External tissue support and fluid–structure simulation in blood flows

A model of mechanical loading of the lungs including gravity and a balancing heterogeneous pleural pressure

Recent years have seen the development of multiple in silico lung models, notably with the aim of improving patient care for pulmonary diseases. These models vary in complexity and typically only consider the implementation of pleural pressure, a depression that keeps the lungs inflated. Gravity, often considered negligible compared to pleural pressure, has been largely overlooked, also due to the complexity of formulating physiological boundary conditions to counterbalance it. However, gravity is known to affect pulmonary functions, such as ventilation. In this study, we incorporated gravity into a recent lung poromechanical model. To do so, in addition to the gravitational body force, we proposed novel boundary conditions consisting in a heterogeneous pleural pressure field constrained to counterbalance gravity to reach global equilibrium of applied forces. We assessed the impact of gravity on the global and local behavior of the model, including the pressure-volume response and porosity field. Our findings reveal that gravity, despite being small, influences lung response. Specifically, the inclusion of gravity in our model led to the emergence of heterogeneities in deformation and stress distribution, compatible with in vivo imaging data. This could provide valuable insights for predicting the progression of certain pulmonary diseases by correlating areas subjected to higher deformation and stresses with disease evolution patterns.

Toward a physiological model of vascular wall vibrations in the arteriovenous fistula

The mechanism behind hemodialysis arteriovenous fistula (AVF) failure remains poorly understood, despite previous efforts to correlate altered hemodynamics with vascular remodeling. We have recently demonstrated that transitional flow induces high-frequency vibrations in the AVF wall, albeit with a simplified model. This study addresses the key limitations of our original fluid-structure interaction (FSI) approach, aiming to evaluate the vibration response using a more realistic model. A 3D AVF geometry was generated from contrast-free MRI and high-fidelity FSI simulations were performed. Patient-specific inflow and pressure were incorporated, and a three-term Mooney-Rivlin model was fitted using experimental data. The viscoelastic effect of perivascular tissue was modeled with Robin boundary conditions. Prescribing pulsatile inflow and pressure resulted in a substantial increase in vein displacement ( + 400 %) and strain ( + 317 %), with a higher maximum spectral frequency becoming visible above -42 dB (from 200 to 500 Hz). Transitioning from Saint Venant-Kirchhoff to Mooney-Rivlin model led to displacement amplitudes exceeding 10 micrometers and had a substantial impact on strain ( + 116 %). Robin boundary conditions significantly damped high-frequency displacement ( - 60 %). Incorporating venous tissue properties increased vibrations by 91%, extending up to 700 Hz, with a maximum strain of 0.158. Notably, our results show localized, high levels of vibration at the inner curvature of the vein, a site known for experiencing pronounced remodeling. Our findings, consistent with experimental and clinical reports of bruits and thrills, underscore the significance of incorporating physiologically plausible modeling approaches to investigate the role of wall vibrations in AVF remodeling and failure.

Central Artery Hemodynamics in Angiotensin II-Induced Hypertension and Effects of Anesthesia

Systemic hypertension is a strong risk factor for cardiovascular, neurovascular, and renovascular diseases. Central artery stiffness is both an initiator and indicator of hypertension, thus revealing a critical relationship between the wall mechanics and hemodynamics. Mice have emerged as a critical animal model for studying effects of hypertension and much has been learned. Regardless of the specific mouse model, data on changes in cardiac function and hemodynamics are necessarily measured under anesthesia. Here, we present a new experimental-computational workflow to estimate awake cardiovascular conditions from anesthetized data, which was then used to quantify effects of chronic angiotensin II-induced hypertension relative to normotension in wild-type mice. We found that isoflurane anesthesia had a greater impact on depressing hemodynamics in angiotensin II-infused mice than in controls, which led to unexpected results when comparing anesthetized results between the two groups of mice. Through comparison of the awake simulations, however, in vivo relevant effects of angiotensin II-infusion on global and regional vascular structure, properties, and hemodynamics were found to be qualitatively consistent with expectations. Specifically, we found an increased in vivo vascular stiffness in the descending thoracic aorta and suprarenal abdominal aorta, leading to increases in pulse pressure in the distal aorta. These insights allow characterization of the impact of regionally varying vascular remodeling on hemodynamics and mouse-to-mouse variations due to induced hypertension.

Simulating impaired left ventricular-arterial coupling in aging and disease: a systematic review

Aortic stenosis, hypertension, and left ventricular hypertrophy often coexist in the elderly, causing a detrimental mismatch in coupling between the heart and vasculature known as ventricular-vascular (VA) coupling. Impaired left VA coupling, a critical aspect of cardiovascular dysfunction in aging and disease, poses significant challenges for optimal cardiovascular performance. This systematic review aims to assess the impact of simulating and studying this coupling through computational models. By conducting a comprehensive analysis of 34 relevant articles obtained from esteemed databases such as Web of Science, Scopus, and PubMed until July 14, 2022, we explore various modeling techniques and simulation approaches employed to unravel the complex mechanisms underlying this impairment. Our review highlights the essential role of computational models in providing detailed insights beyond clinical observations, enabling a deeper understanding of the cardiovascular system. By elucidating the existing models of the heart (3D, 2D, and 0D), cardiac valves, and blood vessels (3D, 1D, and 0D), as well as discussing mechanical boundary conditions, model parameterization and validation, coupling approaches, computer resources and diverse applications, we establish a comprehensive overview of the field. The descriptions as well as the pros and cons on the choices of different dimensionality in heart, valve, and circulation are provided. Crucially, we emphasize the significance of evaluating heart-vessel interaction in pathological conditions and propose future research directions, such as the development of fully coupled personalized multidimensional models, integration of deep learning techniques, and comprehensive assessment of confounding effects on biomarkers.

Hemodynamic effects of entry and exit tear size in aortic dissection evaluated with in vitro magnetic resonance imaging and fluid-structure interaction simulation

Understanding the complex interplay between morphologic and hemodynamic features in aortic dissection is critical for risk stratification and for the development of individualized therapy. This work evaluates the effects of entry and exit tear size on the hemodynamics in type B aortic dissection by comparing fluid-structure interaction (FSI) simulations with in vitro 4D-flow magnetic resonance imaging (MRI). A baseline patient-specific 3D-printed model and two variants with modified tear size (smaller entry tear, smaller exit tear) were embedded into a flow- and pressure-controlled setup to perform MRI as well as 12-point catheter-based pressure measurements. The same models defined the wall and fluid domains for FSI simulations, for which boundary conditions were matched with measured data. Results showed exceptionally well matched complex flow patterns between 4D-flow MRI and FSI simulations. Compared to the baseline model, false lumen flow volume decreased with either a smaller entry tear (- 17.8 and - 18.5%, for FSI simulation and 4D-flow MRI, respectively) or smaller exit tear (- 16.0 and - 17.3%). True to false lumen pressure difference (initially 11.0 and 7.9 mmHg, for FSI simulation and catheter-based pressure measurements, respectively) increased with a smaller entry tear (28.9 and 14.6 mmHg), and became negative with a smaller exit tear (- 20.6 and - 13.2 mmHg). This work establishes quantitative and qualitative effects of entry or exit tear size on hemodynamics in aortic dissection, with particularly notable impact observed on FL pressurization. FSI simulations demonstrate acceptable qualitative and quantitative agreement with flow imaging, supporting its deployment in clinical studies.

