C. Alberto Figueroa

Effect of Curvature on Displacement Forces Acting on Aortic Endografts: A 3-Dimensional Computational Analysis

Purpose: To determine the effect of curvature on the magnitude and direction of displacement forces acting on aortic endografts in 3-dimensional (3D) computational models. Method: A 3D computer model was constructed based on magnetic resonance angiography data from a patient with an infrarenal aortic aneurysm. Computational fluid dynamics tools were used to simulate realistic flow and pressure conditions of the patient. An aortic endograft was deployed in the model, and the displacement forces acting on the endograft were calculated and expressed in Newtons (N). Additional models were created to determine the effects of reducing endograft curvature, neck angulation, and iliac angulation on displacement forces. Results: The aortic endograft had a curved configuration as a result of the patient‘s anatomy, with curvature in the anterolateral direction. Total displacement force acting on the endograft was 5.0 N, with 28% of the force in a downward (caudal) direction and 72% of the force in a sideways (anterolateral) direction. Elimination of endograft curvature (planar graft configuration) reduced total displacement force to 0.8 N, with the largest component of force (70%) acting in the sideways direction. Straightening the aortic neck in the curved endograft configuration reduced the total force acting on the endograft to 4.2 N, with a reduction of the sideways component to 55% of the total force. Straightening the iliac limbs of the endograft reduced the total force acting on the endograft to 2.1 N but increased the sideways component to 91% of the total force. Conclusion: The largest component of the force acting on the aortic endograft is in the sideways direction, with respect to the blood flow, rather than in the downward (caudal) direction as is commonly assumed. Increased curvature of the aortic endograft increases the magnitude of the sideways displacement force. The degree of angulation of the proximal and distal ends of the endograft influence the magnitude and direction of displacement force. These factors may have a significant influence on the propensity of endografts to migrate in vivo.

Computational Simulations for Aortic Coarctation: Representative Results From a Sampling of Patients

Treatments for coarctation of the aorta (CoA) can alleviate blood pressure (BP) gradients (Δ), but long-term morbidity still exists that can be explained by altered indices of hemodynamics and biomechanics. We introduce a technique to increase our understanding of these indices for CoA under resting and nonresting conditions, quantify their contribution to morbidity, and evaluate treatment options. Patient-specific computational fluid dynamics (CFD) models were created from imaging and BP data for one normal and four CoA patients (moderate native CoA: Δ12 mmHg, severe native CoA: Δ25 mmHg and postoperative end-to-end and end-to-side patients: Δ0 mmHg). Simulations incorporated vessel deformation, downstream vascular resistance and compliance. Indices including cyclic strain, time-averaged wall shear stress (TAWSS), and oscillatory shear index (OSI) were quantified. Simulations replicated resting BP and blood flow data. BP during simulated exercise for the normal patient matched reported values. Greatest exercise-induced increases in systolic BP and mean and peak ΔBP occurred for the moderate native CoA patient (SBP: 115 to 154 mmHg; mean and peak ΔBP: 31 and 73 mmHg). Cyclic strain was elevated proximal to the coarctation for native CoA patients, but reduced throughout the aorta after treatment. A greater percentage of vessels was exposed to subnormal TAWSS or elevated OSI for CoA patients. Local patterns of these indices reported to correlate with atherosclerosis in normal patients were accentuated by CoA. These results apply CFD to a range of CoA patients for the first time and provide the foundation for future progress in this area.

A Systematic Comparison between 1-D and 3-D Hemodynamics in Compliant Arterial Models

We present a systematic comparison of computational hemodynamics in arteries between a one-dimensional (1-D) and a three-dimensional (3-D) formulation with deformable vessel walls. The simulations were performed using a series of idealized compliant arterial models representing the common carotid artery, thoracic aorta, aortic bifurcation, and full aorta from the arch to the iliac bifurcation. The formulations share identical inflow and outflow boundary conditions and have compatible material laws. We also present an iterative algorithm to select the parameters for the outflow boundary conditions by using the 1-D theory to achieve a desired systolic and diastolic pressure at a particular vessel. This 1-D/3-D framework can be used to efficiently determine material and boundary condition parameters for 3-D subject-specific arterial models with deformable vessel walls. Finally, we explore the impact of different anatomical features and hemodynamic conditions on the numerical predictions. The results show good agreement between the two formulations, especially during the diastolic phase of the cycle.

