Patient-Specific Aneurysms Rupture Prediction Using CFD Modelling With Strain Energy Function

2013 ◽  
Author(s):  
A. H. Embong ◽  
A. M. Al-Jumaily ◽  
Giri Mahadevan ◽  
Shukei Sugita ◽  
Andrew Lowe
Keyword(s):  
Vessel Wall ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Wall Stress ◽  
Aneurysm Rupture ◽  
Patient Specific ◽  
Cfd Model ◽  
Cfd Modelling ◽  
Strain Relationship ◽  
Strain Function

This paper proposes a new Patient-Specific Aneurysm CFD Model (PSAM) which is based on the energy strain function combined with dilated vessel wall stress-strain relationship to predict aneurysm rupture. The PSAM relies on the available mechanical properties and parameters obtained from a personalized model. A personalized model is developed based on instantaneous arterial deformations obtained from Doppler Ultrasound (US) images at 6–9 MHz. It is shown that PSAM has the ability to correlate the deformation wall energy based on continuous patient-specifics in predicting rupture.

Three-Dimensional Stress Distribution in Arteries

1983 ◽  
Vol 105 (3) ◽  
pp. 268-274 ◽  
Author(s):  
C. J. Chuong ◽  
Y. C. Fung
Keyword(s):  
Experimental Data ◽  
Stress Distribution ◽  
Vessel Wall ◽  
Strain Energy ◽  
Arterial Wall ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Exponential Form ◽  
Strain Relationship ◽  
Longitudinal Stretch

A three-dimensional stress-strain relationship derived from a strain energy function of the exponential form is proposed for the arterial wall. The material constants are identified from experimental data on rabbit arteries subjected to inflation and longitudinal stretch in the physiological range. The objectives are: 1) to show that such a procedure is feasible and practical, and 2) to call attention to the very large variations in stresses and strains across the vessel wall under the assumptions that the tissue is incompressible and stress-free when all external load is removed.

Abdominal Aortic Aneurysm Growth: The Association of Aortic Wall Mechanics and Geometry

2011 ◽  
Author(s):  
Christopher B. Washington ◽  
Judy Shum ◽  
Satish C. Muluk ◽  
Ender A. Finol
Keyword(s):  
Wall Stress ◽  
Abdominal Ultrasound ◽  
Aneurysm Rupture ◽  
Computational Method ◽  
Maximum Diameter ◽  
Patient Specific ◽  
Element Analysis ◽  
Wall Strength ◽  
Aneurysm Growth ◽  
Peak Wall Stress

In an effort to prevent rupture, patients with known AAA undergo periodic abdominal ultrasound or CT scan surveillance. When the aneurysm grows to a diameter of 5.0–5.5 cm or is shown to expand at a rate greater than 1 cm/yr, elective operative repair is undertaken. While this strategy certainly prevents a number of potentially catastrophic ruptures, AAA rupture can occur at sizes less than 5 cm. From a biomechanical standpoint, aneurysm rupture occurs when wall stress exceeds wall strength. By using non-invasive techniques, such as finite element analysis (FEA), wall stress can be estimated for patient specific AAA models, which can perhaps more carefully predict the rupture potential of a given aneurysm, regardless of size. FEA is a computational method that can be used to evaluate complicated structures such as aneurysms. To this end, it was reported earlier that AAA peak wall stress provides a better assessment of rupture risk than the commonly used maximum diameter criterion [1]. What has yet to be examined, however, is the relationship between wall stress and AAA geometry during aneurysm growth. Such finding has the potential for providing individualized predictions of AAA rupture potential during patient surveillance. The purpose of this study is to estimate peak wall stress for an AAA under surveillance and evaluate its potential correlation with geometric features characteristic of the aneurysm’s morphology.

