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Three-Dimensional Geometrical Characterization of Cerebral Aneurysms
Abstract
The risk of rupture of cerebral aneurysms has been correlated with the size of the aneurysm sac. It is conceivable that geometrical shape, not just size may also be related to aneurysm rupture potential. Further, aneurysm shape may also be a factor in deciding on treatment modalities, i.e., to clip or coil. However, our ability to make use of available information on aneurysm shape remains poor. In this study, methods were developed to quantify the seemingly arbitrary three-dimensional geometry of the aneurysm sac, using differential and computational geometry techniques. From computed tomography angiography (CTA) data, the three-dimensional geometry of five unruptured human cerebral aneurysms was reconstructed. Various indices (maximum diameter, neck diameter, height, aspect ratio, bottleneck factor, bulge location, volume, surface area, Gaussian and mean curvatures, isoperimetric ratio, and convexity ratio) were utilized to characterize the geometry of these aneurysm surfaces and four size-matched hypothetical control aneurysms. The physical meanings of various indices and their possible role as prognosticators for rupture risk and presurgical planning were discussed.
... The ''local-shape'' patching was based on the Gaussian, , and mean, , curvatures of a surface (see Fig. 4a and b, respectively, illustrating these fields for the luminal surface of case rICA2), following the classification presented by Ma et al. [48]. The Gaussian curvature, given in mm −2 , defines elliptic ( > 0, sphere-like), parabolic ( = 0, cylindric-like), or hyperbolic ( < 0, saddle-like) points of the surface. ...
... The local-shape classification used here is shown in the table in Fig. 4c -comparing with the classification given by Ma et al. [48], we only employed the ones found on the aneurysms, although others are possible, such as parabolic and planar surfaces. This classification yielded a map of the types of regions spanning the vascular surface, including the aneurysms (see Fig. 4c). ...
... As can be seen in Fig. 4a and b, both and are ''noisy'' fields. As explained in Ma et al. [48], curvatures are second-order quantities in nature that depend on the coordinates of the surface points. Hence, their computation for discretized surfaces leads to noisy fields, and, more importantly, the surface mesh refinement level may affect the evaluation of the curvatures. ...
The properties of intracranial aneurysms (IAs) walls are known to be driven by the underlying hemodynamics adjacent to the IA sac. Different pathways exist explaining the connections between hemodynamics and local tissue properties. The emergence of such theories is essential if one wishes to compute the mechanical response of a patient-specific IA wall and predict its rupture. Apart from the hemodynamics and tissue properties, one could assume that the mechanical response also depends on the local morphology, more specifically, the curvature of the luminal surface, with larger values at highly-curved wall portions. Nonetheless, this contradicts observations of IA rupture sites more often found at the dome, where the curvature is lower. This seeming contradiction indicates a complex interaction between the hemodynamics adjacent to the aneurysm wall, its morphology, and mechanical response, which warrants further investigation. This was the main goal of this work. We accomplished this by analysing the stress and stretch fields in different regions of the wall for a sample of IAs, which have been classified based on particular hemodynamics conditions and lumen curvature. Pulsatile numerical simulations were performed using the one-way fluid-solid interaction strategy implemented in OpenFOAM (solids4foam toolbox). We found that the variable best correlated with regions of high stress and stretch was the lumen curvature. Additionally, our data suggest a connection between the local curvature and particular hemodynamics conditions adjacent to the wall, indicating that the lumen curvature is a property that could be used to assess both mechanical response and hemodynamic conditions, and, moreover, suggest new rupture indicators based on the curvature.
... By using the surface extracted from the imaging examinations, i.e. corresponding to the undeformed configuration, we characterised the sample morphologically by computing size metrics (maximum sac height, maximum sac diameter, aneurysm neck diameter, sac area and sac-enclosed volume) and shape metrics (aspect ratio, undulation, non-sphericity, and ellipticity indices) as defined by Ma et al. [42], Raghavan et al. [43], and Dhar et al. [44]. We also computed curvature-based indices proposed by Ma et al. [42] defined as surface-averages and L2-norms of the Gaussian, K, and mean, H, curvatures, labeled, respectively, GAA, MAA, GLN , and MLN (the "AA" and "LN" stand for "area-average" and "L2-norm", respectively). ...
... By using the surface extracted from the imaging examinations, i.e. corresponding to the undeformed configuration, we characterised the sample morphologically by computing size metrics (maximum sac height, maximum sac diameter, aneurysm neck diameter, sac area and sac-enclosed volume) and shape metrics (aspect ratio, undulation, non-sphericity, and ellipticity indices) as defined by Ma et al. [42], Raghavan et al. [43], and Dhar et al. [44]. We also computed curvature-based indices proposed by Ma et al. [42] defined as surface-averages and L2-norms of the Gaussian, K, and mean, H, curvatures, labeled, respectively, GAA, MAA, GLN , and MLN (the "AA" and "LN" stand for "area-average" and "L2-norm", respectively). ...
... The "local-shape" patching was based on the Gaussian, K, and mean, H, curvatures of a surface (see Fig. 4a and b, respectively, illustrating these fields for case rICA2), following the classification presented by Ma et al. [42]. The Gaussian curvature, given in mm −2 , defines elliptic (K > 0, sphere-like), parabolic (K = 0, cylindric-like), or hyperbolic (K < 0, saddle-like) points of the surface. ...
The properties of intracranial aneurysms (IAs) walls are known to be driven by the underlying hemodynamics adjacent to the IA sac. Different pathways exist explaining the connections between hemodynamics and local tissue properties. The emergence of such theories is essential if one wishes to compute the mechanical response of a patient-specific IA wall and predict its rupture. Apart from the hemodynamics and tissue properties, one could assume that the mechanical response also depends on the local morphology, more specifically, the wall curvature, with larger values at highly-curved wall portions. Nonetheless, this contradicts observations of IA rupture sites more often found at the dome, where the curvature is lower. This seeming contradiction indicates a complex interaction between local hemodynamics, wall morphology, and mechanical response, which warrants further investigation. This was the main goal of this work. We accomplished this by analysing the stress and stretch fields in different regions of the wall for a sample of IAs, which have been classified based on particular local hemodynamics and local curvature. Pulsatile numerical simulations were performed using the one-way fluid-solid interaction strategy implemented in OpenFOAM (solids4foam toolbox). We found that the variable best correlated with regions of high stress and stretch was the wall curvature. Additionally, our data suggest a connection between the local curvature and local hemodynamics, indicating that the curvature is a property that could be used to assess both mechanical response and hemodynamic conditions, and, moreover, to suggest new metrics based on the curvature to predict the likelihood of rupture.
... An example of the resulting patching is shown in Fig. 8.3b. 3. Finally, a "local-shape" patching based on the principal curvatures of the luminal surface, κ 1 and κ 2 , which are related to its fundamental forms. Based on them, more commonly used measures of curvatures are the Gaussian and mean curvatures, defined as follows: Figure 8.3 -Examples of the three types of patching used to locally analyze the mechanical response of IAs walls for case urICA1: (a) the phenotypic classification used to base the abnormal-hemodynamics wall model; (b) the "physician-oriented" patching into "neck", "body", "dome" as defined by Salimi Ashkezari et al. (193); (c) based on the Gaussian, K, and mean, H, curvature fields of the lumen surface, a "local shape characterization" based on the one proposed by Ma et al. (157). and Additionally, as can be seen in Fig. 8.3c, both K and H fields have a "noisy" behavior. ...
... Curvature-based metrics were introduced, in the context of saccular IAs, primarily by Ma et al. (157) with four indices computed as surface-averages and L2-norms of K and H -labeled GAA, MAA, GLN, and MLN (the "AA" and "LN" stand for "area-average" and "L2-norm", respectively. See Section A.1 of Appendix A for their mathematical definitions). ...
... Two important 3D size metrics are the area of the sac surface, A ia , and the volume enclosured by it and the ostium surface, V ia . Moreover, an important entity in the 3D characterization of IAs is its convex hull (157). This can be imagined as the smallest convex surface that encompasses S ia (literally, imagine an "elastic membrane" that covers the aneurysm surface), with surface area S ch and volume V ch . ...
Intracranial aneurysms (IAs) are abnormalities formed in the cerebral arteries characterized by outpouching regions of their walls. The danger with these lesions occurs if they rupture, which causes intracranial hemorrhage and possibly leads to the death of the patient, presenting a mortality rate as high as 50 %. The rupture event is hard to predict, though, and, currently, surgical treatments also pose risks to the patient. Numerical simulations of the blood flow inside IAs have been extensively used to study them because of the well-known connections between hemodynamics and their inception, growth, and rupture. Physically, although it should be modeled as a Fluid-Solid Interaction (FSI) problem, the majority of those works have solely focused on the hemodynamics while either ignoring the wall tissue motion entirely, through rigid-wall modeling, or using limited assumptions for it. One possible explanation is the scarcity of measurements of their wall mechanical properties and also its thickness, which limits the use of better modeling options. Consequently, few works have investigated the impact of tissue modeling on their mechanical response, an important endeavor to try to predict the likelihood of rupture, because it is a wall-exclusive event that theoretically depends on the level of stress. In this context, this work investigated the influence of different hyperelastic laws and the material properties and thickness heterogeneity on the wall mechanics of IAs, given their rupture status. Pulsatile numerical simulations with patient-specific vascular geometries harboring Ias were carried out using the one-way fluid-solid interaction solution strategy implemented in solids4foam, an extension of OpenFOAM ® , in which the blood flow is solved and applied as the driving force of the wall motion. First, it was found that different wall morphology models yielded smaller absolute differences in the mechanical response than different hyperelastic laws. Second, the stretch levels of IAs walls were more sensitive to the hyperelastic laws and material constants than the stress, especially for ruptured IAs, allowing the identification of these by the higher stretch levels instead of stress levels. Additionally, the morphology variable that best correlated with regions of high stress and stretch was the wall curvature. Finally, these findings could be used to guide modeling decisions on IA simulations and also suggest new metrics based on the wall curvature to predict the likelihood of rupture.
... In this study, we used 6 indices for size (dome volume, dome surface area, neck diameter, maximum diameter, aneurysm height, aneurysm size) and 6 indices for shape (aspect ratio, ellipticity index, non-sphericity index, undulation index, conicity parameter, bottleneck factor). These well-established GIs have been previously reviewed by Ma et al. (16), Raghavan et al. (19), and Berkowitz (23). Table 1 provides a summary of these features. ...
... Distribution-derived features characterize the variation of local shape properties evaluated across points p of a surface S. For this study, we considered two such properties, curvature and writhe, both of which have been used already to characterize IAs (16,19,20). ...
... We used VTK (18) to compute the local curvature values for discrete surface meshes, which we subsequently aggregated as described in Table 1. A total of 8 different curvature-derived features are evaluated, which include the well-known metrics for total Gaussian and Mean curvature GLN and MLN (16), and two novel metrics. ...
Background
To date, it remains difficult for clinicians to reliably assess the disease status of intracranial aneurysms. As an aneurysm's 3D shape is strongly dependent on the underlying formation processes, it is believed that the presence of certain shape features mirrors the disease status of the aneurysm wall. Currently, clinicians associate irregular shape with wall instability. However, no consensus exists about which shape features reliably predict instability. In this study, we present a benchmark to identify shape features providing the highest predictive power for aneurysm rupture status.
Methods
3D models of aneurysms were extracted from medical imaging data (3D rotational angiographies) using a standardized protocol. For these aneurysm models, we calculated a set of metrics characterizing the 3D shape: Geometry indices (such as undulation, ellipticity and non-sphericity); writhe- and curvature-based metrics; as well as indices based on Zernike moments. Using statistical learning methods, we investigated the association between shape features and aneurysm disease status. This processing was applied to a clinical dataset of 750 aneurysms (261 ruptured, 474 unruptured) registered in the AneuX morphology database. We report here statistical performance metrics [including the area under curve (AUC)] for morphometric models to discriminate between ruptured and unruptured aneurysms.
Results
The non-sphericity index NSI (AUC = 0.80), normalized Zernike energies ZNsurf (AUC = 0.80) and the modified writhe-index W¯meanL1 (AUC = 0.78) exhibited the strongest association with rupture status. The combination of predictors further improved the predictive performance (without location: AUC = 0.82, with location AUC = 0.87). The anatomical location was a good predictor for rupture status on its own (AUC = 0.78). Different protocols to isolate the aneurysm dome did not affect the prediction performance. We identified problems regarding generalizability if trained models are applied to datasets with different selection biases.
Conclusions
Morphology provided a clear indication of the aneurysm disease status, with parameters measuring shape (especially irregularity) being better predictors than size. Quantitative measurement of shape, alone or in conjunction with information about aneurysm location, has the potential to improve the clinical assessment of intracranial aneurysms.
... Classification accuracy increases to 90.3% in Fig 9D and 92.8±1.7% in Fig 9E. As shown in Fig 10A, there is no significant difference amongst size predictors such as aortic volume, surface area, median and maximum diameters shown in Fig 5, as well as Gaussiancurvature based size measures like the L2-norm of the Gaussian curvature (GLN) and the area-averaged Gaussian curvature (GAA) [40,60,61], see SI Other Shape Metrics. There is a major difference with shape measures: clinical shape measures, which are based on the aortic centerline and include tortuosity index [21,43,44,62], question mark angle [44,63], cross-sectional eccentricity [42,64], and mean centerline curvature [43], significantly underperform δK in aortic disease state classification (Fig 10B). ...
... There is a major difference with shape measures: clinical shape measures, which are based on the aortic centerline and include tortuosity index [21,43,44,62], question mark angle [44,63], cross-sectional eccentricity [42,64], and mean centerline curvature [43], significantly underperform δK in aortic disease state classification (Fig 10B). Similarly, δK outperforms other shape measures described in the biomedical engineering literature including the sphericity index (χ) [65], flatness index (γ) [65], Gaussian curvature (κ g ) [40,41], area-averaged mean curvature (MAA), and L2-norm of the mean curvature (MLN) [40,60,61] (Fig 10C). ...
