Shape-based tracking of left ventricular wall motion

Regional dynamics of fractal dimension of the left ventricular endocardium from cine computed tomography images

We present a method to leverage the high fidelity of computed tomography (CT) to quantify regional left ventricular function using topography variation of the endocardium as a surrogate measure of strain. 4DCT images of 10 normal and 10 abnormal subjects, acquired with standard clinical protocols, are used. The topography of the endocardium is characterized by its regional values of fractal dimension (F D ), computed using a box-counting algorithm developed in-house. The averageF D in each of the 16 American Heart Association segments is calculated for each subject as a function of time over the cardiac cycle. The normal subjects show a peak systolic percentage change inF D of 5.9 % ± 2 % in all free-wall segments, whereas the abnormal cohort experiences a change of 2 % ± 1.2 % ( p < 0.00001 ). Septal segments, being smooth, do not undergo large changes inF D . Additionally, a principal component analysis is performed on the temporal profiles ofF D to highlight the possibility for unsupervised classification of normal and abnormal function. The method developed is free from manual contouring and does not require any feature tracking or registration algorithms. TheF D values in the free-wall segments correlated well with radial strain and with endocardial regional shortening measurements.

A 3D interactive multi-object segmentation tool using local robust statistics driven active contours

Extracting anatomical and functional significant structures renders one of the important tasks for both the theoretical study of the medical image analysis, and the clinical and practical community. In the past, much work has been dedicated only to the algorithmic development. Nevertheless, for clinical end users, a well designed algorithm with an interactive software is necessary for an algorithm to be utilized in their daily work. Furthermore, the software would better be open sourced in order to be used and validated by not only the authors but also the entire community. Therefore, the contribution of the present work is twofolds: first, we propose a new robust statistics based conformal metric and the conformal area driven multiple active contour framework, to simultaneously extract multiple targets from MR and CT medical imagery in 3D. Second, an open source graphically interactive 3D segmentation tool based on the aforementioned contour evolution is implemented and is publicly available for end users on multiple platforms. In using this software for the segmentation task, the process is initiated by the user drawn strokes (seeds) in the target region in the image. Then, the local robust statistics are used to describe the object features, and such features are learned adaptively from the seeds under a non-parametric estimation scheme. Subsequently, several active contours evolve simultaneously with their interactions being motivated by the principles of action and reaction-this not only guarantees mutual exclusiveness among the contours, but also no longer relies upon the assumption that the multiple objects fill the entire image domain, which was tacitly or explicitly assumed in many previous works. In doing so, the contours interact and converge to equilibrium at the desired positions of the desired multiple objects. Furthermore, with the aim of not only validating the algorithm and the software, but also demonstrating how the tool is to be used, we provide the reader reproducible experiments that demonstrate the capability of the proposed segmentation tool on several public available data sets.

DRAMMS: Deformable registration via attribute matching and mutual-saliency weighting

A general-purpose deformable registration algorithm referred to as "DRAMMS" is presented in this paper. DRAMMS bridges the gap between the traditional voxel-wise methods and landmark/feature-based methods with primarily two contributions. First, DRAMMS renders each voxel relatively distinctively identifiable by a rich set of attributes, therefore largely reducing matching ambiguities. In particular, a set of multi-scale and multi-orientation Gabor attributes are extracted and the optimal components are selected, so that they form a highly distinctive morphological signature reflecting the anatomical and geometric context around each voxel. Moreover, the way in which the optimal Gabor attributes are constructed is independent of the underlying image modalities or contents, which renders DRAMMS generally applicable to diverse registration tasks. A second contribution of DRAMMS is that it modulates the registration by assigning higher weights to those voxels having higher ability to establish unique (hence reliable) correspondences across images, therefore reducing the negative impact of those regions that are less capable of finding correspondences (such as outlier regions). A continuously-valued weighting function named "mutual-saliency" is developed to reflect the matching uniqueness between a pair of voxels implied by the tentative transformation. As a result, voxels do not contribute equally as in most voxel-wise methods, nor in isolation as in landmark/feature-based methods. Instead, they contribute according to the continuously-valued mutual-saliency map, which dynamically evolves during the registration process. Experiments in simulated images, inter-subject images, single-/multi-modality images, from brain, heart, and prostate have demonstrated the general applicability and the accuracy of DRAMMS.

