Computational Methods and Software for Bioelectric Field Problems, In Biomedical Engineering Handbook, 4, Vol. 1, Ch. 43, Edited by J.D. Bronzino and D.R. Peterson, CRC Press, pp. 1--28. 2015.
Computer modeling and simulation continue to become more important in the field of bioengineering. The reasons for this growing importance are manyfold. First, mathematical modeling has been shown to be a substantial tool for the investigation of complex biophysical phenomena. Second, since the level of complexity one can model parallels the existing hardware configurations, advances in computer architecture have made it feasible to apply the computational paradigm to complex biophysical systems. Hence, while biological complexity continues to outstrip the capabilities of even the largest computational systems, the computational methodology has taken hold in bioengineering and has been used successfully to suggest physiologically and clinically important scenarios and results.
This chapter provides an overview of numerical techniques that can be applied to a class of bioelectric field problems. Bioelectric field problems are found in a wide variety of biomedical applications, which range from single cells, to organs, up to models that incorporate partial to full human structures. We describe some general modeling techniques that will be applicable, in part, to all the aforementioned applications. We focus our study on a class of bioelectric volume conductor problems that arise in electrocardiography (ECG) and electroencephalography (EEG).
We begin by stating the mathematical formulation for a bioelectric volume conductor, continue by describing the model construction process, and follow with sections on numerical solutions and computational considerations. We continue with a section on error analysis coupled with a brief introduction to adaptive methods. We conclude with a section on software.
Visualization, In Encyclopedia of Applied and Computational Mathematics, Edited by Björn Engquist, Springer, pp. 1537-1546. 2015.
M. Kim, C.D. Hansen.
Surface Flow Visualization using the Closest Point Embedding, In 2015 IEEE Pacific Visualization Symposium, April, 2015.
In this paper, we introduce a novel flow visualization technique for arbitrary surfaces. This new technique utilizes the closest point embedding to represent the surface, which allows for accurate particle advection on the surface as well as supports the unsteady flow line integral convolution (UFLIC) technique on the surface. This global approach is faster than previous parameterization techniques and prevents the visual artifacts associated with image-based approaches.
Keywords: vector field, flow visualization
M. Kim, C.D. Hansen.
GPU Surface Extraction with the Closest Point Embedding, In Proceedings of IS&T/SPIE Visualization and Data Analysis, 2015, February, 2015.
Isosurface extraction is a fundamental technique used for both surface reconstruction and mesh generation. One method to extract well-formed isosurfaces is a particle system; unfortunately, particle systems can be slow. In this paper, we introduce an enhanced parallel particle system that uses the closest point embedding as the surface representation to speedup the particle system for isosurface extraction. The closest point embedding is used in the Closest Point Method (CPM), a technique that uses a standard three dimensional numerical PDE solver on two dimensional embedded surfaces. To fully take advantage of the closest point embedding, it is coupled with a Barnes-Hut tree code on the GPU. This new technique produces well-formed, conformal unstructured triangular and tetrahedral meshes from labeled multi-material volume datasets. Further, this new parallel implementation of the particle system is faster than any known methods for conformal multi-material mesh extraction. The resulting speed-ups gained in this implementation can reduce the time from labeled data to mesh from hours to minutes and benefits users, such as bioengineers, who employ triangular and tetrahedral meshes.
Keywords: scalar field methods, GPGPU, curvature based, scientific visualization
R.M. Kirby, M. Berzins, J.S. Hesthaven (Editors).
Spectral and High Order Methods for Partial Differential Equations, Subtitled Selected Papers from the ICOSAHOM'14 Conference, June 23-27, 2014, Salt Lake City, UT, USA., In Lecture Notes in Computational Science and Engineering, Springer, 2015.
O. A. von Lilienfeld, R. Ramakrishanan, M., A. Knoll.
Fourier Series of Atomic Radial Distribution Functions: A Molecular Fingerprint for Machine Learning Models of Quantum Chemical Properties, In International Journal of Quantum Chemistry, Wiley Online Library, 2015.
We introduce a fingerprint representation of molecules based on a Fourier series of atomic radial distribution functions. This fingerprint is unique (except for chirality), continuous, and differentiable with respect to atomic coordinates and nuclear charges. It is invariant with respect to translation, rotation, and nuclear permutation, and requires no pre-conceived knowledge about chemical bonding, topology, or electronic orbitals. As such it meets many important criteria for a good molecular representation, suggesting its usefulness for machine learning models of molecular properties trained across chemical compound space. To assess the performance of this new descriptor we have trained machine learning models of molecular enthalpies of atomization for training sets with up to 10 k organic molecules, drawn at random from a published set of 134 k organic molecules with an average atomization enthalpy of over 1770 kcal/mol. We validate the descriptor on all remaining molecules of the 134 k set. For a training set of 10k molecules the fingerprint descriptor achieves a mean absolute error of 8.0 kcal/mol, respectively. This is slightly worse than the performance attained using the Coulomb matrix, another popular alternative, reaching 6.2 kcal/mol for the same training and test sets.