Assessing turbulent effects in ascending aorta in presence of bicuspid aortic valve

Aortic valves with bicuspids have two rather than three leaflets, which is a congenital heart condition. About 0.5-2% of people have a bicuspid aortic valve. Blood flow through the aorta is commonly believed to be laminar, although aortic valve disorders can cause turbulent transitions. Understanding the impact of turbulence is crucial for foreseeing how the disease will progress. The study's objective was use large eddy simulation to provide a thorough analysis of the turbulence in bicuspid aortic valve dysfunction. Using a large eddy simulation, the blood flow patterns of the bicuspid and tricuspid aortic valves were compared, and significant discrepancies were found. The velocity field in flow in bicuspid configurations was asymmetrically distributed toward the ascending aorta. In tricuspid aortic valve (TAV) the flow, on the other hand, was symmetrical within the same aortic segment. Moreover, we looked into standard deviation, Q-criterion, viscosity ratio and wall shear stresses for each cases to understand transition to turbulence. Our findings indicate that in the bicuspid aortic valve (BAV) case, the fluid-dynamic abnormalities increase. The global turbulent kinetic energy and time-averaged wall shear stress for the TAV and BAV scenarios were also examined. We discovered that the global turbulent kinetic energy was higher in the BAV case compared to TAV, in addition to the increased wall shear stress induced by the BAV in the ascending aorta.

Calibration of the Mechanical Boundary Conditions for a Patient-Specific Thoracic Aorta Model Including the Heart Motion Effect

OBJECTIVE

We propose a procedure for calibrating 4 parameters governing the mechanical boundary conditions (BCs) of a thoracic aorta (TA) model derived from one patient with ascending aortic aneurysm. The BCs reproduce the visco-elastic structural support provided by the soft tissue and the spine and allow for the inclusion of the heart motion effect.

METHODS

We first segment the TA from magnetic resonance imaging (MRI) angiography and derive the heart motion by tracking the aortic annulus from cine-MRI. A rigid-wall fluid-dynamic simulation is performed to derive the time-varying wall pressure field. We build the finite element model considering patient-specific material properties and imposing the derived pressure field and the motion at the annulus boundary. The calibration, which involves the zero-pressure state computation, is based on purely structural simulations. After obtaining the vessel boundaries from the cine-MRI sequences, an iterative procedure is performed to minimize the distance between them and the corresponding boundaries derived from the deformed structural model. A strongly-coupled fluid-structure interaction (FSI) analysis is finally performed with the tuned parameters and compared to the purely structural simulation.

RESULTS AND CONCLUSION

The calibration with structural simulations allows to reduce maximum and mean distances between image-derived and simulation-derived boundaries from 8.64 mm to 6.37 mm and from 2.24 mm to 1.83 mm, respectively. The maximum root mean square error between the deformed structural and FSI surface meshes is 0.19 mm. This procedure may prove crucial for increasing the model fidelity in replicating the real aortic root kinematics.

Three-Dimensional Characterization of Aortic Root Motion by Vascular Deformation Mapping

The aorta is in constant motion due to the combination of cyclic loading and unloading with its mechanical coupling to the contractile left ventricle (LV) myocardium. This aortic root motion has been proposed as a marker for aortic disease progression. Aortic root motion extraction techniques have been mostly based on 2D image analysis and have thus lacked a rigorous description of the different components of aortic root motion (e.g., axial versus in-plane). In this study, we utilized a novel technique termed vascular deformation mapping (VDM(D)) to extract 3D aortic root motion from dynamic computed tomography angiography images. Aortic root displacement (axial and in-plane), area ratio and distensibility, axial tilt, aortic rotation, and LV/Ao angles were extracted and compared for four different subject groups: non-aneurysmal, TAA, Marfan, and repair. The repair group showed smaller aortic root displacement, aortic rotation, and distensibility than the other groups. The repair group was also the only group that showed a larger relative in-plane displacement than relative axial displacement. The Marfan group showed the largest heterogeneity in aortic root displacement, distensibility, and age. The non-aneurysmal group showed a negative correlation between age and distensibility, consistent with previous studies. Our results revealed a strong positive correlation between LV/Ao angle and relative axial displacement and a strong negative correlation between LV/Ao angle and relative in-plane displacement. VDM(D)-derived 3D aortic root motion can be used in future studies to define improved boundary conditions for aortic wall stress analysis.

Temporal evolution of mechanical stimuli from vascular remodeling in response to the severity and duration of aortic coarctation in a preclinical model

Coarctation of the aorta (CoA) is one of the most common congenital cardiovascular diseases. CoA patients frequently undergo surgical repair, but hypertension (HTN) is still common. The current treatment guideline has revealed irreversible changes in structure and function, yet revised severity guidelines have not been proposed. Our objective was to quantify temporal alterations in mechanical stimuli and changes in arterial geometry in response to the range of CoA severities and durations (i.e. age of treatment) seen clinically. Rabbits were exposed to CoA resulting in peak-to-peak blood pressure gradient (BPGpp) severities of ≤ 10, 10-20, and ≥ 20 mmHg for a duration of ~ 1, 3, or 20 weeks using permanent, dissolvable, and rapidly dissolvable sutures. Elastic moduli and thickness were estimated from imaging and longitudinal fluid-structure interaction (FSI) simulations were conducted at different ages using geometries and boundary conditions from experimentally measured data. Mechanical stimuli were characterized including blood flow velocity patterns, wall tension, and radial strain. Experimental results show vascular alternations including thickening and stiffening proximal to the coarctation with increasing severity and/or duration of CoA. FSI simulations indicate wall tension in the proximal region increases markedly with coarctation severity. Importantly, even mild CoA induced stimuli for remodeling that exceeds values seen in adulthood if not treated early and using a BPGpp lower than the current clinical threshold. The findings are aligned with observations from other species and provide some guidance for the values of mechanical stimuli that could be used to predict the likelihood of HTN in human patients with CoA.

Beyond CFD: Emerging methodologies for predictive simulation in cardiovascular health and disease

Physics-based computational models of the cardiovascular system are increasingly used to simulate hemodynamics, tissue mechanics, and physiology in evolving healthy and diseased states. While predictive models using computational fluid dynamics (CFD) originated primarily for use in surgical planning, their application now extends well beyond this purpose. In this review, we describe an increasingly wide range of modeling applications aimed at uncovering fundamental mechanisms of disease progression and development, performing model-guided design, and generating testable hypotheses to drive targeted experiments. Increasingly, models are incorporating multiple physical processes spanning a wide range of time and length scales in the heart and vasculature. With these expanded capabilities, clinical adoption of patient-specific modeling in congenital and acquired cardiovascular disease is also increasing, impacting clinical care and treatment decisions in complex congenital heart disease, coronary artery disease, vascular surgery, pulmonary artery disease, and medical device design. In support of these efforts, we discuss recent advances in modeling methodology, which are most impactful when driven by clinical needs. We describe pivotal recent developments in image processing, fluid-structure interaction, modeling under uncertainty, and reduced order modeling to enable simulations in clinically relevant timeframes. In all these areas, we argue that traditional CFD alone is insufficient to tackle increasingly complex clinical and biological problems across scales and systems. Rather, CFD should be coupled with appropriate multiscale biological, physical, and physiological models needed to produce comprehensive, impactful models of mechanobiological systems and complex clinical scenarios. With this perspective, we finally outline open problems and future challenges in the field.