DRAMMS: deformable registration via attribute matching and mutual-saliency weighting

A general-purpose deformable registration algorithm referred to as "DRAMMS" is presented in this paper. DRAMMS adds to the literature of registration methods that bridge between the traditional voxel-wise methods and landmark/feature-based methods. In particular, DRAMMS extracts Gabor attributes at each voxel and selects the optimal components, so that they form a highly distinctive morphological signature reflecting the anatomical context around each voxel in a multi-scale and multi-resolution fashion. Compared with intensity or mutual-information based methods, the high-dimensional optimal Gabor attributes render different anatomical regions relatively distinctively identifiable and therefore help establish more accurate and reliable correspondence. Moreover, the optimal Gabor attribute vector is constructed in a way that generalizes well, i.e., it can be applied to different registration tasks, regardless of the image contents under registration. A second characteristic of DRAMMS is that it is based on a cost function that weights different voxel pairs according to a metric referred to as "mutual-saliency", which reflects the uniqueness (reliability) of anatomical correspondences implied by the tentative transformation. As a result, image voxels do not contribute equally to the optimization process, as in most voxel-wise methods, or in a binary selection fashion, as in most landmark/feature-based methods. Instead, they contribute according to a continuously-valued mutual-saliency map, which is dynamically updated during the algorithm's evolution. The general applicability and accuracy of DRAMMS are demonstrated by experiments in simulated images, inter-subject images, single-/multi-modality images, and longitudinal images, from human and mouse brains, breast, heart, and prostate.

Quantitative analysis of left ventricular performance from sequences of cardiac magnetic resonance imaging using active mesh model

In this study, the local and global left ventricular function are estimated by fitting three-dimensional active mesh model (3D-AMM) to the initial sparse displacement which is measured from an establishing point correspondence procedure. To evaluate the performance of the algorithm, eight image sequences were used and the results were compared with those reported by other researchers. The findings were consistent with previously published values and the clinical evidence as well. The results demonstrated the superiority of the novel strategy with respect to formerly presented algorithm reported by author et al. Furthermore, the results are comparable to the current state-of-the-art methods.

New echocardiographic imaging method based on the bandwidth of the ultrasound Doppler signal with applications in blood/tissue segmentation in the left ventricle

A new imaging method, Bandwidth Imaging, which is related to the bandwidth of the ultrasound Doppler signal is proposed as a classification function for blood and tissue signal in transthoracial echocardiography in the left ventricle. An in vivo experiment is presented, where the apparent error rate of Bandwidth Imaging is compared with the apparent error rate of Second-Harmonic Imaging on 15 healthy men. The apparent error rates are calculated from the 16 myocardial wall segments defined in [M.D., Cerqueira, N.J. Weissman, V. Dilsizian, A.K. Jacobs, S. Kaul, W.K. Laskey, D.J. Pennell, J.A. Rumberger, T. Ryan, M.S. Verani, Standardized myocardial segmentation and nomenclature for tomographic imaging of the heart, Circulation (2002) 539-542]. A hypothesis test of Bandwidth Imaging having lower apparent error rate than Second-Harmonic Imaging is proved for a p-value of 0.94 in three segments in end diastole and in one segment in end systole. When data was averaged by a structural element of five radial, three lateral and four temporal samples the numbers of segments increased to nine in end diastole and to six in end systole. This experiment indicates that Bandwidth Imaging can supply additional information for automatic border detection routines on endocardium.

Learning the dynamics and time-recursive boundary detection of deformable objects

We propose a principled framework for recursively segmenting deformable objects across a sequence of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle. The approach involves a technique for learning the system dynamics together with methods of particle-based smoothing as well as nonparametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart. The dynamic system state is a low-dimensional representation of the boundary, and the boundary estimation involves incorporating curve evolution into recursive state estimation. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past and future boundary estimates. Although this paper focuses on left ventricle segmentation, the method generalizes to temporally segmenting any deformable object.

Robust shape tracking with multiple models in ultrasound images

This paper addresses object tracking in ultrasound images using a robust multiple model tracker. The proposed tracker has the following features: 1) it uses multiple dynamic models to track the evolution of the object boundary, and 2) it models invalid observations (outliers), reducing their influence on the shape estimates. The problem considered in this paper is the tracking of the left ventricle which is known to be a challenging problem. The heart motion presents two phases (diastole and systole) with different dynamics, the multiple models used in this tracker try to solve this difficulty. In addition, ultrasound images are corrupted by strong multiplicative noise which prevents the use of standard deformable models. Robust estimation techniques are used to address this difficulty. The multiple model data association (MMDA) tracker proposed in this paper is based on a bank of nonlinear filters, organized in a tree structure. The algorithm determines which model is active at each instant of time and updates its state by propagating the probability distribution, using robust estimation techniques.

Segmentation of the left ventricle of the heart in 3-D+t MRI data using an optimized nonrigid temporal model

Modern medical imaging modalities provide large amounts of information in both the spatial and temporal domains and the incorporation of this information in a coherent algorithmic framework is a significant challenge. In this paper, we present a novel and intuitive approach to combine 3-D spatial and temporal (3-D + time) magnetic resonance imaging (MRI) data in an integrated segmentation algorithm to extract the myocardium of the left ventricle. A novel level-set segmentation process is developed that simultaneously delineates and tracks the boundaries of the left ventricle muscle. By encoding prior knowledge about cardiac temporal evolution in a parametric framework, an expectation-maximization algorithm optimally tracks the myocardial deformation over the cardiac cycle. The expectation step deforms the level-set function while the maximization step updates the prior temporal model parameters to perform the segmentation in a nonrigid sense.

Segmenting and tracking the left ventricle by learning the dynamics in cardiac images

Having accurate left ventricle (LV) segmentations across a cardiac cycle provides useful quantitative (e.g. ejection fraction) and qualitative information for diagnosis of certain heart conditions. Existing LV segmentation techniques are founded mostly upon algorithms for segmenting static images. In order to exploit the dynamic structure of the heart in a principled manner, we approach the problem of LV segmentation as a recursive estimation problem. In our framework, LV boundaries constitute the dynamic system state to be estimated, and a sequence of observed cardiac images constitute the data. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past segmentations. This requires a dynamical system model of the LV, which we propose to learn from training data through an information-theoretic approach. To incorporate the learned dynamic model into our segmentation framework and obtain predictions, we use ideas from particle filtering. Our framework uses a curve evolution method to combine such predictions with the observed images to estimate the LV boundaries at each time. We demonstrate the effectiveness of the proposed approach on a large set of cardiac images. We observe that our approach provides more accurate segmentations than those from static image segmentation techniques, especially when the observed data are of limited quality.

Boosting and nonparametric based tracking of tagged MRI cardiac boundaries

In this paper we present an accurate cardiac boundary tracking method for 2D tagged MRI time sequences. This method naturally integrates the motion and the static local appearance features and generates accurate boundary criteria via a boosting approach. We extend the conventional Adaboost classifier into a posterior probability form, which can be embedded in a particle filtering-based shape tracking framework. To make the tracking process more robust and faster, we use a PCA subspace shape representation to constrain the shape variation and lower the dimensionality. We also learn two shape-dynamic models for systole and diastole separately, to predict the shape evolution. Our tracking method incorporates the static appearance, the motion appearance, the shape constraints, and the dynamic prediction in a unified way. The proposed method has been implemented on 50 tagged MRI sequences. The experimental results show the accuracy and robustness of our approach.

State-space analysis of cardiac motion with biomechanical constraints

Quantitative estimation of nonrigid motion from image sequences has important technical and practical significance. State-space analysis provides powerful and convenient ways to construct and incorporate the physically meaningful system dynamics of an object, the image-derived observations, and the process and measurement noise disturbances. In this paper, we present a biomechanical-model constrained state-space analysis framework for the multiframe estimation of the periodic cardiac motion and deformation. The physical constraints take the roles as spatial regulator of the myocardial behavior and spatial filter/interpolator of the data measurements, while techniques from statistical filtering theory impose spatiotemporal constraints to facilitate the incorporation of multiframe information to generate optimal estimates of the heart kinematics. Physiologically meaningful results have been achieved from estimated displacement fields and strain maps using in vivo left ventricular magnetic resonance tagging and phase contrast image sequences, which provide the tag-tag and tag-boundary displacement inputs, and the mid-wall instantaneous velocity information and boundary displacement measures, respectively.

