From 4D medical images (CT, MRI, and Ultrasound) to 4D structured mesh models of the left ventricular endocardium for patient-specific simulations

With cardiovascular disease (CVD) remaining the primary cause of death worldwide, early detection of CVDs becomes essential. The intracardiac flow is an important component of ventricular function, motion kinetics, wash-out of ventricular chambers, and ventricular energetics. Coupling between Computational Fluid Dynamics (CFD) simulations and medical images can play a fundamental role in terms of patient-specific diagnostic tools. From a technical perspective, CFD simulations with moving boundaries could easily lead to negative volumes errors and the sudden failure of the simulation. The generation of high-quality 4D meshes (3D in space + time) with 1-to-l vertex becomes essential to perform a CFD simulation with moving boundaries. In this context, we developed a semiautomatic morphing tool able to create 4D high-quality structured meshes starting from a segmented 4D dataset. To prove the versatility and efficiency, the method was tested on three different 4D datasets (Ultrasound, MRI, and CT) by evaluating the quality and accuracy of the resulting 4D meshes. Furthermore, an estimation of some physiological quantities is accomplished for the 4D CT reconstruction. Future research will aim at extending the region of interest, further automation of the meshing algorithm, and generating structured hexahedral mesh models both for the blood and myocardial volume

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

Meshless deformable models for LV motion analysis

We propose a novel meshless deformable model for in vivo cardiac left ventricle (LV) 3D motion estimation. As a relatively new technology, tagged MRI (tMRI) provides a direct and noninvasive way to reveal local deformation of the myocardium, which creates a large amount of heart motion data which requiring quantitative analysis. In our study, we sample the heart motion sparsely at intersections of three sets of orthogonal tagging planes and then use a new meshless deformable model to recover the dense 3D motion of the myocardium temporally during the cardiac cycle. We compute external forces at tag intersections based on tracked local motion and redistribute the force to meshless particles throughout the myocardium. Internal constraint forces at particles are derived from local strain energy using a Moving Least Squares (MLS) method. The dense 3D motion field is then computed and updated using the Lagrange equation. The new model avoids the singularity problem of mesh-based models and is capable of tracking large deformation with high efficiency and accuracy. In particular, the model performs well even when the control points (tag intersections) are relatively sparse. We tested the performance of the meshless model on a numerical phantom, as well as in vivo heart data of healthy subjects and patients. The experimental results show that the meshless deformable model can fully recover the myocardium motion in 3D. 1

Real-time 3D reconstruction of non-rigid shapes with a single moving camera

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper describes a real-time sequential method to simultaneously recover the camera motion and the 3D shape of deformable objects from a calibrated monocular video. For this purpose, we consider the Navier-Cauchy equations used in 3D linear elasticity and solved by finite elements, to model the time-varying shape per frame. These equations are embedded in an extended Kalman filter, resulting in sequential Bayesian estimation approach. We represent the shape, with unknown material properties, as a combination of elastic elements whose nodal points correspond to salient points in the image. The global rigidity of the shape is encoded by a stiffness matrix, computed after assembling each of these elements. With this piecewise model, we can linearly relate the 3D displacements with the 3D acting forces that cause the object deformation, assumed to be normally distributed. While standard finite-element-method techniques require imposing boundary conditions to solve the resulting linear system, in this work we eliminate this requirement by modeling the compliance matrix with a generalized pseudoinverse that enforces a pre-fixed rank. Our framework also ensures surface continuity without the need for a post-processing step to stitch all the piecewise reconstructions into a global smooth shape. We present experimental results using both synthetic and real videos for different scenarios ranging from isometric to elastic deformations. We also show the consistency of the estimation with respect to 3D ground truth data, include several experiments assessing robustness against artifacts and finally, provide an experimental validation of our performance in real time at frame rate for small mapsPeer ReviewedPostprint (author's final draft

General Dynamic Surface Reconstruction: Application to the 3D Segmentation of the Left Ventricle

