Eulerian polynomials and polynomial congruences

We prove that the Eulerian polynomial satisfies certain polynomial congruences. Furthermore, these congruences characterize the Eulerian polynomial

Eulerian polynomials and polynomial congruences

We prove that the Eulerian polynomial satisfies certain polynomial congruences. Furthermore, these congruences characterize the Eulerian polynomial

Modified Subtraction Coronary CT Angiography Method for Patients Unable to Perform Long Breath-Holds: A Preliminary Study.

Rationale and ObjectivesSevere calcifications of the coronary arteries are still a major challenge in coronary computed tomography (CT) angiography (CCTA). Subtraction CCTA using a 320-detector row CT scanner has recently been introduced for patients with severe calcifications. However, the conventional subtraction CCTA method requires a long breath-holding time of approximately 20–40 seconds. This is a major problem in clinical practice because many patients may not be able to perform such a long breath-hold. We explored a modified subtraction CCTA method with a short breath-holding time to overcome this problem.Materials and MethodsThis study was approved by our institutional review board, and all patients gave written informed consent. A total of 12 patients with a coronary calcium score of >400 were enrolled in this study. All patients were unable to hold their breath for more than 20 seconds. Modified subtraction CCTA was performed using the bolus-tracking method. The acquisition protocol was adjusted so that the mask scan was acquired 10 seconds after the postcontrast scan during a single breath-hold. The subtraction image was obtained by subtracting the mask image data from the postcontrast image data. The breath-holding times were recorded. Enhancement of the coronary arteries in the subtraction images was assessed. Subjective image quality was evaluated in a total of 32 segments using a 4-point scale.ResultsThe mean breath-holding time was 12.8 ± 0.8 seconds (range, 12–14 seconds). The average CT number in the coronary arteries was 288.6 ± 80.5 Hounsfield units (HU) in the subtraction images. Average image quality was significantly increased from 2.1 ± 0.9 with conventional CCTA to 3.1 ± 0.7 with subtraction CCTA (P < 0.001). With subtraction CCTA, the number of non-diagnostic segments was significantly reduced from 53% to 19% (P = 0.001).ConclusionsThis preliminary study has shown that our modified subtraction CCTA method allows the breath-holding time to be shortened to <15 seconds. This may substantially improve the success rate of subtraction CCTA by reducing artifacts and allowing this technique to be applied to patients who are unable to perform a long breath-hold