SIMPLIFIED MATHEMATICAL MODEL OF A MAGNETIC SYSTEM WITH A CIRCULAR MAGNETIC CONDUCTOR

A simplified design of a magnetic system with a circular magnetic core is presented and its mathematical model is developed to determine the magnetic flux. Transition from a cylindrical coordinate system to a rectangular coordinate system.

Analysis of Seismic Wavefield Characteristics in 3D Tunnel Models Based on the 3D Staggered-Grid Finite-Difference Scheme in the Cylindrical Coordinate System

The accurate prediction of the geological conditions ahead of a tunnel plays an important role in tunnel construction. Among all forward geological prospecting methods, the seismic detection method is widely applied. However, due to the characteristics of the tunnel and the complexity of the geological conditions, the seismic wavefield is complicated. Carrying out a more realistic forward modeling method is vital for fully understanding the law of seismic wave propagation and the characteristics of seismic wavefield in the tunnel. In this paper, the 3D staggered-grid finite-difference scheme in the cylindrical coordinate system based on the decoupled nonconversion elastic wave equation is used to carry out the numerical simulation. This method can avoid the diffraction interferences produced at the edges of the tunnel face in the Cartesian coordinate system. Based on this forward modeling method, the characteristics of wavefield and propagation laws of seismic waves under three kinds of common typical unfavorable geological models were explored, which can provide theoretical guidance to seismic data interpretation of tunnel seismic forward prospecting in practice.

Efficient Computation of Heat Distribution of Processed Materials under Laser Irradiation

In this paper, a solution is provided to solve the heat conduction equation in the three-dimensional cylinder region, where the laser intensity of the material irradiation surface is expressed as a Gaussian distribution. Based on the symmetry of heat distribution, firstly, the form of the heat equation in the common rectangular coordinate system is changed to another form in the two-dimensional cylindrical coordinate system. Secondly, the ADI with the backward Euler method and with Crank–Nicolson method are established to discretize the model in the cylindrical coordinate system, after which the simulation results are obtained, where the first kind of boundary value condition is used to verify the accuracy of these two algorithms. Then, the above two methods are used to solve the model with the third kind of boundary value condition. Finally, the comparison is performed with the results obtained by the MATLAB’s PDETOOL, which shows that the solution is more feasible and efficient.

Femoral Tunnel Placement Analysis in ACL Reconstruction Through Use of a Novel 3-Dimensional Reference With Biplanar Stereoradiographic Imaging

Background: The femoral-sided anatomic footprint of the anterior cruciate ligament (ACL) has been widely studied during the past decades. Nonanatomic placement is an important cause of ACL reconstruction (ACLR) failure. Purpose: To describe femoral tunnel placement in ACLR through use of a comprehensive 3-dimensional (3D) cylindrical coordinate system combining both the traditional clockface technique and the quadrant method. Our objective was to validate this technique and evaluate its reproducibility. Study Design: Descriptive laboratory study. Methods: The EOS Imaging System was used to make 3D models of the knee for 37 patients who had undergone ACLR. We designed an automated cylindrical reference software program individualized to the distal femoral morphology of each patient. Cylinder parameters were collected from 2 observers’ series of 3D models. Each independent observer also manually measured the corresponding parameters using a lateral view of the 3D contours and a 2-dimensional stereoradiographic image for the corresponding patient. Results: The average cylinder produced from the first observer’s EOS 3D models had a 30.0° orientation (95% CI, 28.4°-31.5°), 40.4 mm length (95% CI, 39.3-41.4 mm), and 19.3 mm diameter (95% CI, 18.6-20.0 mm). For the second observer, these measurements were 29.7° (95% CI, 28.1°-31.3°), 40.7 mm (95% CI, 39.7-41.8 mm), and 19.7 mm (95% CI, 18.8-20.6 mm), respectively. Our method showed moderate intertest intraclass correlation among all 3 measuring techniques for both length ( r = 0.68) and diameter ( r = 0.63) but poor correlation for orientation ( r = 0.44). In terms of interobserver reproducibility of the automated EOS 3D method, similar results were obtained: moderate to excellent correlations for length ( r = 0.95; P < .001) and diameter ( r = 0.66; P < .001) but poor correlation for orientation ( r = 0.29; P < .08). With this reference system, we were able to describe the placement of each individual femoral tunnel aperture, averaging a difference of less than 10 mm from the historical anatomic description by Bernard et al. Conclusion: This novel 3D cylindrical coordinate system using biplanar, stereoradiographic, low-irradiation imaging showed a precision comparable with standard manual measurements for ACLR femoral tunnel placement. Our results also suggest that automated cylinders issued from EOS 3D models show adequate accuracy and reproducibility. Clinical Relevance: This technique will open multiple possibilities in ACLR femoral tunnel placement in terms of preoperative planning, postoperative feedback, and even intraoperative guidance with augmented reality.