Multi-scale computational model of three-dimensional hemodynamics within a deformable full-body arterial network

In this article, we present a computational multi-scale model of fully three-dimensional and unsteady hemodynamics within the primary large arteries in the human. Computed tomography image data from two different patients were used to reconstruct a nearly complete network of the major arteries from head to foot. A linearized coupled-momentum method for fluid-structure-interaction was used to describe vessel wall deformability and a multi-domain method for outflow boundary condition specification was used to account for the distal circulation. We demonstrated that physiologically realistic results can be obtained from the model by comparing simulated quantities such as regional blood flow, pressure and flow waveforms, and pulse wave velocities to known values in the literature. We also simulated the impact of age-related arterial stiffening on wave propagation phenomena by progressively increasing the stiffness of the central arteries and found that the predicted effects on pressure amplification and pulse wave velocity are in agreement with findings in the clinical literature. This work demonstrates the feasibility of three-dimensional techniques for simulating hemodynamics in a full-body compliant arterial network.

Magnitude and Direction of Pulsatile Displacement Forces Acting on Thoracic Aortic Endografts

Purpose: To assess 3-dimensional (3D) pulsatile displacement forces (DF) acting on thoracic endografts using 3D computational techniques. Methods: A novel computational method to quantitate the pulsatile 3D flow and pressure fields and aortic wall dynamics in patient-specific anatomical models based on cardiac-gated computed tomography (CT) scans was used to construct simulations of the proximal and mid-descending thoracic aorta. Endografts of varying lengths and diameters were implanted in these patient-specific models. The magnitude and direction of the DF vector were calculated and expressed in Newtons (N). This DF included the effects of both the pressure and shearing stresses of blood. Results: The magnitude of DF increased with endografts of increasing diameter and length. A 36-mm endograft in the mid-descending aorta had a mean DF of 21.7 N with a peak systolic DF of 27.8 N and an end-diastolic DF of 16.7 N. Conversely, a 30-mm endograft in the proximal descending aorta had a mean DF of 14.9 N, with peak systolic and end-diastolic DFs of 18.9 and 11.5, respectively. The orientation of the DF acting on the endograft varied depending on aortic angulation and tortuosity; in general, the vector was perpendicular to the greater curvature of the endograft rather than along the downstream longitudinal centerline axis of the aorta as is commonly believed. The DF vector pointed primarily in the cranial direction for the proximal descending endograft and in the sideways direction for the mid-descending endograft simulation. Furthermore, it was shown that elevated pressure plays an important role in the magnitude and direction of DF; an increase in mean blood pressure resulted in an approximately linearly proportional increase in DF. Conclusion: The orientation of the DF varies depending on curvature and location of the endograft, but in all instances, it is in the cranial rather than caudal direction on axial imaging. This is counter to the intuitive notion that displacement forces act in the downward direction of blood flow. Therefore, we postulate that migration of thoracic endografts may be different from abdominal endografts since it may involve upward rather than downward movement of the graft. Computational methods can enhance the understanding of the magnitude and orientation of the loads experienced in vivo by thoracic aortic endografts and therefore improve their design and performance.

