A bending energy model for measurement of cardiac shape deformity

An Energetic Approach to Modeling Cytoskeletal Architecture in Maturing Cardiomyocytes

Through a variety of mechanisms, a healthy heart is able to regulate its structure and dynamics across multiple length scales. Disruption of these mechanisms can have a cascading effect, resulting in severe structural and/or functional changes that permeate across different length scales. Due to this hierarchical structure, there is interest in understanding how the components at the various scales coordinate and influence each other. However, much is unknown regarding how myofibril bundles are organized within a densely packed cell and the influence of the subcellular components on the architecture that is formed. To elucidate potential factors influencing cytoskeletal development, we proposed a computational model that integrated interactions at both the cellular and subcellular scale to predict the location of individual myofibril bundles that contributed to the formation of an energetically favorable cytoskeletal network. Our model was tested and validated using experimental metrics derived from analyzing single-cell cardiomyocytes. We demonstrated that our model-generated networks were capable of reproducing the variation observed in experimental cells at different length scales as a result of the stochasticity inherent in the different interactions between the various cellular components. Additionally, we showed that incorporating length-scale parameters resulted in physical constraints that directed cytoskeletal architecture toward a structurally consistent motif. Understanding the mechanisms guiding the formation and organization of the cytoskeleton in individual cardiomyocytes can aid tissue engineers toward developing functional cardiac tissue.

BENDING LOSS REGULARIZED NETWORK FOR NUCLEI SEGMENTATION IN HISTOPATHOLOGY IMAGES

Separating overlapped nuclei is a major challenge in histopathology image analysis. Recently published approaches have achieved promising overall performance on public datasets; however, their performance in segmenting overlapped nuclei are limited. To address the issue, we propose the bending loss regularized network for nuclei segmentation. The proposed bending loss defines high penalties to contour points with large curvatures, and applies small penalties to contour points with small curvature. Minimizing the bending loss can avoid generating contours that encompass multiple nuclei. The proposed approach is validated on the MoNuSeg dataset using five quantitative metrics. It outperforms six state-of-the-art approaches on the following metrics: Aggregate Jaccard Index, Dice, Recognition Quality, and Panoptic Quality.

Computer-aided diagnosis of emphysema in COPD patients: neural-network-based analysis of lung shape in digital chest radiographs

Several abnormalities of the shape of lung fields (depression and flattening of the diaphragmatic contours, increased retrosternal space) are indicative of emphysema and can be accurately imaged by digital chest radiography. In this work, we aimed at developing computational descriptors of the shape of the lung silhouette able to capture the alterations associated with emphysema. We analyzed two-sided digital chest radiographs from a sample of 160 patients with chronic obstructive pulmonary disease (COPD), 60 of which were affected by emphysema, and from 160 subjects with normal lung function. Two different description schemes were considered: a first one based on lung-silhouette curvature features, and a second one based on a minimal-polyline approximation of the lung shape. Both descriptors were employed to recognize alterations of the lung shape using classifiers based on multilayer neural networks of the feed-forward type. Results indicate that pulmonary emphysema can be reliably diagnosed or excluded by using digital chest radiographs and a proper computational aid. Two-sided chest radiographs provide more accurate discrimination than single-view analysis. The minimal-polyline approximation provided significantly better results than those obtained from curvature-based features. Emphysema was detected, in the entire dataset, with an accuracy of about 90% (sensitivity 88%, specificity 90%) by using the minimal-polyline approximation.

On curvature estimation of ISO surfaces in 3D gray-value images and the computation of shape descriptors

In this paper, we present a novel method to estimate curvature of iso gray-level surfaces in gray-value images. Our method succeeds where standard isophote curvature estimation methods fail. There is neither a segmentation of the surface needed nor a parametric model assumed. Our estimator works on the orientation field of the surface. This orientation field and a description of local structure is obtained by the Gradient Structure Tensor. The estimated orientation field has discontinuities mod pi. It is mapped via the Knutsson mapping to a continuous representation. The principal curvatures of the surface, a coordinate invariant property, are computed in this mapped representation. From these curvatures, locally the bending energy is computed to describe the surface shape. An extensive evaluation shows that our curvature estimation is robust even in the presence of noise, independent of the scale of the object and furthermore the relative error stays small.

Local force model for cardiac dynamics analysis from volumetric image sequences

We propose a local force model based on the kinetics of the left ventricle (LV) surfaces to characterize the complex nonrigid motion that the heart undergoes. The left ventricle motion is analyzed in a coarse-to-fine fashion. First, global motion and deformation are analyzed and compensated with hierarchical surface modeling. Then, we propose a physics-based model of local deformation derived from the dynamics of independent point masses driven by local external force. Experimental results show that the ensembles of the estimated point mass trajectories match well with the realistic left ventricle surface dynamics.

