Computation of 3-D velocity fields from 3-D cine CT images of a human heart

SHAPE-REGULARIZED UNSUPERVISED LEFT VENTRICULAR MOTION NETWORK WITH SEGMENTATION CAPABILITY IN 3D+TIME ECHOCARDIOGRAPHY

Accurate motion estimation and segmentation of the left ventricle from medical images are important tasks for quantitative evaluation of cardiovascular health. Echocardiography offers a cost-efficient and non-invasive modality for examining the heart, but provides additional challenges for automated analyses due to the low signal-to-noise ratio inherent in ultrasound imaging. In this work, we propose a shape regularized convolutional neural network for estimating dense displacement fields between sequential 3D B-mode echocardiography images with the capability of also predicting left ventricular segmentation masks. Manually traced segmentations are used as a guide to assist in the unsupervised estimation of displacement between a source and a target image while also serving as labels to train the network to additionally predict segmentations. To enforce realistic cardiac motion patterns, a flow incompressibility term is also incorporated to penalize divergence. Our proposed network is evaluated on an in vivo canine 3D+t B-mode echocardiographic dataset. It is shown that the shape regularizer improves the motion estimation performance of the network and our overall model performs favorably against competing methods.

A Semi-supervised Joint Network for Simultaneous Left Ventricular Motion Tracking and Segmentation in 4D Echocardiography

This work presents a novel deep learning method to combine segmentation and motion tracking in 4D echocardiography. The network iteratively trains a motion branch and a segmentation branch. The motion branch is initially trained entirely unsupervised and learns to roughly map the displacements between a source and a target frame. The estimated displacement maps are then used to generate pseudo-ground truth labels to train the segmentation branch. The labels predicted by the trained segmentation branch are fed back into the motion branch and act as landmarks to help retrain the branch to produce smoother displacement estimations. These smoothed out displacements are then used to obtain smoother pseudo-labels to retrain the segmentation branch. Additionally, a biomechanically-inspired incompressibility constraint is implemented in order to encourage more realistic cardiac motion. The proposed method is evaluated against other approaches using synthetic and in-vivo canine studies. Both the segmentation and motion tracking results of our model perform favorably against competing methods.

3D Hermite Transform Optical Flow Estimation inLeft Ventricle CT Sequences

Heart diseases are the most important causes of death in the world and over the years, thestudy of cardiac movement has been carried out mainly in two dimensions, however, it is important toconsider that the deformations due to the movement of the heart occur in a three-dimensional space.The 3D + t analysis allows to describe most of the motions of the heart, for example, the twistingmotion that takes place on every beat cycle that allows us identifying abnormalities of the heartwalls. Therefore, it is necessary to develop algorithms that help specialists understand the cardiacmovement. In this work, we developed a new approach to determine the cardiac movement inthree dimensions using a differential optical flow approach in which we use the steered Hermitetransform (SHT) which allows us to decompose cardiac volumes taking advantage of it as a model ofthe human vision system (HVS). Our proposal was tested in complete cardiac computed tomography(CT) volumes ( 3D + t), as well as its respective left ventricular segmentation. The robustness tonoise was tested with good results. The evaluation of the results was carried out through errors inforwarding reconstruction, from the volume at time t to time t + 1 using the optical flow obtained(interpolation errors). The parameters were tuned extensively. In the case of the 2D algorithm, theinterpolation errors and normalized interpolation errors are very close and below the values reportedin ground truth flows. In the case of the 3D algorithm, the results were compared with another similarmethod in 3D and the interpolation errors remained below 0.1. These results of interpolation errorsfor complete cardiac volumes and the left ventricle are shown graphically for clarity. Finally, a seriesof graphs are observed where the characteristic of contraction and dilation of the left ventricle isevident through the representation of the 3D optical flow.

Flow network tracking for spatiotemporal and periodic point matching: Applied to cardiac motion analysis

The accurate quantification of left ventricular (LV) deformation/strain shows significant promise for quantitatively assessing cardiac function for use in diagnosis and therapy planning. However, accurate estimation of the displacement of myocardial tissue and hence LV strain has been challenging due to a variety of issues, including those related to deriving tracking tokens from images and following tissue locations over the entire cardiac cycle. In this work, we propose a point matching scheme where correspondences are modeled as flow through a graphical network. Myocardial surface points are set up as nodes in the network and edges define neighborhood relationships temporally. The novelty lies in the constraints that are imposed on the matching scheme, which render the correspondences one-to-one through the entire cardiac cycle, and not just two consecutive frames. The constraints also encourage motion to be cyclic, which an important characteristic of LV motion. We validate our method by applying it to the estimation of quantitative LV displacement and strain estimation using 8 synthetic and 8 open-chested canine 4D echocardiographic image sequences, the latter with sonomicrometric crystals implanted on the LV wall. We were able to achieve excellent tracking accuracy on the synthetic dataset and observed a good correlation with crystal-based strains on the in-vivo data.

