A Combined Analytical and Computational approach towards Mechanophenotyping of Biological Cells using Poroelasticity and Machine Learning

Abstract

Mechanical properties are vital biomarkers for the health state of biological cells and indirectly human health. Mathematical and computational models relating the mechanical properties of cells with their deformation are valuable tools for understanding and predicting cellular behavior. Numerous models and techniques have been developed to measure the stiffness and viscosity of biological cells. Recent experimental investigations demonstrated that biological cells are poroelastic materials of solid networks bathed with cytosol liquid in the pores (Moeendarbary et al. (2013), Nature Materials). However, a mathematical model relating the deformation of poroelastic cell material with Young's modulus of Solid networks has not been reported yet to the best of our knowledge. This paper presents a combined mathematical and computational approach to the mechanophenotyping of biological cells. First, an analytical model is presented that considers the poroelastic nature of cells and relates Young's modulus of solid network with cell deformation. The developed model has been validated by predicting its Young’s Modulus based on the experimental data on deformation characteristics of cells squeezing through constriction microchannel. Model’s predicted Young’s Modulus for three different cell lines; HeLa, MCF-10A, and MDAMB-231 are \(153.64\pm 60.3 \text{k}\text{P}\text{a}, 97.84 \pm 41.7 \text{k}\text{P}\text{a}, \text{a}\text{n}\text{d} 67.9 \pm 48.8 \text{k}\text{P}\text{a}\) respectively, which matches well with the measurements reported using conventional techniques in literature. Furthermore, two artificial neural network (ANN) models are developed to predict Young's modulus and viscosity of cells based on measured deformation parameters for HeLa, MCF 10A, and MDA MB-231 cells. The neural network with an architecture of 4-8-9-1 is found to be best suited for Young's modulus predictions with \(R\sim0.974\). In contrast, the 4-7-8-1 architecture could provide better results for viscosity predictions of the given cell lines with \(R\sim0.999\). Further, a linear Support Vector Machine (SVM) model is also presented to classify the three given cell lines based on their initial diameter and elongation behavior in the constriction microchannel. To the best of our knowledge, this is the first study to present a poroelasticity-based mathematical model for biological cells predicting cell stiffness based on their deformation characteristics. Additionally, it is the first one to explore the classification of different cell lines based on their elongation ratio, derived from the analysis of static images within a constriction channel, eliminating the need for time-based studies. This combined analytical and computational approach can prove to be very useful for the direct estimation of mechanical properties of cells based on their squeezing behavior through constriction microchannel.