Magnetic Resonance Imaging–based biomechanical simulation of cartilage: A systematic review

Seyedpour, Seyed Morteza; Nafisi, Sara; Nabati, Mehdi; Pierce, David M.; Reichenbach, Jürgen R.; Ricken, Tim

doi:10.1016/j.jmbbm.2021.104963

Cited by 10 publications

(1 citation statement)

References 121 publications

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“…Multiscale models thus arise naturally since soft tissues derive their macroscopic properties from hierarchical interactions within their heterogeneous microstructures. We can perform experiments to quantify mechanical properties and biology of tissues, and imaging can be used to estimate tissue structure [1][2][3] and even strains [4,5]; however, only computational models can estimate intra-tissue stresses because the required in vivo experiments are impossible or unsafe. To facilitate mechanistic understanding and improved analyses (e.g.…”

Section: Introductionmentioning

confidence: 99%

Finite Elements of Multiscale Mixtures (FE2M) in Three Dimensions: Theory, Numerical Implementation, and Analyses

Almasi,

Ricken,

Pierce

2024

Preprint

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The remarkable macro-mechanics of many soft tissues and fluid-saturated, porous engineered materials derive from the complex micro-mechanics of their constituents interacting. To facilitate mechanistic understanding and improved analyses (e.g. of experimental results) of the multi-scale mechanics of such materials we aimed to establish a computational framework specific to heterogeneous, fluid-saturated, soft tissues and engineered materials. The FE2 method is a general approach in finite elements (FEs) to describe the behavior of heterogeneous materials that circumvents the macroscopic constitutive model, instead a micro-scale representative volume element (RVE) analyses uses the same FE formulation to describe the nonlinear material behaviors resulting from the microstructure. We combined the theory of mixtures and the FE2 method (i.e. finite elements of multiscale mixtures, the FE2M method) to solve 3-D, two-scale, non-linear, coupled, and time-dependent boundary value problems for poroelastic materials. We established this multi-scale framework within FEBio (University of Utah) to perform finite element discretizations of boundary value problems on both macro- and micro-scales and thus facilitate new studies of fluid-saturated, biphasic/poroelastic materials. We investigated the performance of our FE2M framework using numerical experiments, specifically 3-D simulations of square plates with regular circular holes and included two different boundary conditions. Specifically, we studied the error behaviors, convergence rates, and run times, as well as the influence of size effects, i.e. the difference in scale between the macroscale (global) models and the microscale (local) RVE models for biphasic materials. Our results show that there is a size effect but that, with careful application of the framework, we can make the error arbitrarily small. Our FE2M framework is ideally suited to bridge the joint, tissue, and intra-tissue scales inherent in the biomechanics of soft tissues, but have not yet been applied to multi-phase, heterogeneous and fibrous materials. We provide free, public access to our FE2M framework as a plugin for FEBio, including a short user manual and input files for simple test cases, at github.uconn.edu/imLab/FE2M Resources.

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Section: Introductionmentioning

confidence: 99%

Finite Elements of Multiscale Mixtures (FE2M) in Three Dimensions: Theory, Numerical Implementation, and Analyses

Almasi,

Ricken,

Pierce

2024

Preprint

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Phase transition in porous materials: effects of material parameters and deformation regime on mass conservativity

Brodbeck,

Suditsch,

Seyedpour

et al. 2024

Comput Mech

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Phase transition in porous materials is relevant within different engineering applications, such as freezing in saturated soil or pancake sea ice. Mathematical descriptions of such processes can be derived based on Biot’s consolidation theory or the Theory of Porous Media. Depending on parameters such as density ratio, permeability or compressibility of the solid matrix, either small or finite deformations occur. Numerical solution procedures for the general, finite deformation case, suffers from instabilities and high computational costs. Simplifications, assuming small deformations, increases stability and computational efficiency. Within this work shortcomings of simplified theories based on Biot and linearisations of the Theory of Porous Media (TPM) are systematically studied. In order to determine the interaction of the different model parameters a non-dimensional model for poro-elasticity is presented. Based on a characteristic test-case including phase-transition and consolidation, the simplified models are compared to the fully non-linear TPM, focusing on mass errors as well as the time behaviour of the solution. Taking further into account the efficiency of discretisation based on different primal variables and finite-element-spaces, a guideline for selecting an appropriate combination of model, kinematic assumption and discretisation scheme is presented.

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A coupled multiscale description of seasonal Physical–BioGeoChemical dynamics in Southern Ocean Marginal Ice Zone

Pathak,

Seyedpour,

Kutschan

et al. 2025

Environmental Modelling & Software

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Magnetic Resonance Imaging–based biomechanical simulation of cartilage: A systematic review

Cited by 10 publications

References 121 publications

Finite Elements of Multiscale Mixtures (FE2M) in Three Dimensions: Theory, Numerical Implementation, and Analyses

Finite Elements of Multiscale Mixtures (FE2M) in Three Dimensions: Theory, Numerical Implementation, and Analyses

Phase transition in porous materials: effects of material parameters and deformation regime on mass conservativity

A coupled multiscale description of seasonal Physical–BioGeoChemical dynamics in Southern Ocean Marginal Ice Zone

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