Computational geometry for patient-specific reconstruction and meshing of blood vessels from MR and CT angiography

A novel patient-specific model to compute coronary fractional flow reserve

The fractional flow reserve (FFR) is a widely used clinical index to evaluate the functional severity of coronary stenosis. A computer simulation method based on patients' computed tomography (CT) data is a plausible non-invasive approach for computing the FFR. This method can provide a detailed solution for the stenosed coronary hemodynamics by coupling computational fluid dynamics (CFD) with the lumped parameter model (LPM) of the cardiovascular system. In this work, we have implemented a simple computational method to compute the FFR. As this method uses only coronary arteries for the CFD model and includes only the LPM of the coronary vascular system, it provides simpler boundary conditions for the coronary geometry and is computationally more efficient than existing approaches. To test the efficacy of this method, we simulated a three-dimensional straight vessel using CFD coupled with the LPM. The computed results were compared with those of the LPM. To validate this method in terms of clinically realistic geometry, a patient-specific model of stenosed coronary arteries was constructed from CT images, and the computed FFR was compared with clinically measured results. We evaluated the effect of a model aorta on the computed FFR and compared this with a model without the aorta. Computationally, the model without the aorta was more efficient than that with the aorta, reducing the CPU time required for computing a cardiac cycle to 43.4%.

Considerations for numerical modeling of the pulmonary circulation--a review with a focus on pulmonary hypertension

Both in academic research and in clinical settings, virtual simulation of the cardiovascular system can be used to rapidly assess complex multivariable interactions between blood vessels, blood flow, and the heart. Moreover, metrics that can only be predicted with computational simulations (e.g., mechanical wall stress, oscillatory shear index, etc.) can be used to assess disease progression, for presurgical planning, and for interventional outcomes. Because the pulmonary vasculature is susceptible to a wide range of pathologies that directly impact and are affected by the hemodynamics (e.g., pulmonary hypertension), the ability to develop numerical models of pulmonary blood flow can be invaluable to the clinical scientist. Pulmonary hypertension is a devastating disease that can directly benefit from computational hemodynamics when used for diagnosis and basic research. In the present work, we provide a clinical overview of pulmonary hypertension with a focus on the hemodynamics, current treatments, and their limitations. Even with a rich history in computational modeling of the human circulation, hemodynamics in the pulmonary vasculature remains largely unexplored. Thus, we review the tasks involved in developing a computational model of pulmonary blood flow, namely vasculature reconstruction, meshing, and boundary conditions. We also address how inconsistencies between models can result in drastically different flow solutions and suggest avenues for future research opportunities. In its current state, the interpretation of this modeling technology can be subjective in a research environment and impractical for clinical practice. Therefore, considerations must be taken into account to make modeling reliable and reproducible in a laboratory setting and amenable to the vascular clinic. Finally, we discuss relevant existing models and how they have been used to gain insight into cardiopulmonary physiology and pathology.

Cardiovascular and lung mesh generation based on centerlines

We present a fully automatic procedure for the mesh generation of tubular geometries such as blood vessels or airways. The procedure is implemented in the open-source Gmsh software and relies on a centerline description of the input geometry. The presented method can generate different type of meshes: isotropic tetrahedral meshes, anisotropic tetrahedral meshes, and mixed hexahedral/tetrahedral meshes. Additionally, a multiple layered arterial wall can be generated with a variable thickness. All the generated meshes rely on a mesh size field and a mesh metric that is based on centerline descriptions, namely the distance to the centerlines and a local reference system based on the tangent and the normal directions to the centerlines. Different examples show that the proposed method is very efficient and robust and leads to high quality computational meshes.

Lagrangian analysis of hemodynamics data from FSI simulation

We present the computation of lagrangian-based flow characterization measures for time-dependent, deformable-wall, finite-element blood flow simulations. Applicability of the algorithm is demonstrated in a fluid-structure interaction simulation of blood flow through a total cavopulmonary connection (Fontan procedure), and results are compared with a rigid-vessel simulation. Specifically, we report on several important lagrangian-based measures including flow distributions, finite-time Lyapunov exponent fields, particle residence time, and exposure time calculations. Overall, strong similarity in lagrangian measures of the flow between deformable and rigid-vessel models was observed.

Vessel bifurcation localization based on intraoperative three-dimensional ultrasound and catheter path for image-guided catheter intervention of oral cancers

We present a method to localize intraoperative target vessel bifurcations under bones for ultrasound (US) image-guided catheter interventions. A catheter path is recorded to acquire skeletons for the target vessel bifurcations that cannot be imaged by intraoperative US. The catheter path is combined with the centerlines of the three-dimensional (3D) US image to construct a preliminary skeleton. Based on the preliminary skeleton, the orientations of target vessels are determined by registration with the preoperative image and the bifurcations were localized by computing the vessel length. An accurate intraoperative vessel skeleton is obtained for correcting the preoperative image to compensate for vessel deformation. A reality check of the proposed method was performed in a phantom experiment. Reasonable results were obtained. The in vivo experiment verified the clinical workflow of the proposed method in an in vivo environment. The accuracy of the centerline length of the vessel for localizing the target artery bifurcation was 2.4mm. These results suggest that the proposed method can allow the catheter tip to stop at the target artery bifurcations and enter into the target arteries. This method can be applied for virtual reality-enhanced image-guided catheter intervention of oral cancers.

A shell-based inverse approach of stress analysis in intracranial aneurysms

Predicting pressure induced wall stress in intracranial aneurysms continues to be of interest for aneurysm safety assessment. In quasi-static analysis, there are two distinct approaches that one may take, the forward approach and the inverse approach. The inverse approach starts from a deformed configuration and thus is naturally suited to image-based, patient-specific analysis. Early studies by the authors' team suggested that the inverse approach, in the context of estimating the wall stress in cerebral aneurysms, depends weakly on the material description. In this article, we present a population study to further demonstrate the inverse method, in particular, the remarkable feature of insensitivity to material properties. Twenty-six aneurysm models derived from patient-specific images were employed in the study. Wall stresses were predicted in both the inverse and forward approaches using three material models. Results showed that, while forward computation yielded up to ~100% stress difference between some materials, the inverse solutions stayed close across materials. The inverse method, in addition to being methodologically accurate in dealing with pre-deformations, has the added convenience of insensitivity to uncertainties in wall tissue properties. New insight into the stress-geometry relation was also discussed.

Sensitivity of Quantified Intracranial Aneurysm Geometry to Imaging Modality

The objective of this study is to assess the sensitivity of intracranial aneurysm geometry to the modality of imaging. Four imaging modalities-3D rotational angiography (3DRA), computed tomography angiography (CTA), contrast enhanced magnetic resonance angiography (CE-MRA), and time-of-flight magnetic resonance angiography (TOF-MRA)-were assessed using data from a flow phantom and human subjects. A silicone flow phantom of the head and neck arteries with a 10 mm ACOM aneurysm was imaged using all four modalities under steady flow conditions. Three human subjects with mid to large sized intracranial aneurysm who had a 3DRA scan and one of CTA, CE-MRA, or TOF-MRA performed within a day were also studied. The aneurysm and contiguous vasculature were segmented for all available scans and geometric measures of their size (5 indices) and shape (6 indices) were estimated and compared. Visually, the size and shape of segmented 3D models of the aneurysms were similar across scan modalities for both the human subjects and the flow phantom. Consequently, the computed indices were consistent across modalities in the key morphometric indices. In conclusion, quantified indices of 3D geometry of the mid to large sized intracranial aneurysms investigated in this small study population are not sensitive to scanning modality.

On the role of modeling choices in estimation of cerebral aneurysm wall tension

OBJECTIVE

To assess various approaches to estimating pressure-induced wall tension in intracranial aneurysms (IA) and their effect on the stratification of subjects in a study population.

METHODS

Three-dimensional models of 26 IAs (9 ruptured and 17 unruptured) were segmented from Computed Tomography Angiography (CTA) images. Wall tension distributions in these patient-specific geometric models were estimated based on various approaches such as differences in morphological detail utilized or modeling choices made. For all subjects in the study population, the peak wall tension was estimated using all investigated approaches and were compared to a reference approach-nonlinear finite element (FE) analysis using the Fung anisotropic model with regionally varying material fiber directions. Comparisons between approaches were focused toward assessing the similarity in stratification of IAs within the population based on peak wall tension.

RESULTS

The stratification of IAs tension deviated to some extent from the reference approach as less geometric detail was incorporated. Interestingly, the size of the cerebral aneurysm as captured by a single size measure was the predominant determinant of peak wall tension-based stratification. Within FE approaches, simplifications to isotropy, material linearity and geometric linearity caused a gradual deviation from the reference estimates, but it was minimal and resulted in little to no impact on stratifications of IAs.

CONCLUSION

Differences in modeling choices made without patient-specificity in parameters of such models had little impact on tension-based IA stratification in this population. Increasing morphological detail did impact the estimated peak wall tension, but size was the predominant determinant.