A Comparative Study of Biomechanical and Geometrical Attributes of Abdominal Aortic Aneurysms in the Asian and Caucasian Populations

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Tejas Canchi ◽  
Sourav S. Patnaik ◽  
Hong N. Nguyen ◽  
E. Y. K. Ng ◽  
Sriram Narayanan ◽  
...  
Keyword(s):  
Wall Thickness ◽  
Gaussian Curvature ◽  
Wall Stress ◽  
Aneurysm Rupture ◽  
Aortic Aneurysms ◽  
Patient Specific ◽  
Backward Elimination ◽  
Abdominal Aortic ◽  
Highly Correlated ◽  
Peak Wall Stress

Abstract In this work, we provide a quantitative assessment of the biomechanical and geometric features that characterize abdominal aortic aneurysm (AAA) models generated from 19 Asian and 19 Caucasian diameter-matched AAA patients. 3D patient-specific finite element models were generated and used to compute peak wall stress (PWS), 99th percentile wall stress (99th WS), and spatially averaged wall stress (AWS) for each AAA. In addition, 51 global geometric indices were calculated, which quantify the wall thickness, shape, and curvature of each AAA. The indices were correlated with 99th WS (the only biomechanical metric that exhibited significant association with geometric indices) using Spearman's correlation and subsequently with multivariate linear regression using backward elimination. For the Asian AAA group, 99th WS was highly correlated (R2 = 0.77) with three geometric indices, namely tortuosity, intraluminal thrombus volume, and area-averaged Gaussian curvature. Similarly, 99th WS in the Caucasian AAA group was highly correlated (R2 = 0.87) with six geometric indices, namely maximum AAA diameter, distal neck diameter, diameter–height ratio, minimum wall thickness variance, mode of the wall thickness variance, and area-averaged Gaussian curvature. Significant differences were found between the two groups for ten geometric indices; however, no differences were found for any of their respective biomechanical attributes. Assuming maximum AAA diameter as the most predictive metric for wall stress was found to be imprecise: 24% and 28% accuracy for the Asian and Caucasian groups, respectively. This investigation reveals that geometric indices other than maximum AAA diameter can serve as predictors of wall stress, and potentially for assessment of aneurysm rupture risk, in the Asian and Caucasian AAA populations.

Local Mechanical Properties of Abdominal Aortic Aneurysms

2008 ◽  
Author(s):  
Evelyne van Dam ◽  
Marcel Rutten ◽  
Frans van de Vosse
Keyword(s):  
Mechanical Properties ◽  
Stress Analysis ◽  
Vessel Wall ◽  
Computational Models ◽  
Wall Stress ◽  
Abdominal Aortic Aneurysms ◽  
Aortic Aneurysms ◽  
Patient Specific ◽  
Rupture Risk ◽  
Abdominal Aortic

Rupture risk of abdominal aortic aneurysms (AAA) based on wall stress analysis may be superior to the currently used diameter-based rupture risk prediction [4; 5; 6; 7]. In patient specific computational models for wall stress analysis, the geometry of the aneurysm is obtained from CT or MR images. The wall thickness and mechanical properties are mostly assumed to be homogeneous. The pathological AAA vessel wall may contain collageneous areas, but also calcifications, cholesterol crystals and large amounts of fat cells. No research has yet focused yet on the differences in mechanical properties of the components present within the degrading AAA vessel wall.

scholarly journals A generalized strain approach to anisotropic elasticity

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
M. H. B. M. Shariff
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Single Variable ◽  
Energy Functions ◽  
Anisotropic Strain ◽  
Strain Energy Functions ◽  
Strain Function

AbstractThis work proposes a generalized Lagrangian strain function $$f_\alpha$$ f α (that depends on modified stretches) and a volumetric strain function $$g_\alpha$$ g α (that depends on the determinant of the deformation tensor) to characterize isotropic/anisotropic strain energy functions. With the aid of a spectral approach, the single-variable strain functions enable the development of strain energy functions that are consistent with their infinitesimal counterparts, including the development of a strain energy function for the general anisotropic material that contains the general 4th order classical stiffness tensor. The generality of the single-variable strain functions sets a platform for future development of adequate specific forms of the isotropic/anisotropic strain energy function; future modellers only require to construct specific forms of the functions $$f_\alpha$$ f α and $$g_\alpha$$ g α to model their strain energy functions. The spectral invariants used in the constitutive equation have a clear physical interpretation, which is attractive, in aiding experiment design and the construction of specific forms of the strain energy. Some previous strain energy functions that appeared in the literature can be considered as special cases of the proposed generalized strain energy function. The resulting constitutive equations can be easily converted, to allow the mechanical influence of compressed fibres to be excluded or partial excluded and to model fibre dispersion in collagenous soft tissues. Implementation of the constitutive equations in Finite Element software is discussed. The suggested crude specific strain function forms are able to fit the theory well with experimental data and managed to predict several sets of experimental data.