A hybrid Eulerian-Lagrangian approach for thickness, correspondence, and gridding of annular tissues

We present a novel approach to efficiently compute thickness, correspondence, and gridding of tissues between two simply connected boundaries. The solution of Laplace's equation within the tissue region provides a harmonic function whose gradient flow determines the correspondence trajectories going from one boundary to the other. The proposed method uses and expands upon two recently introduced techniques in order to compute thickness and correspondences based on these trajectories. Pairs of partial differential equations are efficiently computed within an Eulerian framework and combined with a Lagrangian approach so that correspondences trajectories are partially constructed when necessary. Examples are presented in order to compare the performance of this method with those of the pure Lagrangian and pure Eulerian approaches. Results show that the proposed technique takes advantage of both the speed of the Eulerian approach and the accuracy of the Lagrangian approach.

Cardiac motion analysis using nonlinear biomechanical constraints

Quantitative assessment of the motion and deformation variability of the heart has important implications for the understanding, diagnosis, and treatment of cardiac diseases. Various existing image-based approaches typically rely on linear constraining models which are however physically implausible. In this paper, we present a biomechnically constrained framework for the estimation of left ventricle deformation from medical image sequences using more realistic nonlinear geometry and material models. Once the myocardial boundaries and the sparse corresponding boundary points are derived from an active region model, we construct the cardiac dynamics where the left ventricle is modelled as an Mooney-Rivlin material undergoing large deformation. We then rely on the Newmark scheme to perform frame-to-frame estimation of the cardiac motion/deformation parameters. Experiments have been performed with 3D cardiac MR image sequences with very encouraging results.

LV Shape and Motion: B-Spline-Based Deformable Model and Sequential Motion Decomposition

In this paper, we extend a previous work by J. Park and propose a uniform framework to reconstruct left ventricle (LV) geometry/motion from tagged MR images. In our work, the LV is modeled as a generalized prolate spheroid, and its motion is decomposed into four components-global translation, polar radial/z-axis compression, twisting, and bending. By formulating model parameters as tensor products of B-splines, we develop efficient algorithms to quickly reconstruct LV geometry/motion from extracted boundary contours and tracked planar tags. Experiments on both synthesized and in vivo data are also reported.

An information fusion framework for robust shape tracking

Abstract-Existing methods for incorporating subspace model constraints in shape tracking use only partial information from the measurements and model distribution. We propose a unified framework for robust shape tracking, optimally fusing heteroscedastic uncertainties or noise from measurement, system dynamics, and a subspace model. The resulting nonorthogonal subspace projection and fusion are natural extensions of the traditional model constraint using orthogonal projection. We present two motion measurement algorithms and introduce alternative solutions for measurement uncertainty estimation. We build shape models offline from training data and exploit information from the ground truth initialization online through a strong model adaptation. Our framework is applied for tracking in echocardiograms where the motion estimation errors are heteroscedastic in nature, each heart has a distinct shape, and the relative motions of epicardial and endocardial borders reveal crucial diagnostic features. The proposed method significantly outperforms the existing shape-space-constrained tracking algorithm. Due to the complete treatment of heteroscedastic uncertainties, the strong model adaptation, and the coupled tracking of double-contours, robust performance is observed even on the most challenging cases.

