Prestressing in finite deformation abdominal aortic aneurysm simulation

Fluid-structure interactions of peripheral arteries using a coupled in silico and in vitro approach

Vascular compliance is considered both a cause and a consequence of cardiovascular disease and a significant factor in the mid- and long-term patency of vascular grafts. However, the biomechanical effects of localised changes in compliance cannot be satisfactorily studied with the available medical imaging technologies or surgical simulation materials. To address this unmet need, we developed a coupled silico-vitro platform which allows for the validation of numerical fluid-structure interaction results as a numerical model and physical prototype. This numerical one-way and two-way fluid-structure interaction study is based on a three-dimensional computer model of an idealised femoral artery which is validated against patient measurements derived from the literature. The numerical results are then compared with experimental values collected from compliant arterial phantoms via direct pressurisation and ring tensile testing. Phantoms within a compliance range of 1.4-68.0%/100 mmHg were fabricated via additive manufacturing and silicone casting, then mechanically characterised via ring tensile testing and optical analysis under direct pressurisation with moderately statistically significant differences in measured compliance ranging between 10 and 20% for the two methods. One-way fluid-structure interaction coupling underestimated arterial wall compliance by up to 14.7% compared with two-way coupled models. Overall, Solaris™ (Smooth-On) matched the compliance range of the numerical and in vivo patient models most closely out of the tested silicone materials. Our approach is promising for vascular applications where mechanical compliance is especially important, such as the study of diseases which commonly affect arterial wall stiffness, such as atherosclerosis, and the model-based design, surgical training, and optimisation of vascular prostheses.

Biomechanical Characterisation of Thoracic Ascending Aorta with Preserved Pre-Stresses

Mechanical properties of an aneurysmatic thoracic aorta are potential markers of future growth and remodelling and can help to estimate the risk of rupture. Aortic geometries obtained from routine medical imaging do not display wall stress distribution and mechanical properties. Mechanical properties for a given vessel may be determined from medical images at different physiological pressures using inverse finite element analysis. However, without considering pre-stresses, the estimation of mechanical properties will lack accuracy. In the present paper, we propose and evaluate a mechanical parameter identification technique, which recovers pre-stresses by determining the zero-pressure configuration of the aortic geometry. We first validated the method on a cylindrical geometry and subsequently applied it to a realistic aortic geometry. The verification of the assessed parameters was performed using synthetically generated reference data for both geometries. The method was able to estimate the true mechanical properties with an accuracy ranging from 98% to 99%.

A quarter of a century biomechanical rupture risk assessment of abdominal aortic aneurysms. Achievements, clinical relevance, and ongoing developments

Abdominal aortic aneurysm (AAA) disease, the local enlargement of the infrarenal aorta, is a serious condition that causes many deaths, especially in men exceeding 65 years of age. Over the past quarter of a century, computational biomechanical models have been developed towards the assessment of AAA risk of rupture, technology that is now on the verge of being integrated within the clinical decision-making process. The modeling of AAA requires a holistic understanding of the clinical problem, in order to set appropriate modeling assumptions and to draw sound conclusions from the simulation results. In this article we summarize and critically discuss the proposed modeling approaches and report the outcome of clinical validation studies for a number of biomechanics-based rupture risk indices. Whilst most of the aspects concerning computational mechanics have already been settled, it is the exploration of the failure properties of the AAA wall and the acquisition of robust input data for simulations that has the greatest potential for the further improvement of this technology.

Assessment of shape-based features ability to predict the ascending aortic aneurysm growth

The current guidelines for the ascending aortic aneurysm (AsAA) treatment recommend surgery mainly according to the maximum diameter assessment. This criterion has already proven to be often inefficient in identifying patients at high risk of aneurysm growth and rupture. In this study, we propose a method to compute a set of local shape features that, in addition to the maximum diameter D, are intended to improve the classification performances for the ascending aortic aneurysm growth risk assessment. Apart from D, these are the ratio DCR between D and the length of the ascending aorta centerline, the ratio EILR between the length of the external and the internal lines and the tortuosity T. 50 patients with two 3D acquisitions at least 6 months apart were segmented and the growth rate (GR) with the shape features related to the first exam computed. The correlation between them has been investigated. After, the dataset was divided into two classes according to the growth rate value. We used six different classifiers with input data exclusively from the first exam to predict the class to which each patient belonged. A first classification was performed using only D and a second with all the shape features together. The performances have been evaluated by computing accuracy, sensitivity, specificity, area under the receiver operating characteristic curve (AUROC) and positive (negative) likelihood ratio LHR+ (LHR-). A positive correlation was observed between growth rate and DCR (r = 0.511, p = 1.3e-4) and between GR and EILR (r = 0.472, p = 2.7e-4). Overall, the classifiers based on the four metrics outperformed the same ones based only on D. Among the diameter-based classifiers, k-nearest neighbours (KNN) reported the best accuracy (86%), sensitivity (55.6%), AUROC (0.74), LHR+ (7.62) and LHR- (0.48). Concerning the classifiers based on the four shape features, we obtained the best accuracy (94%), sensitivity (66.7%), specificity (100%), AUROC (0.94), LHR+ (+∞) and LHR- (0.33) with support vector machine (SVM). This demonstrates how automatic shape features detection combined with risk classification criteria could be crucial in planning the follow-up of patients with ascending aortic aneurysm and in predicting the possible dangerous progression of the disease.

Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications

Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.

Estimation of the zero-pressure computational start shape of atherosclerotic plaques: Improving the backward displacement method with deformation gradient tensor

Advances in medical imaging have enabled patient-specific biomechanical modelling of arterial lesions such as atherosclerosis and aneurysm. Geometry acquired from in-vivo imaging is already pressurized and a zero-pressure computational start shape needs to be identified. The backward displacement algorithm was proposed to solve this inverse problem, utilizing fixed-point iterations to gradually approach the start shape. However, classical fixed-point implementations were reported with suboptimal convergence properties under large deformations. In this paper, a dynamic learning rate guided by the deformation gradient tensor was introduced to control the geometry update. The effectiveness of this new algorithm was demonstrated for both idealized and patient-specific models. The proposed algorithm led to faster convergence by accelerating the initial steps and helped to avoid the non-convergence in large-deformation problems.

