Model Reduction As a Tool for Elucidating Key Dynamics in a Neutrophil Model of Inflammation and Cancer

Mathematical models able to capture clinically-relevant dynamics and data can be powerful tools to aid clinicians in evaluating the effect of a medical intervention on patient response.  We recently published a model of neutrophil and granulocyte-stimulating factor (G-CSF) dynamics that captures both fast (endotoxin challenge, inflammation) and slow (docetaxel chemotherapy, cancer) responses.  This model, which reproduces the underlying biology of the neutrophil signaling cascade in both inflammation and cancer, is of high order (16 ordinary differential equations) and has multiple saturation nonlinearities.  This complex structure is not a priori parametrically identifiable and is intimidating to the intended user:  clinicians.  We use model reduction techniques, both algorithmic and heuristic, that preserve input-output behavior of the model while simplifying the interpretation of the model states by focusing on key physical variables with clinical relevance.  The result is a system of lower equation and parameter orders with clearer interpretation in the context of clinical observations and practice.