Designed especially for neurobiologists, FluoRender is an interactive tool for multi-channel fluorescence microscopy data visualization and analysis.
Deep brain stimulation
BrainStimulator is a set of networks that are used in SCIRun to perform simulations of brain stimulation such as transcranial direct current stimulation (tDCS) and magnetic transcranial stimulation (TMS).
Developing software tools for science has always been a central vision of the SCI Institute.

Biomedical Computing

Biomedical computing combines the diagnostic and investigative aspects of biology and medical science with the power and problem-solving capabilities of modern computing. Computers are used to accelerate research learning, simulate patient behavior and visualize complex biological models.


chris

Chris Johnson

Inverse Problems
Computational Electrophysiology
rob

Rob MacLeod

ECG Imaging
Cardiac Disease
Computational Electrophysiology
jeff

Jeff Weiss

Computational Biomechanics
orly

Orly Alter

Computational Biology
bidone

Tamara Bidone

Computational Models
Simulations of Biological Systems
Multi-Physics Models of Cancer Cells

amir

Amir Arzani

Cardiovascular biomechanics
Biotransport
Scientific machine learning

Centers and Labs:


Funded Research Projects:



Publications in Biomedical Computing:


Extensions to a manifold learning framework for time-series analysis on dynamic manifolds in bioelectric signals
B. Erem, R.M. Orellana, D.E. Hyde, J.M. Peters, F.H. Duffy, P. Stovicek, S.K. Warfield, R.S. MacLeod, G. Tadmor, D.H. Brooks. In Physical Review E, Vol. 93, No. 4, American Physical Society, apr, 2016.
DOI: 10.1103/physreve.93.042218

This paper addresses the challenge of extracting meaningful information from measured bioelectric signals generated by complex, large scale physiological systems such as the brain or the heart. We focus on a combination of the well-known Laplacian eigenmaps machine learning approach with dynamical systems ideas to analyze emergent dynamic behaviors. The method reconstructs the abstract dynamical system phase-space geometry of the embedded measurements and tracks changes in physiological conditions or activities through changes in that geometry. It is geared to extract information from the joint behavior of time traces obtained from large sensor arrays, such as those used in multiple-electrode ECG and EEG, and explore the geometrical structure of the low dimensional embedding of moving time windows of those joint snapshots. Our main contribution is a method for mapping vectors from the phase space to the data domain. We present cases to evaluate the methods, including a synthetic example using the chaotic Lorenz system, several sets of cardiac measurements from both canine and human hearts, and measurements from a human brain.



Optimization of focality and direction in dense electrode array transcranial direct currentstimulation (tDCS)
S. Guler, M. Dannhauer, B. Erem, R.S. Macleod, D. Tucker, S. Turovets, P. Luu, D. Erdogmus, D. Brooks. In Journal of Neural Engineering, Vol. 13, No. 3, IOP Publishing, pp. 036020. May, 2016.
DOI: 10.1088/1741-2560/13/3/036020

OBJECTIVE:
Transcranial direct current stimulation (tDCS) aims to alter brain function non-invasively via electrodes placed on the scalp. Conventional tDCS uses two relatively large patch electrodes to deliver electrical current to the brain region of interest (ROI). Recent studies have shown that using dense arrays containing up to 512 smaller electrodes may increase the precision of targeting ROIs. However, this creates a need for methods to determine effective and safe stimulus patterns as the number of degrees of freedom is much higher with such arrays. Several approaches to this problem have appeared in the literature. In this paper, we describe a new method for calculating optimal electrode stimulus patterns for targeted and directional modulation in dense array tDCS which differs in some important aspects with methods reported to date.

APPROACH:
We optimize stimulus pattern of dense arrays with fixed electrode placement to maximize the current density in a particular direction in the ROI. We impose a flexible set of safety constraints on the current power in the brain, individual electrode currents, and total injected current, to protect subject safety. The proposed optimization problem is convex and thus efficiently solved using existing optimization software to find unique and globally optimal electrode stimulus patterns.