Validation of the Reduced Unified Continuum Formulation Against In Vitro 4D-Flow MRI

We previously introduced and verified the reduced unified continuum formulation for vascular fluid-structure interaction (FSI) against Womersley's deformable wall theory. Our present work seeks to investigate its performance in a patient-specific aortic setting in which assumptions of idealized geometries and velocity profiles are invalid. Specifically, we leveraged 2D magnetic resonance imaging (MRI) and 4D-flow MRI to extract high-resolution anatomical and hemodynamic information from an in vitro flow circuit embedding a compliant 3D-printed aortic phantom. To accurately reflect experimental conditions, we numerically implemented viscoelastic external tissue support, vascular tissue prestressing, and skew boundary conditions enabling in-plane vascular motion at each inlet and outlet. Validation of our formulation is achieved through close quantitative agreement in pressures, lumen area changes, pulse wave velocity, and early systolic velocities, as well as qualitative agreement in late systolic flow structures. Our validated suite of FSI techniques offers a computationally efficient approach for numerical simulation of vascular hemodynamics. This study is among the first to validate a cardiovascular FSI formulation against an in vitro flow circuit involving a compliant vascular phantom of complex patient-specific anatomy.

The effect of terminal impedance on aortic morphology and hemodynamics: an in vitro phantom study using flow field visualization

To investigate the risk factors for aortic dissection tearing, we fabricated a simplified patient-specific aortic silicone phantom using the brush-spin-coating method. The aortic phantom only includes the aorta from the ascending aorta to the descending aorta, without other branches. We designed two experiments to investigate the alteration of aortic morphology and intravascular hemodynamics using the particle image velocimetry method. The results revealed dilation and elongation of the aortic phantom, especially the ascending aorta, after the phantom's terminal resistance was increased. Additionally, the particle image velocimetry results demonstrated an increased vortex region, which caused the inner side of the aortic wall to become scoured by blood. This study suggests that the deformation of the inner side aortic wall and the change in hemodynamics in response to the increased terminal resistance may be a risk factor for aortic tearing and should be monitored.

Inverse problems in blood flow modeling: A review

Mathematical and computational modeling of the cardiovascular system is increasingly providing non-invasive alternatives to traditional invasive clinical procedures. Moreover, it has the potential for generating additional diagnostic markers. In blood flow computations, the personalization of spatially distributed (i.e., 3D) models is a key step which relies on the formulation and numerical solution of inverse problems using clinical data, typically medical images for measuring both anatomy and function of the vasculature. In the last years, the development and application of inverse methods has rapidly expanded most likely due to the increased availability of data in clinical centers and the growing interest of modelers and clinicians in collaborating. Therefore, this work aims to provide a wide and comparative overview of literature within the last decade. We review the current state of the art of inverse problems in blood flows, focusing on studies considering fully dimensional fluid and fluid-solid models. The relevant physical models and hemodynamic measurement techniques are introduced, followed by a survey of mathematical data assimilation approaches used to solve different kinds of inverse problems, namely state and parameter estimation. An exhaustive discussion of the literature of the last decade is presented, structured by types of problems, models and available data.

Experimental and Mouse-Specific Computational Models of the Fbln4SMKO Mouse to Identify Potential Biomarkers for Ascending Thoracic Aortic Aneurysm

PURPOSE

To use computational methods to explore geometric, mechanical, and fluidic biomarkers that could correlate with mouse lifespan in the Fbln4SMKO mouse. Mouse lifespan was used as a surrogate for risk of a severe cardiovascular event in cases of ascending thoracic aortic aneurysm.

METHODS

Image-based, mouse-specific fluid-structure-interaction models were developed for Fbln4SMKO mice (n = 10) at ages two and six months. The results of the simulations were used to quantify potential biofluidic biomarkers, complementing the geometrical biomarkers obtained directly from the images.

RESULTS

Comparing the different geometrical and biofluidic biomarkers to the mouse lifespan, it was found that mean oscillatory shear index (OSImin) and minimum time-averaged wall shear stress (TAWSSmin) at six months showed the largest correlation with lifespan (r2 = 0.70, 0.56), with both correlations being positive (i.e., mice with high OSImean and high TAWSSmin tended to live longer). When change between two and six months was considered, the change in TAWSSmin showed a much stronger correlation than OSImean (r2 = 0.75 vs. 0.24), and the correlation was negative (i.e., mice with increasing TAWSSmin over this period tended to live less long).

CONCLUSION

The results highlight potential biomarkers of ATAA outcomes that can be obtained through noninvasive imaging and computational simulations, and they illustrate the potential synergy between small-animal and computational models.

A coupling strategy for a first 3D-1D model of the cardiovascular system to study the effects of pulse wave propagation on cardiac function

A key factor governing the mechanical performance of the heart is the bidirectional coupling with the vascular system, where alterations in vascular properties modulate the pulsatile load imposed on the heart. Current models of cardiac electromechanics (EM) use simplified 0D representations of the vascular system when coupling to anatomically accurate 3D EM models is considered. However, these ignore important effects related to pulse wave transmission. Accounting for these effects requires 1D models, but a 3D-1D coupling remains challenging. In this work, we propose a novel, stable strategy to couple a 3D cardiac EM model to a 1D model of blood flow in the largest systemic arteries. For the first time, a personalised coupled 3D-1D model of left ventricle and arterial system is built and used in numerical benchmarks to demonstrate robustness and accuracy of our scheme over a range of time steps. Validation of the coupled model is performed by investigating the coupled system's physiological response to variations in the arterial system affecting pulse wave propagation, comprising aortic stiffening, aortic stenosis or bifurcations causing wave reflections. Our first 3D-1D coupled model is shown to be efficient and robust, with negligible additional computational costs compared to 3D-0D models. We further demonstrate that the calibrated 3D-1D model produces simulated data that match with clinical data under baseline conditions, and that known physiological responses to alterations in vascular resistance and stiffness are correctly replicated. Thus, using our coupled 3D-1D model will be beneficial in modelling studies investigating wave propagation phenomena.

Blood-Artery Interaction in Calcified Aortas and Abdominal Aortic Aneurysms

A stabilized FSI method is presented for coupling shear-rate dependent model of blood with finitely deforming anisotropic hyperelastic model of arteries. The blood-artery coupling conditions are weakly enforced to accommodate non-matching blood-artery meshes which provides great flexibility in independent discretization of fluid and solid subdomains in the patient-specific geometric models. The variationally derived interface coupling terms play an important role in the concurrent solution of the nonlinear mixed-field problem across non-matching discretizations. Two test cases are presented that investigate the effect of growth of aortic aneurysm on local changes in blood flow and stress concentrations in calcified arteries under pulsating flows to highlight the clinical relevance of the proposed method for cardiovascular applications.

Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications

Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.

Virtual Transcatheter Interventions for Peripheral Pulmonary Artery Stenosis in Williams and Alagille Syndromes

Background

Despite favorable outcomes of surgical pulmonary artery (PA) reconstruction, isolated proximal stenting of the central PAs is common clinical practice for patients with peripheral PA stenosis in association with Williams and Alagille syndromes. Given the technical challenges of PA reconstruction and the morbidities associated with transcatheter interventions, the hemodynamic consequences of all treatment strategies must be rigorously assessed. Our study aims to model, assess, and predict hemodynamic outcomes of transcatheter interventions in these patients.

Methods and Results

Isolated proximal and “extensive” interventions (stenting and/or balloon angioplasty of proximal and lobar vessels) were performed in silico on 6 patient‐specific PA models. Autoregulatory adaptation of the cardiac output and downstream arterial resistance was modeled in response to intervention‐induced hemodynamic perturbations. Postintervention computational fluid dynamics predictions were validated in 2 stented patients and quantitatively assessed in 4 surgical patients. Our computational methods accurately predicted postinterventional PA pressures, the primary indicators of success for treatment of peripheral PA stenosis. Proximal and extensive treatment achieved median reductions of 14% and 40% in main PA systolic pressure, 27% and 56% in pulmonary vascular resistance, and 10% and 45% in right ventricular stroke work, respectively.

