Narrow Results

Recently, the simplified spherical harmonics equations (SP_N) model has attracted much attention in modeling the light propagation in small tissue geometries at visible and near-infrared wavelengths. In this paper, we report an efficient numerical method for fluorescence molecular tomography (FMT) that combines the advantage of SP_N model and adaptive hp finite element method (hp-FEM). For purposes of comparison, hp-FEM and h-FEM are, respectively applied to the reconstruction process with diffusion approximation and SP_N model. Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are designed to evaluate the reconstruction methods in terms of the location and the reconstructed fluorescent yield. The experimental results demonstrate that hp-FEM with SP_N model, yield more accurate results than h-FEM with diffusion approximation model does. The phantom experiments show the potential and feasibility of the proposed approach in FMT applications.

Signal channelization enables efficient frequency domain processing and is a mainstay of astronomical signal processing, but applications that require high time resolution necessitate reconstruction of the original wide band signal. In a previous paper, a near-perfect method of reconstructing a time-limited input signal from the output of an oversampled polyphase filterbank (PFB) was described. Here, we consider the case where continuous signals are processed. We show that the most simplistic approach, which utilizes non-overlapping windows and a fast Fourier transform (FFT) channelizer, introduces large errors whose magnitude can equal the signal. The ringing introduced by truncation at the end of a block, combined with the cyclic nature of FFTs, leads to errors that are concentrated at block boundaries. These localized errors can be heavily suppressed by utilizing overlapping windows and nearly completely eliminated by apodizing the data blocks with a Tukey window. After these improvements, the much smaller residual error is concentrated at the PFB channel boundaries and is due to adjacent channels having different gain slopes at the channel boundary. Increasing the channel passband equalizes the gain slope at the channel boundary, and the error is reduced further. With these changes, errors as low as −100dB are achieved, and the method of reconstructing the channelized data meets the stringent signal purity requirement for astronomical applications such as radio pulsar timing.

Part I of this paper presents analytic solutions for reconstructing the excitation forces that act on the interior surfaces of a finite solid rectangular enclosure with the fluid loading effect taken into consideration, given vibroacoustic data in the exterior region. The reason for selecting a simple structure is to facilitate the reconstruction of excitation forces. To validate these analytic solutions, we apply the reciprocity principle and demonstrate that when the resultant excitation forces are used to excite the enclosure from the inside, the same vibroacoustic responses in the exterior region in exterior region can be obtained. To illustrate this point, we consider the case in which the top panel of a rectangular box is connected to the side walls through simply-supported boundary conditions, and the rest surfaces are rigid. The top surface of this box may be excited into vibrations by any type of excitation forces from the inside with the fluid loading effect taken into consideration. Note that for arbitrarily shaped structures under arbitrary boundary conditions, numerical solutions can be obtained. Therefore, it is possible to determine the excitation forces acting inside an enclosure based on the vibroacoustic information collected in the exterior. The knowledge of the excitation forces is critically important, because it can lead to optimal mitigation strategies to mitigate undesirable noise and vibrations.

Part II of this study presents numerical simulations of reconstructing the excitation forces acting on the interior surface of an enclosure, based on the vibroacoustic information collected in the exterior region. Various types of excitation forces such as distributed, line, and point forces are considered. Moreover, fluid loading inside the enclosure is considered in the numerical simulations. Analytical proofs show that fluid loading has no impact on excitation forces, but has significant impacts on structural vibrations. This is especially true when the density of fluid medium inside an enclosure is high. Results demonstrate that when excitation forces are continuous, the accuracy in reconstruction may be very high. When excitation forces contain abrupt changes or discontinuities, for example, line and point force, the accuracy in reconstruction may be significantly reduced. This is because many expansion terms are required to properly describe the discontinuities of excitations. On the other hand, discretization grids are fixed a priori. When fixed discretization grids are used together with an increasing number of expansion terms, aliasing may occur that may completely distort the reconstructed excitation forces.

