Coupled B-snake grids and constrained thin-plate splines for analysis of 2-D tissue deformations from tagged MRI

Four-dimensional processing of deformable cardiac PET data

A four-dimensional deformable motion algorithm is described for use in the motion compensation of gated cardiac positron emission tomography. The algorithm makes use of temporal continuity and a non-uniform elastic material model to provide improved estimates of heart motion between time frames. Temporal continuity is utilized in two ways. First, incremental motion fields between adjacent time frames are calculated to improve estimation of long-range motion between distant time frames. Second, a consistency criterion is used to insure that the image match between distant time frames is consistent with the deformations used to match adjacent time frames. The consistency requirement augments the algorithm's ability to estimate motion between noisy time frames, and the concatenated incremental motion fields improve estimation for large deformations. The estimated motion fields are used to establish a voxel correspondence between volumes and to produce a motion-compensated composite volume.

Simulation of tagged MR images with linear tetrahedral solid elements

Computer simulation of tagged magnetic resonance (MR) images is presented using signals derived from connected solid triangular or tetrahedral elements. Simulation provides precisely-known deformations for validating tag quantification algorithms. MR imaging signal is derived by Fourier-transforming over a standard element, then mapping to actual elements via transformations. Linear intensity variations over the element are interpolated from vertex intensities determined by tag calculations.

Imaging longitudinal cardiac strain on short-axis images using strain-encoded MRI

This article presents a new method for measuring longitudinal strain in a short-axis section of the heart using harmonic phase magnetic resonance imaging (HARP-MRI). The heart is tagged using 1-1 SPAMM at end-diastole with tag surfaces parallel to a short-axis imaging plane. Two or more images are acquired such that the images have different phase encodings in a direction orthogonal to the image plane. A dense map of the longitudinal strain can be computed from these images using a simple, fast computation. Simulations are conducted to study the effect of noise and the choice of out-of-plane phase encoding values. Longitudinal strains acquired from a normal human male are shown.

Fast LV motion estimation using subspace approximation techniques

Cardiac motion estimation is very important in understanding cardiac dynamics and in noninvasive diagnosis of heart disease. Magnetic resonance (MR) imaging tagging is a technique for measuring heart deformations. In cardiac tagged MR images, a set of dark lines are noninvasively encoded within myocardial tissue providing the means for measurement of deformations of the heart. The points along tag lines measured in different frames and in different directions carry important information for determining the three-dimensional nonrigid movement of left ventricle. However, these measurements are sparse and, therefore, multidimensional interpolation techniques are needed to reconstruct a dense displacement field. In this paper, a novel subspace approximation technique is used to accomplish this task. We formulate the displacement estimation as a variational problem and then project the solution into spline subspaces. Efficient numerical methods are derived by taking advantages of B-spline properties. The proposed technique significantly improves our previous results reported in [3] with respect to computational time. The method is applied to a temporal sequence of two-dimensional images and is validated with simulated and in vivo heart data.

Estimation of 3D left ventricular deformation from echocardiography

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 a transversely isotropic 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.

Tag surface reconstruction and tracking of myocardial beads from SPAMM-MRI with parametric B-spline surfaces

Magnetic resonance imaging (MRI) is unique in its ability to noninvasively and selectively alter tissue magnetization, and create tag planes intersecting image slices. The resulting grid of signal voids allows for tracking deformations of tissues in otherwise homogeneous-signal myocardial regions. In this paper, we propose a specific spatial modulation of magnetization (SPAMM) imaging protocol together with efficient techniques for measurement of three-dimensional (3-D) motion of material points of the human heart (referred to as myocardial beads) from images collected with the SPAMM method. The techniques make use of tagged images in orthogonal views by explicitly reconstructing 3-D B-spline surface representation of tag planes (tag planes in two orthogonal orientations intersecting the short-axis (SA) image slices and tag planes in an orientation orthogonal to the short-axis tag planes intersecting long-axis (LA) image slices). The developed methods allow for viewing deformations of 3-D tag surfaces, spatial correspondence of long-axis and short-axis image slice and tag positions, as well as nonrigid movement of myocardial beads as a function of time.

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

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

Investigating intrinsic myocardial mechanics: the role of MR tagging, velocity phase mapping, and diffusion imaging

Assessment of myocardial mechanics is an integral part of understanding and predicting heart disease. This review covers the two most common magnetic resonance (MR) methods used to measure myocardial motion: myocardial tagging and myocardial velocity mapping. Myocardial tagging has been well established in clinical research, despite its time-consuming postprocessing procedure. Myocardial velocity mapping uses the phase shifts of the spins to encode the velocity into the MR signal. This means that once the myocardial contours have been segmented, the data can be automatically processed to obtain quantitative measurements. Diffusion MR also has found applications in cardiac imaging, with preliminary results of myocardial fiber architecture being obtained recently. These three different MR techniques have provided valuable insights into the assessment of intrinsic cardiac mechanics. J. Magn. Reson. Imaging 2000;12:873-883.

