Title: Linking Rheological Properties to Topological Texture Analysis in Microscopy Images of Dynamic Casein Gelation

Abstract:

This study introduces a new computational framework that combines Topological Data Analysis (TDA), Differential Box Counting (DBC), Multifractal Partition (MFP), and Local Binary Patterns (LBP). The toolkit was applied to time-lapse super-resolution STED microscopy images capturing the gelation of sodium caseinate, triggered by glucono-delta-lactone (GDL), at temperatures of 30°C and 40°C, using two distinct GDL concentrations (1.8% and 3.5% w/v).

TDA monitored topological loops—closed, ring-like structures that indicate protein network interconnectivity—through max-Betti-1 curves. These curves identified three distinct phases: an initial lag phase characterized by dispersed aggregates, a sharp decay that aligned with network percolation and the sol-gel transition observed in rheological measurements, and a subsequent increase post-gelation that corresponded to network rearrangements. The validity of these topological shifts was confirmed by DBC and MFP, both of which successfully detected alterations in spatial heterogeneity and structural complexity.

Prior to experimental application, the toolbox was validated using simulated fractal images. Collectively, these metrics offered high sensitivity to subtle microstructural changes, complementing the averaged bulk mechanical responses obtained through traditional rheology. This integrated methodology serves as a robust quantitative instrument for analyzing complex microstructures and evolving dynamics in food and material science. The associated code is accessible at https://github.com/Zahratabatabaei/Delifood_CV_paper.git

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC