SCIENTIFIC COMPUTING AND IMAGING INSTITUTE
at the University of Utah

In the field of uncertainty quantification, uncertainty in the governing equations may assume two forms: aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty can be characterised by known probability distributions whilst epistemic uncertainty arises from a lack of knowledge of probabilistic information. While extensive research efforts have been devoted to the numerical treatment of aleatory uncertainty, little attention has been given to the quantification of epistemic uncertainty. In this paper, we propose a numerical framework for quantification of epistemic uncertainty. The proposed methodology does not require any probabilistic information on uncertain input parameters. The method only necessitates an estimate of the range of the uncertain variables that encapsulates the true range of the input variables with overwhelming probability. To quantify the epistemic uncertainty, we solve an encapsulation problem, which is a solution to the original governing equations defined on the estimated range of the input variables. We discuss solution strategies for solving the encapsulation problem and the sufficient conditions under which the numerical solution can serve as a good estimator for capturing the effects of the epistemic uncertainty. In the case where probability distributions of the epistemic variables become known a posteriori, we can use the information to post-process the solution and evaluate solution statistics. Convergence results are also established for such cases, along with strategies for dealing with mixed aleatory and epistemic uncertainty. Several numerical examples are presented to demonstrate the procedure and properties of the proposed methodology.

Keywords: Uncertainty quantification, Epistemic uncertainty, Generalized polynomial chaos, Stochastic collocation, Encapsulation problem

The use of (a posteriori) error estimates is a fundamental tool in the application of adaptive numerical methods across a range of fluid flow problems. Such estimates are incomplete however, in that they do not necessarily indicate where to refine in order to achieve the most impact on the error, nor what type of refinement (for example h-refinement or p-refinement) will be best. This paper extends preliminary work of the authors (Comm Comp Phys, 2010;7:631–8), which uses adjoint-based sensitivity estimates in order to address these questions, to include application with p-refinement to arbitrary order and the use of practical a posteriori estimates. Results are presented which demonstrate that the proposed approach can guide both the h-refinement and the p-refinement processes, to yield improvements in the adaptive strategy compared to the use of more orthodox criteria.

BACKGROUND:
Total subcutaneous implantable subcutaneous defibrillators are in development, but optimal electrode configurations are not known.

OBJECTIVE:
We used image-based finite element models (FEM) to predict the myocardial electric field generated during defibrillation shocks (pseudo-DFT) in a wide variety of reported and innovative subcutaneous electrode positions to determine factors affecting optimal lead positions for subcutaneous implantable cardioverter-defibrillators (S-ICD).

METHODS:
An image-based FEM of an adult man was used to predict pseudo-DFTs across a wide range of technically feasible S-ICD electrode placements. Generator location, lead location, length, geometry and orientation, and spatial relation of electrodes to ventricular mass were systematically varied. Best electrode configurations were determined, and spatial factors contributing to low pseudo-DFTs were identified using regression and general linear models.

RESULTS:
A total of 122 single-electrode/array configurations and 28 dual-electrode configurations were simulated. Pseudo-DFTs for single-electrode orientations ranged from 0.60 to 16.0 (mean 2.65 +/- 2.48) times that predicted for the base case, an anterior-posterior configuration recently tested clinically. A total of 32 of 150 tested configurations (21%) had pseudo-DFT ratios /=1, indicating the possibility of multiple novel, efficient, and clinically relevant orientations. Favorable alignment of lead-generator vector with ventricular myocardium and increased lead length were the most important factors correlated with pseudo-DFT, accounting for 70% of the predicted variation (R(2) = 0.70, each factor P < .05) in a combined general linear modl in which parameter estimates were calculated for each factor.

CONCLUSION:
Further exploration of novel and efficient electrode configurations may be of value in the development of the S-ICD technologies and implant procedure. FEM modeling suggests that the choice of configurations that maximize shock vector alignment with the center of myocardial mass and use of longer leads is more likely to result in lower DFT.

In this paper we present a novel approach to generate proxy geometry for slice based volume rendering. The basic idea is derived from the behavior of a ray-caster and is a simple extension of the well known 2D object-aligned texture stack based technique. From this our novel scheme inherits the advantage that it enables hardware-based volume rendering for devices that do not support 3D textures. On these devices previous object-aligned 2D texture based approaches suffered from disturbing view angle dependent stack-switching artifacts which are avoided by our novel method. Our approach also shows benefits compared to the widely used view aligned slicing algorithm as it avoids jagged boundary artifacts and increases performance.

BACKGROUND:
Atrial fibrosis is a hallmark of atrial structural remodeling (SRM) and leads to structural and functional impairment of left atrial (LA) and persistence of atrial fibrillation (AF). This study was conducted to assess LA reverse remodeling after catheter ablation of AF in mild and moderate-severe LA SRM.

