Non-minimum-phase dynamics in an inflammation model

Inflammation is the innate immune system’s response to tissue damage caused by trauma or infection. Thinking about it as the quickly receding rash after an insect bite detracts from the major antagonistic role it plays in medicine. As Baldur Tumi Baldursson of the National University Hospital of Iceland put it, `I tell my students, your work is inflammation. Practically all of internal medicine is just fighting inflammation.’

Inflammation is a complex process involving different cell types, mediator molecules and changes in the permeability of capillaries and affected tissue. This reaction has to be ramped up quickly to defend our body, but it must also be kept under strict control to prevent immune cells causing tissue damage themselves. On occasion, things go wrong and a patient is left with chronic, abnormal inflammation: inflammatory bowel disease, coeliac disease or rheumatoid arthritis are a few debilitating examples.

A mathematical model of inflammation control

These notes extend the findings of three researchers from Britain—Joanne Dunster (Reading), Helen Byrne (Oxford) and John King (Nottingham)—using control theoretical insights, and perhaps contribute a new aspect to our understanding of the problem. Their 2014 paper1 drew attention to a shift from understanding inflammation resolution as a passive process to an active, anti-inflammatory mechanism. Continue reading