An Optical Flow-Based Approach for Minimally Divergent Velocimetry Data Interpolation

Three-dimensional (3D) biomedical image sets are often acquired with in-plane pixel spacings that are far less than the out-of-plane spacings between images. The resultant anisotropy, which can be detrimental in many applications, can be decreased using image interpolation. Optical flow and/or other registration-based interpolators have proven useful in such interpolation roles in the past. When acquired images are comprised of signals that describe the flow velocity of fluids, additional information is available to guide the interpolation process. In this paper, we present an optical-flow based framework for image interpolation that also minimizes resultant divergence in the interpolated data.

Left and right ventricular hemodynamic forces in healthy volunteers and elite athletes assessed with 4D flow magnetic resonance imaging

Intracardiac blood flow is driven by hemodynamic forces that are exchanged between the blood and myocardium. Previous studies have been limited to 2D measurements or investigated only left ventricular (LV) forces. Right ventricular (RV) forces and their mechanistic contribution to asymmetric redirection of flow in the RV have not been measured. We therefore aimed to quantify 3D hemodynamic forces in both ventricles in a cohort of healthy subjects, using magnetic resonance imaging 4D flow measurements. Twenty five controls, 14 elite endurance athletes, and 2 patients with LV dyssynchrony were included. 4D flow data were used as input for the Navier-Stokes equations to compute hemodynamic forces over the entire cardiac cycle. Hemodynamic forces were found in a qualitatively consistent pattern in all healthy subjects, with variations in amplitude. LV forces were mainly aligned along the apical-basal longitudinal axis, with an additional component aimed toward the aortic valve during systole. Conversely, RV forces were found in both longitudinal and short-axis planes, with a systolic force component driving a slingshot-like acceleration that explains the mechanism behind the redirection of blood flow toward the pulmonary valve. No differences were found between controls and athletes when indexing forces to ventricular volumes, indicating that cardiac force expenditures are tuned to accelerate blood similarly in small and large hearts. Patients’ forces differed from controls in both timing and amplitude. Normal cardiac pumping is associated with specific force patterns for both ventricles, and deviation from these forces may be a sensitive marker of ventricular dysfunction. Reference values are provided for future studies.

NEW & NOTEWORTHY Biventricular hemodynamic forces were quantified for the first time in healthy controls and elite athletes (n = 39). Hemodynamic forces constitute a slingshot-like mechanism in the right ventricle, redirecting blood flow toward the pulmonary circulation. Force patterns were similar between healthy subjects and athletes, indicating potential utility as a cardiac function biomarker.

Sparsity and Biomechanics Inspired Integration of Shape and Speckle Tracking for Cardiac Deformation Analysis

Cardiac motion analysis, particularly of the left ventricle (LV), can provide valuable information regarding the functional state of the heart. We propose a strategy of combining shape tracking and speckle tracking based displacements to calculate the dense deformation field of the myocardium. We introduce the use and effects of l₁ regularization, which induces sparsity, in our integration method. We also introduce regularization to make the dense fields more adhering to cardiac biomechanics. Finally, we motivate the necessity of temporal coherence in the dense fields and demonstrate a way of doing so. We test our method on ultrasound (US) images acquired from six open-chested canine hearts. Baseline and post-occlusion strain results are presented for an animal, where we were able to detect significant change in the ischemic region. Six sets of strain results were also compared to strains obtained from tagged magnetic resonance (MR) data. Median correlation (with MR-tagging) coefficients of 0.73 and 0.82 were obtained for radial and circumferential strains respectively.

Strain analysis from 4-D cardiac CT image data

Strain is a discriminative parameter of regional myocardial dysfunction. Despite the large body of research on myocardial strain analysis in echocardiography and MR images, such techniques have not often been applied to cardiac CT data. Reasons for this include the challenges of sparse image deformation clues and the low temporal resolution. In the current study, we propose an algorithm that uses cardiac CT data to evaluate the mechanical function of the left ventricle. The algorithm is based on a deformable LV model that contains both the myocardium and the blood pool regions and that accounts for the elasticity and incompressibility of the myocardium with the rapid contraction of the blood pool. Our algorithm uses the image intensities of the trabeculle and papillary muscles as well as the border edges in an optical flow manner to extract the 3-D velocities. The resulting strains and rotational values derived from a set of normal patients correlate highly with values from the research literature. We validated our algorithm against 2-D speckle tracking analysis and against visual scores obtained by an expert. Our study shows that strain analysis using CT data can be used in clinical practice.