MAIN RESULTS:
Solutions for four anatomical ROIs based on a realistic head model are shown as exemplary results. To illustrate the differences between our approach and previously introduced methods, we compare our method with two of the other leading methods in the literature. We also report on extensive simulations that show the effect of the values chosen for each proposed safety constraint bound on the optimized stimulus patterns.

SIGNIFICANCE:
The proposed optimization approach employs volume based ROIs, easily adapts to different sets of safety constraints, and takes negligible time to compute. An in-depth comparison study gives insight into the relationship between different objective criteria and optimized stimulus patterns. In addition, the analysis of the interaction between optimized stimulus patterns and safety constraint bounds suggests that more precise current localization in the ROI, with improved safety criterion, may be achieved by careful selection of the constraint bounds.



Quantitative comparison of cortical bone thickness using correspondence-based shape modeling in patients with cam femoroacetabular impingement
P.R. Atkins, S.Y. Elhabian, P. Agrawal, M.D. Harris, R.T. Whitaker, J.A. Weiss, C.L. Peters, A.E. Anderson. In Journal of Orthopaedic Research, Wiley-Blackwell, Nov, 2016.
DOI: 10.1002/jor.23468

The proximal femur is abnormally shaped in patients with cam-type femoroacetabular impingement (FAI). Impingement
may elicit bone remodeling at the proximal femur, causing increases in cortical bone thickness. We used correspondence-based shape modeling to quantify and compare cortical thickness between cam patients and controls for the location of the cam lesion and the proximal femur. Computed tomography images were segmented for 45 controls and 28 cam-type FAI patients. The segmentations were input to a correspondence-based shape model to identify the region of the cam lesion. Median cortical thickness data over the region of the cam lesion and the proximal femur were compared between mixed-gender and gender-specific groups. Median [interquartile range] thickness was significantly greater in FAI patients than controls in the cam lesion (1.47 [0.64] vs. 1.13 [0.22] mm, respectively; p < 0.001) and proximal femur (1.28 [0.30] vs. 0.97 [0.22] mm, respectively; p < 0.001). Maximum thickness in the region of the cam lesion was more anterior and less lateral (p < 0.001) in FAI patients. Male FAI patients had increased thickness compared to male controls in the cam lesion (1.47 [0.72] vs. 1.10 [0.19] mm, respectively; p < 0.001) and proximal femur (1.25 [0.29] vs. 0.94 [0.17] mm, respectively; p < 0.001). Thickness was not significantly different between male and female controls. Clinical significance: Studies of non-pathologic cadavers have provided guidelines regarding safe surgical resection depth for FAI patients. However, our results suggest impingement induces cortical thickening in cam patients, which may strengthen the proximal femur. Thus, these previously established guidelines may be too conservative.



The role of blood vessels in high-resolution volume conductor head modeling of EEG
L.D.J. Fiederer, J. Vorwerk, F. Lucka, M. Dannhauer, S. Yang, M. Dümpelmann, A. Schulze-Bonhage, A. Aertsen, O. Speck, C.H. Wolters, T. Ball. In NeuroImage, Vol. 128, Elsevier, pp. 193--208. March, 2016.
DOI: 10.1016/j.neuroimage.2015.12.041

