Diffusion-weighted images based on echo planar sequences suffer from distortions due to field inhomogeneities from susceptibility differences as well as from eddy currents arising from diffusion gradients. In this paper, a novel approach using nonlinear warping based on optic flow to correct distortions of baseline and diffusion weighted echo planar images (EPI) acquired at 3 T is presented. The distortion correction was estimated by warping the echo planar images to the anatomically correct T 2 -weighted fast spin echo images (T2-FSE). A global histogram intensity matching of the T2-FSE precedes the base line EPI image distortion correction. A local intensity-matching algorithm was used to transform labeled T2-FSE regions to match intensities of diffusion-weighted EPI images prior to distortion correction of these images. Evaluation was performed using three methods: ( Echo planar imaging (EPI) based diffusion tensor acquisition suffers from geometric distortions due to both local magnetic field inhomogeneities and eddy current effects that arise from the large diffusion gradients required to obtain diffusion-weighted images. Previous work in distortion correction of echo planar images have included specially tailored pulse sequences, phantom correction data, and B-spline based deformation (1-3). Approaches that rely on acquiring phase maps are based on correction algorithms using the known relationship between spatial distortions and the local inhomogeneity (measured in the phase maps) (4,5). The major drawback to this approach is the difficulty of rapidly acquiring reliable field maps as well the complexity of phaseunwrapping algorithms. In purely image-based postprocessing algorithms, cubic B-spline approaches with constrained unidirectional free-form deformation have been implemented successfully (2,3).Prior work in reducing the effects of eddy currents include gradient pre-emphasis, special pulse sequences, and postprocessing methods. Reese et al. (6) propose a sequence modification incorporating a second refocusing pulse to the single-shot spin-echo EPI sequence to reduce eddy current effects in diffusion MR acquisition. This method very effectively nullifies eddy currents that contain a single exponential decay. Although greatly reduced, multiexponential eddy currents with similar decay constants are not completely eliminated. Several groups have used global affine transformations to align images from a diffusion-weighted set to a baseline image with no diffusion weighting (7,8). A cost function (based on correlation type similarity measures or mutual information) is used to determine the affine transformation parameters required to align the diffusion-weighted images to the target image, the corresponding baseline echo planar image with no diffusion sensitization (7-9). Andersson and Skare (10) proposed a cost function that minimizes residual error of estimation in diffusion tensor measurement. This latter group has recently extended corrections to include susceptibility-induced field distortions by in...
Time-lapse aerial photography over the Central Business Districts (CBD) of Austin and Dallas, Texas, has been employed to determine the averages of concentration, speed and fraction of vehicles stopped and to examine the relations among such network-wide averages including the flow which was measured on the ground simultaneously. The results have indicated that the average flow in a street network may indeed be expressed as the product of the space mean speed and concentration. Simultaneous ground experiments have also been conducted in the Austin CBD to investigate the reasonableness of the assumptions of the “two-fluid model,” a curvilinear relation between the trip time and stop time per unit distance, which may be used in characterizing the quality of traffic service in urban street networks. As a result of these simultaneous ground experiments and aerial observations, the assumptions of the model have been verified. Moreover, relations between the fraction of vehicles stopped and concentration as well as between speed and concentration have allowed the two-fluid model to be used to compare the quality of traffic service in various street networks under the same level of concentration. The two-fluid model may then be used to predict, for a given change in vehicular concentration in a street network, the resulting changes in the averages of speed, fraction of vehicles stopped, flow, etc. This is particularly useful as a performance model in urban planning where for a given concentration it is desirable to predict the resulting traffic conditions.
A series of vehicular traffic experiments conducted in Austin, Texas, shows the reasonableness of the two assumptions in the two-fluid (moving and stopped vehicles) model of town traffic. The observational data support the assumption that the average speed in an urban street network is proportional to the fraction of the vehicles moving raised to a power and is also in agreement with the supposition that during relatively uniform periods the traffic is ergodic. An important consequence is that the average of the fraction of time stopped for a test vehicle circulating in a street network is approximately equal to the average fraction of the vehicles stopped in the system during the same test period. The parameters of the two-fluid model and the observed ranges of trip time and stop time per unit distance have been shown to be effective in assessing or rank ordering the relative quality of traffic service in a number of Texas cities; comparisons are made with various cities around the world. The two-fluid methodology appears to be useful in a preliminary “before”/“after” study during which signal timing changes were made. Finally, a preliminary analysis of aerial photographic data in two cities allows the determination of an additional two-fluid model parameter, p, in the relation stating that the fraction of vehicles stopped is given by the ratio of concentration to the jam or maximum concentration raised to a power, p. It is suggested that this parameter may be useful in describing the relative quality of various traffic systems.
Left ventricular remodeling during the development of heart failure is a strong predictor of cardiovascular mortality. However, methods to objectively quantify remodeling-associated shape changes are not routinely available but may be possible with new computational anatomy tools. In this study, we analyzed and compared multi-detector computed tomographic (MDCT) images of ventricular shape at endsystole (ES) and end-diastole (ED) to determine whether regional structural characteristics could be identified and, as a proof of principle, whether differences in hearts of patients with anterior myocardial infarction (MI) and ischemic cardiomyopathy (ICM) could be distinguished from those with global nonischemic cardiomyopathy (NICM). MDCT images of hearts from 11 patients (5 with ICM) with ejection fractions (EF) > 35% were analyzed. An average ventricular shape model (template) was constructed for each cardiac phase by bringing heart shapes into correspondence using linear and nonlinear image matching algorithms. Next, transformation fields were computed between the template image and individual heart images in the population. Principal component analysis (PCA) method was used to quantify ventricular shape differences described by the transformation vector fields. Statistical analysis of PCA coefficients revealed significant ventricular shape differences at ED (p = 0.03) and ES (p = 0.03). For validation, a second set of 14 EF-matched patients (8 with ICM) were evaluated. The discrimination rule learned from the training data set was able to differentiate ICM from NICM patients (p = 0.008). Application of a novel shape analysis method to in vivo human cardiac images acquired on a clinical scanner is feasible and can quantify regional shape differences at end-systole in remodeled myopathic human myocardium. This approach may be useful in identifying differences in the remodeling process between ICM and NICM populations and possibly in differentiating the populations.
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