Daniel Balzani

Parallel simulation of patient‐specific atherosclerotic arteries for the enhancement of intravascular ultrasound diagnostics

Purpose – The purpose of this paper is to present a computational framework for the simulation of patient‐specific atherosclerotic arterial walls. Such simulations provide information regarding the mechanical stress distribution inside the arterial wall and may therefore enable improved medical indications for or against medical treatment. In detail, the paper aims to provide a framework which takes into account patient‐specific geometric models obtained by in vivo measurements, as well as a fast solution strategy, giving realistic numerical results obtained in reasonable time.Design/methodology/approach – A method is proposed for the construction of three‐dimensional geometrical models of atherosclerotic arteries based on intravascular ultrasound virtual histology data combined with angiographic X‐ray images, which are obtained on a routine basis in the diagnostics and medical treatment of cardiovascular diseases. These models serve as a basis for finite element simulations where a large number of unknow...

FE 2 -Simulation of Microheterogeneous Steels Based on Statistically Similar RVEs

A main problem of direct homogenization methods is the high computational cost, when we have to deal with large random microstructures. This leads to a large number of history variables which needs a large amount of memory, and moreover a high computation time. We focus on random microstructures consisting of a continuous matrix phase with a high number of embedded inclusions. In this contribution a method is presented for the construction of statistically similar representative volume elements (SSRVEs) which are characterized by a much less complexity than usual random RVEs in order to obtain an efficient simulation tool. The basic idea of the underlying procedure is to find a simplified SSRVE, whose selected statistical measures under consideration are as close as possible to the ones of the original microstructure.

Computational model for the cell-mechanical response of the osteocyte cytoskeleton based on self-stabilizing tensegrity structures

The mechanism by which mechanical stimulation on osteocytes results in biochemical signals that initiate the remodeling process inside living bone tissue is largely unknown. Even the type of stimulation acting on these cells is not yet clearly identified. However, the cytoskeleton of osteocytes is suggested to play a major role in the mechanosensory process due to the direct connection to the nucleus. In this paper, a computational approach to model and simulate the cell structure of osteocytes based on self-stabilizing tensegrity structures is suggested. The computational model of the cell consists of the major components with respect to mechanical aspects: the integrins that connect the cell with the extracellular bone matrix, and different types of protein fibers (microtubules and intermediate filaments) that form the cytoskeleton, the membrane-cytoskeleton (microfilaments), the nucleus and the centrosome. The proposed geometrical cell models represent the cell in its physiological environment which is necessary in order to give a statement on the cell behavior in vivo. Studies on the mechanical response of osteocytes after physiological loading and in particular the mechanical response of the nucleus show that the load acting on the nucleus is rising with increasing deformation applied to the integrins.

Selective enzymatic removal of elastin and collagen from human abdominal aortas: Uniaxial mechanical response and constitutive modeling

The ability to selectively remove the structurally most relevant components of arterial wall tissues such as collagen and elastin enables ex vivo biomechanical testing of the remaining tissues, with the aim of assessing their individual mechanical contributions. Resulting passive material parameters can be utilized in mathematical models of the cardiovascular system. Using eighteen wall specimens from non-atherosclerotic human abdominal aortas (55 ± 11 years; 9 female, 9 male), we tested enzymatic approaches for the selective digestion of collagen and elastin, focusing on their application to human abdominal aortic wall tissues from different patients with varying sample morphologies. The study resulted in an improved protocol for elastin removal, showing how the enzymatic process is affected by inadequate addition of trypsin inhibitor. We applied the resulting protocol to circumferential and axial specimens from the media and the adventitia, and performed cyclic uniaxial extension tests in the physiological and supra-physiological loading domain. The collagenase-treated samples showed a (linear) response without distinct softening behavior, while the elastase-treated samples exhibited a nonlinear, anisotropic response with pronounced remanent deformations (continuous softening), presumably caused by some sliding of collagen fibers within the damaged regions of the collagen network. In addition, our data showed that the stiffness in the initial linear stress-stretch regime at low loads is lower in elastin-free tissue compared to control samples (i.e. collagen uncrimping requires less force than the stretching of elastin), experimentally confirming that elastin is responsible for the initial stiffness in elastic arteries. Utilizing a continuum mechanical description to mathematically capture the experimental results we concluded that the inclusion of a damage model for the non-collagenous matrix material is, in general, not necessary. To model the softening behavior, continuous damage was included in the fibers by adding a damage variable which led to remanent strains through the consideration of damage.

Comparative analysis of damage functions for soft tissues: Properties at damage initialization

In this paper several damage equations are analysed with respect to their properties at damage initialization. This is particularly important for soft biological tissues since two different loading regimes have to be clearly distinguished: the physiological domain where no damage evolution should be considered and the supra-physiological domain where damage evolves. At the transition between these two domains the behaviour of different damage models may influence the convergence of the Newton iteration when solving, for example, nonlinear finite element problems. It is shown that the model proposed by Balzani et al. (Comput Meth Appl Mech Eng 2012; 213–216: 139–151) a priori ensures smooth tangent moduli. In addition to that, a new damage function is proposed able to describe a slow damage evolution at damage initialization also providing smooth tangent moduli. Using this new damage function the approach given by Balzani et al. (Acta Biomater 2006; 2(6): 609–618) can also be modified such that smooth tangent moduli are guaranteed. Numerical analyses of a circumferentially overstretched artery are performed and show that no convergence problems are observed at the transition from the undamaged to the damaged domain, even when a model is used that has non-smooth tangent moduli.

Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains.

