Modeling the Local Viscoelastic Behavior of Living Cells Under Nanoindentation Tests

Abstract

Aiming at multiscale numerical investigations of fibrous connective tissues, the present work proposes a finite strain viscoelastic model suitable to represent the local mechanical response of living cells in conjunction with finite element simulations of nanoindentation tests. The material model is formulated in a thermodynamically consistent framework based on a variational constitutive approach. As a case of study, a numerical investigation of the local compressible response of fibroblast cells is addressed. Moreover, a set of cyclic, stress relaxation and creep experiments are simulated in order to investigate the capability of the model to predict rate dependence of cells, showing sound agreement with experimental data. The proposed model may be used as a suitable tool for a better understanding of stiffness and energetic dissipation of cells. KeywordsLiving cells, Viscoelasticity, Constitutive model, AFM nanoindentation, Multiscale. Modeling the Local Viscoelastic Behavior of Living Cells Under Nanoindentation Tests 1 INTRODUCTIONWithstanding mechanical loadings is the primary function of many biological connective tissues such as tendons, ligaments and cartilage. The mechanical response to external loadings are highly dependent on their hierarchical microstructure, cellular organization and interactions between one another (Lavagnino et al., 2015).On its hierarchy inside the tissue, cells are subjected to a complex mechanical environment (Qi et al., 2006) phology are usually known as mechanotransduction mechanisms (Lavagnino et al., 2015; Wang, 2006).Regardless their physiological functions, living cells are structural units holding particular nonlinear behaviors, including viscous and plastic effects (Bonakdar et al., 2016; Haase and Pelling, 2015; Nawaz et al., 2012). Accordingly, cells may present important mechanical contributions in the macroscopic response of tissues, where multiscale analysis can be employed to investigate these micromechanical behaviors.In multiscale numerical analyses based on representative volume elements (RVE), the homogenized behavior relies strongly on how accurate the behavior of each material phase is represented by corresponding specific material models. In addition, these models must show sound agreement with experimental data at that scale, specifically in cases where these phases present nonlinear behavior and are subjected to finite strains.Several measurement techniques have been employed to assess the mechanical response of living cells, such as micropipette aspiration, magnetic and optical tweezers and atomic force microscopy (AFM) indentation, also known as nanoindentation test (Haase and Pelling, 2015; Janmey and McCulloch, 2007; Kollmannsberger and Fabry, 2011). Among these experimental methods, the later provides a convenient structure to finite element simulations. For instance, whereas the cell sample can be considered locally as a homogenous medium, the tip of the indenter is modeled as a rigid body.With these motivations in mind and aiming futur...

Nonlinear Elastic and Inelastic Properties of Cells

“…Recently, a FEM model was employed to simulate various nano-indentation experiments of fibroblast cells with cyclic, stress relaxation, and creep tests (Fig. 7(c)) [171]. This study showed viscoelastic behaviors of fibroblasts arising in response to those mechanical signals, consistent with experimental observations (Fig.…”

An investigation of coupled solution algorithms for finite‐strain poroviscoelasticity applied to soft biological tissues

“…In the present investigation, the viscoelastic model used for the solid skeleton was formulated within a thermodynamically consistent variational framework, whose details can be found elsewhere. [42][43][44][45][46][47] Considering the time-discrete version of this constitutive formulation, given a time increment 𝛥t = t n+1 − t n , a deformation gradient F n+1 and a set of internal variables 𝜶 n , the main goal of the constitutive algorithm is to update the internal variables to their current state t n+1 and evaluate the stress state afterwards.…”

Mechanical characterization of hydrolysis effects on the stiffness of bioabsorbable polymeric filaments: An experimental and modeling approach based on a simple constitutive damage model

“…Detailed discussion on this subject can be found elsewhere. [22][23][24][25][26][27] A.1. Variational constitutive updates.…”

“…Regarding the constitutive modeling approach, a thermodynamically consistent variational framework well-established in literature was employed herein. 3,22-27 A specific strain energy and a proper dissipation damage potential are proposed to model the tested material. Moreover, a nonlinear curve fitting procedure based on Particle Swarm Optimization (PSO) was used to identify the constitutive parameters in view of the experimental data.…”