Reconstruction of the electrical sources of human EEG activity at high spatio-temporal accuracy is an important aim in neuroscience and neurological diagnostics. Over the last decades, numerous studies have demonstrated that realistic modeling of head anatomy improves the accuracy of source reconstruction of EEG signals. For example, including a cerebro-spinal fluid compartment and the anisotropy of white matter electrical conductivity were both shown to significantly reduce modeling errors. Here, we for the first time quantify the role of detailed reconstructions of the cerebral blood vessels in volume conductor head modeling for EEG. To study the role of the highly arborized cerebral blood vessels, we created a submillimeter head model based on ultra-high-field-strength (7T) structural MRI datasets. Blood vessels (arteries and emissary/intraosseous veins) were segmented using Frangi multi-scale vesselness filtering. The final head model consisted of a geometry-adapted cubic mesh with over 17×10(6) nodes. We solved the forward model using a finite-element-method (FEM) transfer matrix approach, which allowed reducing computation times substantially and quantified the importance of the blood vessel compartment by computing forward and inverse errors resulting from ignoring the blood vessels. Our results show that ignoring emissary veins piercing the skull leads to focal localization errors of approx. 5 to 15mm. Large errors (>2cm) were observed due to the carotid arteries and the dense arterial vasculature in areas such as in the insula or in the medial temporal lobe. Thus, in such predisposed areas, errors caused by neglecting blood vessels can reach similar magnitudes as those previously reported for neglecting white matter anisotropy, the CSF or the dura - structures which are generally considered important components of realistic EEG head models. Our findings thus imply that including a realistic blood vessel compartment in EEG head models will be helpful to improve the accuracy of EEG source analyses particularly when high accuracies in brain areas with dense vasculature are required.



Increased Susceptibility to Atrial Fibrillation Secondary to Atrial Fibrosis in Transgenic Goats Expressing Transforming Growth Factor-β1
I.A. Polejaeva, R. Ranjan, C.J. Davies, M. Regouski, J. Hall, A.L. Olsen, Q. Meng, H.M. Rutigliano, D.J. Dosdall, N.A. Angel, F.B. Sachse, T. Seidel, A.J. Thomas, R. Stott, K.E. Panter, P.M. Lee, A.J. Van Wettere, J.R. Stevens, Z. Wang, R.S. Macleod, N.F. Marrouche, K.L. White. In Journal of Cardiovascular Electrophysiology, Vol. 27, No. 10, Wiley-Blackwell, pp. 1220--1229. Aug, 2016.
DOI: 10.1111/jce.13049

Introduction
Large animal models of progressive atrial fibrosis would provide an attractive platform to study relationship between structural and electrical remodeling in atrial fibrillation (AF). Here we established a new transgenic goat model of AF with cardiac specific overexpression of TGF-β1 and investigated the changes in the cardiac structure and function leading to AF.

Methods and Results
Transgenic goats with cardiac specific overexpression of constitutively active TGF-β1 were generated by somatic cell nuclear transfer. We examined myocardial tissue, ECGs, echocardiographic data, and AF susceptibility in transgenic and wild-type control goats. Transgenic goats exhibited significant increase in fibrosis and myocyte diameters in the atria compared to controls, but not in the ventricles. P-wave duration was significantly greater in transgenic animals starting at 12 months of age, but no significant chamber enlargement was detected, suggesting conduction slowing in the atria. Furthermore, this transgenic goat model exhibited a significant increase in AF vulnerability. Six of 8 transgenic goats (75%) were susceptible to AF induction and exhibited sustained AF (>2 minutes), whereas none of 6 controls displayed sustained AF (P < 0.01). Length of induced AF episodes was also significantly greater in the transgenic group compared to controls (687 ± 212.02 seconds vs. 2.50 ± 0.88 seconds, P < 0.0001), but no persistent or permanent AF was observed.

Conclusion
A novel transgenic goat model with a substrate for AF was generated. In this model, cardiac overexpression of TGF-β1 led to an increase in fibrosis and myocyte size in the atria, and to progressive P-wave prolongation. We suggest that these factors underlie increased AF susceptibility.



Spatial organization of acute myocardial ischemia
K. Aras B. Burton, D. Swenson, R.S. MacLeod. In Journal of Electrocardiology, Vol. 49, No. 3, Elsevier, pp. 323–336. May, 2016.

