A discrete approach for modeling degraded elastic fibers in aortic dissection - Rolf-Pissarczyk, Malte; Li, Kewei; Fleischmann, Dominik; Holzapfel, Gerhard A. (Computer Methods in Applied Mechanics and Engineering, 2021)
The initiation and propagation of aortic dissection have not yet been fully elucidated. An essential role is attributed to the degradation of inter-lamellar elastic fibers in the aortic media which causes a significant lowering of the radial strength. Inter-lamellar elastic fibers are aligned radially and contribute mainly to the cohesion of the lamellar units in the aortic media. Computational studies that consider these pathological findings during aortic dissection are rare. In this study, we propose a constitutive model which incorporates the degeneration of inter-lamellar elastic fibers. For this purpose, the recently introduced discrete fiber dispersion model is applied to include symmetrically dispersed inter-lamellar elastic fibers in a strain–energy function. Damaged or degraded elastic fibers are excluded from the strain–energy function by introducing a degradation parameter. Subsequently, the proposed model is implemented in a finite element program and verified with two representative numerical examples, uniaxial extension and simple shear. An aortic dissection geometry with two distinct layers, motivated from patient data, is then created to study the influence of degraded radially-directed elastic fibers on the stress distribution in an aortic dissection. In summary, the presented constitutive model is able to capture the degradation of inter-lamellar elastic fibers during aortic dissection. Moreover, the finite element analysis results of the patient-data motivated geometry suggest a possible mechanism triggering the dissection propagation.
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Keywords: Aortic dissection; Constitutive modeling; Discrete fiber dispersion model; Elastic fibers; Fibrous tissue; Finite element analysis

A general model for anisotropic pseudo-elasticity and viscoelasticity at finite strains - Wollner, Maximilian P.; Terzano, Michele; Rolf-Pissarczyk, Malte; Holzapfel, Gerhard A. (Journal of the Mechanics and Physics of Solids, 2023)
Given the growing demand for simulating anisotropic material behavior at finite strains, constitutive modeling is in a challenging position to combine descriptive capabilities for several inelastic phenomena with the numerical feasibility for real-world applications. In this article, we develop a material model capable of reproducing anisotropy, viscoelasticity, stress softening, and permanent set by merging several pre-existing frameworks. Each constitutive effect is discussed separately in terms of its thermodynamics and mechanical interpretation and successively built on top of each other. Here, the pseudo-elastic approach to permanent set occupies a special place, with a novel discussion of its applicability to generic deformations. We show that the formulation does not lead to physical behavior in general, but can be constrained in such a way to produce appropriate stress predictions in an average sense. Examples of the stress response in several different deformation modes are visualized throughout. The capabilities and possible shortcomings of the formulation are highlighted and at the end a simple numerical algorithm for stress computation is presented.
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Keywords: Anisotropy; Continuum mechanics; Finite viscoelasticity; Material modeling; Pseudo-elasticity; Structure tensor

A reparameterization-invariant Bayesian framework for uncertainty estimation and calibration of simple materials - Wollner, Maximilian P.; Rolf-Pissarczyk, Malte; Holzapfel, Gerhard A. (Computational Mechanics, 2025)
In this work, we attempt to formalize the many concepts involved in the calibration of constitutive models to experimental data, restricting ourselves to the class of simple materials and spatially-homogeneous experiments. To begin with, we revisit the widely used method of least-squares and discuss its ambiguities and shortcomings. Here, Bayesian inference presents an alternative and closely-related approach to parameter identification, which we introduce with the help of a simple mechanical example using Student’s t-distribution. We then derive a reparameterization-invariant posterior for the probabilistic calibration of a simple material given a general collection of spatially-homogeneous experiments, which constitutes the main result of the work. The proposed Bayesian framework is subsequently applied to a simple but illustrative example: parameter identification in a three-term Ogden model to the classic Treloar data on rubber. Finally, the general properties of the posterior and the results of its application invite a discussion about the subtleties and consequences of model calibration in continuum mechanics, such as the information content of different experimental setups or the interaction between number of experimental data versus number of material parameters.
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Keywords: Bayesian inference; Constitutive modeling; Model calibration; Noninformative prior; Nonlinear solid mechanics; Uncertainty estimation

