The effect of inlet waveforms on computational hemodynamics of patient-specific intracranial aneurysms

Due to the lack of patient-specific inlet flow waveform measurements, most computational fluid dynamics (CFD) simulations of intracranial aneurysms usually employ waveforms that are not patient-specific as inlet boundary conditions for the computational model. The current study examined how this assumption affects the predicted hemodynamics in patient-specific aneurysm geometries. We examined wall shear stress (WSS) and oscillatory shear index (OSI), the two most widely studied hemodynamic quantities that have been shown to predict aneurysm rupture, as well as maximal WSS (MWSS), energy loss (EL) and pressure loss coefficient (PLc). Sixteen pulsatile CFD simulations were carried out on four typical saccular aneurysms using 4 different waveforms and an identical inflow rate as inlet boundary conditions. Our results demonstrated that under the same mean inflow rate, different waveforms produced almost identical WSS distributions and WSS magnitudes, similar OSI distributions but drastically different OSI magnitudes. The OSI magnitude is correlated with the pulsatility index of the waveform. Furthermore, there is a linear relationship between aneurysm-averaged OSI values calculated from one waveform and those calculated from another waveform. In addition, different waveforms produced similar MWSS, EL and PLc in each aneurysm. In conclusion, inlet waveform has minimal effects on WSS, OSI distribution, MWSS, EL and PLc and a strong effect on OSI magnitude, but aneurysm-averaged OSI from different waveforms has a strong linear correlation with each other across different aneurysms, indicating that for the same aneurysm cohort, different waveforms can consistently stratify (rank) OSI of aneurysms.     

Hemodynamic simulation of intracranial aneurysm growth with virtual silk stent implantation

Abstract

Longitudinal hemodynamic assessment of intracranial aneurysms (IAs) with endovascular treatment is essential for clinical decision making. We proposed a hemodynamic simulation method to explore the hemodynamic characteristics of a certain growth process of IA with virtual Silk stent implantation. Eight growth point models of IA were created by applying a bidirectional linear growing algorithm on patient 3D rotational angiography images. Simulated experiments showed that the WSS and velocity were significantly decreased with virtual Silk stent implantation at all growth points considered. The simulations revealed the flow pattern and WSS characteristics of IA growth.     

Uncertainty propagation of phase contrast-MRI derived inlet boundary conditions in computational hemodynamics models of thoracic aorta

This study investigates the impact that uncertainty in phase contrast-MRI derived inlet boundary conditions has on patient-specific computational hemodynamics models of the healthy human thoracic aorta. By means of Monte Carlo simulations, we provide advice on where, when and how, it is important to account for this source of uncertainty. The study shows that the uncertainty propagates not only to the intravascular flow, but also to the shear stress distribution at the vessel wall. More specifically, the results show an increase in the uncertainty of the predicted output variables, with respect to the input uncertainty, more marked for blood pressure and wall shear stress. The methodological approach proposed here can be easily extended to study uncertainty propagation in both healthy and pathological computational hemodynamic models.     

A reproducible swine model of a surgically created saccular thoracic aortic aneurysm

A reproducible swine thoracic aortic aneurysm (TAA) model is useful for investigating new therapeutic interventions. We report a surgical method for creating a reproducible swine saccular TAA model. We used eight female swine weighing 20–25 kg (LWD; ternary species). All procedures were performed under general anesthesia and involved left thoracotomy. Following aortic cross-clamping, the thoracic aorta was surgically dissected and the media and intima were resected, and the dissection plane was extended by spreading the outer layer for aneurysmal space. Subsequently, only the adventitial layer of the aorta was sutured. At 2 weeks after these procedures, angiography and computed tomography were performed. After follow-up imaging, the model animals were euthanized. Macroscopic, histological, and immunohistological examinations were performed. All model animals survived, and a saccular TAA was confirmed by follow-up imaging in all cases. The mean length of the shorter and the longer aortic diameter after the procedure were 14.01 ± 1.0 mm and 18.35 ± 1.4 mm, respectively (P<0.001). The rate of increase in the aortic diameter was 131.7 ± 13.8%, and the mean length of aneurysmal change at thoracic aorta was 22.4 ± 1.9 mm. Histological examination revealed intimal tears and defects of elastic fibers in the media. Immunostaining revealed MMP-2 and MMP-9 expressions at the aneurysm site. We report our surgical method for creating a swine saccular TAA model. Our model animal may be useful to investigate new therapeutic interventions for aortic disease.     

