In this article, a new level set model is proposed for the segmentation of biomedical images. The image energy of the proposed model is derived from a robust image gradient feature which gives the active contour a global representation of the geometric configuration, making it more robust in dealing with image noise, weak edges, and initial configurations. Statistical shape information is incorporated using nonparametric shape density distribution, which allows the shape model to handle relatively large shape variations. The segmentation of various shapes from both synthetic and real images depict the robustness and efficiency of the proposed method.

We propose an automatic algorithm for the reconstruction of patient-specific cardiac mesh models with 1-to-1 vertex correspondence. In this framework, a series of 3D meshes depicting the endocardial surface of the heart at each time step is constructed, based on a set of border delineated magnetic resonance imaging (MRI) data of the whole cardiac cycle. The key contribution in this work involves a novel reconstruction technique to generate a 4D (i.e., spatial–temporal) model of the heart with 1-to-1 vertex mapping throughout the time frames. The reconstructed 3D model from the first time step is used as a base template model and then deformed to fit the segmented contours from the subsequent time steps. A method to determine a tree-based connectivity relationship is proposed to ensure robust mapping during mesh deformation. The novel feature is the ability to handle intra- and inter-frame 2D topology changes of the contours, which manifests as a series of merging and splitting of contours when the images are viewed either in a spatial or temporal sequence. Our algorithm has been tested on five acquisitions of cardiac MRI and can successfully reconstruct the full 4D heart model in around 30 minutes per subject. The generated 4D heart model conforms very well with the input segmented contours and the mesh element shape is of reasonably good quality. The work is important in the support of downstream computational simulation activities.

Accurate and robust extraction of the left ventricle (LV) cavity is a key step for quantitative analysis of cardiac functions. In this study, we propose an improved LV cavity segmentation method that incorporates a dynamic shape constraint into the weighting function of the random walks algorithm. The method involves an iterative process that updates an intermediate result to the desired solution. The shape constraint restricts the solution space of the segmentation result, such that the robustness of the algorithm is increased to handle misleading information that emanates from noise, weak boundaries, and clutter. Our experiments on real cardiac magnetic resonance images demonstrate that the proposed method obtains better segmentation performance than standard method.

Evaluation of right ventricular (RV) structure and function is of importance in the management of most cardiac disorders. But the segmentation of RV has always been consid- ered challenging due to low contrast of the myocardium with surrounding and high shape variability of the RV. In this paper, we present a 2D + T active contour model for segmentation and tracking of RV endocardium on cardiac magnetic resonance (MR) images. To take into account the temporal information between adjacent frames, we propose to integrate the time-dependent constraints into the energy functional of the classical gradient vector flow (GVF). As a result, the prior motion knowledge of RV is introduced in the deformation process through the time-dependent constraints in the proposed GVF-T model. A weighting parameter is introduced to adjust the weight of the temporal information against the image data itself. The additional external edge forces retrieved from the temporal constraints may be useful for the RV segmentation, such that lead to a better segmentation performance. The effectiveness of the proposed approach is supported by experimental results on synthetic and cardiac MR images.

We propose an automatic algorithm for the reconstruction of a set of patient-specific dynamic cardiac mesh model with 1-to-1 mesh correspondence over the whole cardiac cycle. This work focus on both the reconstruction technique of the initial 3D model of the heart and also the consistent mapping of the vertex positions throughout all the 3D meshes. This process is technically more challenging due to the wide interval spacing between MRI images as compared to CT images, making overlapping blood vessels much harder to discern. We propose a tree-based connectivity data structure to perform a filtering process to eliminate weak connections between contours on adjacent slices. The reconstructed 3D model from the first time step is used as a base template model, and deformed to fit the segmented contours in the next time step. Our algorithm has been tested on an actual acquisition of cardiac MRI images over one cardiac cycle.

This study aimed to assess the feasibility of using the regional uniformity of the left ventricle (LV) wall stress (WS) to diagnose patients with myocardial infarction. We present a novel method using a similarity map that measures the degree of uniformity in nominal systolic WS across pairs of segments within the same patient. The values of the nominal WS are computed at each vertex point from a 1-to-1 corresponding mesh pair of the LV at the end-diastole (ED) and end-systole (ES) phases. The 3D geometries of the LV at ED and ES are reconstructed from border-delineated MRI images and the 1-to-1 mesh generated using a strain-energy minimization approach. The LV is then partitioned into 16 segments based on published clinical standard and the nominal WS histogram distribution for each of the segment was computed. A similarity index is then computed for each pair of histogram distributions to generate a 16-by-16 similarity map. Based on our initial study involving 12 MI patients and 9 controls, we observed uniformity for intra- regional comparisons in the controls compared against the patients. Our results suggest that the regional uniformity of the nominal systolic WS in the form of a similarity map can potentially be used as a discriminant between MI patients and normal controls.

