(444f) A Dynamical Systems Approach to Modeling the Inflammatory Response in Sepsis

Sepsis, a high mortality syndrome, is responsible for a significant amount of healthcare resource consumption in the United States. Slow advancement in therapies for sepsis can be partially attributed to poor timing of intervention due to the lack of ability to assess when the patient was infected as well as the current state of patient inflammation. We introduce a mathematical model that uses temporal cytokine IL-6 and IL-10 clinical data to capture the human pro-inflammatory and anti-inflammatory response in sepsis. The model developed can be used by clinicians to understand the dynamics of the inflammatory response and assess patient-specific options for therapeutic intervention.

Methods

Cytokine measurements were collected from the Protocol-Based Care for Early Septic Shock (ProCESS) trial. A cohort of 130 subjects were selected based on the criteria that IL-6 and IL-10 measurements were available at 0, 6, and 24 hours after trial enrollment (n=35 having an additional 72-hour measurement available). Furthermore, this cohort consisted of two patient subgroups: (1) those with IL-6 and IL-10 concentrations that were non-monotonic over the first 24 hours (n=31); and (2) those with monotonically decreasing cytokine levels over the first 24 hours (n=104). Treatment arm differences were not considered when selecting the cohort since there was found to be no significant difference in mortality between the three treatment arms.

The pro- and anti-inflammatory responses to infection were modeled as damped second-order dynamical systems in response to a unit impulse, which represents infection at time zero. Two time constant parameters (Ï„₁, Ï„₂) and a gain parameter (K) of the second-order dynamical system were fit to each of the IL-6 and IL-10 responses. Temporal biomarker data is based on trial enrollment rather than disease time zero (left-censored) and therefore the data was shifted forward in hourly increments 0-24 hours during the parameter estimation procedure. Constraints were implemented to restrict the parameter space to values that result in physiologically feasible cytokine peaks (time of peak greater than 6 hours) and to capture the faster time to peak for IL-6 (vs. IL-10) following infection onset. To examine more biologically relevant representations of infection, symmetric triangular pulse inputs with unity area and durations ranging from 0-48 hours were also applied to the system.

The parameter estimation objective is to minimize the weighted sum of squared error between the measured and model-simulated cytokine concentrations. Penalty terms were included in the objective in order to ensure that cytokine responses returned to zero by 168 hours and to constrain model-simulated patient trajectories to be consistent with measured data below the lower limit of quantitation. Parameter estimates were found using the fmincon nonlinear programming solver in MATLAB and the algorithm was started at multiple initial points in parameter space in order to reduce the probability converging to a local minimum.

Results

Analysis of objective value versus the shift time of clinical data demonstrated a monotonically decreasing profile from fits with a zero time-shift. ANOVA and multiple pairwise comparisons of objective value distributions demonstrated that the objective value distributions over 0-7 hours were statistically different (p<.05), however, distributional means between 8-24 hours were insignificantly different (p>.05). This suggests that the onset of the dynamical system (onset of infection) is at least 8 hours prior to clinical presentation. The initial speed of the pro-inflammatory and anti-inflammatory responses to infection are captured and reflected through the smaller time constant parameter (Ï„₁). The model reveals patient-to-patient variability in inflammatory dynamics up to 10 days after infection onset. For example, some subjects have fast dynamic response that ends within a few days, whereas others have a sustained inflammatory response that lasts greater than a week. The effect of triggering the second order system with triangular waves of infection was also investigated. Patients with non-monotonic IL-6 and IL-10 concentrations (n=31) over clinical time were considered initially, nine of which had four measurements available for each biomarker. The model demonstrated the ability to capture individual patient cytokine trajectories and reveal interpatient differences in infection time and response gains. This knowledge opens the possibility for appropriately timed and scaled modulation of the inflammatory response to infection.

Summary

The mathematical model utilizes potent inflammatory mediators, IL-6 and IL-10, to describe the inflammatory response during sepsis. The model structure reveals interpatient variability in infection time, inflammatory response duration, and magnitude of inflammation. Clinicians could use the results of this model as a guide to develop an appropriate therapeutic regimen that tailors patient health outcome.