• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.327-355
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• 2016

A new analytical derivation of the elastodynamic point load solutions for an isotropic multi-layered half-space is presented by means of the precise integration method (PIM) and the approach of dual vector. The time-harmonic external load is prescribed either on the external boundary or in the interior of the solid medium. Starting with the axisymmetric governing motion equations in a cylindrical coordinate system, a second order ordinary differential matrix equation can be gained by making use of the Hankel integral transform. Employing the technique of dual vector, the second order ordinary differential matrix equation can be simplified into a first-order one. The approach of PIM is implemented to obtain the solutions of the ordinary differential matrix equation in the Hankel integral transform domain. The PIM is a highly accurate algorithm to solve sets of first-order ordinary differential equations and any desired accuracy of the dynamic point load solutions can be achieved. The numerical simulation is based on algebraic matrix operation. As a result, the computational effort is reduced to a great extent and the computation is unconditionally stable. Selected numerical trials are given to validate the accuracy and applicability of the proposed approach. More examples are discussed to portray the dependence of the load-displacement response on the isotropic parameters of the multi-layered media, the depth of external load and the frequency of excitation.

• Geophysics and Geophysical Exploration
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• v.25 no.1
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• pp.38-43
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• 2022

In case axial symmetrical bodies with varying cross sections such as volcanic conduits and unexploded ordnance (UXO), it is efficient to approximate them by adding the response of thin disks perpendicular to the axis of symmetry. To compute the vector magnetic and magnetic gradient tensor respones by such bodies, it is necessary to derive an analytical expression of the circular disk. Therefore, in this study, we drive closed-form expressions of the vector magnetic and magnetic gradient tensor due to a circular disk. First, the vector magnetic field is obtained from the existing gravity gradient tensor using Poisson's relation where the gravity gradient tensor due to the same disk with a constant density can be transformed into a magnetic field. Then, the magnetic gradient tensor is derived by differentiating the vector magnetic field with respect to the cylindrical coordinates converted from the Cartesian coordinate system. Finally, both the vector magnetic and magnetic gradient tensors are derived using Lipschitz-Hankel type integrals based on the axial symmetry of the circular disk.

• Journal of Korean Neurosurgical Society
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• v.62 no.4
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• pp.476-486
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• 2019

Objective : The functional information of $^{11}C$-methionine positron emission tomography (MET-PET) images can be applied for Gamma knife radiosurgery (GKR) and its image quality may affect defining the tumor. This study conducted the phantom-based evaluation for geometric accuracy and functional characteristic of diagnostic MET-PET image co-registered with stereotactic image in Leksell $GammaPlan^{(R)}$ (LGP) and also investigated clinical application of these images in metastatic brain tumors. Methods : Two types of cylindrical acrylic phantoms fabricated in-house were used for this study : the phantom with an array-shaped axial rod insert and the phantom with different sized tube indicators. The phantoms were mounted on the stereotactic frame and scanned using computed tomography (CT), magnetic resonance imaging (MRI), and PET system. Three-dimensional coordinate values on co-registered MET-PET images were compared with those on stereotactic CT image in LGP. MET uptake values of different sized indicators inside phantom were evaluated. We also evaluated the CT and MRI co-registered stereotactic MET-PET images with MR-enhancing volume and PET-metabolic tumor volume (MTV) in 14 metastatic brain tumors. Results : Imaging distortion of MET-PET was maintained stable at less than approximately 3% on mean value. There was no statistical difference in the geometric accuracy according to co-registered reference stereotactic images. In functional characteristic study for MET-PET image, the indicator on the lateral side of the phantom exhibited higher uptake than that on the medial side. This effect decreased as the size of the object increased. In 14 metastatic tumors, the median matching percentage between MR-enhancing volume and PET-MTV was 36.8% on PET/MR fusion images and 39.9% on PET/CT fusion images. Conclusion : The geometric accuracy of the diagnostic MET-PET co-registered with stereotactic MR in LGP is acceptable on phantom-based study. However, the MET-PET images could the limitations in providing exact stereotactic information in clinical study.