Aquesta tesi descriu la nostra contribució a la reconstrucció tridimensional de les superfícies interna i externa del ventricle esquerre humà. La reconstrucció és un primer procés dins d'una aplicació global de Realitat Virtual dissenyada com una important eina de diagnòstic per a hospitals. L'aplicació parteix de la reconstrucció de les superfícies i proveeix a l'expert de manipulació interactiva del model en temps real, a més de càlculs de volums i de altres paràmetres d'interès. El procés de recuperació de les superfícies es caracteritza per la seva velocitat de convergència, la suavitat a les malles finals i la precisió respecte de les dades recuperades. Donat que el diagnòstic de patologies cardíaques requereix d'experiència, temps i molt coneixement professional, la simulació és un procés clau que millora la eficiència.Els nostres algorismes i implementacions han estat aplicats a dades sintètiques i reals amb diferències relatives a la quantitat de dades inexistents, casuístiques presents a casos patològics i anormals. Els conjunts de dades inclouen adquisicions d'instants concrets i de cicles cardíacs complets. La bondat del sistema de reconstrucció ha estat avaluada mitjançant paràmetres mèdics per a poder comparar els nostres resultats finals amb aquells derivats a partir de programari típic utilitzat pels professionals de la medicina.A més de l'aplicació directa al diagnòstic mèdic, la nostra metodologia permet reconstruccions de tipus genèric en el camp dels Gràfics 3D per ordinador. Les nostres reconstruccions permeten generar models tridimensionals amb un baix cost en quant a la interacció manual necessària i a la càrrega computacional associada. Altrament, el nostre mètode pot entendre's com un robust algorisme de triangularització que construeix superfícies partint de núvols de punts que poden obtenir-se d'escàners làser o sensors magnètics, per exemple.Esta tesis describe nuestra contribución a la reconstrucción tridimensional de las superficies interna y externa del ventrículo izquierdo humano. La reconstrucción es un primer proceso que forma parte de una aplicación global de Realidad Virtual diseñada como una importante herramienta de diagnóstico para hospitales. La aplicación parte de la reconstrucción de las superficies y provee al experto de manipulación interactiva del modelo en tiempo real, además de cálculos de volúmenes y de otros parámetros de interés. El proceso de recuperación de las superficies se caracteriza por su velocidad de convergencia, la suavidad en las mallas finales y la precisión respecto de los datos recuperados. Dado que el diagnóstico de patologías cardíacas requiere experiencia, tiempo y mucho conocimiento profesional, la simulación es un proceso clave que mejora la eficiencia.Nuestros algoritmos e implementaciones han sido aplicados a datos sintéticos y reales con diferencias en cuanto a la cantidad de datos inexistentes, casuística presente en casos patológicos y anormales. Los conjuntos de datos incluyen adquisiciones de instantes concretos y de ciclos cardíacos completos. La bondad del sistema de reconstrucción ha sido evaluada mediante parámetros médicos para poder comparar nuestros resultados finales con aquellos derivados a partir de programario típico utilizado por los profesionales de la medicina.Además de la aplicación directa al diagnóstico médico, nuestra metodología permite reconstrucciones de tipo genérico en el campo de los Gráficos 3D por ordenador. Nuestras reconstrucciones permiten generar modelos tridimensionales con un bajo coste en cuanto a la interacción manual necesaria y a la carga computacional asociada. Por otra parte, nuestro método puede entenderse como un robusto algoritmo de triangularización que construye superficies a partir de nubes de puntos que pueden obtenerse a partir de escáneres láser o sensores magnéticos, por ejemplo.This thesis describes a contribution to the three-dimensional reconstruction of the internal and external surfaces of the human's left ventricle. The reconstruction is a first process fitting in a complete VR application that will serve as an important diagnosis tool for hospitals. Beginning with the surfaces reconstruction, the application will provide volume and interactive real-time manipulation to the model. We focus on speed, precision and smoothness for the final surfaces. As long as heart diseases diagnosis requires experience, time and professional knowledge, simulation is a key-process that enlarges efficiency.The algorithms and implementations have been applied to both synthetic and real datasets with differences regarding missing data, present in cases where pathologies and abnormalities arise. The datasets include single acquisitions and complete cardiac cycles. The goodness of the reconstructions has been evaluated with medical parameters in order to compare our results with those retrieved by typical software used by physicians.Besides the direct application to medicine diagnosis, our methodology is suitable for generic reconstructions in the field of computer graphics. Our reconstructions can serve for getting 3D models at low cost, in terms of manual interaction and CPU computation overhead. Furthermore, our method is a robust tessellation algorithm that builds surfaces from clouds of points that can be retrieved from laser scanners or magnetic sensors, among other available hardware