Patient-specific computational modeling of endovascular aneurysm repair: State of the art and future directions

Endovascular aortic repair (EVAR) has become the preferred intervention option for aortic aneurysms and dissections. This is because EVAR is much less invasive than the alternative open surgery repair. While in-hospital mortality rates are smaller for EVAR than open repair (1%-2% vs. 3%-5%), the early benefits of EVAR are lost after 3 years due to larger rates of complications in the EVAR group. Clinicians follow instructions for use (IFU) when possible, but are left with personal experience on how to best proceed and what choices to make with respect to stent-graft (SG) model choice, sizing, procedural options, and their implications on long-term outcomes. Computational modeling of SG deployment in EVAR and tissue remodeling after intervention offers an alternative way of testing SG designs in silico, in a personalized way before intervention, to ultimately select the strategies leading to better outcomes. Further, computational modeling can be used in the optimal design of SGs in cases of complex geometries. In this review, we address some of the difficulties and successes associated with computational modeling of EVAR procedures. There is still work to be done in all areas of EVAR in silico modeling, including model validation, before models can be applied in the clinic, but much progress has already been made. Critical to clinical implementation are current efforts focusing on developing fast algorithms that can achieve (near) real-time solutions, as well as ways of dealing with inherent uncertainties related to patient aortic wall degradation on an individualized basis. We are optimistic that EVAR modeling in the clinic will soon become a reality to help clinicians optimize EVAR interventions and ultimately reduce EVAR-associated complications.

Patient-Specific Biomechanics in Marfan Ascending Thoracic Aortic Aneurysms

BACKGROUND

Guidelines for Sinus of Valsalva-thoracic aortic aneurysms (SOV-TAA) in Marfan syndrome recommend size-based criteria for elective surgical repair. Biomechanics may provide a better prediction of dissection risk than diameter. Our aim was to determine magnitudes of wall stress in the aortic root of Marfan patients using finite element analyses.

METHODS

Forty-six Marfan patients underwent patient-specific 3D SOV-TAA geometry reconstruction using imaging data. Finite element analyses were performed to determine wall stress distributions at SOV, sinotubular junction (STJ), and ascending aorta (AscAo) at systole.

RESULTS

Peak circumferential stresses were 432.8±111kPa, 408.1±88.3kPa, and 321.9±83.8kPa at the SOV, STJ, and AscAo, respectively with significant differences between SOV and AscAo (p<3.08E-07), and STJ and AscAo (p<2.26E-06). Peak longitudinal wall stresses were 352±73.9kPa, 277.5±89.5kPa, and 200.6±81kPa at SOV, STJ, and AscAo, respectively with significant differences between SOV and STJ (p< 6.01E-06), SOV and AscAo (p< 9.79E-13), and STJ and AscAo (p< 3.34E-07). Diameter was not correlated to wall stresses. Comparison of wall stresses in aneurysm <5cm vs ≥5cm and <4.5cm vs ≥4.5 showed no significant differences in wall stresses in the circumferential or longitudinal direction.

CONCLUSIONS

Peak wall stresses in Marfan SOV-TAA were greatest in SOV than STJ than AscAo. Diameter was poorly correlated to peak stresses such that current guidelines with 5cm cutoff had significant overlap in peak stresses in patients with <5cm vs ≥5cm. Use of patient-specific Marfan aneurysm models may identify patients with high wall stresses and small aneurysms who could benefit from earlier surgical repair to prevent aortic dissection.

Biomechanical rupture risk assessment of abdominal aortic aneurysms using clinical data: A patient-specific, probabilistic framework and comparative case-control study

We present a data-informed, highly personalized, probabilistic approach for the quantification of abdominal aortic aneurysm (AAA) rupture risk. Our novel framework builds upon a comprehensive database of tensile test results that were carried out on 305 AAA tissue samples from 139 patients, as well as corresponding non-invasively and clinically accessible patient-specific data. Based on this, a multivariate regression model is created to obtain a probabilistic description of personalized vessel wall properties associated with a prospective AAA patient. We formulate a probabilistic rupture risk index that consistently incorporates the available statistical information and generalizes existing approaches. For the efficient evaluation of this index, a flexible Kriging-based surrogate model with an active training process is proposed. In a case-control study, the methodology is applied on a total of 36 retrospective, diameter matched asymptomatic (group 1, n = 18) and known symptomatic/ruptured (group 2, n = 18) cohort of AAA patients. Finally, we show its efficacy to discriminate between the two groups and demonstrate competitive performance in comparison to existing deterministic and probabilistic biomechanical indices.

Influence of coupled hemodynamics-arterial wall interaction on compliance in a realistic pulmonary artery with variable intravascular wall properties

Pulmonary hypertension is characterized by elevation of pulmonary artery (PA) pressure (p) and structural remodeling of the PA wall, leading to reduction in arterial compliance (c). As a step towards improving diagnosis of pulmonary disease, we use the PA branch geometry (main pulmonary artery (MPA) branching into left (LPA) and right (RPA) pulmonary arteries) obtained from MRI in conjunction with an inverse algorithm to obtain the pre-stress level in the artery walls. Next, a coupled blood-wall interaction (BWI) calculation provides hemodynamic information as well as compliance of the PA walls. We show that the computed load-free geometry from the inverse algorithm exhibits a 27.8% lower inner diameter (d) and 18.5% lower outer d compared to the in vivo geometry from MRI. Further, the mean p computed from the BWI computation in the main PA (p_MPA-n) is within 4% of the mean p_MPA-e (n-numerical; e-experimental). Also, the mean Q computed in the left PA (Q_LPA-n) is within 10% of the mean Q_LPA-e. Finally, the compliance c_MPA-n is computed to be 27% lower than c_MPA-e, while the c_LPA-n is computed to be 20.4% lower than c_LPA-e. Importantly, the PA shows significant intra-vascular variation in compliance, with the MPA showing higher overall compliance compared to the LPA (3.5-4 times).

