Biomechanical Modeling and of ascending thoracic aortic aneurysm

Academic Paper, 2018
6 Pages, Grade: 4,4

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Bio mechanical Modeling and of Ascending Thoracic Aortic


Cardiovascular diseases account for the most cause of death over the globe annually, summarized by the World Health Organization. An aortic aneurysm is one of the cardiovascular diseases with localized abnormal growth of a blood vessel with the primary risk of aneurysm rupturing or aortic wall dissecting. The precise pathological pathway for disease progression in aneurysm formation is not completely understood; however, biomechanically, disrupted blood flow from a diseased heart valve and thrombus formation potential in the dissection could contribute to the increased risk. The current ascending thoracic aortic aneurysm (ATAA) management rely heavily on ATAA diameter and blood pressure rather than biomechanical and hemodynamical parameters including arterial wall deformation or wall shear stress (WSS). Therefore, this thesis firstly evaluated the biomechanical contributions to ATAA progression under the influence of anatomy, hypertension, and hematocrit using fully coupled fluid-structure interaction (FSI) with arterial wall anisotropy to provide additional information in patient evaluations. The investigation was then extended to study the effect of blood rheology on the hemodynamics of a bileaflet mechanical heart valve with particle image velocimetry (PIV) validation. Finally, the rheological experimentations were conducted to analyze the coagulation process and the interactions between heparinized blood and the anticoagulation reversal agents. The ATAA analysis showed significant variations in the maximum WSS despite minimal differences in flow velocity between normotension and hypertension. The three different ATAA models identified different aortic expansions that were not uniform under pulsatile pressure and a geometry depended on elevated wall stress under hypertension. The investigation on the heart valve revealed the hematocrit influenced the shear stress distributions over a cardiac cycle.

The structural stresses in the mechanical valve were affected by the shear stress distributions in the blood flow. Par meter dependencies study indicated that the hematocrit is influential when conducting patient-specific modeling of prosthetic heart valves. Finally, the use of small amplitude oscillatory shear (SAOS) rheometry for studying blood coagulation provided a comprehensive assessment with the combination of multiple rheological parameters for untreated and heparin neutralized blood. The coagulation characterization could be used towards the existing FSI models to account for blood clot formations in future studies.

Note: The presented paper has been translated from Mandarin.

1. Introduction

When an artery abnormally enlarges locally, the disease is typically identified as an aneurysm. An ascending thoracic aortic aneurysm (ATAA) is an aneurysm at the ascending part of the thoracic aorta, which is the largest artery bridging the heart and the rest of the body. The current clinical ATAA managements rely mostly on aneurysm diameter, blood pressure, and lifestyle; however, other mechanical and biological factors can also contribute to aneurysm progression. To investigate the biomechanical influence on ATAAs, computer models were built to simulate blood flow through ATAA and a mechanical heart valve. It was found that the aneurysm's geometrical characteristic, hypertension, and hematocrit can all affect the mechanical load and fluid- induced stress on ATAA and heart valve. Furthermore, experiments and characterizations on the blood coagulation process were conducted for future integration to the existing computer models for simulating blood flow through ATAA and heart valve with potential blood coagulation.

Cardiovascular mortality accounts for a major proportion of total deaths in industrialized societies. In the US alone, it accounted for approximately 31% of the total mortality in 2014 with approximately ten thousand people dying because of aortic aneurysm and dissection. An aortic aneurysm occurs when an aorta enlarges abnormally at a localized region. When the enlargement occurs around the thoracic aorta, it is classified as thoracic aortic aneurysm (TAA). By the same token, when the enlargement occurs around the abdominal aorta, it is classified as abdominal aortic aneurysm(AAA).

The complications of aortic aneurysm are significant and are of considerable concern as the prevalence of the condition is increasing. Blood pressure is a critical parameter that predicts aortic enlargements in conjunction with other factors such as the imbalance between protein synthesis and degradation of matrix proteins. While several other well known risk factors, such as age, gender, smoking and genetics, may lead to the development of TAA formation, the precise causes, physical or biochemical, of aneurysm formations is unknown in most cases.

