Patient-specific finite element analysis of ascending aorta aneurysms

Guidelines for mechanistic modeling and analysis in cardiovascular research

Computational, or in silico, models are an effective, noninvasive tool for investigating cardiovascular function. These models can be used in the analysis of experimental and clinical data to identify possible mechanisms of (ab)normal cardiovascular physiology. Recent advances in computing power and data management have led to innovative and complex modeling frameworks that simulate cardiovascular function across multiple scales. While commonly used in multiple disciplines, there is a lack of concise guidelines for the implementation of computer models in cardiovascular research. In line with recent calls for more reproducible research, it is imperative that scientists adhere to credible practices when developing and applying computational models to their research. The goal of this manuscript is to provide a consensus document that identifies best practices for in silico computational modeling in cardiovascular research. These guidelines provide the necessary methods for mechanistic model development, model analysis, and formal model calibration using fundamentals from statistics. We outline rigorous practices for computational, mechanistic modeling in cardiovascular research and discuss its synergistic value to experimental and clinical data.

Vascular Remodeling During Late-Gestation Pregnancy: An In-Vitro Assessment of the Murine Ascending Thoracic Aorta

Maternal mortality due to cardiovascular disease is a rising concern in the U.S. Pregnancy triggers changes in the circulatory system, potentially influencing the structure of the central vasculature. Evidence suggests a link between a woman's pregnancy history and future cardiovascular health, but our understanding remains limited. To fill this gap, we examined the passive mechanics of the murine ascending thoracic aorta during late gestation. By performing biaxial mechanical testing on the ascending aorta, we were able to characterize the mechanical properties of both control and late-gestation tissues. By examining mechanical, structural, and geometric properties, we confirmed that remodeling of the aortic wall occurred. Morphological and mechanical properties of the tissue indicated an outward expansion of the tissue, as reflected in changes in wall thickness (∼12% increase) and luminal diameter (∼6% increase) at its physiologically loaded state in the pregnant group. With these geometric adaptations and despite increased hemodynamic loads, pregnancy did not induce significant changes in the tensile wall stress at the similar physiological pressure levels of the pregnant and control tissues. The alterations also included reduced intrinsic stiffness in the circumferential direction (∼18%) and reduced structural stiffness (∼26%) in the pregnant group. The observed vascular remodeling maintained the elastic stored energy of the aortic wall under systolic loads, indicating preservation of vascular function. Data from our study of pregnancy-related vascular remodeling will provide valuable insights for future investigations of maternal cardiovascular health.

Mechanics of ascending aortic aneurysms based on a modulus of elasticity dependent on aneurysm diameter and pressure

The mechanical stresses and strains are examined, in ascending thoracic aortic aneurysm (aTAA) models, in a patient-specific aTAA as well as in healthy thoracic aortic models, via Finite Element Analysis. The aneurysms are assumed spherical, 1.5 mm thick, with diameters between 47 mm and 80 mm, eccentrically positioned. The geometry and wall thickness distribution of the aorta along its length are based on open literature data for an average patient age of 66.25 years, accounting for the Body Surface Area (BSA) parameter. The vessel wall material is assumed isotropic and incompressible, with its Young's modulus varying with the aneurysm diameter and the applied intraluminal pressure (120 mmHg to 240 mmHg). In the aTAAs, peak stresses were found to increase nonlinearly with aneurysm diameter (for a given pressure) tending to reach a plateau, appearing at the proximal area of the aneurysm, whereas lower stresses were found at its distal part and even smaller at the aneurysm maximum diameter. Regarding the patient-specific aTAA model, the peak stresses appeared at the distal part of the aneurysm where a tear of the intima layer was detected during surgical intervention. Peak strains exhibited for each pressure a maximum at a certain aneurysm diameter beyond which they dropped so that essentially the vessel wall's distensibility was thus reduced. Examining more than 100 geometry cases and employing a failure stress criterion, the rupture diameter thresholds were estimated to be 65, 52.5, 50 and 47.5 mm for a pressure of 120, 160, 200 and 240 mmHg respectively.

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.

Synergistic Integration of Deep Neural Networks and Finite Element Method with Applications of Nonlinear Large Deformation Biomechanics

Patient-specific finite element analysis (FEA) holds great promise in advancing the prognosis of cardiovascular diseases by providing detailed biomechanical insights such as high-fidelity stress and deformation on a patient-specific basis. Albeit feasible, FEA that incorporates three-dimensional, complex patient-specific geometry can be time-consuming and unsuitable for time-sensitive clinical applications. To mitigate this challenge, machine learning (ML) models, e.g., deep neural networks (DNNs), have been increasingly utilized as potential alternatives to finite element method (FEM) for biomechanical analysis. So far, efforts have been made in two main directions: (1) learning the input-to-output mapping of traditional FEM solvers and replacing FEM with data-driven ML surrogate models; (2) solving equilibrium equations using physics-informed loss functions of neural networks. While these two existing strategies have shown improved performance in terms of speed or scalability, ML models have not yet provided practical advantages over traditional FEM due to generalization issues. This has led us to the question: instead of abandoning or replacing the traditional FEM framework that can reliably solve biomechanical problems, can we integrate FEM and DNNs to enhance performance? In this study, we propose a synergistic integration of DNNs and FEM to overcome their individual limitations. Using biomechanical analysis of the human aorta as the test bed, we demonstrated two novel integrative strategies in forward and inverse problems. For the forward problem, we developed DNNs with state-of-the-art architectures to predict a nodal displacement field, and this initial DNN solution was then updated by a FEM-based refinement process, yielding a fast and accurate computing framework. For the inverse problem of heterogeneous material parameter identification, our method employs DNN as a regularizer of the spatial distribution of material parameters, aiding the optimizer in locating the optimal solution. In our demonstrative examples, despite that the DNN-only forward models yielded small displacement errors in most test cases; stress errors were considerably large, and for some test cases, the peak stress errors were greater than 50%. Our DNN-FEM integration eliminated these non-negligible errors in DNN-only models and was magnitudes faster than the FEM-only approach. Additionally, compared to FEM-only inverse method with errors greater than 50%, our DNN-FEM inverse approach significantly improved the parameter identification accuracy and reduced the errors to less than 1%.

Effect of Nonlinear Hyperelastic Property of Arterial Tissues on the Pulse Wave Velocity Based on the Unified-Fiber-Distribution (UFD) Model

Pulse wave velocity (PWV) is a key, independent risk factor for future cardiovascular events. The Moens-Korteweg equation describes the relation between PWV and the stiffness of arterial tissue with an assumption of isotopic linear elastic property of the arterial wall. However, the arterial tissue exhibits highly nonlinear and anisotropic mechanical behaviors. There is a limited study regarding the effect of arterial nonlinear and anisotropic properties on the PWV. In this study, we investigated the impact of the arterial nonlinear hyperelastic properties on the PWV, based on our recently developed unified-fiber-distribution (UFD) model. The UFD model considers the fibers (embedded in the matrix of the tissue) as a unified distribution, which expects to be more physically consistent with the real fiber distribution than existing models that separate the fiber distribution into two/several fiber families. With the UFD model, we fitted the measured relation between the PWV and blood pressure which obtained a good accuracy. We also modeled the aging effect on the PWV based on observations that the stiffening of arterial tissue increases with aging, and the results agree well with experimental data. In addition, we did parameter studies on the dependence of the PWV on the arterial properties of fiber initial stiffness, fiber distribution, and matrix stiffness. The results indicate the PWV increases with increasing overall fiber component in the circumferential direction. The dependences of the PWV on the fiber initial stiffness, and matrix stiffness are not monotonic and change with different blood pressure. The results of this study could provide new insights into arterial property changes and disease information from the clinical measured PWV data.