Effect of aortic taper on patterns of blood flow and wall shear stress in rabbits: association with age

OBJECTIVE

The distribution of atherosclerotic lesions changes with age in human and rabbit aortas. We investigated if this can be explained by changes in patterns of blood flow and wall shear stress.

METHODS

The luminal geometry of thoracic aortas from immature and mature rabbits was obtained by micro-CT of vascular corrosion casts. Blood flow was computed and average maps of wall shear stress were derived.

RESULTS

The branch anatomy of the aortic arch varied widely between animals. Wall shear was increased downstream and to a lesser extent upstream of intercostal branch ostia, and a stripe of high shear was located on the dorsal descending aortic wall. The stripe was associated with two vortices generated by aortic arch curvature; their persistence into the descending aorta depended on aortic taper and was more pronounced in mature geometries. These results were not sensitive to the modelling assumptions.

CONCLUSIONS

Blood flow characteristics in the rabbit aorta were affected by the degree of taper, which tends to increase with age in the aortic arch and strengthens secondary flows into the descending aorta. Previously-observed lesion distributions correlated better with high than low shear, and age-related changes around branch ostia were not explained by the flow patterns.

Three-dimensional image quantification as a new morphometry method for tissue engineering

Morphological analysis is an essential step in verifying the success of a tissue engineering strategy where the presence of a desired cellular phenotype must be determined. While morphometry has transitioned from observational grading to computational quantification, established quantitative methods eliminate information by relying on two-dimensional (2D) analysis to describe three-dimensional (3D) niches. In this study, we demonstrate the validity and utility of 3D morphological quantification using two common angiogenesis assays in our fibrin-based in vitro model: (1) the microcarrier bead assay with human mesenchymal stem cells and (2) the rat aortic ring outgrowth assay. The quantification method is based on collecting and segmenting fluorescent confocal z-stacks into 3D models with 3D Slicer, an open-source magnetic resonance imaging/computed tomography analysis program. Data from 3D models are then processed into biologically relevant metrics in MATLAB for statistical analysis. Metrics include descriptive parameters such as vascular network length, volume, number of network segments, and degree of network branching. Our results indicate that 2D measures are significantly different than their 3D counterparts unless the vascular network exhibits anisotropic growth along the plane of imaging. Additionally, the statistical outcomes of 3D morphological quantification agreed with our initial qualitative observations among different test groups. This novel quantification approach generates more spatially accurate and objective measures, representing an important step toward improving the reliability of morphological comparisons.

Role of aortic stent graft oversizing and barb characteristics on folding

OBJECTIVE

To evaluate folding in infrarenal stent grafts in relation to oversizing, barb angle, and barb length using computed tomography images of stent grafts deployed in explanted bovine aortas.

METHODS

Computed tomography data from an in vitro investigation on the effect of oversizing of 4% to 45% (n = 19), barb length of 2 to 7 mm (n = 11), and barb angle of 10° to 90° (n = 7) on device fixation were examined for instances of folding. Folding was classified as circumferential or longitudinal and quantified on an ordinal scale based on codified criteria. Cumulative fold ranking from 0 (no fold) to 6 (two severe folds) for each deployment was used as the measure of folding observed.

RESULTS

Of the 37 cases, cumulative mean ± standard deviation fold ranking for stent grafts oversized >30% (n = 5) was significantly greater than the rest (3.4 ± 1.7 vs 0.5 ± 1.2, respectively; Mann-Whitney U test; P < .005). When barb length was varied from 2 to 7 mm (oversizing held at 10%-20%), folding was noted in one of 11 cases. Similarly, when barb angle was varied from 0° (vertical) to 90° (horizontal), folding was not noted in any of the seven cases. The pullout force was not significantly different between stent grafts with and without folding (5.4 ± 1.95 vs 5.12 ± 1.89 N, respectively; P > .5). At least one instance of folding was noted in the seven of seven (100%) stent grafts with oversizing >23.5% and in only five of 30 (14%) stent grafts with oversizing <23.5%.

CONCLUSIONS

Stent graft folding was prevalent when oversized >30%. Large variations in barb length and angle did not aggravate folding risk when oversized within the recommended range of 10% to 20%.

