Finite element and photoelastic modelling of an abdominal aortic aneurysm: a comparative study

Rupture prediction of abdominal aortic aneurysms (AAAs) remains a clinical challenge. Finite element analysis (FEA) may allow for improved identification for intervention timing, but the method needs further substantiation. In this study, experimental photoelastic method and finite element techniques were compared using an idealised AAA geometry. There was good agreement between the numerical and experimental results. At the proximal and distal end of the AAA model, the maximum differences in principle strain for an internal pressure of 120 mmHg had differences ranging from 0.03 to 10.01%. The maximum difference in principle strain for the photoelastic and the finite element model at a pressure of 120 mmHg was 0.167 and 0.158, respectively. The current research strengthens the case for using FEA as an adjunct to the current clinical practice of utilising diameter measurement for intervention timing.     

Use of the photoelastic method and finite element analysis in the assessment of wall strain in abdominal aortic aneurysm models

Abdominal aortic aneurysm (AAA) is a significant health problem. Current clinical rupture-risk relies primarily on the maximum diameter of the AAA and also growth rate. However, AAAs are a patient-specific problem and recently, numerical tools have been employed to estimate rupture-potential. Alternatively, experimental assessment of AAA biomechanics receives less attention, yet, rigorous validation of numerical tools is required prior to clinical acceptance. This paper examines the use of the photoelastic method to assess wall strain and its validation using finite element analysis (FEA) in a small number of patient-specific AAA models. Experimental models were manufactured in-house using the injection-moulding procedure together with a commercially available photoelastic material. The material was mechanically characterised prior to testing, with models examined under three loading regimes (80, 120 and 160mmHg). Each experimental model was imaged using computed tomography (CT) and reconstructed in three dimensions (3D) for numerical analyses. Experimental wall strain was measured and numerical wall strain calculated with finite element analysis (FEA). Results were qualitatively and quantitatively compared. There was good qualitative agreement between the experimental and numerical methods, with similar trends apparent throughout all models at all pressures. Overall, acceptable percentage errors between the techniques were observed for all models. Median errors of -6.5%, -0.4% and 3.9% for the models at 80, 120 and 160mmHg pressures, respectively, were determined. The photoelastic method is a very useful experimental tool that provides instant, easy to interpret, information regarding wall strain. The technique is useful for validation of numerical AAA studies.     

Stereoscopically observed deformations of a compliant abdominal aortic aneurysm model

A new experimental setup has been implemented to precisely measure the deformations of an entire model abdominal aortic aneurysm (AAA). This setup addresses a gap between the computational and experimental models of AAA that have aimed at improving the limited understanding of aneurysm development and rupture. The experimental validation of the deformations from computational approaches has been limited by a lack of consideration of the large and varied deformations that AAAs undergo in response to physiologic flow and pressure. To address the issue of experimentally validating these calculated deformations, a stereoscopic imaging system utilizing two cameras was constructed to measure model aneurysm displacement in response to pressurization. The three model shapes, consisting of a healthy aorta, an AAA with bifurcation, and an AAA without bifurcation, were also evaluated with computational solid mechanical modeling using finite elements to assess the impact of differences between material properties and for comparison against the experimental inflations. The device demonstrated adequate accuracy (surface points were located to within 0.07?mm) for capturing local variation while allowing the full length of the aneurysm sac to be observed at once. The experimental model AAA demonstrated realistic aneurysm behavior by having cyclic strains consistent with reported clinical observations between pressures 80 and 120?mm Hg. These strains are 1-2%, and the local spatial variations in experimental strain were less than predicted by the computational models. The three different models demonstrated that the asymmetric bifurcation creates displacement differences but not cyclic strain differences within the aneurysm sac. The technique and device captured regional variations of strain that are unobservable with diameter measures alone. It also allowed the calculation of local strain and removed rigid body motion effects on the strain calculation. The results of the computations show that an asymmetric aortic bifurcation created displacement differences but not cyclic strain differences within the aneurysm sac.     

Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability

Knowledge of the wall stresses in an abdominal aortic aneurysm (AAA) may be helpful in evaluating the need for surgical intervention to avoid rupture. This must be preceded by the development of a more suitable finite strain constitutive model for AAA, as none currently exists. Additionally, reliable stress analysis of in vivo AAA for the purposes of clinical diagnostics requires patient-specific values of the material parameters, which are difficult to determine noninvasively. The purpose of this work, therefore, was three-fold: (1) to develop a finite strain constitutive model for AAA; (2) to estimate the variation of model parameters within a sample population; and (3) to evaluate the sensitivity of computed stress distribution in AAA due to this biologic variation. We propose here a two parameter, hyperelastic, isotropic, incompressible material model and utilize experimental data from 69 freshly excised AAA specimens to both develop the functional form of the model and estimate its material parameters. Parametric analyses were performed via repeated finite element computations to determine the effect of varying each of the two model parameters on the stress distribution in a three-dimensional AAA model. The agreement between experimental data and the proposed functional form of the constitutive law was very good (R2 > 0.9). Our finite element simulations showed that the computed AAA wall stresses changed by only 4% or less when both the parameters were varied within the 95% confidence intervals for the patient population studied. This observation indicates that in lieu of the patient-specific material parameters, which are difficult to determine the use of population mean values is sufficiently accurate for the model to be reasonably employed in a clinical setting. We believe that this is an important advancement toward the development of a computational tool for the estimation of rupture potential for individual AAA, for which there is great clinical need.     

Identification of rupture locations in patient-specific abdominal aortic aneurysms using experimental and computational techniques

In the event of abdominal aortic aneurysm (AAA) rupture, the outcome is often death. This paper aims to experimentally identify the rupture locations of in vitro AAA models and validate these rupture sites using finite element analysis (FEA). Silicone rubber AAA models were manufactured using two different materials (Sylgard 160 and Sylgard 170, Dow Corning) and imaged using computed tomography (CT). Experimental models were inflated until rupture with high speed photography used to capture the site of rupture. 3D reconstructions from CT scans and subsequent FEA of these models enabled the wall stress and wall thickness to be determined for each of the geometries. Experimental models ruptured at regions of inflection, not at regions of maximum diameter. Rupture pressures (mean±SD) for the Sylgard 160 and Sylgard 170 models were 650.6±195.1 mmHg and 410.7±159.9 mmHg, respectively. Computational models accurately predicted the locations of rupture. Peak wall stress for the Sylgard 160 and Sylgard 170 models was 2.15±0.26 MPa at an internal pressure of 650 mmHg and 1.69±0.38 MPa at an internal pressure of 410 mmHg, respectively. Mean wall thickness of all models was 2.19±0.40 mm, with a mean wall thickness at the location of rupture of 1.85±0.33 and 1.71±0.29 mm for the Sylgard 160 and Sylgard 170 materials, respectively. Rupture occurred at the location of peak stress in 80% (16/20) of cases and at high stress regions but not peak stress in 10% (2/20) of cases. 10% (2/20) of models had defects in the AAA wall which moved the rupture location away from regions of elevated stress. The results presented may further contribute to the understanding of AAA biomechanics and ultimately AAA rupture prediction.     

Finite element analysis to characterize how varying patellar loading influences pressure applied to cartilage: model evaluation

A finite element analysis (FEA) modeling technique has been developed to characterize how varying the orientation of the patellar tendon influences the patellofemoral pressure distribution. To evaluate the accuracy of the technique, models were created from MRI images to represent five knees that were previously tested in vitro to determine the influence of hamstrings loading on patellofemoral contact pressures. Hamstrings loading increased the lateral and posterior orientation of the patellar tendon. Each model was loaded at 40°, 60°, and 80° of flexion with quadriceps force vectors representing the experimental loading conditions. The orientation of the patellar tendon was represented for the loaded and unloaded hamstrings conditions based on experimental measures of tibiofemoral alignment. Similar to the experimental data, simulated loading of the hamstrings within the FEA models shifted the center of pressure laterally and increased the maximum lateral pressure. Significant (p < 0.05) differences were identified for the center of pressure and maximum lateral pressure from paired t-tests carried out at the individual flexion angles. The ability to replicate experimental trends indicates that the FEA models can be used for future studies focused on determining how variations in the orientation of the patellar tendon related to anatomical or loading variations or surgical procedures influence the patellofemoral pressure distribution.     