A comparative study of methods used to generate the arterial fiber structure in a clinically relevant numerical analysis

The advanced constitutive material models of artery wall require the definition of the mean collagen fiber directions in the material configuration. There are several proposed methods; however, it is unclear how much does the fiber structures obtained by these methods differ one from the other and how much this difference may affect the results of the structural analysis of a clinically relevant scenario. Therefore, in this paper, we address this issue by presenting the results of the comparative study of our developed and currently state-of-the-art fiber definition methods. In addition, we present the verification of our developed numerical model that incorporates the extended Holzapfel-Gasser-Ogden (HGO) constitutive material model and the generalized prestressing algorithm (GPA). In the case of the patient-specific internal carotid artery (ICA), the percentage error of the mean fiber directions defined by different methods does not exceed 17.73% (at least 0.05%, at most 81.82%) and has negligible effect on the stress levels, as the percentage error of the mean circumferential Cauchy stress does not exceed 0.1%. Both fiber definition methods produce comparable fiber structure, but our proposed method has an advantage, as it does not depend on method and software used to model the arterial wall mechanics.

Biobanking: Objectives, Requirements, and Future Challenges-Experiences from the Munich Vascular Biobank

Collecting biological tissue samples in a biobank grants a unique opportunity to validate diagnostic and therapeutic strategies for translational and clinical research. In the present work, we provide our long-standing experience in establishing and maintaining a biobank of vascular tissue samples, including the evaluation of tissue quality, especially in formalin-fixed paraffin-embedded specimens (FFPE). Our Munich Vascular Biobank includes, thus far, vascular biomaterial from patients with high-grade carotid artery stenosis (n = 1567), peripheral arterial disease (n = 703), and abdominal aortic aneurysm (n = 481) from our Department of Vascular and Endovascular Surgery (January 2004–December 2018). Vascular tissue samples are continuously processed and characterized to assess tissue morphology, histological quality, cellular composition, inflammation, calcification, neovascularization, and the content of elastin and collagen fibers. Atherosclerotic plaques are further classified in accordance with the American Heart Association (AHA), and plaque stability is determined. In order to assess the quality of RNA from FFPE tissue samples over time (2009–2018), RNA integrity number (RIN) and the extent of RNA fragmentation were evaluated. Expression analysis was performed with two housekeeping genes—glyceraldehyde 3-phosphate dehydrogenase (GAPDH) and beta-actin (ACTB)—using TaqMan-based quantitative reverse-transcription polymerase chain reaction (qRT)-PCR. FFPE biospecimens demonstrated unaltered RNA stability over time for up to 10 years. Furthermore, we provide a protocol for processing tissue samples in our Munich Vascular Biobank. In this work, we demonstrate that biobanking is an important tool not only for scientific research but also for clinical usage and personalized medicine.

Adaptation of cardiovascular system stent implants

Time-consuming design and manufacturing processes are a serious disadvantage when adapting human cardiovascular implants as they cause unacceptable delays after the decision to intervene surgically has been made. An ideal cardiovascular implant should have a broad range of characteristics such as strength, viscoelasticity and blood compatibility. The present research proposes the sequence of the geometrical adaptation procedures and presents their results. The adaptation starts from the identification of a person's current health status while performing abdominal aortic aneurysm (AAA) imaging, which is a point of departure for the mathematical model of a cardiovascular implant. The computerized tomography scan shows the patient-specific geometry parameters of AAA and helps to create a model using COMSOL Multiphysics software. The initial parameters for flow simulation are taken from the results of a patient survey. The simulation results allow choosing the available shape of an implant which ensures a non-turbulent flow. These parameters are essential for the design and manufacturing of an implant prototype which should be tested experimentally for the assurance that the mathematical model is adequate to a physical one. The article gives a focused description of competences and means that are necessary to achieve the shortest possible preparation of the adapted cardiovascular implant for the surgery.

The impact of personalized probabilistic wall thickness models on peak wall stress in abdominal aortic aneurysms

If computational models are ever to be used in high-stakes decision making in clinical practice, the use of personalized models and predictive simulation techniques is a must. This entails rigorous quantification of uncertainties as well as harnessing available patient-specific data to the greatest extent possible. Although researchers are beginning to realize that taking uncertainty in model input parameters into account is a necessity, the predominantly used probabilistic description for these uncertain parameters is based on elementary random variable models. In this work, we set out for a comparison of different probabilistic models for uncertain input parameters using the example of an uncertain wall thickness in finite element models of abdominal aortic aneurysms. We provide the first comparison between a random variable and a random field model for the aortic wall and investigate the impact on the probability distribution of the computed peak wall stress. Moreover, we show that the uncertainty about the prevailing peak wall stress can be reduced if noninvasively available, patient-specific data are harnessed for the construction of the probabilistic wall thickness model.

Fiber-reinforced computational model of the aortic root incorporating thoracic aorta and coronary structures

Cardiovascular diseases are still the leading causes of death in the developed world. The decline in the mortality associated with circulatory system diseases is accredited to development of new diagnostic and prognostic tools. It is well known that there is an inter relationship between the aortic valve impairment and pathologies of the aorta and coronary vessels. However, due to the limitations of the current tools, the possible link is not fully elucidated. Following our previous model of the aortic root including the coronaries, in this study, we have further developed the global aspect of the model by incorporating the anatomical structure of the thoracic aorta. This model is different from all the previous studies in the sense that inclusion of the coronary structures and thoracic aorta into the natural aortic valve introduces the notion of globality into the model enabling us to explore the possible link between the regional pathologies. The developed model was first validated using the available data in the literature under physiological conditions. Then, to provide a support for the possible association between the localized cardiovascular pathologies and global variations in hemodynamic conditions, we simulated the model for two pathological conditions including moderate and severe aortic valve stenoses. The findings revealed that malformations of the aortic valve are associated with development of low wall shear stress regions and helical blood flow in thoracic aorta that are considered major contributors to aortic pathologies.

MRI-based patient-specific human carotid atherosclerotic vessel material property variations in patients, vessel location and long-term follow up

Background

Image-based computational models are widely used to determine atherosclerotic plaque stress/strain conditions and investigate their association with plaque progression and rupture. However, patient-specific vessel material properties are in general lacking in those models, limiting the accuracy of their stress/strain measurements. A noninvasive approach of combining in vivo 3D multi-contrast and Cine magnetic resonance imaging (MRI) and computational modeling was introduced to quantify patient-specific carotid plaque material properties for potential plaque model improvements. Vessel material property variation in patients, along vessel segment, and between baseline and follow up were investigated.