Virtual Interventions for Image-based Blood Flow Computation

Image-based blood flow computation provides great promise for evaluation of vascular devices and assessment of surgical procedures. However, many previous studies employ idealized arterial and device models or only patient-specific models from the image data after device deployment, since the tools for model construction are unavailable or limited and tedious to use. Moreover, in contrast to retrospective studies from existing data, there is a pressing need for prospective analysis with the goal of surgical planning. Therefore, it is necessary to construct models with deployed devices in a fast, virtual and interactive fashion. The goal of this paper is to develop new geometric methods to deploy stents or stent grafts virtually to patient-specific geometric models constructed from a 3D segmentation of medical images. A triangular surface representing the vessel lumen boundary is extracted from the segmentation. The diseased portion is either clipped and replaced by the surface of a deployed device or rerouted in the case of a bypass graft. For diseased arteries close to bifurcations, bifurcated device models are generated. A method to map a 2D strut pattern on the surface of a device is also presented. We demonstrate three applications of our methods in personalized surgical planning for aortic aneurysms, aortic coarctation, and coronary artery stenosis using blood flow computation. Our approach enables prospective model construction and may help to expand the throughput required by routine clinical uses in the future.

Anatomical labeling of the anterior circulation of the Circle of Willis using maximum a posteriori classification

Automated anatomical labeling of the arteries forming the Circle of Willis is of great interest as facilitates inter-subject comparison required to discover geometric risk factors for the development of vascular pathologies. In this paper, we present a method for anatomical labeling of vessels forming anterior part of the Circle of Willis by detecting the five main vessel bifurcations. The method is first trained on a set of pre-labeled examples, where it learns local bifurcation features as well as global variation in the anatomy of the extracted vascular trees. Then the labeling of the target vascular tree is formulated as maximum a posteriori solution where the classifications of individual bifurcations are regularized by the prior learned knowledge of the tree they span. The method was evaluated by cross-validation on 30 subjects, which showed the vascular trees were correctly anatomically labeled in 90% of cases. The proposed method can naturally handle anatomical variations and is shown to be suitable for labeling arterial segments of Circle of Willis.

Simulation of blood flow in deformable vessels using subject-specific geometry and spatially varying wall properties

Simulation of blood flow using image-based models and computational fluid dynamics has found widespread application to quantifying hemodynamic factors relevant to the initiation and progression of cardiovascular diseases and for planning interventions. Methods for creating subject-specific geometric models from medical imaging data have improved substantially in the last decade but for many problems, still require significant user interaction. In addition, while fluid-structure interaction methods are being employed to model blood flow and vessel wall dynamics, tissue properties are often assumed to be uniform. In this paper, we propose a novel workflow for simulating blood flow using subject-specific geometry and spatially varying wall properties. The geometric model construction is based on 3D segmentation and geometric processing. Variable wall properties are assigned to the model based on combining centerline-based and surface-based methods. We finally demonstrate these new methods using an idealized cylindrical model and two subject-specific vascular models with thoracic and cerebral aneurysms.

3D quantitative evaluation of atherosclerotic plaque based on rotational angiography

BACKGROUND AND PURPOSE

Atherosclerosis is a systemic disease that has been shown to cause various cardiovascular diseases and stroke. However, technologies to evaluate the volume of atherosclerotic plaque are limited. We present a method for determination of 3D plaque volume based on RA.

MATERIALS AND METHODS

3DRA images obtained from patients were used to evaluate the plaque. Six patients who were diagnosed with atherosclerotic lesions were included. The PR model developed for 3DRA was applied to analyze the geometry of the vessel and calculate the plaque volume. To validate the present method, we tested computer-generated phantoms with different degrees of stenosis.

RESULTS

Application of PR to clinical cases allowed the estimation of plaque morphology and quantification of plaque volume. Technique validation showed that on average, PR can rebuild 92% of the plaque and provide satisfactory determination of plaque volume.

CONCLUSIONS

A new approach to obtain plaque volume based on 3DRA is presented. The initial tests in 6 clinical cases and validation with different phantoms showed that this method is feasible. Further validation in a larger clinical series is required to assess the ultimate value of the present technique.

Scan-Rescan reproducibility of carotid bifurcation geometry from routine contrast-enhanced MR angiography

PURPOSE

To demonstrate the feasibility of rapid and reliable geometric characterization of normal carotid bifurcation geometry from routine 3D contrast-enhanced magnetic resonance (MR) angiograms.

MATERIALS AND METHODS

Repeat scans of 61 participants, acquired as part of the Atherosclerosis Risk in Communities (ARIC) Carotid MRI substudy, were digitally segmented using automated 3D level set methods, relying on an operator only to select the branch endpoints and thresholds for the 3D lumen surface initialization. Geometric factors characterizing the 3D lumen geometry were then extracted automatically.