A computational framework for investigating the positional stability of aortic endografts

Endovascular aneurysm repair (Greenhalgh in N Engl J Med 362(20):1863–1871, 2010) techniques have revolutionized the treatment of thoracic and abdominal aortic aneurysm disease, greatly reducing the perioperative mortality and morbidity associated with open surgical repair techniques. However, EVAR is not free of important complications such as late device migration, endoleak formation and fracture of device components that may result in adverse events such as aneurysm enlargement, need for long-term imaging surveillance and secondary interventions or even death. These complications result from the device inability to withstand the hemodynamics of blood flow and to keep its originally intended post-operative position over time. Understanding the in vivo biomechanical working environment experienced by endografts is a critical factor in improving their long-term performance. To date, no study has investigated the mechanics of contact between device and aorta in a three-dimensional setting. In this work, we developed a comprehensive Computational Solid Mechanics and Computational Fluid Dynamics framework to investigate the mechanics of endograft positional stability. The main building blocks of this framework are: (1) Three-dimensional non-planar aortic and stent-graft geometrical models, (2) Realistic multi-material constitutive laws for aorta, stent, and graft, (3) Physiological values for blood flow and pressure, and (4) Frictional model to describe the contact between the endograft and the aorta. We introduce a new metric for numerical quantification of the positional stability of the endograft. Lastly, in the results section, we test the framework by investigating the impact of several factors that are clinically known to affect endograft stability.

Preliminary 3D computational analysis of the relationship between aortic displacement force and direction of endograft movement

OBJECTIVE Endograft migration is usually described as a downward displacement of the endograft with respect to the renal arteries. However, change in endograft position is actually a complex process in three-dimensional (3D) space. Currently, there are no established techniques to define such positional changes over time. The purpose of this study is to determine whether the direction of aortic endograft movement as observed in follow-up computed tomography (CT) scans is related to the directional displacement force acting on the endograft. METHODS We quantitated the 3D positional change over time of five abdominal endografts by determining the endograft centroid at baseline (postoperative scan) and on follow-up CT scans. The time interval between CT scans for the 5 patients ranged from 8 months to 8 years. We then used 3D image segmentation and computational fluid dynamics (CFD) techniques to quantitate the pulsatile displacement force (in Newtons [N]) acting on the endografts in the postoperative configurations. Finally, we calculated a correlation metric between the direction of the displacement force vector and the endograft movement by computing the cosine of the angle of these two vectors. RESULTS The average 3D movement of the endograft centroid was 18 mm (range, 9-29 mm) with greater movement in patients with longer follow-up times. In all cases, the movement of the endograft had significant components in all three spatial directions: Two of the endografts had the largest component of movement in the transverse direction, whereas three endografts had the largest component of movement in the axial direction. The magnitude and orientation of the endograft displacement force varied depending on aortic angulation and hemodynamic conditions. The average magnitude of displacement force for all endografts was 5.8 N (range, 3.7-9.5 N). The orientation of displacement force was in general perpendicular to the greatest curvature of the endograft. The average correlation metric, defined as the cosine of the angle between the displacement force and the endograft centroid movement, was 0.38 (range, 0.08-0.66). CONCLUSIONS Computational methods applied to patient-specific postoperative image data can be used to quantitate 3D displacement force and movement of endografts over time. It appears that endograft movement is related to the magnitude and direction of the displacement force acting on aortic endografts. These methods can be used to increase our understanding of clinical endograft migration.

Central Artery Stiffness in Hypertension and Aging: A Problem With Cause and Consequence