Wall stress and flow dynamics in abdominal aortic aneurysms: finite element analysis vs. fluid–structure interaction

Abdominal aortic aneurysm (AAA) rupture is the clinical manifestation of an induced force exceeding the resistance provided by the strength of the arterial wall. This force is most frequently assumed to be the product of a uniform luminal pressure acting along the diseased wall. However fluid dynamics is a known contributor to the pathogenesis of AAAs, and the dynamic interaction of blood flow and the arterial wall represents the in vivo environment at the macro-scale. The primary objective of this investigation is to assess the significance of assuming an arbitrary estimated peak fluid pressure inside the aneurysm sac for the evaluation of AAA wall mechanics, as compared with the non-uniform pressure resulting from a coupled fluid–structure interaction (FSI) analysis. In addition, a finite element approach is utilised to estimate the effects of asymmetry and wall thickness on the wall stress and fluid dynamics of ten idealised AAA models and one non-aneurysmal control. Five degrees of asymmetry with uniform and variable wall thickness are used. Each was modelled under a static pressure-deformation analysis, as well as a transient FSI. The results show that the inclusion of fluid flow yields a maximum AAA wall stress up to 20% higher compared to that obtained with a static wall stress analysis with an assumed peak luminal pressure of 117 mmHg. The variable wall models have a maximum wall stress nearly four times that of a uniform wall thickness, and also increasing with asymmetry in both instances. The inclusion of an axial stretch and external pressure to the computational domain decreases the wall stress by 17%.     

Wall stress and flow dynamics in abdominal aortic aneurysms: finite element analysis vs. fluid-structure interaction

Abdominal aortic aneurysm (AAA) rupture is the clinical manifestation of an induced force exceeding the resistance provided by the strength of the arterial wall. This force is most frequently assumed to be the product of a uniform luminal pressure acting along the diseased wall. However fluid dynamics is a known contributor to the pathogenesis of AAAs, and the dynamic interaction of blood flow and the arterial wall represents the in vivo environment at the macro-scale. The primary objective of this investigation is to assess the significance of assuming an arbitrary estimated peak fluid pressure inside the aneurysm sac for the evaluation of AAA wall mechanics, as compared with the non-uniform pressure resulting from a coupled fluid-structure interaction (FSI) analysis. In addition, a finite element approach is utilised to estimate the effects of asymmetry and wall thickness on the wall stress and fluid dynamics of ten idealised AAA models and one non-aneurysmal control. Five degrees of asymmetry with uniform and variable wall thickness are used. Each was modelled under a static pressure-deformation analysis, as well as a transient FSI. The results show that the inclusion of fluid flow yields a maximum AAA wall stress up to 20% higher compared to that obtained with a static wall stress analysis with an assumed peak luminal pressure of 117 mmHg. The variable wall models have a maximum wall stress nearly four times that of a uniform wall thickness, and also increasing with asymmetry in both instances. The inclusion of an axial stretch and external pressure to the computational domain decreases the wall stress by 17%.     

A comparison of modelling techniques for computing wall stress in abdominal aortic aneurysms

Background  

Aneurysms, in particular abdominal aortic aneurysms (AAA), form a significant portion of cardiovascular related deaths. There is much debate as to the most suitable tool for rupture prediction and interventional surgery of AAAs, and currently maximum diameter is used clinically as the determining factor for surgical intervention. Stress analysis techniques, such as finite element analysis (FEA) to compute the wall stress in patient-specific AAAs, have been regarded by some authors to be more clinically important than the use of a "one-size-fits-all" maximum diameter criterion, since some small AAAs have been shown to have higher wall stress than larger AAAs and have been known to rupture.     