Two-dimensional spatial and temporal displacement and deformation field fitting from cardiac magnetic resonance tagging

Tagged magnetic resonance imaging is a specially developed technique to noninvasively assess contractile function of the heart. Several methods have been developed to estimate myocardial deformation from tagged image data. Most of these methods do not explicitly impose a continuity constraint through time although myocardial motion is a continuous physical phenomenon. In this paper, we propose to model the spatio-temporal myocardial displacement field by a cosine series model fitted to the entire tagged dataset. The method has been implemented in two dimensions (2D)+time. Its accuracy was successively evaluated on actual tagged data and on a simulated two-dimensional (2D) moving heart model. The simulations show that an overall theoretical mean accuracy of 0.1 mm can be attained with adequate model orders. The influence of the tagging pattern was evaluated and computing time is provided as a function of the model complexity and data size. This method provides an analytical and hierarchical model of the 2D+time deformation inside the myocardium. It was applied to actual tagged data from a healthy subject and from a patient with ischemia. The results demonstrate the adequacy of the proposed model for this evaluation.

Four-dimensional B-spline based motion analysis of tagged MR images: introduction and in vivo validation

In MRI tagging, magnetic tags-spatially encoded magnetic saturation planes-are created within tissues acting as temporary markers. Their deformation pattern provides useful qualitative and quantitative information about the functional properties of underlying tissue and allows non-invasive analysis of mechanical function. The measured displacement at a given tag point contains only unidirectional information; in order to track the full 3D motion, these data have to be combined with information from other orthogonal tag sets over all time frames. Here, we provide a method to describe the motion of the heart using a four-dimensional tensor product of B-splines. In vivo validation of this tracking algorithm is performed using different tagging sets on the same heart. Using the validation results, the appropriate control point density was determined for normal cardiac motion tracking. Since our motion fields are parametric and based on an image plane based Cartesian coordinate system, trajectories or other derived values (velocity, acceleration, strains ...) can be calculated for any desired point within the volume spanned by the control points. This method does not rely on specific chamber geometry, so the motion of any tagged structure can be tracked. Examples of displacement and strain analysis for both ventricles are also presented.

Dynamics of errors in 3D motion estimation and implications for strain-tensor imaging in acoustic elastography

For the purpose of quantifying the noise in acoustic elastography, a displacement covariance matrix is derived analytically for the cross-correlation based 3D motion estimator. Static deformation induced in tissue from an external mechanical source is represented by a second-order strain tensor. A generalized 3D model is introduced for the ultrasonic echo signals. The components of the covariance matrix are related to the variances of the displacement errors and the errors made in estimating the elements of the strain tensor. The results are combined to investigate the dependences of these errors on the experimental and signal-processing parameters as well as to determine the effects of one strain component on the estimation of the other. The expressions are evaluated for special cases of axial strain estimation in the presence of axial, axial-shear and lateral-shear type deformations in 2D. The signals are shown to decorrelate with any of these deformations, with strengths depending on the reorganization and interaction of tissue scatterers with the ultrasonic point spread function following the deformation. Conditions that favour the improvements in motion estimation performance are discussed, and advantages gained by signal companding and pulse compression are illustrated.

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

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

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

Cardiac motion tracking using CINE harmonic phase (HARP) magnetic resonance imaging

This article introduces a new image processing technique for rapid analysis of tagged cardiac magnetic resonance image sequences. The method uses isolated spectral peaks in SPAMM-tagged magnetic resonance images, which contain information about cardiac motion. The inverse Fourier transform of a spectral peak is a complex image whose calculated angle is called a harmonic phase (HARP) image. It is shown how two HARP image sequences can be used to automatically and accurately track material points through time. A rapid, semiautomated procedure to calculate circumferential and radial Lagrangian strain from tracked points is described. This new computational approach permits rapid analysis and visualization of myocardial strain within 5-10 min after the scan is complete. Its performance is demonstrated on MR image sequences reflecting both normal and abnormal cardiac motion. Results from the new method are shown to compare very well with a previously validated tracking algorithm. Magn Reson Med 42:1048-1060, 1999.

Spatio-temporal tracking of myocardial deformations with a 4-D B-spline model from tagged MRI

Accurate delineation of the volumetric motion of the 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 four-dimensional (4-D) 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 4-D tracking. Important advantages of the model are that reconstruction of tag surfaces, three-dimensional (3-D) material point localization, as well as displacement reconstruction are all achieved in a single step. The generated 3-D displacement fields are validated with a cardiac motion simulator, and 3-D motion fields capturing in vivo deformations in a porcine model with posterolateral myocardial infarction are illustrated.