RESULTS

Of 122 scans, 117 could be segmented within 5 minutes each, with 40% being of sufficiently high quality to require less than 2 minutes each. Irrespective of scan quality, geometric factors were found to be highly reproducible, with intraclass correlation coefficients (ICCs) typically above 0.9. The reconstructed lumen surfaces were reproducible to <0.3 mm on average, comparable to previous MRI-based reproducibility studies. Owing to the automated nature of the analysis, operator reliability was near-perfect (ICC >0.99), with lumen surface differences <0.1 mm.

CONCLUSION

The 3D geometry of the carotid bifurcation can be characterized rapidly and with a high degree of consistency, even for suboptimal image qualities. This bodes well for large-scale retrospective or prospective studies aimed at teasing out the influence of local vs. systemic risk factors for early atherosclerosis.

Virtual stent grafting in personalized surgical planning for treatment of aortic aneurysms using image-based computational fluid dynamics

Image-based computational fluid dynamics provides great promise for evaluation of vascular devices and assessment of surgical procedures. However, many previous studies employ idealized arterial and device models or patient-specific models with a limited number of cases, since the model construction process is tedious and time-consuming. Moreover, in contrast to retrospective studies from existing image data, there is a pressing need of prospective analysis with the goal of surgical planning. Therefore, it is necessary to construct models with implanted devices in a fast, virtual and interactive fashion. The goal of this paper is to develop new geometric methods to deploy stent grafts virtually to patient-specific models constructed from direct 3D segmentation of medical images. A triangular surface representing vessel lumen boundary is extracted from the segmentation. The diseased portion is then clipped and replaced by the surface of a virtual stent graft following the centerline obtained from the clipped portion. A Y-shape stent graft is employed in case of bifurcated arteries. A method to map a 2D strut pattern on the stent graft is also presented. We demonstrate the application of our methods to quantify wall shear stresses and forces acting on stent grafts in personalized surgical planning for endovascular treatment of thoracic and abdominal aortic aneurysms. Our approach enables prospective model construction and may help to increase its throughput required by routine clinical uses in the future.

Automatic identification of internal carotid artery from 3DRA images

Geometric characteristics and arrangement of the cerebral vessels are assumed to be related to the development of vascular diseases. Identifying anatomical segments and bifurcations of the cerebral vasculature allows the comparison of these characteristics across and within subjects. In this paper, we focus on the automatic identification of internal carotid artery (ICA) from 3D rotational angiographic images. The steps of the proposed method are the following: Arterial vascular tree is first segmented and centerlines are computed. From a set of centerlines, vascular tree topology is constructed and its bifurcations geometrically characterized. Finally, ICA terminal bifurcation is detected, which enables ICA identification. To detect ICA terminal bifurcation, a support vector machine classifier is trained. We processed 82 images to obtain 274 feature vectors of bifurcations around the ICA. 10×5-fold cross-validation showed an average accuracy of 99.6%, with 99.5% specificity and 100% sensitivity. The two most discriminating bifurcation features were: radius ratio between the smaller branch and its parent vessel, and the long-axis component of the smaller branch vector.

Uncluttered single-image visualization of the abdominal aortic vessel tree: method and evaluation

PURPOSE

The authors develop a method to visualize the abdominal aorta and its branches, obtained by CT or MR angiography, in a single 2D stylistic image without overlap among branches.

METHODS

The abdominal aortic vasculature is modeled as an articulated object whose underlying topology is a rooted tree. The inputs to the algorithm are the 3D centerlines of the abdominal aorta, its branches, and their associated diameter information. The visualization problem is formulated as an optimization problem that finds a spatial configuration of the bounding boxes of the centerlines most similar to the projection of the input into a given viewing direction (e.g., anteroposterior), while not introducing intersections among the boxes. The optimization algorithm minimizes a score function regarding the overlap of the bounding boxes and the deviation from the input. The output of the algorithm is used to produce a stylistic visualization, made of the 2D centerlines modulated by the associated diameter information, on a plane. The authors performed a preliminary evaluation by asking three radiologists to label 366 arterial branches from the 30 visualizations of five cases produced by the method. Each of the five patients was presented in six different variant images, selected from ten variants with the three lowest and three highest scores. For each label, they assigned confidence and distortion ratings (low/medium/high). They studied the association between the quantitative metrics measured from the visualization and the subjective ratings by the radiologists.

RESULTS

All resulting visualizations were free from branch overlaps. Labeling accuracies of the three readers were 93.4%, 94.5%, and 95.4%, respectively. For the total of 1098 samples, the distortion ratings were low: 77.39%, medium: 10.48%, and high: 12.12%. The confidence ratings were low: 5.56%, medium: 16.50%, and high: 77.94%. The association study shows that the proposed quantitative metrics can predict a reader's subjective ratings and suggests that the visualization with the lowest score should be selected for readers.