A Structural Strain Energy Function for Vascular Tissue Considering Elastin Anisotropy

2007 ◽  
Author(s):  
Rana Rezakhaniha ◽  
Nikos Stergiopulos
Keyword(s):  
Energy Function ◽  
Constitutive Equations ◽  
Vessel Wall ◽  
Strain Energy ◽  
Vascular Tissue ◽  
Strain Energy Function ◽  
Nonlinear Properties ◽  
Wide Range ◽  
Nonlinear Elastic ◽  
Structural Strain

The vessel wall exhibits relatively strong nonlinear properties and undergoes a wide range of deformations. Identification of a strain energy function (SEF) is the preferred method to describe the complex nonlinear elastic properties of the vascular tissue. Once the strain energy function is known, constitutive equations can be obtained.

Aortic Wall Mechanics: A Geometry-Driven Problem

2011 ◽  
Author(s):  
Samarth S. Raut ◽  
Peng Liu ◽  
Anirban Jana ◽  
Ender A. Finol
Keyword(s):  
Risk Assessment ◽  
Aortic Wall ◽  
Wall Stress ◽  
Aneurysm Rupture ◽  
Intraluminal Pressure ◽  
Wall Material ◽  
Patient Specific ◽  
Rupture Risk ◽  
Constitutive Material Model ◽  
Constitutive Material

Abdominal Aortic Aneurysm (AAA) is a vascular disease that occurs predominantly in people over 60 years of age. The rupture of an AAA is a catastrophic event associated with up to a 90% mortality rate. Hence, it is important for vascular surgeons to justify the risk of repair vis-à-vis the risk of aneurysm rupture. In clinical practice, rupture risk assessment is based on measuring the maximum aneurysm diameter where 5.5 cm is accepted as the critical size for recommending (surgical or endovascular) intervention. However, this criterion is based on an extensive history of evidence-based medicine rather than an individualized assessment of the aneurysm’s potential to rupture. Primary among the biomechanical factors associated with the rupture assessment of an AAA is mechanical wall stress, which is dependent on the accuracy of the geometry reconstruction, intraluminal pressure loading and the constitutive material model used for the aortic wall. We hypothesize that in unruptured, asymptomatic AAA, the wall mechanics is the outcome of primarily the patient specific aneurysm shape and to a lesser extent, the constitutive material property model used to characterize the vascular wall. Evaluating the relative contributions of wall material properties and AAA geometry to wall mechanics estimation will increase our understanding of the factors that influence peak wall stress as an indicator for rupture risk assessment. In the present work, we evaluate the aforementioned hypothesis using a size-matched approach.

Quantifying the Structural and Mechanical Changes in Elastase Degraded Arteries as an In Vitro Model of Aortic Aneurysm

2011 ◽  
Author(s):  
Ming-Jay Chow ◽  
Jarred Raymund Mondonedo ◽  
Katherine Yanhang Zhang
Keyword(s):  
Aortic Aneurysm ◽  
Structural Changes ◽  
Strain Energy Function ◽  
Wall Stress ◽  
Aneurysm Rupture ◽  
Aortic Tissue ◽  
Clinical Practices ◽  
Abdominal Aortic ◽  
Wall Stiffness

Common characteristics of aortic aneurysm include loss of elastin/smooth muscle cells, increase in fibrillary collagen, and increase in artery diameter [5]. Because of the high mortality rate of aneurysm rupture, it is desirable to be able to predict when a patient should have surgery to repair the dilated tissue. Current clinical practices involve predicting aneurysm rupture based on artery expansion rate and diameter. However, other parameters such as wall stiffness and peak wall stress may offer better predictions as to when an aneurysm will fail [8]. Previous studies have investigated the differences in elastin and collagen content of abdominal aortic tissue with and without abdominal aortic aneurysm (AAA) [1]. In another study, human aortic aneurysm tissue was tested in a biaxial tensile tester and the resulting stress strain curves were fitted using Fung type exponential strain energy function [7]. More extensive modeling of aneurysm tissue has been done by modifying the Holzapfel model to incorporate a parameter that characterizes the tissue weakening before the failure of the inner elastic laminae, ground matrix, or collagen fibers themselves [6]. Previous studies have found compositional and mechanical differences between aneurysm and healthy tissue. In addition, good structurally based models for arteries that are developing aneurysm exist but these are mostly theoretical [6]. In order to improve aneurysm rupture prediction techniques, a better understanding of how structural changes affect the mechanical properties of the artery is necessary.