Clinical imaging modalities are a mainstay of modern disease management, but the full utilization of imaging-based data remains elusive. Aortic disease is defined by anatomic scalars quantifying aortic size, even though aortic disease progression initiates complex shape changes. We present an imaging-based geometric descriptor, inspired by fundamental ideas from topology and soft-matter physics that captures dynamic shape evolution. The aorta is reduced to a two-dimensional mathematical surface in space whose geometry is fully characterized by the local principal curvatures. Disease causes deviation from the smooth bent cylindrical shape of normal aortas, leading to a family of highly heterogeneous surfaces of varying shapes and sizes. To deconvolute changes in shape from size, the shape is characterized using integrated Gaussian curvature or total curvature. The fluctuation in total curvature (δK) across aortic surfaces captures heterogeneous morphologic evolution by characterizing local shape changes. We discover that aortic morphology evolves with a power-law defined behavior with rapidly increasing δK forming the hallmark of aortic disease. Divergent δK is seen for highly diseased aortas indicative of impending topologic catastrophe or aortic rupture. We also show that aortic size (surface area or enclosed aortic volume) scales as a generalized cylinder for all shapes. Classification accuracy for predicting aortic disease state (normal, diseased with successful surgery, and diseased with failed surgical outcomes) is 92.8±1.7%. The analysis of δK can be applied on any three-dimensional geometric structure and thus may be extended to other clinical problems of characterizing disease through captured anatomic changes.
... Based on the ostium and dome area, medical studies derive several morphological descriptors, which allow a more differentiated classification of the aneurysm morphology concerning risk evaluation and decision-making [68,84,159,232,311,402]. Here, a distinction between 1D and 2D descriptors is made, where some groups use in-house tools to compute the descriptors semi-automatically [84,212]. ...
... As 1D descriptors allow no reliable risk estimation, clinical studies evaluated 2D descriptors for rupture risk assessment [68,84,159,232,311,402]. Statistically significant differences between ruptured and non-ruptured aneurysms were detected according to the aspect ratio, undulation index, non-sphericity index, and aneurysm/parent artery ratio. ...
Cerebral aneurysms are weak vessel areas that can bulge out and balloon, caused by a pathologically altered structure of the vascular wall. They bear the risk of rupture, leading to internal bleeding causing high risks of mortality. Although most aneurysms will never rupture, the potential risk of bleeding makes the detection and risk-assessment of aneurysms a critical issue. Imaging methods are used for the detection and localization of aneurysms. The decision as to whether or not aneurysms should be treated must be carefully considered, as there is a risk of fatal outcome during surgery. Their initiation and progression depend strongly on the interplay of vascular morphology and hemodynamics. Unfortunately, the processes causing aneurysm growth and rupture are not well understood. Blood flow simulations can obtain information about the patient-specific hemodynamics.
It is also the basis for the development for new, low-risk treatment options since treatment success depends on blood flow characteristics. In clinical routine, risk assessment and treatment planning are just based on morphological characteristics
of an aneurysm and its surrounding vasculature. However, this information allows no reliable evaluation of the aneurysm state. To improve decision-making, medical and biomedical researchers analyze simulated flow data, which are multi-attribute data with high spatial and temporal complexity. The data exploration is performed quantitatively and qualitatively, where the former focuses on the evaluation of specific scalar values such as pressure or wall thickness and the latter focuses
on the analysis of flow patterns such as vortices. Correlations between qualitative and quantitative characteristics can be revealed and formed into hypotheses that can lead to a better understanding of the internal aneurysm procedures. However, the visual exploration of flow data is a time-consuming process, which is affected by visual clutter and occlusions. The goal of our work is to develop computer-aided methods that support the quantitative and qualitative visual exploration of morphological and hemodynamic characteristics in cerebral aneurysm data sets. Since this is an interdisciplinary process involving both physicians and fluid mechanics experts, redundancy-free management of aneurysm data sets is required to enable efficient analysis of the information. We developed a consistent structure to document aneurysm data sets, where users can search for specific cohorts, and individual cases can be analyzed more detailed to assess the aneurysm state as well as to weigh different treatment scenarios. The prerequisite for the visual exploration is the extraction of the ostium, which is a curved surface that separates the parent vessel from an aneurysm. We provide an automatic determination of the ostium. Based on this several other morphological descriptors are computed automatically. Besides an analysis of morphological aspects,
the aneurysm data exploration comprises four more parts: a simultaneous evaluation of wall- and flow-related characteristics, a simultaneous analysis of multiple scalar information on the aneurysm wall, the analysis of mechanical wall processes as well as a qualitative characterization of the internal flow behavior. We provide methods for each of these parts: occlusion-free depictions of the vessel morphology and internal blood flow, interactive 2D and 3D visualizations to explore multi-attribute
correlations, comparative glyph-based visualizations to explore mechanical wall forces and automatic classification of qualitative flow patterns. Our methods were designed and evaluated in collaboration with domain experts who confirmed their usefulness and clinical necessity.
... Further advancements in diagnostic and measurement techniques have led new ways to study aneurysms in greater detail. Well-defined aneurysm morphologies and characterization methods have been used to find correlation to aneurysm risk of rupture [14,[26][27][28]. Their work found that aneurysm morphological indicators such as aspect ratio, undulation index, non-sphericity index, and bottleneck factor have greater risk of rupture. ...
... The aneurysm geometries were designed to be spherical in shape with maximum aneurysm sac diameter ( ) and neck diameter ( ) to be 13.87 mm for the first model, and = 13.87 mm and = 8.69 mm for the second model. The aneurysm size dimensions were used describe a non-dimensional parameter, bottleneck factor ( ) [27], to differentiate the models. ...
Aneurysms are abnormal expansion of weakened blood vessels which can be debilitating or fatal upon rupture. Previous studies have shown that hemodynamics play a role in aneurysm formation, growth and rupture. Therefore, the objective of this work is to investigate the impact of flow structures on vortex strength, impinging location, and wall shear stress for two aneurysm models. For this study, experiments were performed on two different, idealized, rigid, and saccular aneurysm models characterized by BF ratios of 1.0 and 1.6. The vortical structures formation and movement were altered by changing peak Reynolds number (Rep) from 50 and 270 and Womersley number (α) from 2, and 5 on both aneurysm models. Velocity field measurements were performed on the mid-plane location of the aneurysm models using Particle Image Velocimetry (PIV). The results showed presence of vortical structures which formed, grew, and dissipated at different phases in the flow cycle. The behavior of these vortical structures impacted the impinging locations where increased frequency of impingement points at the distal neck could be seen for α=5 than α=2 flow scenarios. The wall shear stress results showed that the distal neck experienced elevated stresses during the vortex formation phases of the flow cycle for BF=1.0 and 1.6 models.
... Global curvature indices have been previously quantified for patient-specific aortic aneurysm models to assess the role of geometry in aneurysm rupture risk [11,12]. Similar global curvature metrics have been computed for cerebral aneurysm models [30]. For PH RV models, we studied the feasibility of using comparable metrics to assess changes in RV geometry. ...
... Short-axis view of RV endocardial wall models at the EDV of the cardiac cycle for a representative (a) PH subject and (b) control subject. 1, 2, and 3 indicate the location of the free wall, interventricular septum, and ventricular apex for both models, respectivelyTable 3Local surface shape characteristics based on combinations of mean (M) and Gaussian (G) curvatures (adapted from Ma et al.[30]) ...
Pulmonary hypertension (PH) is a chronic progressive disease diagnosed when the pressure in the main pulmonary artery, assessed by right heart catheterization, is greater than 25 mmHg. Changes in the pulmonary vasculature due to the high pressure yield an increase in the right ventricle (RV) afterload. RV models were obtained from segmentation of cardiac magnetic resonance images at baseline and 1-year follow up for a pilot study that involved 12 PH and 7 control subjects. The models were used to create surface meshes and compute the principal, mean, and Gaussian curvatures. Ten global curvature indices were calculated for RV endocardial wall reconstructions at the end-diastolic volume (EDV) and end-systolic volume (ESV) phases of the cardiac cycle. Data analysis was performed to discern if there are significant differences in the curvature indices between controls and the PH group, as well as between the baseline and follow-up phases for the PH subjects. Six curvature indices, namely the Gaussian curvature at ESV, the mean curvature at EDV and ESV, the L2-norm of the mean curvature at ESV, and the L2-norm of the major principal curvature at EDV and ESV, were found to be significantly different between controls and PH subjects (p < 0.05). We infer that these geometry measures could be used as indicators of RV endocardial wall morphology changes. Two global parameters, the Gaussian and mean curvatures at ESV, showed significant change at the one-year follow up for the PH subjects (p < 0.05).
... For example, Ujiie et al. [20] have shown that aneurysms with an aspect ratio greater than 1.6 have a greater risk of rupture. Aneurysm shapes were further characterized by Ma et al. [21] and Raghavan et al. [22], these studies also suggest that aneurysms with a diameter !7 mm and morphological indicators such as aspect ratio, undulation index, and nonsphericity index are associated with increased risk of rupture. These clinical studies have led the way for experimental and computational work to investigate possible factors leading to aneurysm growth and rupture. ...
... This suggests controlled inflow scenarios and allowed us to systematically study the impact of Re-and a in the aneurysm region. The bottleneck factor [21,22] used for the model is one, and the model was fabricated using borosilicate glass to allow index matching with the fluid. The fluid used in this study was a mixture of glycerin and water and has been successfully used in several previous investigations [11,35,38,39,41,56]. ...
Aneurysms are localized expansions of weakened blood vessels that can be debilitating or fatal upon rupture. Previous studies have shown that flow in an aneurysm exhibits complex flow structures that are correlated with its inflow conditions. Therefore, the objective of this study was to demonstrate the application of Proper Orthogonal Decomposition (POD) to study the impact of different inflow conditions on energetic flow structures and their temporal behavior in an aneurysm. To achieve this objective, experiments were performed on an idealized rigid sidewall aneurysm model. A piston pump system was used for precise inflow control, i.e., peak Reynolds number () and Womersley number () were varied from 50-270 and 2-5, respectively. The velocity flow field measurements at the mid-plane location of the idealized aneurysm model were performed using Particle Image Velocimetry (PIV). The results demonstrate the efficacy of POD in decomposing complex data, and POD was able to capture the energetic flow structures unique to each studied inflow condition. Furthermore, the time-varying coefficient results highlighted the interplay between the coefficients and their corresponding POD modes, which in turn helped explain how POD modes impact certain flow features. The low-order reconstruction results were able to capture the flow evolution and provide information on complex flow in an aneurysm. The POD and low-order reconstruction results also indicated that vortex formation, evolution, and convection varied with an increase in , while vortex strength and formation of secondary structures were correlated with an increase in .
... Approximately 20-30% of patients have multiple aneurysms (9). Aneurysm rupture leads to subarachnoid hemorrhage (SAH), with high rates of mortality and a morbidity rate of 50% for survivors (10,11). A growing aneurysm may cause a mass effect due to impingement on brain tissue or cranial nerves; thrombotic aneurysms may also cause distal thromboemboli. ...
... Despite numerous studies on the subject, assessing the risk of aneurysm rupture remains a clinical challenge. As discussed in Section 1.1, most UIAs remain stable, with approximately 10-15% showing growth in longitudinal studies (13,14), but since an aneurysm rupture leads to high mortality and morbidity rates (10,11), most UIAs are currently treated even if the probability of rupture may be negligible. Risk stratification scores such as those from the ISUIA and UCAS and PHASES, UIATS, and ELAPSS, mentioned above (7,21,(24)(25)(26), are based on a combination of aneurysm location (e.g., posterior or anterior), morphology (e.g., size, shape), and clinical factors (e.g., comorbidities, age, gender, smoking status, family history). ...
In the last two decades, numerous studies have conducted patient-specific computations of blood flow dynamics in cerebral aneurysms and reported correlations between various hemodynamic metrics and aneurysmal disease progression or treatment outcomes. Nevertheless, intra-aneurysmal flow analysis has not been adopted in current clinical practice, and hemodynamic factors usually are not considered in clinical decision making. This review presents the state of the art in cerebral aneurysm imaging and image-based modeling, discussing the advantages and limitations of each approach and focusing on the translational value of hemodynamic analysis. Combining imaging and modeling data obtained from different flow modalities can improve the accuracy and fidelity of resulting velocity fields and flow-derived factors that are thought to affect aneurysmal disease progression. It is expected that predictive models utilizing hemodynamic factors in combination with patient medical history and morphological data will outperform current risk scores and treatment guidelines. Possible future directions include novel approaches enabling data assimilation and multimodality analysis of cerebral aneurysm hemodynamics.
Expected final online publication date for the Annual Review of Biomedical Engineering, Volume 22 is June 4, 2020. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
... The 4D-flow MRI showed that lesion dimension and form had an effect on aneurysm hemodynamics, implying that 4D-flow MRI might help with the categorization of specific aneurysms. Ma et al. 6 investigated the three-dimensional geometry of five cerebral aneurysms obtained from computed tomography angiography. The team compared the hypothetical shapes, such as hemispherical, spherical, and ellipsoid with the real aneurysms of irregular shapes. ...
An efficient screening method for detecting and assessing aneurysms is magnetic resonance imaging. The current study examines the flow through aneurysmal sacs with six distinct shapes. The study assumes that a strong magnetic field is present in order to create an internal environment for magnetic resonance imaging equipment. The flow properties are investigated, including cell Reynolds number, pressure, and velocity. The study concluded that the globous and bilobar configurations are more susceptible to sac burst and horizontal neck expansion, respectively. The extent of the recirculation zone formed in the globous sac is relatively high. The pressure difference in bilobar, in contrast to other configurations, noticed at the distal node of the aneurysm neck is in the range of 0.089%–0.443%. Magnetic flux density, magnetization vector, magnetic field norm, and Lorentz force magnitude are investigated in the context of magnetic field attributes. The ellipse of transition at the aneurysmal sac's neck is found, along with its dimensions. The size of the ellipse formed denotes the extent of percolation of the magnetic flux into the aneurysms. The most veiled version of the geometry is determined to be multilobar by analyzing the amount of magnetic field line seepage into the sac during magnetic resonance imaging. The weak formulation, the creation of a climate akin to that of the magnetic resonance imaging machine's interior, and the investigation of magnetic field entities during blood flow in the presence of a strong magnetic field are the novel aspects of this work.