Robust real-time myocardial border tracking for echocardiography: an information fusion approach

Ultrasound is a main noninvasive modality for the assessment of the heart function. Wall tracking from ultrasound data is, however, inherently difficult due to weak echoes, clutter, poor signal-to-noise ratio, and signal dropouts. To cope with these artifacts, pretrained shape models can be applied to constrain the tracking. However, existing methods for incorporating subspace shape constraints in myocardial border tracking use only partial information from the model distribution, and do not exploit spatially varying uncertainties from feature tracking. In this paper, we propose a complete fusion formulation in the information space for robust shape tracking, optimally resolving uncertainties from the system dynamics, heteroscedastic measurement noise, and subspace shape model. We also exploit information from the ground truth initialization where this is available. The new framework is applied for tracking of myocardial borders in very noisy echocardiography sequences. Numerous myocardium tracking experiments validate the theory and show the potential of very accurate wall motion measurements. The proposed framework outperforms the traditional shape-space-constrained tracking algorithm by a significant margin. Due to the optimal fusion of different sources of uncertainties, robust performance is observed even for the most challenging cases.

Stochastic finite element framework for simultaneous estimation of cardiac kinematic functions and material parameters

A stochastic finite element framework is presented for the simultaneous estimation of the cardiac kinematic functions and material model parameters from periodic medical image sequences. While existing biomechanics studies of the myocardial material constitutive laws have assumed known tissue kinematic measurements, and image analysis efforts on cardiac kinematic functions have relied on fixed constraining models of mathematical or mechanical nature, we illustrate through synthetic data that a probabilistic joint estimation strategy is needed to achieve more robust and accurate analysis of the kinematic functions and material parameters at the same time. For a particular a priori constraining material model with uncertain subject-dependent parameters and a posteriori noisy imaging based observations, our strategy combines the stochastic differential equations of the myocardial dynamics with the finite element method, and the material parameters and the imaging data are treated as random variables with known prior statistics. After the conversion to state space representation, the extended Kalman filtering procedures are adopted to linearize the equations and to provide the joint estimates in an approximate optimal sense. The estimation bias and convergence issues are addressed, and we conclude experimentally that it is possible to adopt this biomechanical model based multiframe estimation approach to achieve converged estimates because of the periodic nature of the cardiac dynamics. The effort is validated using synthetic data sequence with known kinematics and material parameters. Further, under linear elastic material model, estimation results using canine magnetic resonance phase contrast image sequences are presented, which are in very good agreement with histological tissue staining results, the current gold standards.

An Eulerian PDE approach for computing tissue thickness

We outline an Eulerian framework for computing the thickness of tissues between two simply connected boundaries that does not require landmark points or parameterizations of either boundary. Thickness is defined as the length of correspondence trajectories, which run from one tissue boundary to the other, and which follow a smooth vector field constructed in the region between the boundaries. A pair of partial differential equations (PDEs) that are guided by this vector field are then solved over this region, and the sum of their solutions yields the thickness of the tissue region. Unlike other approaches, this approach does not require explicit construction of any correspondence trajectories. An efficient, stable, and computationally fast solution to these PDEs is found by careful selection of finite differences according to an upwinding condition. The behavior and performance of our method is demonstrated on two simulations and two magnetic resonance imaging data sets in two and three dimensions. These experiments reveal very good performance and show strong potential for application in tissue thickness visualization and quantification.

Biomechanical dynamics of the heart with MRI

Magnetic resonance imaging (MRI) provides a noninvasive way to evaluate the biomechanical dynamics of the heart. MRI can provide spatially registered tomographic images of the heart in different phases of the cardiac cycle, which can be used to assess global cardiac function and regional endocardial surface motion. In addition, MRI can provide detailed information on the patterns of motion within the heart wall, permitting calculation of the evolution of regional strain and related motion variables within the wall. These show consistent patterns of spatial and temporal variation in normal subjects, which are affected by alterations of function due to disease. Although still an evolving technique, MRI shows promise as a new method for research and clinical evaluation of cardiac dynamics.

Estimation of 3-D left ventricular deformation from medical images using biomechanical models

The quantitative estimation of regional cardiac deformation from three-dimensional (3-D) image sequences has important clinical implications for the assessment of viability in the heart wall. We present here a generic methodology for estimating soft tissue deformation which integrates image-derived information with biomechanical models, and apply it to the problem of cardiac deformation estimation. The method is image modality independent. The images are segmented interactively and then initial correspondence is established using a shape-tracking approach. A dense motion field is then estimated using a transversely isotropic, linear-elastic model, which accounts for the muscle fiber directions in the left ventricle. The dense motion field is in turn used to calculate the deformation of the heart wall in terms of strain in cardiac specific directions. The strains obtained using this approach in open-chest dogs before and after coronary occlusion, exhibit a high correlation with strains produced in the same animals using implanted markers. Further, they show good agreement with previously published results in the literature. This proposed method provides quantitative regional 3-D estimates of heart deformation.