Relative accuracy of spin-image-based registration of partial capitate bones in 4DCT of the wrist

In image-based biomechanical analyses, registration transformations are the data of interest. In dynamic 4DCT imaging the capitate is often partially imaged. While alignment of incomplete objects poses a significant registration challenge, the established spin-image surface-matching algorithm can be utilized to align two surfaces representing disparate but overlapping portions of an object. For this reason the spin-image algorithm was chosen for the registration of partial bone geometry in 4DCT of the wrist. Registrations were performed on eleven 4DCT datasets using complete and partial capitate meshes generated by cropping complete meshes. Relative accuracy was assessed as the difference between partial- and complete-geometry registrations. Accurate registration of partial capitates geometry was achieved with 55% of the proximal capitate geometry on average, and in some cases as little as 35%. Requisite geometry depends on feature salience and imaging resolution, however the spin-image algorithm should be considered a valuable tool for biomechanists and image analysts.

Deformable image registration for temporal subtraction of chest radiographs

PURPOSE

Temporal subtraction images constructed from image registration can facilitate the visualization of pathologic changes. In this study, we propose a deformable image registration (DIR) framework for creating temporal subtraction images of chest radiographs.

METHODS

We developed a DIR methodology using two different image similarity metrics, varying flow (VF) and compressible flow (CF). The proposed registration method consists of block matching, filtering, and interpolation. Specifically, corresponding point pairs between reference and target images are initially determined by minimizing a nonlinear least squares formulation using grid-searching optimization. A two-step filtering process, including least median of squares filtering and backward matching filtering, is then applied to the estimated point matches in order to remove erroneous matches. Finally, moving least squares is used to generate a full displacement field from the filtered point pairs.

RESULTS

We applied the proposed DIR method to 10 pairs of clinical chest radiographs and compared it with the demons and B-spline algorithms using the five-point rating score method. The average quality scores were 2.7 and 3 for the demons and B-spline methods, but 3.5 and 4.1 for the VF and CF methods. In addition, subtraction images improved the visual perception of abnormalities in the lungs by using the proposed method.

CONCLUSION

The VF and CF models achieved a higher accuracy than the demons and the B-spline methods. Furthermore, the proposed methodology demonstrated the ability to create clinically acceptable temporal subtraction chest radiographs that enhance interval changes and can be used to detect abnormalities such as non-small cell lung cancer.

Radial basis functions for combining shape and speckle tracking in 4D echocardiography

Quantitative analysis of left ventricular deformation can provide valuable information about the extent of disease as well as the efficacy of treatment. In this work, we develop an adaptive multi-level compactly supported radial basis approach for deformation analysis in 3D+time echocardiography. Our method combines displacement information from shape tracking of myocardial boundaries (derived from B-mode data) with mid-wall displacements from radio-frequency-based ultrasound speckle tracking. We evaluate our methods on open-chest canines (N=8) and show that our combined approach is better correlated to magnetic resonance tagging-derived strains than either individual method. We also are able to identify regions of myocardial infarction (confirmed by postmortem analysis) using radial strain values obtained with our approach.

Quantification of smoothing requirement for 3D optic flow calculation of volumetric images

Complexities of dynamic volumetric imaging challenge the available computer vision techniques on a number of different fronts. This paper examines the relationship between the estimation accuracy and required amount of smoothness for a general solution from a robust statistics perspective. We show that a (surprisingly) small amount of local smoothing is required to satisfy both the necessary and sufficient conditions for accurate optic flow estimation. This notion is called "just enough" smoothing, and its proper implementation has a profound effect on the preservation of local information in processing 3D dynamic scans. To demonstrate the effect of "just enough" smoothing, a robust 3D optic flow method with quantized local smoothing is presented, and the effect of local smoothing on the accuracy of motion estimation in dynamic lung CT images is examined using both synthetic and real image sequences with ground truth.

A reference dataset for deformable image registration spatial accuracy evaluation using the COPDgene study archive

Landmark point-pairs provide a strategy to assess deformable image registration (DIR) accuracy in terms of the spatial registration of the underlying anatomy depicted in medical images. In this study, we propose to augment a publicly available database (www.dir-lab.com) of medical images with large sets of manually identified anatomic feature pairs between breath-hold computed tomography (BH-CT) images for DIR spatial accuracy evaluation. Ten BH-CT image pairs were randomly selected from the COPDgene study cases. Each patient had received CT imaging of the entire thorax in the supine position at one-fourth dose normal expiration and maximum effort full dose inspiration. Using dedicated in-house software, an imaging expert manually identified large sets of anatomic feature pairs between images. Estimates of inter- and intra-observer spatial variation in feature localization were determined by repeat measurements of multiple observers over subsets of randomly selected features. 7298 anatomic landmark features were manually paired between the 10 sets of images. Quantity of feature pairs per case ranged from 447 to 1172. Average 3D Euclidean landmark displacements varied substantially among cases, ranging from 12.29 (SD: 6.39) to 30.90 (SD: 14.05) mm. Repeat registration of uniformly sampled subsets of 150 landmarks for each case yielded estimates of observer localization error, which ranged in average from 0.58 (SD: 0.87) to 1.06 (SD: 2.38) mm for each case. The additions to the online web database (www.dir-lab.com) described in this work will broaden the applicability of the reference data, providing a freely available common dataset for targeted critical evaluation of DIR spatial accuracy performance in multiple clinical settings. Estimates of observer variance in feature localization suggest consistent spatial accuracy for all observers across both four-dimensional CT and COPDgene patient cohorts.

