Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

Coupling biomechanics to a cellular level model: An approach to patient-specific image driven multi-scale and multi-physics tumor simulation

Modeling of tumor growth has been performed according to various approaches addressing different biocomplexity levels and spatiotemporal scales. Mathematical treatments range from partial differential equation based diffusion models to rule-based cellular level simulators, aiming at both improving our quantitative understanding of the underlying biological processes and, in the mid- and long term, constructing reliable multi-scale predictive platforms to support patient-individualized treatment planning and optimization. The aim of this paper is to establish a multi-scale and multi-physics approach to tumor modeling taking into account both the cellular and the macroscopic mechanical level. Therefore, an already developed biomodel of clinical tumor growth and response to treatment is self-consistently coupled with a biomechanical model. Results are presented for the free growth case of the imageable component of an initially point-like glioblastoma multiforme tumor. The composite model leads to significant tumor shape corrections that are achieved through the utilization of environmental pressure information and the application of biomechanical principles. Using the ratio of smallest to largest moment of inertia of the tumor material to quantify the effect of our coupled approach, we have found a tumor shape correction of 20\% by coupling biomechanics to the cellular simulator as compared to a cellular simulation without preferred growth directions. We conclude that the integration of the two models provides additional morphological insight into realistic tumor growth behavior. Therefore, it might be used for the development of an advanced oncosimulator focusing on tumor types for which morphology plays an important role in surgical and/or radio-therapeutic treatment planning.

A Fully Bayesian Approach for Combining Multilevel Failure Information in Fault Tree Quantification and Corresponding Optimal Resource Allocation

This paper presents a fully Bayesian approach that simultaneously combines basic event and statistically independent higher event-level failure data in fault tree quantification. Such higher-level data could correspond to train, sub-system or system failure events. The full Bayesian approach also allows the highest-level data that are usually available for existing facilities to be automatically propagated to lower levels. A simple example illustrates the proposed approach. The optimal allocation of resources for collecting additional data from a choice of different level events is also presented. The optimization is achieved using a genetic algorithm.

Effect of X-ray tube parameters, iodine concentration, and patient size on image quality in pulmonary computed tomography angiography: a chest-phantom-study

OBJECTIVES: The aim of this phantom study was to evaluate the contrast-to-noise ratio (CNR) in pulmonary computed tomography (CT)-angiography for 300 and 400 mg iodine/mL contrast media using variable x-ray tube parameters and patient sizes. We also analyzed the possible strategies of dose reduction in patients with different sizes. MATERIALS AND METHODS: The segmental pulmonary arteries were simulated by plastic tubes filled with 1:30 diluted solutions of 300 and 400 mg iodine/mL contrast media in a chest phantom mimicking thick, intermediate, and thin patients. Volume scanning was done with a CT scanner at 80, 100, 120, and 140 kVp. Tube current-time products (mAs) varied between 50 and 120% of the optimal value given by the built-in automatic dose optimization protocol. Attenuation values and CNR for both contrast media were evaluated and compared with the volume CT dose index (CTDI(vol)). Figure of merit, calculated as CNR/CTDIvol, was used to quantify image quality improvement per exposure risk to the patient. RESULTS: Attenuation of iodinated contrast media increased both with decreasing tube voltage and patient size. A CTDIvol reduction by 44% was achieved in the thin phantom with the use of 80 instead of 140 kVp without deterioration of CNR. Figure of merit correlated with kVp in the thin phantom (r = -0.897 to -0.999; P < 0.05) but not in the intermediate and thick phantoms (P = 0.09-0.71), reflecting a decreasing benefit of tube voltage reduction on image quality as the thickness of the phantom increased. Compared with the 300 mg iodine/mL concentration, the same CNR for 400 mg iodine/mL contrast medium was achieved at a lower CTDIvol by 18 to 40%, depending on phantom size and applied tube voltage. CONCLUSIONS: Low kVp protocols for pulmonary embolism are potentially advantageous especially in thin and, to a lesser extent, in intermediate patients. Thin patients profit from low voltage protocols preserving a good CNR at a lower exposure. The use of 80 kVp in obese patients may be problematic because of the limitation of the tube current available, reduced CNR, and high skin dose. The high CNR of the 400 mg iodine/mL contrast medium together with lower tube energy and/or current can be used for exposure reduction.