Longitudinal versus circumferential biomechanical behavior of the aneurysmal ascending aorta

OBJECTIVES

We evaluate the independent effects of patient and aortic tissue characteristics on biaxial physiologic mechanical metrics in aneurysmal and nonaneurysmal tissues, and uniaxial failure metrics in aneurysmal tissue, comparing longitudinal and circumferential behavior.

METHODS

From February 2017 to October 2022, 382 aortic specimens were collected from 134 patients; 268 specimens underwent biaxial testing, and 114 specimens underwent uniaxial testing. Biaxial testing evaluated Green-Lagrange transition strain and low and high tangent moduli. Uniaxial testing evaluated failure stretch, Cauchy stress, and low and high tangent moduli. Longitudinal gradient boosting models were implemented to estimate mechanical metrics and covariates of importance.

RESULTS

On biaxial testing, nonaneurysmal tissue was less deformable and exhibited a lower transition strain than aneurysmal tissue in the longitudinal (0.18 vs 0.30, P < .001) and circumferential (0.25 vs 0.30, P = .01) directions. Older age and increasing ascending aortic length contributed most to predicting transition strain. On uniaxial testing, longitudinal specimens failed at lower stretch (1.4 vs 1.5, P = .003) and Cauchy stress (1.0 vs 1.9 kPa, P < .001) than circumferential specimens. Failure stretch and Cauchy stress were most strongly associated with tissue orientation and decreased sharply with older age. Age, ascending aortic length, and tissue thickness were the most frequent covariates predicting mechanical metrics across 10 prediction models.

CONCLUSIONS

Age was the strongest predictor of mechanical behavior. After adjusting for age, nonaneurysmal tissue was less deformable than aneurysmal tissue. Differences in longitudinal and circumferential mechanics contribute to tissue dysfunction and failure in ascending aneurysms. This highlights the need to better understand the effects of age, ascending aortic length, and thickness on clinical aortic behavior.

A review on the biomechanical behaviour of the aorta

Large aortic aneurysm and acute and chronic aortic dissection are pathologies of the aorta requiring surgery. Recent advances in medical intervention have improved patient outcomes; however, a clear understanding of the mechanisms leading to aortic failure and, hence, a better understanding of failure risk, is still missing. Biomechanical analysis of the aorta could provide insights into the development and progression of aortic abnormalities, giving clinicians a powerful tool in risk stratification. The complexity of the aortic system presents significant challenges for a biomechanical study and requires various approaches to analyse the aorta. To address this, here we present a holistic review of the biomechanical studies of the aorta by categorising articles into four broad approaches, namely theoretical, in vivo, experimental and combined investigations. Experimental studies that focus on identifying mechanical properties of the aortic tissue are also included. By reviewing the literature and discussing drawbacks, limitations and future challenges in each area, we hope to present a more complete picture of the state-of-the-art of aortic biomechanics to stimulate research on critical topics. Combining experimental modalities and computational approaches could lead to more comprehensive results in risk prediction for the aortic system.

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.

Ascending Aortic Volume: A Feasible Indicator for Ascending Aortic Aneurysm Elective Surgery?

Diameter-based criterion have been widely adopted for preventive surgery of ascending thoracic aortic aneurysm (ATAA). However, recent and growing evidence has shown that diameter-based methods may not be sufficient for identifying patients who are at risk of an ATAA. In this study, fluid-structure interaction (FSI) analysis was performed on one-hundred ATAA geometries reconstructed from clinical data to examine the relationship between hemodynamic conditions, ascending aortic volume (AAV), ascending aortic curvature, and aortic ratios measured from the reconstructed 3D models. The simulated hemodynamic and biomechanical parameters were compared among different groups of ATAA geometries classified based on AAV. The ATAAs with enlarged AAV showed significantly compromised hemodynamic conditions and higher mechanical wall stress. The maximum oscillatory shear index (OSI), particle residence time (PRT) and wall stress (WS) were significantly higher in enlarged ATAAs compared with controls (0.498 [0.497, 0.499] vs 0.499 [0.498, 0.499], p = 0.002, 312.847 [207.445, 519.391] vs 996.047 [640.644, 1573.140], p < 0.001, 769.680 [668.745, 879.795] vs 1072.000 [873.060, 1280.000] kPa, p < 0.001, respectively). Values were reported as median with interquartile range (IQR). AAV was also found to be more strongly correlated with these parameters compared to maximum diameter. The correlation coefficient between AAV and average WS was as high as 0.92 (p < 0.004), suggesting that AAV might be a feasible risk identifier for ATAAs. STATEMENT OF SIGNIFICANCE: Ascending thoracic aortic aneurysm is associated with the risk of dissection or rupture, creating life-threatening conditions. Current surgical intervention guidelines are purely diameter based. Recently, many studies proposed to incorporate other morphological parameters into the current clinical guidelines to better prevent severe adverse aortic events like rupture or dissection. The purpose of this study is to gain a better understanding of the relationship between morphological parameters and hemodynamic parameters in ascending aortic aneurysms using fluid-solid-interaction analysis on patient-specific geometries. Our results suggest that ascending aortic volume may be a better indicator for surgical intervention as it shows a stronger association with pathogenic hemodynamic conditions.

Effect of Aging, Sex, and Gene (Fbln5) on Arterial Stiffness of Mice: 20 Weeks Adult Fbln5-knockout Mice Have Older Arteries than 100 Weeks Wild-Type Mice

The arterial stiffening is a strong independent predictor of cardiovascular risk and has been used to characterize the biological age of arteries ('arterial age'). Here we revealed that the Fbln5 gene knockout (Fbln5 ^-/- ) significantly increases the arterial stiffening for both male and female mice. We also showed that the arterial stiffening increases with natural aging, but the stiffening effect of Fbln5 ^-/- is much more severe than aging. The arterial stiffening of 20 weeks old mice with Fbln5 ^-/- is much higher than that at 100 weeks in wild-type (Fbln5 ^+/+ ) mice, which indicates that 20 weeks mice (equivalent to ∼26 years old humans) with Fbln5 ^-/- have older arteries than 100 weeks wild-type mice (equivalent to ∼77 years humans). Histological microstructure changes of elastic fibers in the arterial tissue elucidate the underlying mechanism of the increase of arterial stiffening due to Fbln5-knockout and aging. These findings provide new insights to reverse 'arterial age' due to abnormal mutations of Fbln5 gene and natural aging. This work is based on a total of 128 biaxial testing samples of mouse arteries and our recently developed unified-fiber-distribution (UFD) model. The UFD model considers the fibers in the arterial tissue as a unified distribution, which is more physically consistent with the real fiber distribution of arterial tissues than the popular fiber-family-based models (e.g., the well-know Gasser-Ogden-Holzapfel [GOH] model) that separate the fiber distribution into several fiber families. Thus, the UFD model achieves better accuracies with less material parameters. To our best knowledge, the UFD model is the only existing accurate model that could capture the property/stiffness differences between different groups of the experimental data discussed here.

Synergistic Integration of Deep Neural Networks and Finite Element Method with Applications for Biomechanical Analysis of Human Aorta

Motivation: Patient-specific finite element analysis (FEA) has the potential to aid in the prognosis of cardiovascular diseases by providing accurate stress and deformation analysis in various scenarios. It is known that patient-specific FEA is time-consuming and unsuitable for time-sensitive clinical applications. To mitigate this challenge, machine learning (ML) techniques, including deep neural networks (DNNs), have been developed to construct fast FEA surrogates. However, due to the data-driven nature of these ML models, they may not generalize well on new data, leading to unacceptable errors.