METHODS:
Catheter ablation was performed in 68 patients (age 62 ± 14 years, 68% males) with paroxysmal (n = 26) and persistent (n = 42) AF. The patients were divided into group 1 with mild LA SRM (10%, n = 37) by delayed enhancement magnetic resonance imaging (DEMRI). Two-dimensional echocardiography, LA strain, and strain rate during left ventricular systole by velocity vector imaging were performed pre and at 6 ± 3 months postablation. The long-term outcome was monitored for 12 months.

RESULTS:
Patients in group 1 were younger (57 ± 15 vs 66 ± 13 years, P = .009) with a male predominance (80% vs 57%, P < .05) as compared to group 2. Postablation, group 1 had significant increase in average LA strain (??: 14% vs 4%, P < .05) and strain rate (??: 0.5 vs 0.1 cm/s, P < .05) as compared to group 2. There was a trend toward more patients with persistent AF in group 2 (68% vs 55%, P = .2), but it was not statistically significant. Group 2 had more AF recurrences (41% vs 16%, P = .02) at 12 months after ablation.

CONCLUSION:
Mild preablation LA SRM by DEMRI predicts favorable LA structural and functional reverse remodeling and long-term success after catheter ablation of AF, irrespective of the paroxysmal or persistent nature of AF.

The goal of our work is to support experts in the process of hypotheses generation concerning the roles of genes in diseases. For a deeper understanding of the complex interdependencies between genes, it is important to bring gene expressions (measurements) into context with pathways. Pathways, which are models of biological processes, are available in online databases. In these databases, large networks are decomposed into small sub-graphs for better manageability. This simplification results in a loss of context, as pathways are interconnected and genes can occur in multiple instances scattered over the network. Our main goal is therefore to present all relevant information, i.e., gene expressions, the relations between expression and pathways and between multiple pathways in a simple, yet effective way. To achieve this we employ two different multiple-view approaches. Traditional multiple views are used for large datasets or highly interactive visualizations, while a 2.5D technique is employed to support a seamless navigation of multiple pathways which simultaneously links to the expression of the contained genes. This approach facilitates the understanding of the interconnection of pathways, and enables a non-distracting relation to gene expression data. We evaluated Caleydo with a group of users from the life science community. Users were asked to perform three tasks: pathway exploration, gene expression analysis and information comparison with and without visual links, which had to be conducted in four different conditions. Evaluation results show that the system can improve the process of understanding the complex network of pathways and the individual effects of gene expression regulation considerably. Especially the quality of the available contextual information and the spatial organization was rated good for the presented 2.5D setup.

When analyzing multidimensional, quantitative data, the comparison of two or more groups of dimensions is a common task. Typical sources of such data are experiments in biology, physics or engineering, which are conducted in different configurations and use replicates to ensure statistically significant results.  One common way to analyze this data is to filter it using statistical methods and then run clustering algorithms to group similar values. The clustering results can be visualized using heat maps, which show differences between groups as changes in color. However, in cases where groups of dimensions have an a priori meaning, it is not desirable to cluster all dimensions combined, since a clustering algorithm can fragment continuous blocks of records.  Furthermore, identifying relevant elements in heat maps becomes  more difficult as the number of dimensions increases. To aid in such situations, we have developed Matchmaker, a visualization technique that allows researchers to arbitrarily  arrange and  compare multiple groups of dimensions at the same time.  We create separate groups of dimensions which can be clustered individually, and place them in an arrangement of heat maps reminiscent of parallel coordinates. To identify relations, we render bundled curves and ribbons between related records in different groups. We then allow interactive drill-downs using enlarged detail views of the data, which enable in-depth comparisons of clusters between groups. To reduce visual clutter, we minimize crossings between the views. This paper concludes with two case studies. The first demonstrates the value of our technique for the comparison of clustering algorithms. In the second, biologists use our system to investigate why certain strains of mice develop liver disease while others remain healthy, informally showing the efficacy of our system  when analyzing multidimensional data containing distinct groups of dimensions.

Evaluation of failure probability of a given system requires sampling of the system response and can be computationally expensive. Therefore it is desirable to construct an accurate surrogate model for the system response and subsequently to sample the surrogate model. In this paper we discuss the properties of this approach. We demonstrate that the straightforward sampling of a surrogate model can lead to erroneous results, no matter how accurate the surrogate model is. We then propose a hybrid approach by sampling both the surrogate model in a “large” portion of the probability space and the original system in a “small” portion. The resulting algorithm is significantly more efficient than the traditional sampling method, and is more accurate and robust than the straightforward surrogate model approach. Rigorous convergence proof is established for the hybrid approach, and practical implementation is discussed. Numerical examples are provided to verify the theoretical findings and demonstrate the efficiency gain of the approach.

Keywords: Failure probability, Sampling, Polynomial chaos, Stochastic computation