41 research outputs found
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Sampling bounds for 2-D vector field tomography
The tomographic mapping of a 2-D vector field from line-integral data in the discrete domain requires the uniform sampling of the continuous Radon domain parameter space. In this paper we use sampling theory and derive limits for the sampling steps of the Radon parameters, so that no information is lost. It is shown that if Îx is the sampling interval of the reconstruction region and xmax is the maximum value of domain parameter x, the steps one should use to sample Radon parameters Ď and θ should be: ÎĎ⤠Îx/â2 and Îθâ¤Îx/((â2+2)|xmax|). Experiments show that when the proposed sampling bounds are violated, the reconstruction accuracy of the vector field deteriorates. We further demonstrate that the employment of a scanning geometry that satisfies the proposed sampling requirements also increases the resilience to noise
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Full tomographic reconstruction of 2D vector fields using discrete integral data
Vector field tomography is a field that has received considerable attention in recent decades. It deals with the problem of the determination of a vector field from non-invasive integral data. These data are modelled by the vectorial Radon transform. Previous attempts at solving this reconstruction problem showed that tomographic data alone are insufficient for determining a 2D band-limited vector field completely and uniquely. This paper describes a method that allows one to recover both components of a 2D vector field based only on integral data, by solving a system of linear equations. We carry out the analysis in the digital domain and we take advantage of the redundancy in the projection data, since these may be viewed as weighted sums of the local vector field's Cartesian components. The potential of the introduced method is demonstrated by presenting examples of vector field reconstruction
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Improved 2-D vector field reconstruction using virtual sensors and the Radon transform
This paper describes a method that allows one to recover both components of a 2-D vector field based on boundary information only, by solving a system of linear equations. The analysis is carried out in the digital domain and takes advantage of the redundancy in the boundary data, since these may be viewed as weighted sums of the local vector fieldâs Cartesian components. Furthermore, a sampling of lines is used in order to combine the available measurements along continuous tracing lines with the digitised 2-D space where the solution is sought. A significant enhancement in the performance of the proposed algorithm is achieved by using, apart from real data, also boundary data obtained at virtual sensors. The potential of the proposed method is demonstrated by presenting an example of vector field reconstruction
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Virtual sensors for 2D vector field tomography
We consider the application of tomography to the reconstruction of 2-D vector fields. The most convenient sensor configuration in such problems is the regular positioning along the domain boundary. However, the most accurate reconstructions are obtained by sampling uniformly the Radon parameter domain rather than the border of the reconstruction domain. This dictates a prohibitively large number of sensors and impractical sensor positioning. In this paper, we propose uniform placement of the sensors along the boundary of the reconstruction domain and interpolation of the measurements for the positions that correspond to uniform sampling in the Radon domain. We demonstrate that when the cubic spline interpolation method is used, a 60 times reduction in the number of sensors may be achieved with only about 10% increase in the error with which the vector field is estimated. The reconstruction error by using the same sensors and ignoring the necessity of uniform sampling in the Radon domain is in fact higher by about 30%. The effects of noise are also examined
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Quantitative analysis of hypertrophic myocardium using diffusion tensor magnetic resonance imaging
Systemic hypertension is a causative factor in left ventricular hypertrophy (LVH). This study is motivated by the potential to reverse or manage the dysfunction associated with structural remodeling of the myocardium in this pathology. Using diffusion tensor magnetic resonance imaging, we present an analysis of myocardial fiber and laminar sheet orientation in ex vivo hypertrophic (6 SHR) and normal (5 WKY) rat hearts using the covariance of the diffusion tensor. First, an atlas of normal cardiac microstructure was formed using the WKY b0 images. Then, the SHR and WKY b0 hearts were registered to the atlas. The acquired deformation fields were applied to the SHR and WKY heart tensor fields followed by the preservation of principal direction (PPD) reorientation strategy. A mean tensor field was then formed from the registered WKY tensor images. Calculating the covariance of the registered tensor images about this mean for each heart, the hypertrophic myocardium exhibited significantly increased myocardial fiber derangement (p Âź 0.017) with a mean dispersion of 38.7 deg, and an increased dispersion of the laminar sheet normal (p = 0.030) of 54.8 deg compared with 34.8 deg and 51.8 deg, respectively, in the normal hearts. Results demonstrate significantly altered myocardial fiber and laminar sheet structure in rats with hypertensive LVH
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A level set approach to segmenting a deforming myocardium from dynamically acquired SPECT projection data
Dynamic cardiac single photon emission computed tomography (SPECT) offers an effective way for observing fundamental physiological functions of organs and could aid in the early diagnosis of cardiovascular disease, in particular, for those patients with minimal disease. This would improve the chances of recovery by initiating appropriate therapy and an altered life style. To make dynamic cardiac SPECT viable with present clinical scanners methods need to be developed that reconstruct time activity curves from dynamically moving organs representing the change of tracer concentration as a function of time from projection data acquired from slowly rotating gamma cameras. This type of data analysis faces the challenge of modeling both rigid and non-rigid body deformation as well as modeling of a time varying tracer concentration. In the work presented here, we develop methods for segmenting the beating heart using an approach based upon level sets, which can deal naturally with topological changes. A variational formulation of the level set method was implemented. This allowed the inclusion of a priori information and was computationally efficient. The algorithm was first evaluated with simulated dynamic cardiac image data. The MCAT phantom was used to generate data containing 32 time frames over one cardiac cycle. Each frame had a matrix size of 64Ă64Ă32 voxels with a resolution of 6.25 mm. Starting with an initial estimate of the boundary, the algorithm then converged to an accurate segmentation of the deforming heart. The initial estimate was not important and we could segment simultaneously both interior and exterior boundaries. This algorithm forms the foundation for the segmentation of the boundary of the deforming myocardium directly from projection data
Diffusion tensor magnetic resonance imaging-derived myocardial fiber disarray in hypertensive left ventricular hypertrophy: visualization, quantification and the effect on mechanical function
Left ventricular hypertrophy induced by systemic hypertension is generally regarded a morphological precursor of unfortunate cardiovascular events. Myocardial fiber disarray has been long recognized as a prevalent hallmark of this pathology. In this chapter, ex vivo diffusion tensor magnetic resonance imaging is employed to delineate the regional loss of myocardial organization that is present in the excised heart of a spontaneously hypertensive rat, as opposed to a control. Fiber tracking results are provided that illustrate in great detail the alterations in the integrity of cardiac muscle microstructure due to the disease. A quantitative analysis is also performed. Another contribution of this chapter is the model-based assessment of the role of the myofiber disarray in modulating the mechanical properties of the myocardium. The results of this study improve our understanding of the structural remodeling mechanisms that are associated with hypetensive left ventricular hypertrophy and their role
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