A Numerical Implementation to Predict Residual Strains from the Homogeneous Stress Hypothesis with Application to Abdominal Aortic Aneurysms

Wall stress analysis of abdominal aortic aneurysm (AAA) is a promising method of identifying AAAs at high risk of rupture. However, neglecting residual strains (RS) in the load-free configuration of patient-specific finite element analysis models is a sever limitation that strongly affects the computed wall stresses. Although several methods for including RS have been proposed, they cannot be directly applied to patient-specific AAA simulations. RS in the AAA wall are predicted through volumetric tissue growth that aims at satisfying the homogeneous stress hypothesis at mean arterial pressure load. Tissue growth is interpolated linearly across the wall thickness and aneurysm tissues are described by isotropic constitutive formulations. The total deformation is multiplicatively split into elastic and growth contributions, and a staggered schema is used to solve the field variables. The algorithm is validated qualitatively at a cylindrical artery model and then applied to patient-specific AAAs (n = 5). The induced RS state is fully three-dimensional and in qualitative agreement with experimental observations, i.e., wall strips that were excised from the load-free wall showed stress-releasing-deformations that are typically seen in laboratory experiments. Compared to RS-free simulations, the proposed algorithm reduced the von Mises stress gradient across the wall by a tenfold. Accounting for RS leads to homogenized wall stresses, which apart from reducing the peak wall stress (PWS) also shifted its location in some cases. The present study demonstrated that the homogeneous stress hypothesis can be effectively used to predict RS in the load-free configuration of the vascular wall. The proposed algorithm leads to a fast and robust prediction of RS, which is fully capable for a patient-specific AAA rupture risk assessment. Neglecting RS leads to non-realistic wall stress values that severely overestimate the PWS.     

Non-Invasive Determination of Zero-Pressure Geometry of Arterial Aneurysms

Arterial aneurysms are in a pre-deformed state in vivo under non-zero pressure. The ability to determine their zero pressure geometry may help in improving accuracy of determination of stress distribution and reverse estimation of material properties from dynamic imaging data. An approximate method to recover the zero pressure geometry of the AAA is proposed. This method is motivated by the observation that the patterns in displacement field for a given AAA are strikingly consistent in an AAA under all physiological pressures. The basic principle is to leverage this observation to iteratively identify the geometry that when subjected to the in vivo pressure, will recover the geometry reconstructed from in vivo imaging. The methodology is demonstrated and validated using patient-specific AAA models.     

Role of Re-entry Tears on the Dynamics of Type B Dissection Flap

Mortality during follow-up after acute Type B aortic dissection is substantial with aortic expansion observed in over 59% of the patients. Lumen pressure differential is considered a prime contributing factor for aortic dilation after propagation. The objective of the study was to evaluate the relationship between changes in vessel geometry with and without lumen pressure differential post propagation in an ex vivo porcine model with comparison with patient clinical data. A pulse duplicator system was utilized to propagate the dissection within descending thoracic porcine aortic vessels for set proximal (%circumference of the entry tear: 40%, axial length: 2 cm) and re-entry (50% of distal vessel circumference) tear geometry. Measurements of lumen pressure differential were made along with quantification of vessel geometry (n = 16). The magnitude of mean lumen pressure difference measured after propagation was low (~ 5 mmHg) with higher pressures measured in false lumen and as anticipated the pressure difference approached zero after the creation of distal re-entry tear. False lumen Dissection Ratio (FDR) defined as arc length of dissected wall divided by arc length of dissection flap, had mean value of 1.59 ± 0.01 at pressure of 120/80 mmHg post propagation with increasing values with increase in pulse pressure that was not rescued with the creation of distal re-entry tear (p < 0.01). An average FDR of 1.87 ± 0.27 was measured in patients with acute Type B dissection. Higher FDR value (FDR = 1 implies zero dissection) in the presence of distal re-entry tear demonstrates an acute change in vessel morphology in response to the dissection independent of local pressure changes challenges the re-apposition of the aortic wall.     