Methods

In vivo 3D multi-contrast and Cine MRI carotid plaque data were acquired from 8 patients with follow-up (18 months) with written informed consent obtained. 3D thin-layer models and an established iterative procedure were used to determine parameter values of the Mooney-Rivlin models for the 81slices from 16 plaque samples. Effective Young’s Modulus (YM) values were calculated for comparison and analysis.

Results

Average Effective Young’s Modulus (YM) and circumferential shrinkage rate (C-Shrink) value of the 81 slices was 411kPa and 5.62%, respectively. Slice YM value varied from 70 kPa (softest) to 1284 kPa (stiffest), a 1734% difference. Average slice YM values by vessel varied from 109 kPa (softest) to 922 kPa (stiffest), a 746% difference. Location-wise, the maximum slice YM variation rate within a vessel was 311% (149 kPa vs. 613 kPa). The average slice YM variation rate for the 16 vessels was 134%. The average variation of YM values for all patients from baseline to follow up was 61.0%. The range of the variation of YM values was [-28.4%, 215%]. For plaque progression study, YM at follow-up showed negative correlation with plaque progression measured by wall thickness increase (WTI) (r = -0.7764, p = 0.0235). Wall thickness at baseline correlated with WTI negatively, with r = -0.5253 (p = 0.1813). Plaque burden at baseline correlated with YM change between baseline and follow-up, with r = 0.5939 (p = 0.1205).

Conclusion

In vivo carotid vessel material properties have large variations from patient to patient, along the diseased segment within a patient, and with time. The use of patient-specific, location specific and time-specific material properties in plaque models could potentially improve the accuracy of model stress/strain calculations.

Evaluation of Hemodynamics in a Prestressed and Compliant Tapered Femoral Artery Using an Optimization-Based Inverse Algorithm

The important factors that affect the arterial wall compliance are the tissue properties of the arterial wall, the in vivo pulsatile pressure, and the prestressed condition of the artery. It is necessary to obtain the load-free geometry for determining the physiological level of prestress in the arterial wall. The previously developed optimization-based inverse algorithm was improved to obtain the load-free geometry and the wall prestress of an idealized tapered femoral artery of a dog under varying arterial wall properties. The compliance of the artery was also evaluated over a range of systemic pressures (72.5–140.7 mmHg), associated blood flows, and artery wall properties using the prestressed arterial geometry. The results showed that the computed load-free outer diameter at the inlet of the tapered artery was 6.7%, 9.0%, and 12% smaller than the corresponding in vivo diameter for the 25% softer, baseline, and 25% stiffer arterial wall properties, respectively. In contrast, the variations in the prestressed geometry and circumferential wall prestress were less than 2% for variable arterial wall properties. The computed compliance at the inlet of the prestressed artery for the baseline arterial wall property was 0.34%, 0.19%, and 0.13% diameter change/mmHg for time-averaged pressures of 72.5, 104.1, and 140.7 mmHg, respectively. However, the variation in compliance due to the change in arterial wall property was less than 6%. The load-free and prestressed geometries of the idealized tapered femoral artery were accurately (error within 1.2% of the in vivo geometry) computed under variable arterial wall properties using the modified inverse algorithm. Based on the blood-arterial wall interaction results, the arterial wall compliance was influenced significantly by the change in average pressure. In contrast, the change in arterial wall property did not influence the arterial wall compliance.

A Methodology for the Derivation of Unloaded Abdominal Aortic Aneurysm Geometry With Experimental Validation

In this work, we present a novel method for the derivation of the unloaded geometry of an abdominal aortic aneurysm (AAA) from a pressurized geometry in turn obtained by 3D reconstruction of computed tomography (CT) images. The approach was experimentally validated with an aneurysm phantom loaded with gauge pressures of 80, 120, and 140 mm Hg. The unloaded phantom geometries estimated from these pressurized states were compared to the actual unloaded phantom geometry, resulting in mean nodal surface distances of up to 3.9% of the maximum aneurysm diameter. An in-silico verification was also performed using a patient-specific AAA mesh, resulting in maximum nodal surface distances of 8 μm after running the algorithm for eight iterations. The methodology was then applied to 12 patient-specific AAA for which their corresponding unloaded geometries were generated in 5-8 iterations. The wall mechanics resulting from finite element analysis of the pressurized (CT image-based) and unloaded geometries were compared to quantify the relative importance of using an unloaded geometry for AAA biomechanics. The pressurized AAA models underestimate peak wall stress (quantified by the first principal stress component) on average by 15% compared to the unloaded AAA models. The validation and application of the method, readily compatible with any finite element solver, underscores the importance of generating the unloaded AAA volume mesh prior to using wall stress as a biomechanical marker for rupture risk assessment.

Quantify patient-specific coronary material property and its impact on stress/strain calculations using in vivo IVUS data and 3D FSI models: a pilot study

Computational models have been used to calculate plaque stress and strain for plaque progression and rupture investigations. An intravascular ultrasound (IVUS)-based modeling approach is proposed to quantify in vivo vessel material properties for more accurate stress/strain calculations. In vivo Cine IVUS and VH-IVUS coronary plaque data were acquired from one patient with informed consent obtained. Cine IVUS data and 3D thin-slice models with axial stretch were used to determine patient-specific vessel material properties. Twenty full 3D fluid-structure interaction models with ex vivo and in vivo material properties and various axial and circumferential shrink combinations were constructed to investigate the material stiffness impact on stress/strain calculations. The approximate circumferential Young's modulus over stretch ratio interval [1.0, 1.1] for an ex vivo human plaque sample and two slices (S6 and S18) from our IVUS data were 1631, 641, and 346 kPa, respectively. Average lumen stress/strain values from models using ex vivo, S6 and S18 materials with 5 % axial shrink and proper circumferential shrink were 72.76, 81.37, 101.84 kPa and 0.0668, 0.1046, and 0.1489, respectively. The average cap strain values from S18 material models were 150-180 % higher than those from the ex vivo material models. The corresponding percentages for the average cap stress values were 50-75 %. Dropping axial and circumferential shrink consideration led to stress and strain over-estimations. In vivo vessel material properties may be considerably softer than those from ex vivo data. Material stiffness variations may cause 50-75 % stress and 150-180 % strain variations.