... Additionally, mechanical tests have shown that the wall tissue has negligible bending stiffness (Humphrey and Canham, 2000). Therefore, membrane elements with triangular mesh are used for strain calculation (Ma et al., 2004), and the IAs (Patients 1 to 4) with irregular pulsation were meshed into 10414, 7322, 8196 and 4554 elements, respectively. Due to the complex structure and composition of the aneurysm, the surface deformation of IAs exhibits a complex mechanical behaviour, with the largest deformations usually occurring where irregular pulsation occurs, which is also likely to be where the aneurysm wall is weaker. ...
... Definition of morphological parameters. *DV CH and DA CH are the volume and outer area of the convex hull of the aneurysm 34,35 . Volume to the ostium area (VOA) DV /NA www.nature.com/scientificreports/ ...
Cerebral aneurysms are a silent yet prevalent condition that affects a significant global population. Their development can be attributed to various factors, presentations, and treatment approaches. The importance of selecting the appropriate treatment becomes evident upon diagnosis, as the severity of the disease guides the course of action. Cerebral aneurysms are particularly vulnerable in the circle of Willis and pose a significant concern due to the potential for rupture, which can lead to irreversible consequences, including fatality. The primary objective of this study is to predict the rupture status of cerebral aneurysms. To achieve this, we leverage a comprehensive dataset that incorporates clinical and morphological data extracted from 3D real geometries of previous patients. The aim of this research is to provide valuable insights that can help make informed decisions during the treatment process and potentially save the lives of future patients. Diagnosing and predicting aneurysm rupture based solely on brain scans is a significant challenge with limited reliability, even for experienced physicians. However, by employing statistical methods and machine learning techniques, we can assist physicians in making more confident predictions regarding rupture likelihood and selecting appropriate treatment strategies. To achieve this, we used 5 classification machine learning algorithms and trained them on a substantial database comprising 708 cerebral aneurysms. The dataset comprised 3 clinical features and 35 morphological parameters, including 8 novel morphological features introduced for the first time in this study. Our models demonstrated exceptional performance in predicting cerebral aneurysm rupture, with accuracy ranging from 0.76 to 0.82 and precision score from 0.79 to 0.83 for the test dataset. As the data are sensitive and the condition is critical, recall is prioritized as the more crucial parameter over accuracy and precision, and our models achieved outstanding recall score ranging from 0.85 to 0.92. Overall, the best model was Support Vector Machin with an accuracy and precision of 0.82, recall of 0.92 for the testing dataset and the area under curve of 0.84. The ellipticity index, size ratio, and shape irregularity are pivotal features in predicting aneurysm rupture, respectively, contributing significantly to our understanding of this complex condition. Among the multitude of parameters under investigation, these are particularly important. In this study, the ideal roundness parameter was introduced as a novel consideration and ranked fifth among all 38 parameters. Neck circumference and outlet numbers from the new parameters were also deemed significant contributors.
... In addition to WSS metrics, some morphological parameters of aneurysm were considered, which included aneurysm dome area (DA), volume (V aneu ), nonsphericity index [NSI, NSI = 1-(18π) 1/3 V aneu 2/3 /A], height (H, the longest perpendicular distance to the neck plane), width (W, the largest diameter perpendicular to H), diameter of the aneurysm neck (D neck ), height-to-width ratio (HWR, HWR = H/W), aspect ratio (AR, AR = H/D neck ), and bottleneck factor (BF, BF = W/D neck ) (Ma et al., 2004;Chien et al., 2018;Xin et al., 2022). ...
Anterior communicating artery (ACoA) aneurysms are more prone to rupture compared to aneurysms present in other cerebral arteries. We hypothesize that systemic blood flow in the cerebral artery network plays an important role in shaping intra-aneurysmal hemodynamic environment thereby affecting the rupture risk of ACoA aneurysms. The majority of existing numerical studies in this field employed local modeling methods where the physical boundaries of a model are confined to the aneurysm region, which, though having the benefit of reducing computational cost, may compromise the physiological fidelity of numerical results due to insufficient account of systemic cerebral arterial hemodynamics. In the present study, we firstly carried out numerical experiments to address the difference between the outcomes of local and global modeling methods, demonstrating that local modeling confined to the aneurysm region results in inaccurate predictions of hemodynamic parameters compared with global modeling of the ACoA aneurysm as part of the cerebral artery network. Motivated by this finding, we built global hemodynamic models for 40 ACoA aneurysms (including 20 ruptured and 20 unruptured ones) based on medical image data. Statistical analysis of the computed hemodynamic data revealed that maximum wall shear stress (WSS), minimum WSS divergence, and maximum WSS gradient differed significantly between the ruptured and unruptured ACoA aneurysms. Optimal threshold values of high/low WSS metrics were determined through a series of statistical tests. In the meantime, some morphological parameters of aneurysms, such as large nonsphericity index, aspect ratio, and bottleneck factor, were found to be associated closely with aneurysm rupture. Furthermore, multivariate logistic regression analyses were performed to derive models combining hemodynamic and morphological parameters for discriminating the rupture status of aneurysms. The capability of the models in rupture status discrimination was high, with the area under the receiver operating characteristic curve reaching up to 0.9. The findings of the study suggest that global modeling of the cerebral artery network is essential for reliable quantification of hemodynamics in ACoA aneurysms, disturbed WSS and irregular aneurysm morphology are associated closely with aneurysm rupture, and multivariate models integrating hemodynamic and morphological parameters have high potential for assessing the rupture risk of ACoA aneurysms.
... Aspect ratio (AR) and bottleneck factor (BF) were calculated for each aneurysm: however it is important to note that there is some variation in these calculations, given the different aneurysmal forms (i.e. saccular, multilobular and fusiform) (Ma et al., 2004;Shum et al., 2011). The values are Type 1 (AR:1.71; ...
Thrombosis is an important contributor to cerebral aneurysm growth and progression. A number of sophisticated multiscale and multiphase in silico models have been developed with a view towards interventional planning. Many of these models are able to account for clotting outcomes, but do not provide detailed insight into the role of flow during clot development. In this study, we present idealised, two-dimensional in silico cerebral fibrin clot model based on computational fluid dynamics (CFD), biochemical modelling and variable porosity, permeability, and diffusivity. The model captures fibrin clot growth in cerebral aneurysms over a period at least 1000 s in five different geometries. The fibrin clot growth results were compared to an experiment presented in literature. The biochemistry was found to be more sensitive to mesh size compared to the haemodynamics, while larger timesteps overpredicted clot size in pulsatile flow. When variable diffusivity was used, the predicted clot size was 25.4% lesser than that with constant diffusivity. The predicted clot size in pulsatile flow was 14.6% greater than in plug flow. Different vortex modes were observed in plug and pulsatile flow; the latter presented smaller intermediate modes where the main vortex was smaller and less likely to disrupt the growing fibrin clot. Furthermore, smaller vortex modes were seen to support fibrin clot propagation across geometries. The model clearly demonstrates how the growing fibrin clot alters vortical structures within the aneurysm sac and how this changing flow, in turn, shapes the growing fibrin clot.
... Investigaciones previas han intentado implementar diferentes sistemas de puntuaciones. (19,20) Estos instrumentos no han tenido gran aceptación por varios motivos: han presentado limitaciones porque no abarcan todos los tipos de aneurismas intracraneales como los pequeños y gigantes y es un hecho conocido que existen diferencias estructurales y hemodinámicas entre aneurismas pequeños, grandes y gigantes; algunos de estos instrumentos fueron diseñados para grupos poblacionales y entornos específicos lo cual puede modificar la validez predictiva cuando son aplicados en entornos diferentes debido a las variaciones descritas en cuanto a variablidad interobservador, geometría y mediciones de los aneurismas. (21) Otros investigadores han tratado de construir instrumentos basados en modelos usando dinámica computacional de fluidos y parámetros hemodinámicos. ...
Fundamento:
la estratificación del riesgo de rotura de los aneurismas intracraneales es importante para decidir la conducta ante aquellos pacientes con aneurismas que son incidentales o asintomáticos. No existe consenso para determinar la realización de intervención quirúrgica o seguimiento médico de estos pacientes.
Objetivo:
elaborar un instrumento predictivo de rotura de aneurismas intracraneales incidentales.
Métodos:
se incluyó una muestra de 152 pacientes con diagnóstico, mediante angiografía por tomografía axial computarizada, de aneurismas intracraneales saculares rotos (n=138) y no rotos(n=22). Se trabajó con 160 imágenes de aneurismas intracraneales. Los 152 pacientes fueron divididos, al azar, en un grupo de desarrollo que corrrespondió a 95 pacientes, 100 imágenes de aneurismas y un grupo de validación que incluyó 57 pacientes con 60 imágenes de aneurismas. Se realizaron mediciones y segmentaciones de los aneurismas; se obtuvieron nueve factores morfológicos. Se realizó una combinación multivariante, mediante regresión logística múltiple, que expresó seis factores demográficos, clínicos y mofológicos predictivos obtenidos de los expedientes clínicos de los pacientes. La selección para inclusión de los factores fue realizada a partir de un consenso de 15 expertos con más de 15 años de experiencia en el tema. Se confeccionó un nomograma representativo del modelo con los predictores significativos. Se evaluó la calibración y la precisión del instrumento predictivo representado por un modelo y su nomograma.
Resultados:
el instrumento quedó conformado por cinco predictores que resultaron estadísticamente significativos asociados con la rotura en el análisis multivariado: el sexo femenino, la razón de aspecto, el mayor ancho del domo, el volumen, y el índice de no esfericidad. El nomograma mostró una buena calibración y discriminación (grupo de entrenamiento: área bajo la curva = 99 %; grupo de validación área bajo la curva=99 % ).
Conclusiones:
el instrumento predictivo, validado y representado por el nomograma es un modelo útil para estratificar el riesgo de rotura de aneurismas. Puede emplearse para el seguimiento de aneurismas considerados de menor riesgo.
... The volume of the aneurysm is tessellated into finite elements where each element acts as a spring-mass system with K and M which are the parameters that determine natural frequency. This study aims at finding the correlation between natural frequency and rupture status, as shape based morphological parameters of aneurysms 24,25,26 offer a key role in predicting rupture potential. ...
Neurosurgeons often encounter dilemmas in the clinical management of cerebral aneurysms owing to an uncertainty of their rupture status and rupture risk. This study evaluates the influence of natural frequency of an aneurysm, as a novel morphological parameter to understand and analyze rupture status and risk prediction. In this work, we employ the natural frequency of 20 idealized and 50 patient specific aneurysms. The natural frequency of patient specific aneurysms is then compared against their rupture status. A strong correlation was observed between various morphological indicators and natural frequency for ideal and patient specific geometries. A statistical analysis with both Mann Whitney U test and T-test for rupture status against natural frequency has given a p-value less than 0.01 indicating a strong correlation between them. The correlation of morphological parameters with natural frequency from Pearson correlation coefficient and T-test suggests a holistic reflection of their effects on the natural frequency of an aneurysm. Thus, natural frequency could be a good indicator to discern the rupture potential of an aneurysm. The correlation between rupture status and natural frequency makes it a novel parameter that can differentiate between ruptured and unruptured patient specific aneurysms.
... Traditionally only 2D information from neuroimaging was utilized in the interpreting and measuring IAs (Rayz and Cohen-Gadol, 2020), which neglected the complex 3D structure of IAs and may lead to measurement bias and inconsistency (Rajabzadeh-Oghaz et al., 2017. Studies have shown that morphological metrics derived based on 3D information are more accurate and consistent than 2D manual measurement (Ma et al., 2004;Ryu et al., 2011;Rajabzadeh-Oghaz et al., 2018). However, recent studies have revealed that the morphology metrics alone may not be sufficient for predicting the rupture risks of IA, especially in small unruptured IAs (Abboud et al., 2017;Korja et al., 2017;Longo et al., 2017;Hu et al., 2021;Ren et al., 2022). ...
The manual identification and segmentation of intracranial aneurysms (IAs) involved in the 3D reconstruction procedure are labor-intensive and prone to human errors. To meet the demands for routine clinical management and large cohort studies of IAs, fast and accurate patient-specific IA reconstruction becomes a research Frontier. In this study, a deep-learning-based framework for IA identification and segmentation was developed, and the impacts of image pre-processing and convolutional neural network (CNN) architectures on the framework’s performance were investigated. Three-dimensional (3D) segmentation-dedicated architectures, including 3D UNet, VNet, and 3D Res-UNet were evaluated. The dataset used in this study included 101 sets of anonymized cranial computed tomography angiography (CTA) images with 140 IA cases. After the labeling and image pre-processing, a training set and test set containing 112 and 28 IA lesions were used to train and evaluate the convolutional neural network mentioned above. The performances of three convolutional neural networks were compared in terms of training performance, segmentation performance, and segmentation efficiency using multiple quantitative metrics. All the convolutional neural networks showed a non-zero voxel-wise recall (V-Recall) at the case level. Among them, 3D UNet exhibited a better overall segmentation performance under the relatively small sample size. The automatic segmentation results based on 3D UNet reached an average V-Recall of 0.797 ± 0.140 (3.5% and 17.3% higher than that of VNet and 3D Res-UNet), as well as an average dice similarity coefficient (DSC) of 0.818 ± 0.100, which was 4.1%, and 11.7% higher than VNet and 3D Res-UNet. Moreover, the average Hausdorff distance (HD) of the 3D UNet was 3.323 ± 3.212 voxels, which was 8.3% and 17.3% lower than that of VNet and 3D Res-UNet. The three-dimensional deviation analysis results also showed that the segmentations of 3D UNet had the smallest deviation with a max distance of +1.4760/−2.3854 mm, an average distance of 0.3480 mm, a standard deviation (STD) of 0.5978 mm, a root mean square (RMS) of 0.7269 mm. In addition, the average segmentation time (AST) of the 3D UNet was 0.053s, equal to that of 3D Res-UNet and 8.62% shorter than VNet. The results from this study suggested that the proposed deep learning framework integrated with 3D UNet can provide fast and accurate IA identification and segmentation.
... It enables the reconstruction of three-dimensional patient-specific configurations, which can help with measurement gathering at various stages of treatment. These geometries, in particular, can help with rupture risk assessment, which is typically based on aneurysm diameter and dome-neck area ratio (AR) [32,33]. Surgical planning, such as surgical intervention and stent insertion, is influenced by the geometric features of intracerebral aneurysms [34]. ...