Introduction
Myocardial ischemia is a pathological condition initiated by supply and demand imbalance of the blood to the heart. Previous studies suggest that ischemia originates in the subendocardium, i.e., that nontransmural ischemia is limited to the subendocardium. By contrast, we hypothesized that acute myocardial ischemia is not limited to the subendocardium and sought to document its spatial distribution in an animal preparation. The goal of these experiments was to investigate the spatial organization of ischemia and its relationship to the resulting shifts in ST segment potentials during short episodes of acute ischemia.

Methods
We conducted acute ischemia studies in open-chest canines (N = 19) and swines (N = 10), which entailed creating carefully controlled ischemia using demand, supply or complete occlusion ischemia protocols and recording intramyocardial and epicardial potentials. Elevation of the potentials at 40% of the ST segment between the J-point and the peak of the T-wave (ST40%) provided the metric for local ischemia. The threshold for ischemic ST segment elevations was defined as two standard deviations away from the baseline values.

Results
The relative frequency of occurrence of acute ischemia was higher in the subendocardium (78% for canines and 94% for swines) and the mid-wall (87% for canines and 97% for swines) in comparison with the subepicardium (30% for canines and 22% for swines). In addition, acute ischemia was seen arising throughout the myocardium (distributed pattern) in 87% of the canine and 94% of the swine episodes. Alternately, acute ischemia was seen originating only in the subendocardium (subendocardial pattern) in 13% of the canine episodes and 6% of the swine episodes (p < 0.05).

Conclusions
Our findings suggest that the spatial distribution of acute ischemia is a complex phenomenon arising throughout the myocardial wall and is not limited to the subendocardium.



muView: A Visual Analysis System for Exploring Uncertainty in Myocardial Ischemia Simulations
P. Rosen, B. Burton, K. Potter, C.R. Johnson. In Visualization in Medicine and Life Sciences III, Springer Nature, pp. 49--69. 2016.
DOI: 10.1007/978-3-319-24523-2_3

In this paper we describe the Myocardial Uncertainty Viewer (muView or µView) system for exploring data stemming from the simulation of cardiac ischemia. The simulation uses a collection of conductivity values to understand how ischemic regions effect the undamaged anisotropic heart tissue. The data resulting from the simulation is multi-valued and volumetric, and thus, for every data point, we have a collection of samples describing cardiac electrical properties. µView combines a suite of visual analysis methods to explore the area surrounding the ischemic zone and identify how perturbations of variables change the propagation of their effects. In addition to presenting a collection of visualization techniques, which individually highlight different aspects of the data, the coordinated view system forms a cohesive environment for exploring the simulations.We also discuss the findings of our study, which are helping to steer further development of the simulation and strengthening our collaboration with the biomedical engineers attempting to understand the phenomenon.



Virtual Electrophysiological Study of Atrial Fibrillation in Fibrotic Remodeling
K. S. McDowell, S. Zahid, F. Vadakkumpadan, J. Blauer, R. S. MacLeod, N. A. Trayanova. In PLoS ONE, Vol. 10, No. 2, Public Library of Science, pp. 1-16. May, 2015.
DOI: doi.org/10.1371/journal.pone.0117110

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.



The use of stimulation field models for deep brain stimulation programming
C. R. Butson, C. C. McIntyre. In Brain Stimulation, Vol. 8, No. 5, Elsevier BV, pp. 976--978. September, 2015.
DOI: 10.1016/j.brs.2015.06.005



Proceedings of the Second Annual Deep Brain Stimulation Think Tank: What's in the Pipeline
A. Gunduz, H. Morita, P. J. Rossi, W. L. Allen, R. L. Alterman, H. Bronte-Stewart, C. R. Butson, D. Charles, S. Deckers, C. de Hemptinne, M. DeLong, D. Dougherty, J. Ellrich, K. D. Foote, J. Giordano, W. Goodman, B. D. Greenberg, D. Greene, R. Gross, J. W. Judy, E. Karst, A. Kent, B. Kopell, A. Lang, A. Lozano, C. Lungu, K. E. Lyons, A. Machado, H. Martens, C. McIntyre, H. Min, J. Neimat, J. Ostrem, S. Pannu, F. Ponce, N. Pouratian, D. Reymers, L. Schrock, S. Sheth, L. Shih, S. Stanslaski, G. K. Steinke, P. Stypulkowski, A. I. Tröster, L. Verhagen, H. Walker, M. S. Okun. In International Journal of Neuroscience, Vol. 125, No. 7, Taylor & Francis, pp. 475-485. 2015.
DOI: 10.3109/00207454.2014.999268
PubMed ID: 25526555