The complications of aortic aneurysm are significant and are of considerable concern as the prevalence of the condition is increasing. Blood pressure is a critical parameter that predicts aortic enlargements in conjunction with other factors such as the imbalance between protein synthesis and degradation of matrix proteins. While several other well known risk factors, such as age, gender, smoking and genetics, may lead to the development of TAA formation, the precise causes, physical or biochemical, of aneurysm formations is unknown in most cases.

The current standard practices for patients, who have aortic aneurysms and dissections, are primarily managed by evaluating the size of the dilated blood vessels as well as patients' blood pressures. More specifically, the assessments and managements of TAA, ascending thoracic aortic aneurysm (ATAA), and AAA relies heavily on the diameter of an aneurysm and blood pressure rather than biomechanical and hemodynamic parameters such as arterial wall deformation or wall shear stress. However, in some circumstances, the patients with smaller vessel diameter may develop an aortic dissection before blood vessel diameter reaches the recommended threshold for surgery. Once a surgical option is deemed to be suitable, an open procedure remains the gold standard for a treatment. Given an approximately 30% of the patient population are not suitable for open procedures due to potential complications, the risk of surgery is preferred over the risk of further developments of aneurysms and dissections. One of the potential alternative treatment option of aortic aneurysm would be endovascular aortic repair (EVAR), which avoid the need of introducing open surgical procedures with the increased risk. However, EVAR is not risk-free as the stent graft relies on the outward expansion force generated from the stent frame, the imperfections from the repair would introduce further series complications including endovascular leakages and retrograde dissections.

Ascending aortic curvature, aortic stiffness, peak wall stress (PWS), as well as wall shear stress (WSS) are biomechanical factors that may provide information for the disease predictions. Unfortunately, besides the aortic geometries, most of these factors cannot easily be directly measured in vivo . A method for calculation of arterial wall stress, blood flow velocity, and WSS would be of considerable value for disease assessments.

Although the size of the aorta has been studied in TAA; the impact of increasing aortic arch curvature has received less attention. The curvature might dramatically increase the force experience by ascending aorta even if under the conditions of lower systole pressure and smaller vessel diameter. Data suggest that the aorta and aortic aneurysm might be influenced considerably by its geometrical configuration but this has not been studied in detail. It is reasonable to begin an investigation on aortic aneurysm from a biomechanical perspective and to consider blood vessel displacement under pulsatile blood pressure. Since arterial wall stiffness increase with aging especially in patient with hypertension, investigation of aortic wall stress should provide important insights on how the stress is distributed.

In addition, evaluation of PWS, or overall arterial wall stress, should assist in identifying regions of the aorta that are subject to high stress rendering them at high risk for aneurysm rupture and/or dissection.

1.1 ATAA Pathology

While the exact disease pathway for the progression of an aneurysm is still unclear, there are several key factors identified that prompt the aneurysm developments. As proposed by Shimizu et al. for the progression of aneurysms, there should be a two-step process where the normal healthy blood vessel undergoes initial aortic wall damage after the first trigger due to environmental or genetic events.

A second trigger, which is caused by environmental factors, would be followed such that the progression of an aneurysm is continued. Although their work is limited to the investigation of AAA, the same process for TAA and ATAA may apply . The primary cause of ATAA progression is the degradation of the media layer, which has decreased elastin concentration and reduced smooth muscle cells. Since the environmental factors are the second trigger, it can be argued that biochemical or biomechanical factors are the main factors in ATAA progression. As ascending thoracic aorta receives the highest amount of the blood flow from the heart, the investigation of ATAA progression from the biomechanics point of view could provide further clinical insights for the patients.

