Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.

Automatic modeling of pectus excavatum corrective prosthesis using artificial neural networks

Pectus excavatum is the most common deformity of the thorax. Pre-operative diagnosis usually includes Computed Tomography (CT) to successfully employ a thoracic prosthesis for anterior chest wall remodeling. Aiming at the elimination of radiation exposure, this paper presents a novel methodology for the replacement of CT by a 3D laser scanner (radiation-free) for prosthesis modeling. The complete elimination of CT is based on an accurate determination of ribs position and prosthesis placement region through skin surface points. The developed solution resorts to a normalized and combined outcome of an artificial neural network (ANN) set. Each ANN model was trained with data vectors from 165 male patients and using soft tissue thicknesses (STT) comprising information from the skin and rib cage (automatically determined by image processing algorithms). Tests revealed that ribs position for prosthesis placement and modeling can be estimated with an average error of 5.0 ± 3.6 mm. One also showed that the ANN performance can be improved by introducing a manually determined initial STT value in the ANN normalization procedure (average error of 2.82 ± 0.76 mm). Such error range is well below current prosthesis manual modeling (approximately 11 mm), which can provide a valuable and radiation-free procedure for prosthesis personalization.

Automatic modeling of pectus excavatum corrective prosthesis using artificial neural networks

Pectus excavatum is the most common deformity of the thorax. Pre-operative diagnosis usually includes Computed Tomography (CT) to successfully employ a thoracic prosthesis for anterior chest wall remodeling. Aiming at the elimination of radiation exposure, this paper presents a novel methodology for the replacement of CT by a 3D laser scanner (radiation-free) for prosthesis modeling. The complete elimination of CT is based on an accurate determination of ribs position and prosthesis placement region through skin surface points. The developed solution resorts to a normalized and combined outcome of an artificial neural network (ANN) set. Each ANN model was trained with data vectors from 165 male patients and using soft tissue thicknesses (STT) comprising information from the skin and rib cage (automatically determined by image processing algorithms). Tests revealed that ribs position for prosthesis placement and modeling can be estimated with an average error of 5.0 ± 3.6 mm. One also showed that the ANN performance can be improved by introducing a manually determined initial STT value in the ANN normalization procedure (average error of 2.82 ± 0.76 mm). Such error range is well below current prosthesis manual modeling (approximately 11 mm), which can provide a valuable and radiation-free procedure for prosthesis personalization.

Artificial neural networks for automatic modelling of the pectus excavatum corrective prosthesis

Pectus excavatum is the most common deformity of the thorax and usually comprises Computed Tomography (CT) examination for pre-operative diagnosis. Aiming at the elimination of the high amounts of CT radiation exposure, this work presents a new methodology for the replacement of CT by a laser scanner (radiation-free) in the treatment of pectus excavatum using personally modeled prosthesis. The complete elimination of CT involves the determination of ribs external outline, at the maximum sternum depression point for prosthesis placement, based on chest wall skin surface information, acquired by a laser scanner. The developed solution resorts to artificial neural networks trained with data vectors from 165 patients. Scaled Conjugate Gradient, Levenberg-Marquardt, Resilient Back propagation and One Step Secant gradient learning algorithms were used. The training procedure was performed using the soft tissue thicknesses, determined using image processing techniques that automatically segment the skin and rib cage. The developed solution was then used to determine the ribs outline in data from 20 patient scanners. Tests revealed that ribs position can be estimated with an average error of about 6.82±5.7 mm for the left and right side of the patient. Such an error range is well below current prosthesis manual modeling (11.7±4.01 mm) even without CT imagiology, indicating a considerable step forward towards CT replacement by a 3D scanner for prosthesis personalization.

Improving The Robustness Of Interventional 4D Ultrasound Segmentation Through The Use Of Personalized Shape Priors

While fluoroscopy is still the most widely used imaging modality to guide cardiac interventions, the fusion of pre-operative Magnetic Resonance Imaging (MRI) with real-time intra-operative ultrasound (US) is rapidly gaining clinical acceptance as a viable, radiation-free alternative. In order to improve the detection of the left ventricular (LV) surface in 4D ultrasound, we propose to take advantage of the pre-operative MRI scans to extract a realistic geometrical model representing the patients cardiac anatomy. This could serve as prior information in the interventional setting, allowing to increase the accuracy of the anatomy extraction step in US data. We have made use of a real-time 3D segmentation framework used in the recent past to solve the LV segmentation problem in MR and US data independently and we take advantage of this common link to introduce the prior information as a soft penalty term in the ultrasound segmentation algorithm. We tested the proposed algorithm in a clinical dataset of 38 patients undergoing both MR and US scans. The introduction of the personalized shape prior improves the accuracy and robustness of the LV segmentation, as supported by the error reduction when compared to core lab manual segmentation of the same US sequences.