Immersed boundary-finite element model of fluid-structure interaction in the aortic root

It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to e-volve as increasingly detailed in vivo imaging data become available. Herein, we describe a fluid-structure interaction model of the aortic root, including the aortic valve leaflets, the sinsuses of Valsalva, the aortic annulus, and the sinotubular junction, that employs a version of Peskin's immersed boundary (IB) method with a finite element (FE) description of the structural elasticity. As in earlier work, we use a fiber-based model of the valve leaflets, but this study extends earlier IB models of the aortic root by employing an incompressible hyperelastic model of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backward displacement method that determines the unloaded configurations of the root model. Our model yields realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations indicate that although the detailed leaflet and root kinematics show some grid sensitivity, our IB model of the aortic root nonetheless produces essentially grid-converged flow rates and pressures at practical grid spacings for the high-Reynolds number flows of the aortic root. These results thereby clarify minimum grid resolutions required by such models when used as stand-alone models of the aortic valve as well as when used to provide models of the outflow valves in models of left ventricular fluid dynamics.

On the effect of preload and pre-stretch on hemodynamic simulations: an integrative approach

In this work, we address the simulation of three-dimensional arterial blood flow and its effect on the stress state of arterial walls. The novel contribution is the unprecedented combination of several modeling techniques to account for (1) the fact that known configurations for the arterial wall are in a preloaded state, (2) the compliance of the vessel segments, (3) proper boundary data over the non-physical interfaces resulting from the isolation of an arterial district from the rest of the arterial tree, (4) the presence of surrounding tissues in which the vessel is embedded and (5) residual stress state due to pre-stretch. Firstly, we formulate both the forward mechanical problem when the reference (zero-load) configuration is assumed to be known and, the preload problem arising when the known domain is a configuration at equilibrium with a certain load state (typically due to internal pressure and tethering forces). Then, two additional complexities are faced: the fluid-structure interaction problem that follows when the compliant vessels are coupled with the blood flow, and the introduction of non-physical boundaries coming from the artificial isolation of the arterial district from the original vessel. This, in turn, posses the problem of coupling dimensionally heterogeneous models to incorporate the effect of upstream and downstream systemic impedances. Additionally, a viscoelastic support on the external surface of the vessel is also incorporated. Two examples are presented to quantify in a physiologically consistent scenario the differences in simulation results when either considering or not the preload state of arterial walls. These computational simulations shed light on the validity of simplifying hypotheses in most hemodynamic models.

[Contribution of mathematical models and biomechanical properties in predicting the risk of abdominal aortic aneurysm rupture]

INTRODUCTION

Rupture is the worst outcome of abdominal aortic aneurysm (AAA). The decision to operate should include counterbalancing the risk of aneurysm rupture against the risk of aneurysm repair, within the context of a patient's overall life expectancy. Current surgical guidelines are based on population studies, and important variables are missed in predicting individual risk of rupture.

METHODS

In this literature review, we focused on the contribution of biomechanical and mathematical models in predicting risk of AAA rupture.

RESULTS

Anatomical features as diameter asymmetry and lack of tortuosity are shown to be anatomical risk factors of rupture. Wall stiffness (due to modifications of elastin and collagen composition) and increased inflammatory response are also factors that affect the structural integrity of the AAA wall. Biomechanical studies showed that wall strength is lower in ruptured than non-ruptured AAA. Intra-luminal thrombus also has a big role to play in the occurrence of rupture. Current mathematical models allow more variables to be included in predicting individual risk of rupture.

CONCLUSION

Moving away from using maximal transverse diameter of the AAA as a unique predictive factor and instead including biological, structural and biomechanical variables in predicting individual risk of rupture will be essential in the future and will help gain precision and accuracy in surgical indications.

Finite element simulation of the insertion of guidewires during an EVAR procedure: example of a complex patient case, a first step toward patient-specific parameterized models

Deformations of the vascular structure due to the insertion of tools during endovascular treatment of aneurysms of the abdominal aorta, unless properly anticipated during the preoperative planning phase, may be the source of intraoperative or postoperative complications. We propose here an explicit finite element simulation method which enables one to predict such deformations. This method is based on a mechanical model of the vascular structure which takes into account the nonlinear behavior of the arterial wall, the prestressing effect induced by the blood pressure and the mechanical support of the surrounding organs and structures. An analysis of the model sensitivity to the parameters used to represent this environment is done. This allows determining the parameters that have the largest influence on the quality of the prediction and also provides realistic values for each of them as no experimental data are available in the literature. Moreover, for the first time, the results are compared with 3D intraoperative data. This is done for a patient-specific case with a complex anatomy in order to assess the feasibility of the method. Finally, the predictive capability of the simulation is evaluated on a group of nine patients. The error between the final simulated and intraoperatively measured tool positions was 2.1 mm after the calibration phase on one patient. It results in a 4.6 ± 2.5 mm in average error for the blind evaluation on nine patients.

Effect of Intraluminal Thrombus Asymmetrical Deposition on Abdominal Aortic Aneurysm Growth Rate

Purpose: To determine the relationship between asymmetrical intraluminal thrombus (ILT) deposition in abdominal aortic aneurysm (AAA) and growth rate and to explore its biomechanical perspective. Methods: Thirty-four patients with AAA underwent at least 2 computed tomography scans during surveillance. The volumes of the AAA (VAAA) and thrombus (VILT) and the maximum thrombus thickness (ILTthick) were computed. Thrombus distribution was evaluated by introducing the asymmetrical thrombus deposition index (ATDI), with positive and negative values (–1<ATDI<1) associated with anterior and posterior ILT deposition, respectively. Finite element analysis was applied to estimate wall stress. Aneurysms were divided into high and low growth rate groups based on the cohort’s median growth rate, and the abovementioned parameters were compared between groups. Results: Most AAAs had asymmetrical anterior thrombus deposition. The high and low growth rate groups did not present significant differences in maximum diameter, VAAA, VILT, or maximum ILTthick. However, the high growth rate group had significantly higher ATDI (p=0.02). The ATDI<0 group (posterior ILT distribution) presented a significantly lower median growth rate compared to that of ATDI≥0 group (anterior or symmetrical ILT deposition; p=0.029). The specificity of an ATDI<0 criterion for identifying AAAs with a growth rate below the cohort median was 89%. The ATDI<0 group had a significantly lower posterior maximum wall stress compared with that of the ATDI≥0 group (p=0.03). Overall peak wall stress did not differ between groups. Conclusion: Posterior thrombus deposition in AAAs is associated with significantly lower growth rate and lower posterior maximum wall stress compared with that of AAAs with anterior thrombus deposition and could potentially indicate a lower rupture risk.