S. Liu, D. Maljovec, Bei Wang, P. T. Bremer, V. Pascucci.
Visualizing High-Dimensional Data: Advances in the Past Decade, In State of The Art Report, Eurographics Conference on Visualization (EuroVis), 2015.
Massive simulations and arrays of sensing devices, in combination with increasing computing resources, have generated large, complex, high-dimensional datasets used to study phenomena across numerous fields of study. Visualization plays an important role in exploring such datasets. We provide a comprehensive survey of advances in high-dimensional data visualization over the past 15 years. We aim at providing actionable guidance for data practitioners to navigate through a modular view of the recent advances, allowing the creation of new visualizations along the enriched information visualization pipeline and identifying future opportunities for visualization research.
S. Liu, Bei Wang, J. J. Thiagarajan, P. T. Bremer, V. Pascucci.
Visual Exploration of High-Dimensional Data through Subspace Analysis and Dynamic Projections, In Computer Graphics Forum, Vol. 34, No. 3, Wiley-Blackwell, pp. 271--280. June, 2015.
We introduce a novel interactive framework for visualizing and exploring high-dimensional datasets based on subspace analysis and dynamic projections. We assume the high-dimensional dataset can be represented by a mixture of low-dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that create smooth animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real-world examples to demonstrate the novelty and usability of our proposed framework.
Note: map3d: Interactive scientific visualization tool for bioengineering data. Scientific Computing and Imaging Institute (SCI), Download from: http://www.sci.utah.edu/cibc/software.html, 2015.
K.S. McDowell, S. Zahid, F. Vadakkumpadan, J.J. Blauer, R.S. MacLeod, N.A. Trayanova.
Virtual Electrophysiological Study of Atrial Fibrillation in Fibrotic Remodeling, In PLoS ONE, Vol. 10, No. 2, pp. e0117110. February, 2015.
Research has indicated that atrial fibrillation (AF) ablation failure is related to the presence of atrial fibrosis. However it remains unclear whether this information can be successfully used in predicting the optimal ablation targets for AF termination. We aimed to provide a proof-of-concept that patient-specific virtual electrophysiological study that combines i) atrial structure and fibrosis distribution from clinical MRI and ii) modeling of atrial electrophysiology, could be used to predict: (1) how fibrosis distribution determines the locations from which paced beats degrade into AF; (2) the dynamic behavior of persistent AF rotors; and (3) the optimal ablation targets in each patient. Four MRI-based patient-specific models of fibrotic left atria were generated, ranging in fibrosis amount. Virtual electrophysiological studies were performed in these models, and where AF was inducible, the dynamics of AF were used to determine the ablation locations that render AF non-inducible. In 2 of the 4 models patient-specific models AF was induced; in these models the distance between a given pacing location and the closest fibrotic region determined whether AF was inducible from that particular location, with only the mid-range distances resulting in arrhythmia. Phase singularities of persistent rotors were found to move within restricted regions of tissue, which were independent of the pacing location from which AF was induced. Electrophysiological sensitivity analysis demonstrated that these regions changed little with variations in electrophysiological parameters. Patient-specific distribution of fibrosis was thus found to be a critical component of AF initiation and maintenance. When the restricted regions encompassing the meander of the persistent phase singularities were modeled as ablation lesions, AF could no longer be induced. The study demonstrates that a patient-specific modeling approach to identify non-invasively AF ablation targets prior to the clinical procedure is feasible.
S. McKenna, M. Meyer, C. Gregg, S. Gerber.
s-CorrPlot: An Interactive Scatterplot for Exploring Correlation, In Journal of Computational and Graphical Statistics, 2015.
The degree of correlation between variables is used in many data analysis applications as a key measure of interdependence. The most common techniques for exploratory analysis of pairwise correlation in multivariate datasets, like scatterplot matrices and clustered heatmaps, however, do not scale well to large datasets, either computationally or visually. We present a new visualization that is capable of encoding pairwise correlation between hundreds of thousands variables, called the s-CorrPlot. The s-CorrPlot encodes correlation spatially between variables as points on scatterplot using the geometric structure underlying Pearson's correlation. Furthermore, we extend the s-CorrPlot with interactive techniques that enable animation of the scatterplot to new projections of the correlation space, as illustrated in the companion video in Supplemental Materials. We provide the s-CorrPlot as an open-source R-package and validate its effectiveness through a variety of methods including a case study with a biology collaborator.