Background: Cerebral aneurysm is the basic cause of sub-arachnoid hemorrhage; Computed tomographic angiogram is the non-invasive approach to diagnose aneurysm by reconstructing the image in 3D dimension making it possible to locate the aneurysm and differentiate it from other arteries. Objective: Focus of this study was to investigate the accuracy of CTA to detect the aneurysm, its type, location and size. Material and method: Data of 50 patients was taken retrospectively with cost-benefit approach that undergoes non-invasive CTA through Aquilion 64-slices CT machine under post-processing work station. Results: This retrospective study is taken with 50 patients, with a 38 percent positive predictive value and a 62 percent negative predictive value, multi-slice CT properly revealed substantial aneurysm in 19 of 50 cases. Conclusion: 64-slices CT provides high diagnostic accuracy for detecting the aneurysm in cerebral arteries with a non-invasive angiogram procedure.
... It enables the reconstruction of three-dimensional patient-specific configurations, which can help with measurement gathering at various stages of treatment. These geometries, in particular, can help with rupture risk assessment, which is typically based on aneurysm diameter and dome-neck area ratio (AR) [32,33]. Surgical planning, such as surgical intervention and stent insertion, is influenced by the geometric features of intracerebral aneurysms [34]. ...
Background: Cerebral aneurysm is the basic cause of sub-arachnoid hemorrhage; Computed tomographic angiogram is the non-invasive approach to diagnose aneurysm by reconstructing the image in 3D dimension making it possible to locate the aneurysm and differentiate it from other arteries. Objective: Focus of this study was to investigate the accuracy of CTA to detect the aneurysm, its type, location and size. Material and method: Data of 50 patients was taken retrospectively with cost-benefit approach that undergoes non-invasive CTA through Aquilion 64-slices CT machine under post-processing work station. Results: This retrospective study is taken with 50 patients, with a 38 percent positive predictive value and a 62 percent negative predictive value, multi-slice CT properly revealed substantial aneurysm in 19 of 50 cases. Conclusion: 64-slices CT provides high diagnostic accuracy for detecting the aneurysm in cerebral arteries with a non-invasive angiogram procedure.
... For instance, earlier studies used aneurysm size to quantify likelihood of rupture [19,20]. With advancements in technology and computational capabilities, other studies used non-dimensional geometrical characterization of different sizes and shapes to identify aneurysms with low and high risk of rupture [21][22][23]. A few studies have focused on hemodynamics, using computational [24][25][26] and experimental [27][28][29][30] approaches, and identified hemodynamics as playing an important role in aneurysm behavior, particularly in aneurysm progression and rupture. ...
Aneurysms are localized expansions of blood vessels which can be fatal upon rupture. Studies have shown that aneurysm flows exhibit complex flow phenomena which consist of single or multiple vortical structures that move within the flow cycle. Understanding the complex flow behaviors of aneurysms remain challenging. Thus, the goal of this study is to quantify the flow behavior and extract physical insights into aneurysm flows using advance data decomposition methods, Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). The velocity field data were obtained by performing 2D Particle Image Velocimetry (2D PIV) on the mid-plane of an idealized, rigid, saccular aneurysm model. The input flow conditions were set to Rep=50 and 150 for a fixed α=2 using a precisely controlled piston pump system. POD was used to quantify the spatial features of the flows, while DMD was used to obtain insight on the dynamics. The results obtained from POD and DMD showed the capability of both methods to quantify the flow field, with the modes obtained providing different insights into the flow evolution in the aneurysm. The curve-fitting step of the POD time-varying coefficients, and the appropriate selection of DMD modes based on their energy contribution, allowed the mathematical flow models from POD and DMD to reconstruct flow fields at any given time step. This can be used for validation of numerical or computational data.
... For example, aneurysmal diseases (e.g., cerebral or aortic) lead to very complex 3D morphologies. Prior attempts in characterizing their geometry have revealed the complexity in geometric features [13,14]. Alternatively, occlusive diseases, such as, vulnerable coronary artery plaques or peripheral vascular p. 3 disease can also create very complex shapes [15][16][17]. ...
Recent progress in machine learning (ML), together with advanced computational power, have provided new research opportunities in cardiovascular modeling. While classifying patient outcomes and medical image segmentation with ML have already shown significant promising results, ML for the prediction of biomechanics such as blood flow or tissue dynamics is in its infancy. This perspective article discusses some of the challenges in using ML for replacing well-established physics-based models in cardiovascular biomechanics. Specifically, we discuss the large landscape of input features in 3D patient-specific modeling as well as the high-dimensional output space of field variables that vary in space and time. We argue that the end purpose of such ML models needs to be clearly defined and the tradeoff between the loss in accuracy and the gained speedup carefully interpreted in the context of translational modeling. We also discuss several exciting venues where ML could be strategically used to augment traditional physics-based modeling in cardiovascular biomechanics. In these applications, ML is not replacing physics-based modeling, but providing opportunities to solve ill-defined problems, improve measurement data quality, enable a solution to computationally expensive problems, and interpret complex spatiotemporal data by extracting hidden patterns. In summary, we suggest a strategic integration of ML in cardiovascular biomechanics modeling where the ML model is not the end goal but rather a tool to facilitate enhanced modeling.
... To characterize the aneurysm hemodynamics and geometry, we computed 15 flow variables and 10 geometric parameters defined on the aneurysm region. 14,15 Additionally, the aneurysm anatomic characteristics (location, morphology, and multiplicity) and patient demographics (population, sex, and age) were described by 6 categoric variables (numeric in the case of age). ...
Background and purpose:
Many small, regularly shaped cerebral aneurysms rupture; however, they usually receive a low score based on current risk-assessment methods. Our goal was to identify patient and aneurysm characteristics associated with rupture of small, regularly shaped aneurysms and to develop and validate predictive models of rupture in this aneurysm subpopulation.
Materials and methods:
Cross-sectional data from 1079 aneurysms smaller than 7 mm with regular shapes (without blebs) were used to train predictive models for aneurysm rupture using machine learning methods. These models were based on the patient population, aneurysm location, and hemodynamic and geometric characteristics derived from image-based computational fluid dynamics models. An independent data set with 102 small, regularly shaped aneurysms was used for validation.
Results:
Adverse hemodynamic environments characterized by strong, concentrated inflow jets, high speed, complex and unstable flow patterns, and concentrated, oscillatory, and heterogeneous wall shear stress patterns were associated with rupture in small, regularly shaped aneurysms. Additionally, ruptured aneurysms were larger and more elongated than unruptured aneurysms in this subset. A total of 5 hemodynamic and 6 geometric parameters along with aneurysm location, multiplicity, and morphology, were used as predictive variables. The best machine learning rupture prediction-model achieved a good performance with an area under the curve of 0.84 on the external validation data set.
Conclusions:
This study demonstrated the potential of using predictive machine learning models based on aneurysm-specific hemodynamic, geometric, and anatomic characteristics for identifying small, regularly shaped aneurysms prone to rupture.
... The aneurysm geometries were spherical in shape, with maximum aneurysm sac diameters (D max ) and neck diameters (D neck ) at 13.87 mm for the model in Figure 1a and 13.87 mm and 8.69 mm for the model in Figure 1b. For this study, the aneurysm dimensions were characterized using bottleneck factor (BF) [59] to provide a distinction between the models and their flow characteristics. The BF is the ratio of the maximum aneurysm diameter to the neck diameter opening, which provides BF = 1.0 for the model in Figure 1a and BF = 1.6 in Figure 1b. ...
Aneurysms are abnormal ballooning of a blood vessel. Previous studies have shown presence of complex flow structures in aneurysms. The objective of this study was to quantify the flow features observed in two selected saccular aneurysm geometries over a range of inflow conditions using Proper Orthogonal Decomposition (POD). For this purpose, two rigid-wall saccular aneurysm models geometries were used (i.e., the bottleneck factor of 1 and 1.6), and the inflow conditions were varied using a peak Reynolds number (Rep) from 50 and 270 and Womersley number (α) from 2 and 5. The velocity flow field data for the studied aneurysm geometries were acquired using Particle Image Velocimetry (PIV). The average flow field from the PIV measurement showed that the model geometry and Rep have more significant impact on the average flow field than the variations in α. The POD results showed that the method was able to quantify the flow field characteristics between the two model geometries. The mode shapes obtained showed different spatial structures for each inflow scenarios and models. The POD energy results showed that more than 80% of the fluctuating kinetic energy were captured within five POD modes for BF=1.0 flow scenarios, while they were captured within ten modes for BF=1.6. The time varying coefficient results showed the complex interplay of POD modes at different inflow scenarios, highlighting important modes at different phases of the flow cycle. The low-order reconstruction results showed that the vortical structure either proceeded outward or stayed within the aneurysm, and this behavior was highly dependent on α, Rep, and model geometry that were not evident in average PIV results.
... The importance of this procedure is shown in previous works [6], where the authors argue that wall thickness and asymmetry of the aorta have a large impact on the distribution of wall friction (WSS). Previous studies [14,15,16] suggest finite element methods (FEM) to provide the surface reconstruction of anatomical structures. ...
Abdominal aortic aneurysm is a serious disease which course is accompanied by the development of health complications and often leads to patient death due to aortic rupture. One of the powerful methods to estimate the risk of rupture is three-dimensional patient-specific hemodynamic analysis. In this study, we develop a software tool based on deep learning and CFD methods to perform automated computational hemodynamics with patient-specific geometry reconstructed from computed tomography images.
... In this context, Computational Fluid Dynamics (CFD) has been widely used to simulate the flow in virtual and patient-specific aneurysms geometries and vessel networks. The simulations have been used to improve the understanding of the flow dynamics and to correlate morphological and hemodynamic discriminants with aneurysm rupture [15][16][17][18][19]. While several CFD studies have been performed using aneurysm geometries obtained at a single instant of time, few studies have considered the time evolution of IAs [20,21]. ...
In the last two decades, the application of computational fluid dynamics (CFD) to study the blood flow in intracranial aneurysms has gained popularity since hemodynamics plays a key role in the inception, growth, and rupture of these aneurysms. Although the rupture event has been the main focus of these studies, other researches have shown the importance of hemodynamics also on the initiation and growth of intracranial aneurysms. However, due to the lack of follow up examinations of a single aneurysm case, these studies are scarcer. In this work, two consecutive examinations of an unruptured lateral aneurysm followed up for 5 years were used to investigate the growth of the aneurysm by using CFD . By simulating the flow in these two geometries and in the virtually reconstructed hypothetical healthy vasculature, correlations between hemodynamic parameters and the growth of the aneurysm were evaluated. The results showed that the inception of the aneurysm correlated positively with high wall shear stress (WSS) and high positive WSS spatial gradient, as other studies also suggest. Furthermore, and most importantly, as different biological pathways may explain the influence of hemodynamics on the growth process, the results also pointed out that the hemodynamic effects that drove the subsequent growth of the aneurysm have changed to a combination of low WSS and high oscillatory shear index (OSI) . Thus, even though the driving mechanisms observed during each period are distinct, they strongly agree with two main theories that currently explain aneurysm inception and growth.
... The interest in blood flow simulations and hemodynamic variables-as well as the precise morphology of the brain aneurysms-has been increasingly pursued over the last two decades. [3][4][5][6][7][8][9] Image-based CFD can analyze the effects of hemodynamic forces on the initiation, growth, and rupture of cerebral aneurysms. 7,[10][11][12][13][14] Nevertheless, it is necessary to translate research findings into clinical settings. ...
Objective:
To analyze the reliability and accuracy of morphological measurements of software employed to three-dimensionally reconstruct aneurysms and vessels (VMTKlab, version 1.6.1,) with computed tomography angiography (CTA) as the source of images. Agreement with measurements from three-dimensional digital subtraction angiography (3 D-DSA) was evaluated.
Methods:
We evaluated 40 patients presenting with aneurysmal subarachnoid hemorrhage (aSAH). We analyzed four main variables of the aneurysm morphology: absolute height (size), neck (maximum neck width), perpendicular height, and maximum width. The CTA images were uploaded to the software and then segmented to reconstruct the aneurysm. This new method was compared to the current gold standard-3D reconstruction of pretreatment cerebral angiography. We used intraclass correlation coefficient (ICC) and Bland-Altman plot analyses to evaluate the agreement between these methods.
Results:
The ICCs obtained for absolute height, neck, perpendicular height, and maximum width were 0.85, 0.57, 0.85, and 0.89, respectively. This implied good agreement except for the neck of the aneurysm (moderate agreement). Bland-Altman plots are presented for the four indexes. The average of the differences was not significant in terms of absolute height, perpendicular height, and maximum width indicating good agreement. However, it was significant for the neck of the aneurysm.
Conclusions:
We report good agreement between the values generated using VMTKlab and cerebral angiography for three of the four main variables. Discrepancies in neck diameter are not surprising and its underestimation with a traditional delineation from cerebral angiography has been reported before.
... An approach mimicking manual IA isolation is by positioning a cutting plane. In past clinical practice the cutting plane was chosen manually with the help of the 3D visualization software [17]. Jerman et al. [11] developed method that automatically positions the cutting plane (ACP). ...
Predicting rupture risk and deciding on optimal treatment plan for intracranial aneurysms (IAs) is possible by quantification of their size and shape. For this purpose the IA has to be isolated from 3D angiogram. State-of-the-art methods perform IA isolation by encoding neurosurgeon’s intuition about former non-dilated vessel anatomy through principled approaches like fitting a cutting plane to vasculature surface, using Gaussian curvature and vessel centerline distance constraints, by deformable contours or graph cuts guided by the curvature or restricted by Voronoi surface decomposition and similar. However, the large variability of IAs and their parent vasculature configurations often leads to failure or non-intuitive isolation. Manual corrections are thus required, but suffer from poor reproducibility. In this paper, we aim to increase the accuracy, robustness and reproducibility of IA isolation through two stage deep learning based segmentation of vascular surface. The surface was represented by local patches in form of point clouds, which were fed into first stage multilayer neural network (MNN) to obtain descriptors invariant to point ordering, rotation and scale. Binary classifier as second stage MNN was used to isolate surface belonging to the IA. Method validation was based on 57 3D-DSA, 28 CTA and 5 MRA images, where cross-modality-validation showed high segmentation sensitivity of 0.985, a substantial improvement over 0.830 obtained for the state-of-the-art method on the same datasets. Visual analysis of IA isolation and its high accuracy and reliability consistent across CTA, MRA and 3D-DSA scans confirmed the clinical applicability of proposed method.