It is known that fluid shear stress would initiate the remodeling of blood vessels as well as create damage to blood cell; however, to physically measure fluid shear stress without influencing fluid flow in real-time can be very challenging. Due to the shear stress generated under pulsatile blood flow, it was shown that the endothelial cells and the adhesion of the neutrophils to endothelial cells responded to the gradients of WSS and potentially influenced the stability of the atherosclerotic plaque. Given the main components of blood are red blood cells (erythrocytes), white blood cells (leukocytes), platelets (thrombocytes), and plasma, the biomechanical factors should have majority effects on these four components. Combining the evidence of blood damage under high shear stress and the thrombus generation under shear flow, one can argue that platelets initiate thrombus formation due to abnormal hemodynamics under pathological conditions.

A further investigation reveals that there is a close biophysical connection between the interaction of platelets and fluid shear stress. Briefly, the increase in blood shear stress would cause platelets to release and upregulate tissue growth factors. Specifically, human aortic smooth muscle cell (SMC) apoptosis has been observed with the overexpression of connective tissue growth factor (CTGF), which is released by platelets or other mechanical stimuli. Additionally, CTGF has been shown to increase the risk of a cardiovascular event and proposed as an independent risk predictor for the atherosclerotic disease. 4D magnetic resonance imaging (MRI) study has revealed a potential linkage by concluding that the bicuspid aortic valve (BAV) patients with aortic dilation are experiencing higher shear stress than the patients with tricuspid aortic valve (TAV).

1.2 Aortic Valve disease ൮

BAV is the most common congenital defect affecting up to 2% of the population with complications associated to aortic stenosis, regurgitation, and the dilation of the ascending thoracic aorta, which is the most relevant to the current study. With severe aortic stenosis, the aortic valve would typically have to be replaced with an artificial heart valve, either with a mechanical heart valve or a bioprosthetic tissue valve. In the study investigated the number of patients receiving aortic valve replacement by Roberts and Ko, approximately 49% (458 out of 932) of the patient had a BAV. When BAV is associated with the dilation of the ascending thoracic aorta, the growth rate of the aorta for BAV patients is higher than aneurysm patients with a TAV. As the arterial wall stresses and the fluid shear stresses contribute to the pathogenesis of BAV, hemodynamical influence in both BAV and ATAA is identified as one of the key factors for the disease progression. The use of 4D MRI has concluded that BAV patients had a significant difference in the shear stress at the arterial wall and the generation of helical flow across the aortic arch from the ascending thoracic aorta. The earlier study concludes the curvature of the aortic arch would play an important role in the generation of secondary flow patterns such as helical flows. Therefore, the formation and progression of an ATAA could not only be caused by altered hemodynamics with a defective BAV but also due to the geometrical curvatures of the aorta generating helical flows.

2. Biomechanical Characterizations of Aortic Wall

As the heart mechanically pumps the blood flow through the aorta and distributes the blood to all parts of the body, a deeper understanding in the biomechanical interactions between the aortic wall and the blood would further bridge the gap between the progression of an aneurysm and the management of a patient. With a better understanding of an aneurysm development, it is possible to better predict the outcome of the patients by translating the knowledge to clinical settings.

Mechanical loadings including forces, stresses, and deformations are some of the biomechanical factors that would have a more direct influence on aneurysm's progression. To account for the force transfer, the internal wall stress, as well as the structural deformation for biological soft tissue, it is essential to consider how the material composition of tissue would affect the overall tissue properties under various loading conditions. For the case of the aorta, it is understood that each layer consists of various portion of elastin and collagen that provide overall structural support.

The arterial wall consists of three main layers: intima, media, and adventitia. Each layer, separated by elastic lamina, has its own characteristic that provides the overall structural function of the arterial wall. For example, intima primarily provides internal protection of the blood vessel with a smooth endothelial cell layer, elastin, and fibre-reinforced layer. Media, which is considered as transversely isotropic, provides the flexibility to expand and contract under pulsatile blood flow with smooth muscle. Adventitia provides external structural support for the blood vessel with an anisotropic collagen fibre layer. The distribution of microstructures, such as elastin fibres and collagen fibres has been shown to be one of the main contributors that affect the macroscopic biomechanics of arterial wal.