Model-based processing scheme for quantitative 4-D cardiac MRI analysis

In this paper, we present an integrated model-based processing scheme for cardiac magnetic resonance imaging (MRI), embedded in an interactive computing environment suitable for quantitative cardiac analysis, which provides a set of functions for the extraction, modeling, and visualization of cardiac shape and deformation. The methods apply four-dimensional (4-D) processing (three spatial and one temporal) to multiphase multislice MRI acquisitions and produce a continuous 4-D model of the myocardial surface deformation. The model is used to measure diagnostically useful parameters, such as wall motion, myocardial thicking, and myocardial mass measurements. The proposed model-based shape extraction method has the advantage of integrating local information into an overall representation and produces a robust description of cardiac cavities. A learning segmentation process that incorporates a generating-shrinking neural network is combined with a spatiotemporal parametric modeling method through functional basis decomposition. A multiscale approach is adopted, which uses at each step a coarse-scale model defined at the previous step in order to constrain the boundary detection. The representation accuracy starts from a coarse but smooth estimation of the approximate cardiac shape and is gradually increased to the desired detail. The main advantages of the proposed methods are efficiency, lack of uncertainty about convergence, and robustness to image artifacts. Experimental results obtained from application to clinical multislice multiphase MRI examinations of normal volunteers and patients with medical record of myocardial infarction were satisfactory in terms of accuracy and robustness.

A shape-space-based approach to tracking myocardial borders and quantifying regional left-ventricular function applied in echocardiography

This paper presents a new semi-automatic method for quantifying regional heart function from two-dimensional echocardiography. In the approach, we first track the endocardial and epicardial boundaries using a new variant of the dynamic snake approach. The tracked borders are then decomposed into clinically meaningful regional parameters, using a novel interpretational shape-space motivated by the 16-segment model used in clinical practice for qualitative assessment of heart function. We show how a quantitative and automatic scoring scheme for the endocardial excursion and myocardial thickening can be derived from this. Results illustrating our approach on apical long-axis two-chamber-view data from a patient with a myocardial infarct in the apical anterior/inferior region of the heart are presented. In a case study (five patients, nine data sets) the performance of the tracking and interpretation techniques are compared with manual delineations of borders using a number of quantitative measures of regional comparison.

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.

Fusion of physically-based registration and deformation modeling for nonrigid motion analysis

In our previous work, we used finite element models to determine nonrigid motion parameters and recover unknown local properties of objects given correspondence data recovered with snakes or other tracking models. In this paper, we present a novel multiscale approach to recovery of nonrigid motion from sequences of registered intensity and range images. The main idea of our approach is that a finite element (FEM) model incorporating material properties of the object can naturally handle both registration and deformation modeling using a single model-driving strategy. The method includes a multiscale iterative algorithm based on analysis of the undirected Hausdorff distance to recover correspondences. The method is evaluated with respect to speed and accuracy. Noise sensitivity issues are addressed. Advantages of the proposed approach are demonstrated using man-made elastic materials and human skin motion. Experiments with regular grid features are used for performance comparison with a conventional approach (separate snakes and FEM models). It is shown, however, that the new method does not require a sampling/correspondence template and can adapt the model to available object features. Usefulness of the method is presented not only in the context of tracking and motion analysis, but also for a burn scar detection application.

Three-dimensional transesophageal echocardiography (TEE) and other future directions

As faster imaging systems enter the market, three-dimensional echocardiography is gearing up to become a useful tool in assisting the clinician to image the heart in many innovative projections. What started out as a novel idea of displaying a three-dimensional anatomic picture of the heart now provides a multitude of views of the heart and its structures. Information gained from anatomic and dynamic data has helped clinicians and surgeons in making clinical decisions. In the future, this imaging modality may become a routine imaging modality for assessing cardiac pathology and may serve to increase understanding of the dynamics of the heart.