Initial stress and nonlinear material behavior in patient-specific AAA wall stress analysis

Rupture risk estimation of abdominal aortic aneurysms (AAA) is currently based on the maximum diameter of the AAA. A more critical approach is based on AAA wall stress analysis. For that, in most cases, the AAA geometry is obtained from CT-data and treated as a stress free geometry. However, during CT imaging, the AAA is subjected to a time-averaged blood pressure and is therefore not stress free. The aim of this study is to evaluate the effect of neglecting these initial stresses (IS) on the patient-specific AAA wall stress as computed by finite element analysis. Additionally, the contribution of the nonlinear material behavior of the AAA wall is evaluated.Thirty patients with maximum AAA diameters below the current surgery criterion were scanned with contrast-enhanced CT and the AAA's were segmented from the image data. The mean arterial blood pressure (MAP) was measured immediately after the CT-scan and used to compute the IS corresponding with the CT geometry and MAP. Comparisons were made between wall stress obtained with and without IS and with linear and nonlinear material properties.On average, AAA wall stresses as computed with IS were higher than without IS. This was also the case for the stresses computed with the nonlinear material model compared to the linear material model. However, omitting initial stress and material nonlinearity in AAA wall stress computations leads to different effects in the resulting wall stress for each AAA. Therefore, provided that other assumptions made are not predominant, IS cannot be discarded and a nonlinear material model should be used in future patient-specific AAA wall stress analyses.     

Modeling pulsatile flow in aortic aneurysms: effect of non-Newtonian properties of blood

Pulsatile flow in an axisymmetric rigid-walled model of an abdominal aorta aneurysm was analyzed numerically for various aneurysm dilations using physiologically realistic resting waveform at time-averaged Reynolds number of 300 and peak Reynolds number of 1607. Discretization of the governing equations was achieved using a finite element scheme based on the Galerkin method of weighted residuals. Comparisons with previously published work on the basis of special cases were performed and found to be in excellent agreement. Our findings indicate that the velocity fields are significantly affected by non-Newtonian properties in pathologically altered configurations. Non-Newtonian fluid shear stress is found to be greater than Newtonian fluid shear stress during peak systole. Further, the maximum shear stress is found to occur near the distal end of AAA during peak systole. The impact of non-Newtonian blood flow characteristics on pressure compared to Newtonian model is found insignificant under resting conditions. Viscous and inertial forces associated with blood flow are responsible for the changes in the wall that result in thrombus deposition and dilation while rupture of AAA is more likely determined by much larger mechanical stresses imposed by pulsatile pressure on the wall of AAA.     

The influence of data shape acquisition process and geometric accuracy of the mandible for numerical simulation

Computer-aided technologies have allowed new 3D modelling capabilities and engineering analyses based on experimental and numerical simulation. It has enormous potential for product development, such as biomedical instrumentation and implants. However, due to the complex shapes of anatomical structures, the accuracy of these technologies plays an important key role for adequate and accurate finite element analysis (FEA). The objective of this study was to determine the influence of the geometry variability between two digital models of a human model of the mandible. Two different shape acquisition techniques, CT scan and 3D laser scan, were assessed. A total of 130 points were controlled and the deviations between the measured points of the physical and 3D virtual models were assessed. The results of the FEA study showed a relative difference of 20% for the maximum displacement and 10% for the maximum strain between the two geometries.     

Anisotropic AAA: Computational comparison between four and two fiber family material models

Abdominal aortic aneurysm (AAA) is a cardiovascular disease with high incidence among elderly population. Biomechanical computational analyses can provide fundamental insights into AAA pathogenesis and clinical management, but modeling should be sufficiently accurate. Several constitutive models of the AAA wall are present in the literature, and some of them seem to well describe the experimental behavior of the aneurysmatic human aorta. In this work we compare a two (2FF) and a four (4FF) fiber families constitutive models of the AAA wall. Both these models satisfactorily fit literature data from biaxial tests on the aneurysmatic tissue. To investigate the peculiar characteristics of these models, we considered the problem of AAA inflation, and solved it by implementing the constitutive equations in a finite element code. A 20% axial stretch was imposed to the aneurysm ends, to simulate the physiological condition. Although fitted on the same dataset, the two material models lead to considerably different outcomes. In particular, adopting a 4FF strain energy function (SEF), an increase of the circumferential stress values can be observed, while higher axial stresses are recorded for the 2FF model. These differences can be attributed to the intrinsic characteristics of the SEFs and to the effective stress field, with respect to the one experienced in biaxial experimental tests on which the fitting is based. In fact the two SEFs appear similar within the region of the stress-strain experimental data, but become different outside it, as in case of aneurysms, due to the effects of the data extrapolation process. It is suggested that experimental data should be obtained for conditions similar to those of the application for which they are intended.     