Assessment of Aortic Dissection Remodeling with Patient-Specific Fluid-Structure Interaction Models - Bäumler, Kathrin; Rolf-Pissarczyk, Malte; Schussnig, Richard; Fries, Thomas-Peter; Mistelbauer, Gabriel; Pfaller, Martin R.; Marsden, Alison L.; Fleischmann, Dominik; Holzapfel, Gerhard A. (IEEE transactions on bio-medical engineering, 2025)
Aortic dissection leads to late complications due tochronic degeneration and dilatation of the false lumen. This study examines the interaction between hemodynamics and long-term remodeling of a patient's aortic dissection, tracked from pre-dissection to the chronic phase using CT angiography. Fluid-structure interaction models with tissue prestress, external support, and anisotropic properties were used to analyze hemodynamic markers. Each aortic wall layer had distinct thicknesses and material properties. The boundary conditions were guided by in vitro 4D-flow MRI and the patient's blood pressure. Aortic dilatation was most significant distal to the left subclavian artery, reaching 6 cm in the chronic phase. Simulations quantified the flow jet velocity through the entry tear, which peaked at 185 cm/s in the subacute phase and decreased to 123 to 133 cm/s in the chronic phase, corresponding to an increased entry tear size. Flow jet impingement on the false lumen resulted in a localized pressure increase of 11 and 2 mmHg in the subacute and chronic phases, with wall shear stress reaching 4 Pa. These hemodynamic changes appear to be the main drivers of aortic growth and morphological changes. Despite moderate overall flap movement, in-plane displacement increased from 0.6 to 1.8 mm as disease progressed, which was associated with an overall increase in aortic diameter. Simulations with a significant reduction in flap stiffness during the subacute phase resulted in increased flap motion up to 9.5 mm. Although these results are based on a single patient, they suggest a strong relationship between hemodynamics and aortic growth.
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Keywords: anisotropy; Aortic dissection; computational hemodynamics; fluid-structure interaction; patient-specific simulation; pre-dissection; remodeling

Detection, segmentation, simulation and visualization of aortic dissections: A review - Pepe, Antonio; Li, Jianning; Rolf-Pissarczyk, Malte; Gsaxner, Christina; Chen, Xiaojun; Holzapfel, Gerhard A.; Egger, Jan (Medical Image Analysis, 2020)
Aortic dissection (AD) is a condition of the main artery of the human body, resulting in the formation of a new flow channel, or false lumen. The disease is usually diagnosed with a computed tomography angiography scan during the acute phase. A better understanding of the causes of AD requires knowledge of the aortic geometry (segmentation), including the true and false lumina, which is very time-consuming to reconstruct when performed manually on a slice-by-slice basis. Hence, different automatic and semi-automatic medical image analysis approaches have been proposed for this task over the last years. In this review, we present and discuss these computing techniques used to segment dissected aortas, also in regard to the detection and visualization of clinically relevant information and features from dissected aortas for customized patient-specific treatments.
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Keywords: Aorta; Computed tomography; Detection; Dissection; Segmentation; Simulation; Visualization