... Similarly, the geometry of the aneurysm was characterized by computing variables that capture different aspects of the aneurysm geometry, 16 including: aneurysm sac size (Asize, SR, GAA), aneurysm neck size (Nsize), aneurysm elongation (AR, VOR, BF), and aneurysm shape distortion relative to a spherical shape (NSI, CR) and surface irregularity (UI). More details are presented in Supplementary Table I. ...
Background
Although it is generally believed that blebs represent weaker spots in the walls of intracranial aneurysms (IAs), it is largely unknown which aneurysm characteristics favor their development.
Objective
To investigate possible associations between aneurysm hemodynamic and geometric characteristics and the development of blebs in intracranial aneurysms.
Methods
A total of 270 IAs in 199 patients selected for surgical clipping were studied. Blebs were visually identified and interactively marked on patient-specific vascular models constructed from presurgical images. Blebs were then deleted from the vascular reconstruction to approximate the aneurysm before bleb formation. Computational fluid dynamics studies were performed in these models and in cases without blebs. Hemodynamic and geometric characteristics of aneurysms with and without blebs were compared.
Results
A total of 173 aneurysms had no blebs, while 97 aneurysms had a total of 122 blebs. Aneurysms favoring bleb formation had stronger (p<0.0001) and more concentrated inflow jets (p<0.0001), higher flow velocity (p=0.0061), more complex (p<0.0001) and unstable (p=0.0157) flow patterns, larger maximum wall shear stress (WSS; p<0.0001), more concentrated (p=0.0005) and oscillatory (p=0.0004) WSS distribution, and a more heterogeneous WSS field (p<0.0001), than aneurysms without blebs. They were also larger (p<0.0001), more elongated (p<0.0001), had wider necks (p=0.0002), and more distorted and irregular shapes (p<0.0001).
Conclusions
Strong and concentrated inflow jets, high-speed, complex, and unstable flow patterns, and concentrated, oscillatory, and heterogeneous WSS patterns favor the formation of blebs in IAs. Blebs are more likely to form in large, elongated, and irregularly shaped aneurysms. These adverse characteristics could be considered signs of aneurysm instability when evaluating aneurysms for conservative observation or treatment.
... When analyzing the IA rupture risk, many studies evaluated their morphology with respect to the rupture state [7,12,16]. Niemann et al. [17] investigated the potential of 22 morphological features for aneurysm rupture risk prediction. Although the best model had an accuracy of only 69%, several features showed high association toward rupture risk. ...
PurposeMedical case-based reasoning solves problems by applying experience gained from the outcome of previous treatments of the same kind. Particularly for complex treatment decisions, for example, incidentally found intracranial aneurysms (IAs), it can support the medical expert. IAs bear the risk of rupture and may lead to subarachnoidal hemorrhages. Treatment needs to be considered carefully, since it may entail unnecessary complications for IAs with low rupture risk. With a rupture risk prediction based on previous cases, the treatment decision can be supported.Methods
We present an interactive visual exploration tool for the case-based reasoning of IAs. In presence of a new aneurysm of interest, our application provides visual analytics techniques to identify the most similar cases with respect to morphology. The clinical expert can obtain the treatment, including the treatment outcome, for these cases and transfer it to the aneurysm of interest. Our application comprises a heatmap visualization, an adapted scatterplot matrix and fully or partially directed graphs with a circle- or force-directed layout to guide the interactive selection process. To fit the demands of clinical applications, we further integrated an interactive identification of outlier cases as well as an interactive attribute selection for the similarity calculation. A questionnaire evaluation with six trained physicians was used.ResultOur application allows for case-based reasoning of IAs based on a reference data set. Three classifiers summarize the rupture state of the most similar cases. Medical experts positively evaluated the application.Conclusion
Our case-based reasoning application combined with visual analytic techniques allows for representation of similar IAs to support the clinician. The graphical representation was rated very useful and provides visual information of the similarity of the k most similar cases.
... For the automated radiomic description, we derived quantitative morphometric data for each aneurysm dome. [22,28] Most notably, we computed aneurysm size (aSz), the non-sphericity index (NSI), and the normalized total Gaussian curvature (GLN). aSz is the maximum diameter of the aneurysm dome. ...
Background:
Morphological irregularity is linked to intracranial aneurysm wall instability and manifests in the lumen shape. Yet there is currently no consent on how to assess shape irregularity. The aims of this work are to quantify irregularity as perceived by clinicians, to break down irregularity into morphological attributes, and to relate these to clinically relevant factors such as rupture status, aneurysm location, and patient age or sex.
Methods:
Thirteen clinicians and 26 laypersons assessed 134 aneurysm lumen segmentations in terms of overall perceived irregularity and five different morphological attributes (presence/absence of a rough surface, blebs, lobules, asymmetry, complex geometry of the parent vasculature). We examined rater agreement and compared the ratings with clinical factors by means of regression analysis or binary classification.
Results:
Using rank-based aggregation, the irregularity ratings of clinicians and laypersons did not differ statistically. Perceived irregularity showed good agreement with curvature (coefficient of determination R2 = 0.68 ± 0.08) and was modeled very accurately using the five morphological rating attributes plus shape elongation (R2 = 0.95 ± 0.02). In agreement with previous studies, irregularity was associated with aneurysm rupture status (AUC = 0.81 ± 0.08); adding aneurysm location as an explanatory variable increased the AUC to 0.87 ± 0.09. Besides irregularity, perceived asymmetry, presence of blebs or lobules, aneurysm size, non-sphericity, and curvature were linked to rupture. No association was found between morphology and any of patient sex, age, and history of smoking or hypertension. Aneurysm size was linked to morphology.
Conclusions:
Irregular lumen shape carries significant information on the aneurysm's disease status. Irregularity constitutes a continuous parameter that shows a strong association with the rupture status. To improve the objectivity of morphological assessment, we suggest examining shape through six different morphological attributes, which can characterize irregularity accurately.
... An approach mimicking manual IA isolation is by positioning a cutting plane. In past clinical practice the cutting plane was chosen manually with the help of the 3D visualization software [17]. Jerman et al. [11] developed method that automatically positions the cutting plane (ACP). ...
Predicting rupture risk and deciding on optimal treatment plan for intracranial aneurysms (IAs) is possible by quantification of their size and shape. For this purpose the IA has to be isolated from 3D angiogram. State-of-the-art methods perform IA isolation by encoding neurosurgeon's intuition about former non-dilated vessel anatomy through principled approaches like fitting a cutting plane to vasculature surface, using Gaussian curvature and vessel centerline distance constraints, by deformable contours or graph cuts guided by the curvature or restricted by Voronoi surface decomposition and similar. However, the large variability of IAs and their parent vasculature configurations often leads to failure or non-intuitive isolation. Manual corrections are thus required, but suffer from poor reproducibility. In this paper, we aim to increase the accuracy, robustness and reproducibility of IA isolation through two stage deep learning based segmentation of vascular surface. The surface was represented by local patches in form of point clouds, which were fed into first stage multilayer neural network (MNN) to obtain descriptors invariant to point ordering, rotation and scale. Binary classifier as second stage MNN was used to isolate surface belonging to the IA. Method validation was based on 57 DSA, 28 CTA and 5 MRA images, where cross-validation showed high segmentation sensitivity of 0.985, a substantial improvement over 0.830 obtained for the state-of-the-art method on the same datasets. Visual analysis of IA isolation and its high accuracy and reliability consistent across CTA and DSA scans confirmed the clinical applicability of proposed method.
... These characteristics were calculated according to previous work. 25,26 The determined hemodynamic characteristics were related to aneurysm inflow (inflow concentration index), intrasaccular flow (maximum velocity, mean vorticity [VO], mean shear rate, and vortex core-line length [CLL]), flow instability (proper orthogonal decomposition entropy), and aneurysm wall shear stress (maximal, mean WSS, shear concentration index, low shear area [LSA], and mean and maximum oscillatory shear index [OSI]). These characteristics were calculated according to the methods described by Mut et al. 27 We also calculated the Population, Hypertension, Age, Size, Earlier Subarachnoid Hemorrhage, and Site (PHASES) 4 and ELAPSS 12 scores to estimate the risk of rupture and growth in the population. ...
Background and purpose:
Aneurysm growth has been related to higher rupture risk. A better understanding of the characteristics related to growth may assist in the treatment decisions of unruptured intracranial aneurysms. This study aimed to identify morphologic and hemodynamic characteristics associated with aneurysm growth and to determine whether these characteristics deviate further from those of stable aneurysms after growth.
Materials and methods:
We included 81 stable and 56 growing aneurysms. 3D vascular models were segmented on CTA, MRA, or 3D rotational angiographic images. With these models, we performed computational fluid dynamics simulations. Morphologic (size, size ratios, and shape) and hemodynamic (inflow, vorticity, shear stress, oscillatory shear index, flow instability) characteristics were automatically calculated. We compared the characteristics between aneurysms that were stable and those that had grown at baseline and final imaging. The significance level after Bonferroni correction was P < .002.
Results:
At baseline, no significant differences between aneurysms that were stable and those that had grown were detected (P > .002). Significant differences between aneurysms that were stable and those that had grown were seen at the final imaging for shear rate, aneurysm velocity, vorticity, and mean wall shear stress (P < .002). The latter was 11.5 (interquartile range, 5.4-18.8 dyne/cm2) compared with 17.5 (interquartile range, 11.2-29.9 dyne/cm2) in stable aneurysms (P = .001). Additionally, a trend toward lower area weighted average Gaussian curvature in aneurysms that had grown was observed with a median of 6.0 (interquartile range, 3.2-10.7 cm-2) compared with 10.4 (interquartile range, 5.0-21.2 cm-2) in stable aneurysms (P = .004).
Conclusions:
Morphologic and hemodynamic characteristics at baseline were not associated with aneurysm growth in our population. After growth, almost all indices increase toward values associated with higher rupture risks. Therefore, we stress the importance of longitudinal imaging and repeat risk assessment in unruptured aneurysms.
... In this context, CFD has been widely used to simulate the flow in virtual and patient-specific aneurysms geometries and vessel networks. The simulations have been used to improve the understanding of the flow dynamics and to correlate morphological and hemodynamic discriminants with aneurysm rupture (Ma et al., 2004;Dhar et al., 2008;Xiang et al., 2011;Cebral et al., 2011b,a). While several CFD studies were performed on aneurysm geometries of a single instant in time, few studies have considered the time evolution of intracranial aneurysms, but the ones that do only had available a single geometry of the aneurysm temporal evolution (Boussel et al., 2008;Sforza et al., 2011), possibly because most available exams used are retrospective. ...
Aneurysms are dilated and thin regions of arterial walls of the human vascular system. One of the most common type of aneurysm occurs on brain arteries in the circle of Willis. Their cause have been investigated for a long time, and researchers agree that hemodynamic effects play a key role in the initiation, growth, and rupture of brain aneurysms. With the development of scanning techniques of the cerebral vascular system, it has been possible to obtain the geometry of aneurysms, allowing Computational Fluid Dynamics (CFD) to be used for the solution of the blood flow. Since then, several researchers have been investigating the influence of biological and hemodynamic variables on aneurysms rupture, considering arteries and aneurysms as rigid walls. However, fewer studies analyze the initiation and growth of intracranial aneurysms and the importance of hemodynamics in this process, probably due to the lack of availability of consecutive exams of a single aneurysm case. In this work, by using two available exams at different instants of time of a single aneurysm case and also by virtually reconstructing the healthy vasculature, we used CFD results to assess whether hemodynamic parameters can be correlated with aneurysm initiation and growth.
... 78 Additional morphological parameters have been used with varying applicability. 79 In this era of technological advancements and the development of novel imaging software, more sophisticated combinations of geometric variables have been emerging. This could lead to the development of an imaging-based predictive test that uses the morphological characteristics of an individual aneurysm and computes the adjusted risk of rupture with an acceptable area under the curve. ...
Cerebral aneurysms (CAs) are characterized by a pathological wall structure with internal elastic lamina and media disruption, which leads to focal weakened pouches of the arterial wall. The prevalence of unruptured CAs has been estimated to be 2%-5% in the general population. During the past few decades, the pathophysiological mechanisms behind the formation, growth, and rupture of CAs have been the focus of numerous research studies. In the present review, we have summarized the inflammatory pathways, genetics, and risk factors for the formation, growth, and rupture of CAs. In addition, we have discussed the concepts of geometric indexes, flow patterns, and fluid dynamics that govern CA development.
Background
False lumen changes (FLCs) are the main reference for the prognosis judgment and treatment plan selection for type IIa superior mesenteric artery dissection (SMAD).
Methods
For this retrospective study, 55 patients with symptomatic type IIa SMAD were included. Computational fluid dynamics (CFD) analysis was used to explore the hemodynamic basis of FLCs. Correlation and multiple linear regression analyses were performed to identify clinical, morphological and hemodynamic factors associated with FLCs.
Results
The FLCs of patients with successful conservative treatment ( n = 29) are significantly higher than those with failed conservative treatment ( n = 26) (58.5 ± 21.1% vs 10.9 ± 17.4%, p < 0.0001). Positive correlations were seen between FLCs and the morphological parameters false lumen length (FLL)/dissection entrance length (DEL) and FLL. In terms of hemodynamic parameters, negative correlations were seen between FLCs and time-averaged wall shear stress (TAWSS), vorticity, and high areas of TAWSS and vorticity, whereas positive correlations were seen between FLCs and oscillatory shear index (OSI), relative residence time (RRT), and high areas of OSI and RRT. Multiple linear regression analysis identified symptom duration (odds ratio [OR], 0.93; 95% CI, 0.91–0.96; p < 0.0001), FLL/DEL (OR, 1.30; 95% CI, 1.01–1.67; p = 0.044), and high RRT area (OR, 2.03; 95% CI, 1.48–2.78; p < 0.0001) as predictors of FLCs.
Conclusion
The clinical predictor symptom duration, morphological factor FLL/DEL, and the hemodynamic factor high RRT area can serve as predictors of FLCs in patients with symptomatic type IIa SMAD.