The proceedings of the 2nd Annual Deep Brain Stimulation Think Tank summarize the most contemporary clinical, electrophysiological, and computational work on DBS for the treatment of neurological and neuropsychiatric disease and represent the insights of a unique multidisciplinary ensemble of expert neurologists, neurosurgeons, neuropsychologists, psychiatrists, scientists, engineers and members of industry. Presentations and discussions covered a broad range of topics, including advocacy for DBS, improving clinical outcomes, innovations in computational models of DBS, understanding of the neurophysiology of Parkinson's disease (PD) and Tourette syndrome (TS) and evolving sensor and device technologies.



Poor scar formation after ablation is associated with atrial fibrillation recurrence,
B.R. Parmar, T.R. Jarrett, E.G. Kholmovski, N. Hu, D. Parker, R.S. MacLeod, N.F. Marrouche, R. Ranjan. In Journal of Interventional Cardiac Electrophysiology, Vol. 44, No. 3, pp. 247-256. December, 2015.

Purpose
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.

Methods
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.

Results
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.

Conclusions
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.



Generation of Combined-Modality Tetrahedral Meshes
K. Gillette, J.D. Tate, B. Kindall, P. Van Dam, E. Kholmovski, R.S. MacLeod. In Computing in Cardiology, 2015.

Registering and combining anatomical components from different image modalities, like MRI and CT that have different tissue contrast, could result in patient-specific models that more closely represent underlying anatomical structures.

In this study, we combined a pair of CT and MRI scans of a pig thorax to make a tetrahedral mesh and compared different registration techniques including rigid, affine, thin plate spline morphing (TPSM), and iterative closest point (ICP), to  superimpose the segmented bones from the CT scan on the soft tissues segmented from the MRI. The TPSM and affine-registered bones remained close to, but not overlapping, important soft tissue.

Simulation models, including an ECG forward model and a defibrillation model, were computed on generated multi-modality meshes after TPSM and affine registration and compared to those based on the original torso mesh.



A Kalman Filtering Perspective for Multiatlas Segmentation
Y. Gao, L. Zhu, J. Cates, R. S. MacLeod, S. Bouix,, A. Tannenbaum. In SIAM J. Imaging Sciences, Vol. 8, No. 2, pp. 1007-1029. 2015.
DOI: 10.1137/130933423

In multiatlas segmentation, one typically registers several atlases to the novel image, and their respective segmented label images are transformed and fused to form the final segmentation. In this work, we provide a new dynamical system perspective for multiatlas segmentation, inspired by the following fact: The transformation that aligns the current atlas to the novel image can be not only computed by direct registration but also inferred from the transformation that aligns the previous atlas to the image together with the transformation between the two atlases. This process is similar to the global positioning system on a vehicle, which gets position by inquiring from the satellite and by employing the previous location and velocity—neither answer in isolation being perfect. To solve this problem, a dynamical system scheme is crucial to combine the two pieces of information; for example, a Kalman filtering scheme is used. Accordingly, in this work, a Kalman multiatlas segmentation is proposed to stabilize the global/affine registration step. The contributions of this work are twofold. First, it provides a new dynamical systematic perspective for standard independent multiatlas registrations, and it is solved by Kalman filtering. Second, with very little extra computation, it can be combined with most existing multiatlas segmentation schemes for better registration/segmentation accuracy.



