Publications

Traction force microscopy (TFM) quantifies cellular forces at the cell-extracellular matrix interface, yet elastic formulations neglect viscous dissipation and can misinterpret cellular forces on viscoelastic substrates. We introduce a semi-analytical 2D viscoelastic TFM (veTFM) that generalizes the Boussinesq framework of elastic TFM to Generalized Maxwell (GMX) substrates with one or two components. By combining Fourier and Laplace transforms, veTFM quantifies time-resolved tractions in finite-thickness substrates and resolves stress-free reference and substrate pre-stress. We derive criteria for when elastic regimes remain valid in this framework. This positions veTFM as a scalable extension of standard 2D TFM (eTFM) to viscoelastic substrates, identifying when eTFM remains sufficient, which elastic limit applies, and when full viscoelastic quantification is required. Applied to beating cardiomyocytes, epithelial cells, and dermal fibroblasts cultured on linear-polyacrylamide and alginate viscoelastic hydrogels, veTFM shows that the elastic or viscoelastic regime engaged by the cell depends on timescale matching between the loading rate and the substrate's relaxation times. Notably, for the Generalized Maxwell substrates analyzed here, viscoelastic traction magnitudes scale with the substrate's total dissipation rather than individual relaxation times, with total dissipation setting traction magnitude and timescale matching determining whether the cell engages the substrate in an elastic or viscoelastic regime.

JTD Keywords: Biomaterials, Cell, Cell-material interactions, Extracellular-matrix viscoelasticity, Focal adhesions, Guide, Hydrogels, Numerical inversion, Semi-analytical methods, Stress relaxation, Viscoelastic hydrogels, Viscoelastic traction force microscopy

Tuning of the crosslink density (CLD) in the rubber compounds is very crucial for optimizing the physical and mechanical properties of the ultimate rubber products. Conventionally, CLD can be measured via rheological methods such as moving die rheometer (MDR), via mechanical tests such as temperature scanning stress relaxation analysis (TSSR), or via direct swelling experiments using Flory–Rehner approach. In the current study, two novel techniques, focused ion beam - scanning electron microscopy (FIB-SEM) processing, with simultaneous energy dispersive X-ray spectrometry (EDS) mapping analysis and scanning acoustic microscopy (SAM) were combined and correlated to conventional methods on a model recipe of ethylene propylene diene monomer (EPDM) compound having different sulphur contents. Depending on the applied technique, the increase in the crosslink density with sulphur content was found to be 1.7 fold for the Flory–Rehner approach and 1.2 fold for both TSSR and MDR. It is directly monitored from the FIB-SEM-EDS analysis that the sulphur distribution and agglomeration behavior increased in line with ZnO content, which is an indirect indication of the rise in crosslink density. The impedance maps of the crosslinked samples obtained through SAM analysis revealed that the impedance of the samples increased with the increasing sulphur content, which can be attributed to higher level of crosslink density. A quantified correlation was obtained between SAM images and the crosslink density of the samples. It was shown that SAM is a promising tool for practical and non-destructive analysis for determining the formation of crosslink density of the rubbers. © The Author(s) 2022.

JTD Keywords: blends, compressibility, crosslink density, cure characteristics, ethylene propylene diene monomer, focused ion beam, mechanical-properties, morphology, natural-rubber, particles, scanning acoustic microscopy, scanning electron microscopy, sulfur, thermal-stability, vulcanization, Composite soft materials, Cross-link densities, Crosslink density, Crosslinking, Density (specific gravity), Ethylene, Ethylene propylene diene monomer, Flory-rehner, Focused ion beam - scanning electron microscopy, Focused ion beam-scanning electron microscopies, Ii-vi semiconductors, Monomers, Moving die rheometers, Physical and mechanical properties, Propylene, Relaxation analysis, Rubber, Scanning acoustic microscopy, Scanning electron microscopy, Stress relaxation, Sulfur contents, Temperature scanning stress relaxations, Zinc oxide