Methods

We propose a synergistic integration of DNNs and finite element method (FEM) to overcome each other’s limitations. We demonstrated this novel integrative strategy in forward and inverse problems. For the forward problem, we developed DNNs using state-of-the-art architectures, and DNN outputs were then refined by FEM to ensure accuracy. For the inverse problem of heterogeneous material parameter identification, our method employs a DNN as regularization for the inverse analysis process to avoid erroneous material parameter distribution.

Results

We tested our methods on biomechanical analysis of the human aorta. For the forward problem, the DNN-only models yielded acceptable stress errors in majority of test cases; yet, for some test cases that could be out of the training distribution (OOD), the peak stress errors were larger than 50%. The DNN-FEM integration eliminated the large errors for these OOD cases. Moreover, the DNN-FEM integration was magnitudes faster than the FEM-only approach. For the inverse problem, the FEM-only inverse method led to errors larger than 50%, and our DNN-FEM integration significantly improved performance on the inverse problem with errors less than 1%.

PyTorch-FEA: Autograd-enabled Finite Element Analysis Methods with Applications for Biomechanical Analysis of Human Aorta

Motivation

Finite-element analysis (FEA) is widely used as a standard tool for stress and deformation analysis of solid structures, including human tissues and organs. For instance, FEA can be applied at a patient-specific level to assist in medical diagnosis and treatment planning, such as risk assessment of thoracic aortic aneurysm rupture/dissection. These FEA-based biomechanical assessments often involve both forward and inverse mechanics problems. Current commercial FEA software packages (e.g., Abaqus) and inverse methods exhibit performance issues in either accuracy or speed.

Methods

In this study, we propose and develop a new library of FEA code and methods, named PyTorch-FEA, by taking advantage of autograd, an automatic differentiation mechanism in PyTorch. We develop a class of PyTorch-FEA functionalities to solve forward and inverse problems with improved loss functions, and we demonstrate the capability of PyTorch-FEA in a series of applications related to human aorta biomechanics. In one of the inverse methods, we combine PyTorch-FEA with deep neural networks (DNNs) to further improve performance.

Results

We applied PyTorch-FEA in four fundamental applications for biomechanical analysis of human aorta. In the forward analysis, PyTorch-FEA achieved a significant reduction in computational time without compromising accuracy compared with Abaqus, a commercial FEA package. Compared to other inverse methods, inverse analysis with PyTorch-FEA achieves better performance in either accuracy or speed, or both if combined with DNNs.

Finite element modeling of meniscal tears using continuum damage mechanics and digital image correlation

Meniscal tears are a common, painful, and debilitating knee injury with limited treatment options. Computational models that predict meniscal tears may help advance injury prevention and repair, but first these models must be validated using experimental data. Here we simulated meniscal tears with finite element analysis using continuum damage mechanics (CDM) in a transversely isotropic hyperelastic material. Finite element models were built to recreate the coupon geometry and loading conditions of forty uniaxial tensile experiments of human meniscus that were pulled to failure either parallel or perpendicular to the preferred fiber orientation. Two damage criteria were evaluated for all experiments: von Mises stress and maximum normal Lagrange strain. After we successfully fit all models to experimental force-displacement curves (grip-to-grip), we compared model predicted strains in the tear region at ultimate tensile strength to the strains measured experimentally with digital image correlation (DIC). In general, the damage models underpredicted the strains measured in the tear region, but models using von Mises stress damage criterion had better overall predictions and more accurately simulated experimental tear patterns. For the first time, this study has used DIC to expose strengths and weaknesses of using CDM to model failure behavior in soft fibrous tissue.

Residual strains in ascending thoracic aortic aneurysms: The effect of valve type, layer, and circumferential quadrant

The stress distribution in ascending thoracic aortic aneurysms is determined by the mechanical properties, geometry, loading conditions, and zero-stress state of the aneurysmal aorta. Our objective was to fully characterize the zero-stress state of the aneurysmal aorta in twelve tricuspid aortic valve patients and eight (age/aortic diameter-matched) bicuspid aortic valve patients, for which little data are available. Opening angles and residual stretches were measured for the intact wall and individual layers according to quadrant and were similar in the two patient groups. The intact-wall and medial opening angles were comparable; their circumferential but not their axial ones peaked in the left lateral quadrant, with non-significant regional differences in the other layers. The intima's circumferential opening angles were the highest of all layers (∼300 deg) and the adventitia's the lowest (∼165 deg), with lesser layer differences in the axial opening angles. Upon radially cutting aortic rings, the released circumferential residual stretches were tensile (of large magnitude) externally and compressive (of small magnitude) internally, unlike the axial residual stretches released when cutting intact-wall strips, whose magnitude was small externally and large internally. Nevertheless, large circumferential compressive residual stretches were released in the adventitia upon layer dissection, counteracting the large circumferential tensile stretches of the intact wall externally. Moreover, the large axial tensile residual stretches of the intima counteracted the large axial compressive stretches of the intact wall internally. These layer-specific residual stretches may moderate the in-vivo stress gradients across wall thickness, serving as a protective mechanism against aortic dissection or rupture.

Association of diameter and wall stresses of tricuspid aortic valve ascending thoracic aortic aneurysms

OBJECTIVE

Ascending thoracic aortic aneurysms carry a risk of acute type A dissection. Elective repair guidelines are designed around size thresholds, but the 1-dimensional parameter of maximum diameter cannot predict acute events in small aneurysms. Biomechanically, dissection can occur when wall stress exceeds strength. Patient-specific ascending thoracic aortic aneurysm wall stresses may be a better predictor of dissection. Our aim was to compare wall stresses in tricuspid aortic valve-associated ascending thoracic aortic aneurysms based on diameter.

METHODS

Patients with tricuspid aortic valve-associated ascending thoracic aortic aneurysm and diameter 4.0 cm or greater (n = 221) were divided into groups by 0.5-cm diameter increments. Three-dimensional geometries were reconstructed from computed tomography images, and finite element models were developed taking into account prestress geometries. A fiber-embedded hyperelastic material model was applied to obtain longitudinal and circumferential wall stress distributions under systolic pressure. Median stresses with interquartile ranges were determined. The Kruskal-Wallis test was used for comparisons between size groups.

RESULTS

Peak longitudinal wall stresses for tricuspid aortic valve-associated ascending thoracic aortic aneurysm were 290 (265-323) kPa for size 4.0 to 4.4 cm versus 330 (296-359) kPa for 4.5 to 4.9 cm versus 339 (320-373) kPa for 5.0 to 5.4 cm versus 318 (293-351) kPa for 5.5 to 5.9 cm versus 373 (363-449) kPa for 6.0 cm or greater (P = 8.7e-8). Peak circumferential wall stresses were 460 (421-543) kPa for size 4.0 to 4.4 cm versus 503 (453-569) kPa for 4.5 to 4.9 cm versus 549 (430-588) kPa for 5.0 to 5.4 cm versus 540 (471-608) kPa for 5.5 to 5.9 cm versus 596 (506-649) kPa for 6.0 cm or greater (P = .0007).

CONCLUSIONS

Circumferential and longitudinal wall stresses are higher as diameter increases, but size groups had large overlap of stress ranges. Wall stress thresholds based on aneurysm wall strength may be a better predictor of patient-specific risk of dissection than diameter in small ascending thoracic aortic aneurysms.

Interplay between Artificial Intelligence and Biomechanics Modeling in the Cardiovascular Disease Prediction

Cardiovascular disease (CVD) is the most common cause of morbidity and mortality worldwide, and early accurate diagnosis is the key point for improving and optimizing the prognosis of CVD. Recent progress in artificial intelligence (AI), especially machine learning (ML) technology, makes it possible to predict CVD. In this review, we first briefly introduced the overview development of artificial intelligence. Then we summarized some ML applications in cardiovascular diseases, including ML-based models to directly predict CVD based on risk factors or medical imaging findings and the ML-based hemodynamics with vascular geometries, equations, and methods for indirect assessment of CVD. We also discussed case studies where ML could be used as the surrogate for computational fluid dynamics in data-driven models and physics-driven models. ML models could be a surrogate for computational fluid dynamics, accelerate the process of disease prediction, and reduce manual intervention. Lastly, we briefly summarized the research difficulties and prospected the future development of AI technology in cardiovascular diseases.

