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Architected metamaterials such as foams and lattices exhibit a wide range of properties governed by microstructural instabilities and emerging phase transformations. Their macroscopic response--including energy dissipation during impact,…
We provide an adaptive finite element approximation for a model of quasi-static crack growth in dimension two. The discrete setting consists of integral functionals that are defined on continuous, piecewise affine functions, where the…
A patient-specific fluid-structure interaction (FSI) model of a phase-contrast magnetic resonance angiography (PC-MRA) imaged arteriovenous fistula is presented. The numerical model is developed and simulated using a commercial multiphysics…
A coupled system of nonlinear mixed-type equations modeling early stages of angiogenesis is analyzed in a bounded domain. The system consists of stochastic differential equations describing the movement of the positions of the tip and stalk…
We develop a finite element method for the vector Laplacian based on the covariant derivative of tangential vector fields on surfaces embedded in $\mathbb{R}^3$. Closely related operators arise in models of flow on surfaces as well as…
Surface growth, i.e., the addition or removal of mass from the boundary of a solid body, occurs in a wide range of processes, including the growth of biological tissues, solidification and melting, and additive manufacturing. To understand…
A general model is formulated for elasto-plastic materials undergoing linear kinematic hardening to describe microstructure evolution associated with phase transformations. Using infinitesimal strain theory, the model is based on…
A coarse-grained computational procedure based on the Finite Element Method is proposed to calculate the normal modes and mechanical response of proteins and their supramolecular assemblies. Motivated by the elastic network model, proteins…
A mathematical model of atherosclerosis of a blood vessel is advanced with regard for the entry of low-density lipoproteins (LDLs) into blood. For the first time, the influence of cytokines on the inflammation of a blood vessel at the…
Arterial tissue consists of multiple structurally important constituents that have individual material properties and associated stress-free configurations that evolve over time. This gives rise to residual stresses contributing to the…
Shape memory materials have gained considerable attention thanks to their ability to change physical properties when subjected to external stimuli such as temperature, pH, humidity, electromagnetic fields, etc. These materials are…
Coronary artery stenosis is a critical health risk, and its precise identification in Coronary Angiography (CAG) can significantly aid medical practitioners in accurately evaluating the severity of a patient's condition. The complexity of…
Assessing the severity of stenoses in coronary angiography is critical to the patient's health, as coronary stenosis is an underlying factor in heart failure. Current practice for grading coronary lesions, i.e. fractional flow reserve (FFR)…
Aims: The presence of coronary tandem lesions poses a significant challenge for the accurate diagnosis and management of coronary artery diseases. This study set out to provide a deeper understanding of the haemodynamic interactions between…
Unconditionally stable finite element methods for Darcy flow are derived by adding least-squares residual forms of the governing equations to the classical mixed formulations. The proposed methods are free of mesh dependent stabilization…
Uncertainty estimations are presented of the response of a multiscale in-stent restenosis model, as obtained by both non-intrusive and semi-intrusive uncertainty quantification. The in-stent restenosis model is a fully coupled multiscale…
Local hemodynamic forces play an important role in determining the functional significance of coronary arterial stenosis and understanding the mechanism of coronary disease progression. Computational fluid dynamics (CFD) have been widely…
This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of…
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…
Deformation modeling of cardiac muscle is an important issue in the field of cardiac analysis. For this reason, many approaches have been developed to best estimate the cardiac muscle deformation, and to obtain a practical model to use in…