Four-Dimensional Image Reconstruction Strategies in Cardiac-Gated and Respiratory-Gated PET Imaging

Cardiac and respiratory movements pose significant challenges to image quality and quantitative accuracy in PET imaging. Cardiac and/or respiratory gating attempt to address this issue, but instead lead to enhanced noise levels. Direct four-dimensional (4D) PET image reconstruction incorporating motion compensation has the potential to minimize noise amplification while removing considerable motion blur. A wide-ranging choice of such techniques is reviewed in this work. Future opportunities and the challenges facing the adoption of 4D PET reconstruction and its role in basic and clinical research are also discussed.

Least median of squares filtering of locally optimal point matches for compressible flow image registration

Compressible flow based image registration operates under the assumption that the mass of the imaged material is conserved from one image to the next. Depending on how the mass conservation assumption is modeled, the performance of existing compressible flow methods is limited by factors such as image quality, noise, large magnitude voxel displacements, and computational requirements. The Least Median of Squares Filtered Compressible Flow (LFC) method introduced here is based on a localized, nonlinear least squares, compressible flow model that describes the displacement of a single voxel that lends itself to a simple grid search (block matching) optimization strategy. Spatially inaccurate grid search point matches, corresponding to erroneous local minimizers of the nonlinear compressible flow model, are removed by a novel filtering approach based on least median of squares fitting and the forward search outlier detection method. The spatial accuracy of the method is measured using ten thoracic CT image sets and large samples of expert determined landmarks (available at www.dir-lab.com). The LFC method produces an average error within the intra-observer error on eight of the ten cases, indicating that the method is capable of achieving a high spatial accuracy for thoracic CT registration.

Cardiac motion and deformation recovery from MRI: a review

Magnetic resonance imaging (MRI) is a highly advanced and sophisticated imaging modality for cardiac motion tracking and analysis, capable of providing 3D analysis of global and regional cardiac function with great accuracy and reproducibility. In the past few years, numerous efforts have been devoted to cardiac motion recovery and deformation analysis from MR image sequences. Many approaches have been proposed for tracking cardiac motion and for computing deformation parameters and mechanical properties of the heart from a variety of cardiac MR imaging techniques. In this paper, an updated and critical review of cardiac motion tracking methods including major references and those proposed in the past ten years is provided. The MR imaging and analysis techniques surveyed are based on cine MRI, tagged MRI, phase contrast MRI, DENSE, and SENC. This paper can serve as a tutorial for new researchers entering the field.

On the Usage of GPUs for Efficient Motion Estimation in Medical Image Sequences

Images are ubiquitous in biomedical applications from basic research to clinical practice. With the rapid increase in resolution, dimensionality of the images and the need for real-time performance in many applications, computational requirements demand proper exploitation of multicore architectures. Towards this, GPU-specific implementations of image analysis algorithms are particularly promising. In this paper, we investigate the mapping of an enhanced motion estimation algorithm to novel GPU-specific architectures, the resulting challenges and benefits therein. Using a database of three-dimensional image sequences, we show that the mapping leads to substantial performance gains, up to a factor of 60, and can provide near-real-time experience. We also show how architectural peculiarities of these devices can be best exploited in the benefit of algorithms, most specifically for addressing the challenges related to their access patterns and different memory configurations. Finally, we evaluate the performance of the algorithm on three different GPU architectures and perform a comprehensive analysis of the results.

Force estimation and prediction from time-varying density images

We present methods for estimating forces which drive motion observed in density image sequences. Using these forces, we also present methods for predicting velocity and density evolution. To do this, we formulate and apply a Minimum Energy Flow (MEF) method which is capable of estimating both incompressible and compressible flows from time-varying density images. Both the MEF and force-estimation techniques are applied to experimentally obtained density images, spanning spatial scales from micrometers to several kilometers. Using density image sequences describing cell splitting, for example, we show that cell division is driven by gradients in apparent pressure within a cell. Using density image sequences of fish shoals, we also quantify 1) intershoal dynamics such as coalescence of fish groups over tens of kilometers, 2) fish mass flow between different parts of a large shoal, and 3) the stresses acting on large fish shoals.