Imaging three-dimensional cardiac function

The three-dimensional (3-D) nature of myocardial deformations is dependent on ventricular geometry, muscle fiber architecture, wall stresses, and myocardial-material properties. The imaging modalities of X-ray angiography, echocardiography, computed tomography, and magnetic resonance (MR) imaging (MRI) are described in the context of visualizing and quantifying cardiac mechanical function. The quantification of ventricular anatomy and cavity volumes is then reviewed, and surface reconstructions in three dimensions are demonstrated. The imaging of myocardial wall motion is discussed, with an emphasis on current MRI and tissue Doppler imaging techniques and their potential clinical applications. Calculation of 3-D regional strains from motion maps is reviewed and illustrated with clinical MRI tagging results. We conclude by presenting a promising technique to assess myocardial-fiber architecture, and we outline its potential applications, in conjunction with quantification of anatomy and regional strains, for the determination of myocardial stress and work distributions. The quantification of multiple components of 3-D cardiac function has potential for both fundamental-science and clinical applications.

Quantification of 3-D regional myocardial deformation: shape-based analysis of magnetic resonance images

A comprehensive three-dimensional (3-D) shape-based approach for quantification of regional myocardial deformations was evaluated in a canine model (n = 8 dogs) with the use of cine magnetic resonance imaging. The shape of the endocardial and epicardial surfaces was used to track the 3-D trajectories of a dense field of points over the cardiac cycle. The shape-based surface displacements are integrated with a continuum biomechanics model incorporating myofiber architecture to estimate both cardiac- and fiber-specific endocardial and epicardial strains and shears for 24 left ventricular regions. Whereas radial and circumferential end-systolic strains were fairly uniform, there was a significant apex-to-base gradient in longitudinal strain and radial-longitudinal shear. We also observed transmural epicardial-to-endocardial gradients in both cardiac- and fiber-specific strains. The increase in endocardial strain was accompanied by increases in radial-longitudinal shear and radial-fiber shears in the endocardium, supporting previous theories of regional myocardial deformation that predict considerable sliding between myocardial fibers.

Multiframe temporal estimation of cardiac nonrigid motion

A robust, flexible system for tracking the point to point nonrigid motion of the left ventricular (LV) endocardial wall in image sequences has been developed. This system is unique in its ability to model motion trajectories across multiple frames. The foundation of this system is an adaptive transversal filter based on the recursive least-squares algorithm. This filter facilitates the integration of models for periodicity and proximal smoothness as appropriate using a contour-based description of the object's boundaries. A set of correspondences between contours and an associated set of correspondence quality measures comprise the input to the system. Frame-to-frame relationships from two different frames of reference are derived and analyzed using synthetic and actual images. Two multiframe temporal models, both based on a sum of sinusoids, are derived. Illustrative examples of the system's output are presented for quantitative analysis. Validation of the system is performed by comparing computed trajectory estimates with the trajectories of physical markers implanted in the LV wall. Sample case studies of marker trajectory comparisons are presented. Ensemble statistics from comparisons with 15 marker trajectories are acquired and analyzed. A multiframe temporal model without spatial periodicity constraints was determined to provide excellent performance with the least computational cost. A multiframe spatiotemporal model provided the best performance based on statistical standard deviation, although at significant computational expense.

Assessment of left ventricular cardiac shape by the use of volumetric curvature analysis from 3D echocardiography

A method for three-dimensional shape analysis of left ventricle (LV) is presented in this article. The method uses three-dimensional transesophageal echocardiography (TEE) as the source to derive the 3D wire-frame model and the related shape descriptors. The shape descriptors developed in this article include regional surface changing (RSC), global surface curvature (GSC), surface distance (SD), normalized surface distance (ND), and effective radius (ER) of the endocardial surface. Based on these shape descriptors, the shape of LV could be sketched in both static and dynamic manner. The results show that the new approach provides a robust but easy method to quantify regional and global LV shape from 2D and 3D echocardiograms.

Precision of myocardial contour estimation from tagged MR images with a "black-blood" technique

RATIONALE AND OBJECTIVES

The authors determined whether blood presaturation of tagged magnetic resonance (MR) images affects identification of left ventricular endocardial borders.

MATERIALS AND METHODS

Three healthy volunteers underwent MR imaging performed with a breath-hold segmented spoiled gradient-recalled-echo sequence with tissue tagging. Two saturation pulses (in the basal and apical regions) were used to generate black-blood images. Manual segmentation of endocardial contours on black-blood and white-blood images was performed independently by five observers.