Conclusions

In patients with Williams and Alagille syndromes, extensive transcatheter intervention is required to sufficiently reduce PA pressures and right ventricular stroke work. Transcatheter therapy was shown to be ineffective for long‐segment stenosis and pales hemodynamically in comparison with published outcomes of surgical reconstruction. Regardless of the chosen strategy, a virtual treatment planning platform could identify lesions most critical for optimizing right ventricular afterload.

Patient-Specific Fluid-Structure Simulations of Anomalous Aortic Origin of Right Coronary Arteries

Objectives

Anomalous aortic origin of the right coronary artery (AAORCA) may cause ischemia and sudden death. However, the specific anatomic indications for surgery are unclear, so dobutamine-stress instantaneous wave-free ratio (iFR) is increasingly used. Meanwhile, advances in fluid–structure interaction (FSI) modeling can simulate the pulsatile hemodynamics and tissue deformation. We sought to evaluate the feasibility of simulating the resting and dobutamine-stress iFR in AAORCA using patient-specific FSI models and to visualize the mechanism of ischemia within the intramural geometry and associated lumen narrowing.

Methods

We developed 6 patient-specific FSI models of AAORCA using SimVascular software. Three-dimensional geometries were segmented from coronary computed tomography angiography. Vascular outlets were coupled to lumped-parameter networks that included dynamic compression of the coronary microvasculature and were tuned to each patient's vitals and cardiac output.

Results

All cases were interarterial, and 5 of 6 had an intramural course. Measured iFRs ranged from 0.95 to 0.98 at rest and 0.80 to 0.95 under dobutamine stress. After we tuned the distal coronary resistances to achieve a stress flow rate triple that at rest, the simulations adequately matched the measured iFRs (r = 0.85, root-mean-square error = 0.04). The intramural lumen remained narrowed with simulated stress and resulted in lower iFRs without needing external compression from the pulmonary root.

Conclusions

Patient-specific FSI modeling of AAORCA is a promising, noninvasive method to assess the iFR reduction caused by intramural geometries and inform surgical intervention. However, the models’ sensitivity to distal coronary resistance suggests that quantitative stress-perfusion imaging may augment virtual and invasive iFR studies.

About prestretch in homogenized constrained mixture models simulating growth and remodeling in patient-specific aortic geometries

Evolution of mechanical and structural properties in the Ascending Thoracic Aorta (ATA) is the results of complex mechanobiological processes. In this work, we address some numerical challenges in order to elaborate computational models of these processes. For that, we extend the state of the art of homogenized constrained mixture (hCM) models. In these models, prestretches are assigned to the mixed constituents in order to ensure local mechanical equilibrium macroscopically, and to maintain a homeostatic level of tension in collagen fibers microscopically. Although the initial prestretches were assumed as homogeneous in idealized straight tubes, more elaborate prestretch distributions need to be considered for curved geometrical models such as patient-specific ATA. Therefore, we introduce prestretches having a three-dimensional gradient across the ATA geometry in the homeostatic reference state. We test different schemes with the objective to ensure stable growth and remodeling (G&R) simulations on patient-specific curved vessels. In these simulations, aneurysm progression is triggered by tissue changes in the constituents such as mass degradation of intramural elastin. The results show that the initial prestretches are not only critical for the stability of numerical simulations, but they also affect the G&R response. Eventually, we submit that initial conditions required for G&R simulations need to be identified regionally for ensuring realistic patient-specific predictions of aneurysm progression.

Fully-Coupled FSI Computational Analyses in the Ascending Thoracic Aorta Using Patient-Specific Conditions and Anisotropic Material Properties

Computational hemodynamics has become increasingly important within the context of precision medicine, providing major insight in cardiovascular pathologies. However, finding appropriate compromise between speed and accuracy remains challenging in computational hemodynamics for an extensive use in decision making. For example, in the ascending thoracic aorta, interactions between the blood and the aortic wall must be taken into account for the sake of accuracy, but these fluid structure interactions (FSI) induce significant computational costs, especially when the tissue exhibits a hyperelastic and anisotropic response. The objective of the current study is to use the Small On Large (SOL) theory to linearize the anisotropic hyperelastic behavior in order to propose a reduced-order model for FSI simulations of the aorta. The SOL method is tested for fully-coupled FSI simulations in a patient-specific aortic geometry presenting an Ascending Thoracic Aortic Aneurysm (aTAA). The same model is also simulated with a fully-coupled FSI with non-linear material behavior, without SOL linearization. Eventually, the results and computational times with and without the SOL are compared. The SOL approach is demonstrated to provide a significant reduction of computational costs for FSI analysis in the aTAA, and the results in terms of stress state distribution are comparable. The method is implemented in ANSYS and will be further evaluated for clinical applications.

Comparative Study of Human and Murine Aortic Biomechanics and Hemodynamics in Vascular Aging

Introduction: Aging has many effects on the cardiovascular system, including changes in structure (aortic composition, and thus stiffening) and function (increased proximal blood pressure, and thus cardiac afterload). Mouse models are often used to gain insight into vascular aging and mechanisms of disease as they allow invasive assessments that are impractical in humans. Translation of results from murine models to humans can be limited, however, due to species-specific anatomical, biomechanical, and hemodynamic differences. In this study, we built fluid-solid-interaction (FSI) models of the aorta, informed by biomechanical and imaging data, to compare wall mechanics and hemodynamics in humans and mice at two equivalent ages: young and older adults. Methods: For the humans, 3-D computational models were created using wall property data from the literature as well as patient-specific magnetic resonance imaging (MRI) and non-invasive hemodynamic data; for the mice, comparable models were created using population-based properties and hemodynamics as well as subject-specific anatomies. Global aortic hemodynamics and wall stiffness were compared between humans and mice across age groups. Results: For young adult subjects, we found differences between species in pulse pressure amplification, compliance and resistance distribution, and aortic stiffness gradient. We also found differences in response to aging between species. Generally, the human spatial gradients of stiffness and pulse pressure across the aorta diminished with age, while they increased for the mice. Conclusion: These results highlight key differences in vascular aging between human and mice, and it is important to acknowledge these when using mouse models for cardiovascular research.

Computational simulation-derived hemodynamic and biomechanical properties of the pulmonary arterial tree early in the course of ventricular septal defects

Untreated ventricular septal defects (VSDs) can lead to pulmonary arterial hypertension (PAH) characterized by elevated pulmonary artery (PA) pressure and vascular remodeling, known as PAH associated with congenital heart disease (PAH-CHD). Though previous studies have investigated hemodynamic effects on vascular mechanobiology in late-stage PAH, hemodynamics leading to PAH-CHD initiation have not been fully quantified. We hypothesize that abnormal hemodynamics from left-to-right shunting in early stage VSDs affects PA biomechanical properties leading to PAH initiation. To model PA hemodynamics in healthy, small, moderate, and large VSD conditions prior to the onset of vascular remodeling, computational fluid dynamics simulations were performed using a 3D finite element model of a healthy 1-year-old's proximal PAs and a body-surface-area-scaled 0D distal PA tree. VSD conditions were modeled with increased pulmonary blood flow to represent degrees of left-to-right shunting. In the proximal PAs, pressure, flow, strain, and wall shear stress (WSS) increased with increasing VSD size; oscillatory shear index decreased with increasing VSD size in the larger PA vessels. WSS was higher in smaller diameter vessels and increased with VSD size, with the large VSD condition exhibiting WSS >100 dyn/cm[Formula: see text], well above values typically used to study dysfunctional mechanotransduction pathways in PAH. This study is the first to estimate hemodynamic and biomechanical metrics in the entire pediatric PA tree with VSD severity at the stage leading to PAH initiation and has implications for future studies assessing effects of abnormal mechanical stimuli on endothelial cells and vascular wall mechanics that occur during PAH-CHD initiation and progression.