Interaction of the Blood Components with Ascending Thoracic Aortic Aneurysm Wall: Biomechanical and Fluid Analyses

BACKGROUND

Ascending thoracic aortic aneurysm (ATAA) is an asymptomatic localized dilation of the aorta that is prone to rupture with a high rate of mortality. While diameter is the main risk factor for rupture assessment, it has been shown that the peak wall stress from finite element (FE) simulations may contribute to refinement of clinical decisions. In FE simulations, the intraluminal boundary condition is a single-phase blood flow that interacts with the thoracic aorta (TA). However, the blood is consisted of red blood cells (RBCs), white blood cells (WBCs), and plasma that interacts with the TA wall, so it may affect the resultant stresses and strains in the TA, as well as hemodynamics of the blood.

METHODS

In this study, discrete elements were distributed in the TA lumen to represent the blood components and mechanically coupled using fluid-structure interaction (FSI). Healthy and aneurysmal human TA tissues were subjected to axial and circumferential tensile loadings, and the hyperelastic mechanical properties were assigned to the TA and ATAA FE models.

RESULTS

The ATAA showed larger tensile and shear stresses but smaller fluid velocity compared to the ATA. The blood components experienced smaller shear stress in interaction with the ATAA wall compared to TA. The computational fluid dynamics showed smaller blood velocity and wall shear stress compared to the FSI.

CONCLUSIONS

This study is a first proof of concept, and future investigations will aim at validating the novel methodology to derive a more reliable ATAA rupture risk assessment considering the interaction of the blood components with the TA wall.

Bovine Aortic Arch, A High-Risk Variant

The bovine aortic arch is a vascular variant related to an increased incidence of vascular and neurological complications. It should be ruled out in patients with vague neurological symptoms without a clear etiology. Our case is of a 72-year-old female patient who presented with a syncopal episode; the workup incidentally showed the aortic arch bovine variant with evidence of ischemic white matter disease more than expected for age. After reviewing the related literature, we suggest that this aortic variant is likely an independent risk factor for multiple vascular complications. A close follow-up is essential, and screening should be considered for symptomatic family members.

Medical Image-Based Computational Fluid Dynamics and Fluid-Structure Interaction Analysis in Vascular Diseases

Hemodynamic factors, induced by pulsatile blood flow, play a crucial role in vascular health and diseases, such as the initiation and progression of atherosclerosis. Computational fluid dynamics, finite element analysis, and fluid-structure interaction simulations have been widely used to quantify detailed hemodynamic forces based on vascular images commonly obtained from computed tomography angiography, magnetic resonance imaging, ultrasound, and optical coherence tomography. In this review, we focus on methods for obtaining accurate hemodynamic factors that regulate the structure and function of vascular endothelial and smooth muscle cells. We describe the multiple steps and recent advances in a typical patient-specific simulation pipeline, including medical imaging, image processing, spatial discretization to generate computational mesh, setting up boundary conditions and solver parameters, visualization and extraction of hemodynamic factors, and statistical analysis. These steps have not been standardized and thus have unavoidable uncertainties that should be thoroughly evaluated. We also discuss the recent development of combining patient-specific models with machine-learning methods to obtain hemodynamic factors faster and cheaper than conventional methods. These critical advances widen the use of biomechanical simulation tools in the research and potential personalized care of vascular diseases.

Simulating progressive intramural damage leading to aortic dissection using DeepONet: an operator-regression neural network

Aortic dissection progresses mainly via delamination of the medial layer of the wall. Notwithstanding the complexity of this process, insight has been gleaned by studying in vitro and in silico the progression of dissection driven by quasi-static pressurization of the intramural space by fluid injection, which demonstrates that the differential propensity of dissection along the aorta can be affected by spatial distributions of structurally significant interlamellar struts that connect adjacent elastic lamellae. In particular, diverse histological microstructures may lead to differential mechanical behaviour during dissection, including the pressure-volume relationship of the injected fluid and the displacement field between adjacent lamellae. In this study, we develop a data-driven surrogate model of the delamination process for differential strut distributions using DeepONet, a new operator-regression neural network. This surrogate model is trained to predict the pressure-volume curve of the injected fluid and the damage progression within the wall given a spatial distribution of struts, with in silico data generated using a phase-field finite-element model. The results show that DeepONet can provide accurate predictions for diverse strut distributions, indicating that this composite branch-trunk neural network can effectively extract the underlying functional relationship between distinctive microstructures and their mechanical properties. More broadly, DeepONet can facilitate surrogate model-based analyses to quantify biological variability, improve inverse design and predict mechanical properties based on multi-modality experimental data.

Ascending thoracic aortic aneurysm growth is minimal at sizes that do not meet criteria for surgical repair

BACKGROUND

Historic studies of nonsyndromic ascending thoracic aortic aneurysms (aTAAs) reported that the typical aTAA growth rate was approximately 0.6 mm/year, but data were limited due to relatively few studies using computed tomography (CT) imaging. Our purpose was to reevaluate the annual growth rate of nonsyndromic aTAAs that do not meet criteria for surgical repair in veterans in the contemporary era, using modern CT imaging suitable for highly accurate and reproducible aneurysm measurement.

METHODS

Nonsurgical patients (diameter <5.5 cm) undergoing aneurysm surveillance at a Veterans Affairs Medical Center with repeat CT imaging performed 3 to 5 years apart were identified. Maximum diameter was determined by a single radiologist using multiplanar reformat-based measurements. Average rate of aneurysm growth was evaluated based on longest available follow-up.

RESULTS

Sixty-seven patients were included. Average follow-up time was 4.06±0.83 years. Patients were exclusively male, with average age of 68.1±6.0 years, and the majority had a history of smoking (n=52, 78%), hypertension (n=52, 78%), and dyslipidemia (n=48, 72%). Average baseline aneurysm diameter was 44.0±3.2 mm and average growth rate was 0.11±0.31 mm/year, with no difference in growth rate between patients with initial diameter ≤45 vs. >45 mm. Only 3 patients experienced clinically significant changes in diameter with magnitude greater than 5% of baseline.

CONCLUSIONS

In this veteran population, most patients did not experience significant annual aneurysm growth over up to 5 years of follow-up, regardless of initial diameter. Thus, in the modern era, aTAAs may not grow as quickly as previously described, which will be important in determining appropriate intervals for aneurysm surveillance based upon risk-benefit ratio.

Atlas-Based Evaluation of Hemodynamic in Ascending Thoracic Aortic Aneurysms

Atlas-based analyses of patients with cardiovascular diseases have recently been explored to understand the mechanistic link between shape and pathophysiology. The construction of probabilistic atlases is based on statistical shape modeling (SSM) to assess key anatomic features for a given patient population. Such an approach is relevant to study the complex nature of the ascending thoracic aortic aneurysm (ATAA) as characterized by different patterns of aortic shapes and valve phenotypes. This study was carried out to develop an SSM of the dilated aorta with both bicuspid aortic valve (BAV) and tricuspid aortic valve (TAV), and then assess the computational hemodynamic of virtual models obtained by the deformation of the mean template for specific shape boundaries (i.e., ±1.5 standard deviation, σ). Simulations demonstrated remarkable changes in the velocity streamlines, blood pressure, and fluid shear stress with the principal shape modes such as the aortic size (Mode 1), vessel tortuosity (Mode 2), and aortic valve morphologies (Mode 3). The atlas-based disease assessment can represent a powerful tool to reveal important insights on ATAA-derived hemodynamic, especially for aneurysms which are considered to have borderline anatomies, and thus challenging decision-making. The utilization of SSMs for creating probabilistic patient cohorts can facilitate the understanding of the heterogenous nature of the dilated ascending aorta.