Efficient computational modelling of smooth muscle orientation and function in the aorta - Rolf-Pissarczyk, Malte; Wollner, Maximilian P.; Pacheco, Douglas R.Q.; Holzapfel, Gerhard A. (Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2021)
Understanding the mechanical effects of smooth muscle cell (SMC) contraction on the initiation and the propagation of cardiovascular diseases such as aortic dissection is critical. Framed by elastic lamellar sheets in the lamellar unit, there are SMCs in the media with a distinct radial tilt, which indicates their contribution to the radial strength. However, the mechanical effects of this type of anisotropy have not been fully discussed. Therefore, in this study, we propose a constitutive framework that models the passive and active mechanics of the aorta, taking into account the dispersed nature of the aortic constituents by applying the discrete fibre dispersion method. We suggest an isoparametric approach by evaluating various numerical integration methods and introducing a non-uniform discretization of the unit hemisphere to increase its computational efficiency. Finally, the constitutive parameters are fitted to layer-specific experimental data and initial computational results are briefly presented. The radial tilt of SMCs is also analysed, which has a noticeable influence on the mechanical behaviour of the aorta. In the absence of sufficient experimental data, the results indicate that the active contribution of SMCs has a remarkable impact on the mechanics of the healthy aorta.
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Keywords: constitutive modelling; contraction; discrete fibre dispersion model; fibre dispersion; smooth muscle cell

Fluid‐Structure Interaction Simulations of Aortic Dissection - Schussnig, Richard; Rolf-Pissarczyk, Malte; Holzapfel, Gerhard A.; Fries, Thomas-Peter (Proceedings in Applied Mathematics and Mechanics, 2021)
The numerical modeling of aortic dissection (AD) is a particularly challenging biomechanical application, since the underlying coupling of tissue deformation and blood flow has to be considered, leading to a fluid-structure interaction (FSI) problem. To improve clinical relevance, patient-specific data and state-of-the-art constitutive models have to be incorporated. Computational methods to consider for tissue prestress and fiber orientation are presented herei

Mechanisms of aortic dissection: From pathological changes to experimental and in silico models - Rolf-Pissarczyk, Malte; Schussnig, Richard; Fries, Thomas-Peter; Fleischmann, Dominik; Elefteriades, John A.; Humphrey, Jay D.; Holzapfel, Gerhard A. (Progress in Materials Science, 2025)
Aortic dissection continues to be responsible for significant morbidity and mortality, although recent advances in medical data assimilation and in experimental and in silico models have improved our understanding of the initiation and progression of the accumulation of blood within the aortic wall. Hence, there remains a pressing necessity for innovative and enhanced models to more accurately characterize the associated pathological changes. Early on, experimental models were employed to uncover mechanisms in aortic dissection, such as hemodynamic changes and alterations in wall microstructure, and to assess the efficacy of medical implants. While experimental models were once the only option available, more recently they are also being used to validate in silico models. Based on an improved understanding of the deteriorated microstructure of the aortic wall, numerous multiscale material models have been proposed in recent decades to study the state of stress in dissected aortas, including the changes associated with damage and failure. Furthermore, when integrated with accessible patient-derived medical data, in silico models prove to be an invaluable tool for identifying correlations between hemodynamics, wall stresses, or thrombus formation in the deteriorated aortic wall. They are also advantageous for model-guided design of medical implants with the aim of evaluating the deployment and migration of implants in patients. Nonetheless, the utility of in silico models depends largely on patient-derived medical data, such as chosen boundary conditions or tissue properties. In this review article, our objective is to provide a thorough summary of medical data elucidating the pathological alterations associated with this disease. Concurrently, we aim to assess experimental models, as well as multiscale material and patient data-informed in silico models, that investigate various aspects of aortic dissection. In conclusion, we present a discourse on future perspectives, encompassing aspects of disease modeling, numerical challenges, and clinical applications, with a particular focus on aortic dissection. The aspiration is to inspire future studies, deepen our comprehension of the disease, and ultimately shape clinical care and treatment decisions.
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Keywords: Aortic dissection; Computational fluid dynamics; Computational mechanics; Computational modeling; Damage mechanics; Fluid-structure interaction; Hemodynamics; Material characterization; Microstructure; Morphology; Patient-specific simulation