RESULTS

Endocardial borders were better identified on black-blood images compared with white-blood images, especially in the early systolic phases. Interobserver variability in contour estimation was significantly higher for white-blood images (P < .001) and was twice that for corresponding black-blood images during early systole. Contour variability appeared to be affected mainly by tag-to-myocardium contrast (P = .009) and myocardium-to-chamber contrast (P = .05).

CONCLUSION

Blood presaturation of tagged MR images improves reliability of contour segmentation.

Shape-based tracking of left ventricular wall motion

An approach for tracking and quantifying the nonrigid, nonuniform motion of the left ventricular (LV) endocardial wall from two-dimensional (2-D) cardiac image sequences, on a point-by-point basis over the entire cardiac cycle, is presented. Given a set of boundaries, motion computation involves first matching local segments on one contour to segments on the next contour in the sequence using a shape-based strategy. Results from the match process are incorporated with a smoothness term into an optimization functional. The global minimum of this functional is found, resulting in a smooth flow field that is consistent with the match data. The computation is performed for all pairs of frames in the temporal sequence and equally sampled points on one contour are tracked throughout the sequence, resulting in a composite flow field over the entire sequence. Two perspectives on characterizing the optimization functional are presented which result in a tradeoff resolved by the confidence in the initial boundary segmentation. Experimental results for contours derived from diagnostic image sequences of three different imaging modalities are presented. A comparison of trajectory estimates with trajectories of gold-standard markers implanted in the LV wall are presented for validation. The results of this comparison confirm that although cardiac motion is a three-dimensional (3-D) problem, two-dimensional (2-D) analysis provides a rich testing ground for algorithm development.

Fusion of short-axis and long-axis cardiac MR images

A method for fusion of the short-axis and long-axis cardiac MR images into an isotropic volume image is introduced. A volume image obtained by this method contains the left ventricular (LV) cavity in one piece, facilitating measurement of its shape and volume. The main goal in this image fusion is to reconstruct the LV cavity in volume form and in high resolution. The accuracy of the method is measured using a synthetic image, and examples of image fusion using real images are presented.

Two-dimensional rigid-body kinematics using image contour registration

A method for calculating two-dimensional rigid-body kinematic parameters using shape features is presented. Proposed applications include the noninvasive quantification of planar joint motion in vivo. By using digitized images (computed tomographs, radiographs, etc.) of a bone contour at two positions, the contour curvatures can be 'best-fit' to obtain a one-to-one mapping or registration of the bone images. This produces a dense field of displacement vectors from which planar rigid-body kinematic parameters can be estimated. Accuracy was studied using radiographic images of cadaveric femoral bone. The two motions of pure rotation with a fixed center of rotation and of pure translation were simulated. For pure rotation, error in rotation was independent of the rotation magnitude, with an average (n = 10) error of 0.3 +/- 0.8 degrees. The translation error averaged 0.9 +/- 0.5 mm. For pure translation, the error in rotation was -0.01 +/- 0.69 degrees and the error in translation was -0.62 +/- 0.98 mm (n = 10). This novel method has broad applications in the field of planar kinematics, especially in cases for which marker fixation is neither possible nor practical.

Automatic determination of LV orientation from SPECT data

Presents a new method to determine the orientation or pose of the left ventricle (LV) of the heart from cardiac SPECT (single photon emission computed tomography) data. This proposed approach offers an accurate, fast, and robust delineation of the LV long-axis. The location and shape of the generated long-axis can then be utilized to define automatically the tomographic slices for enhanced visualization and quantification of the clinical data. The methodology is broadly composed of two main steps: (1) volume segmentation of cardiac SPECT data; and (2) topological goniometry, a novel approach incorporating volume visualization and computer graphics ideas to determine the overall shape of 3-D objects. The outcome of the algorithm is a 3-D curve representing the overall pose of the LV long-axis. Experimental results on both phantom and clinical data (50 technetium-99m and 74 thallium-201) are presented. An interactive graphical interface to visualize the volume (3-D) data, the left ventricle, and its pose is an integral part of the overall methodology. This technique is completely data driven and expeditious, making it viable for routine clinical use.

Determining cardiac velocity fields and intraventricular pressure distribution from a sequence of ultrafast CT cardiac images

A method of computing the velocity field and pressure distribution from a sequence of ultrafast CT (UFCT) cardiac images is demonstrated. UFCT multi-slice cine imaging gives a series of tomographic slices covering the volume of the heart at a rate of 17 frames per second. The complete volume data set can be modeled using equations of continuum theory and through regularization, velocity vectors of both blood and tissue can be determined at each voxel in the volume. The authors present a technique to determine the pressure distribution throughout the volume of the left ventricle using the computed velocity field. A numerical algorithm is developed by discretizing the pressure Poisson equation (PPE), which Is based on the Navier-Stokes equation. The algorithm is evaluated using a mathematical phantom of known velocity and pressure-Couette flow. It is shown that the algorithm based on the PPE can reconstruct the pressure distribution using only the velocity data. Furthermore, the PPE is shown to be robust in the presence of noise. The velocity field and pressure distribution derived from a UFCT study of a patient are also presented.