The effect of angulation in abdominal aortic aneurysms: fluid–structure interaction simulations of idealized geometries

Abdominal aortic aneurysm (AAA) represents a degenerative disease process of the abdominal aorta that results in dilation and permanent remodeling of the arterial wall. A fluid structure interaction (FSI) parametric study was conducted to evaluate the progression of aneurysmal disease and its possible implications on risk of rupture. Two parametric studies were conducted using (i) the iliac bifurcation angle and (ii) the AAA neck angulation. Idealized streamlined AAA geometries were employed. The simulations were carried out using both isotropic and anisotropic wall material models. The parameters were based on CT scans measurements obtained from a population of patients. The results indicate that the peak wall stresses increased with increasing iliac and neck inlet angles. Wall shear stress (WSS) and fluid pressure were analyzed and correlated with the wall stresses for both sets of studies. An adaptation response of a temporary reduction of the peak wall stresses seem to correlate to a certain extent with increasing iliac angles. For the neck angulation studies it appears that a breakdown from symmetric vortices at the AAA inlet into a single larger vortex significantly increases the wall stress. Our parametric FSI study demonstrates the adaptation response during aneurysmal disease progression and its possible effects on the AAA risk of rupture. This dependence on geometric parameters of the AAA can be used as an additional diagnostic tool to help clinicians reach informed decisions in establishing whether a risky surgical intervention is warranted.     

A novel approach for local abdominal aortic aneurysm growth quantification

Although aneurysm size still remains the most accepted predictor of rupture risk, abdominal aortic aneurysms (AAAs) with maximum diameter smaller than 5 cm may also rupture. Growth rate is an additional marker for rupture risk as it potentially reflects an undesirable wall remodeling that leads to fast regional growth. Currently, an indication for surgery is an expansion rate >10 mm/year, measured as change in maximum diameter over time. However, as AAA expansion is non-uniform, it is questionable whether measurement of maximum diameter change over time can capture increased localized remodeling activity. A method for estimating AAA surface area growth is introduced, providing a better measure of local wall deformation. The proposed approach is based on the non-rigid iterative closest point algorithm. Optimization and validation is performed using 12 patient-specific AAA geometries artificially deformed to produce a target surface with known nodal displacements. Mesh density sensitivity, range of uncertainty, and method limitations are discussed. Application to ten AAA patient-specific follow-ups suggested that maximum diameter growth does not correlate strongly with the maximum surface growth (R ² = 0.614), which is not always colocated with maximum diameter, or uniformly distributed. Surface growth quantification could reinforce the quality of aneurysm surveillance programs.     

腹主动脉瘤的数值计算模型比较研究

目的分别采用纯流体模型和流固耦合模型来计算腹主动脉瘤的血流动力学特征,比较两种数值模型的不同,并讨论在研究腹主动脉瘤中的应用。方法使用Gambit 2.2.30和COMSOL Multiphysics 4.2建立腹主动脉瘤的理想模型,分别基于有限体的方法分析纯流体模型,基于任意拉格朗日-欧拉算法(Arbitrary Lagrangian-Eulerian)计算流固耦合模型。结果同样的入口速度下,纯流体模型出现4个涡流和6个局部压力集中;流固耦合模型只有2个涡流和局部压力集中,且涡流中心更接近腹主动脉瘤的远端。在边界层分离点、血流回帖位置以及腹主动脉瘤的近端和远端,两种模型均出现壁剪切力极值。血管壁的最大形变和最大壁应力出现在腹主动脉瘤的近端和远端。结论两种模型的涡流个数和涡流中心的位置均不一样,与瘤体的生长有着密切的关联;流固耦合模型中的最大壁剪切力比纯流体模型要小36%;最大壁应力和最大血管壁的形变量与出口血压呈正相关。在研究血管瘤生长与血流动力学的关系时需要考虑使用流固耦合模型。     

A patient-specific computational model of fluid-structure interaction in abdominal aortic aneurysms