Mechanical characterization of dissected and dilated human ascending aorta using Fung-type hyperelastic models with pre-identified initial tangent moduli for low-stress distensibility

Ascending aortic dissection (AD) is a potentially fatal vascular disease associated with degradation and fragmentation of the elastic fibers in the aortic media, increasing low-stress distensibility, and a dilated aorta may lead to dissection. In this study, a Fung-type hyperelastic model was formulated incorporating the initial tangent moduli (ITM) of stress-strain curves as an index of low-stress distensibility. ITM were correlated with the material constants by linearizing incompressible stress-strain relationships at zero strain. For uniaxial loading tests, the robustness of the material constants was examined in the stress ranges of 0-200, 0-180, and 0-160 kPa and to the ITM values of 100%, 95%, and 90%. Examination revealed stable changes in the material constants of 80% of the specimens. For equibiaxial stretch tests, the material constants were determined for each curve of the isotropic and anisotropic deformation groups by pre-identifying the ITM and minimizing fitting errors using isotropic or anisotropic models. The errors for all groups were <6% using a transversely isotropic model, and <10% for an orthotropic model. Comparisons with experimental curves showed that Fung-type models described both the ITM and significant stiffening at high stress levels. The mechanical characteristics of the aorta in the stage prior/posterior to dissection is such that while hardening occurs under both low- and high-stress levels with an increase in collagen content as an aging response, softening occurs under low-stress conditions due to histological abnormalities such as elastin deficiency and fragmentation. Numerical simulations using Fung-type models implied that elastic fiber degeneration and fragmentation in AD tissues reduced not only the low-stress stiffness but also the elastic stiffness with superimposed shear. The latter stiffness was modulated by the stiffening at high stress levels in tensile deformation behavior and normal-strain state under physiological loading conditions, and therefore provides further insight into wall rupture.

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.

Computation of a probabilistic and anisotropic failure metric on the aortic wall using a machine learning-based surrogate model

Scalar-valued failure metrics are commonly used to assess the risk of aortic aneurysm rupture and dissection, which occurs under hypertensive blood pressures brought on by extreme emotional or physical stress. To compute failure metrics under an elevated blood pressure, a classical patient-specific computer model consists of multiple computation steps involving inverse and forward analyses. These classical procedures may be impractical for time-sensitive clinical applications that require prompt feedback to clinicians. In this study, we developed a machine learning-based surrogate model to directly predict a probabilistic and anisotropic failure metric, namely failure probability (FP), on the aortic wall using aorta geometries at the systolic and diastolic phases. Ascending thoracic aortic aneurysm (ATAA) geometries of 60 patients were obtained from their CT scans, and biaxial mechanical testing data of ATAA tissues from 79 patients were collected. Finite element simulations were used to generate datasets for training, validation, and testing of the ML-surrogate model. The testing results demonstrated that the ML-surrogate can compute the maximum FP failure metric, with 0.42% normalized mean absolute error, in 1 s. To compare the performance of the ML-predicted probabilistic FP metric with other isotropic or deterministic metrics, a numerical case study was performed using synthetic "baseline" data. Our results showed that the probabilistic FP metric had more discriminative power than the deterministic Tsai-Hill metric, isotropic maximum principal stress, and aortic diameter criterion.

Development of an FEA framework for analysis of subject-specific aortic compliance based on 4D flow MRI

This paper presents a subject-specific in-silico framework in which we uncover the relationship between the spatially varying constituents of the aorta and the non-linear compliance of the vessel during the cardiac cycle uncovered through our MRI investigations. A microstructurally motivated constitutive model is developed, and simulations reveal that internal vessel contractility, due to pre-stretched elastin and actively generated smooth muscle cell stress, must be incorporated, along with collagen strain stiffening, in order to accurately predict the non-linear pressure-area relationship observed in-vivo. Modelling of elastin and smooth muscle cell contractility allows for the identification of the reference vessel configuration at zero-lumen pressure, in addition to accurately predicting high- and low-compliance regimes under a physiological range of pressures. This modelling approach is also shown to capture the key features of elastin digestion and SMC activation experiments. The volume fractions of the constituent components of the aortic material model were computed so that the in-silico pressure-area curves accurately predict the corresponding MRI data at each location. Simulations reveal that collagen and smooth muscle volume fractions increase distally, while elastin volume fraction decreases distally, consistent with reported histological data. Furthermore, the strain at which collagen transitions from low to high stiffness is lower in the abdominal aorta, again supporting the histological finding that collagen waviness is lower distally. The analyses presented in this paper provide new insights into the heterogeneous structure-function relationship that underlies aortic biomechanics. Furthermore, this subject-specific MRI/FEA methodology provides a foundation for personalised in-silico clinical analysis and tailored aortic device development. STATEMENT OF SIGNIFICANCE: This study provides a significant advance in in-silico medicine by capturing the structure/function relationship of the subject-specific human aorta presented in our previous MRI analyses. A physiologically based aortic constitutive model is developed, and simulations reveal that internal vessel contractility must be incorporated, along with collagen strain stiffening, to accurately predict the in-vivo non-linear pressure-area relationship. Furthermore, this is the first subject-specific model to predict spatial variation in the volume fractions of aortic wall constituents. Previous studies perform phenomenological hyperelastic curve fits to medical imaging data and ignore the prestress contribution of elastin, collagen, and SMCs and the associated zero-pressure reference state of the vessel. This novel MRI/FEA framework can be used as an in-silico diagnostic tool for the early stage detection of aortic pathologies.

Influence of Material Model and Aortic Root Motion in Finite Element Analysis of Two Exemplary Cases of Proximal Aortic Dissection

The risk of type-A dissection is increased in subjects with connective tissue disorders and dilatation of the proximal aorta. The location and extents of vessel wall tears in these patients could be potentially missed during prospective imaging studies. The objective of this study is to estimate the distribution of systolic wall stress in two exemplary cases of proximal dissection using finite element analysis (FEA) and evaluate the sensitivity of the distribution to the choice of anisotropic material model and root motion. FEA was performed for predissection aortas, without prior knowledge of the origin and extents of vessel wall tear. The stress distribution was evaluated along the wall tear in the postdissection aortas. The stress distribution was compared for the Fung and Holzapfel models with and without root motion. For the subject with spiral dissection, peak stress coincided with the origin of the tear in the sinotubular junction. For the case with root dissection, maximum stress was obtained at the distal end of the tear. The FEA predicted tear pressure was 20% higher for the subject with root dissection as compared to the case with spiral dissection. The predicted tear pressure was higher (9-11%) for root motions up to 10 mm. The Holzapfel model predicted a tear pressure that was lower (8-15%) than the Fung model. The FEA results showed that both material response and root motion could potentially influence the predicted dissection pressure of the proximal aorta at least for conditions tested in this study.

