Robust Cardiac Motion Estimation using Ultrafast Ultrasound Data: A Low-Rank-Topology-Preserving Approach

Cardiac motion estimation is an important diagnostic tool to detect heart diseases and it has been explored with modalities such as MRI and conventional ultrasound (US) sequences. US cardiac motion estimation still presents challenges because of the complex motion patterns and the presence of noise. In this work, we propose a novel approach to estimate the cardiac motion using ultrafast ultrasound data. -- Our solution is based on a variational formulation characterized by the L2-regularized class. The displacement is represented by a lattice of b-splines and we ensure robustness by applying a maximum likelihood type estimator. While this is an important part of our solution, the main highlight of this paper is to combine a low-rank data representation with topology preservation. Low-rank data representation (achieved by finding the k-dominant singular values of a Casorati Matrix arranged from the data sequence) speeds up the global solution and achieves noise reduction. On the other hand, topology preservation (achieved by monitoring the Jacobian determinant) allows to radically rule out distortions while carefully controlling the size of allowed expansions and contractions. Our variational approach is carried out on a realistic dataset as well as on a simulated one. We demonstrate how our proposed variational solution deals with complex deformations through careful numerical experiments. While maintaining the accuracy of the solution, the low-rank preprocessing is shown to speed up the convergence of the variational problem. Beyond cardiac motion estimation, our approach is promising for the analysis of other organs that experience motion.Comment: 15 pages, 10 figures, Physics in Medicine and Biology, 201

Analysis of myocardial motion using generalized spline models and tagged magnetic resonance images

Heart wall motion abnormalities are the very sensitive indicators of common heart diseases, such as myocardial infarction and ischemia. Regional strain analysis is especially important in diagnosing local abnormalities and mechanical changes in the myocardium. In this work, we present a complete method for the analysis of cardiac motion and the evaluation of regional strain in the left ventricular wall. The method is based on the generalized spline models and tagged magnetic resonance images (MRI) of the left ventricle. The whole method combines dynamical tracking of tag deformation, simulating cardiac movement and accurately computing the regional strain distribution. More specifically, the analysis of cardiac motion is performed in three stages. Firstly, material points within the myocardium are tracked over time using a semi-automated snake-based tag tracking algorithm developed for this purpose. This procedure is repeated in three orthogonal axes so as to generate a set of one-dimensional sample measurements of the displacement field. The 3D-displacement field is then reconstructed from this sample set by using a generalized vector spline model. The spline reconstruction of the displacement field is explicitly expressed as a linear combination of a spline kernel function associated with each sample point and a polynomial term. Finally, the strain tensor (linear or nonlinear) with three direct components and three shear components is calculated by applying a differential operator directly to the displacement function. The proposed method is computationally effective and easy to perform on tagged MR images. The preliminary study has shown potential advantages of using this method for the analysis of myocardial motion and the quantification of regional strain

Modelling mitral valvular dynamics–current trend and future directions

Dysfunction of mitral valve causes morbidity and premature mortality and remains a leading medical problem worldwide. Computational modelling aims to understand the biomechanics of human mitral valve and could lead to the development of new treatment, prevention and diagnosis of mitral valve diseases. Compared with the aortic valve, the mitral valve has been much less studied owing to its highly complex structure and strong interaction with the blood flow and the ventricles. However, the interest in mitral valve modelling is growing, and the sophistication level is increasing with the advanced development of computational technology and imaging tools. This review summarises the state-of-the-art modelling of the mitral valve, including static and dynamics models, models with fluid-structure interaction, and models with the left ventricle interaction. Challenges and future directions are also discussed

On motion in dynamic magnetic resonance imaging: Applications in cardiac function and abdominal diffusion