CONCLUSIONS

The method for eliminating misleading false intersections in 2D projections of the abdominal aortic tree conserves the overall shape and does not diminish accurate identifiability of the branches.

Region-based geometric modelling of human airways and arterial vessels

Anatomically precise geometric models of human airways and arterial vessels play a critical role in the analysis of air and blood flows in human bodies. The established geometric modelling methods become invalid when the model consists of bronchioles or small vessels. This paper presents a new method for reconstructing the entire airway tree and carotid vessels from point clouds obtained from CT or MR images. A novel layer-by-layer searching algorithm has been developed to recognize branches of the airway tree and arterial vessels from the point clouds. Instead of applying uniform accuracy to all branches regardless of the number of available points, the surface patches on each branch are constructed adaptively based on the number of available elemental points, which leads to the elimination of distortions occurring at small bronchi and vessels.

A framework for geometric analysis of vascular structures: application to cerebral aneurysms

There is well-documented evidence that vascular geometry has a major impact in blood flow dynamics and consequently in the development of vascular diseases, like atherosclerosis and cerebral aneurysmal disease. The study of vascular geometry and the identification of geometric features associated with a specific pathological condition can therefore shed light into the mechanisms involved in the pathogenesis and progression of the disease. Although the development of medical imaging technologies is providing increasing amounts of data on the three-dimensional morphology of the in vivo vasculature, robust and objective tools for quantitative analysis of vascular geometry are still lacking. In this paper, we present a framework for the geometric analysis of vascular structures, in particular for the quantification of the geometric relationships between the elements of a vascular network based on the definition of centerlines. The framework is founded upon solid computational geometry criteria, which confer robustness of the analysis with respect to the high variability of in vivo vascular geometry. The techniques presented are readily available as part of the VMTK, an open source framework for image segmentation, geometric characterization, mesh generation and computational hemodynamics specifically developed for the analysis of vascular structures. As part of the Aneurisk project, we present the application of the present framework to the characterization of the geometric relationships between cerebral aneurysms and their parent vasculature.

Quantification of carotid vessel wall and plaque thickness change using 3D ultrasound images

Quantitative measurements of carotid plaque burden progression or regression are important in monitoring patients and in evaluation of new treatment options. 3D ultrasound (US) has been used to monitor the progression or regression of carotid artery plaques. This paper reports on the development and application of a method used to analyze changes in carotid plaque morphology from 3D US. The technique used is evaluated using manual segmentations of the arterial wall and lumen from 3D US images acquired in two imaging sessions. To reduce the effect of segmentation variability, segmentation was performed five times each for the wall and lumen. The mean wall and lumen surfaces, computed from this set of five segmentations, were matched on a point-by-point basis, and the distance between each pair of corresponding points served as an estimate of the combined thickness of the plaque, intima, and media (vessel-wall-plus-plaque thickness or VWT). The VWT maps associated with the first and the second US images were compared and the differences of VWT were obtained at each vertex. The 3D VWT and VWT-Change maps may provide important information for evaluating the location of plaque progression in relation to the localized disturbances of flow pattern, such as oscillatory shear, and regression in response to medical treatments.

Multiscale vascular surface model generation from medical imaging data using hierarchical features

Computational fluid dynamics (CFD) modeling of blood flow from image-based patient specific models can provide useful physiologic information for guiding clinical decision making. A novel method for the generation of image-based, 3-D, multiscale vascular surface models for CFD is presented. The method generates multiscale surfaces based on either a linear triangulated or a globally smooth nonuniform rational B-spline (NURB) representation. A robust local curvature analysis is combined with a novel global feature analysis to set mesh element size. The method is particularly useful for CFD modeling of complex vascular geometries that have a wide range of vasculature size scales, in conditions where 1) initial surface mesh density is an important consideration for balancing surface accuracy with manageable size volumetric meshes, 2) adaptive mesh refinement based on flow features makes an underlying explicit smooth surface representation desirable, and 3) semi-automated detection and trimming of a large number of inlet and outlet vessels expedites model construction.