This chapter presents an image gradient based approach to perform 2D and 3D deformable model segmentation using level set. The 2D method uses an external force field that is based on magnetostatics and hypothesized magnetic interactions between the active contour and object boundaries. The major contribution of the method is that the interaction of its forces can greatly improve the active contour in capturing complex geometries and dealing with difficult initializations, weak edges and broken boundaries. This method is then generalized to 3D by reformulating its external force based on geometrical interactions between the relative geometries of the deformable model and the object boundary characterized by image gradient. The evolution of the deformable model is solved using the level set method so that topological changes are handled automatically. The relative geometrical configurations between the deformable model and the object boundaries contribute to a dynamic vector force field that changes accordingly as the deformable model evolves. The geometrically induced dynamic interaction force has been shown to greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries, and it gives the deformable model a high invariancy in initialization configurations. The voxel interactions across the whole image domain provide a global view of the object boundary representation, giving the external force a long attraction range. The bidirectionality of the external force field allows the new deformable model to deal with arbitrary cross-boundary initializations, and facilitates the handling of weak edges and broken boundaries.

We present a method for the reconstruction of vascular geometries from medical images. Image denoising is performed using vessel enhancing diffusion, which can smooth out image noise and enhance vessel structures. The Canny edge detection technique which produces object edges with single pixel width is used for accurate detection of the lumen boundaries. The image gradients are then used to compute the geometric potential field which gives a global representation of the geometric configuration. The deformable model uses a regional constraint to suppress calcified regions for accurate segmentation of the vessel geometries. The proposed framework show high accuracy when applied to the segmentation of the carotid arteries from CT images.

The segmentation of shapes from biomedical images has a wide range of uses such as image based modelling and bioimage analysis. In this paper, an active contour model is proposed for the segmentation of N-dimensional biomedical images. The proposed model uses a curvature smoothing flow and an image attraction force derived from the interactions between the geometries of the active contour model and the image objects. The active contour model is formulated using the level set method so as to handle topological changes automatically. The magnitude and orientation of the image attraction force is based on the relative geometric configurations between the active contour model and the image object boundaries. The vector force field is therefore dynamic, and the active contour model can propagate through narrow structures to segment complex shapes efficiently. The proposed model utilizes pixel interactions across the image domain, which gives a coherent representation of the image object shapes. This allows the active contour model to be robust to image noise and weak object edges. The proposed model is compared against widely used active contour models in the segmentation of anatomical shapes from biomedical images. It is shown that the proposed model has several advantages over existing techniques and can be used for the segmentation of biomedical images efficiently.

We propose a new level set segmentation method with statistical shape prior using a variational approach. The image energy is derived from a robust image gradient feature. This gives the active contour a global representation of the geometric configuration, making it more robust to image noise, weak edges and initial configurations. Statistical shape information is incorporated using nonparametric shape density distribution, which allows the model to handle relatively large shape variations. Comparative examples using both synthetic and real images show the robustness and efficiency of the proposed method.

In this paper, a robust and semi-automatic modelling pipeline for blood flow through subject-specific arterial geometries is presented. The framework developed consists of image segmentation, domain discretization (meshing) and fluid dynamics. All the three subtopics of the pipeline are explained using an example of flow through a severely stenosed human carotid artery. In the Introduction, the state-of-the-art of both image segmentation and meshing is presented in some detail, and wherever possible the advantages and disadvantages of the existing methods are analysed. Followed by this, the deformable model used for image segmentation is presented. This model is based upon a geometrical potential force (GPF), which is a function of the image. Both the GPF calculation and level set determination are explained. Following the image segmentation method, a semi-automatic meshing method used in the present study is explained in full detail. All the relevant techniques required to generate a valid domain discretization are presented. These techniques include generating a valid surface mesh, skeletonization, mesh cropping, boundary layer mesh construction and various mesh cosmetic methods that are essential for generating a high-quality domain discretization. After presenting the mesh generation procedure, how to generate flow boundary conditions for both the inlets and outlets of a geometry is explained in detail. This is followed by a brief note on the flow solver, before studying the blood flow through the carotid artery with a severe stenosis.