Numerical analysis of the hemodynamics of rat aorta based on magnetic resonance imaging and fluid-structure interaction

Murine models have been widely used to investigate the mechanobiology of aortic atherosclerosis and dissections, which develop preferably at different anatomic locations of aorta. Based MRI and finite element analysis with fluid-structure interaction, we numerically investigated factors that may affect the blood flow and structural mechanics of rat aorta. The results indicated that aortic root motion greatly increases time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), relative residence time (RRT), displacement of the aorta, and enhances helical flow pattern but has limited influence on effective stress, which is highly modulated by blood pressure. Moreover, the influence of the motion component on these indicators is different with axial motion more obvious than planar motion. Surrounding fixation of the intercostal arteries and the branch vessels on aortic arch would reduce the influence of aortic root motion. The compliance of the aorta has different influences at different regions, leading to decrease in TAWSS and helical flow, increase in OSI, RRT at the aortic arch, but has reversed effects on the branch vessels. When compared with the steady flow, the pulsatile blood flow would obviously increase the WSS, the displacement, and the effective stress in most regions. In conclusion, to accurately quantify the blood flow and structural mechanics of rat aorta, the motion of the aortic root, the compliance of aortic wall, and the pulsation of blood flow should be considered. However, when only focusing on the effective stress in rat aorta, the motion of the aortic root may be neglected.

A surrogate model for plaque modeling in carotids based on Robin conditions calibrated by cine MRI data

We propose a surrogate model for the fluid-structure interaction (FSI) problem for the study of blood dynamics in carotid arteries in presence of plaque. This is based on the integration of a numerical model with subject-specific data and clinical imaging. We propose to model the plaque as part of the tissues surrounding the vessel wall through the application of an elastic support boundary condition. In order to characterize the plaque and other surrounding tissues, such as the close-by jugular vein, the elastic parameters of the boundary condition were spatially differentiated and their values were estimated by minimizing the discrepancies between computed vessel displacements and reference values obtained from CINE Magnetic Resonance Imaging data. We applied the model to three subjects with a degree of stenosis greater than 70%. We found that accounting for both plaque and jugular vein in the estimation of the elastic parameters increases the accuracy. In particular, in all patients, mismatches between computed and in vivo measured wall displacements were one to two orders of magnitude lower than the spatial resolution of the original MRI data. These results confirmed the validity of the proposed surrogate plaque model. We also compared fluid-dynamics results with those obtained in a fixed wall setting and in a full FSI model, used as gold standard, highlighting the better accordance of our results in comparison to the rigid ones.

Arterial pulse wave propagation across stenoses and aneurysms: assessment of one-dimensional simulations against three-dimensional simulations and in vitro measurements

One-dimensional (1-D) arterial blood flow modelling was tested in a series of idealized vascular geometries representing the abdominal aorta, common carotid and iliac arteries with different sizes of stenoses and/or aneurysms. Three-dimensional (3-D) modelling and in vitro measurements were used as ground truth to assess the accuracy of 1-D model pressure and flow waves. The 1-D and 3-D formulations shared identical boundary conditions and had equivalent vascular geometries and material properties. The parameters of an experimental set-up of the abdominal aorta for different aneurysm sizes were matched in corresponding 1-D models. Results show the ability of 1-D modelling to capture the main features of pressure and flow waves, pressure drop across the stenoses and energy dissipation across aneurysms observed in the 3-D and experimental models. Under physiological Reynolds numbers (Re), root mean square errors were smaller than 5.4% for pressure and 7.3% for the flow, for stenosis and aneurysm sizes of up to 85% and 400%, respectively. Relative errors increased with the increasing stenosis and aneurysm size, aneurysm length and Re, and decreasing stenosis length. All data generated in this study are freely available and provide a valuable resource for future research.

Numerical study of hemodynamics in a complete coronary bypass with venous and arterial grafts and different degrees of stenosis

Cardiovascular diseases are among the leading causes of death in the world. The coronary blockage is one of most common types of these diseases that in the majority of cases has been treated by bypass surgery. In the bypass surgery, a graft is implemented to alter the blocked coronary and allow the blood supply process. The hemodynamic characteristics of the bypass strongly depend on the geometry and mechanical properties of the graft. In the present study, the fluid-structure interaction (FSI) analysis is conducted to investigate the bypass performance for a thoracic artery as well as a saphenous vein graft. Blood flow introduces a pressure on the walls of the graft which behaves as a hyperelastic material. A complete coronary bypass with stenosis degrees of 70% and 100% is modeled. To consider the nonlinear stress-strain behavior of the grafts, a five parameter Mooney-Rivlin hyperplastic model is implemented for the structural analysis and blood is assumed to behave as a Newtonian fluid. The simulations are performed for a structured grid to solve the governing equations using finite element method (FEM). The results show that wall shear stress (WSS) for saphenous vein is larger than that of thoracic artery while the total deformation of the thoracic artery is larger compared to the saphenous vein. Also, for the venous grafts or lower stenosis degree, the oscillatory shear index (OSI) is higher at both left and right anastomoses meaning that venous grafts as well as lower degree of stenosis are more critical in terms of restenosis.

A flexible framework for sequential estimation of model parameters in computational hemodynamics

A major challenge in constructing three dimensional patient specific hemodynamic models is the calibration of model parameters to match patient data on flow, pressure, wall motion, etc. acquired in the clinic. Current workflows are manual and time-consuming. This work presents a flexible computational framework for model parameter estimation in cardiovascular flows that relies on the following fundamental contributions. (i) A Reduced-Order Unscented Kalman Filter (ROUKF) model for data assimilation for wall material and simple lumped parameter network (LPN) boundary condition model parameters. (ii) A constrained least squares augmentation (ROUKF-CLS) for more complex LPNs. (iii) A "Netlist" implementation, supporting easy filtering of parameters in such complex LPNs. The ROUKF algorithm is demonstrated using non-invasive patient-specific data on anatomy, flow and pressure from a healthy volunteer. The ROUKF-CLS algorithm is demonstrated using synthetic data on a coronary LPN. The methods described in this paper have been implemented as part of the CRIMSON hemodynamics software package.

Amplified Flow Imaging (aFlow): A Novel MRI-Based Tool to Unravel the Coupled Dynamics Between the Human Brain and Cerebrovasculature

With each heartbeat, periodic variations in arterial blood pressure are transmitted along the vasculature, resulting in localized deformations of the arterial wall and its surrounding tissue. Quantification of such motions may help understand various cerebrovascular conditions, yet it has proven technically challenging thus far. We introduce a new image processing algorithm called amplified Flow (aFlow) which allows to study the coupled brain-blood flow motion by combining the amplification of cine and 4D flow MRI. By incorporating a modal analysis technique known as dynamic mode decomposition into the algorithm, aFlow is able to capture the characteristics of transient events present in the brain and arterial wall deformation. Validating aFlow, we tested it on phantom simulations mimicking arterial walls motion and observed that aFlow displays almost twice higher SNR than its predecessor amplified MRI (aMRI). We then applied aFlow to 4D flow and cine MRI datasets of 5 healthy subjects, finding high correlations between blood flow velocity and tissue deformation in selected brain regions, with correlation values r = 0.61 , 0.59, 0.52 for the pons, frontal and occipital lobe ( ). Finally, we explored the potential diagnostic applicability of aFlow by studying intracranial aneurysm dynamics, which seems to be indicative of rupture risk. In two patients, aFlow successfully visualized the imperceptible aneurysm wall motion, additionally quantifying the increase in the high frequency wall displacement after a one-year follow-up period (20%, 76%). These preliminary data suggest that aFlow may provide a novel imaging biomarker for the assessment of aneurysms evolution, with important potential diagnostic implications.