Modelling the anisotropic inelastic response of polymeric scaffolds for in situ tissue engineering applications - Terzano, Michele; Wollner, Maximilian P.; Kainz, Manuel P.; Rolf-Pissarczyk, Malte; Götzen, Nils; Holzapfel, Gerhard A. (Journal of the Royal Society Interface, 2023)
In situ tissue engineering offers an innovative solution for replacement valves and grafts in cardiovascular medicine. In this approach, a scaffold, which can be obtained by polymer electrospinning, is implanted into the human body and then infiltrated by cells, eventually replacing the scaffold with native tissue. In silico simulations of the whole process in patient-specific models, including implantation, growth and degradation, are very attractive to study the factors that might influence the end result. In our research, we focused on the mechanical behaviour of the polymeric scaffold and its short-term response. Following a recently proposed constitutive model for the anisotropic inelastic behaviour of fibrous polymeric materials, we present here its numerical implementation in a finite element framework. The numerical model is developed as user material for commercial finite element software. The verification of the implementation is performed for elementary deformations. Furthermore, a parallel-plate test is proposed as a large-scale representative example, and the model is validated by comparison with experiments.
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Keywords: anisotropy; electrospinning; endogenous tissue restoration; tissue engineering; viscoelasticity

Morphological parameters affecting false lumen thrombosis following type B aortic dissection: a systematic study based on simulations of idealized models - Jafarinia, Alireza; Melito, Gian Marco; Müller, Thomas Stephan; Rolf-Pissarczyk, Malte; Holzapfel, Gerhard A.; Brenn, Günter; Ellermann, Katrin; Hochrainer, Thomas (Biomechanics and Modeling in Mechanobiology, 2023)
Type B aortic dissection (TBAD) carries a high risk of complications, particularly with a partially thrombosed or patent false lumen (FL). Therefore, uncovering the risk factors leading to FL thrombosis is crucial to identify high-risk patients. Although studies have shown that morphological parameters of the dissected aorta are related to FL thrombosis, often conflicting results have been reported. We show that recent models of thrombus evolution in combination with sensitivity analysis methods can provide valuable insights into how combinations of morphological parameters affect the prospect of FL thrombosis. Based on clinical data, an idealized geometry of a TBAD is generated and parameterized. After implementing the thrombus model in computational fluid dynamics simulations, a global sensitivity analysis for selected morphological parameters is performed. We then introduce dimensionless morphological parameters to scale the results to individual patients. The sensitivity analysis demonstrates that the most sensitive parameters influencing FL thrombosis are the FL diameter and the size and location of intimal tears. A higher risk of partial thrombosis is observed when the FL diameter is larger than the true lumen diameter. Reducing the ratio of the distal to proximal tear size increases the risk of FL patency. In summary, these parameters play a dominant role in classifying morphologies into patent, partially thrombosed, and fully thrombosed FL. In this study, we point out the predictive role of morphological parameters for FL thrombosis in TBAD and show that the results are in good agreement with available clinical studies.
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Keywords: Aortic dissection; Global sensitivity analysis; Morphological parametrization; Thrombus classification; Thrombus formation