Tag and contour detection in tagged MR images of the left ventricle

Tracking magnetic resonance tags in myocardial tissue promises to be an effective tool for the assessment of myocardial motion. The authors describe a hierarchy of image processing steps which rapidly detects both the contours of the myocardial boundaries of the left ventricle and the tags within the myocardium. The method works on both short axis and long axis images containing radial and parallel tag patterns, respectively. Left ventricular boundaries are detected by first removing the tags using morphological closing and then selecting candidate edge points. The best inner and outer boundaries are found using a dynamic program that minimizes a nonlinear combination of several local cost functions. Tags are tracked by matching a template of their expected profile using a least squares estimate. Since blood pooling, contiguous and adjacent tissue, and motion artifacts sometimes cause detection errors, a graphical user interface was developed to allow user correction of anomalous points. The authors present results on several tagged images of a human. A fully automated run generally finds the endocardial boundary and the tag lines extremely well, requiring very little manual correction. The epicardial boundary sometimes requires more intervention to obtain an acceptable result. These methods are currently being used in the analysis of cardiac strain and as a basis for the analysis of alternate tag geometries.

Application of form features in digital cell analysis of non-Hodgkin's lymphomas

The form of a biological cell nucleus can be characterized by the well-known circularity factor, which is derived from the area of an object and its circumference. More sophisticated form features are introduced, which are calculated from the curvature of an object ("bending energy") or from invariant moments. To investigate the sensitivity of the various form features on controlled changes of form and the behaviour under rotation and scaling, algebraic curves similar to the form of real nucleus profiles are generated. Analysis of the shape characteristics of biological cells requires an extraction of the boundaries of the nuclei. This was performed by an edge detection algorithm using eight gradient masks followed by a contour tracing procedure with feedback. The suitability of the introduced form features for classification of different nucleus profiles of non-Hodgkin's lymphomas (NHL) was tested using a Bayes classifier.

Modelling the growth of solid tumours and incorporating a method for their classification using nonlinear elasticity theory

Medically, tumours are classified into two important classes--benign and malignant. Generally speaking, the two classes display different behaviour with regard to their rate and manner of growth and subsequent possible spread. In this paper, we formulate a new approach to tumour growth using results and techniques from nonlinear elasticity theory. A mathematical model is given for the growth of a solid tumour using membrane and thick-shell theory. A central feature of the model is the characterisation of the material composition of the model through the use of a strain-energy function, thus permitting a mathematical description of the degree of differentiation of the tumour explicitly in the model. Conditions are given in terms of the strain-energy function for the processes of invasion and metastasis occurring in a tumour, being interpreted as the bifurcation modes of the spherical shell which the tumour is essentially modelled as. Our results are compared with actual experimental results and with the general behaviour shown by benign and malignant tumours. Finally, we use these results in conjunction with aspects of surface morphogenesis of tumours (in particular, the Gaussian and mean curvatures of the surface of a solid tumour) in an attempt to produce a mathematical formulation and description of the important medical processes of staging and grading cancers. We hope that this approach may form the basis of a practical application.

A mathematical model for the growth and classification of a solid tumor: a new approach via nonlinear elasticity theory using strain-energy functions

Medically, tumors are classified into two important classes--benign and malignant. Generally speaking, the two classes display different behaviour with regard to their rate and manner of growth and subsequent possible spread. In this paper, we formulate a new approach to tumor growth using results and techniques from nonlinear elasticity theory. A mathematical model is given for the growth of a solid tumor using membrane and thick-shell theory. A central feature of the model is the characterization of the material composition of the tumor through the use of a strain energy function, thus permitting a mathematical description of the degree of differentiation of the tumor explicitly in the model. Conditions are given in terms of the strain energy function for the processes of invasion and metastasis occurring in a tumor, being interpreted as the bifurcation modes of the spherical shell, which the tumor is essentially modeled as. Our results are compared with actual medical experimental results and with the general behavior shown by benign and malignant tumors. Finally, we use these results in conjunction with aspects of surface morphogenesis of tumors (in particular, the Gaussian and mean curvatures of the surface of a solid tumor) in an attempt to produce a mathematical formulation and description of the important medical processes of staging and grading cancers. We hope that this approach may form the basis of a practical application.