Fig 1.
Erythema pattern and modeling of erythema development.
(A) Process of the inflammatory response for erythema development. Upon stimulation, keratinocytes and resident immune cells secrete pro-inflammatory mediators that induce the production of pro- and anti-inflammatory mediators. Pro-inflammatory mediators dilate local blood vessels. The dilation appears as redness on the skin surface, developing erythema. (B–H) Photographs of erythema with linear [24] (B), reticular [25] (C), circular [26] (D), annular [27] (E), polycyclic [28] (F), arcuate [29](G), or gyrate patterns [30] (H). (I) A model for regulatory feedback between pro- and anti-inflammatory mediators. (J) A representation of simulation in the skin. The skin surface is partitioned into square regions. Erythema is initiated by keratinocytes and immune cells in the skin through secreting pro-inflammatory mediators. The area of microinflammation with a high concentration of pro-inflammatory mediators is considered as a “seed” region, and its projection to the surface is colored in red.
Table 1.
System parameters and their interpretations.
Fig 2.
Simulated time courses of the healthy fading patterns.
Spatiotemporal evolution of pro-inflammatory mediator levels (a) upon initial stimulation in linear (A), reticular (B), and circular areas (C and D). The parameter values for these simulations are listed in S2(A)Table.
Table 2.
Erythema patterns observed in eleven diseases.
Fig 3.
Simulated time courses of the five types of expanding patterns.
Pro-inflammatory mediator levels (a). The initial stage of the inflamed area (row 1) consisted of three seed areas. Later forms of the disease (rows 2–5) correspond to circular (A), annular (B), polycyclic (C), arcuate (D), or gyrate patterns (E). The parameter values for these simulations are listed in S2(B) Table.
Fig 4.
Pattern selection in the parameter space of pro- and anti-inflammatory mediator productions.
Fading (F), arcuate (Ar), polycyclic (P), gyrate (G), annular (An) and circular (C) patterns emerged as the steady state (Eq 2) at the parameter values of qa and pi (A), ra and qi (B). pa = 0.05, ra = 0.8, qi = 6.0 for (A) and pa = 0.05, qa = 3.0, pi = 0.12 for (B). In all the simulations, Da = Di = 0.3. (C) Summary for all the analyzed parameter space regarding the mediator production (see also S2 and S3 Figs), indicating the characteristic imbalance by each expanding pattern.
Fig 5.
Dynamical characters underlying the five expanding and fading pattern types.
The phase space of pro- and anti-inflammatory mediator concentrations (a, i) depicts the time course (green curve) upon stimulation and the nullclines (red curve for da/dt = 0 in Eq 2A; blue curve for di/dt = 0 in Eq 2B; Da = Di = 0). The intersections of the nullclines indicate steady states, where filled and hollow circles represent stable and unstable states, respectively. The time course shows convergence to a stable steady state upon a supra-threshold stimulation at the initial condition (a = 1.0, i =0.01). Vector fields are also shown to represent mediator dynamics at the respective concentration. The parameter values for each simulation are listed in S2 Table.