Direct and inverse identification of constitutive parameters from the structure of soft tissues.

Part 2: dispersed arrangement of collagen fibers

authored by: Markus von Hoegen, Michele Marino, Jörg Schröder, Peter Wriggers
Abstract: This paper investigates on the relationship between the arrangement of collagen fibers within soft tissues and parameters of constitutive models. Starting from numerical experiments based on biaxial loading conditions, the study addresses both the direct (from structure to mechanics) and the inverse (from mechanics to structure) problems, solved introducing optimization problems for model calibration and regression analysis. A campaign of parametric analyses is conducted in order to consider fibers distributions with different main orientation and angular dispersion. Different anisotropic constitutive models are employed, accounting for fibers dispersion either with a generalized structural approach or with an increasing number of strain energy terms. Benchmark data sets, toward which constitutive models are fitted, are built by employing a multiscale description of fiber nonlinearities and accounting for fibers dispersion with an angular integration method. Results show how the optimal values of constitutive parameters obtained from model calibration vary as a function of fibers arrangement and testing protocol. Moreover, the fitting capabilities of constitutive models are discussed. A novel strategy for model calibration is also proposed, in order to obtain a robust accuracy with respect to different loading conditions starting from a low number of mechanical tests. Furthermore, novel results useful for the inverse determination of the mean angle and the variance of fibers distribution are obtained. Therefore, the study contributes: to better design procedures for model calibration; to account for mechanical alterations due to remodeling mechanisms; and to gain structural information in a nondestructive way.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): University of Duisburg-Essen
Type: Article
Journal: Biomechanics and Modeling in Mechanobiology
Volume: 18
Pages: 897-920
No. of pages: 24
ISSN: 1617-7959
Publication date: 15.08.2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Mechanical Engineering, Biotechnology, Modelling and Simulation
Electronic version(s): https://doi.org/10.1007/s10237-019-01119-3 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{5097f3a9f4b04bf7bcaf0aaaad4fdf2c,
title = "Direct and inverse identification of constitutive parameters from the structure of soft tissues.: Part 2: dispersed arrangement of collagen fibers",
abstract = "This paper investigates on the relationship between the arrangement of collagen fibers within soft tissues and parameters of constitutive models. Starting from numerical experiments based on biaxial loading conditions, the study addresses both the direct (from structure to mechanics) and the inverse (from mechanics to structure) problems, solved introducing optimization problems for model calibration and regression analysis. A campaign of parametric analyses is conducted in order to consider fibers distributions with different main orientation and angular dispersion. Different anisotropic constitutive models are employed, accounting for fibers dispersion either with a generalized structural approach or with an increasing number of strain energy terms. Benchmark data sets, toward which constitutive models are fitted, are built by employing a multiscale description of fiber nonlinearities and accounting for fibers dispersion with an angular integration method. Results show how the optimal values of constitutive parameters obtained from model calibration vary as a function of fibers arrangement and testing protocol. Moreover, the fitting capabilities of constitutive models are discussed. A novel strategy for model calibration is also proposed, in order to obtain a robust accuracy with respect to different loading conditions starting from a low number of mechanical tests. Furthermore, novel results useful for the inverse determination of the mean angle and the variance of fibers distribution are obtained. Therefore, the study contributes: to better design procedures for model calibration; to account for mechanical alterations due to remodeling mechanisms; and to gain structural information in a nondestructive way.",
keywords = "Constitutive models, Fiber dispersion, Inverse analysis, Parameters identification, Soft tissue mechanics, Regression Analysis, Algorithms, Models, Biological, Fibrillar Collagens/physiology, Organ Specificity",
author = "{von Hoegen}, Markus and Michele Marino and J{\"o}rg Schr{\"o}der and Peter Wriggers",
note = "Funding Information: M. Marino acknowledges that this work has been carried out within the framework of the SMART BIOTECS alliance between the Technical University of Braunschweig and the Leibniz University of Hannover. This initiative is financially supported by the Ministry of Science and Culture (MWK) of Lower Saxony, Germany.",
year = "2019",
month = aug,
day = "15",
doi = "10.1007/s10237-019-01119-3",
language = "English",
volume = "18",
pages = "897--920",
journal = "Biomechanics and Modeling in Mechanobiology",
issn = "1617-7959",
publisher = "Springer Verlag",
number = "4",
}