Biomechanical rupture risk assessment of abdominal aortic aneurysms using clinical data: A patient-specific, probabilistic framework and comparative case-control study

We present a data-informed, highly personalized, probabilistic approach for the quantification of abdominal aortic aneurysm (AAA) rupture risk. Our novel framework builds upon a comprehensive database of tensile test results that were carried out on 305 AAA tissue samples from 139 patients, as well as corresponding non-invasively and clinically accessible patient-specific data. Based on this, a multivariate regression model is created to obtain a probabilistic description of personalized vessel wall properties associated with a prospective AAA patient. We formulate a probabilistic rupture risk index that consistently incorporates the available statistical information and generalizes existing approaches. For the efficient evaluation of this index, a flexible Kriging-based surrogate model with an active training process is proposed. In a case-control study, the methodology is applied on a total of 36 retrospective, diameter matched asymptomatic (group 1, n = 18) and known symptomatic/ruptured (group 2, n = 18) cohort of AAA patients. Finally, we show its efficacy to discriminate between the two groups and demonstrate competitive performance in comparison to existing deterministic and probabilistic biomechanical indices.

An Introductory Overview of Image-Based Computational Modeling in Personalized Cardiovascular Medicine

Cardiovascular diseases account for the number one cause of deaths in the world. Part of the reason for such grim statistics is our limited understanding of the underlying mechanisms causing these devastating pathologies, which is made difficult by the invasiveness of the procedures associated with their diagnosis (e.g., inserting catheters into the coronal artery to measure blood flow to the heart). Likewise, it is also difficult to design and test assistive devices without implanting them in vivo. However, with the recent advancements made in biomedical scanning technologies and computer simulations, image-based modeling (IBM) has arisen as the next logical step in the evolution of non-invasive patient-specific cardiovascular medicine. Yet, due to its novelty, it is still relatively unknown outside of the niche field. Therefore, the goal of this manuscript is to review the current state-of-the-art and the limitations of the methods used in this area of research, as well as their applications to personalized cardiovascular investigations and treatments. Specifically, the modeling of three different physics – electrophysiology, biomechanics and hemodynamics – used in the cardiovascular IBM is discussed in the context of the physiology that each one of them describes and the mechanisms of the underlying cardiac diseases that they can provide insight into. Only the “bare-bones” of the modeling approaches are discussed in order to make this introductory material more accessible to an outside observer. Additionally, the imaging methods, the aspects of the unique cardiac anatomy derived from them, and their relation to the modeling algorithms are reviewed. Finally, conclusions are drawn about the future evolution of these methods and their potential toward revolutionizing the non-invasive diagnosis, virtual design of treatments/assistive devices, and increasing our understanding of these lethal cardiovascular diseases.

A nonlinear rotation-free shell formulation with prestressing for vascular biomechanics

We implement a nonlinear rotation-free shell formulation capable of handling large deformations for applications in vascular biomechanics. The formulation employs a previously reported shell element that calculates both the membrane and bending behavior via displacement degrees of freedom for a triangular element. The thickness stretch is statically condensed to enforce vessel wall incompressibility via a plane stress condition. Consequently, the formulation allows incorporation of appropriate 3D constitutive material models. We also incorporate external tissue support conditions to model the effect of surrounding tissue. We present theoretical and variational details of the formulation and verify our implementation against axisymmetric results and literature data. We also adapt a previously reported prestress methodology to identify the unloaded configuration corresponding to the medically imaged in vivo vessel geometry. We verify the prestress methodology in an idealized bifurcation model and demonstrate the significance of including prestress. Lastly, we demonstrate the robustness of our formulation via its application to mouse-specific models of arterial mechanics using an experimentally informed four-fiber constitutive model.

Numerical simulation of magnetic nano drug targeting to atherosclerosis: Effect of plaque morphology (stenosis degree and shoulder length)

BACKGROUND AND OBJECTIVE

Nanoparticle-mediated targeted drug delivery is a promising option for treatment of atherosclerosis. However, the drug targeting may be affected by multiple factors. Considerable attentions have been focused on the influences of external factors, e.g., magnetic field, drug-loaded particle, but internal factors, e.g., plaque morphology (stenosis degree and shoulder length), have not received any attention yet. Therefore, we investigate the impact of plaque morphology on magnetic nanoparticles targeting under the action of an external field.

METHOD

Numerical simulation, based on Eulerian-Lagrangian coupled Fluid-Solid Interaction, is performed in ANSYS Workbench platform. Blood flow is solved by Navier-Stokes equation, particles are tracked by discrete phase model, and the incorporated effect is obtained by two-way method. Plaques with varying stenosis degrees and shoulder lengths are acquired by manually modifying the geometry of patient-specific. The quantified variables include targeted delivery efficiency (deposition+adhesive strength) of particles and plaque injury characterized by temporal-spatial averaged shear stress (TAWSS¯) during the process of drug transport, in which the critical deposition velocity is determined by plaques and particles, the DEFINE_DPM_BC and User Defined Memory are employed to evaluate whether the particles are deposited, and to store the total number and the adhesive strength of particles deposited on the plaque.

RESULTS

Results signify that, with an increment of plaque stenosis degree, the deposition of particle and the adhesive strength between particle and plaque decrease, while the TAWSS¯ increases. Furthermore, for the same stenosis degree, with the increase of plaque shoulder length, the deposition and the adhesive strength of particle increase, and the TAWSS¯ decreases.

CONCLUSIONS

Results demonstrates that the plaque with smaller stenosis degree or longer shoulder length may achieve a better treatment effect in view of the higher targeted delivery efficiency of particles and the lighter shear damage to plaque itself during the process of drug transport.

The effect of the elongation of the proximal aorta on the estimation of the aortic wall distensibility

The compliance of the proximal aortic wall is a major determinant of cardiac afterload. Aortic compliance is often estimated based on cross-sectional area changes over the pulse pressure, under the assumption of a negligible longitudinal stretch during the pulse. However, the proximal aorta is subjected to significant axial stretch during cardiac contraction. In the present study, we sought to evaluate the importance of axial stretch on compliance estimation by undertaking both an in silico and an in vivo approach. In the computational analysis, we developed a 3-D finite element model of the proximal aorta and investigated the discrepancy between the actual wall compliance to the value estimated after neglecting the longitudinal stretch of the aorta. A parameter sensitivity analysis was further conducted to show how increased material stiffness and increased aortic root motion might amplify the estimation errors (discrepancies between actual and estimated distensibility ranging from − 20 to − 62%). Axial and circumferential aortic deformation during ventricular contraction was also evaluated in vivo based on MR images of the aorta of 3 healthy young volunteers. The in vivo results were in good qualitative agreement with the computational analysis (underestimation errors ranging from − 26 to − 44%, with increased errors reflecting higher aortic root displacement). Both the in silico and in vivo findings suggest that neglecting the longitudinal strain during contraction might lead to severe underestimation of local aortic compliance, particularly in the case of women who tend to have higher aortic root motion or in subjects with stiff aortas.