It is well summarized in Tsamis et al. and Back et al. that elastin and collagen content would be affected by age, diseases, genetic or developmental defects including, hypertension, aneurysm, dissection, atherosclerosis, bicuspid aortic valve, Marfan syndrome, and other factors [61,65]. Specifically for the aortic aneurysm cases, the overall elastin content would decrease withfragmented, disrupted, and irre gular elastin while the overall collagen content would remain the same with thin scattered collagen fibres. The change in elastin and collagen content would result in a less anisotropic aorta. Similarly, for the aortic dissection cases, elastin and collagen concentration also decrease and thus affecting the aorta' s global response to pulsatile pressure. It was also shown that structure integrity would be adversely affected by elastin removal and aneurysm remodeling in the media layer. The tissue toughness of the media layer of the ATAA was shown to be independent of different regions of the aneurysm but depended on both the collagen and elastin fibres.

To further understand the progression of arterial diseases and construct physical models from a biomechanics perspective, it would be necessary to determine the macroscopic material properties of the arterial wall. Recently, many research groups have used uniaxial or biaxial tensile measurements to model the properties of the aortic wall using constitutive equations that account for hyper-elasticity or anisotropy. The characterization of the arterial wall can, therefore, be categorized into isotropic linear elastic material, isotropic hyper-elastic material, and anisotropic hyper-elastic material as discussed in the following sections.

2.1 Isotropic linear elastic material

The constitutive equation of an isotropic elastic material is a simple linear relationship between stress and strain. This relationship is known as Hooke's Law where the given material is characterized by only Young' s modulus and Poisson's ratio. Assuming isothermal condition. Since the strain, or more specifically the engineering strain, used in linear elastic relationship is only valid when deformation is small and within linear range. Therefore, depending on various stress-strain definitions, it is recommended to apply the true (instantaneous changes) stress and true strain relationship for soft tissue experiments.

Fluid-structure interaction (FSI) methods has been used for investigating the arterial wall stress under pulsatile blood flow with an assumption of a linear elastic arterial wall. The assumption of applying isotropic linear elastic material to the arterial wall was made to compensate more relevant global evaluation on aneurysm rupture, asymmetry and wall thickness, stent graft implantation, and multiple arterial layers. Additionally, a uniform aortic wall thickness of a single arterial wall layer could be assumed.

Torii et al. compared the single layer linear elastic and hyper-elastic cerebral aneurysm model and concluded that the hyper-elastic model resulted in a 36% smaller maximum displacement, but with similar displacement patterns, compare with the linear elastic model [74]. To address the rupture risk due to the arterial wall thickness and asymmetry, Scotti et al. found that the non-uniform wall thickness model would result in up to four times greater wall stress, thus increasing AAA rupture risk based on the von Mises failure stress criteria. It is therefore recommended to accurately reproduce the aortic geometry when predicting the biomechanics of aortic aneurysm.

Similarly, Li and Kleistreuer numerically investigated the biomechanics of AAA before and after endovascular stent graft implantation and analyzed the wall stress and aneurysm sac pressure. The use of fully coupled FSI for both AAA and endovascular stent graft resulted in a significant decrease in maximum wall stress for stented AAA when compare with non-stented AAA. The authors also discussed that from their preliminary studies, aneurysm sac pressure and wall stress might increase by 60% with an increase of only 3% endoleak volume as well as a greater endograft drag force from aortic geometrical factors.

Nevertheless, smce the arterial wall structure consists of three layers and most biomechanics investigation on aortic aneurysm is modeled as an equivalent single wall layer, Gao et al. considered the multilayer mechanics of arterial wall and analyze stress distribution across each arterial layer. The authors presented an idealized aorta, from the ascending aorta to the descending aorta, (without the aortic branches) with a three-layered aortic wall with a corresponding thickness ratio of 1/6/3 (media thickness of 1.2mm) and isotropic linear elastic properties (Eintima= 2.98 MPa, Emedia = 8.95 MPa, Eadventitia= 2.98 MPa). The circumferential stress was concluded to be directly related to blood pressure resulting in high composite stress around ascending aorta and highest stress at the media layer, suggesting the formation of an aortic dissection.