腹主动脉瘤生长过程的蠕变力学模型

基于增强对腹主动脉瘤生长过程的理解、为腹主动脉瘤临床手术提供参考的目的,本文根据腹主动脉瘤的生长物理机制,提出了以蠕变力学为基础模拟腹主动脉瘤生长过程的模型.建立了腹主动脉瘤简化模型,利用有限元方法进行模拟计算.结果显示蠕变模型能够有效模拟腹主动脉瘤生长过程中的形态变化.参数优化模型模拟结果符合临床统计数据所示的腹主动脉瘤生长过程.本文还讨论了腹主动脉材料力学参数对模型的影响.     

The influence of data shape acquisition process and geometric accuracy of the mandible for numerical simulation

Computer-aided technologies have allowed new 3D modelling capabilities and engineering analyses based on experimental and numerical simulation. It has enormous potential for product development, such as biomedical instrumentation and implants. However, due to the complex shapes of anatomical structures, the accuracy of these technologies plays an important key role for adequate and accurate finite element analysis (FEA).

The objective of this study was to determine the influence of the geometry variability between two digital models of a human model of the mandible. Two different shape acquisition techniques, CT scan and 3D laser scan, were assessed. A total of 130 points were controlled and the deviations between the measured points of the physical and 3D virtual models were assessed.

The results of the FEA study showed a relative difference of 20% for the maximum displacement and 10% for the maximum strain between the two geometries.     

3D reconstruction and manufacture of real abdominal aortic aneurysms: from CT scan to silicone model

Abdominal aortic aneurysm (AAA) can be defined as a permanent and irreversible dilation of the infrarenal aorta. AAAs are often considered to be an aorta with a diameter 1.5 times the normal infrarenal aorta diameter. This paper describes a technique to manufacture realistic silicone AAA models for use with experimental studies. This paper is concerned with the reconstruction and manufacturing process of patient-specific AAAs. 3D reconstruction from computed tomography scan data allows the AAA to be created. Mould sets are then designed for these AAA models utilizing computer aided designcomputer aided manufacture techniques and combined with the injection-moulding method. Silicone rubber forms the basis of the resulting AAA model. Assessment of wall thickness and overall percentage difference from the final silicone model to that of the computer-generated model was performed. In these realistic AAA models, wall thickness was found to vary by an average of 9.21%. The percentage difference in wall thickness recorded can be attributed to the contraction of the casting wax and the expansion of the silicone during model manufacture. This method may be used in conjunction with wall stress studies using the photoelastic method or in fluid dynamic studies using a laser-Doppler anemometry. In conclusion, these patient-specific rubber AAA models can be used in experimental investigations, but should be assessed for wall thickness variability once manufactured.     

Computational analysis of biomechanical contributors to possible endovascular graft failure

This paper evaluates numerically coupled blood flow and wall structure interactions in a representative stented abdominal aortic aneurysm (AAA) model, leading potentially to endovascular graft (EVG) failure. A total of 12 biomechanical contributors to possible EVG migration were considered. The results show that after EVG insertion for the given model, the peak AAA sac-pressure was reduced to 14.2 mmHg (11.8% of p_lumen), and hence the maximum von Mises wall stress and wall deformation dropped by factors of 20 and 10, respectively. Thus, an EVG can significantly reduce sac pressure, mechanical stress, pulsatile wall motion, and the maximum diameter in AAAs and hence prevent AAA rupture effectively. In the absence of endoleaks, elevated sac-pressure can still be caused by fluid-structure interactions between the EVG, stagnant blood, and AAA wall. EVG migration forces vary from 1.4 to 7 N for different EVG geometries, material properties, and hemodynamic conditions. AAA-neck angle, iliac bifurcation angle, neck aorta-to-iliac diameter ratio, EVG size, aorto-uni-iliac EVG, and hypertension play important roles in generating forces potentially leading to EVG migration.     