Dose optimization approach to fast X-ray microtomography of the lung alveoli

A basic prerequisite for in vivo X-ray imaging of the lung is the exact determination of radiation dose. Achieving resolutions of the order of micrometres may become particularly challenging owing to increased dose, which in the worst case can be lethal for the imaged animal model. A framework for linking image quality to radiation dose in order to optimize experimental parameters with respect to dose reduction is presented. The approach may find application for current and future in vivo studies to facilitate proper experiment planning and radiation risk assessment on the one hand and exploit imaging capabilities on the other.

X-ray image calibration and its application to clinical orthopedics.

X-ray imaging is one of the most commonly used medical imaging modality. Albeit X-ray radiographs provide important clinical information for diagnosis, planning and post-operative follow-up, the challenging interpretation due to its 2D projection characteristics and the unknown magnification factor constrain the full benefit of X-ray imaging. In order to overcome these drawbacks, we proposed here an easy-to-use X-ray calibration object and developed an optimization method to robustly find correspondences between the 3D fiducials of the calibration object and their 2D projections. In this work we present all the details of this outlined concept. Moreover, we demonstrate the potential of using such a method to precisely extract information from calibrated X-ray radiographs for two different orthopedic applications: post-operative acetabular cup implant orientation measurement and 3D vertebral body displacement measurement during preoperative traction tests. In the first application, we have achieved a clinically acceptable accuracy of below 1° for both anteversion and inclination angles, where in the second application an average displacement of 8.06±3.71 mm was measured. The results of both applications indicate the importance of using X-ray calibration in the clinical routine.

Acute onset incomitant image disparity modifies saccadic and vergence eye movements.

New-onset impairment of ocular motility will cause incomitant strabismus, i.e., a gaze-dependent ocular misalignment. This ocular misalignment will cause retinal disparity, that is, a deviation of the spatial position of an image on the retina of both eyes, which is a trigger for a vergence eye movement that results in ocular realignment. If the vergence movement fails, the eyes remain misaligned, resulting in double vision. Adaptive processes to such incomitant vergence stimuli are poorly understood. In this study, we have investigated the physiological oculomotor response of saccadic and vergence eye movements in healthy individuals after shifting gaze from a viewing position without image disparity into a field of view with increased image disparity, thus in conditions mimicking incomitance. Repetitive saccadic eye movements into a visual field with increased stimulus disparity lead to a rapid modification of the oculomotor response: (a) Saccades showed immediate disconjugacy (p < 0.001) resulting in decreased retinal image disparity at the end of a saccade. (b) Vergence kinetics improved over time (p < 0.001). This modified oculomotor response enables a more prompt restoration of ocular alignment in new-onset incomitance.

Automatic X-ray landmark detection and shape segmentation via data-driven joint estimation of image displacements

In this paper, we propose a new method for fully-automatic landmark detection and shape segmentation in X-ray images. To detect landmarks, we estimate the displacements from some randomly sampled image patches to the (unknown) landmark positions, and then we integrate these predictions via a voting scheme. Our key contribution is a new algorithm for estimating these displacements. Different from other methods where each image patch independently predicts its displacement, we jointly estimate the displacements from all patches together in a data driven way, by considering not only the training data but also geometric constraints on the test image. The displacements estimation is formulated as a convex optimization problem that can be solved efficiently. Finally, we use the sparse shape composition model as the a priori information to regularize the landmark positions and thus generate the segmented shape contour. We validate our method on X-ray image datasets of three different anatomical structures: complete femur, proximal femur and pelvis. Experiments show that our method is accurate and robust in landmark detection, and, combined with the shape model, gives a better or comparable performance in shape segmentation compared to state-of-the art methods. Finally, a preliminary study using CT data shows the extensibility of our method to 3D data.