It is generally believed that knowledge of the wall stress distribution could help to find better rupture risk predictors of abdominal aortic aneurysms (AAAs). Although AAA wall stress results from combined action between blood, wall and intraluminal thrombus, previously published models for patient-specific assessment of the wall stress predominantly did not include fluid-dynamic effects. In order to facilitate the incorporation of fluid–structure interaction in the assessment of AAA wall stress, in this paper, a method for generating patient-specific hexahedral finite element meshes of the AAA lumen and wall is presented. The applicability of the meshes is illustrated by simulations of the wall stress, blood velocity distribution and wall shear stress in a characteristic AAA. The presented method yields a flexible, semi-automated approach for generating patient-specific hexahedral meshes of the AAA lumen and wall with predefined element distributions. The combined fluid/solid mesh allows for simulations of AAA blood dynamics and AAA wall mechanics and the interaction between the two. The mechanical quantities computed in these simulations need to be validated in a clinical setting, after which they could be included in clinical trials in search of risk factors for AAA rupture.     

The Effects of Anisotropy on the Stress Analyses of Patient-Specific Abdominal Aortic Aneurysms

The local dilation of the infrarenal abdominal aorta, termed an abdominal aortic aneurysm (AAA), is often times asymptomatic and may eventually result in rupture—an event associated with a significant mortality rate. The estimation of in-vivo stresses within AAAs has been proposed as a useful tool to predict the likelihood of rupture. For the current work, a previously-derived anisotropic relation for the AAA wall was implemented into patient-specific finite element simulations of AAA. There were 35 AAAs simulated in the current work which were broken up into three groups: elective repairs (n = 21), non-ruptured repairs (n = 5), and ruptured repairs (n = 9). Peak stresses and strains were compared using the anisotropic and isotropic constitutive relations. There were significant increases in peak stress when using the anisotropic relationship (p < 0.001), even in the absence of the ILT (p = 0.014). Rutpured AAAs resulted in elevated peak stresses as compared to non-ruptured AAAs when using both the isotropic and anisotropic simulations, however these comparisons did not reach significance (p _ani = 0.55, p _iso = 0.73). While neither the isotropic or anisotropic simulations were able to significantly discriminate ruptured vs. non-ruptured AAAs, the lower p-value when using the anisotropic model suggests including it into patient-specific AAAs may help better identify AAAs at high risk.     

Simulation of abdominal aortic aneurysm growth with updating hemodynamic loads using a realistic geometry

Advances in modeling vascular tissue growth and remodeling (G&R) as well as medical imaging usher in a great potential for integrative computational mechanics to revolutionize the clinical treatment of cardiovascular diseases. A computational model of abdominal aortic aneurysm (AAA) enlargement has been previously developed based on realistic geometric models. In this work, we couple the computational simulation of AAA growth with the hemodynamics simulation in a stepwise, iterative manner and study the interrelation between the changes in wall shear stress (WSS) and arterial wall evolution. The G&R simulation computes a long-term vascular adaptation with constant hemodynamic loads, derived from the previous hemodynamics simulation, while the subsequent hemodynamics simulation computes hemodynamic loads on the vessel wall during the cardiac cycle using the evolved geometry. We hypothesize that low WSS promotes degradation of elastin during the progression of an AAA. It is shown that shear stress-induced degradation of elastin elevates wall stress and accelerates AAA enlargement. Regions of higher expansion correlate with regions of low WSS. Our results show that despite the crucial role of stress-mediated collagen turnover in compensating the loss of elastin, AAA enlargement can be accelerated through the effect of WSS. The present study is able to account for computational models of image-based AAA growth as well as important hemodynamic parameters with relatively low computational expense. We suggest that the present computational framework, in spite of its limitations, provides a useful foundation for future studies which may yield new insight into how aneurysms grow and rupture.     