High Wall Shear Stress can Predict Wall Degradation in Ascending Aortic Aneurysms: An Integrated Biomechanics Study

Background: Blood flow patterns can alter material properties of ascending thoracic aortic aneurysms (ATAA) via vascular wall remodeling. This study examines the relationship between wall shear stress (WSS) obtained from image-based computational modelling with tissue-derived mechanical and microstructural properties of the ATAA wall using segmental analysis. Methods: Ten patients undergoing surgery for ATAA were recruited. Exclusions: bicuspid aortopathy, connective tissue disease. All patients had pre-operative 4-dimensional flow magnetic resonance imaging (4D-MRI), allowing for patient-specific computational fluid dynamics (CFD) analysis and anatomically precise WSS mapping of ATAA regions (6-12 segments per patient). ATAA samples were obtained from surgery and subjected to region-specific tensile and peel testing (matched to WSS segments). Computational pathology was used to characterize elastin/collagen abundance and smooth muscle cell (SMC) count. Results: Elevated values of WSS were predictive of: reduced wall thickness [coef -0.0489, 95% CI (-0.0905, -0.00727), p = 0.022] and dissection energy function (longitudinal) [-15,0, 95% CI (-33.00, -2.98), p = 0.048]. High WSS values also predicted higher ultimate tensile strength [coef 0.136, 95% CI (0 0.001, 0.270), p = 0.048]. Additionally, elevated WSS also predicted a reduction in elastin levels [coef -0.276, 95% (CI -0.531, -0.020), p = 0.035] and lower SMC count ([oef -6.19, 95% CI (-11.41, -0.98), p = 0.021]. WSS was found to have no effect on collagen abundance or circumferential mechanical properties. Conclusions: Our study suggests an association between elevated WSS values and aortic wall degradation in ATAA disease. Further studies might help identify threshold values to predict acute aortic events.

A Novel Anisotropic Failure Criterion With Dispersed Fiber Orientations for Aortic Tissues

Accurate failure criteria play a fundamental role in biomechanical analyses of aortic wall rupture and dissection. Experimental investigations have demonstrated a significant difference of aortic wall strengths in the circumferential and axial directions. Therefore, the isotropic von Mises stress and maximum principal stress, commonly used in computational analysis of the aortic wall, are inadequate for modeling of anisotropic failure properties. In this study, we propose a novel stress-based anisotropic failure criterion with dispersed fiber orientations. In the new failure criterion, the overall failure metric is computed by using angular integration (AI) of failure metrics in all directions. Affine rotations of fiber orientations due to finite deformation are taken into account in an anisotropic hyperelastic constitutive model. To examine fitting capability of the failure criterion, a set of off-axis uniaxial tension tests were performed on aortic tissues of four porcine individuals and 18 human ascending thoracic aortic aneurysm (ATAA) patients. The dispersed fiber failure criterion demonstrates a good fitting capability with the off-axis testing data. Under simulated biaxial stress conditions, the dispersed fiber failure criterion predicts a smaller failure envelope comparing to those predicted by the traditional anisotropic criteria without fiber dispersion, which highlights the potentially important role of fiber dispersion in the failure of the aortic wall. Our results suggest that the deformation-dependent fiber orientations need to be considered when wall strength determined from uniaxial tests are used for in vivo biomechanical analysis. More investigations are needed to determine biaxial failure properties of the aortic wall.

Matrix Metalloproteinase-2 Isoforms Differ within the Aortic Wall of Ascending Aortic Aneurysms Associated with Bicuspid Aortic Valve

The pathogenesis of ascending thoracic aortic aneurysm (aTAA) is thought to differ between patients with bicuspid aortic valve (BAV) and tricuspid aortic valve (TAV), and one of the causes is different hemodynamics. Influenced by hemodynamics, the tissue levels of proteins associated with aTAA might differ between aTAAs with BAV and TAV and between different localities within the aortic wall. We therefore analyzed aTAA tissue levels of MMP-2 (matrix metalloproteinase-2) isoforms (Pro-MMP-2, active MMP-2, and total MMP-2) and tissue levels of MMP-14, TIMP-2 (tissue inhibitor of metalloproteinase-2), MMP-9, and TIMP-1 in 19 patients with BAV and 23 patients with TAV via gelatin zymography and enzyme-linked immunosorbent assay (ELISA), respectively. TAV and BAV groups' protein levels did not differ significantly. Whereas the TAV group exhibited no significant differences in protein levels between the aneurysm's anterior and posterior parts, the BAV group revealed significantly higher levels of Pro-MMP-2, total MMP-2, and TIMP-2 in the aneurysm's posterior parts (mean Pro-MMP-2 200.52 arbitrary units (AU) versus 161.12 AU, p=0.007; mean total MMP-2 235.22 AU versus 193.68 AU, p=0.002; mean TIMP-2 26.90 ng/ml versus 25.36 ng/ml, p=0.009), whereas the other proteins did not differ significantly within the aortic wall. Thus, MMPs are distributed more heterogeneously within the aortic wall of aTAAs associated with BAV than in those associated with TAV, which is a new aspect for understanding the underlying pathogenesis. This heterogeneous protein level distribution might be attributable to differences in the underlying pathogenesis, especially hemodynamics. This result is important for further studies as it will be essential to specify the location of samples to ensure data comparability regarding the main goals of understanding the pathogenesis of aTAA, optimizing treatments, and establishing a screening method for its potentially deadly complications.

Wall Stress Distribution in Bicuspid Aortic Valve-Associated Ascending Thoracic Aortic Aneurysms

BACKGROUND

Bicuspid aortic valve-associated ascending thoracic aortic aneurysms (BAV-aTAAs) carry a risk of acute type A dissection. Biomechanically, dissection may occur when wall stress exceeds wall strength. Our aim was to develop patient-specific computational models of BAV-aTAAs to determine magnitudes of wall stress by anatomic regions.

METHODS

Patients with BAV-aTAA diameter greater than 4.5 cm (n = 41) underwent electrocardiogram-gated computed tomography angiography. Three-dimensional aneurysm geometries were reconstructed after accounting for prestress and loaded to systemic pressure. Finite element analyses were performed with fiber-embedded hyperelastic material model using LS-DYNA software (LSTC Inc, Livermore, CA) to obtain wall stress distributions. The 99th percentile longitudinal and circumferential stresses were determined at systole.

RESULTS

The 99th percentile longitudinal wall stresses for BAV-aTAAs at sinuses of Valsalva, sinotubular junction (STJ), and ascending aorta were 361 ± 59.8 kPa, 295 ± 67.2 kPa, and 224 ± 37.6 kPa, respectively, with significant differences in ascending aorta vs sinuses (P< 1 × 10-13) and STJ (P < 1 × 10-6). The 99th percentile circumferential wall stresses were 474 ± 88.2 kPa, 634 ± 181.9 kPa, and 381 ± 54.0 kPa for sinuses, the STJ, and the ascending aorta, respectively, with significant differences in the ascending aorta vs sinuses (P = .002) and STJ (P < 1 × 10-13).

CONCLUSIONS

Wall stresses, both circumferential and longitudinal, were greater in the aortic root, sinuses, and STJ than in the ascending aorta on BAV-aTAAs. These results fill a fundamental knowledge gap regarding biomechanical stress distribution in BAV-aTAA patients, which when related to wall strength may provide prognostication of aTAA dissection risk by patient-specific modeling.

Multimodality Imaging-Based Characterization of Regional Material Properties in a Murine Model of Aortic Dissection

Chronic infusion of angiotensin-II in atheroprone (ApoE-/-) mice provides a reproducible model of dissection in the suprarenal abdominal aorta, often with a false lumen and intramural thrombus that thickens the wall. Such lesions exhibit complex morphologies, with different regions characterized by localized changes in wall composition, microstructure, and properties. We sought to quantify the multiaxial mechanical properties of murine dissecting aneurysm samples by combining in vitro extension-distension data with full-field multimodality measurements of wall strain and thickness to inform an inverse material characterization using the virtual fields method. A key advance is the use of a digital volume correlation approach that allows for characterization of properties not only along and around the lesion, but also across its wall. Specifically, deformations are measured at the adventitial surface by tracking motions of a speckle pattern using a custom panoramic digital image correlation technique while deformations throughout the wall and thrombus are inferred from optical coherence tomography. These measurements are registered and combined in 3D to reconstruct the reference geometry and compute the 3D finite strain fields in response to pressurization. Results reveal dramatic regional variations in material stiffness and strain energy, which reflect local changes in constituent area fractions obtained from histology but emphasize the complexity of lesion morphology and damage within the dissected wall. This is the first point-wise biomechanical characterization of such complex, heterogeneous arterial segments. Because matrix remodeling is critical to the formation and growth of these lesions, we submit that quantification of regional material properties will increase the understanding of pathological mechanical mechanisms underlying aortic dissection.

