Digital Quantification of Surface–Biofilm Interactions via Persistent Homology: Beyond Conventional Absorbance Measurements

Crystal violet (CV) absorbance measurement is the most widely used method for quantifying biofilm formation on material surfaces. However, this conventional approach yields only a bulk measure of total biomass and suffers from substantial data scatter, failing to capture the spatial heterogeneity inherent in biofilm colonization. In this study, we introduce persistent homology (PH), a tool from topological data analysis, as a digital framework for extracting structural information directly from photographs of CV-stained specimens. Three substrate conditions were examined: bare carbon steel (SS400), chromium-plated steel (Cr/SS400), and alkoxysilane-resin-coated chromium-plated steel (Permeate/Cr/SS400). CV-stained surface images were converted to scalar intensity maps using the CIELAB a*−b* channel, followed by sublevel-set filtration and union-find tracking to generate persistence diagrams. Zero-dimensional features (H₀) quantified the number and independence of biofilm colonies, while first-dimensional features (H₁) characterized the development of valley structures between colonies. Both H₀ and H₁ total persistence decreased in the order SS400 > Cr/SS400 > Permeate/Cr/SS400, revealing that the Permeate coating suppresses not only biofilm adhesion but also the maturation and three-dimensional structural development of attached biofilms — a distinction invisible to conventional absorbance measurements. H₀ mean persistence was further identified as a potential indicator of biofilm maturation stage. This image-based topological approach offers a cost-effective, reproducible digital tool for evaluating anti-biofilm performance of surface treatments.