This article surveys deformable models, a promising and vigorously researched computer-assisted medical image analysis technique. Among model-based techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They have proven to be effective in segmenting, matching, and tracking anatomic structures by exploiting (bottom-up) constraints derived from the image data together with (top-down) a priori knowledge about the location, size, and shape of these structures. Deformable models are capable of accommodating the significant variability of biological structures over time and across different individuals. Furthermore, they support highly intuitive interaction mechanisms that, when necessary, allow medical scientists and practitioners to bring their expertise to bear on the model-based image interpretation task. This article reviews the rapidly expanding body of work on the development and application of deformable models to problems of fundamental importance in medical image analysis, includingsegmentation, shape representation, matching, and motion tracking.

We present a new method for analyzing the motion of the heart's left ventricle (LV) from tagged magnetic resonance imaging (MRI) data. Our technique is based on the development of a new class of physics-based deformable models whose parameters are functions. They allow the definition of new parameterized primitives and parameterized deformations which can capture the local shape variation of a complex object. Furthermore, these parameters are intuitive and require no complex post-processing in order to be used by a physician. Using a physics-based approach, we convert the geometric models into dynamic models that deform due to forces exerted from the datapoints and conform to the given dataset. We present experiments involving the extraction of the shape and motion of the LV's mid-wall during systole from tagged MRI data based on a few parameter functions. Furthermore, by plotting the variations over time of the extracted LV model parameters from normal and abnormal heart data along t...

We present a new approach for the analysis of the left ventricular shape and motion that is based on the development of a new class of volumetric deformable models. We estimate the deformation and complex motion of the left ventricle (LV) in terms of a few parameters that are functions and whose values vary locally across the LV. These parameters capture the radial and longitudinal contraction, the axial twisting, and the long-axis deformation. Using Lagrangian dynamics and the finite element theory, we convert these volumetric primitives into dynamic models that deform due to forces exerted by the datapoints. We present experiments where we used magnetic tagging (MRI-SPAMM) to acquire datapoints from the LV during systole. By applying our method to MRI-SPAMM datapoints, we were able to characterize both locally and globally the 3D shape and motion of the LV in a clinically useful way. In addition, based on the model parameters we were able to extract quantitative differences between n...

The quantitative estimation of regional cardiac deformation from 3D image sequences has important clinical implications for the assessment of viability in the heart wall. Such estimates have so far been obtained almost exclusively from Magnetic Resonance (MR) images, specifically MR tagging. In this paper we describe a methodology for estimating cardiac deformations from 3D echocardiography (3DE). The images are segmented interactively and then initial correspondence is established using a shape-tracking approach. A dense motion field is then estimated using an anisotropic linear elastic model, which accounts for the 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, show good agreement with previously published results in the literature. They also exhibit a high correlation with strains produced in the same animals using implanted sonomicrometers. This proposed method provides quantitative regional 3D estimates of heart deformation from ultrasound images. 1

MRI is unique in its ability to non-invasively and selectively alter tissue magnetization, and create tagged patterns within a deforming body such as the heart muscle. The resulting patterns define a time-varying curvilinear coordinate system on the tissue, which we track with coupled B-snake grids.

To date, MRI-SPAMM data from different image slices have been analyzed independently. In this paper, we propose an approach for 3D tag localization and tracking of SPAMM data by a novel deformable B-solid. The solid is defined in terms of a 3D tensor product B-spline. The iso-parametric curves of the B-spline solid have special importance. These are termed implicit snakes as they deform under image forces from tag lines in different image slices. The localization and tracking of tag lines is performed under constraints of continuity and smoothness of the B-solid. To track motion from boundaries and restrict image forces to the myocardium, a volumetric model is employed as a pair of coupled endocardial and epicardial B-spline surfaces. To recover deformations of the Left Ventricle (LV) an energy-minimization problem is posed where both tag and LV boundary data are used. The framework has been implemented on tag data from Short Axis (SA) cardiac images, as well as SA LV boundaries, and i...

This paper describes a computational simulator for use in cardiac imaging using tagged magnetic resonance imaging. The simulator incorporates a 13-parameter model of left-ventricular motion due to Arts et al. (1992) and applies it to a confocal prolate spherical shell, resembling the shape of the left ventricle. Using parameters determined in other work, our model can be made to assume a configuration representing one of 60 phases in the cardiac cycle. In this paper, we determine the inverse motion map analytically, allowing pointwise correspondences to be made between two points at any two times. Using this mathematical relationship, we simulate the (tagged) magnetic resonance imaging process using a standard (tagged) spin-echo imaging equation. Image sequences can be synthesized at arbitrary orientations at any phase. We currently synthesize a SPAMM tag pattern with arbitrary spatial frequency, but other patterns can be readily incorporated. To accommodate two-dimensional motion esti...

Accurate delineation of the volumetric motion of Left-Ventricle (LV) of the heart from tagged Magnetic Resonance Imaging (MRI) is an important area of research. We have built a system that takes extracted tag line features from short-axis (SA) and long-axis (LA) image sequences as input, and fits a 4D time-varying B-spline model to the data by simultaneously fitting the model knot solids to MRI frames via matching three sequences of solid knot planes to the LV tag planes for 4D tracking. An important advantage of the model is that 3D material point localization and displacement reconstruction is achieved in a single step. The generated 3D displacement fields are validated with a cardiac motion simulator, and 3D motion fields capturing in-vivo deformations in a porcine model with anterior myocardial infarction are illustrated. Keywords: Cardiac Motion, Tagged MRI, B-spline Deformable Model, Myocardial Infarction. 1 Introduction Noninvasive imaging techniques for assessing the dynamic ...

In this paper, we propose a new approach for tracking the deformation of the Left Ventricular (LV) myocardium from two-dimensional Magnetic Resonance (MR) phase contrast velocity fields. The use of phase contrast MR velocity data in cardiac motion problems has been introduced by others [1] and shown to be potentially useful for tracking discrete tissue elements, and therefore characterizing LV motion. However, we show here that these velocity data i.) are extremely noisy near the LV borders and ii.) cannot alone be used to estimate the motion and the deformation of the entire myocardium due to noise in the velocity fields. In this new approach, we use the natural spatial constraints of the endocardial and epicardial contours, detected semi-automatically in each image frame, to help remove noisy velocity vectors at the LV contours. The information from both the boundaries and the phase contrast velocity data is then integrated into a deforming mesh that is placed over the myocardium at ...

A major issue in cardiac imaging is the assessment of cardiac function and particularly the identification of ischemic or infarcted tissues. We present in this article a method to reconstruct the displacement field of the left ventricular (LV) motion using 4D planispheric transformations of time and space combined in a first step with B-spline tensor products. Because of the 4D modeling, a) it is possible to include any tag plane direction as input data. b) The use of planispheric coordinates makes the numerical evaluation more stable as compared to prolate spheroidal coordinates, the equivalent focal point being much further from the apical area of the heart. This therefore avoids mathematical instability when the material points of the myocardium are too close to the apical focus. c) In the temporal modeling, a simple adaptation is possible to changing temporal dynamics, suchasintroduced by ectopic pacing or rapid filling after systole. d) Finally, the strain analysis and displacemen...