La imagen por resonancia magnética (MRI), hoy en día, representa una potente herramienta para el diagnóstico clínico debido a su flexibilidad y sensibilidad a un amplio rango de propiedades del tejido. Sus principales ventajas son su sobresaliente versatilidad y su capacidad para proporcionar alto contraste entre tejidos blandos. Gracias a esa versatilidad, la MRI se puede emplear para observar diferentes fenómenos físicos dentro del cuerpo humano combinando distintos tipos de pulsos dentro de la secuencia. Esto ha permitido crear distintas modalidades con múltiples aplicaciones tanto biológicas como clínicas. La adquisición de MR es, sin embargo, un proceso lento, lo que conlleva una solución de compromiso entre resolución y tiempo de adquisición (Lima da Cruz, 2016; Royuela-del Val, 2017). Debido a esto, la presencia de movimiento fisiológico durante la adquisición puede conllevar una grave degradación de la calidad de imagen, así como un incremento del tiempo de adquisición, aumentando así tambien la incomodidad del paciente. Esta limitación práctica representa un gran obstáculo para la viabilidad clínica de la MRI. En esta Tesis Doctoral se abordan dos problemas de interés en el campo de la MRI en los que el movimiento fisiológico tiene un papel protagonista. Éstos son, por un lado, la estimación robusta de parámetros de rotación y esfuerzo miocárdico a partir de imágenes de MR-Tagging dinámica para el diagnóstico y clasificación de cardiomiopatías y, por otro, la reconstrucción de mapas del coeficiente de difusión aparente (ADC) a alta resolución y con alta relación señal a ruido (SNR) a partir de adquisiciones de imagen ponderada en difusión (DWI) multiparamétrica en el hígado.Departamento de Teoría de la Señal y Comunicaciones e Ingeniería TelemáticaDoctorado en Tecnologías de la Información y las Telecomunicacione

Phenomenological model of diffuse global and regional atrophy using finite-element methods

The main goal of this work is the generation of ground-truth data for the validation of atrophy measurement techniques, commonly used in the study of neurodegenerative diseases such as dementia. Several techniques have been used to measure atrophy in cross-sectional and longitudinal studies, but it is extremely difficult to compare their performance since they have been applied to different patient populations. Furthermore, assessment of performance based on phantom measurements or simple scaled images overestimates these techniques' ability to capture the complexity of neurodegeneration of the human brain. We propose a method for atrophy simulation in structural magnetic resonance (MR) images based on finite-element methods. The method produces cohorts of brain images with known change that is physically and clinically plausible, providing data for objective evaluation of atrophy measurement techniques. Atrophy is simulated in different tissue compartments or in different neuroanatomical structures with a phenomenological model. This model of diffuse global and regional atrophy is based on volumetric measurements such as the brain or the hippocampus, from patients with known disease and guided by clinical knowledge of the relative pathological involvement of regions and tissues. The consequent biomechanical readjustment of structures is modelled using conventional physics-based techniques based on biomechanical tissue properties and simulating plausible tissue deformations with finite-element methods. A thermoelastic model of tissue deformation is employed, controlling the rate of progression of atrophy by means of a set of thermal coefficients, each one corresponding to a different type of tissue. Tissue characterization is performed by means of the meshing of a labelled brain atlas, creating a reference volumetric mesh that will be introduced to a finite-element solver to create the simulated deformations. Preliminary work on the simulation of acquisition artefa- - cts is also presented. Cross-sectional and

Analysis of cardiac motion using MRI and nonrigid image registration

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MR imaging of left-ventricular function : novel image acquisition and analysis techniques.

