Inflammation dynamics of atopic dermatitis: Phase transition and scaling law of remission time

Atopic dermatitis (AD) is a prevalent skin disorder affecting individuals globally, with many patients experiencing a range of symptoms. A pronounced clinical phenomenon associated with AD is the cyclic alternation of two distinct phases in time: inflammation and remission, depending on patients' immune response and skin permeability. Frequent and relatively long inflammatory times lead to symptoms that can severely deteriorate the quality of life for the patient. Through mathematical modeling, we find that patients with similar AD symptoms can be categorized into two phases depending on the skin permeability and immune response that constitute the most clinically relevant parameter plane: the inflammatory time is shorter or longer than the remission time, respectively and the transition between the two phases is of the second-order type. In the parameter plane, a critical threshold curve emerges, which separates the two phases. Computing the frequency and duration of the inflammatory response, we uncover a logarithmic scaling law governing the inflammatory and remission times and discuss its clinical implications. In particular, when the skin condition is managed to be near the phase transition point, the benefits of treatment are more pronounced. However, at this stage, the effectiveness of skincare in reducing flare-ups tends to be less noticeable, making it difficult to evaluate the success of the treatment, largely due to the nature of logarithmic decay in the remission time. Our study provides insights into the mechanisms of AD that can enhance diagnostic accuracy and treatment by understanding the alternation between inflammation and remission periods.