Influence of inlet boundary conditions on the local haemodynamics of intracranial aneurysms

Haemodynamics is believed to play an important role in the initiation, growth and rupture of intracranial aneurysms. In this context, computational haemodynamics has been extensively used in an effort to establish correlations between flow variables and clinical outcome. It is common practice in the application of Dirichlet boundary conditions at domain inlets to specify transient velocities as either a flat (plug) profile or a spatially developed profile based on Womersley's analytical solution. This paper provides comparative haemodynamics measures for three typical cerebral aneurysms.

Three dimentional rotational angiography images of aneurysms at three common locations, viz. basilar artery tip, internal carotid artery and middle cerebral artery were obtained. The computational tools being developed in the European project @neurIST were used to reconstruct the fluid domains and solve the unsteady Navier–Stokes equations, using in turn Womersley and plug-flow inlet velocity profiles. The effects of these assumptions were analysed and compared in terms of relevant haemodynamic variables within the aneurismal sac. For the aneurysm at the basilar tip geometries with different extensions of the afferent vasculature were considered to study the plausibility of a fully-developed axial flow at the inlet boundaries.

The study shows that assumptions made on the velocity profile while specifying inlet boundary conditions have little influence on the local haemodynamics in the aneurysm, provided that a sufficient extension of the afferent vasculature is considered and that geometry is the primary determinant of the flow field within the aneurismal sac. For real geometries the Womersley profile is at best an unnecessary over-complication, and may even be worse than the plug profile in some anatomical locations (e.g. basilar confluence).     

Stratification of a population of intracranial aneurysms using blood flow metrics

Indices of the intra-aneurysm hemodynamic environment have been proposed as potentially indicative of their longitudinal outcome. To be useful, the indices need to be used to stratify large study populations and tested against known outcomes. The first objective was to compile the diverse hemodynamic indices reported in the literature. Furthermore, as morphology is often the only patient-specific information available in large population studies, the second objective was to assess how the ranking of aneurysms in a population is affected by the use of steady flow simulation as an approximation to pulsatile flow simulation, even though the former is clearly non-physiological. Sixteen indices of aneurysmal hemodynamics reported in the literature were compiled and refined where needed. It was noted that, in the literature, these global indices of flow were always time-averaged over the cardiac cycle. Steady and pulsatile flow simulations were performed on a population of 198 patient-specific and 30 idealised aneurysm models. All proposed hemodynamic indices were estimated and compared between the two simulations. It was found that steady and pulsatile flow simulations had a strong linear dependence (r ≥ 0.99 for 14 indices; r ≥ 0.97 for 2 others) and rank the aneurysms in an almost identical fashion (ρ ≥ 0.99 for 14 indices; ρ ≥ 0.96 for other 2). When geometry is the only measured piece of information available, stratification of aneurysms based on hemodynamic indices reduces to being a physically grounded substitute for stratification of aneurysms based on morphology. Under such circumstances, steady flow simulations may be just as effective as pulsatile flow simulation for estimating most key indices currently reported in the literature.     

A computational model for prediction of clot platelet content in flow-diverted intracranial aneurysms

Treatment of intracranial aneurysms with flow-diverting stents is a safe and minimally invasive technique. The goal is stable embolisation that facilitates stent endothelialisation, and elimination of the aneurysm. However, it is not fully understood why some aneurysms fail to develop a stable clot even with sufficient levels of flow reduction. Computational prediction of thrombus formation dynamics can help predict the post-operative response in such challenging cases. In this work, we propose a new model of thrombus formation and platelet dynamics inside intracranial aneurysms. Our novel contribution combines platelet activation and transport with fibrin generation, which is key to characterising stable and unstable thrombus. The model is based on two types of thrombus inside aneurysms: red thrombus (fibrin- and erythrocyte-rich) can be found in unstable clots, while white thrombus (fibrin- and platelet-rich) can be found in stable clots. The thrombus generation model is coupled to a CFD model and the flow-induced platelet index (FiPi) is defined as a quantitative measure of clot stability. Our model is validated against an in vitro phantom study of two flow-diverting stents with different sizing. We demonstrate that our model accurately predicts the lower thrombus stability in the oversized stent scenario. This opens possibilities for using computational simulations to improve endovascular treatment planning and reduce adverse events, such as delayed haemorrhage of flow-diverted aneurysms.     