Note: NCR Toolset: A collection of software tools for the reconstruction and visualization of neural circuitry from electron microscopy data. Scientific Computing and Imaging Institute (SCI). Download from: http://www.sci.utah.edu/software.html, 2015.
C. Nobre, A. Lex.
OceanPaths: Visualizing Multivariate Oceanography Data, In Eurographics Conference on Visualization (EuroVis) - Short Papers, Edited by E. Bertini, J. Kennedy, E. Puppo, The Eurographics Association, 2015.
Geographical datasets are ubiquitous in oceanography. While map-based visualizations are useful for many different domains, they can suffer from cluttering and overplotting issues when used for multivariate data sets. As a result, spatial data exploration in oceanography has often been restricted to multiple maps showing various depths or time intervals. This lack of interactive exploration often hinders efforts to expose correlations between properties of oceanographic features, specifically currents. OceanPaths provides powerful interaction and exploration methods for spatial, multivariate oceanography datasets to remedy these situations. Fundamentally, our method allows users to define pathways, typically following currents, along which the variation of the high-dimensional data can be plotted efficiently. We present a case study conducted by domain experts to underscore the usefulness of OceanPaths in uncovering trends and correlations in oceanographic data sets.
I. OguzI, J. Cates, M. Datar, B. Paniagua, T. Fletcher, C. Vachet, M. Styner, R. Whitaker.
Entropy-based particle correspondence for shape populations, In International Journal of Computer Assisted Radiology and Surgery, Springer, pp. 1-12. December, 2015.
Statistical shape analysis of anatomical structures plays an important role in many medical image analysis applications such as understanding the structural changes in anatomy in various stages of growth or disease. Establishing accurate correspondence across object populations is essential for such statistical shape analysis studies.
In this paper, we present an entropy-based correspondence framework for computing point-based correspondence among populations of surfaces in a groupwise manner. This robust framework is parameterization-free and computationally efficient. We review the core principles of this method as well as various extensions to deal effectively with surfaces of complex geometry and application-driven correspondence metrics.
We apply our method to synthetic and biological datasets to illustrate the concepts proposed and compare the performance of our framework to existing techniques.
Through the numerous extensions and variations presented here, we create a very flexible framework that can effectively handle objects of various topologies, multi-object complexes, open surfaces, and objects of complex geometry such as high-curvature regions or extremely thin features.
B.R. Parmar, T.R. Jarrett, E.G. Kholmovski, N. Hu, D. Parker, R.S. MacLeod, N.F. Marrouche, R. Ranjan.
Poor scar formation after ablation is associated with atrial fibrillation recurrence, In Journal of Interventional Cardiac Electrophysiology, Vol. 44, No. 3, pp. 247-256. December, 2015.
Patients routinely undergo ablation for atrial fibrillation (AF) but the recurrence rate remains high. We explored in this study whether poor scar formation as seen on late-gadolinium enhancement magnetic resonance imaging (LGE-MRI) correlates with AF recurrence following ablation.
We retrospectively identified 94 consecutive patients who underwent their initial ablation for AF at our institution and had pre-procedural magnetic resonance angiography (MRA) merged with left atrial (LA) anatomy in an electroanatomic mapping (EAM) system, ablated areas marked intraprocedurally in EAM, 3-month post-ablation LGE-MRI for assessment of scar, and minimum of 3-months of clinical follow-up. Ablated area was quantified retrospectively in EAM and scarred area was quantified in the 3-month post-ablation LGE-MRI.
With the mean follow-up of 336 days, 26 out of 94 patients had AF recurrence. Age, hypertension, and heart failure were not associated with AF recurrence, but LA size and difference between EAM ablated area and LGE-MRI scar area was associated with higher AF recurrence. For each percent higher difference between EAM ablated area and LGE-MRI scar area, there was a 7–9 % higher AF recurrence (p values 0.001–0.003) depending on the multivariate analysis.
In AF ablation, poor scar formation as seen on LGE-MRI was associated with AF recurrence. Improved mapping and ablation techniques are necessary to achieve the desired LA scar and reduce AF recurrence.
B. Peterson, N. Xiao, J. Holmen, S. Chaganti, A. Pakki, J. Schmidt, D. Sunderland, A. Humphrey, M. Berzins.
Developing Uintah’s Runtime System For Forthcoming Architectures, Subtitled Refereed paper presented at the RESPA 15 Workshop at SuperComputing 2015 Austin Texas, SCI Institute, 2015.