Variational Stereo Imaging of Oceanic Waves with Statistical Constraints

An image processing observational technique for the stereoscopic reconstruction of the wave form of oceanic sea states is developed. The technique incorporates the enforcement of any given statistical wave law modeling the quasi Gaussianity of oceanic waves observed in nature. The problem is posed in a variational optimization framework, where the desired wave form is obtained as the minimizer of a cost functional that combines image observations, smoothness priors and a weak statistical constraint. The minimizer is obtained combining gradient descent and multigrid methods on the necessary optimality equations of the cost functional. Robust photometric error criteria and a spatial intensity compensation model are also developed to improve the performance of the presented image matching strategy. The weak statistical constraint is thoroughly evaluated in combination with other elements presented to reconstruct and enforce constraints on experimental stereo data, demonstrating the improvement in the estimation of the observed ocean surface.

In-loop Feature Tracking for Structure and Motion with Out-of-core Optimization

In this paper, a novel and approach for obtaining 3D models from video sequences captured with hand-held cameras is addressed. We define a pipeline that robustly deals with different types of sequences and acquiring devices. Our system follows a divide and conquer approach: after a frame decimation that pre-conditions the input sequence, the video is split into short-length clips. This allows to parallelize the reconstruction step which translates into a reduction in the amount of computational resources required. The short length of the clips allows an intensive search for the best solution at each step of reconstruction which robustifies the system. The process of feature tracking is embedded within the reconstruction loop for each clip as opposed to other approaches. A final registration step, merges all the processed clips to the same coordinate frame

Efficient Model-based 3D Tracking by Using Direct Image Registration

This thesis deals with the problem of efficiently tracking 3D objects in sequences of images. We tackle the efficient 3D tracking problem by using direct image registration. This problem is posed as an iterative optimization procedure that minimizes a brightness error norm. We review the most popular iterative methods for image registration in the literature, turning our attention to those algorithms that use efficient optimization techniques. Two forms of efficient registration algorithms are investigated. The first type comprises the additive registration algorithms: these algorithms incrementally compute the motion parameters by linearly approximating the brightness error function. We centre our attention on Hager and Belhumeur’s factorization-based algorithm for image registration. We propose a fundamental requirement that factorization-based algorithms must satisfy to guarantee good convergence, and introduce a systematic procedure that automatically computes the factorization. Finally, we also bring out two warp functions to register rigid and nonrigid 3D targets that satisfy the requirement. The second type comprises the compositional registration algorithms, where the brightness function error is written by using function composition. We study the current approaches to compositional image alignment, and we emphasize the importance of the Inverse Compositional method, which is known to be the most efficient image registration algorithm. We introduce a new algorithm, the Efficient Forward Compositional image registration: this algorithm avoids the necessity of inverting the warping function, and provides a new interpretation of the working mechanisms of the inverse compositional alignment. By using this information, we propose two fundamental requirements that guarantee the convergence of compositional image registration methods. Finally, we support our claims by using extensive experimental testing with synthetic and real-world data. We propose a distinction between image registration and tracking when using efficient algorithms. We show that, depending whether the fundamental requirements are hold, some efficient algorithms are eligible for image registration but not for tracking.