Pulsatile arterial wall-blood flow interaction with wall pre-stress computed using an inverse algorithm

Background

The computation of arterial wall deformation and stresses under physiologic conditions requires a coupled compliant arterial wall-blood flow interaction model. The in-vivo arterial wall motion is constrained by tethering from the surrounding tissues. This tethering, together with the average in-vivo pressure, results in wall pre-stress. For an accurate simulation of the physiologic conditions, it is important to incorporate the wall pre-stress in the computational model. The computation of wall pre-stress is complex, as the un-loaded and un-tethered arterial shape with residual stress is unknown. In this study, the arterial wall deformation and stresses in a canine femoral artery under pulsatile pressure was computed after incorporating the wall pre-stresses. A nonlinear least square optimization based inverse algorithm was developed to compute the in-vivo wall pre-stress.

Methods

First, the proposed inverse algorithm was used to obtain the un-loaded and un-tethered arterial geometry from the unstressed in-vivo geometry. Then, the un-loaded, and un-tethered arterial geometry was pre-stressed by applying a mean in-vivo pressure of 104.5 mmHg and an axial stretch of 48% from the un-tethered length. Finally, the physiologic pressure pulse was applied at the inlet and the outlet of the pre-stressed configuration to calculate the in-vivo deformation and stresses. The wall material properties were modeled with an incompressible, Mooney-Rivlin model derived from previously published experimental stress-strain data (Attinger et al., 1968).

Results

The un-loaded and un-tethered artery geometry computed by the inverse algorithm had a length, inner diameter and thickness of 35.14 mm, 3.10 mm and 0.435 mm, respectively. The pre-stressed arterial wall geometry was obtained by applying the in-vivo axial-stretch and average in-vivo pressure to the un-loaded and un-tethered geometry. The length of the pre-stressed artery, 51.99 mm, was within 0.01 mm (0.019%) of the in-vivo length of 52.0 mm; the inner diameter of 3.603 mm was within 0.003 mm (0.08%) of the corresponding in-vivo diameter of 3.6 mm, and the thickness of 0.269 mm was within 0.0015 mm (0.55%) of the in-vivo thickness of 0.27 mm. Under physiologic pulsatile pressure applied to the pre-stressed artery, the time averaged longitudinal stress was found to be 42.5% higher than the circumferential stresses. The results of this study are similar to the results reported by Zhang et al., (2005) for the left anterior descending coronary artery.

Conclusions

An inverse method was adopted to compute physiologic pre-stress in the arterial wall before conducting pulsatile hemodynamic calculations. The wall stresses were higher in magnitude in the longitudinal direction, under physiologic pressure after incorporating the effect of in-vivo axial stretch and pressure loading.

Abdominal aortic aneurysm: from clinical imaging to realistic replicas

The goal of this work is to develop a framework for manufacturing nonuniform wall thickness replicas of abdominal aortic aneurysms (AAAs). The methodology was based on the use of computed tomography (CT) images for virtual modeling, additive manufacturing for the initial physical replica, and a vacuum casting process and range of polyurethane resins for the final rubberlike phantom. The average wall thickness of the resulting AAA phantom was compared with the average thickness of the corresponding patient-specific virtual model, obtaining an average dimensional mismatch of 180 μm (11.14%). The material characterization of the artery was determined from uniaxial tensile tests as various combinations of polyurethane resins were chosen due to their similarity with ex vivo AAA mechanical behavior in the physiological stress configuration. The proposed methodology yields AAA phantoms with nonuniform wall thickness using a fast and low-cost process. These replicas may be used in benchtop experiments to validate deformations obtained with numerical simulations using finite element analysis, or to validate optical methods developed to image ex vivo arterial deformations during pressure-inflation testing.

A generalized prestressing algorithm for finite element simulations of preloaded geometries with application to the aorta

Finite element models reconstructed from medical imaging data, for example, computed tomography or MRI scans, generally represent geometries under in vivo load. Classical finite element approaches start from an unloaded reference configuration. We present a generalized prestressing algorithm based on a concept introduced by Gee et al. (Int. J. Num. Meth. Biomed. Eng. 26:52-72, 2012) in which an incremental update of the displacement field in the classical approach is replaced by an incremental update of the deformation gradient field. Our generalized algorithm can be implemented in existing finite element codes with relatively low implementation effort on the element level and is suitable for material models formulated in the current or initial configurations. Applicable to any finite element simulations started from preloaded geometries, we demonstrate the algorithm and its convergence properties on an academic example and on a segment of a thoracic aorta meshed from MRI data. Furthermore, we present an example to discuss the influence of neglecting prestresses in geometries obtained from medical images, a topic on which conflicting statements are found in the literature.

Computational modeling of cardiac valve function and intervention

In the past two decades, major advances have been made in the clinical evaluation and treatment of valvular heart disease owing to the advent of noninvasive cardiac imaging modalities. In clinical practice, valvular disease evaluation is typically performed on two-dimensional (2D) images, even though most imaging modalities offer three-dimensional (3D) volumetric, time-resolved data. Such 3D data offer researchers the possibility to reconstruct the 3D geometry of heart valves at a patient-specific level. When these data are integrated with computational models, native heart valve biomechanical function can be investigated, and preoperative planning tools can be developed. In this review, we outline the advances in valve geometry reconstruction, tissue property modeling, and loading and boundary definitions for the purpose of realistic computational structural analysis of cardiac valve function and intervention.

Plaque hemorrhage in carotid artery disease: pathogenesis, clinical and biomechanical considerations

Stroke remains the most prevalent disabling illness today, with internal carotid artery luminal stenosis due to atheroma formation responsible for the majority of ischemic cerebrovascular events. Severity of luminal stenosis continues to dictate both patient risk stratification and the likelihood of surgical intervention. But there is growing evidence to suggest that plaque morphology may help improve pre-existing risk stratification criteria. Plaque components such a fibrous tissue, lipid rich necrotic core and calcium have been well investigated but plaque hemorrhage (PH) has been somewhat overlooked. In this review we discuss the pathogenesis of PH, its role in dictating plaque vulnerability, PH imaging techniques, marterial properties of atherosclerotic tissues, in particular, those obtained based on in vivo measurements and effect of PH in modulating local biomechanics.