Pulmonary kinematics from image data: a review

The effects of certain lung pathologies include alterations in lung physiology negatively affecting pulmonary compliance. Current approaches to diagnosis and treatment assessment of lung disease commonly rely on pulmonary function testing. Such testing is limited to global measures of lung function, neglecting regional measurements, which are critical for early diagnosis and localization of disease. Increased accessibility to medical image acquisition strategies with high spatiotemporal resolution coupled with the development of sophisticated intensity-based and geometric registration techniques has resulted in the recent exploration of modeling pulmonary motion for calculating local measures of deformation. In this review, the authors provide a broad overview of such research efforts for the estimation of pulmonary deformation. This includes discussion of various techniques, current trends in validation approaches, and the public availability of software and data resources.

Quantitative study of cardiac motion estimation and abnormality classification in emission computed tomography

Quantitative description of cardiac motion is desirable to assist in detecting myocardial abnormalities from gated myocardial perfusion (GMP) emission computed tomography (ECT) images. While "optical flow" type of cardiac motion estimation (ME) techniques have been developed in the past, there has been no quantitative evaluation of their performance. Moreover, no investigation has been performed in terms of applying an ME technique to quantify cardiac motion abnormalities. Using the four-dimensional NCAT beating heart phantom with known built-in motion, the current work aimed at addressing the aforementioned two issues. A three-dimensional cardiac ME technique was developed to search for a motion vector field (MVF) that establishes voxel-by-voxel correspondence between two GMP ECT images. The weighted myocardial strain energy served as the constraint in the process to minimize the difference between one intensity image and the MVF warped other. We studied the convergence of the ME technique using different initial estimates and cost functions. The dependence of estimated MVF on the initialization was attributed to the tangential motion that is undetectable while not suppressed by the strain energy constraint. We optimized the strain energy constraint weighting using noise-free phantom images and noisy reconstructed images, the former against the known MVF and the later in the task of regional motion classification. While the results from the above two studies well coincide with each other, we also demonstrated that upon appropriate optimization the ME method has the capability of serving as a computer motion observer in separating simulated noisy reconstructed GMP SPECT images corresponding to hearts with and without regional motion abnormalities.

Robust processing of optical flow of fluids

This paper proposes a new approach, coupling physical models and image estimation techniques, for modelling the movement of fluids. The fluid flow is characterized by turbulent movement and dynamically changing patterns which poses challenges to existing optical flow estimation methods. The proposed methodology, which relies on Navier-Stokes equations, is used for processing fluid optical flow by using a succession of stages such as advection, diffusion and mass conservation. A robust diffusion step jointly considering the local data geometry and its statistics is embedded in the proposed framework. The diffusion kernel is Gaussian with the covariance matrix defined by the local second derivatives. Such an anisotropic kernel is able to implicitly detect changes in the vector field orientation and to diffuse accordingly. A new approach is developed for detecting fluid flow structures such as vortices. The proposed methodology is applied on artificially generated vector fields as well as on various image sequences.

Comparison of 3D OS-EM and 4D MAP-RBI-EM reconstruction algorithms for cardiac motion abnormality classification using a motion observer

Using a heart motion observer, we compared the performance of two image reconstruction techniques, a 3D OS-EM algorithm with post Butterworth spatial filtering and a 4D MAP-RBI-EM algorithm. The task was to classify gated myocardial perfusion (GMP) SPECT images of beating hearts with or without regional motion abnormalities. Noise-free simulated GMP SPECT projection data was generated from two 4D NCAT beating heart phantom models, one with normal motion and the other with a 50% motion defect in a pie-shaped wedge region-of-interest (ROI) in the anterior-lateral left ventricular wall. The projection data were scaled to clinical GMP SPECT count level before Poisson noise was simulated to generate 40 noise realizations. The noise-free and noisy projection data were reconstructed using the two reconstruction algorithms, parameters chosen to optimize the tradeoff between image bias and noise. As a motion observer, a 3D motion estimation method previously developed was applied to estimate the radial motion on the ROI from two adjacent gates. The receiver operating characteristic (ROC) curves were computed for radial motion magnitudes corresponding to each reconstruction technique. The area under the ROC curve (AUC) was calculated as an index for classification of regional motion. The reconstructed images with better bias and noise tradeoff were found to offer better classification for hearts with or without regional motion defects. The 3D cardiac motion estimation algorithm, serving as a heart motion observer, was better able to distinguish the abnormal from the normal regional motion in GMP SPECT images obtained from the 4D MAP-RBI-EM algorithm than from the 3D OS-EM algorithm with post Butterworth spatial filtering.

