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A previously described two-dimensional k-space method for large-scale calculation of acoustic wave propagation in tissues is extended to three dimensions. The three-dimensional method contains all of the two-dimensional method features that allow accurate and stable calculation of propagation. These features are spectral calculation of spatial derivatives, temporal correction that produces exact propagation in a homogeneous medium, staggered spatial and temporal grids, and a perfectly matched boundary layer. Spectral evaluation of spatial derivatives is accomplished using a fast Fourier transform in three dimensions. This computational bottleneck requires all-to-all communication; execution time in a parallel implementation is therefore sensitive to node interconnect latency and bandwidth. Accuracy of the three-dimensional method is evaluated through comparisons with exact solutions for media having spherical inhomogeneities. Large-scale calculations in three dimensions were performed by distributing the nearly 50 variables per voxel that are used to implement the method over a cluster of computers. Two computer clusters used to evaluate method accuracy are compared. Comparisons of k-space calculations with exact methods including absorption highlight the need to model accurately the medium dispersion relationships, especially in large-scale media. Accurately modeled media allow the k-space method to calculate acoustic propagation in tissues over hundreds of wavelengths.

Correction of aberration in ultrasound imaging uses the response of a point reflector or its equivalent to characterize the aberration. Because a point reflector is usually unavailable, its equivalent is obtained using statistical methods, such as processing reflections from multiple focal regions in a random medium. However, the validity of methods that use reflections from multiple points is limited to isoplanatic patches for which the aberration is essentially the same. In this study, aberration is modeled by an offset phase screen to relax the isoplanatic restriction. Methods are developed to determine the depth and phase of the screen and to use the model for compensation of aberration as the beam is steered. Use of the model to enhance the performance of the noted statistical estimation procedure is also described. Experimental results obtained with tissue-mimicking phantoms that implement different models and produce different amounts of aberration are presented to show the efficacy of these methods. The improvement in b-scan resolution realized with the model is illustrated. The results show that the isoplanatic patch assumption for estimation of aberration can be relaxed and that propagation-path characteristics and aberration estimation are closely related.

Clustering is necessary for data aggregation, hierarchical routing, optimizing sleep patterns, election of extremal sensors, optimizing coverage and resource allocation, reuse of frequency bands and codes, and conserving energy. Optimal clustering is typically an NP-hard problem. Solutions to NP-hard problems involve searches through vast spaces of possible solutions. Evolutionary algorithms have been applied successfully to a variety of NP-hard problems. We explore one such approach, Particle Swarm Optimization (PSO), an evolutionary programming technique where a 'swarm' of test solutions, analogous to a natural swarm of bees, ants or termites, is allowed to interact and cooperate to find the best solution to the given problem. We use the PSO approach to cluster sensors in a sensor network. The energy efficiency of our clustering in a data-aggregation type sensor network deployment is tested using a modified LEACH-C code. The PSO technique with a recursive bisection algorithm is tested against random search and simulated annealing; the PSO technique is shown to be robust. We further investigate developing a distributed version of the PSO algorithm for clustering optimally a wireless sensor network.

A 40 × 35 × 25-mm3 specimen of human breast consisting mostly of fat and connective tissue was imaged using a 3-T magnetic resonance scanner. The resolutions in the image plane and in the orthogonal direction were 130 μm and 150 μm, respectively. Initial processing to prepare the data for segmentation consisted of contrast inversion, interpolation, and noise reduction. Noise reduction used a multilevel bidirectional median filter to preserve edges. The volume of data was segmented into regions of fat and connective tissue by using a combination of local and global thresholding. Local thresholding was performed to preserve fine detail, while global thresholding was performed to minimize the interclass variance between voxels classified as background and voxels classified as object. After smoothing the data to avoid aliasing artifacts, the segmented data volume was visualized using iso-surfaces. The isosurfaces were enhanced using transparency, lighting, shading, reflectance, and animation. Computations of pulse propagation through the model illustrate its utility for the study of ultrasound aberration. The results show the feasibility of using the described combination of methods to demonstrate tissue morphology in a form that provides insight about the way ultrasound beams are aberrated in three dimensions by tissue.

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In this paper, we explore methods to generate optimal network topologies for wireless sensor networks (WSNs) with and without obstacles. Specifically, we investigate a dense network with n sensor nodes and m = n b (0 < b < 1) helping nodes, and assess the impact of topology on its throughput capacity. For networks without obstacles, we find that uniformly distributed sensor nodes and regularly distributed helping nodes have some advantages in improving the throughput capacity. We also explore properties of networks composed of some isomorphic sub-networks. For networks with obstacles, we assume there are M = Θ(n v) (0 < v ≤ 1) arbitrarily or randomly distributed obstacles, which block cells they are located in, i.e., sensor nodes cannot be placed in these cells and nodes' communication cannot cross them directly. We find that the overall throughput capacity is bounded by the transmission burden in areas around these blocked cells and introduce a novel algorithm of complexity O(M) to generate optimal sensor nodes' topologies for any given obstacles' distributions. We further analyze its performance for regularly distributed obstacles, which can be taken to estimate the lower bound of the algorithm's performance.

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