Three-dimensional traction microscopy with a fiber-based constitutive model

Song, Dawei; Hugenberg, Nicholas; Oberai, Assad A.

doi:10.1016/j.cma.2019.112579

Cited by 21 publications

(15 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, while the hyperelastic Neo-Hookean model can be used for synthetic, bio-compatible hydrogels, it cannot be used for realistic fibrous ECMs, which often exhibit highly nonlinear response at finite strains. To capture the complex behavior of those materials, more advanced constitutive models, such as the fiber-based homogenization models (e.g., [35,45]), should be used. We believe that the ability to recover tractions in 3D fibrous ECMs, while accounting for both fiber degradation and fiber realignment, will be a significant step forward.…”

Section: Resultsmentioning

confidence: 99%

“…6a). On the other hand, previous studies have shown that for fibrous ECM, cellinduced fiber realignment leads to ECM stiffening, as well as to slow displacement decay and long-range force transmission (e.g., [35,61,62]). Taken together, these results suggest that cells can modulate the range of force transmission in fibrous ECMs through two competing mechanisms-ECM degradation and fiber realignment.…”

Section: Inverse Problem and Error Analysismentioning

confidence: 95%

“…However, it cannot be directly applied to realistic biological tissues, which often contain a significant proportion of fibers and exhibit highly nonlinear response at finite strains [44]. For those cases, more complicated models such as the fiber-based constitutive models (e.g., [35,45,46]) should be used.…”

Section: Constitutive Equations and Ecm Degradationmentioning

confidence: 99%

“…In addition, we assume that ECM degradation is confined within a region proximal to the cell surface, so that the ECM is in its pristine state (i.e., λ = λ 0 and µ = µ 0 ) far from the cell surface. Thus, we consider the following inverse problem: given the displacement field u(x) in the ECM occupying a domain Ω, and at least one point x 0 in the ECM where λ = λ 0 and µ = µ 0 , find µ(x) and λ(x) in Ω such that equations (4), (35), and (36) are satisfied.…”

Section: A1 Inverse Problemmentioning

confidence: 99%

“…These authors also computed tractions exerted by 3T3 cells in dextran-based hydrogel matrices. More recently, Song et al [35] generalized the inverse approach to estimate tractions in fibrous ECMs, making use of a Voigt-type (affine) homogenization model to explicitly account for the fibrous microstructure of the ECM.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Three-dimensional traction microscopy accounting for cell-induced matrix degradation

Song

Seidl

Oberai

2019

Preprint

Self Cite

View full text Add to dashboard Cite

Tractions exerted by cells on the extracellular matrix (ECM) are critical in many important physiological and pathological processes such as embryonic morphogenesis, wound healing, and cancer metastasis. Three-dimensional Traction Microscopy (3DTM) is a tool to quantify cellular tractions by first measuring the displacement field in the ECM in response to these tractions, and then using this measurement to infer tractions. Most applications of 3DTM have assumed that the ECM has spatially-uniform mechanical properties, but cells secrete enzymes that can locally degrade the ECM. In this work, a novel computational method is developed to quantify both cellular tractions and ECM degradation. In particular, the ECM is modeled as a hyperelastic, Neo-Hookean solid, whose material parameters are corrupted by a single degradation parameter. The feasibility of determining both the traction and the degradation parameter is first demonstrated by showing the existence and uniqueness of the solution. An inverse problem is then formulated to determine the nodal values of the traction vector and the degradation parameter, with the objective of minimizing the difference between a predicted and measured displacement field, under the constraint that the predicted displacement field satisfies the equation of equilibrium. The inverse problem is solved by means of a gradient-based optimization approach, and the gradient is computed efficiently using appropriately derived adjoint fields. The computational method is validated in-silico using a geometrically accurate neuronal cell model and synthetic traction and degradation fields. It is found that the method accurately recovers both the traction and degradation fields. Moreover, it is found that neglecting ECM degradation can yield significant errors in traction measurements. Our method can extend the range of applicability of 3DTM.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Inverse Problem and Error Analysismentioning

confidence: 95%

Section: Constitutive Equations and Ecm Degradationmentioning

confidence: 99%

Section: A1 Inverse Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Three-dimensional traction microscopy accounting for cell-induced matrix degradation

Song

Seidl

Oberai

2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

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

View full text Add to dashboard Cite

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.

show abstract

Some Effects of Fiber Dispersion on the Mechanical Response of Incompressible Soft Solids

Sen

2022

J Elast

View full text Add to dashboard Cite

Three-dimensional traction microscopy with a fiber-based constitutive model

Cited by 21 publications

References 44 publications

Three-dimensional traction microscopy accounting for cell-induced matrix degradation

Three-dimensional traction microscopy accounting for cell-induced matrix degradation

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

Some Effects of Fiber Dispersion on the Mechanical Response of Incompressible Soft Solids

Contact Info

Product

Resources

About