An approach to quantitative assessment of hemodynamic differences between unruptured and ruptured ophthalmic artery aneurysms

Background and purpose: Hemodynamic parameters are important in the pathogenesis, evolution and rupture of intracranial aneurysm. Energy loss (EL) has been applied for the rupture risk prediction of artery aneurysms recently. We proposed a new EL and further investigate its effects on the rupture of aneurysms. Materials and methods: Sixty-four patient-specific ophthalmic aneurysm datasets were divided into ruptured and unruptured groups based on their clinical history. Based on patient-specific 3D-DSA data, realistic models were retrospectively reconstructed and then analyzed by using computational fluid dynamic method. Results: The flow field feature EL in ruptured cases was significantly higher than that in unruptured cases. The average wall shear stress (WSS) and the maximum WSS in ruptured cases were higher than those in unruptured cases. Modified pressure loss coefficient (PLC_M) in ruptured cases was slight higher than that in unruptured cases but the difference has no statistical significance. Multivariate logistic regression analysis demonstrated flow field feature EL (p < 0.05) and the maximum WSS (p < 0.05) were the only independently significant variables to predict rupture of ophthalmic aneurysm. There were no differences in PLC_M, the maximum oscillatory shear index (OSI), the average OSI and AR between the two groups. Conclusion: Flow field feature EL may be a reliable factor to predict the rupture risk of aneurysms.     

The Helsinki Rat Microsurgical Sidewall Aneurysm Model

Experimental saccular aneurysm models are necessary for testing novel surgical and endovascular treatment options and devices before they are introduced into clinical practice. Furthermore, experimental models are needed to elucidate the complex aneurysm biology leading to rupture of saccular aneurysms.Several different kinds of experimental models for saccular aneurysms have been established in different species. Many of them, however, require special skills, expensive equipment, or special environments, which limits their widespread use. A simple, robust, and inexpensive experimental model is needed as a standardized tool that can be used in a standardized manner in various institutions.The microsurgical rat abdominal aortic sidewall aneurysm model combines the possibility to study both novel endovascular treatment strategies and the molecular basis of aneurysm biology in a standardized and inexpensive manner. Standardized grafts by means of shape, size, and geometry are harvested from a donor rat''s descending thoracic aorta and then transplanted to a syngenic recipient rat. The aneurysms are sutured end-to-side with continuous or interrupted 9-0 nylon sutures to the infrarenal abdominal aorta.We present step-by-step procedural instructions, information on necessary equipment, and discuss important anatomical and surgical details for successful microsurgical creation of an abdominal aortic sidewall aneurysm in the rat.     

A large-scale comparison of computational models on the residue flexibility for NMR-derived proteins

As an alternative to X-ray crystallography, nuclear magnetic resonance (NMR) has also emerged as the method of choice for studying both protein structure and dynamics in solution. However, little work using computational models such as Gaussian network model (GNM) and machine learning approaches has focused on NMR-derived proteins to predict the residue flexibility, which is represented by the root mean square deviation (RMSD) with respect to the average structure. We provide a large-scale comparison of computational models, including GNM, parameter-free GNM and several linear regression models using local solvent exposures as inputs, based on a dataset of 1609 protein chains whose structures were resolved by NMR. The result again confirmed that the correlation of GNM outputs with raw RMSD values was better than that using B-factors of X-ray data. Nevertheless, it was also concluded that the parameter-free GNM and the solvent exposure based linear regression models performed worse than GNM when predicting RMSD, contrary to results using X-ray data. The discrepancy of residue flexibility prediction between NMR and X-ray data is likely attributable to a combination of their physical and methodological differences.     