New experiments on shear modulus of elasticity of arteries

1994 ◽  
Vol 266 (1) ◽  
pp. H1-H10 ◽  
Author(s):  
S. X. Deng ◽  
J. Tomioka ◽  
J. C. Debes ◽  
Y. C. Fung
Keyword(s):  
Blood Pressure ◽  
Shear Modulus ◽  
Modulus Of Elasticity ◽  
Vessel Wall ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
New Instrument ◽  
Rat Thoracic Aorta ◽  
The Difference

Although the mechanical properties of blood vessels have been studied extensively, the shear modulus of the blood vessel wall is still unknown. New data on the shear modulus of elasticity of rat arteries and its variation with axial stretch and blood pressure are presented. The data were obtained from a new instrument designed and constructed by us to perform simultaneous torsion, inflation, and longitudinal stretching tests. It was found under physiological conditions (pressure = 120 mmHg or 16 kPa; longitudinal stretch = 1.2 relative to zero-stress state), the shear modulus of normal rat thoracic aorta is G = 137 +/- 18 kPa. The difference of shear modulus at body temperature (37 degrees C) and room temperature (25 degrees C) is within 10%. The shear modulus varies significantly with changing longitudinal and circumferential strains in proportion to the strain energy due to these strains. A constitutive equation based on a pseudo strain energy function is proposed. The vessel wall is not transversely isotropic in the incremental sense. When the rat was subjected to high blood pressure due to constriction of its aorta, the shear modulus does not vary significantly with the length of time the animal was subjected to hypertension.

scholarly journals Biaxial vasoactivity of porcine coronary artery

2012 ◽  
Vol 302 (10) ◽  
pp. H2058-H2063 ◽  
Author(s):  
Yunlong Huo ◽  
Yana Cheng ◽  
Xuefeng Zhao ◽  
Xiao Lu ◽  
Ghassan S. Kassab
Keyword(s):  
Coronary Arteries ◽  
Strain Energy ◽  
Error Function ◽  
Strain Energy Function ◽  
Mechanical Tests ◽  
Biaxial Stress ◽  
Stress Strain ◽  
Porcine Coronary Artery ◽  
Strain Relationship ◽  
The Mean

The passive mechanical properties of blood vessel mainly stem from the interaction of collagen and elastin fibers, but vessel constriction is attributed to smooth muscle cell (SMC) contraction. Although the passive properties of coronary arteries have been well characterized, the active biaxial stress-strain relationship is not known. Here, we carry out biaxial (inflation and axial extension) mechanical tests in right coronary arteries that provide the active coronary stress-strain relationship in circumferential and axial directions. Based on the measurements, a biaxial active strain energy function is proposed to quantify the constitutive stress-strain relationship in the physiological range of loading. The strain energy is expressed as a Gauss error function in the physiological pressure range. In K+-induced vasoconstriction, the mean ± SE values of outer diameters at transmural pressure of 80 mmHg were 3.41 ± 0.17 and 3.28 ± 0.24 mm at axial stretch ratios of 1.3 and 1.5, respectively, which were significantly smaller than those in Ca2+-free-induced vasodilated state (i.e., 4.01 ± 0.16 and 3.75 ± 0.20 mm, respectively). The mean ± SE values of the inner and outer diameters in no-load state and the opening angles in zero-stress state were 1.69 ± 0.04 mm and 2.25 ± 0.08 mm and 126 ± 22°, respectively. The active stresses have a maximal value at the passive pressure of 80–100 mmHg and at the active pressure of 140–160 mmHg. Moreover, a mechanical analysis shows a significant reduction of mean stress and strain (averaged through the vessel wall). These findings have important implications for understanding SMC mechanics.

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