Quantitation of left-ventricular asynergy by cardiac ultrasound

The clinical evaluation of regional delays in myocardial motion (myocardial asynchrony) has proved problematic, yet it remains an important functional parameter to evaluate. Prior attempts to quantify regional asynergy have met with limited success, often thwarted by the low temporal resolution of imaging-system data acquisition. If a delay in onset of motion of 30-40 msec is clinically important to measure, then data acquisition at frame rates of 50-100 per second is required. This is out of the current temporal resolution of angiographic, nuclear, or magnetic resonance studies. Only cardiac ultrasound can currently achieve the necessary frame rates. Furthermore, quantitative studies into the accuracy with which a trained observer can identify computed regional myocardial asynchrony in a left-ventricular 2-dimensional (2-D) image have shown that regional delays of < 80 msec are not normally recognized in a moving image. This may be improved to 60 msec when either training is undertaken or comparative image review is used. However, this is still out of the temporal resolution required in clinical practice. Thus, visual interpretation of asynchrony is not sufficiently accurate. Two ultrasound data sets based on either integrated backscatter or Doppler myocardial imaging data may provide the solution. Doppler myocardial imaging is a new ultrasound technique which, in either its pulsed or color Doppler format, can achieve the required temporal resolution (with temporal resolutions of 8 msec and 16 msec, respectively). In contrast, color Doppler myocardial imaging, in its curved M-mode format, can display the timing of events during the cardiac cycle for all in-plane myocardial segments. This should allow the quantitation of regional delay for all systolic and diastolic events. Potentially, asynchrony due to regional ischemia, bundle branch block, ventricular premature beats, and ventricular preexcitation could all be identified and the degree of delay quantified. This overview will aim to establish the potential role of these new ultrasound methodologies in the recognition and quantitation of left-ventricular asynergy and how they might best be introduced into clinical practice.

A METHOD FOR INCREASING PRECISION AND RELIABILITY OF ELASTICITY ANALYSIS IN COMPLICATED BURN SCAR CASES

In this paper we propose a method for increasing precision and reliability of elasticity analysis in complicated burn scar cases. The need for a technique that would help physicians by objectively assessing elastic properties of scars, motivated our original algorithm. This algorithm successfully employed active contours for tracking and finite element models for strain analysis. However, the previous approach considered only one normal area and one abnormal area within the region of interest, and scar shapes which were somewhat simplified. Most burn scars have rather complicated shapes and may include multiple regions with different elastic properties. Hence, we need a method capable of adequately addressing these characteristics. The new method can split the region into more than two localities with different material properties, select and quantify abnormal areas, and apply different forces if it is necessary for a better shape description of the scar. The method also demonstrates the application of scale and mesh refinement techniques in this important domain. It is accomplished by increasing the number of Finite Element Method (FEM) areas as well as the number of elements within the area.

The method is successfully applied to elastic materials and real burn scar cases. We demonstrate all of the proposed techniques and investigate the behavior of elasticity function in a 3-D space. Recovered properties of elastic materials are compared with those obtained by a conventional mechanics-based approach. Scar ratings achieved with the method are correlated against the judgments of physicians.

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.

Shape-based nonrigid correspondence with application to heart motion analysis

A common problem in many biomedical imaging studies is that of finding a correspondence between two plane curves which aligns their shapes. A mathematical formulation and solutions to this problem is proposed in this paper. The formulation exhibits desirable properties. It allows for one-to-one as well as non-one-to-one correspondences, it consistently compares shape, even in nonrigid situations, and it is completely symmetric with respect to the two curves. A numerical implementation of the algorithm for finding the optimal correspondence is also reported. The algorithm is used to estimate nonrigid motion of the endocardium in MRI image sequences of normal and post-infarct dog hearts. The return error (the difference between the starting and ending positions of a point) is used as a performance measure to evaluate the technique. Since heart motion is periodic, the return error is a measure of consistency of the algorithm. Preliminary applications to other data sets are reported as well.