Efficient computational fluid dynamics mesh generation by image registration

Most implementations of computational fluid dynamics (CFD) solutions require a discretisation or meshing of the solution domain. The production from a medical image of a computationally efficient mesh representing the structures of interest can be time consuming and labour-intensive, and remains a major bottleneck in the clinical application of CFD. This paper presents a method for deriving a patient-specific mesh from a medical image. The method uses volumetric registration of a pseudo-image, produced from an idealised template mesh, with the medical image. The registration algorithm used is robust and computationally efficient. The accuracy of the new algorithm is measured in terms of the distance between a registered surface and a known surface, for image data derived from casts of the lumen of two different vessels. The true surface is identified by laser profiling. The average distance between the surface points measured by the laser profiler and the surface of the mapped mesh is better than 0.2 mm. For the images analysed, the new algorithm is shown to be 2-3 times more accurate than a standard published algorithm based on maximising normalised mutual information. Computation times are approximately 18 times faster for the new algorithm than the standard algorithm. Examples of the use of the algorithm on two clinical examples are also given. The registration methodology lends itself immediately to the construction of dynamic mesh models in which vessel wall motion is obtained directly using registration.

Vessels as 4-D curves: global minimal 4-D paths to extract 3-D tubular surfaces and centerlines

In this paper, we propose an innovative approach to the segmentation of tubular structures. This approach combines all of the benefits of minimal path techniques such as global minimizers, fast computation, and powerful incorporation of user input, while also having the capability to represent and detect vessel surfaces directly which so far has been a feature restricted to active contour and surface techniques. The key is to represent the trajectory of a tubular structure not as a 3-D curve but to go up a dimension and represent the entire structure as a 4-D curve. Then we are able to fully exploit minimal path techniques to obtain global minimizing trajectories between two user supplied endpoints in order to reconstruct tubular structures from noisy or low contrast 3-D data without the sensitivity to local minima inherent in most active surface techniques. In contrast to standard purely spatial 3-D minimal path techniques, however, we are able to represent a full tubular surface rather than just a curve which runs through its interior. Our representation also yields a natural notion of a tube's "central curve." We demonstrate and validate the utility of this approach on magnetic resonance (MR) angiography and computed tomography (CT) images of coronary arteries.

Segmentation of 3D tubular objects with adaptive front propagation and minimal tree extraction for 3D medical imaging

We present a new fast approach for segmentation of thin branching structures, like vascular trees, based on Fast-Marching (FM) and Level Set (LS) methods. FM allows segmentation of tubular structures by inflating a "long balloon" from a user given single point. However, when the tubular shape is rather long, the front propagation may blow up through the boundary of the desired shape close to the starting point. Our contribution is focused on a method to propagate only the useful part of the front while freezing the rest of it. We demonstrate its ability to segment quickly and accurately tubular and tree-like structures. We also develop a useful stopping criterion for the causal front propagation. We finally derive an efficient algorithm for extracting an underlying 1D skeleton of the branching objects, with minimal path techniques. Each branch being represented by its centerline, we automatically detect the bifurcations, leading to the "Minimal Tree" representation. This so-called "Minimal Tree" is very useful for visualization and quantification of the pathologies in our anatomical data sets. We illustrate our algorithms by applying it to several arteries datasets.

System for the analysis and visualization of large 3D anatomical trees

Modern micro-CT and multi-detector helical CT scanners can produce high-resolution 3D digital images of various anatomical trees. The large size and complexity of these trees make it essentially impossible to define them interactively. Automatic approaches have been proposed for a few specific problems, but none of these approaches guarantee extracting geometrically accurate multi-generational tree structures. This paper proposes an interactive system for defining and visualizing large anatomical trees and for subsequent quantitative data mining. The system consists of a large number of tools for automatic image analysis, semi-automatic and interactive tree editing, and an assortment of visualization tools. Results are presented for a variety of 3D high-resolution images.

Emerging vascular applications of magnetic resonance imaging: a picture is worth more than a thousand words

Vascular applications of magnetic resonance (MR) imaging are reviewed, with emphasis on algorithms that use nonpictorial information contained in the MR data set. Current clinical vascular practice generally limits use of MR angiography and three-dimensional vessel images to qualitative pictorial rendering without routinely using the available quantitative information contained within the MR data. This review is dedicated to recent advances that include characterization of vessel histology, assessment of carotid plaque vulnerability, characterization of blood flow dynamics, quantitative analysis of disease severity, and prediction of vascular intervention outcome. Examples from histologic preparation, in vitro and in vivo experiments, are discussed, with an emphasis on potential clinical applications and advances in acquisition technology.

A proposed parent vessel geometry-based categorization of saccular intracranial aneurysms: computational flow dynamics analysis of the risk factors for lesion rupture

OBJECT

The authors created a simple, broadly applicable classification of saccular intracranial aneurysms into three categories: sidewall (SW), sidewall with branching vessel (SWBV), and endwall (EW) according to the angiographically documented patterns of their parent arteries. Using computational flow dynamics analysis (CFDA) of simple models representing the three aneurysm categories, the authors analyzed geometry-related risk factors such as neck width, parent artery curvature, and angulation of the branching vessels.