Many cardiac diseases, such as myocardial ischemia, secondary to coronary artery disease, may be identified and localized through the analysis of cardiac deformations. Early efforts for quantifying ventricular wall motion used surgical implantation and tracking of radiopaque markers with X-ray imaging in canine hearts [1]. Such techniques are invasive and affect the regional motion pattern of the ventricular wall during the marker tracking process and, clearly are not feasible clinically. Noninvasive imaging techniques are vital and have been widely applied to the clinic. MRI is a noninvasive imaging technique with the capability to monitor and assess the progression of cardiovascular diseases (CVD) so that effective procedures for the care and treatment of patients can be developed by physicians and researchers. It is 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 imaging sequences. In order to assess cardiac function, there are two categories of indices that are used: global and regional indices. Global indices include ejection fraction, cavity volume, and myocardial mass [2]. They are important indices for cardiac disease diagnosis. However, these global indices are not specific for regional analysis. A quantitative assessment of regional parameters may prove beneficial for the diagnosis of disease and evaluation of severity and the quantification of treatment [3]. Local measures, such as wall deformation and strain in all regions of the heart, can provide objective regional quantification of ventricular wall function and relate to the location and extent of ischemic injury. This dissertation is concerned with the development of novel MR imaging techniques and image postprocessing algorithms to analyze left ventricular deformations. A novel pulse sequence, termed Orthogonal CSPAMM (OCSPAMM), has been proposed which results in the same acquisition time as SPAMM for 2D deformation estimation while keeping the main advantages of CSPAMM [4,5]: i.e., maintaining tag contrast through-out the ECG cycle. Different from CSPAMM, in OCSPAMM the second tagging pulse orientation is rotated 90 degrees relative to the first one so that motion information can be obtained simultaneously in two directions. This reduces the acquisition time by a factor of two as compared to the traditional CSPAMM, in which two separate imaging sequences are applied per acquisition. With the application of OCSPAMM, the effect of tag fading encountered in SPAMM tagging due to Tl relaxation is mitigated and tag deformations can be visualized for the entire cardiac cycle, including diastolic phases. A multilevel B-spline fitting method (MBS) has been proposed which incorporates phase-based displacement information for accurate calculation of 2D motion and strain from tagged MRI [6, 7]. The proposed method combines the advantages of continuity and smoothness of MBS, and makes use of phase information derived from tagged MR images. Compared to previous 2D B-spline-based deformation analysis methods, MBS has the following advantages: 1) It can simultaneously achieve a smooth deformation while accurately approximating the given data set; 2) Computationally, it is very fast; and 3) It can produce more accurate deformation results. Since the tag intersections (intersections between two tag lines) can be extracted accurately and are more or less distributed evenly over the myocardium, MBS has proven effective for 2D cardiac motion tracking. To derive phase-based displacements, 2D HARP and SinMod analysis techniques [8,9] were employed. By producing virtual tags from HARP /SinMod and calculating intersections of virtual tag lines, more data points are obtained. In the reference frame, virtual tag lines are the isoparametric curves of an undeformed 2D B-spline model. In subsequent frames, the locations of intersections of virtual tag lines over the myocardium are updated with phase-based displacement. The advantage of the technique is that in acquiring denser myocardial displacements, it uses both real and virtual tag line intersections. It is fast and more accurate than 2D HARP and SinMod tracking. A novel 3D sine wave modeling (3D SinMod) approach for automatic analysis of 3D cardiac deformations has been proposed [10]. An accelerated 3D complementary spatial modulation of magnetization (CSPAMM) tagging technique [11] was used to acquire complete 3D+t tagged MR data sets of the whole heart (3 dynamic CSPAMM tagged MRI volume with tags in different orientations), in-vivo, in 54 heart beats and within 3 breath-holds. In 3D SinMod, the intensity distribution around each pixel is modeled as a cosine wave front. The principle behind 3D SinMod tracking is that both phase and frequency for each voxel are determined directly from the frequency analysis and the displacement is calculated from the quotient of phase difference and local frequency. The deformation fields clearly demonstrate longitudinal shortening during systole. The contraction of the LV base towards the apex as well as the torsional motion between basal and apical slices is clearly observable from the displacements. 3D SinMod can automatically process the image data to derive measures of motion, deformations, and strains between consecutive pair of tagged volumes in 17 seconds. Therefore, comprehensive 4D imaging and postprocessing for determination of ventricular function is now possible in under 10 minutes. For validation of 3D SinMod, 7 3D+t CSPAMM data sets of healthy subjects have been processed. Comparison of mid-wall contour deformations and circumferential shortening results by 3D SinMod showed good agreement with those by 3D HARP. Tag lines tracked by the proposed technique were also compared with manually delineated ones. The average errors calculated for the systolic phase of the cardiac cycles were in the sub-pixel range

Full Motion and Flow Field Recovery from Echo Doppler Data

We present a new computational method for reconstructing a vector velocity field from scattered, pulsed-wave ultrasound Doppler data. The main difficulty is that the Doppler measurements are incomplete, for they do only capture the velocity component along the beam direction. We thus propose to combine measurements from different beam directions. However, this is not yet sufficient to make the problem well posed because 1) the angle between the directions is typically small and 2) the data is noisy and nonuniformly sampled. We propose to solve this reconstruction problem in the continuous domain using regularization. The reconstruction is formulated as the minimizer of a cost that is a weighted sum of two terms: 1) the sum of squared difference between the Doppler data and the projected velocities 2) a quadratic regularization functional that imposes some smoothness on the velocity field. We express our solution for this minimization problem in a B-spline basis, obtaining a sparse system of equations that can be solved efficiently. Using synthetic phantom data, we demonstrate the significance of tuning the regularization according to the a priori knowledge about the physical property of the motion. Next, we validate our method using real phantom data for which the ground truth is known. We then present reconstruction results obtained from clinical data that originate from 1) blood flow in carotid bifurcation and 2) cardiac wall motion

Data reconciliation of immersive heart inspection

IVUS images are complicated medical datasets suffering from some artifacts caused by the data acquisition method of immersive heart inspection. Data reconciliation, which removes tracing and tracking uncertainties of these datasets, is an important step for the medical application of remodeling the arteries in virtual reality to aid diagnosing and treating heart diseases. This paper provides an empirical data reconciliation method, which fuses the features of the coronary longitudinal movement with motion compensation model. It explains the distortion of the data set well and provides a method to analyze and reconcile the dataset