Applying isotropic linear elastic properties to the aortic wall reduced the modelling complexity while provided an overall macroscopic evaluation on the progression of an aneurysm. However, given the linear elasticity would only be valid within the linear proportional limit, the estimation of the rupture stress for aortic aneurysm would not be accurate as the failure strength is beyond the linear region.

2.2 Isotropic hyper-elastic material

There are several well-established constitutive equations for isotropic hyper-elastic relationship. The main difference between different relationships, besides the material constants, is the method of material properties fittings: exponential or polynomial.

The material constants used in each constitutive equation are determined experimentally with uniaxial and biaxial tension test using cadaveric, surgical, or animal tissue specimens. The collected data from tensional experiments are usually fitted using multivariable least square analysis. Although the anisotropic material relationship would provide better experimental fit, the use of the neo-Hookean model would be sufficient for describing the material behavior of the media layer.

The characterization of the aortic wall model can be extended to the solid mechanics modeling for multilayer stenotic artery modeling with stent deployment or modeling the device-wall interaction in coronary sinus. More specifically, Schiavone et al. conducted a finite element simulation on the stent deployment in the stenotic artery using a combination of constitutive equations to model the transcatheter balloon (Mooney-Rivlin 2- parameter), three arterial wall layers, and plaque.

Their simulations suggested that their artery-plaque-stent system would result in significantly different stress distribution with different stent designs. Furthermore, Zahedmanesh and Lally numerically investigated that blood vessel is more likely to get restenosis if the wall stress is greater.

Studies have modelled the arterial wall as a composite of isotropic hyperelastic materials with the material properties derived from experimental studies. However, given that the elastin, collagen fibres and other components in the media and adventitia layer of the aorta affect the deformation and stress distribution of the arterial wall, considering material anisotropy due to collagen fibres when modelling the arterial wall could result in better predictions.

2.3 Anisotropic hyper-elastic material

To further improve the biomechanics model for arterial wall, anisotropy can be added to the isotropic hyper-elastic model. Such an addition will account for the different fibre groups embedded within each arterial wall layer in order to capture the effect of fibre-reinforced deformation in biological soft tissue. Several key studies on the constitutive equations for modeling the anisotropic hyper-elastic arterial wall has been conducted intensively.

To characterize the material constants, several experimental efforts were carried for the modeling of human aorta and the atherosclerotic plaque. Labrosse et al. conducted biaxial and pressurized vessel test for modeling the anisotropic hyper-elastic constitutive equation for human ascending, descending, and abdominal aorta.

3. In Silico Investigation of Aneurysm Biomechanics

In additional to the biomechanics of aortic wall given that shear stress due to the pulsatile blood flow plays an important role in the disease progression of an aneurysm. High shear stress could lead to an overexpression of CTGF released by platelets and CTGF overexpression would lead to aortic smooth muscle cell apoptosis, which is the signature of media layer degradation in ATAA.

Finite element simulations have focused on the investigation of aneurysm wall stress in patient-specific modeling using data either from computed tomography (CT) imaging or MRI.

Studies focused on the analysis of the aortic wall stress with the use of anisotropic hyperelastic arterial wall modeling, geometrical correction for zero blood pressure, aortic root displacement, and aneurysm expansion prediction.

The accurate hemodynamic analysis in the cardiovascular system is heavily depended on the appropriate interaction modelling between blood and blood vessels; therefore, accurate models for.blood rheology and vessel structures are necessary to account for blood flow distributions and aortic wall stresses.