Computer evaluation of left ventricular wall motion by means of shape-based tracking and symbolic description

Relevant cardiac pathologies manifest themselves as abnormal movements of left ventricular (LV) myocardial wall. An objective quantification is usually accomplished by computer analysis of temporal sequences of LV contours, as obtained by angiography or echography. However the choice of the reference system for measuring motion is still open to discussion. Simple geometric models cannot deal with the non-uniform myocardial fibre structure, which gives rise to non-rigid movements, asynchronous even in normal subjects. Therefore, a new method, Curvature-Motion (CM), was developed for improving motion assessment. Since LV contour shape and position change smoothly throughout the cardiac cycle, the points of curvature extremes are tracked frame-to-frame and selected by exploiting physiologically-based assumptions; then, the points lying among these landmarks are mapped onto sequential contours, according to local displacements and curvature changes. In this way point-trajectories are allowed to be curvilinear and different in systole and diastole. CM gave no significant differences in estimating the known motion of computer-generated contours (R=0.88), unlike other methods commonly adopted (R<0.80). Moreover, for the evaluation of regional wall motion of a preclassified set of angiographic contours, CM showed a greater specificity (88%) and accuracy (90%) with respect to the centre-line method (respectively 83% and 87%). Finally, a fuzzy logic inference system is proposed for translating significant motion patterns from the quantitative form, as provided by the analysis method, into the linguistic terms used by cardiologists in their clinical examinations. This makes the interpretation of quantitative analysis easier and allows medical users to interact with the system for searching particular properties in a single clinical report as well as in a large database.

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.

Physical and geometrical modeling for image-based recovery of left ventricular deformation

Information about left ventricular (LV) mechanical performance is of critical importance in understanding the etiology of ischemic heart disease. Regional measurements derived from non-invasive imaging to assist in assessing this performance have been in use for decades, and certain parameters derived from these measurements often are useful clinically, as they correlate to some extent with gross physiological hypotheses. However, relatively little work has been done to date to carefully understand the relationship of regional myocardial injury to the local mechanical performance of the heart as derived from image data acquired non-invasively for a particular patient in 3 spatial dimensions over time. This paper describes efforts to take advantage of recent developments in 3D non-invasive imaging and biomechanical modeling to design an integrated computational platform capable of assembling a variety of displacement and velocity data derived from each image frame to deform a volumetric model representation of a portion of the myocardium. A brief description of the reasoning behind this strategy an overview of the approach and some initial results are described.

On-line analysis of echocardiographic image sequences

This paper presents a semiautomatic system for the interactive analysis of echocardiographic image sequences, able to provide useful information to cardiologists. The proposed approach combines well known techniques for the detection of left ventricular boundaries with the computation of optical flow. The initial detection of the cavity contour is based on an improved balloon model, with automatic tuning of parameters and optional model-based constraints. The computation of optical flow is performed with a fast correlation technique and the contour tracking is obtained combining motion information provided by the optical flow with model-based constraints and/or a snake-based regularization. The system is able to follow the motion of the ventricular boundaries precisely, to provide several quantitative features of the heartbeat and a dynamic representation of systolic and diastolic motion. Preliminary experimental results are presented and commented on with particular attention to their clinical relevance. Furthermore a distributed implementation of the system suitable for remote examination analysis has been realized and applied to echo images of the carotid artery.

A vision-based technique for objective assessment of burn scars

In this paper a method for the objective assessment of burn scars is proposed. The quantitative measures developed in this research provide an objective way to calculate elastic properties of burn scars relative to the surrounding areas. The approach combines range data and the mechanics and motion dynamics of human tissues. Active contours are employed to locate regions of interest and to find displacements of feature points using automatically established correspondences. Changes in strain distribution over time are evaluated. Given images at two time instances and their corresponding features, the finite element method is used to synthesize strain distributions of the underlying tissues. This results in a physically based framework for motion and strain analysis. Relative elasticity of the burn scar is then recovered using iterative descent search for the best nonlinear finite element model that approximates stretching behavior of the region containing the burn scar. The results from the skin elasticity experiments illustrate the ability to objectively detect differences in elasticity between normal and abnormal tissue. These estimated differences in elasticity are correlated against the subjective judgments of physicians that are presently the practice.