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

• Published in: Engineering with computers Vol. 41; no. 1; pp. 403 - 422
• Main Authors: Apolinar-Fernández, Alejandro, Barrasa-Fano, Jorge, Van Oosterwyck, Hans, Sanz-Herrera, José A.
• Format: Journal Article
• Language: English
• Published: London Springer London 01.02.2025; Springer Nature B.V
• Subjects: CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Cancer; Classical Mechanics; Computer Science; Computer-Aided Engineering (CAD; Control; Degradation; Extracellular matrix; Heterogeneity; Hydrogels; Math. Applications in Chemistry; Mathematical and Computational Engineering; Mechanical properties; Methodology; Microscopy; Modelling; Multiscale analysis; Original Article; Partial differential equations; Systems Theory; Traction force; Finite element method; Nonlinear mechanics; Traction force microscopy; Computational mechanics; Metalloproteinase-induced ECM degradation; Mechanobiology
• ISSN: 0177-0667; 1435-5663; 1435-5663
• DOI: 10.1007/s00366-024-02017-8

3D 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.