Role of Pulse Pressure and Geometry of Primary Entry Tear in Acute Type B Dissection Propagation

The hemodynamic and geometric factors leading to propagation of acute Type B dissections are poorly understood. The objective is to elucidate whether geometric and hemodynamic parameters increase the predilection for aortic dissection propagation. A pulse duplicator set-up was used on porcine aorta with a single entry tear. Mean pressures of 100 and 180 mmHg were used, with pulse pressures ranging from 40 to 200 mmHg. The propagation for varying geometric conditions (%circumference of the entry tear: 15–65%, axial length: 0.5–3.2 cm) were tested for two flap thicknesses (1/3rd and 2/3rd of the thickness of vessel wall, respectively). To assess the effect of pulse and mean pressure on flap dynamics, the %true lumen (TL) cross-sectional area of the entry tear were compared. The % circumference for propagation of thin flap (47 ± 1%) was not significantly different (p = 0.14) from thick flap (44 ± 2%). On the contrary, the axial length of propagation for thin flap (2.57 ± 0.15 cm) was significantly different (p < 0.05) from the thick flap (1.56 ± 0.10 cm). TL compression was observed during systolic phase. For a fixed geometry of entry tear (%circumference = 39 ± 2%; axial length = 1.43 ± 0.13 cm), mean pressure did not have significant (p = 0.84) effect on flap movement. Increase in pulse pressure resulted in a significant change (p = 0.02) in %TL area (52 ± 4%). The energy acting on the false lumen immediately before propagation was calculated as 75 ± 9 J/m² and was fairly uniform across different specimens. Pulse pressure had a significant effect on the flap movement in contrast to mean pressure. Hence, mitigation of pulse pressure and restriction of flap movement may be beneficial in patients with type B acute dissections.     

The Effect of Material Model Formulation in the Stress Analysis of Abdominal Aortic Aneurysms

A reliable estimation of wall stress in Abdominal Aortic Aneurysms (AAAs), requires performing an accurate three-dimensional reconstruction of the medical image-based native geometry and modeling an appropriate constitutive law for the aneurysmal tissue material characterization. A recent study on the biaxial mechanical behavior of human AAA tissue specimens demonstrates that aneurysmal tissue behaves mechanically anisotropic. Results shown in this communication show that the peak wall stress is highly sensitive to the anisotropic model used for the stress analysis. In addition, the present investigation indicates that structural parameters (e.g., collagen fiber orientation) should be determined independently and not by means of non-linear fitting to stress–strain test data. Fiber orientation identified in this manner could lead to overestimated peak wall stresses.     

Towards A Noninvasive Method for Determination of Patient-Specific Wall Strength Distribution in Abdominal Aortic Aneurysms

The spatial distributions of both wall stress and wall strength are required to accurately evaluate the rupture potential for an individual abdominal aortic aneurysm (AAA). The purpose of this study was to develop a statistical model to non-invasively estimate the distribution of AAA wall strength. Seven parameters–namely age, gender, family history of AAA, smoking status, AAA size, local diameter, and local intraluminal thrombus (ILT) thickness–were either directly measured or recorded from the patients hospital chart. Wall strength values corresponding to these predictor variables were calculated from the tensile testing of surgically procured AAA wall specimens. Backwards–stepwise regression techniques were used to identify and eliminate insignificant predictors for wall strength. Linear mixed-effects modeling was used to derive a final statistical model for AAA wall strength, from which 95% confidence intervals on the model parameters were formed. The final statistical model for AAA wall strength consisted of the following variables: sex, family history, ILT thickness, and normalized transverse diameter. Demonstrative application of the model revealed a unique, complex wall strength distribution, with strength values ranging from 56 N/cm² to 133 N/cm². A four-parameter statistical model for the noninvasive estimation of patient-specific AAA wall strength distribution has been successfully developed. The currently developed model represents a first attempt towards the noninvasive assessment of AAA wall strength. Coupling this model with our stress analysis technique may provide a more accurate means to estimate patient-specific rupture potential of AAA.     