Three-dimensional sensitivity assessment of thoracic aortic aneurysm wall stress: a probabilistic finite-element study

OBJECTIVES

In clinical practice, maximum diameter is used as a criterion to estimate aneurysm-rupture risk; however, it is only a general indicator and its value becomes difficult to estimate in the thoracic segment. Improved understanding of aortic aneurysm complexity and biomechanics is needed to achieve advancements in surgical repair techniques. The objective of this study was to determine the maximum wall stress by using imaging-derived data and a specific probabilistic design integrated into finite element (FE) analysis.

METHODS

Computed tomography images of thoracic aortic aneurysms from our database were analysed and the main morphological features were identified by means of a specific automatic routine. Morphological data were used to develop an idealized finite element library of thoracic aortic arch models. Sensitivity analyses were performed by using the geometrical parameters as input variables for a statistical wall stress assessment. Numerical results were compared with those obtained from deterministic analysis on patient-specific three-dimensional reconstructions.

RESULTS

The results showed that in small aneurysms, wall stress values similar to those of large aneurysms can be obtained if a significant eccentricity is achieved. In small aneurysms, the peak stress is primarily affected by the eccentricity of the bulge [correlation coefficient (CC) = 0.86], while for diameters in the range of 50-60 mm, the CC is 0.43 for the eccentricity and 0.72 for the maximum diameter.

CONCLUSIONS

The stress distribution in small aneurysms may contribute to the pathogenesis of aortic rupture and dissections. Our method can provide a novel and efficient procedure for generating computational models to estimate the wall stress in a comparative multivariate manner.

The role of geometric and biomechanical factors in abdominal aortic aneurysm rupture risk assessment

The current clinical management of abdominal aortic aneurysm (AAA) disease is based to a great extent on measuring the aneurysm maximum diameter to decide when timely intervention is required. Decades of clinical evidence show that aneurysm diameter is positively associated with the risk of rupture, but other parameters may also play a role in causing or predisposing the AAA to rupture. Geometric factors such as vessel tortuosity, intraluminal thrombus volume, and wall surface area are implicated in the differentiation of ruptured and unruptured AAAs. Biomechanical factors identified by means of computational modeling techniques, such as peak wall stress, have been positively correlated with rupture risk with a higher accuracy and sensitivity than maximum diameter alone. The objective of this review is to examine these factors, which are found to influence AAA disease progression, clinical management and rupture potential, as well as to highlight on-going research by our group in aneurysm modeling and rupture risk assessment.

In vivo determination of elastic properties of the human aorta based on 4D ultrasound data

Computational analysis of the biomechanics of the vascular system aims at a better understanding of its physiology and pathophysiology. To be of clinical use, however, these models and thus their predictions, have to be patient specific regarding geometry, boundary conditions and material. In this paper we present an approach to determine individual material properties of human aortae based on a new type of in vivo full field displacement data acquired by dimensional time resolved three dimensional ultrasound (4D-US) imaging. We developed a nested iterative Finite Element Updating method to solve two coupled inverse problems: The prestrains that are present in the imaged diastolic configuration of the aortic wall are determined. The solution of this problem is integrated in an iterative method to identify the nonlinear hyperelastic anisotropic material response of the aorta to physiologic deformation states. The method was applied to 4D-US data sets of the abdominal aorta of five healthy volunteers and verified by a numerical experiment. This non-invasive in vivo technique can be regarded as a first step to determine patient individual material properties of the human aorta.

A Quasi-Nonlinear Analysis of the Anisotropic Behaviour of Human Gallbladder Wall

Estimation of biomechanical parameters of soft tissues from noninvasive measurements has clinical significance in patient-specific modeling and disease diagnosis. In this work, we present a quasi-nonlinear method that is used to estimate the elastic moduli of the human gallbladder wall. A forward approach based on a transversely isotropic membrane material model is used, and an inverse iteration is carried out to determine the elastic moduli in the circumferential and longitudinal directions between two successive ultrasound images of gallbladder. The results demonstrate that the human gallbladder behaves in an anisotropic manner, and constitutive models need to incorporate this. The estimated moduli are also nonlinear and patient dependent. Importantly, the peak stress predicted here differs from the earlier estimate from linear membrane theory. As the peak stress inside the gallbladder wall has been found to strongly correlate with acalculous gallbladder pain, reliable mechanical modeling for gallbladder tissue is crucial if this information is to be used in clinical diagnosis.

Measuring and modeling patient-specific distributions of material properties in abdominal aortic aneurysm wall

Both the clinically established diameter criterion and novel approaches of computational finite element (FE) analyses for rupture risk stratification of abdominal aortic aneurysms (AAA) are based on assumptions of population-averaged, uniform material properties for the AAA wall. The presence of inter-patient and intra-patient variations in material properties is known, but has so far not been addressed sufficiently. In order to enable the preoperative estimation of patient-specific AAA wall properties in the future, we investigated the relationship between non-invasively assessable clinical parameters and experimentally measured AAA wall properties. We harvested n = 163 AAA wall specimens (n = 50 patients) during open surgery and recorded the exact excision sites. Specimens were tested for their thickness, elastic properties, and failure loads using uniaxial tensile tests. In addition, 43 non-invasively assessable patient-specific or specimen-specific parameters were obtained from recordings made during surgery and patient charts. Experimental results were correlated with the non-invasively assessable parameters and simple regression models were created to mathematically describe the relationships. Wall thickness was most significantly correlated with the metabolic activity at the excision site assessed by PET/CT (ρ = 0.499, P = 4 × 10(-7)) and to thrombocyte counts from laboratory blood analyses (ρ = 0.445, P = 3 × 10(-9)). Wall thickness was increased in patients suffering from diabetes mellitus, while it was significantly thinner in patients suffering from chronic kidney disease (CKD). Elastic AAA wall properties had significant correlations with the metabolic activity at the excision site (PET/CT), with existent calcifications, and with the diameter of the non-dilated aorta proximal to the AAA. Failure properties (wall strength and failure tension) had correlations with the patient's medical history and with results from laboratory blood analyses. Interestingly, AAA wall failure tension was significantly reduced for patients with CKD and elevated blood levels of potassium and urea, respectively, both of which are associated with kidney disease. This study is a first step to a future preoperative estimation of AAA wall properties. Results can be conveyed to both the diameter criterion and FE analyses to refine rupture risk prediction. The fact that AAA wall from patients suffering from CKD featured reduced failure tension implies an increased AAA rupture risk for this patient group at comparably smaller AAA diameters.