Multiscale Experimental Characterization and Computational Modeling of the Human Aorta - Dalbosco, Misael; Haspinger, Daniel Ch.; Li, Kewei; Murtada, Sae Il; Pukaluk, Anna; Rolf-Pissarczyk, Malte; Sherifova, Selda; Sommer, Gerhard (Solid (Bio)mechanics: Challenges of the Next Decade: A Book Dedicated to Professor Gerhard A. Holzapfel, 2022)
Advanced imaging techniques, novel experimental approaches and sophisticated computational modeling frameworks to characterize and simulate the mechanical behavior of soft biological tissues have dramatically improved in the past decades. Particularly, the advancing of multiphoton microscopy and other imaging techniques has enabled a detailed three-dimensional visualization of the underlying microscopic structure of various biological tissues including arterial walls. In addition, mechanical testing combined with sophisticated microscopy techniques allowed us to quantify the tissue microstructural reorganization and the mechanical response under large deformation simultaneously. Multiscale constitutive models incorporating detailed microstructural information such as the 3D dispersion of collagen fibers in the extracellular matrix and experimentally-derived tissue material properties have been developed and employed in the computational simulations of human aortic tissues under various (patho)physiological conditions. Thus, in this chapter, we review some of the most critical advances and developments in experimental approaches and computational modeling strategies to characterize the mechanical behavior of human aortic tissue. In addition, we discuss future challenges to improve our understanding of the aortic tissue and its related pathologies.
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On the role of tissue mechanics in fluid–structure interaction simulations of patient-specific aortic dissection - Schussnig, Richard; Rolf-Pissarczyk, Malte; Bäumler, Kathrin; Fries, Thomas-Peter; Holzapfel, Gerhard A.; Kronbichler, Martin (International Journal for Numerical Methods in Engineering, 2024)
Modeling an aortic dissection represents a particular challenge from a numerical perspective, especially when it comes to the interaction between solid (aortic wall) and liquid (blood flow). The complexity of patient-specific simulations requires a variety of parameters, modeling assumptions and simplifications that currently hinder their routine use in clinical settings. We present a numerical framework that captures, among other things, the layer-specific anisotropic properties of the aortic wall, the non-Newtonian behavior of blood, patient-specific geometry, and patient-specific flow conditions. We compare hemodynamic indicators and stress measurements in simulations with increasingly complex material models for the vessel tissue ranging from rigid walls to anisotropic hyperelastic materials. We find that for the present geometry and boundary conditions, rigid wall simulations produce different results than fluid–structure interaction simulations. Considering anisotropic fiber contributions in the tissue model, stress measurements in the aortic wall differ, but shear stress-based biomarkers are less affected. In summary, the increasing complexity of the tissue model enables capturing more details. However, an extensive parameter set is also required. Since the simulation results depend on these modeling choices, variations can lead to different recommendations in clinical applications.
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Keywords: anisotropy; aortic dissection; computational medicine; fluid–structure interaction; hemodynamics; patient-specific; vascular flow

Stochastic modeling of inhomogeneities in the aortic wall and uncertainty quantification using a Bayesian encoder–decoder surrogate - Ranftl, Sascha; Rolf-Pissarczyk, Malte; Wolkerstorfer, Gloria; Pepe, Antonio; Egger, Jan; von der Linden, Wolfgang; Holzapfel, Gerhard A. (Computer Methods in Applied Mechanics and Engineering, 2022)
Inhomogeneities in the aortic wall can lead to localized stress accumulations, possibly initiating dissection. In many cases, a dissection results from pathological changes such as fragmentation or loss of elastic fibers. But it has been shown that even the healthy aortic wall has an inherent heterogeneous microstructure. Some parts of the aorta are particularly susceptible to the development of inhomogeneities due to pathological changes, however, the distribution in the aortic wall and the spatial extent, such as size, shape and type, are difficult to predict. Motivated by this observation, we describe the heterogeneous distribution of elastic fiber degradation in the dissected aortic wall using a stochastic constitutive model. For this purpose, random field realizations, which model the stochastic distribution of degraded elastic fibers, are generated over a non-equidistant grid. The random field then serves as input for a uniaxial extension test of the pathological aortic wall, solved with the finite element method. To include the microstructure of the dissected aortic wall, a constitutive model developed in a previous study is applied, which also includes an approach to model the degradation of interlamellar elastic fibers. To then assess the uncertainty in the output stress distribution due to the proposed stochastic constitutive model, a convolutional neural network, specifically a Bayesian encoder–decoder, was used as a surrogate model that maps the random input fields to the output stress distribution obtained from the finite element analysis. The results show that the neural network is able to predict the stress distribution of the finite element analysis while also significantly reducing the computational time. In addition, this provides the probability for exceeding certain rupture stresses within the aortic wall, which could allow for the prediction of delamination or fatal rupture.
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Keywords: Aortic dissection; Bayesian uncertainty quantification; Beta random field; Fibrous tissue; Finite element analysis; Stochastic constitutive modeling