Stiffness estimation and classification of biological cells using constriction microchannel: poroelastic model and machine learning

Mathematical and computational models linking cell mechanical properties with deformation are crucial for understanding cellular behavior. While various techniques measure the stiffness and viscosity of cells, recent experiments suggest that cells exhibit poroelastic behavior, characterized by solid mesh networks immersed in cytosol liquid (Moeendarbary et al. in Nat Mater 12:253–261, 2013. https://doi.org/10.1038/nmat3517). Despite this, a mathematical model relating poroelastic cell deformation and Young's modulus of solid networks has not been reported. This study presents the first poroelasticity-based mathematical model for relating cell deformation with Young’s modulus of solid mesh networks. The model is validated by utilizing the experimental data of the cell’s squeezing behavior through a constriction microchannel. The predicted Young’s modulus for HeLa, MCF-10A, and MDA MB-231 cell lines are 153.64 ± 60.3 kPa, 97.84 ± 41.7 kPa, and 67.9 ± 48.8 kPa, respectively, which matches well with the conventional measurements. Additionally, two artificial neural network (ANN) models were developed which predicted Young's modulus and viscosity for these cell lines based on migration and deformation characteristics through constriction microchannel, achieving high accuracy (R ~ 0.974 and R ~ 0.999, respectively). Further, a linear Support Vector Machine (SVM) model classified cell lines based on initial diameter and elongation in the constriction microchannel measured from static images. The combined analytical and computational approach proposed here offers direct quantitative estimates of cell mechanical properties and cell classification based on their squeezing behavior through constriction microchannel.