Pullout performance of self-tapping medical screws

This study investigates the effect of the pilot hole size, implant depth, synthetic bone density, and screw size on the pullout strength of the self-tapping screw using analytical, finite element, and experimental methodologies. Stress distribution and failure propagation mode around the implant thread zone are also investigated. Based on the finite element analysis (FEA) results, an analytical model for the pullout strength of the self-tapping screw is constructed in terms of the (synthetic) bone mechanical properties, screw size, and the implant depth. The pullout performance of self-tapping screws is discussed. Results from the analytical and finite element models are experimentally validated.     

A planar biaxial constitutive relation for the luminal layer of intra-luminal thrombus in abdominal aortic aneurysms

The rupture risk of abdominal aortic aneurysms (AAAs) is thought to be associated with increased levels of wall stress. Finite element analysis (FEA) allows the prediction of wall stresses in a patient-specific, non-invasive manner. We have recently shown that it is important to include the intra-luminal thrombus (ILT), present in approximately 70% of AAA, into FEA simulations of AAA. All FEA simulations to date assume an isotropic, homogeneous material behavior for this material. The purpose of this work was to investigate the multi-axial biomechanical behavior of ILT and to derive an appropriate constitutive relation. We performed planar biaxial testing on the luminal layer of nine ILT specimens obtained fresh in the operating room (9 patients, mean age 71+/-4.5 years, mean diameter 5.9+/-0.4 cm), and a constitutive relation was derived from this data. Peak stretch and maximum tangential modulus (MTM) values were recorded for the equibiaxial protocol in both the circumferential (theta) and longitudinal (L) directions. Stress contour plots were used to investigate the presence of mechanical anisotropy, after which an appropriate strain energy function was fit to each of the specimen datasets. The peak stretch values for the luminal layer of the ILT were (mean+/-SEM) 1.18+/-0.02 and 1.13+/-0.02 in the theta and L directions, respectively (p=0.14). The MTM values were 20+/-2 and 23+/-3N/cm(2) in the theta and L directions, respectively (p=0.37). From these results and our observation of the symmetry of the stress contour plots for each specimen, we concluded that the use of an isotropic strain energy function for ILT is appropriate. Each specimen data set was then fit to a second-order polynomial strain energy function of the first invariant of the left Cauchy-Green strain tensor, resulting in an accurate fit (average R(2)=0.92+/-0.02; range 0.80-0.99). Comparison of our previously reported, uniaxially derived constitutive relation with the biaxially derived relation derived here shows large differences in the predicted mechanical response, underscoring the importance of the appropriate experimental methods used to derive constitutive relations. Further work is merited in an effort to produce more accurate predictions of wall stresses in patient-specific AAA, and viscoelastic behaviors of the ILT.     

Effects of wall calcifications in patient-specific wall stress analyses of abdominal aortic aneurysms

It is generally acknowledged that rupture of an abdominal aortic aneurysm (AAA) occurs when the stress acting on the wall over the cardiac cycle exceeds the strength of the wall. Peak wall stress computations appear to give a more accurate rupture risk assessment than AAA diameter, which is currently used for a diagnosis. Despite the numerous studies utilizing patient-specific wall stress modeling of AAAs, none investigated the effect of wall calcifications on wall stress. The objective of this study was to evaluate the influence of calcifications on patient-specific finite element stress computations. In addition, we assessed whether the effect of calcifications could be predicted directly from the CT-scans by relating the effect to the amount of calcification present in the AAA wall. For 6 AAAs, the location and extent of calcification was identified from CT-scans. A finite element model was created for each AAA and the areas of calcification were defined node-wise in the mesh of the model. Comparisons are made between maximum principal stress distributions, computed without calcifications and with calcifications with varying material properties. Peak stresses are determined from the stress results and related to a calcification index (CI), a quantification of the amount of calcification in the AAA wall. At calcification sites, local stresses increased, leading to a peak stress increase of 22% in the most severe case. Our results displayed a weak correlation between the CI and the increase in peak stress. Additionally, the results showed a marked influence of the calcification elastic modulus on computed stresses. Inclusion of calcifications in finite element analysis of AAAs resulted in a marked alteration of the stress distributions and should therefore be included in rupture risk assessment. The results also suggest that the location and shape of the calcified regions--not only the relative amount--are considerations that influence the effect on AAA wall stress. The dependency of the effect of the wall stress on the calcification elastic modulus points out the importance of determination of the material properties of calcified AAA wall.