METHODS

The authors performed CFDAs of 68 aneurysmal geometric formations documented on angiograms that had been obtained in patients with 45 ruptured and 23 unruptured lesions. In successfully studied CFDA cases, the wall shear stress, blood velocity, and pressure maps were examined and correlated with aneurysm rupture points. Statistical analysis of the cases involving aneurysm rupture revealed a statistically significant correlation between aneurysm depth and both neck size (p < 0.0001) and caliber of draining arteries (p < 0.0001). Wider-necked aneurysms or those with wider-caliber draining vessels were found to be high-flow lesions that tended to rupture at larger sizes. Smaller-necked aneurysms or those with smaller-caliber draining vessels were found to be low-flow lesions that tended to rupture at smaller sizes. The incidence of ruptured aneurysms with an aspect ratio (depth/neck) exceeding 1.6 was 100% in the SW and SWBV categories, whereas the incidence was only 28.75% for the EW aneurysms.

CONCLUSIONS

The application of standardized categories enables the comparison of results for various aneurysms' geometric formations, thus assisting in their management. The proposed classification system may provide a promising means of understanding the natural history of saccular intracranial aneurysms.

Quantitative analysis of pulmonary airway tree structures

A method for computationally efficient skeletonization of three-dimensional tubular structures is reported. The method is specifically targeting skeletonization of vascular and airway tree structures in medical images but it is general and applicable to many other skeletonization tasks. The developed approach builds on the following novel concepts and properties: fast curve-thinning algorithm to increase computational speed, endpoint re-checking to avoid generation of spurious side branches, depth-and-length sensitive pruning, and exact tree-branch partitioning allowing branch volume and surface measurements. The method was validated in computer and physical phantoms and in vivo CT scans of human lungs. The validation studies demonstrated sub-voxel accuracy of branch point positioning, insensitivity to changes of object orientation, and high reproducibility of derived quantitative indices of the tubular structures offering a significant improvement over previously reported methods (p<<0.001).

Finite element modelling and simulations in cardiovascular mechanics and cardiology: A bibliography 1993–2004

The paper gives a bibliographical review of the finite element modelling and simulations in cardiovascular mechanics and cardiology from the theoretical as well as practical points of views. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1993 and 2004. At the end of this paper, more than 890 references are given dealing with subjects as: Cardiovascular soft tissue modelling; material properties; mechanisms of cardiovascular components; blood flow; artificial components; cardiac diseases examination; surgery; and other topics.

Quantifying 3-D vascular structures in MRA images using hybrid PDE and geometric deformable models

The aim of this paper is to present a hybrid approach to accurate quantification of vascular structures from magnetic resonance angiography (MRA) images using level set methods and deformable geometric models constructed with 3-D Delaunay triangulation. Multiple scale filtering based on the analysis of local intensity structure using the Hessian matrix is used to effectively enhance vessel structures with various diameters. The level set method is then applied to automatically segment vessels enhanced by the filtering with a speed function derived from enhanced MRA images. Since the goal of this paper is to obtain highly accurate vessel borders, suitable for use in fluid flow simulations, in a subsequent step, the vessel surface determined by the level set method is triangulated using 3-D Delaunay triangulation and the resulting surface is used as a parametric deformable model. Energy minimization is then performed within a variational setting with a first-order internal energy; the external energy is derived from 3-D image gradients. Using the proposed method, vessels are accurately segmented from MRA data.

Robust and objective decomposition and mapping of bifurcating vessels

Computational modeling of human arteries has been broadly employed to investigate the relationships between geometry, hemodynamics and vascular disease. Recent developments in modeling techniques have made it possible to perform such analyses on realistic geometries acquired noninvasively and, thus, have opened up the possibility to extend the investigation to populations of subjects. However, for this to be feasible, novel methods for the comparison of the data obtained from large numbers of realistic models in the presence of anatomic variability must be developed. In this paper, we present an automatic technique for the objective comparison of distributions of geometric and hemodynamic quantities over the surface of bifurcating vessels. The method is based on centerlines and consists of robustly decomposing the surface into its constituent branches and mapping each branch onto a template parametric plane. The application of the technique to realistic data demonstrates how similar results are obtained over similar geometries, allowing for proper model-to-model comparison. Thanks to the computational and differential geometry criteria adopted, the method does not depend on user-defined parameters or user interaction, it is flexible with respect to the bifurcation geometry and it is readily extendible to more complex configurations of interconnecting vessels.