Ascending aorta mechanics in bicuspid aortopathy: controversy or fact?

Bicuspid aortic valve is the most common congenital cardiovascular defect, often associated with proximal aortic dilatation, and the ideal management strategy is debated. The inconsistency in previous and present guideline recommendations emphasizes the insufficiency of the maximal diameter as the sole criterion for prophylactic repair. Our ability to guide clinical decisions may improve through an understanding of the mechanical properties of ascending thoracic aortic aneurysms in bicuspid compared to tricuspid aortic valve patients and non-aneurysmal aortas, because dissection and rupture are aortic wall mechanical failures. Such an understanding of the mechanical properties has been attempted by several authors, and this article addresses whether there is a controversy in the accumulated knowledge. The available mechanical studies are briefly reviewed, discussing factors such as age, sex, and the region of mechanical examination that may be responsible for the lack of unanimity in the reported findings. The rationale for acquiring layer-specific properties is presented along with the main results from our recent study. No mechanical vulnerability of ascending thoracic aortic aneurysms was evidenced in bicuspid aortic valve patients, corroborating present conservative guidelines concerning the management of bicuspid aortopathy. Weakening and additional vulnerability was evidenced in aged patients and those with coexisting valve pathology, aortic root dilatation, hypertension, and hyperlipidemia. Discussion of these results from age- and sex-matched subjects, accounting for the region- and layer-specific aortic heterogeneity, in relation to intact wall results and histologic confirmation, helps to reconcile previous findings and affords a universal interpretation of ascending aorta mechanics in bicuspid aortopathy.

A feasibility study of deep learning for predicting hemodynamics of human thoracic aorta

Numerical analysis methods including finite element analysis (FEA), computational fluid dynamics (CFD), and fluid-structure interaction (FSI) analysis have been used to study the biomechanics of human tissues and organs, as well as tissue-medical device interactions, and treatment strategies. However, for patient-specific computational analysis, complex procedures are usually required to set-up the models, and long computing time is needed to perform the simulation, preventing fast feedback to clinicians in time-sensitive clinical applications. In this study, by using machine learning techniques, we developed deep neural networks (DNNs) to directly estimate the steady-state distributions of pressure and flow velocity inside the thoracic aorta. After training on hemodynamic data from CFD simulations, the DNNs take as input a shape of the aorta and directly output the hemodynamic distributions in one second. The trained DNNs are capable of predicting the velocity magnitude field with an average error of 1.9608% and the pressure field with an average error of 1.4269%. This study demonstrates the feasibility and great potential of using DNNs as a fast and accurate surrogate model for hemodynamic analysis of large blood vessels.

Biomechanics of aortic wall failure with a focus on dissection and aneurysm: A review

Aortic dissections and aortic aneurysms are fatal events characterized by structural changes to the aortic wall. The maximum diameter criterion, typically used for aneurysm rupture risk estimations, has been challenged by more sophisticated biomechanically motivated models in the past. Although these models are very helpful for the clinicians in decision-making, they do not attempt to capture material failure. Following a short overview of the microstructure of the aorta, we analyze the failure mechanisms involved in the dissection and rupture by considering also traumatic rupture. We continue with a literature review of experimental studies relevant to quantify tissue strength. More specifically, we summarize more extensively uniaxial tensile, bulge inflation and peeling tests, and we also specify trouser, direct tension and in-plane shear tests. Finally we analyze biomechanically motivated models to predict rupture risk. Based on the findings of the reviewed studies and the rather large variations in tissue strength, we propose that an appropriate material failure criterion for aortic tissues should also reflect the microstructure in order to be effective. STATEMENT OF SIGNIFICANCE: Aortic dissections and aortic aneurysms are fatal events characterized by structural changes to the aortic wall. Despite the advances in medical, biomedical and biomechanical research, the mortality rates of aneurysms and dissections remain high. The present review article summarizes experimental studies that quantify the aortic wall strength and it discusses biomechanically motivated models to predict rupture risk. We identified contradictory observations and a large variation within and between data sets, which may be due to biological variations, different sample sizes, differences in experimental protocols, etc. Based on the findings of the reviewed literature and the rather large variations in tissue strength, it is proposed that an appropriate criterion for aortic failure should also reflect the microstructure.

Identification of in vivo nonlinear anisotropic mechanical properties of ascending thoracic aortic aneurysm from patient-specific CT scans

Accurate identification of in vivo nonlinear, anisotropic mechanical properties of the aortic wall of individual patients remains to be one of the critical challenges in the field of cardiovascular biomechanics. Since only the physiologically loaded states of the aorta are given from in vivo clinical images, inverse approaches, which take into account of the unloaded configuration, are needed for in vivo material parameter identification. Existing inverse methods are computationally expensive, which take days to weeks to complete for a single patient, inhibiting fast feedback for clinicians. Moreover, the current inverse methods have only been evaluated using synthetic data. In this study, we improved our recently developed multi-resolution direct search (MRDS) approach and the computation time cost was reduced to 1~2 hours. Using the improved MRDS approach, we estimated in vivo aortic tissue elastic properties of two ascending thoracic aortic aneurysm (ATAA) patients from pre-operative gated CT scans. For comparison, corresponding surgically-resected aortic wall tissue samples were obtained and subjected to planar biaxial tests. Relatively close matches were achieved for the in vivo-identified and ex vivo-fitted stress-stretch responses. It is hoped that further development of this inverse approach can enable an accurate identification of the in vivo material parameters from in vivo image data.

A deep learning approach to estimate stress distribution: a fast and accurate surrogate of finite-element analysis

Structural finite-element analysis (FEA) has been widely used to study the biomechanics of human tissues and organs, as well as tissue-medical device interactions, and treatment strategies. However, patient-specific FEA models usually require complex procedures to set up and long computing times to obtain final simulation results, preventing prompt feedback to clinicians in time-sensitive clinical applications. In this study, by using machine learning techniques, we developed a deep learning (DL) model to directly estimate the stress distributions of the aorta. The DL model was designed and trained to take the input of FEA and directly output the aortic wall stress distributions, bypassing the FEA calculation process. The trained DL model is capable of predicting the stress distributions with average errors of 0.492% and 0.891% in the Von Mises stress distribution and peak Von Mises stress, respectively. This study marks, to our knowledge, the first study that demonstrates the feasibility and great potential of using the DL technique as a fast and accurate surrogate of FEA for stress analysis.

Computational modeling of bicuspid aortopathy: Towards personalized risk strategies

This paper describes current advances on the application of in-silico for the understanding of bicuspid aortopathy and future perspectives of this technology on routine clinical care. This includes the impact that artificial intelligence can provide to develop computer-based clinical decision support system and that wearable sensors can offer to remotely monitor high-risk bicuspid aortic valve (BAV) patients. First, we discussed the benefit of computational modeling by providing tangible examples of in-silico software products based on computational fluid-dynamic (CFD) and finite-element method (FEM) that are currently transforming the way we diagnose and treat cardiovascular diseases. Then, we presented recent findings on computational hemodynamic and structural mechanics of BAV to highlight the potentiality of patient-specific metrics (not-based on aortic size) to support the clinical-decision making process of BAV-associated aneurysms. Examples of BAV-related personalized healthcare solutions are illustrated.