An aneurysm is a disease condition, which is due to the pathological weakening of an arterial wall. These aneurysms are often found in various branch points and bifurcations of an artery in the cerebral circulation. Most aneurysms come to medical attention, either due to brain hemorrhages caused by rupture or found unruptured. To consider surgically invasive treatment modalities, clinicians need scientific methods such as, hemodynamic analysis to assess rupture risk. The arterial wall loses its structural integrity when wall shear stress (WSS) and other hemodynamic parameters exceed a certain threshold. In the present study, numerical simulations are carried out for unruptured middle cerebral artery (MCA) aneurysms. Three distinct representative sizes are chosen from a larger patient pool of 26 MCA aneurysms. Logically, these aneurysms represent three growth stages of any patient with similar anatomical structure. Simulations are performed to compare the three growth phases (with different aspect ratios) of an aneurysm and correlate their hemodynamic parameters. Simulations with patient specific boundary conditions reveal that, aneurysms with a higher aspect ratio (AR) correspond to an attendant decrease in both time-averaged wall shear stress (TAWSS) and spatial wall shear stress gradients (WSSG). Smaller MCAs were observed to have higher positive wall shear stress divergence (WSSD), exemplifying the tensile nature of arterial wall stretching. Present study identifies positive wall shear stress divergence (PWSSD) to be a potential biomarker for evaluating the growth of an aneurysm.
Background
The presence of blebs increases the rupture risk of intracranial aneurysms (IAs).
Objective
To evaluate whether cross-sectional bleb formation models can identify aneurysms with focalized enlargement in longitudinal series.
Methods
Hemodynamic, geometric, and anatomical variables derived from computational fluid dynamics models of 2265 IAs from a cross-sectional dataset were used to train machine learning (ML) models for bleb development. ML algorithms, including logistic regression, random forest, bagging method, support vector machine, and K-nearest neighbors, were validated using an independent cross-sectional dataset of 266 IAs. The models' ability to identify aneurysms with focalized enlargement was evaluated using a separate longitudinal dataset of 174 IAs. Model performance was quantified by the area under the receiving operating characteristic curve (AUC), the sensitivity and specificity, positive predictive value, negative predictive value, F1 score, balanced accuracy, and misclassification error.
Results
The final model, with three hemodynamic and four geometrical variables, along with aneurysm location and morphology, identified strong inflow jets, non-uniform wall shear stress with high peaks, larger sizes, and elongated shapes as indicators of a higher risk of focal growth over time. The logistic regression model demonstrated the best performance on the longitudinal series, achieving an AUC of 0.9, sensitivity of 85%, specificity of 75%, balanced accuracy of 80%, and a misclassification error of 21%.
Conclusions
Models trained with cross-sectional data can identify aneurysms prone to future focalized growth with good accuracy. These models could potentially be used as early indicators of future risk in clinical practice.
Large deformation of an elastic hollow ellipsoid may be used as the mechanism of a flowmeter. It is seen as being inspired by human biology, when passing through fluid internally. The investigation on this potential was carried out where simply the relationships among pressure drop across an ellipsoid, deformation, flowrate and fluid viscosity were obtained. The elastic hollow ellipsoid was made from Silicone, which has a long axis of 0.05 m, a short axis of 0.03 m, and a wall thickness of 3.5 × 10 ⁻⁴ ± 4.6 × 10 ⁻⁵ m. A monotonic relationship between fluid flowrate and a representative diameter of the ellipsoid was found. Sodium carboxymethyl cellulose (CMC) aqueous solutions were used as a more viscous media so the effect of viscosity was explored. Unlike the firm result on flowrate gauging, it was inconclusive on differentiating the effect of viscosity. When the inlet and the outlet of the fluid were switched over, the geometrical expansion of the ellipsoid was found to be sensitive to the small spatial variation of wall thickness (a non‐uniformity caused by manufacturing limitation). Nevertheless, this work has demonstrated an interesting flowmeter and further explorations on viscosity effect may be warranted.
Objectives
Assessing the risk associated with unruptured intracranial aneurysms (IAs) is essential in clinical decision making. Several geometric risk parameters have been proposed for this purpose. However, performance of these parameters has been inconsistent. This study evaluates the performance and robustness of geometric risk parameters on two datasets and compare it to the uncertainty inherent in assessing these parameters and quantifies interparameter correlations.
Methods
Two datasets containing 244 ruptured and unruptured IA geometries from 178 patients were retrospectively analysed. IAs were stratified by anatomical region, based on the PHASES score locations. 37 geometric risk parameters representing four groups (size, neck, non-dimensional, and curvature parameters) were assessed. Analysis included standardised absolute group differences (SADs) between ruptured and unruptured IAs, ratios of SAD to median relative uncertainty (MRU) associated with the parameters, and interparameter correlation.
Results
The ratio of SAD to MRU was lower for higher dimensional size parameters (ie, areas and volumes) than for one-dimensional size parameters. Non-dimensional size parameters performed comparatively well with regard to SAD and MRU. SAD was higher in the posterior anatomical region. Correlation of parameters was strongest within parameter (sub)groups and between size and curvature parameters, while anatomical region did not strongly affect correlation patterns.
Conclusion
Non-dimensional parameters and few parameters from other groups were comparatively robust, suggesting that they might generalise better to other datasets. The data on discriminative performance and interparameter correlations presented in this study may aid in developing and choosing robust geometric parameters for use in rupture risk models.
Cross-sectional imaging, such as computed tomography (CTA) scans, provide unparalleled visualization of aortic anatomy. However, despite the immense geometric and anatomic detail provided by CTA imaging, surgeons continue to interact with this data in a linear and dimensionally reduced feature space. Aortic pathologies such as aneurysms and dissections are clinically quantified using a single scalar: maximum aortic diameter. To date, not feature of aortic shape has reproducibly captured what surgeons often describe qualitatively when looking at CT scans or when in the operating room observing the physical anatomy. Shape along with size plays a central role in differentiating normal from diseased aortas. We defined a geometric feature space using tools of modern differential geometry that incorporate shape and size. We show that size can be parameterized by l, the radial aortic extent commonly taken as aortic diameter. Size invariant shape is quantified by performing a Gauss map of local regions on the aortic surface and calculating the variance of the total integrated curvature (δK) across each aorta. While we do not inherently study aortic stability as it relates to clinical rupture in this paper, aortas appearing at high δK are clinically classified by size and qualitative appearance as high risk. It is therefor interesting to conjecture that divergence in the (δK,l)-space is a sign of aortic topologic instability. Projection into (δK, l)-space provides two independent variables that show a natural division of the data as it transitions from size to shape dominated behavior, an indictor of aortic fragility.
Purpose:
Blebs are known risk factors for intracranial aneurysm (IA) rupture. We analyzed differences between IAs that ruptured with blebs and those that ruptured without developing blebs to identify distinguishing characteristics among them and suggest possible mechanistic implications.
Methods:
Using image-based models, 25 hemodynamic and geometric parameters were compared between ruptured IAs with and without blebs (n = 673), stratified by location. Hemodynamic and geometric differences between bifurcation and sidewall aneurysms and for aneurysms at five locations were also analyzed.
Results:
Ruptured aneurysms harboring blebs were exposed to higher flow conditions than aneurysms that ruptured without developing blebs, and this was consistent across locations. Bifurcation aneurysms were exposed to higher flow conditions than sidewall aneurysms. They had larger maximum wall shear stress (WSS), more concentrated WSS distribution, and larger numbers of critical points than sidewall aneurysms. Additionally, bifurcation aneurysms were larger, more elongated, and had more distorted shapes than sidewall aneurysms. Aneurysm morphology was associated with aneurysm location (p < 0.01). Flow conditions were different between aneurysm locations.
Conclusion:
Aneurysms at different locations are likely to develop into varying morphologies and thus be exposed to diverse flow conditions that may predispose them to follow distinct pathways towards rupture with or without bleb development. This could explain the diverse rupture rates and bleb presence in aneurysms at different locations.
Objectives:
This study aimed to derive a novel classification of blood flow pattern in AAA based on computational fluid dynamics, and determine the predicting value of flow pattern in abdominal aortic aneurysm (AAA) rupture.
Design:
Age, gender matched case-control study MATERIALS: Case patients were identified as those who underwent emergent endovascular or open repair due to ruptured or impending rupture AAA. Control patients were those age and gender matched AAA patients who were asymptomatic and confirmed unruptured from CTA images from the same period.
Methods:
Classification of blood flow pattern (Type I: non-helical main flow channel with multiple vortices; Type II: non-helical main flow channel with single vortices; Type III, helical main flow channel with helical vortices) and hemodynamic parameters [areas of low wall shear stress (A low WSS), aneurysm pressure drop (Δ pressure), etc.] were derived from computational fluid dynamic (CFD) analyses. Multivariate regression was used to determine independent risk factors of AAA rupture. The incremental discriminant and reclassification abilities for AAA rupture were compared among different models.
Results:
This study included 53 ruptured and 53 intact AAA patients. Ruptured AAA showed higher prevalence of type III flow pattern (60.38% vs. 15.09%, P<.001) compared to intact AAA. Type III flow pattern was associated with a significantly increased risk of aneurysm rupture (OR 10.22, 95%CI 3.43-30.49). Among all predicting models, combination of AAA diameter, hemodynamic parameters (A low WSS or Δ pressure) and flow pattern showed highest discriminant abilities in both overall population (concordance statistic [c-index] .862) and subgroup patients with AAAs <55mm (c-index .972). Compared to AAA diameter, adding flow pattern could significantly improve the reclassification abilities in both overall population (net reclassification index [NRI] .321; p<.001) and subgroup of AAAs < 55mm (NRI .732, P<.001).
Conclusion:
Type III flow pattern was associated with a significantly increased risk of AAA rupture. Integration of blood flow pattern may improve the identification of high-risk aneurysms in both overall population and AAAs smaller than 55mm.
Intracranial aneurysm projected posteriorly is associated with high risk of aneurysm rupture. In order to investigate the biomechanical mechanisms for the adverse event, three-dimension intracranial cerebral aneurysms were constructed based on clinical data, and we numerically compared effect of location, position, size, and shape of aneurysm on hemodynamic conditions including velocity, pressure, and wall shear stress (WSS). The numerical results showed that the aneurysm projected posteriorly even at small sizes led to abnormal hemodynamic environment, which was featured by a local high pressure and stress concentration near aneurysm neck area. Moreover, the one located at the proximal A1 segment and ellipsoidal aneurysm would further worse local hemodynamic environment, causing high local stresses. These findings indicated the potential mechanical mechanism for high rupture rate of the aneurysms projected posteriorly, underscoring importance of early and accurate diagnosis and promptly treatment for improved the clinical outcome, even if these aneurysms are of small sizes.
Background and purpose:
Untreated unruptured intracranial aneurysms are usually followed radiologically to detect aneurysm growth, which is associated with increased rupture risk. The ideal aneurysm size cutoff for defining growth remains unclear and also whether change in morphology should be part of the definition. We investigated the relationship between change in aneurysm size and 3D quantified morphologic changes during follow-up.
Materials and methods:
We performed 3D morphology measurements of unruptured intracranial aneurysms on baseline and follow-up TOF-MRAs. Morphology measurements included surface area, compactness, elongation, flatness, sphericity, shape index, and curvedness. We investigated the relation between morphologic change between baseline and follow-up scans and unruptured intracranial aneurysm growth, with 2D and 3D growth defined as a continuous variable (correlation statistics) and a categoric variable (t test statistics). Categoric growth was defined as ≥1-mm increase in 2D length or width. We assessed unruptured intracranial aneurysms that changed in morphology and the proportion of growing and nongrowing unruptured intracranial aneurysms with statistically significant morphologic change.
Results:
We included 113 patients with 127 unruptured intracranial aneurysms. Continuous growth of unruptured intracranial aneurysms was related to an increase in surface area and flatness and a decrease in the shape index and curvedness. In 15 growing unruptured intracranial aneurysms (12%), curvedness changed significantly compared with nongrowing unruptured intracranial aneurysms. Of the 112 nongrowing unruptured intracranial aneurysms, 10 (9%) changed significantly in morphology (flatness, shape index, and curvedness).
Conclusions:
Growing unruptured intracranial aneurysms show morphologic change. However, nearly 10% of nongrowing unruptured intracranial aneurysms change in morphology, suggesting that they could be unstable. Future studies should investigate the best growth definition including morphologic change and size to predict aneurysm rupture.
Background:
Bleb presence in intracranial aneurysms (IAs) is a known indication of instability and vulnerability.
Objective:
To develop and evaluate predictive models of bleb development in IAs based on hemodynamics, geometry, anatomical location, and patient population.
Methods:
Cross-sectional data (one time point) of 2395 IAs were used for training bleb formation models using machine learning (random forest, support vector machine, logistic regression, k-nearest neighbor, and bagging). Aneurysm hemodynamics and geometry were characterized using image-based computational fluid dynamics. A separate dataset with 266 aneurysms was used for model evaluation. Model performance was quantified by the area under the receiving operating characteristic curve (AUC), true positive rate (TPR), false positive rate (FPR), precision, and balanced accuracy.
Results:
The final model retained 18 variables, including hemodynamic, geometrical, location, multiplicity, and morphology parameters, and patient population. Generally, strong and concentrated inflow jets, high speed, complex and unstable flow patterns, and concentrated, oscillatory, and heterogeneous wall shear stress patterns together with larger, more elongated, and more distorted shapes were associated with bleb formation. The best performance on the validation set was achieved by the random forest model (AUC=0.82, TPR=91%, FPR=36%, misclassification error=27%).
Conclusions:
Based on the premise that aneurysm characteristics prior to bleb formation resemble those derived from vascular reconstructions with their blebs virtually removed, machine learning models can identify aneurysms prone to bleb development with good accuracy. Pending further validation with longitudinal data, these models may prove valuable for assessing the propensity of IAs to progress to vulnerable states and potentially rupturing.
