to reflect current understanding derived from previous experimental, clinical, and computational work, albeit with some simplifications to retain tractability. Nonetheless, any experimental or clinical work aimed at predicting outcome, such as suggesting early-warning signs for patient risk groups and targets for therapeutic interventions, would necessarily proceed based on some theoretical framework, typically reflecting the prevailing scientific viewpoint, which would exert a strong impact on the study performed. Among the advantages of the modeling approach used here in this report, we note that the underlying assumptions are clearly stated (see “
Ordinary differential equation model development” section) and the parameter fitting process does not impose any additional biases; rather, this modeling approach evaluates all model parameters’ contributions to cluster differences, giving all an equal chance to emerge as significant.
Lastly, microglia responses in the acute phase may be a transient phenomenon overshadowed by subsequent chronic elevations [
46,
52], which have been observed as late as 11 months to 17 years post-TBI in humans [
40], and accompanying pathologies; nonetheless, these transients may contribute to long-term influences of acute neuroinflammation on patient outcome [
18].
Stratifying patient subgroups for improved prognosis and treatment
PCA and cluster analysis by R.G. Kumar et al. identified a cluster of individuals (cluster 1) with elevated inflammation with respect PC1 markers. However, the outcomes of cluster 2 individuals in this study were variable, despite negative PC1 scores for the majority [
18]. This work indicates that elevations of PC1 markers (IL-5, IL-6, IL-8, IL-10, sVCAM, sICAM, and sFAS) were predictive of outcome for a subset of the patients in the study; however, other predictive measures were yet to be unveiled to distinguish patient prognosis in cluster 2. In the current study, we grouped cluster 2 patients by 6-month GOS score to investigate differences in their inflammatory and microglial dynamics post-TBI beyond classification of particular acute inflammatory markers. Despite having greater cortisol levels in the first 3 days following TBI, cluster 2B individuals were also projected to be in an immunosuppressed state due to early microglia decay and greater sensitivity to IL-10 in negative feedback mechanisms that control cytokine production.
Our findings on cluster 2B emphasize the important point that microglial responses underlying poor patient outcomes post-TBI are likely heterogeneous; in particular, poor outcomes in some patients might relate to a sub-physiological microglial response. This interpretation of results exemplifies the utility of mathematical modeling in exploring how early patient stratification based on inflammatory marker expression may lead to informed understanding of acute recovery trajectories and guide decision-making for specific immunomodulatory therapy types that may benefit from additional pre-clinical evaluation.