Customized stent-grafts for endovascular aneurysm repair with challenging necks: A numerical proof of concept

Endovascular aortic repair (EVAR) is a challenging intervention whose long-term success strongly depends on the appropriate stent-graft (SG) selection and sizing. Most off-the-shelf SGs are straight and cylindrical. Especially in challenging vessel morphologies, the morphology of off-the-shelf SGs is not able to meet the patient-specific demands. Advanced manufacturing technologies facilitate the development of highly customized SGs. Customized SGs that have the same morphology as the luminal vessel surface could considerably improve the quality of the EVAR outcome with reduced likelihoods of EVAR related complications such as endoleaks type I and SG migration. In this contribution, we use an in silico EVAR methodology that approximates the deployed state of the elastically deformable SG in a hyperelastic, anisotropic vessel. The in silico EVAR results of off-the-shelf SGs and customized SGs are compared qualitatively and quantitatively in terms of mechanical and geometrical parameters such as stent stresses, contact tractions, SG fixation forces and the SG-vessel attachment. In a numerical proof of concept, eight different vessel morphologies, such as a conical vessel, a barrel shaped vessel and a curved vessel, are used to demonstrate the added value of customized SGs compared to off-the-shelf SGs. The numerical investigation has shown large benefits of the highly customized SGs compared to off-the-shelf SGs with respect to a better SG-vessel attachment and a considerable increase in SG fixation forces of up to 50% which indicate decreased likelihoods of EVAR related complications. Hence, this numerical proof of concept motivates further research and development of highly customized SGs for the use in challenging vessel morphologies.

Verification of the coupled-momentum method with Womersley's Deformable Wall analytical solution

In this paper, we perform a verification study of the Coupled-Momentum Method (CMM), a 3D fluid-structure interaction (FSI) model which uses a thin linear elastic membrane and linear kinematics to describe the mechanical behavior of the vessel wall. The verification of this model is done using Womersley's deformable wall analytical solution for pulsatile flow in a semi-infinite cylindrical vessel. This solution is, under certain premises, the analytical solution of the CMM and can thus be used for model verification. For the numerical solution, we employ an impedance boundary condition to define a reflection-free outflow boundary condition and thus mimic the physics of the analytical solution, which is defined on a semi-infinite domain. We first provide a rigorous derivation of Womersley's deformable wall theory via scale analysis. We then illustrate different characteristics of the analytical solution such as space-time wave periodicity and attenuation. Finally, we present the verification tests comparing the CMM with Womersley's theory.

Fluid-structure interaction simulations of patient-specific aortic dissection

Credible computational fluid dynamic (CFD) simulations of aortic dissection are challenging, because the defining parallel flow channels-the true and the false lumen-are separated from each other by a more or less mobile dissection membrane, which is made up of a delaminated portion of the elastic aortic wall. We present a comprehensive numerical framework for CFD simulations of aortic dissection, which captures the complex interplay between physiologic deformation, flow, pressures, and time-averaged wall shear stress (TAWSS) in a patient-specific model. Our numerical model includes (1) two-way fluid-structure interaction (FSI) to describe the dynamic deformation of the vessel wall and dissection flap; (2) prestress and (3) external tissue support of the structural domain to avoid unphysiologic dilation of the aortic wall and stretching of the dissection flap; (4) tethering of the aorta by intercostal and lumbar arteries to restrict translatory motion of the aorta; and a (5) independently defined elastic modulus for the dissection flap and the outer vessel wall to account for their different material properties. The patient-specific aortic geometry is derived from computed tomography angiography (CTA). Three-dimensional phase contrast magnetic resonance imaging (4D flow MRI) and the patient's blood pressure are used to inform physiologically realistic, patient-specific boundary conditions. Our simulations closely capture the cyclical deformation of the dissection membrane, with flow simulations in good agreement with 4D flow MRI. We demonstrate that decreasing flap stiffness from [Formula: see text] to [Formula: see text] kPa (a) increases the displacement of the dissection flap from 1.4 to 13.4 mm, (b) decreases the surface area of TAWSS by a factor of 2.3, (c) decreases the mean pressure difference between true lumen and false lumen by a factor of 0.63, and (d) decreases the true lumen flow rate by up to 20% in the abdominal aorta. We conclude that the mobility of the dissection flap substantially influences local hemodynamics and therefore needs to be accounted for in patient-specific simulations of aortic dissection. Further research to accurately measure flap stiffness and its local variations could help advance future CFD applications.

Simulating ventricular systolic motion in a four-chamber heart model with spatially varying robin boundary conditions to model the effect of the pericardium

The pericardium affects cardiac motion by limiting epicardial displacement normal to the surface. In computational studies, it is important for the model to replicate realistic motion, as this affects the physiological fidelity of the model. Previous computational studies showed that accounting for the effect of the pericardium allows for a more realistic motion simulation. In this study, we describe the mechanism through which the pericardium causes improved cardiac motion. We simulated electrical activation and contraction of the ventricles on a four-chamber heart in the presence and absence of the effect of the pericardium. We simulated the mechanical constraints imposed by the pericardium by applying normal Robin boundary conditions on the ventricular epicardium. We defined a regional scaling of normal springs stiffness based on image-derived motion from CT images. The presence of the pericardium reduced the error between simulated and image-derived end-systolic configurations from 12.8±4.1 mm to 5.7±2.5 mm. First, the pericardium prevents the ventricles from spherising during isovolumic contraction, reducing the outward motion of the free walls normal to the surface and the upwards motion of the apex. Second, by restricting the inward motion of the free and apical walls of the ventricles the pericardium increases atrioventricular plane displacement by four folds during ejection. Our results provide a mechanistic explanation of the importance of the pericardium in physiological simulations of electromechanical cardiac function.

Numerical investigation of the effects of blood rheology and wall elasticity in abdominal aortic aneurysm under pulsatile flow conditions

BACKGROUND

Previous studies on aneurysm modeling have focused on the blood rheology and vessel elasticity separately. The combined effects of blood shear thinning properties and wall elasticity need to be revealed.

OBJECTIVE

To provide insights on how pulsatile hemodynamics vary with blood rheology and vessel elasticity for a developed abdominal aortic aneurysm (AAA).

METHOD

An Arbitrary Lagrangian-Eulerian fluid-solid interaction method is adopted with the Newtonian and the shear thinning Carreau constitutive models for the fluid with the linearly elastic and the hyperelastic Yeoh models for the vessel. Finite element based numerical solver is used to simulate the blood flow in the AAA.

RESULTS

Newtonian model overestimates the velocity values compared to the Carreau model and the difference in the velocity field increases as the shear rate decreases at the instances of the cardiac cycle. The rigid walled simulations display higher deviations in the velocity and wall shear stress with the fluid rheology. The risk indicators show that Newtonian assumption combined with the linearly elastic model may overlook degeneration risk of arterial tissue.

CONCLUSIONS

Newtonian assumption for the blood as well as modelling the arterial wall as linearly elastic lead to significant differences in oscillatory hemodynamic properties with respect to the use of Carreau fluid together with hyperelastic vessel model, even in large vessel aneurysms.

Effect of axial prestretch and adipose tissue on the inflation-extension behavior of the human abdominal aorta

Our study aims to show that perivascular adipose tissue may significantly change the mechanical state of the abdominal aorta. To this end, uniaxial tensile tests with perivascular fat tissue were carried out. In the subsequent regression analysis, stress-strain data were fitted by the polynomial strain energy density. A constitutive model of adipose tissue was used in the analytical simulation of the inflation-extension behavior of the human abdominal aorta. The computational model was based on the theory of the bi-layered thick-walled tube. In addition to the effect of perivascular tissue, the effect of axial prestretch was also studied. It was found that the presence of perivascular tissue reduces the distensibility of the aorta. Axial prestretch applied to the aorta embedded in adipose tissue had an effect opposite to that of adipose tissue. Axially prestrained aorta exhibited higher distensiblity than non-prestrained aorta. It was also shown that the perivascular envelope bears some portion of the pressure loading and thus reduces the mechanical stresses inside the wall of aorta. A similar effect was found for axial prestretch.

