Mathematical Modeling of Lesion Pattern Formation in Dendritic Keratitis

TL;DR

A mathematical model is proposed to elucidate the mechanisms of lesion pattern formation in dendritic keratitis and shows that increased production of infection-suppressive cytokines induces dendritic patterns with terminal bulbs, whereas reduced cytokine levels lead to geographic patterns.

Abstract

Dendritic keratitis is a form of eye infection caused by herpes simplex virus (HSV). The virus spreads via direct cell-to-cell infection among corneal epithelial cells. This leads to the formation of dendritic lesions characterized by terminal bulbs at their tips. Under immunosuppression, the condition may progress to geographic keratitis, which is a map-shaped lesion with dendritic tails. The mechanism of this pattern formation remains to be elucidated. In this study, we propose a mathematical model to elucidate the mechanisms of lesion pattern formation in dendritic keratitis. Our model shows that increased production of infection-suppressive cytokines induces dendritic patterns with terminal bulbs, whereas reduced cytokine levels lead to geographic patterns. Furthermore, altering the spatial distribution of cytokine production can reproduce dendritic tails. By including external cytokine secretion, we could reproduce tapered lesions observed in non-HSV keratitis. By clarifying the mechanisms behind terminal bulb formation and reproducing atypical lesion morphologies, our findings enhance the understanding of herpetic keratitis and highlight the utility of mathematical modeling in ophthalmology.

Figures (12)

• Figure 1: Slit-lamp photographs of dendritic keratitis (a) and geographic keratitis (b), and their corresponding binary images (c, d). Panels (a) and (b) were taken under cobalt-blue illumination after fluorescein staining. Fluorescein dye stains corneal regions where cell-to-cell junctions are disrupted, and visualize diseased epithelial defects Srinivas2023. As a result, the ulcerated epithelial areas appear green, while the surrounding intact corneal surface appears blue. Panels (c) and (d) show binary images generated from (a) and (b), respectively, using the Color Threshold function in ImageJ to enhance lesion visibility. (a)(c) The lesion exhibits a characteristic branching, linear ulcerative pattern with terminal bulbs (arrows) and swollen epithelial borders. (b)(d) The lesion exhibits a broad amoeboid ulcerative pattern (stars). At the lesion periphery, dendritic tails (arrowheads) are observed.
• Figure 2: Slit-lamp photographs of pseudodendritic keratitis of VZV infection. Pseudodendritic keratitis lacks terminal bulbs, and tends to form thinner lesions.
• Figure 3: Conceptual diagrams of variable $u$, $S$ and $v$. (a) Conceptual diagram of variable $u$. We defined $u=1$ for infected cells and $u=0$ for uninfected cells. Uninfected cells ($u=0$) adjacent to infected cells ($u=1$) can probabilistically become infected cells ($u=1$). (b) Conceptual diagram of variable $S$ and $v$. Cytokines are produced from the cytokine-producing area where $S=1$. The cytokine concentration $v$ is high within the region ($S=1$), and spreads to the surrounding area through diffusion.
• Figure 4: Conceptual diagram of the infected region (green) and the cytokine-producing region (blue). The top row represents the infected region (green), while Types A to E show the cytokine-producing regions (blue) in each case. The dashed lines indicate the boundaries of the infected region. The five cases are as follows: (Type A) All infected cells produce cytokines. (Type B) All infected cells and their adjacent uninfected cells produce cytokines. (Type C) Only adjacent uninfected cells produce cytokines. (Type D) Only infected cells located within $n$ layers of the lesion boundary produce cytokines. (Type E) Both infected cells located within $n$ layers of the lesion boundary and their adjacent uninfected cells produce cytokines.
• Figure 5: Conceptual diagram of simulation domain under inflammatory conditions. During inflammation, cytokine-producing cells (e.g., dendritic cells) migrate from the limbus into the cornea and locally release cytokines. In the numerical model, this process is approximated by placing cytokine-producing source regions along the boundary of the simulation domain.