Quantification of Hemodynamics in Abdominal Aortic Aneurysms During Rest and Exercise Using Magnetic Resonance Imaging and Computational Fluid Dynamics

Abdominal aortic aneurysms (AAAs) affect 5–7% of older Americans. We hypothesize that exercise may slow AAA growth by decreasing inflammatory burden, peripheral resistance, and adverse hemodynamic conditions such as low, oscillatory shear stress. In this study, we use magnetic resonance imaging and computational fluid dynamics to describe hemodynamics in eight AAAs during rest and exercise using patient-specific geometric models, flow waveforms, and pressures as well as appropriately resolved finite-element meshes. We report mean wall shear stress (MWSS) and oscillatory shear index (OSI) at four aortic locations (supraceliac, infrarenal, mid-aneurysm, and suprabifurcation) and turbulent kinetic energy over the entire computational domain on meshes containing more than an order of magnitude more elements than previously reported results (mean: 9.0-million elements; SD: 2.3 M; range: 5.7–12.0 M). MWSS was lowest in the aneurysm during rest 2.5 dyn/cm² (SD: 2.1; range: 0.9–6.5), and MWSS increased and OSI decreased at all four locations during exercise. Mild turbulence existed at rest, while moderate aneurysmal turbulence was present during exercise. During both rest and exercise, aortic turbulence was virtually zero superior to the AAA for seven out of eight patients. We postulate that the increased MWSS, decreased OSI, and moderate turbulence present during exercise may attenuate AAA growth.     

In Vivo Three-Dimensional Surface Geometry of Abdominal Aortic Aneurysms

Abdominal aortic aneurysm (AAA) is a local, progressive dilation of the distal aorta that risks rupture until treated. Using the law of Laplace, in vivo assessment of AAA surface geometry could identify regions of high wall tensions as well as provide critical dimensional and shape data for customized endoluminal stent grafts. In this study, six patients with AAA underwent spiral computed tomography imaging and the inner wall of each AAA was identified, digitized, and reconstructed. A biquadric surface patch technique was used to compute the local principal curvatures, which required no assumptions regarding axisymmetry or other shape characteristics of the AAA surface. The spatial distribution of AAA principal curvatures demonstrated substantial axial asymmetry, and included adjacent elliptical and hyperbolic regions. To determine how much the curvature spatial distributions were dependent on tortuosity versus bulging, the effects of AAA tortuosity were removed from the three-dimensional (3D) reconstructions by aligning the centroids of each digitized contour to the z axis. The spatial distribution of principal curvatures of the modified 3D reconstructions were found to be largely axisymmetric, suggesting that much of the surface geometric asymmetry is due to AAA bending. On average, AAA surface area increased by 56% and abdominal aortic length increased by 27% over those for the normal aorta. Our results indicate that AAA surface geometry is highly complex and cannot be simulated by simple axisymmetric models, and suggests an equally complex wall stress distribution. © 1999 Biomedical Engineering Society. PAC99: 8719Rr, 8759Fm, 8757Gg     

On Coupling a Lumped Parameter Heart Model and a Three-Dimensional Finite Element Aorta Model

Aortic flow and pressure result from the interactions between the heart and arterial system. In this work, we considered these interactions by utilizing a lumped parameter heart model as an inflow boundary condition for three-dimensional finite element simulations of aortic blood flow and vessel wall dynamics. The ventricular pressure–volume behavior of the lumped parameter heart model is approximated using a time varying elastance function scaled from a normalized elastance function. When the aortic valve is open, the coupled multidomain method is used to strongly couple the lumped parameter heart model and three-dimensional arterial models and compute ventricular volume, ventricular pressure, aortic flow, and aortic pressure. The shape of the velocity profiles of the inlet boundary and the outlet boundaries that experience retrograde flow are constrained to achieve a robust algorithm. When the aortic valve is closed, the inflow boundary condition is switched to a zero velocity Dirichlet condition. With this method, we obtain physiologically realistic aortic flow and pressure waveforms. We demonstrate this method in a patient-specific model of a normal human thoracic aorta under rest and exercise conditions and an aortic coarctation model under pre- and post-interventions.     

