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In this article, we develop an exponential high order compact alternating direction implicit (EHOC ADI) method for solving three dimensional (3D) unsteady convection-diffusion equations. The method, which requires only a regular seven-point 3D stencil similar to that in the standard second-order methods, is second order accurate in time and fourth-order accurate in space and unconditionally stable. The resulting EHOC ADI scheme in each alternating direction implicit (ADI) solution step corresponding to a strictly diagonally dominant matrix equation can be solved by the application of the one-dimensional tridiagonal Thomas algorithm with a considerable saving in computing time. Numerical experiments for three test problems are carried out to demonstrate the performance of the present method and to compare it with the classical Douglas-Gunn ADI method and the Karaa's high-order compact ADI method.

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Early detection of skull base invasion in nasopharyngeal carcinoma (NPC) is crucial for correct staging, assessing treatment response and contouring the tumor target in radiotherapy planning, as well as improving the patient's prognosis. To compare the diagnostic efficacy of single photon emission computed tomography/computed tomography (SPECT/CT) imaging, magnetic resonance imaging (MRI) and computed tomography (CT) for the detection of skull base invasion in NPC. Sixty untreated patients with histologically proven NPC underwent SPECT/CT imaging, contrast-enhanced MRI and CT. Of the 60 patients, 30 had skull base invasion confirmed by the final results of contrast-enhanced MRI, CT and six-month follow-up imaging (MRI and CT). The diagnostic efficacy of the three imaging modalities in detecting skull base invasion was evaluated. The rates of positive findings of skull base invasion for SPECT/CT, MRI and CT were 53.3%, 48.3% and 33.3%, respectively. The sensitivity, specificity and accuracy were 93.3%, 86.7% and 90.0% for SPECT/CT fusion imaging, 96.7%, 100.0% and 98.3% for contrast-enhanced MRI, and 66.7%, 100.0% and 83.3% for contrast-enhanced CT. MRI showed the best performance for the diagnosis of skull base invasion in nasopharyngeal carcinoma, followed closely by SPECT/CT. SPECT/CT had poorer specificity than that of both MRI and CT, while CT had the lowest sensitivity.