Four-dimensional deformable image registration using trajectory modeling

A four-dimensional deformable image registration (4D DIR) algorithm, referred to as 4D local trajectory modeling (4DLTM), is presented and applied to thoracic 4D computed tomography (4DCT) image sets. The theoretical framework on which this algorithm is built exploits the incremental continuity present in 4DCT component images to calculate a dense set of parameterized voxel trajectories through space as functions of time. The spatial accuracy of the 4DLTM algorithm is compared with an alternative registration approach in which component phase to phase (CPP) DIR is utilized to determine the full displacement between maximum inhale and exhale images. A publically available DIR reference database (http://www.dir-lab.com) is utilized for the spatial accuracy assessment. The database consists of ten 4DCT image sets and corresponding manually identified landmark points between the maximum phases. A subset of points are propagated through the expiratory 4DCT component images. Cubic polynomials were found to provide sufficient flexibility and spatial accuracy for describing the point trajectories through the expiratory phases. The resulting average spatial error between the maximum phases was 1.25 mm for the 4DLTM and 1.44 mm for the CPP. The 4DLTM method captures the long-range motion between 4DCT extremes with high spatial accuracy.

Estimating Myocardial Motion by 4D Image Warping

A method for spatio-temporally smooth and consistent estimation of cardiac motion from MR cine sequences is proposed. Myocardial motion is estimated within a 4-dimensional (4D) registration framework, in which all 3D images obtained at different cardiac phases are simultaneously registered. This facilitates spatio-temporally consistent estimation of motion as opposed to other registration-based algorithms which estimate the motion by sequentially registering one frame to another. To facilitate image matching, an attribute vector (AV) is constructed for each point in the image, and is intended to serve as a "morphological signature" of that point. The AV includes intensity, boundary, and geometric moment invariants (GMIs). Hierarchical registration of two image sequences is achieved by using the most distinctive points for initial registration of two sequences and gradually adding less-distinctive points to refine the registration. Experimental results on real data demonstrate good performance of the proposed method for cardiac image registration and motion estimation. The motion estimation is validated via comparisons with motion estimates obtained from MR images with myocardial tagging.

Characterization of 3-D coronary tree motion from MSCT angiography

This paper describes a method for the characterization of coronary artery motion using multislice computed tomography (MSCT) volume sequences. Coronary trees are first extracted by a spatial vessel tracking method in each volume of MSCT sequence. A point-based matching algorithm, with feature landmarks constraint, is then applied to match the 3-D extracted centerlines between two consecutive instants over a complete cardiac cycle. The transformation functions and correspondence matrices are estimated simultaneously, and allow deformable fitting of the vessels over the volume series. Either point-based or branch-based motion features can be derived. Experiments have been conducted in order to evaluate the performance of the method with a matching error analysis.

4D MAP image reconstruction incorporating organ motion

Four-dimensional respiratory correlated computed tomography (4D RCCT) has been widely used for studying organ motion. Most current algorithms use binning techniques which introduce artifacts that can seriously hamper quantitative motion analysis. In this paper, we develop an algorithm for tracking organ motion which uses raw time-stamped data and simultaneously reconstructs images and estimates deformations in anatomy. This results in a reduction of artifacts and an increase in signal-to-noise ratio (SNR). In the case of CT, the increased SNR enables a reduction in dose to the patient during scanning. This framework also facilitates the incorporation of fundamental physical properties of organ motion, such as the conservation of local tissue volume. We show in this paper that this approach is accurate and robust against noise and irregular breathing for tracking organ motion. A detailed phantom study is presented, demonstrating accuracy and robustness of the algorithm. An example of applying this algorithm to real patient image data is also presented, demonstrating the utility of the algorithm in reducing artifacts.

Incompressible cardiac motion estimation of the left ventricle using tagged MR images

Interpolation from sparse imaging data is typically required to achieve dense, three-dimensional quantification of left ventricular function. Although the heart muscle is known to be incompressible, this fact is ignored by most previous approaches that address this problem. In this paper, we present a method to reconstruct a dense representation of the three-dimensional, incompressible deformation of the left ventricle from tagged MR images acquired in both short-axis and long axis orientations. The approach applies a smoothing, divergence-free, vector spline to interpolate velocity fields at intermediate discrete times such that the collection of velocity fields integrate over time to match the observed displacement components. Through this process, the method yields a dense estimate of a displacement field that matches our observations and also corresponds to an incompressible motion.

A geometry-driven optical flow warping for spatial normalization of cortical surfaces

Spatial normalization is frequently used to map data to a standard coordinate system by removing intersubject morphological differences, thereby allowing for group analysis to be carried out. The work presented in this paper is motivated by the need for an automated cortical surface normalization technique that will automatically identify homologous cortical landmarks and map them to the same coordinates on a standard manifold. The geometry of a cortical surface is analyzed using two shape measures that distinguish the sulcal and gyral regions in a multiscale framework. A multichannel optical flow warping procedure aligns these shape measures between a reference brain and a subject brain, creating the desired normalization. The partial differential equation that carries out the warping is implemented in a Euclidean framework in order to facilitate a multiresolution strategy, thereby permitting large deformations between the two surfaces. The technique is demonstrated by aligning 33 normal cortical surfaces and showing both improved structural alignment in manually labeled sulci and improved functional alignment in positron emission tomography data mapped to the surfaces. A quantitative comparison between our proposed surface-based spatial normalization method and a leading volumetric spatial normalization method is included to show that the surface-based spatial normalization performs better in matching homologous cortical anatomies.