3D Printed Modeling of the Mitral Valve for Catheter-Based Structural Interventions

As catheter-based structural heart interventions become increasingly complex, the ability to effectively model patient-specific valve geometry as well as the potential interaction of an implanted device within that geometry will become increasingly important. Our aim with this investigation was to combine the technologies of high-spatial resolution cardiac imaging, image processing software, and fused multi-material 3D printing, to demonstrate that patient-specific models of the mitral valve apparatus could be created to facilitate functional evaluation of novel trans-catheter mitral valve repair strategies. Clinical 3D transesophageal echocardiography and computed tomography images were acquired for three patients being evaluated for a catheter-based mitral valve repair. Target anatomies were identified, segmented and reconstructed into 3D patient-specific digital models. For each patient, the mitral valve apparatus was digitally reconstructed from a single or fused imaging data set. Using multi-material 3D printing methods, patient-specific anatomic replicas of the mitral valve were created. 3D print materials were selected based on the mechanical testing of elastomeric TangoPlus materials (Stratasys, Eden Prairie, Minnesota, USA) and were compared to freshly harvested porcine leaflet tissue. The effective bending modulus of healthy porcine MV tissue was significantly less than the bending modulus of TangoPlus (p < 0.01). All TangoPlus varieties were less stiff than the maximum tensile elastic modulus of mitral valve tissue (3697.2 ± 385.8 kPa anterior leaflet; 2582.1 ± 374.2 kPa posterior leaflet) (p < 0.01). However, the slopes of the stress-strain toe regions of the mitral valve tissues (532.8 ± 281.9 kPa anterior leaflet; 389.0 ± 156.9 kPa posterior leaflet) were not different than those of the Shore 27, Shore 35, and Shore 27 with Shore 35 blend TangoPlus material (p > 0.95). We have demonstrated that patient-specific mitral valve models can be reconstructed from multi-modality imaging datasets and fabricated using the multi-material 3D printing technology and we provide two examples to show how catheter-based repair devices could be evaluated within specific patient 3D printed valve geometry. However, we recognize that the use of 3D printed models for the development of new therapies, or for specific procedural training has yet to be defined.     

The Quasi-Static Failure Properties of the Abdominal Aortic Aneurysm Wall Estimated by a Mixed Experimental-Numerical Approach

Assessing the risk for abdominal aortic aneurysm (AAA) rupture is critical in the management of aneurysm patients and an individual assessment is possible with the biomechanical rupture risk assessment. Such an assessment could potentially be improved by a constitutive AAA wall model that accounts for irreversible damage-related deformations. Because of that the present study estimated the elastic and inelastic properties of the AAA wall through a mixed experimental-numerical approach. Specifically, finite element (FE) models of bone-shaped tensile specimens were used to merge data from failure testing of the AAA wall with their measured collagen orientation distribution. A histo-mechanical constitutive model for collagen fibers was employed, where plastic fibril sliding determined not only remaining deformations but also weakening of the fiber. The developed FE models were able to replicate the experimentally recorded load–displacement property of all 16 AAA wall specimens that were investigated in the study. Tensile testing in longitudinal direction of the AAA defined a Cauchy strength of 569(SD 411) kPa that was reached at a stretch of 1.436(SD 0.118). The stiffness and strength of specimens decreased with the wall thickness and were elevated (p = 0.018; p = 0.030) in patients with chronic obstructive pulmonary disease (COPD). Smoking affected the tissue parameters that were related to the irreversible deformation response, and no correlation with gender and age was found. The observed effects on the biomechanical properties of the AAA wall could have long-term consequences for the management of aneurysm patients, i.e., specifically they might influence future AAA rupture risk assessments. However, in order to design appropriate clinical validation studies our findings should firstly be verified in a larger patient cohort.     

腹主动脉瘤几何形态对血液动力学影响的三维数值分析

目的研究腹主动脉瘤不同形态学对瘤内血液动力学的影响,为临床预估动脉瘤的破裂提供参考。方法根据动脉瘤影像学上的特点建立不同几何形态的数学模型,采用计算流体动力学(CFD)方法,在周期性脉动速度入流、刚性壁面以及血液为牛顿流体的条件下,对一个心动周期内瘤内流场进行数值分析研究,比较不同几何形态腹主动脉瘤内血液动力学。结果非轴对称模型可造成相对较大的壁面剪应力;带有峰值偏移和曲率半径偏转的腹主动脉瘤,瘤内漩涡的发展变化会随着几何形态的不同而产生变化。结论腹主动脉瘤内流场特征的变化受到不同形态学的影响。