Virtual Electrophysiological Study of Atrial Fibrillation in Fibrotic Remodeling
K.S. McDowell, S. Zahid, F. Vadakkumpadan, J.J. Blauer, R.S. MacLeod, N.A. Trayanova. In PLoS ONE, Vol. 10, No. 2, pp. e0117110. February, 2015.
DOI: 10.1371/journal.pone.0117110

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.



Experimental Data and Geometric Analysis Repository: EDGAR
K.K. Aras, W. Good, J. Tate, B.M. Burton, D.H. Brooks, J. Coll-Font, O. Doessel, W. Schulze, D. Patyogaylo, L. Wang, P. Van Dam,, R.S. MacLeod. In Journal of Electrocardiology, 2015.

Introduction
The "Experimental Data and Geometric Analysis Repository", or EDGAR is an Internet-based archive of curated data that are freely distributed to the international research community for the application and validation of electrocardiographic imaging (ECGI) techniques. The EDGAR project is a collaborative effort by the Consortium for ECG Imaging (CEI, ecg-imaging.org), and focused on two specific aims. One aim is to host an online repository that provides access to a wide spectrum of data, and the second aim is to provide a standard information format for the exchange of these diverse datasets.

Methods
The EDGAR system is composed of two interrelated components: 1) a metadata model, which includes a set of descriptive parameters and information, time signals from both the cardiac source and body-surface, and extensive geometric information, including images, geometric models, and measure locations used during the data acquisition/generation; and 2) a web interface. This web interface provides efficient, search, browsing, and retrieval of data from the repository.

Results
An aggregation of experimental, clinical and simulation data from various centers is being made available through the EDGAR project including experimental data from animal studies provided by the University of Utah (USA), clinical data from multiple human subjects provided by the Charles University Hospital (Czech Republic), and computer simulation data provided by the Karlsruhe Institute of Technology (Germany).

Conclusions
It is our hope that EDGAR will serve as a communal forum for sharing and distribution of cardiac electrophysiology data and geometric models for use in ECGI research.



Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization,
C.D. Hansen, M. Chen, C.R. Johnson, A.E. Kaufman, H. Hagen (Eds.). Mathematics and Visualization, Springer, 2014.
ISBN: 978-1-4471-6496-8



Uncertainty Visualization in Forward and Inverse Cardiac Models
B. Burton, B. Erem, K. Potter, P. Rosen, C.R. Johnson, D. Brooks, R.S. Macleod. In Computing in Cardiology CinC, pp. 57--60. 2013.
ISSN: 2325-8861

Quantification and visualization of uncertainty in cardiac forward and inverse problems with complex geometries is subject to various challenges. Specific to visualization is the observation that occlusion and clutter obscure important regions of interest, making visual assessment difficult. In order to overcome these limitations in uncertainty visualization, we have developed and implemented a collection of novel approaches. To highlight the utility of these techniques, we evaluated the uncertainty associated with two examples of modeling myocardial activity. In one case we studied cardiac potentials during the repolarization phase as a function of variability in tissue conductivities of the ischemic heart (forward case). In a second case, we evaluated uncertainty in reconstructed activation times on the epicardium resulting from variation in the control parameter of Tikhonov regularization (inverse case). To overcome difficulties associated with uncertainty visualization, we implemented linked-view windows and interactive animation to the two respective cases. Through dimensionality reduction and superimposed mean and standard deviation measures over time, we were able to display key features in large ensembles of data and highlight regions of interest where larger uncertainties exist.