A computational model of ameboid deformation and locomotion

Traditional continuum models of ameboid deformation and locomotion are limited by the computational difficulties intrinsic in free boundary conditions. A new model using the immersed boundary method overcomes these difficulties by representing the cell as a force field immersed in fluid domain. The forces can be derived from a direct mechanical interpretation of such cell components as the cell membrane, the actin cortex, and the transmembrane adhesions between the cytoskeleton and the substratum. The numerical cytoskeleton, modeled as a dynamic network of immersed springs, is able to qualitatively model the passive mechanical behavior of a shear-thinning viscoelastic fluid (Bottino 1997). The same network is used to generate active protrusive and contractile forces. When coordinated with the attachment-detachment cycle of the cell's adhesions to the substratum, these forces produce directed locomotion of the model ameba. With this model it is possible to study the effects of altering the numerical parameters upon the motility of the model cell in a manner suggestive of genetic deletion experiments. In the context of this ameboid cell model and its numerical implementation, simulations involving multicellular interaction, detailed internal signaling, and complex substrate geometries are tractable. Received: 5 January 1998 / Revised version: 23 March 1998 / Accepted: 26 March 1998     

The influence of fiber dispersion on the mechanical response of aortic tissues in health and disease: a computational study

Changes in the structural components of aortic tissues have been shown to play a significant role in the pathogenesis of aortic degeneration. Therefore, reliable stress analyses require a suitable and meaningful constitutive model that captures micro-structural changes. As recent data show, in-plane and out-of-plane collagen fiber dispersions vary significantly between healthy and aneurysmatic aortic walls. The aim of this study is to computationally investigate the influence of fiber dispersion on the mechanical response of aortic tissues in health and disease. In particular, the influence of three different fiber dispersions is studied: (i) non-rotationally symmetric dispersion, the most realistic assumption for aortic tissues; (ii) transversely isotropic dispersion, a special case; (iii) perfectly aligned fibers (no dispersion in either plane), another special case. Explicit expressions for the stress and elasticity tensors as needed for the implementation in a finite element code are provided. Three representative numerical examples are studied: planar biaxial extension, inflation of residually stressed and pre-stretched aortic segments and inflation of an idealized abdominal aortic aneurysm (AAA) geometry. For the AAA geometry the case of isotropic dispersion is additionally analyzed. Documented structural and mechanical parameters are taken from human aortas (healthy media/adventitia and AAA). The influence of fiber dispersions upon magnitudes and distributions of stresses and deformations are presented and analyzed. Stresses vary significantly, especially in the AAA case, where material stiffening is significantly influenced by fiber dispersion. The results highlight the need to incorporate the structural differences into finite element simulations to obtain more accurate stress predictions. Additionally, results show the capability of one constitutive model to represent different scenarios of aortic micro-structures allowing future studies of collagen reorientation during disease progression.     

Toward computational determination of peptide-receptor structure.

We introduce a method for docking small flexible ligands of the size of dipeptides and phosphocholine and test it against crystallographic complexes. We then show how the method can be used as the basis for a strategy for solving the much more difficult problem of docking fully flexible peptides in the 8-10-residue size range. After developing the method we apply it to peptide-MHC class I systems and find that the predictions are in accord with biological and crystallographic data.     

Toward ecologically explicit null models of nestedness

A community is "nested" when species assemblages in less rich sites form nonrandom subsets of those at richer sites. Conventional null models used to test for statistically nonrandom nestedness are under- or over-restrictive because they do not sufficiently isolate ecological processes of interest, which hinders ecological inference. We propose a class of null models that are ecologically explicit and interpretable. Expected values of species richness and incidence, rather than observed values, are used to create random presence-absence matrices for hypothesis testing. In our examples, based on six datasets, expected values were derived either by using an individually based random placement model or by fitting empirical models to richness data as a function of environmental covariates. We describe an algorithm for constructing unbiased null matrices, which permitted valid testing of our null models. Our approach avoids the problem of building too much structure into the null model, and enabled us to explicitly test whether observed communities were more nested than would be expected for a system structured solely by species-abundance and species-area or similar relationships. We argue that this test or similar tests are better determinants of whether a system is truly nested; a nested system should contain unique pattern not already predicted by more fundamental ecological principles such as species-area relationships. Most species assemblages we studied were not nested under these null models. Our results suggest that nestedness, beyond that which is explained by passive sampling processes, may not be as widespread as currently believed. These findings may help to improve the utility of nestedness as an ecological concept and conservation tool.     

