A new mathematical model for the propagation of longitudinal guided waves in free transversely isotropic cylinders is developed in this paper. The model uses three scalar potential functions to represent the three wave modes which can propagate inside the cylinder, i.e. compression (P), vertically polarized shear (SV) and horizontally polarized shear (SH) waves. This results in the decoupling of the equations of motion such that SH wave is completely decoupled from P and SV waves. Unlike other models in which the displacement field is guessed a priori, in the new model the resulting partial differential equations are solved by the method of separation of variables and the frequency equation is derived in a systematic manner. The dispersion curves as well as displacement fields inside the cylinder at various frequencies are plotted for longitudinal waves propagating along a number of transversely isotropic cylinders. The results obtained from this mathematical model agree with those obtained from the previous model. The new model has several advantages in comparison with the pervious ones. In this approach the equations are solved systematically and unlike other models, there is no need to guess the form of the final solution. This approach can also be used for solving similar problems which deal with cylindrical shells and multilayered cylinders having either finite or infinite lengths.
Various approaches have been used for model1ing problems dealing with interaction of acoustic/elastic waves with transversely isotropic cylinders. The authors developed the first mathematical model for the scattering of acoustic waves from transversely isotropic cylinders [Honarvar, F., Sinclair, A.N., 1996. Acoustic wave scattering from transversely isotropic cylinders. Journal of the Acoustical Society of America 100, 57-63.]. In the current paper, this model is used for derivation of the frequency equations of longitudinal and flexural wave propagation in free transversely isotropic cylinders. Consistency of this model with the physics of the problem is demonstrated and a systematic solution to the corresponding equations is developed. Numerical results obtained for a number of transversely isotopic cylinders are used for verification of the mathematical model.
We investigated a projection interpolation method for reconstructing dynamic contrast-enhanced (DCE) heart images from undersampled x-ray projections with filtered backprojecton (FBP). This method may facilitate the application of sparse-view dynamic acquisition for ultralow-dose quantitative computed tomography (CT) myocardial perfusion (MP) imaging. We conducted CT perfusion studies on 5 pigs with a standard full-view acquisition protocol (984 projections). We reconstructed DCE heart images with FBP from all and a quarter of the measured projections evenly distributed over 360°. We interpolated the sparse-view (quarter) projections to a full-view setting using a cubic-spline interpolation method before applying FBP to reconstruct the DCE heart images (synthesized full-view). To generate MP maps, we used 3 sets of DCE heart images, and compared mean MP values and biases among the 3 protocols. Compared with synthesized full-view DCE images, sparse-view DCE images were more affected by streak artifacts arising from projection undersampling. Relative to the full-view protocol, mean bias in MP measurement associated with the sparse-view protocol was 10.0 mL/min/100 g (95%CI: −8.9 to 28.9), which was >3 times higher than that associated with the synthesized full-view protocol (3.3 mL/min/100 g, 95% CI: −6.7 to 13.2). The cubic-spline-view interpolation method improved MP measurement from DCE heart images reconstructed from only a quarter of the full projection set. This method can be used with the industry-standard FBP algorithm to reconstruct DCE images of the heart, and it can reduce the radiation dose of a whole-heart quantitative CT MP study to <2 mSv (at 8-cm coverage).
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