Motion estimation for cardiac emission tomography by optical flow methods

This paper describes a new method for estimating the 3D, non-rigid object motion in a time sequence of images. The method is a generalization of a standard optical flow algorithm that is incorporated into a successive quadratic approximation framework. The method was evaluated for gated cardiac emission tomography using images obtained from a mathematical, 4D phantom and a physical, dynamic phantom. The results showed that the proposed method offers improved motion estimation accuracy relative to the standard optical flow method. Convergence of the proposed algorithm was evidenced with a monotonically decreasing objective function value with iteration. Practical application of the motion estimation method in cardiac emission tomography includes quantitative myocardial motion estimation and 4D, motion-compensated image reconstruction.

Haptic rendering of dynamic volumetric data

With current methods for volume haptics in scientific visualization, features in time-varying data can freely move straight through the haptic probe without generating any haptic feedback the algorithms are simply not designed to handle variation with time but consider only the instantaneous configuration when the haptic feedback is calculated. This article introduces haptic rendering of dynamic volumetric data to provide a means for haptic exploration of dynamic behaviour in volumetric data. We show how haptic feedback can be produced that is consistent with volumetric data moving within the virtual environment and with data that, in itself, evolves over time. Haptic interaction with time-varying data is demonstrated by allowing palpation of a CT sequence of a beating human heart.

Motion compensated fan-beam reconstruction for nonrigid transformation

We develop an approximate fan-beam algorithm to reconstruct an object with time-dependent nonrigid transformation such as the heart. The method is in the form of derivative backprojection filtering with compensation of affine transformations on a local basis. Computer simulations showed the proposed method significantly reduces image artifact due to nonrigid motion. Therefore, with very little motion artifact, the proposed method allowed us to reconstruct images from projections over about one motion cycle, resulting in reduced image noise level down to 40% of the current level.

Cortical surface alignment using geometry driven multispectral optical flow

Spatial normalization is frequently used to map data to a standard coordinate system by removing inter-subject morphological differences, thereby allowing for group analysis to be carried out. In this paper, we analyze the geometry of the cortical surface using two shape measures that are the key to distinguish sulcal and gyral regions from each other. Then a multispectral optical flow (OF) warping procedure that aims to align the shape measure maps of an atlas and a subject brain's normalized maps is described. The variational problem to estimate the OF field is solved using a Euclidean framework. After warping one brain given the OF result, we obtain a better structural and functional alignment across multiple brains.

Estimation of images and nonrigid deformations in gated emission CT

In this paper, we propose and test a new iterative algorithm to simultaneously estimate the nonrigid motion vector fields and the emission images for a complete cardiac cycle in gated cardiac emission tomography. We model the myocardium as an elastic material whose motion does not generate large amounts of strain. As a result, our method is based on minimizing an objective function consisting of the negative logarithm of a maximum likelihood image reconstruction term, the standard biomechanical model of strain energy, and an image matching term that ensures a measure of agreement of intensities between frames. Simulations are obtained using data for the four-dimensional (4-D) NCAT phantom. The data models realistic noise levels in a typical gated myocardial perfusion SPECT study. We show that our simultaneous algorithm produces images with improved spatial resolution characteristics and noise properties compared with those obtained from postsmoothed 4-D maximum likelihood methods. The simulations also demonstrate improved motion estimates over motion estimation using independently reconstructed images.

Assessment of Left Ventricular Function in Cardiac MSCT Imaging by a 4D Hierarchical Surface-Volume Matching Process

Multislice computed tomography (MSCT) scanners offer new perspectives for cardiac kinetics evaluation with 4D dynamic sequences of high contrast and spatiotemporal resolutions. A new method is proposed for cardiac motion extraction in multislice CT. Based on a 4D hierarchical surface-volume matching process, it provides the detection of the heart left cavities along the acquired sequence and the estimation of their 3D surface velocity fields. A Markov random field model is defined to find, according to topological descriptors, the best correspondences between a 3D mesh describing the left endocardium at one time and the 3D acquired volume at the following time. The global optimization of the correspondences is realized with a multiresolution process. Results obtained on simulated and real data show the capabilities to extract clinically relevant global and local motion parameters and highlight new perspectives in cardiac computed tomography imaging.