When simulating blood flow in intracranial aneurysms, the Newtonian model seems to be ubiquitous. However, analyzing the results from the few studies on this subject, the doubt remains on whether it is necessary to use non-Newtonian models in wall shear stress (WSS) simulations of cerebral vascular flows. Another open question related to this topic is whether different rheology models would influence the flow parameters for ruptured and unruptured cases, especially because ruptured aneurysms normally have morphological features that could trigger non-Newtonian phenomena in the blood flow due to low shear rates. The objective of this study is to investigate such flows. By using Computational Fluid Dynamics (CFD) in an open-source framework, we simulated an equal number of ruptured and unruptured patient-specific aneurysms to assess the influence of the blood modeling on the main hemodynamic variables associated with aneurysm formation, growth, and rupture. Results for wall shear stress and oscillatory shear index and their metrics were obtained using Casson and Carreau-Yasuda non-Newtonian models and were compared with those obtained using the Newtonian model. We found that the wall shear stress at peak systole is overestimated by more than 50% by using the non-Newtonian models, but its metrics based on time and surface averaged values remain unaffected. On the other hand, the surface-averaged oscillatory shear index (OSI) is underestimated by more than 40% by the non-Newtonian models. In addition, all differences were consistent among all aneurysms cases irrespective of their rupture status.
Early image understanding seeks to derive analytic representations from image intensities. The authors present steps towards this goal by considering the inference of surfaces from three-dimensional images. Only smooth surfaces are considered and the focus is on the coupled problems of inferring the trace points (the points through which the surface passes) and estimating the associated differential structure given by the principal curvature and direction fields over the estimated smooth surfaces. Computation of these fields is based on determining an atlas of local charts or parameterizations at estimated surface points. Algorithm robustness and the stability of results are essential for analyzing real images; to this end, the authors present a functional minimization algorithm utilizing overlapping local charts to refine surface points and curvature estimates, and develop an implementation as an iterative constraint satisfaction procedure based on local surface smoothness properties. Examples of the recovery of local structure are presented for synthetic images degraded by noise and for clinical magnetic resonance images
To investigate the natural history of unruptured aneurysms and predictive risk factors determining subsequent rupture, the authors followed 142 patients with 181 unruptured aneurysms until death or subarachnoid hemorrhage intervened, or for at least 10 years after the unruptured aneurysm was diagnosed. Six patients had a symptomatic aneurysm, five had an incidentally discovered aneurysm, and 131 had multiple aneurysms, of which the ruptured lesion was clipped at the beginning of the follow-up study. The median follow-up time was 13.9 years (range 0.8 to 30.0 years). During 1944 patient-years of follow-up study there were 27 first episodes of hemorrhage from a previously unruptured aneurysm, giving an average annual rupture incidence of 1.4%. Fourteen of these bleeding episodes were fatal. The cumulative rate of bleeding was 10% at 10 years, 26% at 20 years, and 32% at 30 years after the diagnosis.
The only predictor for the rupture was the size of the aneurysm (p = 0.036). However, in patients with multiple aneurysms (the main subgroup) the only variable that tended to predict rupture was the age of the patient: risk of rupture was inversely associated with age (p = 0.080). The median diameter of the aneurysms was 4 mm at the beginning of the follow-up period, both in those with and those without a later hemorrhage. During the angiographic monitoring period, a ruptured aneurysm significantly (p < 0.001) increased in size in 17 patients with hemorrhage but aneurysms did not increase significantly in 14 patients without hemorrhage. In addition, a new aneurysm was found in six of 31 patients. The authors conclude that an unruptured aneurysm should be operated on, irrespective of its size, if it is technically possible and the patient's age and concurrent diseases are not contraindications to surgery.
Our goal was to characterize the geometry of simple-lobed cerebral aneurysms and to find the absolute size of these lesions from angiographic tracings.
Measurements of angiographic neck width (N), dome height (H), dome diameter (D), and semi-axis height (S) were obtained from tracings of 87 simple-lobed lesions located at the basilar bifurcation (BB), middle cerebral (MCA), anterior communicating (AcomA), posterior communicating (PcomA), superior cerebellar (SCA), and posterior cerebral (PCA) arteries. The following ratios were analyzed as subgroups according to location and as a collective sample: dome diameter/dome height (D/H), dome height/neck width (H/N), dome diameter/neck width (D/N), and dome height/semi-axis height (H/S). Using the parent artery as a reference, aneurysm dimensions were normalized to absolute in vivo size. Estimations were validated using angiographic markers.
For the entire sample, mean ratios were D/H = 1.11, D/N = 1.91, and H/N = 1.86. For the H/S ratio, the value was 1.98 for BB, MCA, and PcomA lesions and significantly smaller for the AcomA subgroup, at 1.52. The average sizes (in mm) for these dimensions were N = 3.4 for MCA, 3.0 for AcomA, 3.1 for PcomA, and 6.5 for BB; D = 6.1 for MCA, 5.9 for AcomA, 5.3 for PcomA, and 11.7 for BB; H = 5.6 for MCA, 5.0 for AcomA, 5.3 for PcomA, and 11.3 for BB. On average, BB aneurysms were twice as large as aneurysms at other locations. Good correlations were found between the scaled values for D and N, H and N, and H and D.
These results have been used to characterize the typical simple-lobed aneurysm geometry and to provide a framework for the development of a method of assessment of treatment choice and outcome on the basis of lesion geometry.
Most intracranial saccular aneurysms remain asymptomatic until rupture. Yet, some unruptured lesions present with various symptoms, often related to the compression of a nerve or other intracranial tissue. An obvious question, therefore, is whether or not symptomatic unruptured lesions necessarily have a greater rupture-potential than asymptomatic ones. In this paper, we show numerically that contact constraints can have a protective effect on certain lesions. Specifically, finite element analyses of stress fields in model axisymmetric lesions, with and without the presence of a rigid contacting obstacle at the fundus, reveal that with the exception of near point loads, the constraint decreases the stresses near the fundus. Given that it is well accepted that rupture occurs when wall stress exceeds wall strength, these findings suggest that the rupture-potential will be lower in at least one sub-class of constrained versus comparable unconstrained lesions. Because of the myriad of sizes, shapes, and compositions of saccular aneurysms, however, there is a need to examine this important issue further, hopefully based on an increased awareness for clinical data on lesion-tissue interactions.
ing with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept, ACM Inc., 1515 Broadway, New York, NY 10036 USA, fax +1 (212) 869-0481, or permissions@acm.org. c fl 1996 by the Association for Computing Machinery, Inc. ACM Transactions on Mathematical Software, Vol.22, No. 4 (Dec. 1996), pp. 469-483, http://www.acm.org/pubs/toc/Abstracts/toms/235821.html 2 Delta Geometric algorithms, languages, and systems General Terms: Algorithms, Reliability Additional Key Words and Phrases: convex hull, Delaunay triagulation, Voronoi diagram, halfspace intersection 1. INTRODUCTION The convex hull of a set of points is the smallest convex set that contains the points. The convex hull is a fundamental construction for mathematics and computational geometry. For example, Boardman uses the convex h...
OBJECTIVE : To review our experience and examine the size at which aneurysms ruptured in our patient population.
METHODS : Patient charts and angiograms for all patients admitted with a diagnosis of subarachnoid hemorrhage to the Thomas Jefferson/Wills Eye Hospital between April 1996 and March 2000 were reviewed.
RESULTS : Of the 362 cases reviewed, definite measurements of the ruptured aneurysm were obtained in 245. The data clearly showed that most ruptured aneurysms presenting to our institution were less than 10 mm in diameter. We found that, regardless of location on the circle of Willis, 85.6% of all aneurysms presenting with rupture were less than 10 mm. Review by location shows that aneurysms of the anterior communicating artery most often presented with rupture at sizes less than 10 mm (94.4%). A large number of ruptured posterior communicating artery aneurysms also presented at sizes less than 10 mm (87.5%). This trend continued for all aneurysm sites in our review. The incidence of subarachnoid hemorrhage in Western countries is estimated at 10 per 100,000 people per year. Recent reports have indicated that aneurysms less than 10 mm in size are unlikely to rupture.
CONCLUSION : We argue that the risk of small aneurysms rupturing is not insignificant, especially those of the anterior communicating artery. Our findings indicate that surgery on unruptured aneurysms should not be predicated on aneurysm size alone.
Given a set of points and normals on a surface and a triangulation associated with them a simple scheme for approximating the principal curvatures at these points is developed. The approximation is based on the fact that a surface can locally be represented as the graph of a bivariate function. Quadratic polynomials are used for this local approximation. The principal curvatures at a point on the graph of such a quadratic polynomial is used as the approximation of the principal curvatures at an original surface point.
In a recent study from the Mayo Clinic on the natural history of intact saccular intracranial aneurysms, none of the aneurysms smaller than 10 mm in diameter ruptured. It was concluded that these aneurysms carry a negligible risk for future hemorrhage and that surgery for their repair could not be recommended. These findings and recommendations have been the subject of much controversy. The authors report three patients with previously documented asymptomatic intact saccular intracranial aneurysms smaller than 5 mm in diameter that subsequently ruptured. In Case 1, a 70-year-old man bled from a 4-mm middle cerebral artery aneurysm that had been discovered incidentally 2 1/2 years previously during evaluation of cerebral ischemic symptoms. A 10-mm internal carotid artery aneurysm and a contralateral 4-mm middle cerebral artery aneurysm had not ruptured. Case 2 was that of a 66-year-old woman who bled from a 4-mm pericallosal aneurysm that had been present 9 1/2 years previously when she suffered subarachnoid hemorrhage (SAH) from a 7 x 9-mm posterior inferior cerebellar artery aneurysm. Although the pericallosal aneurysm had not enlarged in the intervening years, a daughter aneurysm had developed. The third patient was a 45-year-old woman who bled from a 4- to 5-mm posterior inferior cerebellar artery aneurysm that had measured approximately 2 mm on an angiogram obtained 4 years previously; at that time she had suffered SAH due to rupture of a 5 x 12-mm posterior communicating artery aneurysm. These cases show that small asymptomatic intact saccular intracranial aneurysms are not innocuous and that careful consideration must be given to their surgical repair and long-term follow-up study.
Computer-generated three-dimensional reconstruction of the intracranial vascular system obtained by contrast-enhanced computerized tomography (CT) has been used in the diagnosis of 20 patients with known or suspected intracranial cerebrovascular disease. This technique allows visualization of the intracranial vasculature without exposing patients to the risks associated with intra-arterial angiography. The color prints and videotape images generated have been used to diagnose the presence of intracranial aneurysms, arteriovenous malformations, and venous angiomas. They have also been used to rule out structural abnormalities in patients with suspected intracranial vascular pathology and to screen patients with a strong family history of intracranial aneurysm. In 11 patients who underwent both three-dimensional CT angiography and intra-arterial angiography, the diagnostic correlation was 100%. No complications from the procedures or from incorrect diagnosis have been encountered. Although this technique requires further development and clinical evaluation, the authors' early experience with three-dimensional CT angiography suggests that this may become a valuable tool in the diagnosis of patients with cerebrovascular disease.
Fifteen patients with high-risk intracranial saccular aneurysms were treated using electrolytically detachable coils introduced via an endovascular approach. The patients ranged in age from 21 to 69 years. The most frequent clinical presentation was subarachnoid hemorrhage (eight cases). Considerable thrombosis of the aneurysm (70% to 100%) was achieved in all 15 patients, and preservation of the parent artery was obtained in 14. Although temporary neurological deterioration due to the technique was recorded in one patient, no permanent neurological deficit was observed in this series and there were no deaths. It is believed that this new technology is a viable alternative in the management of patients with high-risk intracranial saccular aneurysms. It may also play an important role in the occlusion of aneurysms in the acute phase of subarachnoid hemorrhage.
Eleven experimental saccular aneurysms were created on the common carotid artery of swine. Between 3 and 15 days after creation of these aneurysms, they were thrombosed via an endovascular approach, using a very soft detachable platinum coil delivered through a microcatheter positioned within the aneurysm. This detachable platinum coil was soldered to a stainless steel delivery guidewire. Intra-aneurysmal thrombosis was then initiated by applying a low positive direct electric current to the delivery guidewire. Thrombosis occurred because of the attraction of negatively charged white blood cells, red blood cells, platelets, and fibrinogen to the positively charged platinum coil positioned within the aneurysm. The passage of electric current detached the platinum coil within the clotted aneurysm in 4 to 12 minutes. This detachment was elicited by electrolysis of the stainless steel wire nearest to the thrombus-covered platinum coil. Control angiograms obtained 2 to 6 months postembolization confirmed permanent aneurysm occlusion as well as patency of the parent artery in all cases. No angiographic manifestation of untoward distal embolization was noted. Due to the encouraging results of this research, this technique has been applied in selected clinical cases which are described in Part 2 of this study.
A case is presented of an incidentally discovered 6-mm aneurysm that was left untreated and subsequently produced a subarachnoid hemorrhage. The patient had no previous history of intracranial hemorrhage from any other source. A case of this type has not been previously documented in the literature. This experience points out the potential for catastrophe in small unruptured aneurysms found in patients without previous subarachnoid hemorrhage. The extremely low operative morbidity for repair of these types of lesions in otherwise healthy individuals would argue strongly for prophylactic surgery in properly selected patients.
Among the factors that determine the behavior of an intracranial aneurysm is the relationship between its volume and the size of the orifice. The investigative method described herein is the means being used to define that relationship in humans. It is a postmortem study that focuses on unruptured aneurysms. Central to the protocol was a synthetic rubber cast of the aneurysm's interior. The cast was made under normal arterial pressure so that unruptured aneurysms were reexpanded to lifelike size and shape. After the cast was removed intact from the specimen, the lumenal features recorded upon it were verified by comparison with the opened aneurysm. Working now only with the cast, the chamber was cut from the artery through its neck. The orifice area was determined by dividing it, mathematically, into many smaller, measurable forms. Chamber volume was ascertained by a fluid displacement technique. Both measurements were made with magnification and engineering instruments. Casts of ruptured or thrombosed aneurysms gave helpful morphological information, but were of limited value for measurement. The techniques are described, and examples of the initial results are presented.
