Search results for: Soyoon Bak

Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

Abstract:

In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration-free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results are in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes. Semi-Lagrangian method, iteration-free method, nonlinear advection-diffusion equation, second-order backward difference formula

Keywords: Semi-Lagrangian method, iteration free method, nonlinear advection-diffusion equation, second-order backward difference formula

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Authors: Jae Ni Jang, SoYoon Park, Sukhee Park, Yumin Song, Jae Won Kim, Keum Nae Kang, Young Uk Kim

Abstract:

Objectives: Patellofemoral pain syndrome (PFPS) is a common clinical condition characterized by anterior knee pain. Here, we investigated the quadriceps tendon cross-sectional area (QTCSA) as a novel predictor for the diagnosis of PFPS. By examining the association between the QTCSA and PFPS, we aimed to provide a more valuable diagnostic parameter and more equivocal assessment of the diagnostic potential of PFPS by comparing the QTCSA with the quadriceps tendon thickness (QTT), a traditional measure of quadriceps tendon hypertrophy. Patients and Methods: This retrospective study included 30 patients with PFPS and 30 healthy participants who underwent knee magnetic resonance imaging. T1-weighted turbo spin echo transverse magnetic resonance images were obtained. The QTCSA was measured on the axial-angled phases of the images by drawing outlines, and the QTT was measured at the most hypertrophied quadriceps tendon. Results: The average QTT and QTCSA for patients with PFPS (6.33±0.80 mm and 155.77±36.60 mm², respectively) were significantly greater than those for healthy participants (5.77±0.36 mm and 111.90±24.10 mm2, respectively; both P<0.001). We used a receiver operating characteristic curve to confirm the sensitivities and specificities for both the QTT and QTCSA as predictors of PFPS. The optimal diagnostic cutoff value for QTT was 5.98 mm, with a sensitivity of 66.7%, a specificity of 70.0%, and an area under the curve of 0.75 (0.62–0.88). The optimal diagnostic cutoff value for QTCSA was 121.04 mm², with a sensitivity of 73.3%, a specificity of 70.0%, and an area under the curve of 0.83 (0.74–0.93). Conclusion: The QTCSA was found to be a more reliable diagnostic indicator for PFPS than QTT.

Keywords: patellofemoral pain syndrome, quadriceps muscle, hypertrophy, magnetic resonance imaging

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