Systemic hypertension is a risk factor for many diseases affecting the heart, brain, and kidneys. It has long been thought that hypertension leads to a thickening and stiffening of central arteries (ie, stiffness is a consequence), whereas more recent evidence suggests that stiffening precedes hypertension (ie, stiffness is a cause). We submit, however, that consideration of the wall biomechanics and hemodynamics reveals an insidious positive feedback loop that may render it irrelevant whether hypertension causes or is caused by central arterial stiffening. A progressive worsening can ensue in either case, thus any onset of stiffening merits early intervention. Understanding arterial function requires integration of biological and mechanical information.1–4 Stress (a force intensity) is a key concept in biomechanics; it enables one to calculate the stiffness of a material and assess its strength. Mean circumferential stresses in arteries can be estimated using Laplace’s equation: ![Formula][1] (1) where P is pressure, a is the pressurized luminal radius, and h is the whole wall thickness. In vitro experiments reveal nonlinear pressure–radius relations, ![Graphic][2] , hence acute increases in blood pressure increase both wall stress (with a increasing because of wall elasticity and h decreasing because of the near incompressibility) and material stiffness (essentially the slope of the stress–stretch relationship). Such pressure-induced increases in material stiffness increase most clinical measures of arterial stiffness, thus it is important to delineate acute and chronic (remodeling) changes. The latter can arise from mechanobiological responses (eg, altered gene expression) by endothelial cells, smooth muscle cells, and fibroblasts to changes in hemodynamically induced loads, with an apparent goal of preserving homeostatic values of stress and material stiffness3 although often at the expense of increasing structural stiffness (essentially wall thickness times material stiffness). Different metrics are used clinically to assess structural stiffness of central arteries, with carotid-to-femoral pulse wave … [1]: /embed/graphic-1.gif [2]: /embed/inline-graphic-1.gif

Computational analysis of stresses acting on intermodular junctions in thoracic aortic endografts.

Purpose To evaluate the biomechanical and hemodynamic forces acting on the intermodular junctions of a multi-component thoracic endograft and elucidate their influence on the development of type III endoleak due to disconnection of stent-graft segments. Methods Three-dimensional computer models of the thoracic aorta and a 4-component thoracic endograft were constructed using postoperative (baseline) and follow-up computed tomography (CT) data from a 69-year-old patient who developed type III endoleak 4 years after stent-graft placement. Computational fluid dynamics (CFD) techniques were used to quantitate the displacement forces acting on the device. The contact stresses between the different modules of the graft were then quantified using computational solid mechanics (CSM) techniques. Lastly, the intermodular junction frictional stability was evaluated using a Coulomb model. Results The CFD analysis revealed that curvature and length are key determinants of the displacement forces experienced by each endograft and that the first 2 modules were exposed to displacement forces acting in opposite directions in both the lateral and longitudinal axes. The CSM analysis revealed that the highest concentration of stresses occurred at the junction between the first and second modules of the device. Furthermore, the frictional analysis demonstrated that most of the surface area (53%) of this junction had unstable contact. The predicted critical zone of intermodular stress concentration and frictional instability matched the location of the type III endoleak observed in the 4-year follow-up CT image. Conclusion The region of larger intermodular stresses and highest frictional instability correlated with the zone where a type III endoleak developed 4 years after thoracic stent-graft placement. Computational techniques can be helpful in evaluating the risk of endograft migration and potential for modular disconnection and may be useful in improving device placement strategies and endograft design.

Computational simulations of hemodynamic changes within thoracic, coronary, and cerebral arteries following early wall remodeling in response to distal aortic coarctation

Mounting evidence suggests that the pulsatile character of blood pressure and flow within large arteries plays a particularly important role as a mechano-biological stimulus for wall growth and remodeling. Nevertheless, understanding better the highly coupled interactions between evolving wall geometry, structure, and properties and the hemodynamics will require significantly more experimental data. Computational fluid–solid-growth models promise to aid in the design and interpretation of such experiments and to identify candidate mechanobiological mechanisms for the observed arterial adaptations. Motivated by recent aortic coarctation models in animals, we used a computational fluid–solid interaction model to study possible local and systemic effects on the hemodynamics within the thoracic aorta and coronary, carotid, and cerebral arteries due to a distal aortic coarctation and subsequent spatial variations in wall adaptation. In particular, we studied an initial stage of acute cardiac compensation (i.e., maintenance of cardiac output) followed by early arterial wall remodeling (i.e., spatially varying wall thickening and stiffening). Results suggested, for example, that while coarctation increased both the mean and pulse pressure in the proximal vessels, the locations nearest to the coarctation experienced the greatest changes in pulse pressure. In addition, after introducing a spatially varying wall adaptation, pressure, left ventricular work, and wave speed all increased. Finally, vessel wall strain similarly experienced spatial variations consistent with the degree of vascular wall adaptation.