A prerequisite to biomedical analyses of the right ventricular free wall (RVFW) is the characterization of its in vivo geometry and instantaneous wall thickness (WT). We present a method to reconstruct and mathematically model the in vivo RVFW surface geometry using ECG-gated magnetic resonance imaging (MRI). From digitized contours we reconstructed the endo- and epicardial surfaces of the entire heart, and approximated the RVFW surface geometry by local biquadric surface patches. An insurface coordinate system was developed, with respect to which the metric tensor, curvature tensor, major (k2), and minor (k1) principal curvatures were computed. The method was evaluated using MRI data from one dog, which showed that k2 was about 10 times k1, with k2 and k1 approximately perpendicular and parallel to the RV long axis, respectively. During systole, k1 and both principal curvature directions remained essentially unchanged, while k2 revealed only a 7% decrease (rho < 0.05) in the sinus region. These results suggest that while the RVFW undergoes small changes in surface geometry during systole, its overall curvature remained constant. The WT/mean radius of curvature ratio was less than 0.1 during systole throughout the RVFW, indicating it can be idealized as a thin shell.
Rupture of intracranial saccular aneurysms is the most common cause of spontaneous subarachnoid hemorrhage which, despite advances in neurosurgery, continues to result in significant morbidity and mortality. Currently, the decision to treat a diagnosed, unruptured aneurysm is based primarily on the maximum dimension of the lesion even though there is controversy over the 'critical size' (e.g. many 'large' lesions do not rupture whereas some 'small' ones do). There is a need, therefore, for improved predictors of the rupture-potential of these lesions. In this paper, we show that it is highly unlikely that saccular aneurysms expand or rupture due to a limit point instability, and suggest that a rupture-criterion should be based on local multiaxial states of stress or strain. Moreover, our results from nonlinear finite element analyses reveal important roles of lesion shape, material properties, and loading conditions, not just size, in governing the distributions of stress and strain within a sub-class of axisymmetric saccular aneurysms. For example, we find that maximum biaxial stresses and strains are most often at the fundus, where rupture tends to occur, and that maximum stresses increase markedly with increases in lesion size, the ratio of neck diameter to lesion height, and the distending transmural pressure.
The size of intracranial aneurysms is the only characteristic shown to correlate with their rupture. However, the critical size for rupture has varied considerably among previous accounts and remains a point of controversy. Our goal was to identify statistically significant clinical and morphological factors predictive of the occurrence of rupture and aneurysm size in patients referred for endovascular treatment. We retrospectively recorded the following factors from 74 patients who presented with ruptured (40) or unruptured (34) aneurysms: aneurysm morphology (uni/multilobulated), location (anterior/posterior), maximum diameter, diameter of the neck, and the patient's age and sex. We performed stepwise discriminant, and stepwise and logistic regression analysis to identify factors predicting rupture and the size of the aneurysm at rupture. The mean diameter of the ruptured aneurysms was 11.9+/-6.3 mm, range 3.0-33.0 mm, and that of the unruptured aneurysm 13.5+/-5.8 mm, range 5.0-30 mm. Stepwise discriminant analysis identified aneurysm morphology (P < 0.001) and location in the intracranial circulation (P < 0.001) as statistically significant factors in predicting rupture. Stepwise regression analysis revealed that aneurysm morphology and the size of the neck were predictors of aneurysm size at rupture.
The present study was undertaken to explore the relationship between the characteristic geometry of aneurysms prone to rupture and the blood flow patterns therein, using microsurgically produced aneurysms that simulated human middle cerebral artery aneurysms in scale and shape.
We measured in vivo velocity profiles using our 20-MHz, 80-channel, Doppler ultrasound velocimeter. We produced small (< or =5 mm, 5 cases) and large (6-13 mm, 12 cases) aneurysms with round, dumbbell, or multilobular shapes.
The fundamental patterns of intra-aneurysmal flow were composed of inflow, circulating flow, and outflow. The inflow, which entered the aneurysm only during the systolic phase, was strongly influenced by the position and size of the neck and the flow ratio into the distal branches. The outflow was usually nonpulsatile and of low velocity. The circulating flow depended on the aspect ratio (depth/neck width). A single recirculation zone was observed in aneurysms with aspect ratios of less than 1.6. This circulation did not seem to extend to areas with aspect ratios greater than this value; in aneurysms with aspect ratios of more than 1.6, a much slower circulation was observed near the dome. Furthermore, in the dome of dumbbell-shaped aneurysms and daughter aneurysms, no flow was detected. Intra-aneurysmal flow was determined by the aspect ratio, rather than the aneurysm size.
The localized, extremely low-flow condition that was observed in the dome of aneurysms with aspect ratios of more than 1.6 is a common flow characteristic in the geometry of ruptured aneurysms, so great care should be taken for patients with unruptured intracranial aneurysms with aspect ratios of more than 1.6.
Abdominal aortic aneurysm (AAA) is a local, progressive dilation of the distal aorta that risks rupture until treated. Using the law of Laplace, in vivo assessment of AAA surface geometry could identify regions of high wall tensions as well as provide critical dimensional and shape data for customized endoluminal stent grafts. In this study, six patients with AAA underwent spiral computed tomography imaging and the inner wall of each AAA was identified, digitized, and reconstructed. A biquadric surface patch technique was used to compute the local principal curvatures, which required no assumptions regarding axisymmetry or other shape characteristics of the AAA surface. The spatial distribution of AAA principal curvatures demonstrated substantial axial asymmetry, and included adjacent elliptical and hyperbolic regions. To determine how much the curvature spatial distributions were dependent on tortuosity versus bulging, the effects of AAA tortuosity were removed from the three-dimensional (3D) reconstructions by aligning the centroids of each digitized contour to the z axis. The spatial distribution of principal curvatures of the modified 3D reconstructions were found to be largely axisymmetric, suggesting that much of the surface geometric asymmetry is due to AAA bending. On average, AAA surface area increased by 56% and abdominal aortic length increased by 27% over those for the normal aorta. Our results indicate that AAA surface geometry is highly complex and cannot be simulated by simple axisymmetric models, and suggests an equally complex wall stress distribution. © 1999 Biomedical Engineering Society.
PAC99: 8719Rr, 8759Fm, 8757Gg
The goal of this study was to evaluate the utility of volume-rendered helical computerized tomography (CT) angiography in patients with intracranial aneurysms. The authors compared the abilities of CT angiography, digital subtraction (DS) angiography, and three-dimensional time-of-flight magnetic resonance (MR) angiography to characterize aneurysms.
Helical CT angiography was performed in 45 patients with suspected intracranial aneurysms by using volume-rendered multiplanar reformatted (MPR) images. Digital subtraction angiography was performed using biplane angiography. These studies and those performed using MR angiography were interpreted in a blinded manner. Two neurosurgeons and two interventional neuroradiologists independently graded the utility of CT angiography with respect to aneurysm characterization. Fifty-five aneurysms were detected. Of these, 48 were evaluated for treatment. Computerized tomography angiography was judged to be superior to both DS and MR angiography in the evaluation of the arterial branching pattern at the aneurysm neck (compared with DS angiography, p = 0.001, and with MR angiography, p = 0.007), aneurysm neck geometry (compared with DS angiography, p = 0.001, and with MR angiography, p = 0.001), arterial branch incorporation (compared with DS angiography, p = 0.021, and with MR angiography, p = 0.001), mural thrombus (compared with DS angiography, p < 0.001), and mural calcification (compared with DS angiography, p < 0.001, and with MR angiography, p < 0.001). For surgical cases, CT angiography had a significant impact on treatment path (p = 0.001), operative approach (p = 0.001), and preoperative clip selection (p < 0.001). For endovascular cases, CT angiography had an impact on treatment path (p < 0.02), DS angiography study time (p = 0.01), contrast agent usage (p = 0.01), and coil selection (p = 0.02). Computerized tomography angiography provided unique information about 39 (81%) of 48 aneurysms, especially when compared with DS angiography (p = 0.003). The sensitivity and specificity of CT angiography compared with DS angiography was 1. The sensitivity and specificity of CT and DS angiography studies compared with operative findings were 0.98 and 1, respectively.
Computerized tomography angiography is equal to DS angiography in the detection and superior to DS angiography and MR angiography in the characterization of brain aneurysms. Information contained in volume-rendered CT angiography images had a significant impact on case management.
The surface geometry of anatomic structures can have a direct impact upon their mechanical behavior in health and disease. Thus, mechanical analysis requires the accurate quantification of three-dimensional in vivo surface geometry. We present a fully generalized surface fitting method for surface geometric analysis that uses finite element based hermite biquintic polynomial interpolation functions. The method generates a contiguous surface of C2 continuity, allowing computation of the finite strain and curvature tensors over the entire surface with respect to a single in-surface coordinate system. The Sobolev norm, which restricts element length and curvature, was utilized to stabilize the interpolating polynomial at boundaries and in regions of sparse data. A major advantage of the current method is its ability to fully quantify surface deformation from an unstructured grid of data points using a single interpolation scheme. The method was validated by computing both the principal curvature distributions for phantoms of known curvatures and the principal stretch and principal change of curvature distributions for a synthetic spherical patch warping into an ellipsoidal shape. To demonstrate the applicability to biomedical problems, the method was applied to quantify surface curvatures of an abdominal aortic aneurysm and the principal strains and change of curvatures of a deforming bioprosthetic heart valve leaflet. The method proved accurate for the computation of surface curvatures, as well as for strains and curvature change for a surface undergoing large deformations.
The present retrospective study was undertaken to prove the reliability of the aspect ratio (aneurysm depth to aneurysm neck width) for predicting an aneurysmal rupture. The aspect ratio is considered a better geometric index than aneurysm size for determining the intra-aneurysmal blood flow.
We measured the aspect ratios and the sizes of aneurysms, as determined by examining angiographic films magnified 1.4x, in 129 patients with ruptured aneurysms and in 72 patients with 78 unruptured aneurysms. After categorizing the aneurysms into four groups on the basis of their locations (aneurysms of the anterior communicating artery, middle cerebral artery, internal carotid artery-posterior communicating artery [ICA-PComA], and other aneurysms), a statistical analysis of ruptured and unruptured aneurysms was performed.
The mean aneurysm size was found to be statistically significant in the aneurysms at the ICA-PComA and in locations excluding the anterior communicating artery, the middle cerebral artery, and the ICA-PComA. However, the mean aspect ratio was statistically significant at all four locations. In patients with ruptured aneurysms, no ruptured aneurysms with an aspect ratio of less than 1.0 were found. The distribution of the ruptured group versus the unruptured group with an aspect ratio of less than 1.6 at each location was 13 versus 79%, respectively, at the anterior communicating artery, 11 versus 58% at the middle cerebral artery, 11% versus 85% at the ICA-PComA, and 7 versus 81% at other locations.
The aspect ratio between ruptured aneurysms and unruptured aneurysms was found to be statistically significant, and almost 80% of the ruptured aneurysms showed an aspect ratio of more than 1.6, whereas almost 90% of the unruptured aneurysms showed an aspect ratio of less than 1.6. This study therefore suggests that the aspect ratio may be useful in predicting imminent aneurysmal ruptures.
Microstructure of trabecular bone has been examined with a particular emphasis on surface curvatures in two-phase (trabecular and intertrabecular space- i.e., marrow space) structures. Three trabecular bone samples, quantified as "plate-like," "rod-like," and a mixture of these two structural elements according to the structure model index (SMI), were subjected to analysis based on (differential) geometry. A correspondence between the SMI and the mean curvature was found. A method to measure surface curvatures is proposed. The gaussian curvatures averaged over the surfaces for the three analyzed bone structures were all found to be negative, demonstrating their surfaces to be, on average, hyperbolic. In addition, the Euler-Poincaré characteristics and the genus, both characterizing topological features of bone connectivity, were estimated from integral gaussian curvature (Gauss-Bonnet theorem). The three bone microstructures were found to be topologically analogous to spheres with one to three handles.
In this article, pathological, radiological, and clinical information regarding unruptured intracranial aneurysms is reviewed.
Treatment decisions require that surgeons and interventionists take into account information obtained in pathological, radiological, and clinical studies of unruptured aneurysms. The author has performed a detailed review of the literature and has compared, contrasted, and summarized his findings. Unruptured aneurysms may be classified as truly incidental, part of a multiple aneurysm constellation, or symptomatic by virtue of their mass, irritative, or embolic effects. Unruptured aneurysms with clinical pathological profiles resembling those of ruptured lesions should be considered for treatment at a smaller size than unruptured lesions with profiles typical of intact aneurysms, as has been determined at autopsy in patients who have died of other causes. The track record of the surgeon or interventionist and the institution in which treatment is to be performed should be considered while debating treatment options. In cases in which treatment is not performed immediately, ongoing periodic radiological assessment may be wise. Radiological investigations to detect unruptured aneurysms in asymptomatic patients should be restricted to high-prevalence groups such as adults with a strong family history of aneurysms or patients with autosomal dominant polycystic kidney disease. All patients with intact lesions should be strongly advised to discontinue cigarette smoking if they are addicted.
The current state of knowledge about unruptured aneurysms does not support the use of the largest diameter of the lesion as the sole criterion on which to base treatment decisions, although it is of undoubted importance.
Rupture of a previously docu-mented asymptomatic aneurysm enhances the argument for pro-phylactic surgical intervention Signal processing approach to fair surface design Clinical analysis of incidentally discovered unruptured aneurysms
- R A Solomon
- J W Correll
- G . Taubin
- K Sato
- H Onda
- A Oikawa
- M Kagawa
- K Takakura
- N Kobayashi
Solomon, R. A., and J. W. Correll. Rupture of a previously docu-mented asymptomatic aneurysm enhances the argument for pro-phylactic surgical intervention. Surg. Neurol. 30:321–323, 1988. 26 Taubin, G. Signal processing approach to fair surface design. Proc 22nd Ann ACM Conf Comp Graph Interactive Tech Los Angeles, CA, ACM, New York, 9–11 Aug. 1995. 27 Ujiie, H., K. Sato, H. Onda, A. Oikawa, M. Kagawa, K. Takakura, and N. Kobayashi. Clinical analysis of incidentally discovered unruptured aneurysms. Stroke 24:1850–1856, 1993. 28 Ujiie, H., H. Tachibana, O. Hiramatsu, A. L. Hazel, T. Matsumoto, Y. Ogasawara, H. Nakajima, T. Hori, K. Takakura, and F. Kajiya. Effects of size and shape (aspect ratio) on the hemodynamics of saccular aneurysms: A possible index for sur-gical treatment of intracranial aneurysms. Neurosurgery 45:119–