This paper presents analyses of the 3D acoustic fields generated by motorcycles at very low frequencies ($<150$ Hz) at the idle speed and during sudden acceleration. Diagnosis and analyses of sound sources at low frequencies have always been a significant challenge because the directivity of low-frequency sound is very poor. To date, there are no research papers and/or reports that have demonstrated low-frequency sources localization and radiation patterns of any kind at high spatial resolution in 3D space. This study shows that by using sound viewer technologies, which include the passive sonic detection and ranging (SODAR), the Helmholtz equation least squares (HELS) method, advanced signal processing, denoising, etc., the locations of sound sources and visualization of the sound fields can be determined with high spatial resolution, even at frequencies below 150 Hz. In particular, the HELS method allows for reconstructing all the acoustic quantities, including the acoustic pressure, time-averaged acoustic intensity, time-averaged acoustic power on the source surfaces and in 3D space. The hardware needed consists of a 3D array with six free-field precision microphones with pre-amplifiers, a miniature wide-angle camera, an eight-channel digital signal processor and a laptop computer.

This paper presents the experimental validations of reconstructing the characteristics of the excitation forces that act inside a vibrating structure, which includes the location, type, amplitude, and spectrum, based on a single set of measurements of the normal surface velocity on the exterior surface by using the modified Helmholtz Equation Least Squares (HELS) method, as if one could see through this solid structure. Phase I of this paper shows the reconstruction of the vibroacoustic responses in the exterior region of the structure, including the field acoustic pressure, the surface acoustic pressure, the normal surface velocity or Operational Deflection Shape (ODS), the normal component of the time-averaged acoustic intensity, and the time-averaged acoustic power. Phase II of this paper illustrates the reconstruction of the excitation forces with the fluid-loading effects taken into consideration, based on the vibroacoustic responses reconstructed in the exterior region. The significance of the study, namely, the interrelationships among the excitation force, structural vibration, and acoustic radiation is discussed. The knowledge thus acquired may be important for engineers to analyze various complex noise and vibration issues in practice and to come up with the most cost-effective noise and vibration mitigation strategies.

Part II of this paper discusses experimental validations of the reconstructed excitation forces acting inside a vibrating structure with the fluid-loading effect taken into consideration. Specifically, the characteristics of the excitation forces such as their locations, types, amplitudes, and spectra are reconstructed by using the modified Helmholtz Equation Least Squares (HELS) method, based on a single set of measurements of the normal surface velocity on the exterior surfaces, as if one could see through such a solid structure. Since the fluid-loading effect has a direct impact on the vibration responses of a structure, it is not possible to derive analytic solutions to vibration responses of the structure. Therefore, numerical solutions are sought by using the boundary element method (BEM). The fluid-loading effect, a.k.a., the reverberation sound field inside the structure is calculated based on the absorption coefficients and surface areas of the interior objects. The reconstructed excitation forces are then compared to the benchmark values and satisfactory agreements are obtained.

The consensus of the normal magnitude of lumbosacral curve has not been achieved. The Cobb's angle cannot depict the whole contour of this curve. For practical applications, a clearer image of these curves and their aging changes should be further investigated. This study aimed to provide a more consolidate concept of normal lumbosacral curves for clinician through a computerized reconstruction method.

Standing lateral radiographs of lumbosacral spine in 82 normal adults were used for reconstructing the sagittal lumbosacral curves. The geometric characteristics of these curves according to the gender and age groups were studied. Using standing lateral radiographs, reconstruction of the lumbosacral curves was performed through digitization, programming and computation. These curves and related parameters were normalized and averaged for analyzing the differences of gender and age.

The most anteriorward and horizontal vertebrae usually occurred on the L4 and L3 in any gender and age groups. The sacral inclination angle did not change obviously with the increasing ages. A tendency of L1 shifting backward was noted in the age groups of 40 to 60 and above 60 years old. The sagittal lumbosacral curves can be easily reconstructed by digitizing lateral radiographs, The aging changes of lumbosacral curves could be qualitatively described as the flattening of lower lumbar curve and the rearward inclination of upper lumbar curve. The changes occurred obviously above 40 years old. Although individual variations existed, the aging changes and the geometric characteristics such as the most anteriorward or horizontal vertebrae could be used as an important guideline during therapy or surgical correction.