Elastic image mapping for 4-D dose estimation in thoracic radiotherapy

PURPOSE

Demonstrate the path integration of a four-dimensional (4-D) dose distribution onto the 3-D anatomy.

MATERIALS AND METHODS

A computer-generated 4-D thoracic phantom with a lung tumour was constructed. Eight respiratory phases were generated. A radiotherapy treatment plan was applied to all the phases resulting in a 4-D dose distribution. An elastic image registration algorithm was used to find the vector displacement between all the image elements and the end expiration phase. The path-integrated tissue dose distribution and each component dose distribution were compared with the planned dose distribution.

RESULTS

Numerical path integration was performed to calculate the tissue dose distribution. Loss of tumour coverage was the predominant effect observed with tumour motion in this study. The loss was asymmetric and dependent on the tumour trajectory.

CONCLUSION

The elastic image registration allowed an accurate path integration through a 4-D data set to produce an accurate 3-D tissue dose estimate.

Consistent Estimation of Cardiac Motions by 4D Image Registration

A 4D image registration method is proposed for consistent estimation of cardiac motion from MR image sequences. Under this 4D registration framework, all 3D cardiac images taken at different time-points are registered simultaneously, and motion estimated is enforced to be spatiotemporally smooth, thereby overcoming potential limitations of some methods that typically estimate cardiac deformation sequentially from one frame to another, instead of treating the entire set of images as a 4D volume. To facilitate our image matching process, an attribute vector is designed for each point in the image to include intensity, boundary and geometric moment invariants (GMIs). Hierarchical registration of two image sequences is achieved by using the most distinctive points for initial registration of two sequences and gradually adding less-distinctive points for refinement of registration. Experimental results on real data demonstrate good performance of the proposed method in registering cardiac images and estimating motions from cardiac image sequences.

Intrathoracic tumour motion estimation from CT imaging using the 3D optical flow method

The purpose of this work was to develop and validate an automated method for intrathoracic tumour motion estimation from breath-hold computed tomography (BH CT) imaging using the three-dimensional optical flow method (3D OFM). A modified 3D OFM algorithm provided 3D displacement vectors for each voxel which were used to map tumour voxels on expiration BH CT onto inspiration BH CT images. A thoracic phantom and simulated expiration/inspiration BH CT pairs were used for validation. The 3D OFM was applied to the measured inspiration and expiration BH CT images from one lung cancer and one oesophageal cancer patient. The resulting displacements were plotted in histogram format and analysed to provide insight regarding the tumour motion. The phantom tumour displacement was measured as 1.20 and 2.40 cm with full-width at tenth maximum (FWTM) for the distribution of displacement estimates of 0.008 and 0.006 cm, respectively. The maximum error of any single voxel's motion estimate was 1.1 mm along the z-dimension or approximately one-third of the z-dimension voxel size. The simulated BH CT pairs revealed an rms error of less than 0.25 mm. The displacement of the oesophageal tumours was nonuniform and up to 1.4 cm, this was a new finding. A lung tumour maximum displacement of 2.4 cm was found in the case evaluated. In conclusion, 3D OFM provided an accurate estimation of intrathoracic tumour motion, with estimated errors less than the voxel dimension in a simulated motion phantom study. Surprisingly, oesophageal tumour motion was large and nonuniform, with greatest motion occurring at the gastro-oesophageal junction.

Regularization of flow streamlines in multislice phase-contrast MR imaging

Magnetic resonance angiography (MRA) has become an important tool for the clinical evaluation of vascular disease. Flow measurement with phase-contrast (PC) magnetic resonance (MR) imaging provides a powerful method for evaluation of blood velocity information inside vessels. However, image artifacts from complex flow patterns including slow flow, recirculation zone, and pulsatile flow can adversely affect accuracy of results. In this paper, we introduce a new numerical formulation for improving the accuracy of PC velocity fields and corresponding streamlines, based on a physical constraint from fluid dynamics, within a regularization framework. The formulation which makes use of a stream function, automatically enforces continuity constraint of incompressible flow and reconstructs the flow streamlines from PC images. We applied the algorithm to complex MR imaging flow velocities obtained in a flow phantom of an axisymmetric abdominal aortic aneurysm. The algorithm significantly improved streamline results especially inside the recirculation zone, where artifacts are more pronounced. A velocity reconstruction method in primitive variable form is also presented and results are compared with the stream function method. In order to validate flow characteristics derived from PC MR images, we used the FLUENT computational fluid dynamics software package, to simulate flow patterns within the same geometry as our phantom. There was a good agreement between the numerical simulations and recovered PC streamline results. Processed streamlines, in both stream function and primitive variable methods, were more realistic and provided more precise flow patterns than unprocessed PC data. Additionally, the feasibility of the method was demonstrated in the aorta of a normal volunteer.