Although debates are ongoing regarding the effectiveness of different computational approaches between computational fluid dynamics (CFD) and FSI methods for the investigations of aortic biomechanics, the motions of blood vessel induced under physiological pulsatile blood pressure by FSI approach would have different flow distributions than predicted by CFD approaches.

The prediction from CFD would capture the effects of different non-Newtonian models applied to patient-specific geometry were investigated and it was concluded that the Newtonian model underestimates WSS prediction.

Given the importance in WSS, the PSI approach that couples CPD and structural mechanics for modelling blood vessel expansion (Windkessel effect) should be used toward accurate hemodynamic predictions.

Both PSI-CPD comparison studies by Reymond et al. and Crosetto et al. concluded that there was a WSS overestimation from the simulations without the inclusion of the aortic wall. There were multiple PSI studies conducted for modelling cardiovascular system in the past decade. Each of them had a slightly different approach in hemorheological and structural modelling. Earlier PSI studies focused on the assessment of multilayer aortic wall biomechanics.

Gao et al., constructed idealized 3D Newtonian models for the hemodynamics comparison between non-aneurysm and aneurysm model with aortic wall properties assumed as three isotropic linear elastic layers (intima, media, and adventitia). Similarly, Khanafer and Berguer's three-layered isotropic linear elastic aorta model provided insights into peak wall stress in the media layer. The PSI method has also been used recently in the modelling in ATAA geometrical characteristics [107], ATAA with BAV and TAV [108], abdominal aortic aneurysm growth evolution , and local stiffening.

While the studies utilized the advanced material model for the aortic wall (isotropic hyperelastic and anisotropic hyperelastic models), the blood was assumed to be a Newtonian fluid.

As mentioned earlier, WSS prediction is one of the most important biomechanics predictors in ATAA, and FSI model with Newtonian fluid would result in a WSS underestimation. Interestingly, as all the results implied a geometrical dependence in hemodynamic distributions and helical flow development, the quantitative relationship between geometry and hemodynamics is to be further developed for better model predictions and correlations such that the analysis can be translated toward to clinical practice. Nevertheless, for an FSI modelling, the boundary velocity conditions (3D MRI, 1D MRI, fully developed, and plug flow) prescribed in the model would also have a significant influence in time-averaged WSS distributions and oscillatory shear index, which would affect the predicted outcome.

The hyperelastic models for characterizing the aortic wall are used to determine the biomechanical response under physiological loading conditions. Tan et al. investigated the mechanics and hemodynamics of TAA using the single layer isotropic hyperelastic Mooney-Rivlin model, with material constants taken from the experimental work on AAA. The use of laminar-turbulent transition model concluded a 13% lower time-averaged WSS and significantly higher turbulence intensity in the FSI model than the rigid wall model.

On the other hand, Raghavan and Vorp conducted another study on the rupture potential of AAA with freshly excised tissue. They concluding that AAA wall stress would only vary 4% if the material parameters used from Mooney-Rivlin constitutive equation were within 95% confidence intervals. This suggests that the use of mean value from sample population might be sufficient for patient-specific modeling. For advanced numerical simulation, Grytsan et al. have modified the anisotropic arterial wall model and accounted for AAA remodeling under the additional consideration of elastin degradation and adaptation of collagen fibres.

The model considered the hemodynamic changes with the progression of AAA enlargement but without the connection between WSS and AAA remodeling . The time-averaged WSS was not meaningfully influenced by the arterial wall motion due to pulsatile blood flow unless the investigation of instantaneous WSS was considered. Since the magnitude of WSS would affect endothelial cell alignment and potentially cause blood cell damage, a coupled fluid and structure study on WSS is of considerable value given that the local blood recirculation or unbalanced homeostasis could also lead to aneurysm rupture.


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Biomechanical Modeling and of ascending thoracic aortic aneurysm
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biomechanical, modeling
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Hollae Netow (Author), 2018, Biomechanical Modeling and of ascending thoracic aortic aneurysm, Munich, GRIN Verlag,


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