Summary We report a case of massive rectal haemorrhage arising from a single ectatic arterial vessel above the haemorrhoidal cushion in normal rectal mucosa. Use of an anal retractor enable identification of the bleeding vessel and avoided a major laparatomy.
We present a numerical framework for computing nested quadrature rules for various weight functions. The well-known Kronrod method extends the Gauss-Legendre quadrature by adding new optimal nodes to the existing Gauss nodes for integration of higher order polynomials. Our numerical method generalizes the Kronrod rule for any continuous probability density function on real line with finite moments. We develop a bi-level optimization scheme to solve moment-matching conditions for two levels of main and nested rule and use a penalty method to enforce the constraints on the limits of the nodes and weights. We demonstrate our nested quadrature rule for probability measures on finite/infinite and symmetric/asymmetric supports. We generate Gauss-Kronrod-Patterson rules by slightly modifying our algorithm and present results associated with Chebyshev polynomials which are not reported elsewhere. We finally show the application of our nested rules in construction of sparse grids where we validate the accuracy and efficiency of such nested quadrature-based sparse grids on parameterized boundary and initial value problems in multiple dimensions.
Neural operator learning as a means of mapping between complex function spaces has garnered significant attention in the field of computational science and engineering (CS&E). In this paper, we apply Neural operator learning to the time-of-flight ultrasound computed tomography (USCT) problem. We learn the mapping between time-of-flight (TOF) data and the heterogeneous sound speed field using a full-wave solver to generate the training data. This novel application of operator learning circumnavigates the need to solve the computationally intensive iterative inverse problem. The operator learns the non-linear mapping offline and predicts the heterogeneous sound field with a single forward pass through the model. This is the first time operator learning has been used for ultrasound tomography and is the first step in potential real-time predictions of soft tissue distribution for tumor identification in beast imaging.
Numerical algorithms, modern programming techniques, and parallel computing are often taught serially across different courses and different textbooks. The need to integrate concepts and tools usually comes only in employment or in research - after the courses are concluded - forcing the student to synthesise what is perceived to be three independent subfields into one. This book provides a seamless approach to stimulate the student simultaneously through the eyes of multiple disciplines, leading to enhanced understanding of scientific computing as a whole. The book includes both basic as well as advanced topics and places equal emphasis on the discretization of partial differential equations and on solvers. Some of the advanced topics include wavelets, high-order methods, non-symmetric systems, and parallelization of sparse systems. The material covered is suited to students from engineering, computer science, physics and mathematics.
Histologic confirmation of axillary nodal metastases preoperatively avoids a sentinel node biopsy and enables a one step surgical procedure. The aim of this study was to establish the local positive predictive value of axillary ultrasound (AUS) and guided needle core biopsy (NCB) in axillary staging of breast cancer, and to identify factors influencing yield. A prospective audit of 142 consecutive patients (screening and symptomatic) presenting from 1st December 2008–31st May 2009 with breast lesions categorized R4–R5, who underwent a preoperative AUS, and proceeded to surgery was undertaken. Ultrasound-guided NCB was performed on nodes radiologically classified R3–R5. Lymph node size, number, and morphological features were documented. Yield was correlated with tumor size, grade, and histologic type. AUS/NCB was correlated with post surgical pathologic findings to determine sensitivity, specificity, positive and negative predictive value of AUS and NCB. A total of 142 patients underwent surgery, of whom 52 (37%) had lymph node metastases on histology. All had a preoperative AUS, 51 (36%) had abnormal ultrasound findings. 46 (90%) underwent axillary node NCB of which 24 (52%) were positive. The smallest tumor size associated with positive nodes at surgery was 11.5 mm. The sensitivity of AUS was 65%. Specificity was 81%, with a positive predictive value (PPV) of 67% and negative predictive (NPV) value of 80%. Sensitivity of U/S-guided NCB was 75%, with a specificity of 100%, PPV 100% and NPV 64%. Sensitivity of AUS for lobular carcinoma was 36% versus 76% for all other histologies. Sensitivity of NCB for lobular cancer was 33% versus 79% for all other histologies. The most significant factor producing discordance between preoperative AUS and definitive histologic evidence of lymph node metastasis was tumor type. Accurate preoperative lymph node staging was prejudiced by lobular histology (p < 0.0019).
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