SVD Identifies Transcript Length Distribution Functions from DNA Microarray Data and Reveals Evolutionary Forces Globally Affecting GBM Metabolism
N.M. Bertagnolli, J.A. Drake, J.M. Tennessen, O. Alter. In Public Library of Science (PLoS) One, Vol. 8, No. 11, pp. article e78913. November, 2013.
DOI: 10.1371/journal.pone.0078913

To search for evolutionary forces that might act upon transcript length, we use the singular value decomposition (SVD) to identify the length distribution functions of sets and subsets of human and yeast transcripts from profiles of mRNA abundance levels across gel electrophoresis migration distances that were previously measured by DNA microarrays. We show that the SVD identifies the transcript length distribution functions as “asymmetric generalized coherent states” from the DNA microarray data and with no a-priori assumptions. Comparing subsets of human and yeast transcripts of the same gene ontology annotations, we find that in both disparate eukaryotes, transcripts involved in protein synthesis or mitochondrial metabolism are significantly shorter than typical, and in particular, significantly shorter than those involved in glucose metabolism. Comparing the subsets of human transcripts that are overexpressed in glioblastoma multiforme (GBM) or normal brain tissue samples from The Cancer Genome Atlas, we find that GBM maintains normal brain overexpression of significantly short transcripts, enriched in transcripts that are involved in protein synthesis or mitochondrial metabolism, but suppresses normal overexpression of significantly longer transcripts, enriched in transcripts that are involved in glucose metabolism and brain activity. These global relations among transcript length, cellular metabolism and tumor development suggest a previously unrecognized physical mode for tumor and normal cells to differentially regulate metabolism in a transcript length-dependent manner. The identified distribution functions support a previous hypothesis from mathematical modeling of evolutionary forces that act upon transcript length in the manner of the restoring force of the harmonic oscillator.



Graph Diffusion Distance: A Difference Measure for Weighted Graphs Based on the Graph Laplacian Exponential Kernel
D.K. Hammond, Y. Gur, C.R. Johnson. In Proceedings of the IEEE global conference on information and signal processing (GlobalSIP'13), Austin, Texas, pp. 419--422. 2013.
DOI: 10.1109/GlobalSIP.2013.6736904

We propose a novel difference metric, called the graph diffusion distance (GDD), for quantifying the difference between two weighted graphs with the same number of vertices. Our approach is based on measuring the average similarity of heat diffusion on each graph. We compute the graph Laplacian exponential kernel matrices, corresponding to repeatedly solving the heat diffusion problem with initial conditions localized to single vertices. The GDD is then given by the Frobenius norm of the difference of the kernels, at the diffusion time yielding the maximum difference. We study properties of the proposed distance on both synthetic examples, and on real-data graphs representing human anatomical brain connectivity.



Inverse Electrocardiographic Source Localization of Ischemia: An Optimization Framework and Finite Element Solution
D. Wang, R.M. Kirby, R.S. MacLeod, C.R. Johnson. In Journal of Computational Physics, Vol. 250, Academic Press, pp. 403--424. 2013.
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2013.05.027

With the goal of non-invasively localizing cardiac ischemic disease using bodysurface potential recordings, we attempted to reconstruct the transmembrane potential (TMP) throughout the myocardium with the bidomain heart model. The task is an inverse source problem governed by partial differential equations (PDE). Our main contribution is solving the inverse problem within a PDE-constrained optimization framework that enables various physically-based constraints in both equality and inequality forms. We formulated the optimality conditions rigorously in the continuum before deriving finite element discretization, thereby making the optimization independent of discretization choice. Such a formulation was derived for the L2-norm Tikhonov regularization and the total variation minimization. The subsequent numerical optimization was fulfilled by a primal-dual interior-point method tailored to our problem's specific structure. Our simulations used realistic, fiberincluded heart models consisting of up to 18,000 nodes, much finer than any inverse models previously reported. With synthetic ischemia data we localized ischemic regions with roughly a 10% false-negative rate or a 20% false-positive rate under conditions up to 5% input noise. With ischemia data measured from animal experiments, we reconstructed TMPs with roughly 0.9 correlation with the ground truth. While precisely estimating the TMP in general cases remains an open problem, our study shows the feasibility of reconstructing TMP during the ST interval as a means of ischemia localization.

Keywords: cvrti, 2P41 GM103545-14