Three-dimensional modeling of Marfan syndrome with elastic and hyperelastic materials assumptions using fluid-structure interaction

BACKGROUND

Marfan syndrome (MFS) is a genetic disorder of the connective tissue. It most prominently influences the skeletal, cardiovascular, and ocular systems, but all fibrous connective tissue throughout the body can be affected as well.

OBJECTIVE

This study aims to investigate a realistic three-dimensional model of an aorta of a specific patient suffering from MFS by considering elastic and hyperelastic materials for the tissue using fluid-structure interaction (FSI).

METHODS

Isotropic linear elastic and Mooney-Rivlin hyperelastic assumptions are implemented. Linear and nonlinear mechanical properties of the aneurysmal MFS aortic tissue are derived from an uniaxial experimental test.

RESULTS

Vortex generation in the vicinity of the aneurysm region in both elastic and hyperelastic models and the maximum blood velocity at peak flow time is calculated as 0.517 and 0.533 m/s for the two materials, respectively. The blood pressure is not significantly different between the two models (±8 Pa) and the blood pressure difference between the points in the horizontal plane of the aneurysm region is obtained as ±10 Pa for both models. The maximum von Mises stress for the hyperelastic model (2.19 MPa) is 27% more than the elastic one (1.72 MPa) and takes place at the inner curvature and upper part of the aorta and somehow far from the aneurysm region. The wall shear stress (WSS) is also considered for the elastic and hyperelastic assumptions, which is 36.7 Pa for both elastic and hyperelastic models.

CONCLUSION

The aneurysm region in the MFS affects the blood flow and causes the vortex to be generated which consequently affects the blood flow in the downstream by adding some perturbations to the blood flow. The WSS is obtained to be lower in the aneurysm region compared to other regions which indicated vascular remodeling.

Estimation of in vivo constitutive parameters of the aortic wall using a machine learning approach

The patient-specific biomechanical analysis of the aorta requires the quantification of the in vivo mechanical properties of individual patients. Current inverse approaches have attempted to estimate the nonlinear, anisotropic material parameters from in vivo image data using certain optimization schemes. However, since such inverse methods are dependent on iterative nonlinear optimization, these methods are highly computation-intensive. A potential paradigm-changing solution to the bottleneck associated with patient-specific computational modeling is to incorporate machine learning (ML) algorithms to expedite the procedure of in vivo material parameter identification. In this paper, we developed an ML-based approach to estimate the material parameters from three-dimensional aorta geometries obtained at two different blood pressure (i.e., systolic and diastolic) levels. The nonlinear relationship between the two loaded shapes and the constitutive parameters are established by an ML-model, which was trained and tested using finite element (FE) simulation datasets. Cross-validations were used to adjust the ML-model structure on a training/validation dataset. The accuracy of the ML-model was examined using a testing dataset.

On the computation of in vivo transmural mean stress of patient-specific aortic wall

It is well known that residual deformations/stresses alter the mechanical behavior of arteries, e.g., the pressure-diameter curves. In an effort to enable personalized analysis of the aortic wall stress, approaches have been developed to incorporate experimentally derived residual deformations into in vivo loaded geometries in finite element simulations using thick-walled models. Solid elements are typically used to account for "bending-like" residual deformations. Yet, the difficulty in obtaining patient-specific residual deformations and material properties has become one of the biggest challenges of these thick-walled models. In thin-walled models, fortunately, static determinacy offers an appealing prospect that allows for the calculation of the thin-walled membrane stress without patient-specific material properties. The membrane stress can be computed using forward analysis by enforcing an extremely stiff material property as penalty treatment, which is referred to as the forward penalty approach. However, thin-walled membrane elements, which have zero bending stiffness, are incompatible with the residual deformations, and therefore, it is often stated as a limitation of thin-walled models. In this paper, by comparing the predicted stresses from thin-walled models and thick-walled models, we demonstrate that the transmural mean stress is approximately the same for the two models and can be readily obtained from in vivo clinical images without knowing the patient-specific material properties and residual deformations. Computation of patient-specific mean stress can be greatly simplified by using the forward penalty approach, which may be clinically valuable.

Predissection-derived geometric and distensibility indices reveal increased peak longitudinal stress and stiffness in patients sustaining acute type A aortic dissection: Implications for predicting dissection

OBJECTIVE

To assess ascending aortic distensibility and build geometry and distensibility-based patient-specific stress distribution maps in patients sustaining type A aortic dissection (TAAD) using predissection noninvasive imaging.

METHODS

Review of charts from patients undergoing surgical repair of TAAD (n = 351) led to the selection of a subset population (n = 7) with 2 or more predissection computed tomography angiography scans and echocardiograms at least 1 year before dissection. Ascending aortic wall biomechanical properties (aortic strain, distensibility, and stiffness) were compared with age- and size-matched nondissected nonaneurysmal controls. Patient-specific aortic strain served as an input in aortic geometry-based simulated 3-dimensional reconstructions to generate longitudinal and circumferential wall stress maps. Inspection of perioperative dissection scans and intraoperative visual examination confirmed primary tear locations.

RESULTS

Predissection echocardiography revealed ascending aortas of patients sustaining TAAD to exhibit decreased aortic wall strain (14.50 ± 1.13% vs 8.49 ± 1.08%; P < .01), decreased distensibility (4.26 ± 0.44 vs 2.39 ± 0.33 10^-6 cm²·dyne^-1; P < .01), increased stiffness (3.84 ± 0.24 vs 7.48 ± 1.05; P < .001), and increased longitudinal wall stress (246 ± 22 vs 172 ± 37 kPa; P < .01). There was no significant difference in circumferential wall stress. Predissection computed tomography angiography models revealed overlap between regions of increased longitudinal wall stress and primary tear sites.

CONCLUSIONS

Using predissection imaging, we identified increased stiffness and longitudinal wall stress in ascending aortas of patients with dissection. Patient-specific imaging-derived biomechanical property maps like these may be instrumental toward designing better prediction models of aortic dissection potential.

The evaluation of the aortic annulus displacement during cardiac cycle using magnetic resonance imaging

Background

The stress in the ascending aorta results from many biomechanical factors including the geometry of the vessel and its maximum dimensions, arterial blood pressure and longitudinal systolic stretching due to heart motion. The stretching of the ascending aorta resulting from the longitudinal displacement of the aortic annulus during the heart cycle has not been examined in the general population so far. The aim of the study is to evaluate this parameter using cardiovascular magnetic resonance (CMR) imaging in the general population in all age groups.

Methods

The cardiac magnetic resonance images of 73 patients were evaluated. The maximum distance to which the ventriculo-aortic junction was pulled by the contracting heart (LDAA – longitudinal displacement of the aortic annulus) was measured in the cine coronal sequences. Moreover, the maximum dimensions of the aortic root and the ascending aorta were assessed.

Results

The LDAA value was on average 11.6 ± 2.9 mm (range: 3-19 mm; 95% CI: 10.9–12.3 mm) and did not differ between males and females (11.8 ± 2.9 mm vs. 11.2 ± 2.9 mm, p = .408). The diameter of the ascending aorta was 32 ± 6.3 mm (range: 20-57 mm). The maximal dimension of the aortic root was 35 ± 5.1 mm (range: 18-42 mm). There was a statistically significant negative correlation between the LDAA and the age of patients (r = −.38, p = .001). There was no significant correlation between the LDAA and aortic root dimension (r = .1, p = .409) and between the LDAA and diameter of the ascending aorta (r = .16, p = .170).

Conclusions

Human aortic root and ascending aorta are significantly stretched during systole and the distance to which the aorta is stretched decreases with age. The measurement of the longitudinal displacement of the aortic annulus using the CMR is feasible and reproducible.