This paper focuses on the impact of including nasal cavity on airflow through a human upper respiratory tract. A computational study is carried out on a realistic geometry, reconstructed from CT scans of a subject. The geometry includes nasal cavity, pharynx, larynx, trachea and two generations of airway bifurcations below trachea. The unstructured mesh generation procedure is discussed in some length due to the complex nature of the nasal cavity structure and poor scan resolution normally available from hospitals. The fluid dynamic studies have been carried out on the geometry with and without the inclusion of the nasal cavity. The characteristic-based split scheme along with the one-equation Spalart–Allmaras turbulence model is used in its explicit form to obtain flow solutions at steady state. Results reveal that the exclusion of nasal cavity significantly influences the resulting solution. In particular, the location of recirculating flow in the trachea is dramatically different when the truncated geometry is used. In addition, we also address the differences in the solution due to imposed, equally distributed and proportionally distributed flow rates at inlets (both nares). The results show that the differences in flow pattern between the two inlet conditions are not confined to the nasal cavity and nasopharyngeal region, but they propagate down to the trachea.

In this paper, we propose a novel 3-D deformable model that is based upon a geometrically induced external force field which can be conveniently generalized to arbitrary dimensions. This external force field is based upon hypothesized interactions between the relative geometries of the deformable model and the object boundary characterized by image gradient. The evolution of the deformable model is solved using the level set method so that topological changes are handled automatically. The relative geometrical configurations between the deformable model and the object boundaries contribute to a dynamic vector force field that changes accordingly as the deformable model evolves. The geometrically induced dynamic interaction force has been shown to greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries, and it gives the deformable model a high invariancy in initialization configurations. The voxel interactions across the whole image domain provide a global view of the object boundary representation, giving the external force a long attraction range. The bidirectionality of the external force field allows the new deformable model to deal with arbitrary cross-boundary initializations, and facilitates the handling of weak edges and broken boundaries. In addition, we show that by enhancing the geometrical interaction field with a nonlocal edge-preserving algorithm, the new deformable model can effectively overcome image noise. We provide a comparative study on the segmentation of various geometries with different topologies from both synthetic and real images, and show that the proposed method achieves significant improvements against existing image gradient techniques.

It is believed that left ventricular (LV) regional shape is indicative of LV regional function, and cardiac pathologies are often associated with regional alterations in ventricular shape. In this article, we present a set of procedures for evaluating regional LV surface shape from anatomically accurate models reconstructed from cardiac magnetic resonance (MR) images. LV surface curvatures are computed using local surface fitting method, which enables us to assess regional LV shape and its variation. Comparisons are made between normal and diseased hearts. It is illustrated that LV surface curvatures at different regions of the normal heart are higher than those of the diseased heart. Also, the normal heart experiences a larger change in regional curvedness during contraction than the diseased heart. It is believed that with a wide range of dataset being evaluated, this approach will provide a new and efficient way of quantifying LV regional function.

Geometric remodeling of the left ventricle (LV) after myocardial infarction is associated with changes in myocardial wall stress. The objective of this study was to determine the regional curvatures and wall stress based on three-dimensional (3-D) reconstructions of the LV using MRI. Ten patients with ischemic dilated cardiomyopathy (IDCM) and 10 normal subjects underwent MRI scan. The IDCM patients also underwent delayed gadolinium-enhancement imaging to delineate the extent of myocardial infarct. Regional curvedness, local radii of curvature, and wall thickness were calculated. The percent curvedness change between end diastole and end systole was also calculated. In normal heart, a short- and long-axis two-dimensional analysis showed a 41 +/- 11% and 45 +/- 12% increase of the mean of peak systolic wall stress between basal and apical sections, respectively. However, 3-D analysis showed no significant difference in peak systolic wall stress from basal and apical sections (P = 0.298, ANOVA). LV shape differed between IDCM patients and normal subjects in several ways: LV shape was more spherical (sphericity index = 0.62 +/- 0.08 vs. 0.52 +/- 0.06, P < 0.05), curvedness at end diastole (mean for 16 segments = 0.034 +/- 0.0056 vs. 0.040 +/- 0.0071 mm(-1), P < 0.001) and end systole (mean for 16 segments = 0.037 +/- 0.0068 vs. 0.067 +/- 0.020 mm(-1), P < 0.001) was affected by infarction, and peak systolic wall stress was significantly increased at each segment in IDCM patients. The 3-D quantification of regional wall stress by cardiac MRI provides more precise evaluation of cardiac mechanics. Identification of regional curvedness and wall stresses helps delineate the mechanisms of LV remodeling in IDCM and may help guide therapeutic LV restoration.

We propose a new external force field for deformable models which can be conve- niently generalized to high dimensions. The external force field is based on hypothesized interactions between the relative geometries of the deformable model and image gradi- ents. The evolution of the deformable model is solved using the level set method. The dynamic interaction forces between the geometries can greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries, and in dealing with weak image edges. The new deformable model can handle arbi- trary cross-boundary initializations. Here, we show that the proposed method achieve significant improvements when compared against existing state-of-the-art techniques.