B. Peterson, H. K. Dasari, A. Humphrey, J.C. Sutherland, T. Saad, M. Berzins.
Reducing overhead in the Uintah framework to support short-lived tasks on GPU-heterogeneous architectures, In Proceedings of the 5th International Workshop on Domain-Specific Languages and High-Level Frameworks for High Performance Computing (WOLFHPC'15), ACM, pp. 4:1-4:8. 2015.
J. M. Phillips, Bei Wang, Y. Zheng.
Geometric Inference on Kernel Density Estimates, In CoRR, Vol. abs/1307.7760, 2015.
We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and approximate computation in comparison to raw point sets. This is achieved by examining the sublevel sets of the kernel distance
, which isomorphically map to superlevel sets of the kernel density estimate. We prove new properties about the kernel distance, demonstrating stability results and allowing it to inherit reconstruction results from recent advances in distance-based topological reconstruction. Moreover, we provide an algorithm to estimate its topology using weighted Vietoris-Rips complexes.
J.R. Pruett Jr., S. Kandala, S. Hoertel, A.Z. Snyder, J.T. Elison, T. Nishino, E. Feczko, N.U.F. Dosenbach, B. Nardos, J.D. Power, B. Adeyemo, K.N. Botteron, R.C. McKinstry, A.C. Evans, H.C. Hazlett, S.R. Dager, S. Paterson, R.T. Schultz, D.L. Collins, V.S. Fonov, M. Styner, G. Gerig, S. Das, P. Kostopoulos, J.N. Constantino, A.M. Estes, The IBIS Network, S.E. Petersen, B.L. Schlaggar, J. Piven.
Accurate age classification of 6 and 12 month-old infants based on resting-state functional connectivity magnetic resonance imaging data, In Developmental Cognitive Neuroscience, Vol. 12, pp. 123--133. April, 2015.
Human large-scale functional brain networks are hypothesized to undergo significant changes over development. Little is known about these functional architectural changes, particularly during the second half of the first year of life. We used multivariate pattern classification of resting-state functional connectivity magnetic resonance imaging (fcMRI) data obtained in an on-going, multi-site, longitudinal study of brain and behavioral development to explore whether fcMRI data contained information sufficient to classify infant age. Analyses carefully account for the effects of fcMRI motion artifact. Support vector machines (SVMs) classified 6 versus 12 month-old infants (128 datasets) above chance based on fcMRI data alone. Results demonstrate significant changes in measures of brain functional organization that coincide with a special period of dramatic change in infant motor, cognitive, and social development. Explorations of the most different correlations used for SVM lead to two different interpretations about functional connections that support 6 versus 12-month age categorization.
S. Pujol, W. Wells, C. Pierpaoli, C. Brun, J. Gee, G. Cheng, B. Vemuri, O. Commowick, S. Prima, A. Stamm, M. Goubran, A. Khan, T. Peters, P. Neher, K. H. Maier-Hein, Y. Shi, A. Tristan-Vega, G. Veni, R. Whitaker, M. Styner, C.F. Westin, S. Gouttard, I. Norton, L. Chauvin, H. Mamata, G. Gerig, A. Nabavi, A. Golby,, R. Kikinis.
The DTI Challenge: Toward Standardized Evaluation of Diffusion Tensor Imaging Tractography for Neurosurgery, In Journal of Neuroimaging, Wiley, August, 2015.
BACKGROUND AND PURPOSE
Diffusion tensor imaging (DTI) tractography reconstruction of white matter pathways can help guide brain tumor resection. However, DTI tracts are complex mathematical objects and the validity of tractography-derived information in clinical settings has yet to be fully established. To address this issue, we initiated the DTI Challenge, an international working group of clinicians and scientists whose goal was to provide standardized evaluation of tractography methods for neurosurgery. The purpose of this empirical study was to evaluate different tractography techniques in the first DTI Challenge workshop.METHODS
Eight international teams from leading institutions reconstructed the pyramidal tract in four neurosurgical cases presenting with a glioma near the motor cortex. Tractography methods included deterministic, probabilistic, filtered, and global approaches. Standardized evaluation of the tracts consisted in the qualitative review of the pyramidal pathways by a panel of neurosurgeons and DTI experts and the quantitative evaluation of the degree of agreement among methods.RESULTS
The evaluation of tractography reconstructions showed a great interalgorithm variability. Although most methods found projections of the pyramidal tract from the medial portion of the motor strip, only a few algorithms could trace the lateral projections from the hand, face, and tongue area. In addition, the structure of disagreement among methods was similar across hemispheres despite the anatomical distortions caused by pathological tissues.CONCLUSIONS
The DTI Challenge provides a benchmark for the standardized evaluation of tractography methods on neurosurgical data. This study suggests that there are still limitations to the clinical use of tractography for neurosurgical decision making.