Topological texture analysis of microscopy images of dynamic casein gelation and its relation to rheological properties

We present a computational framework integrating longitudinal super-resolution Stimulated Emission Depletion microscopy with Topological Data Analysis (TDA), fractal analysis, and texture descriptors to quantify the dynamic microstructural evolution of protein gelation. Sodium caseinate gelation induced by glucono- \(\delta\) -lactone (GDL) was used as a model system. Two temperatures (30 °C and 40 °C) and GDL concentrations (1.8% and 3.5% w/v) were investigated. The toolbox was first validated on simulated fractal images with controlled structural complexity and subsequently applied to experimental sodium caseinate data. TDA tracked network interconnectivity through max-Betti-1 curves. Results revealed aggregation stages including a lag phase related to dispersed aggregates, a sharp decay coinciding with network percolation and the rheological gel point, and a post-percolation increase associated with network rearrangements. Differential Box Counting and Multifractal Partition revealed the transition from a heterogeneous dispersion to a structurally organized network, while Local Binary Patterns detected post-percolation rearrangements. Overall, the framework captured microstructural transitions represented only indirectly by bulk rheology while resolving early aggregation dynamics inaccessible to conventional techniques. This scalable approach links microstructure with macroscopic functionality and is applicable to diverse soft matter and food systems. Code is available at DOI .