In silico study of vessel and stent-graft parameters on the potential success of endovascular aneurysm repair

The variety of stent-graft (SG) design variables (eg, SG type and degree of SG oversizing) and the complexity of decision making whether a patient is suitable for endovascular aneurysm repair (EVAR) raise the need for the development of predictive tools to assist clinicians in the preinterventional planning phase. Recently, some in silico EVAR methods have been developed to predict the deployed SG configuration. However, only few studies investigated how to assess the in silico EVAR outcome with respect to EVAR complication likelihoods (eg, endoleaks and SG migration). Based on a large literature study, in this contribution, 20 mechanical and geometrical parameters (eg, SG drag force and SG fixation force) are defined to evaluate the quality of the in silico EVAR outcome. For a cohort of n = 146 realizations of parameterized vessel and SG geometries, the in silico EVAR results are studied with respect to these mechanical and geometrical parameters. All degrees of SG oversizing in the range between 5% and 40% are investigated continuously by a computationally efficient parameter continuation approach. The in silico investigations have shown that the mechanical and geometrical parameters are able to indicate candidates at high risk of postinterventional complications. Hence, this study provides the basis for the development of a simulation-based metric to assess the potential success of EVAR based on engineering parameters.

A Spatially Resolved and Quantitative Model of Early Atherosclerosis

Atherosclerosis is a major burden for all societies, and there is a great need for a deeper understanding of involved key inflammatory, immunological and biomechanical processes. A decisive step for the prevention and medical treatment of atherosclerosis is to predict what conditions determine whether early atherosclerotic plaques continue to grow, stagnate or become regressive. The driving biological and mechanobiological mechanisms that determine the stability of plaques are yet not fully understood. We develop a spatially resolved and quantitative mathematical model of key contributors of early atherosclerosis. The stability of atherosclerotic model plaques is assessed to identify and classify progression-prone and progression-resistant atherosclerotic regions based on measurable or computable in vivo inputs, such as blood cholesterol concentrations and wall shear stresses. The model combines Darcy's law for the transmural flow through vessels walls, the Kedem-Katchalsky equations for endothelial fluxes of lipoproteins, a quantitative model of early plaque formation from a recent publication and a novel submodel for macrophage recruitment. The parameterization and analysis of the model suggest that the advective flux of lipoproteins through the endothelium is decisive, while the influence of the advective transport within the artery wall is negligible. Further, regions in arteries with an approximate wall shear stress exposure below 20% of the average exposure and their surroundings are potential regions where progression-prone atherosclerotic plaques develop.

Patient-specific in silico endovascular repair of abdominal aortic aneurysms: application and validation

Non-negligible postinterventional complication rates after endovascular aneurysm repair (EVAR) leave room for further improvements. Since the potential success of EVAR depends on various patient-specific factors, such as the complexity of the vessel geometry and the physiological state of the vessel, in silico models can be a valuable tool in the preinterventional planning phase. A suitable in silico EVAR methodology applied to patient-specific cases can be used to predict stent-graft (SG)-related complications, such as SG migration, endoleaks or tissue remodeling-induced aortic neck dilatation and to improve the selection and sizing process of SGs. In this contribution, we apply an in silico EVAR methodology that predicts the final state of the deployed SG after intervention to three clinical cases. A novel qualitative and quantitative validation methodology, that is based on a comparison between in silico results and postinterventional CT data, is presented. The validation methodology compares average stent diameters pseudo-continuously along the total length of the deployed SG. The validation of the in silico results shows very good agreement proving the potential of using in silico approaches in the preinterventional planning of EVAR. We consider models of bifurcated, marketed SGs as well as sophisticated models of patient-specific vessels that include intraluminal thrombus, calcifications and an anisotropic model for the vessel wall. We exemplarily show the additional benefit and applicability of in silico EVAR approaches to clinical cases by evaluating mechanical quantities with the potential to assess the quality of SG fixation and sealing such as contact tractions between SG and vessel as well as SG-induced tissue overstresses.

An In-Vitro Flow Study Using an Artificial Circle of Willis Model for Validation of an Existing One-Dimensional Numerical Model

A one-dimensional (1D) numerical model has been previously developed to investigate the hemodynamics of blood flow in the entire human vascular network. In the current work, an experimental study of water-glycerin mixture flow in a 3D-printed silicone model of an anatomically accurate, complete circle of Willis (CoW) was conducted to investigate the flow characteristics in comparison with the simulated results by the 1D numerical model. In the experiment, the transient flow and pressure waveforms were measured at 13 selected segments within the flow network for comparisons. In the 1D simulation, the initial parameters of the vessel network were obtained by a direct measurement of the tubes in the experimental setup. The results verified that the 1D numerical model is able to capture the main features of the experimental pressure and flow waveforms with good reliability. The mean flow rates measurement results agree with the predictions of the 1D model with an overall difference of less than 1%. Further experiment might be needed to validate the 1D model in capturing pressure waveforms.

Comparison between a generalized Newtonian model and a network-type multiscale model for hemodynamic behavior in the aortic arch: Validation with 4D MRI data for a case study

Blood is a complex fluid in which the presence of the various constituents leads to significant changes in its rheological properties. Thus, an appropriate non-Newtonian model is advisable; and we choose a Modified version of the rheological model of Phan-Thien and Tanner (MPTT). The different parameters of this model, derived from the rheology of polymers, allow characterization of the non-Newtonian nature of blood, taking into account the behavior of red blood cells in plasma. Using the MPTT model that we implemented in the open access software OpenFOAM, numerical simulations have been performed on blood flow in the thoracic aorta for a healthy patient. We started from a patient-specific model which was constructed from medical images. Exiting flow boundary conditions have been developped, based on a 3-element Windkessel model to approximate physiological conditions. The parameters of the Windkessel model were calibrated with in vivo measurements of flow rate and pressure. The influence of the selected viscosity of red blood cells on the flow and wall shear stress (WSS) was investigated. Results obtained from this model were compared to those of the Newtonian model, and to those of a generalized Newtonian model, as well as to in vivo dynamic data from 4D MRI during a cardiac cycle. Upon evaluating the results, the MPTT model shows better agreement with the MRI data during the systolic and diastolic phases than the Newtonian or generalized Newtonian model, which confirms our interest in using a complex viscoelastic model.

A methodology for in silico endovascular repair of abdominal aortic aneurysms

Endovascular aneurysm repair (EVAR) can involve some unfavorable complications such as endoleaks or stent-graft (SG) migration. Such complications, resulting from the complex mechanical interaction of vascular tissue, SG and blood flow or incompatibility of SG design and vessel geometry, are difficult to predict. Computational vascular mechanics models can be a predictive tool for the selection, sizing and placement process of SGs depending on the patient-specific vessel geometry and hence reduce the risk of potential complications after EVAR. In this contribution, we present a new in silico EVAR methodology to predict the final state of the deployed SG after intervention and evaluate the mechanical state of vessel and SG, such as contact forces and wall stresses. A novel method to account for residual strains and stresses in SGs, resulting from the precompression of stents during the assembly process of SGs, is presented. We suggest a parameter continuation approach to model various different sizes of SGs within one in silico EVAR simulation which can be a valuable tool when investigating the issue of SG oversizing. The applicability and robustness of the proposed methods are demonstrated on the example of a synthetic abdominal aortic aneurysm geometry.