The accurate prediction of transmural stresses in arterial walls requires on the one hand robust and efficient numerical schemes for the solution of boundary value problems including fluid-structure interactions and on the other hand the use of a material model for the vessel wall that is able to capture the relevant features of the material behavior. One of the main contributions of this paper is the application of a highly nonlinear, polyconvex anisotropic structural model for the solid in the context of fluid-structure interaction, together with a suitable discretization. Additionally, the influence of viscoelasticity is investigated. The fluid-structure interaction problem is solved using a monolithic approach; that is, the nonlinear system is solved (after time and space discretizations) as a whole without splitting among its components. The linearized block systems are solved iteratively using parallel domain decomposition preconditioners. A simple - but nonsymmetric - curved geometry is proposed that is demonstrated to be suitable as a benchmark testbed for fluid-structure interaction simulations in biomechanics where nonlinear structural models are used. Based on the curved benchmark geometry, the influence of different material models, spatial discretizations, and meshes of varying refinement is investigated. It turns out that often-used standard displacement elements with linear shape functions are not sufficient to provide good approximations of the arterial wall stresses, whereas for standard displacement elements or F-bar formulations with quadratic shape functions, suitable results are obtained. For the time discretization, a second-order backward differentiation formula scheme is used. It is shown that the curved geometry enables the analysis of non-rotationally symmetric distributions of the mechanical fields. For instance, the maximal shear stresses in the fluid-structure interface are found to be higher in the inner curve that corresponds to clinical observations indicating a high plaque nucleation probability at such locations. Copyright

Construction of Statistically Similar Representative Volume Elements

In computational homogenization approaches the definition of a representative volume element (RVE) strongly influences the performance of the resulting numerical scheme, not only with respect to its physical accuracy but also with respect to the computational effort required. Here, we propose a method for the construction of statistically similar RVEs (SSRVEs), which are characterized by a reduced complexity compared to real microstructures and which therefore lead to computationally less expensive methods. These SSRVEs are obtained by minimizing a least-square functional taking into account differences of statistical measures that characterize the morphology of a real (target) microstructure and the SSRVE. By comparing the mechanical response in a series of numerical investigations it is shown that also the material behavior obtained by considering the real microstructure is well represented by the SSRVEs.

Relaxed incremental variational approach for the modeling of damage-induced stress hysteresis in arterial walls.

In this paper, a three-dimensional relaxed incremental variational damage model is proposed, which enables the description of complex softening hysteresis as observed in supra-physiologically loaded arterial tissues, and which thereby avoids a loss of convexity of the underlying formulation. The proposed model extends the relaxed formulation of Balzani and Ortiz [2012. Relaxed incremental variational formulation for damage at large strains with application to fiber-reinforced materials and materials with truss-like microstructures. Int. J. Numer. Methods Eng. 92, 551-570], such that the typical stress-hysteresis observed in arterial tissues under cyclic loading can be described. This is mainly achieved by constructing a modified one-dimensional model accounting for cyclic loading in the individual fiber direction and numerically homogenizing the response taking into account a fiber orientation distribution function. A new solution strategy for the identification of the convexified stress potential is proposed based on an evolutionary algorithm which leads to an improved robustness compared to solely Newton-based optimization schemes. In order to enable an efficient adjustment of the new model to experimentally observed softening hysteresis, an adjustment scheme using a surrogate model is proposed. Therewith, the relaxed formulation is adjusted to experimental data in the supra-physiological domain of the media and adventitia of a human carotid artery. The performance of the model is then demonstrated in a finite element example of an overstretched artery. Although here three-dimensional thick-walled atherosclerotic arteries are considered, it is emphasized that the formulation can also directly be applied to thin-walled simulations of arteries using shell elements or other fiber-reinforced biomembranes.

Method for the unique identification of hyperelastic material properties using full field measures. Application to the passive myocardium material response

Quantitative measurement of the material properties (eg, stiffness) of biological tissues is poised to become a powerful diagnostic tool. There are currently several methods in the literature to estimating material stiffness, and we extend this work by formulating a framework that leads to uniquely identified material properties. We design an approach to work with full-field displacement data-ie, we assume the displacement field due to the applied forces is known both on the boundaries and also within the interior of the body of interest-and seek stiffness parameters that lead to balanced internal and external forces in a model. For in vivo applications, the displacement data can be acquired clinically using magnetic resonance imaging while the forces may be computed from pressure measurements, eg, through catheterization. We outline a set of conditions under which the least-square force error objective function is convex, yielding uniquely identified material properties. An important component of our framework is a new numerical strategy to formulate polyconvex material energy laws that are linear in the material properties and provide one optimal description of the available experimental data. An outcome of our approach is the analysis of the reliability of the identified material properties, even for material laws that do not admit unique property identification. Lastly, we evaluate our approach using passive myocardium experimental data at the material point and show its application to identifying myocardial stiffness with an in silico experiment modeling the passive filling of the left ventricle.

One-Way and Fully-Coupled FE2 Methods for Heterogeneous Elasticity and Plasticity Problems: Parallel Scalability and an Application to Thermo-Elastoplasticity of Dual-Phase Steels

In this paper, aspects of the two-scale simulation of dual-phase steels are considered. First, we present two-scale simulations applying a top-down one-way coupling to a full thermo-elastoplastic model in order to study the emerging temperature field. We find that, for our purposes, the consideration of thermo-mechanics at the microscale is not necessary. Second, we present highly parallel fully-coupled two-scale FE2 simulations, now neglecting temperature, using up to 458, 752 cores of the JUQUEEN supercomputer at Forschungszentrum Julich. The strong and weak parallel scalability results obtained for heterogeneous nonlinear hyperelasticity exemplify the massively parallel potential of the FE2 multiscale method.