Esmaeil Enjilela

An alternative method for plotting dispersion curves.

Solving the frequency equation and plotting the dispersion curves in problems of wave propagation in cylinders and plates, particularly when the material is anisotropic, are complicated tasks. The traditional numerical methods are usually based on determination of the zeros of the frequency equation by using an iterative find-root algorithm. In this paper, an alternative method is proposed which extracts the solution of the frequency equation in the form of dispersion curves from the three-dimensional illustration of the frequency equation. For this purpose, a three-dimensional representation of the real roots of the frequency equation is first plotted. The dispersion curves, which are the numerical solutions of the frequency equation, are then obtained by a suitable cut in the velocity-frequency plane. The advantages of this method include simplicity, high speed, low possibility of numerical error, and presentation of the results in a graphical form that promotes ease of interpretation. This method is not directly applicable to problems which incorporate high damping or leaky waves. However, if the damping is not very high, it could be a good estimate of the true dispersion curves.

Correlation between helical surface waves and guided modes of an infinite immersed elastic cylinder

Scattering of obliquely incident plane acoustic waves from immersed infinite solid elastic cylinders is a complex phenomenon that involves generation of various types of surface waves on the body of the cylinder. Mitri [F.G. Mitri, Acoustic backscattering enhancement resulting from the interaction of an obliquely incident plane wave with an infinite cylinder, Ultrasonics 50 (2010) 675-682] recently showed that for a solid aluminum cylinder, there exist acoustic backscattering enhancements at a normalized frequency of ka⩽0.1. The incidence angle α(c) at which these enhancements are observed lies between the first (longitudinal) and second (shear) coupling angles of the cylinder. He also confirmed the observations previously reported by the authors that there exist backscattering enhancements of the dipole mode at large angles of incidence where no wave penetration into the cylinder is expected. In this paper, physical explanations are provided for the aforementioned observations by establishing a correlation between helical surface waves generated by oblique insonification of an immersed infinite solid elastic cylinder and the longitudinal and flexural guided modes that can propagate along the cylinder. In particular, it is shown that the backscattering enhancement observed at ka⩽0.1 is due to the excitation of the first longitudinal guided mode travelling at the bar velocity along the cylinder. It is also demonstrated that the dipole resonance mode observed at incidence angles larger than the Rayleigh coupling angle is associated with the first flexural guided mode of the cylinder. The correlation established between the scattering and propagation problems can be used in both numerical and experimental studies of interaction of mechanical waves with cylinders.

Asymmetric and axisymmetric vibrations of finite transversely isotropic circular cylinders

This paper presents an approach for obtaining the exact frequency equations of axisymmetric and asymmetric free vibrations of transversely isotropic circular cylinders. The solution method is based on the three dimensional theory of linear elasticity and uses potential functions. Using this approach, the frequency spectra and vibration mode shapes are plotted for a number of transversely isotropic cylinders. The proposed approach introduces a number of merits compared to earlier approximate and exact solution methods. First, unlike numerically complicated series methods that provide approximate solutions, the proposed approach is exact. Second, combination of scalar functions employed for representing the displacement field is consistent with the physics of the problem. One scalar potential function has been considered for each component of the wave field inside the elastic cylinder. As a result, the solution is systematically divided into coupled and decoupled equations. In addition, by using this approach, there is no need to guess the final of the solution a priori. These merits make the proposed approach suitable for other vibration problems of anisotropic materials.

Refining a region-of-interest within an available CT image

This paper describes a numerical method for refining the image of a region-of-interest (RoI) within an existing tomographic slice, provided that projection data are stored along with the image. Using the attributes of the image, projection values (ray-sums) are adjusted to compensate for the material outside the RoI. Advantage is taken of the high degree of overdetermination of common computed tomography systems to reconstruct an RoI image over smaller pixels. The smaller size of a region-of-interest enables the use of iterative methods for RoI image reconstruction, which are less prone to error propagation. Simulation results are shown for an anthropomorphic head phantom, demonstrating that the introduced approach enhances both the spatial resolution and material contrast of RoI images; without the need to acquire any additional measurements or to alter existing imaging setups and systems.

Transmission-Like Calibration-Free Tomographic Reconstruction With Compton-Scattered Photons

Image-reconstruction with Compton-scattered photons is a nonlinear problem, because it involves both the linear process of scattering and the exponential pre- and post-scatter attenuation. For thin and light objects and with high-energy photons, the exponential terms can be ignored, rendering the problem linear. We show that when attenuation is significant, linearity can also be accomplished by considering scattering as a scaling factor and with subsequent logarithmic transformation, the image-reconstruction problem is converted into a transmission-like problem along the travel lines of incident and scattered radiation. It is shown that this formulation produces images qualitatively reflecting object features in a manner similar to that of backprojection in conventional computed tomography. This is done without the need for calibration or scaling of measurements. The theoretical aspects of the introduced mathematical formulation are developed for idealized pencil-beams, adapted approximately to fan-beam configurations, and applied to imaging with laboratory-acquired measurements. The introduced transmission-like formulation and calibration-free aspects should promote wider use of scatter imaging.

Ultra-low dose quantitative CT myocardial perfusion imaging with sparse-view dynamic acquisition and image reconstruction: A feasibility study

PURPOSE We implemented and validated a compressed sensing (CS) based algorithm for reconstructing dynamic contrast-enhanced (DCE) CT images of the heart from sparsely sampled X-ray projections. METHODS DCE CT imaging of the heart was performed on five normal and ischemic pigs after contrast injection. DCE images were reconstructed with filtered backprojection (FBP) and CS from all projections (984-view) and 1/3 of all projections (328-view), and with CS from 1/4 of all projections (246-view). Myocardial perfusion (MP) measurements with each protocol were compared to those with the reference 984-view FBP protocol. RESULTS Both the 984-view CS and 328-view CS protocols were in good agreements with the reference protocol. The Pearson correlation coefficients of 984-view CS and 328-view CS determined from linear regression analyses were 0.98 and 0.99 respectively. The corresponding mean biases of MP measurement determined from Bland-Altman analyses were 2.7 and 1.2ml/min/100g. When only 328 projections were used for image reconstruction, CS was more accurate than FBP for MP measurement with respect to 984-view FBP. However, CS failed to generate MP maps comparable to those with 984-view FBP when only 246 projections were used for image reconstruction. CONCLUSION DCE heart images reconstructed from one-third of a full projection set with CS were minimally affected by aliasing artifacts, leading to accurate MP measurements with the effective dose reduced to just 33% of conventional full-view FBP method. The proposed CS sparse-view image reconstruction method could facilitate the implementation of sparse-view dynamic acquisition for ultra-low dose CT MP imaging.