Deformable mesh model for cardiac motion estimation from MRI data

Projecte final de carrera realitzat en col.laboració amb l'Illinois Institute of TechnologyThe use of technology in medical applications has expanded tremendously in the last 50 years, playing an important role in diagnosis and treatment of disease. As a consequence of this growth, it has been possible to develop new techniques and processes which allows scientists and physicians to extract potentially life-saving information by peering noninvasively into the human body. One of these techniques, Magnetic Resonance Imaging, has the capacity of providing data which contain information about motion of human tissue. In this project we exploit this characteristic to present a model for estimating left ventricular heart motion through a whole cardiac cycle. The model is based on the utilization of a non-rigid deformable mesh which tracks the intensity variations on the datasets of MRI images. The use of a mesh allows us to interpolate the motion on every point of the myocardial tissue. Although still in his first steps of development, preliminary results here presented demonstrate great potential of our model in terms of efficiency and flexibility versus the other existing models. It constitutes a good alternative for developing full 4D heart models in the future

Sequential non-rigid structure from motion using physical priors

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.We propose a new approach to simultaneously recover camera pose and 3D shape of non-rigid and potentially extensible surfaces from a monocular image sequence. For this purpose, we make use of the Extended Kalman Filter based Simultaneous Localization And Mapping (EKF-SLAM) formulation, a Bayesian optimization framework traditionally used in mobile robotics for estimating camera pose and reconstructing rigid scenarios. In order to extend the problem to a deformable domain we represent the object's surface mechanics by means of Navier's equations, which are solved using a Finite Element Method (FEM). With these main ingredients, we can further model the material's stretching, allowing us to go a step further than most of current techniques, typically constrained to surfaces undergoing isometric deformations. We extensively validate our approach in both real and synthetic experiments, and demonstrate its advantages with respect to competing methods. More specifically, we show that besides simultaneously retrieving camera pose and non-rigid shape, our approach is adequate for both isometric and extensible surfaces, does not require neither batch processing all the frames nor tracking points over the whole sequence and runs at several frames per second.Peer ReviewedPostprint (author's final draft

Foetal echocardiographic segmentation

Congenital heart disease affects just under one percentage of all live births [1]. Those defects that manifest themselves as changes to the cardiac chamber volumes are the motivation for the research presented in this thesis. Blood volume measurements in vivo require delineation of the cardiac chambers and manual tracing of foetal cardiac chambers is very time consuming and operator dependent. This thesis presents a multi region based level set snake deformable model applied in both 2D and 3D which can automatically adapt to some extent towards ultrasound noise such as attenuation, speckle and partial occlusion artefacts. The algorithm presented is named Mumford Shah Sarti Collision Detection (MSSCD). The level set methods presented in this thesis have an optional shape prior term for constraining the segmentation by a template registered to the image in the presence of shadowing and heavy noise. When applied to real data in the absence of the template the MSSCD algorithm is initialised from seed primitives placed at the centre of each cardiac chamber. The voxel statistics inside the chamber is determined before evolution. The MSSCD stops at open boundaries between two chambers as the two approaching level set fronts meet. This has significance when determining volumes for all cardiac compartments since cardiac indices assume that each chamber is treated in isolation. Comparison of the segmentation results from the implemented snakes including a previous level set method in the foetal cardiac literature show that in both 2D and 3D on both real and synthetic data, the MSSCD formulation is better suited to these types of data. All the algorithms tested in this thesis are within 2mm error to manually traced segmentation of the foetal cardiac datasets. This corresponds to less than 10% of the length of a foetal heart. In addition to comparison with manual tracings all the amorphous deformable model segmentations in this thesis are validated using a physical phantom. The volume estimation of the phantom by the MSSCD segmentation is to within 13% of the physically determined volume

Deformable mesh model for cardiac motion estimation from MRI data

Projecte final de carrera realitzat en col.laboració amb l'Illinois Institute of TechnologyThe use of technology in medical applications has expanded tremendously in the last 50 years, playing an important role in diagnosis and treatment of disease. As a consequence of this growth, it has been possible to develop new techniques and processes which allows scientists and physicians to extract potentially life-saving information by peering noninvasively into the human body. One of these techniques, Magnetic Resonance Imaging, has the capacity of providing data which contain information about motion of human tissue. In this project we exploit this characteristic to present a model for estimating left ventricular heart motion through a whole cardiac cycle. The model is based on the utilization of a non-rigid deformable mesh which tracks the intensity variations on the datasets of MRI images. The use of a mesh allows us to interpolate the motion on every point of the myocardial tissue. Although still in his first steps of development, preliminary results here presented demonstrate great potential of our model in terms of efficiency and flexibility versus the other existing models. It constitutes a good alternative for developing full 4D heart models in the future