Applications of image-based, multi-view stereo reconstruction methods = (Aplicaciones de los métodos de reconstrucción estéreo multivista)

These slides present several 3-D reconstruction methods to obtain the geometric structure of a scene that is viewed by multiple cameras. We focus on the combination of the geometric modeling in the image formation process with the use of standard optimization tools to estimate the characteristic parameters that describe the geometry of the 3-D scene. In particular, linear, non-linear and robust methods to estimate the monocular and epipolar geometry are introduced as cornerstones to generate 3-D reconstructions with multiple cameras. Some examples of systems that use this constructive strategy are Bundler, PhotoSynth, VideoSurfing, etc., which are able to obtain 3-D reconstructions with several hundreds or thousands of cameras. En esta presentación se tratan varios métodos de reconstrucción 3-D para la obtención de la estructura geométrica de una escena que es visualizada por varias cámaras. Se enfatiza la combinación de modelado geométrico del proceso de formación de la imagen con el uso de herramientas estándar de optimización para estimar los parámetros característicos que describen la geometría de la escena 3-D. En concreto, se presentan métodos de estimación lineales, no lineales y robustos de las geometrías monocular y epipolar como punto de partida para generar reconstrucciones con tres o más cámaras. Algunos ejemplos de sistemas que utilizan este enfoque constructivo son Bundler, PhotoSynth, VideoSurfing, etc., los cuales, en la práctica pueden llegar a reconstruir una escena con varios cientos o miles de cámaras.

Improving Wishart Classification of Polarimetric SAR Data Using the Hopfield Neural Network Optimization Approach.

This paper proposes the optimization relaxation approach based on the analogue Hopfield Neural Network (HNN) for cluster refinement of pre-classified Polarimetric Synthetic Aperture Radar (PolSAR) image data. We consider the initial classification provided by the maximum-likelihood classifier based on the complex Wishart distribution, which is then supplied to the HNN optimization approach. The goal is to improve the classification results obtained by the Wishart approach. The classification improvement is verified by computing a cluster separability coefficient and a measure of homogeneity within the clusters. During the HNN optimization process, for each iteration and for each pixel, two consistency coefficients are computed, taking into account two types of relations between the pixel under consideration and its corresponding neighbors. Based on these coefficients and on the information coming from the pixel itself, the pixel under study is re-classified. Different experiments are carried out to verify that the proposed approach outperforms other strategies, achieving the best results in terms of separability and a trade-off with the homogeneity preserving relevant structures in the image. The performance is also measured in terms of computational central processing unit (CPU) times.

Three-level cell topology for a multilevel power supply to achieve High

This paper presents an envelope amplifier solution for envelope elimination and restoration (EER), that consists of a series combination of a switch-mode power supply (SMPS), based on three-level voltage cells and a linear regulator. This cell topology offers several advantages over a previously presented envelope amplifier based on a different multilevel topology (two-level voltage cells). The topology of the multilevel converter affects to the whole design of the envelope amplifier and a comparison between both design alternatives regarding the size, complexity and the efficiency of the solution is done. Both envelope amplifier solutions have a bandwidth of 2 MHz with an instantaneous maximum power of 50 W. It is also analyzed the linearity of the three-level cell solution, with critical importance in the EER technique implementation. Additionally, considerations to optimize the design of the envelope amplifier and experimental comparison between both cell topologies are included.

MBIS: Multivariate Bayesian Image Segmentation Tool

We present MBIS (Multivariate Bayesian Image Segmentation tool), a clustering tool based on the mixture of multivariate normal distributions model. MBIS supports multi-channel bias field correction based on a B-spline model. A second methodological novelty is the inclusion of graph-cuts optimization for the stationary anisotropic hidden Markov random field model. Along with MBIS, we release an evaluation framework that contains three different experiments on multi-site data. We first validate the accuracy of segmentation and the estimated bias field for each channel. MBIS outperforms a widely used segmentation tool in a cross-comparison evaluation. The second experiment demonstrates the robustness of results on atlas-free segmentation of two image sets from scan-rescan protocols on 21 healthy subjects. Multivariate segmentation is more replicable than the monospectral counterpart on T1-weighted images. Finally, we provide a third experiment to illustrate how MBIS can be used in a large-scale study of tissue volume change with increasing age in 584 healthy subjects. This last result is meaningful as multivariate segmentation performs robustly without the need for prior knowledge.