Determining the optimal interval for imaging surveillance of ascending aortic aneurysms

BackgroundCardiovascular guidelines recommend (bi-)annual computed tomography (CT) or magnetic resonance imaging (MRI) for surveillance of the diameter of thoracic aortic aneurysms (TAAs). However, no previous study has demonstrated the necessity for this approach. The current study aims to provide patient-specific intervals for imaging follow-up of non-syndromic TAAs.MethodsA total of 332 patients with non-syndromic ascending aortic aneurysms were followed over a median period of 6.7 years. Diameters were assessed using all available imaging techniques (echocardiography, CT and MRI). Growth rates were calculated from the differences between the first and last examinations. The diagnostic accuracy of follow-up protocols was calculated as the percentage of subjects requiring pre-emptive surgery in whom timely identification would have occurred.ResultsThe mean growth rate in our population was 0.2 ± 0.4 mm/year. The highest recorded growth rate was 2.0 mm/year, while 40.6% of patients showed no diameter expansion during follow-up. Females exhibited significantly higher growth rates than men (0.3 ± 0.5 vs 0.2 ± 0.4 mm/year, p = 0.007). Conversely, a bicuspid aortic valve was not associated with more rapid aortic growth. The optimal imaging protocol comprises triennial imaging of aneurysms 40–49 mm in diameter and yearly imaging of those measuring 50–54 mm. This strategy is as accurate as annual follow-up, but reduces the number of imaging examinations by 29.9%.ConclusionsIn our population of patients with non-syndromic TAAs, we found aneurysm growth rates to be lower than those previously reported. Yearly imaging does not lead to changes in the management of small aneurysms. Thus, lower imaging frequencies might be a good alternative approach.     

Imaging mass spectroscopy delineates the thinned and thickened walls of intracranial aneurysms

Object

The wall thickness of intracranial aneurysms (IAs) is heterogeneous. Although thinning of the IA wall is thought to contribute to IA rupture, the underlying mechanism remains poorly understood. Recently, imaging mass spectroscopy (IMS) has been used to reveal the distribution of phospholipids in vascular diseases. To investigate the feature of phospholipid composition of IA walls, we conducted IMS in a rat model of experimentally induced IA.

Stochastic modelling of wall stresses in abdominal aortic aneurysms treated by a gene therapy

A stochastic mechanical model using the membrane theory was used to simulate the in vivo mechanical behaviour of abdominal aortic aneurysms (AAAs) in order to compute the wall stresses after stabilisation by gene therapy. For that, both length and diameter of AAAs rats were measured during their expansion. Four groups of animals, control and treated by an endovascular gene therapy during 3 or 28 days were included. The mechanical problem was solved analytically using the geometric parameters and assuming the shape of aneurysms by a ‘parabolic–exponential curve’. When compared to controls, stress variations in the wall of AAAs for treated arteries during 28 days decreased, while they were nearly constant at day 3. The measured geometric parameters of AAAs were then investigated using probability density functions (pdf) attributed to every random variable. Different trials were useful to define a reliable confidence region in which the probability to have a realisation is equal to 99%. The results demonstrated that the error in the estimation of the stresses can be greater than 28% when parameters uncertainties are not considered in the modelling. The relevance of the proposed approach for the study of AAA growth may be studied further and extended to other treatments aimed at stabilisation AAAs, using biotherapies and pharmacological approaches.     

Toward error analysis of large-scale forest carbon budgets

Quantification of forest carbon sources and sinks is an important part of national inventories of net greenhouse gas emissions. Several such forest carbon budgets have been constructed, but little effort has been made to analyse the sources of error and how these errors propagate to determine the overall uncertainty of projected carbon fluxes. We performed an error analysis for estimates of tree volume and volume change determined by repeated measurements of permanent sample plots for the South‐eastern United States as a step toward assessing errors in the carbon budget constructed by the USDA Forest Service. Error components recognized were: sampling error for sample plot selection; measurement error for tree height and diameter; and regression error for tree volume. Most of the propagated error in volume and volume change estimation was due to sampling error. Error estimates depended on the size of the area examined (single state to region) and the degree to which tree growth and recruit‐ment balanced mortality and harvesting. Approximate regional 95% confidence intervals were 3 455 073 000 ± 39 606 000 (1.1%) m³ for current growing‐stock volume, and 10 616 000 ± 4210 000 (39.7%) m³ years^?1 for growing‐stock volume change. These methods should be useful in further analysis of the sources of error and overall uncertainty in national efforts to quantify carbon fluxes associated with forests and land cover dynamics.