Using in vivo Cine and 3D multi-contrast MRI to determine human atherosclerotic carotid artery material properties and circumferential shrinkage rate and their impact on stress/strain predictions

In vivo magnetic resonance image (MRI)-based computational models have been introduced to calculate atherosclerotic plaque stress and strain conditions for possible rupture predictions. However, patient-specific vessel material properties are lacking in those models, which affects the accuracy of their stress/strain predictions. A noninvasive approach of combining in vivo Cine MRI, multicontrast 3D MRI, and computational modeling was introduced to quantify patient-specific carotid artery material properties and the circumferential shrinkage rate between vessel in vivo and zero-pressure geometries. In vivo Cine and 3D multicontrast MRI carotid plaque data were acquired from 12 patients after informed consent. For each patient, one nearly-circular slice and an iterative procedure were used to quantify parameter values in the modified Mooney-Rivlin model for the vessel and the vessel circumferential shrinkage rate. A sample artery slice with and without a lipid core and three material parameter sets representing stiff, median, and soft materials from our patient data were used to demonstrate the effect of material stiffness and circumferential shrinkage process on stress/strain predictions. Parameter values of the Mooney-Rivlin models for the 12 patients were quantified. The effective Young's modulus (YM, unit: kPa) values varied from 137 (soft), 431 (median), to 1435 (stiff), and corresponding circumferential shrinkages were 32%, 12.6%, and 6%, respectively. Using the sample slice without the lipid core, the maximum plaque stress values (unit: kPa) from the soft and median materials were 153.3 and 96.2, which are 67.7% and 5% higher than that (91.4) from the stiff material, while the maximum plaque strain values from the soft and median materials were 0.71 and 0.293, which are about 700% and 230% higher than that (0.089) from the stiff material, respectively. Without circumferential shrinkages, the maximum plaque stress values (unit: kPa) from the soft, median, and stiff models were inflated to 330.7, 159.2, and 103.6, which were 116%, 65%, and 13% higher than those from models with proper shrinkage. The effective Young's modulus from the 12 human carotid arteries studied varied from 137 kPa to 1435 kPa. The vessel circumferential shrinkage to the zero-pressure condition varied from 6% to 32%. The inclusion of proper shrinkage in models based on in vivo geometry is necessary to avoid over-estimating the stresses and strains by up 100%. Material stiffness had a greater impact on strain (up to 700%) than on stress (up to 70%) predictions. Accurate patient-specific material properties and circumferential shrinkage could considerably improve the accuracy of in vivo MRI-based computational stress/strain predictions.

Importance of initial aortic properties on the evolving regional anisotropy, stiffness and wall thickness of human abdominal aortic aneurysms

Complementary advances in medical imaging, vascular biology and biomechanics promise to enable computational modelling of abdominal aortic aneurysms to play increasingly important roles in clinical decision processes. Using a finite-element-based growth and remodelling model of evolving aneurysm geometry and material properties, we show that regional variations in material anisotropy, stiffness and wall thickness should be expected to arise naturally and thus should be included in analyses of aneurysmal enlargement or wall stress. In addition, by initiating the model from best-fit material parameters estimated for non-aneurysmal aortas from different subjects, we show that the initial state of the aorta may influence strongly the subsequent rate of enlargement, wall thickness, mechanical behaviour and thus stress in the lesion. We submit, therefore, that clinically reliable modelling of the enlargement and overall rupture-potential of aneurysms may require both a better understanding of the mechanobiological processes that govern the evolution of these lesions and new methods of determining the patient-specific state of the pre-aneurysmal aorta (or correlation to currently unaffected portions thereof) through knowledge of demographics, comorbidities, lifestyle, genetics and future non-invasive or minimally invasive tests.

Correlation of biomechanics to tissue reaction in aortic aneurysms assessed by finite elements and [18F]-fluorodeoxyglucose-PET/CT

Mechanobiological interactions are essential for the adaption of the cardiovascular system to altered environmental and internal conditions, but are poorly understood with regard to abdominal aortic aneurysm (AAA) pathogenesis, growth and rupture. In the present study, we therefore calculated mechanical AAA quantities using nonlinear finite element methods and correlated these to [18F]-fluorodeoxyglucose (FDG)-metabolic activity in the AAA wall detected by positron emission tomography/computed tomography (PET/CT). The interplay between mechanics and FDG-metabolic activity was analyzed in terms of maximum values and the three-dimensional spatial relationship, respectively. Fluorodeoxyglucose-positron emission tomography/computed tomography (FDG-PET/CT) data sets of n = 18 AAA patients were studied. Maximum FDG-uptake (SUV max ) in the AAA wall varied from 1.32 to 4.60 (average SUV max 3.31 ± 0.87). Maximum wall stresses and strains ranged from 10.0 to 64.0 N∕cm(2) (38.2 ± 13.8  N∕cm(2)) and from 0.190 to 0.260 (0.222 ± 0.023), respectively. SUV max was significantly correlated to maximum wall stress and strain (SUV max to stress: r = 0.71, p = 0.0005; SUV max to strain: r = 0.66, p = 0.0013). To evaluate the three-dimensional spatial interaction between FDG-uptake and acting wall stress, element-wise correlations were performed. In all but 2 AAAs, positive element-wise correlation of FDG-uptake to wall stress was obtained, with the Pearson's correlation coefficient ranging from -0.168 to 0.738 ( 0.372 ± 0.263). The results indicate that mechanical stresses are correlated quantitatively and spatially to FDG-uptake in the AAA wall. It is hypothesized that unphysiologically increased loading in the AAA wall triggers biological tissue reaction, such as inflammation or regenerative processes, causing elevated FDG-metabolic activity. These findings strongly support experimental hypotheses of mechanotransduction mechanisms in vivo.