Mathematical modeling of community-acquired pneumonia patients

Introduction

Sepsis is defined by the systemic response to an infection, governed by dynamic interactions between the tissues, immune cells and inflammatory mediators. We used the Immunetrics platform to build a large-scale mathematical model that encompasses these biological components. The model incorporates a virtual clinician, an automated system to examine simulated patients' status at clinically relevant intervals and administer standard of care interventions as necessary, thereby altering the dynamics of the disease state. The model reproduces many characteristics of systemic response to an infection, including the time course of cytokines, coagulation factors, clinical markers, early and late organ failure, and early versus late deaths.

Methods

The ordinary differential equation-based model was used to simulate the progression of sepsis over a 30-day hospital stay. This model was fit to published human endotoxemia data as well as data from severely septic community-acquired pneumonia (CAP) patients from the GenIMS study. The model was fit to 15 biomarkers and clinical markers, including mean arterial pressure, , IL-6, and PAI-1. PaO₂, creatinine, TNFα

Results

Figure 1 illustrates simulated output as compared with the median time course data for surviving CAP patients without co-morbidities and for CAP patients without co-morbidities who died between 4 and 8 days after admission. After incorporating changes in physiological and immune function due to patient demographics and co-morbidities (for example, COPD, cardiovascular disease), a handful of parameters were changed to fit the model to median time course data from 14 subgroups. These parameters included pathogen virulence, effectiveness of antibiotics, baseline status of patients at study inclusion, and occurrence of secondary infection. By overlaying variations in the above parameters about the median model, the model can encompass the entire spectrum of patients observed in the GenIMS study. The virtual clinician administers individualized treatment for each simulated patient. The model simulations provide clear evidence of changes in disease progression as a function of differences in treatment.

Figure 1

Comparison of time course data from model simulation (solid line) and median of patients (filled circles) from (a) surviving CAP patients without co-morbidities and (b) CAP patients without co-morbidities dying between 4 and 8 days after admission.

Conclusion

The ability of our model to reproduce a large variety of patients with a relatively small number of parameter changes illustrates the robustness of the underlying biological processes being modeled. The model may help identify real signals in immensely variable and noisy multidimensional sepsis patient data, and distinguish real patient responses from clinical study-site-related variability. This model is currently undergoing further validation. Future capabilities include assessment of risk and benefit of new drugs for sepsis or new treatment strategies (for example, early goal-directed therapy) in different patient cohorts.