Advanced in silico validation framework for three-dimensional traction force microscopy and application to an in vitro model of sprouting angiogenesis

Barrasa‐Fano, Jorge; Shapeti, Apeksha; Jong, Jan de; Ranga, Adrian; Sanz-Herrera, José A.; Oosterwyck, Hans Van

doi:10.1016/j.actbio.2021.03.014

Cited by 20 publications

(21 citation statements)

References 87 publications

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“…The determined traction profile τ recon can then be compared to the initial analytical profile τ . Studies that describe new methods to improve the image processing part of TFM often include a simulation of the bead distribution, sometimes also assuming a specific point spread function [ 18 , 56 , 57 ]. However, noise can also arise from different sources, e.g.…”

Section: Resultsmentioning

confidence: 99%

“…This workflow is known as the direct (or forward ) method (DM). It has been pioneered for 2.5D TFM [ 14 – 16 ], but also has been applied to 3D TFM [ 17 , 18 ] and to elastic beads with embedded markers that are deformed by the traction forces in cell aggregates [ 11 ]. The DM is especially suited to deal with large deformations and non-linear material laws, but it also can be used in the linear regime, which is typically used for 2D or 2.5D TFM on soft elastic substrates.…”

Section: Introductionmentioning

confidence: 99%

“…In order to choose the correct value of the regularization parameter, different schemes have been suggested, including the L-curve criterion or generalized cross-validation [ 22 , 23 ]. The need for explicit regularization can be avoided by using TFM-schemes that effectively filter the deformation data, like image smoothing [ 24 , 25 ] or the Finite Element Method (FEM) [ 17 , 18 , 26 ].…”

Section: Introductionmentioning

confidence: 99%

“…Very rarely however are these different methods directly compared against each other. A notable exception is a recent work that compares FEM-based implementations of the direct and inverse methods for 3D TFM [ 17 , 18 ]. Here we aim at a similar comparison, but for 2.5D TFM and with GF-based methods.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of direct and inverse methods for 2.5D traction force microscopy

Blumberg

Schwarz

2022

PLoS ONE

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Essential cellular processes such as cell adhesion, migration and division strongly depend on mechanical forces. The standard method to measure cell forces is traction force microscopy (TFM) on soft elastic substrates with embedded marker beads. While in 2D TFM one only reconstructs tangential forces, in 2.5D TFM one also considers normal forces. Here we present a systematic comparison between two fundamentally different approaches to 2.5D TFM, which in particular require different methods to deal with noise in the displacement data. In the direct method, one calculates strain and stress tensors directly from the displacement data, which in principle requires a divergence correction. In the inverse method, one minimizes the difference between estimated and measured displacements, which requires some kind of regularization. By calculating the required Green’s functions in Fourier space from Boussinesq-Cerruti potential functions, we first derive a new variant of 2.5D Fourier Transform Traction Cytometry (FTTC). To simulate realistic traction patterns, we make use of an analytical solution for Hertz-like adhesion patches. We find that FTTC works best if only tangential forces are reconstructed, that 2.5D FTTC is more precise for small noise, but that the performance of the direct method approaches the one of 2.5D FTTC for larger noise, before both fail for very large noise. Moreover we find that a divergence correction is not really needed for the direct method and that it profits more from increased resolution than the inverse method.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Comparison of direct and inverse methods for 2.5D traction force microscopy

Blumberg

Schwarz

2022

PLoS ONE

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“…The developed mechanobiological model contains a number of phenomenological parameters with physiological meaning. In fact, these parameters may be measured (or calibrated) using standard experiments of proliferation, diffusion [20], or traction force microscopy [57,58] to account for the contractile behavior of glioblastoma cells. The effect of model parameters on the results was investigated in a parametric analysis, using the same rate of variation (from half to double) for all the parameters.…”

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confidence: 99%

A mechanobiological model for tumor spheroids evolution: application to glioblastoma

Carrasco-Mantis

Castro-Abril

Ranđelović

et al. 2021

Preprint

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Spheroids are in vitro spherical structures of cell aggregates, eventually cultured within a hydrogel matrix, that are used, among other applications, as a technological platform to investigate tumor formation and evolution. Several interesting features can be replicated using this methodology, such as cell communication mechanisms, the effect of gradients of nutrients, or the creation of realistic 3D biological structures. In this paper, we propose a continuum mechanobiological model which accounts for the most relevant phenomena that take place in tumor spheroids evolution under in vitro suspension, namely, nutrients diffusion in the spheroid, kinetics of cellular growth and death, and mechanical interactions among the cells. The model is qualitatively validated, after calibration of the model parameters, versus in vitro experiments of spheroids of different glioblastoma cell lines. This preliminary validation allowed us to conclude that glioblastoma tumor spheroids evolution is mainly driven by mechanical interactions of the cell aggregate and the dynamical evolution of the cell population. In particular, it is concluded that our model is able to explain quite different setups, such as spheroids growth (up to six times the initial configuration for U-87 MG cell line) or shrinking (almost half of the initial configuration for U-251 MG cell line); as the result of the mechanical interplay of cells driven by cellular evolution. Indeed, the main contribution of this work is to link the spheroid evolution with the mechanical activity of cells, coupled with nutrient consumption and the subsequent cell dynamics. All this information can be used to further investigate mechanistic effects in the evolution of tumors and their role in cancer disease.

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Multiphysics modeling of 3D traction force microscopy with application to cancer cell-induced degradation of the extracellular matrix

Apolinar-Fernández,

Barrasa-Fano,

Van Oosterwyck

et al. 2024

Engineering with Computers

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Abstract3D Traction Force Microscopy (3DTFM) constitutes a powerful methodology that enables the computation of realistic forces exerted by cells on the surrounding extracellular matrix (ECM). The ECM is characterized by its highly dynamic structure, which is constantly remodeled in order to regulate most basic cellular functions and processes. Certain pathological processes, such as cancer and metastasis, alter the way the ECM is remodeled. In particular, cancer cells are able to invade its surrounding tissue by the secretion of metalloproteinases that degrade the extracellular matrix to move and migrate towards different tissues, inducing ECM heterogeneity. Typically, 3DTFM studies neglect such heterogeneity and assume homogeneous ECM properties, which can lead to inaccuracies in traction reconstruction. Some studies have implemented ECM degradation models into 3DTFM, but the associated degradation maps are defined in an ad hoc manner. In this paper, we present a novel multiphysics approach to 3DTFM with evolving mechanical properties of the ECM. Our modeling considers a system of partial differential equations based on the mechanisms of activation of diffusive metalloproteinase MMP2 by membrane-bound metalloproteinase MT1-MMP. The obtained ECM density maps in an ECM-mimicking hydrogel are then used to compute the heterogeneous mechanical properties of the hydrogel through a multiscale approach. We perform forward and inverse TFM simulations both accounting for and omitting degradation, and results are compared to ground truth reference solutions in which degradation is considered. The main conclusions resulting from the study are: (i) the inverse methodology yields results that are significantly more accurate than those provided by the forward methodology; (ii) ignoring ECM degradation results in a considerable overestimation of tractions and non negligible errors in all analyzed cases.

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Advanced in silico validation framework for three-dimensional traction force microscopy and application to an in vitro model of sprouting angiogenesis

Cited by 20 publications

References 87 publications

Comparison of direct and inverse methods for 2.5D traction force microscopy

Comparison of direct and inverse methods for 2.5D traction force microscopy

A mechanobiological model for tumor spheroids evolution: application to glioblastoma

Multiphysics modeling of 3D traction force microscopy with application to cancer cell-induced degradation of the extracellular matrix

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