SCI Publications

2011

B. Nelson, R. Haimes, R.M. Kirby. “GPU-Based Interactive Cut-Surface Extraction From High-0rder Finite Element Fields,” In IEEE Transactions on Visualization and Computer Graphics (IEEE Visualization Issue), Vol. 17, No. 12, pp. 1803--1811. 2011.

We present a GPU-based ray-tracing system for the accurate and interactive visualization of cut-surfaces through 3D simulations of physical processes created from spectral/hp high-order finite element methods. When used by the numerical analyst to debug the solver, the ability for the imagery to precisely reflect the data is critical. In practice, the investigator interactively selects from a palette of visualization tools to construct a scene that can answer a query of the data. This is effective as long as the implicit contract of image quality between the individual and the visualization system is upheld. OpenGL rendering of scientific visualizations has worked remarkably well for exploratory visualization for most solver results. This is due to the consistency between the use of first-order representations in the simulation and the linear assumptions inherent in OpenGL (planar fragments and color-space interpolation). Unfortunately, the contract is broken when the solver discretization is of higher-order. There have been attempts to mitigate this through the use of spatial adaptation and/or texture mapping. These methods do a better job of approximating what the imagery should be but are not exact and tend to be view-dependent. This paper introduces new rendering mechanisms that specifically deal with the kinds of native data generated by high-order finite element solvers. The exploratory visualization tools are reassessed and cast in this system with the focus on image accuracy. This is accomplished in a GPU setting to ensure interactivity.

D.J. Swenson, S.E. Geneser, J.G. Stinstra, R.M. Kirby, R.S. MacLeod. “Cardiac Position Sensitivity Study in the Electrocardiographic Forward Problem Using Stochastic Collocation and Boundary Element Methods,” In Annals of Biomedical Engineering, Vol. 39, No. 12, pp. 2900--2910. 2011.
DOI: 10.1007/s10439-011-0391-5
PubMed ID: 21909818
PubMed Central ID: PMC336204

D. Wang, R.M. Kirby, C.R. Johnson. “Finite Element Based Discretization and Regularization Strategies for 3D Inverse Electrocardiography,” In IEEE Transactions for Biomedical Engineering, Vol. 58, No. 6, pp. 1827--1838. 2011.
PubMed ID: 21382763
PubMed Central ID: PMC3109267

We consider the inverse electrocardiographic problem of computing epicardial potentials from a body-surface potential map. We study how to improve numerical approximation of the inverse problem when the finite-element method is used. Being ill-posed, the inverse problem requires different discretization strategies from its corresponding forward problem. We propose refinement guidelines that specifically address the ill-posedness of the problem. The resulting guidelines necessitate the use of hybrid finite elements composed of tetrahedra and prism elements. Also, in order to maintain consistent numerical quality when the inverse problem is discretized into different scales, we propose a new family of regularizers using the variational principle underlying finite-element methods. These variational-formed regularizers serve as an alternative to the traditional Tikhonov regularizers, but preserves the L₂ norm and thereby achieves consistent regularization in multiscale simulations. The variational formulation also enables a simple construction of the discrete gradient operator over irregular meshes, which is difficult to define in traditional discretization schemes. We validated our hybrid element technique and the variational regularizers by simulations on a realistic 3-D torso/heart model with empirical heart data. Results show that discretization based on our proposed strategies mitigates the ill-conditioning and improves the inverse solution, and that the variational formulation may benefit a broader range of potential-based bioelectric problems.

D. Wang, R.M. Kirby, R.S. Macleod, C.R. Johnson. “An optimization framework for inversely estimating myocardial transmembrane potentials and localizing ischemia,” In Proceedings of the International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS), pp. 1680--1683. 2011.
DOI: 10.1109/IEMBS.2011.6090483
PubMed ID: 22254648
PubMed Central ID: PMC3336368

By combining a static bidomain heart model with a torso conduction model, we studied the inverse electrocardiographic problem of computing the transmembrane potentials (TMPs) throughout the myocardium from a body-surface potential map, and then used the recovered potentials to localize myocardial ischemia. Our main contribution is solving the inverse problem within a constrained optimization framework, which is a generalization of previous methods for calculating transmembrane potentials. The framework offers ample flexibility for users to apply various physiologically-based constraints, and is well supported by mature algorithms and solvers developed by the optimization community. By avoiding the traditional inverse ECG approach of building the lead-field matrix, the framework greatly reduces computation cost and, by setting the associated forward problem as a constraint, the framework enables one to flexibly set individualized resolutions for each physical variable, a desirable feature for balancing model accuracy, ill-conditioning and computation tractability. Although the task of computing myocardial TMPs at an arbitrary time instance remains an open problem, we showed that it is possible to obtain TMPs with moderate accuracy during the ST segment by assuming all cardiac cells are at the plateau phase. Moreover, the calculated TMPs yielded a good estimate of ischemic regions, which was of more clinical interest than the voltage values themselves. We conducted finite element simulations of a phantom experiment over a 2D torso model with synthetic ischemic data. Preliminary results indicated that our approach is feasible and suitably accurate for the common case of transmural myocardial ischemia.

C. Yang, D. Xiu, R.M. Kirby. “Visualization of Covariance and Cross-covariance Field,” In International Journal for Uncertainty Quantification, Vol. 3, No. 1, pp. 25--38. 2011.
DOI: 10.1615/Int.J.UncertaintyQuantification.2011003369

We present a numerical technique to visualize covariance and cross-covariance fields of a stochastic simulation. The method is local in the sense that it demonstrates the covariance structure of the solution at a point with its neighboring locations. When coupled with an efficient stochastic simulation solver, our framework allows one to effectively concurrently visualize both the mean and (cross-)covariance information for two-dimensional (spatial) simulation results. Most importantly, the visualization provides the scientist a means to identify interesting correlation structure of the solution field. The mathematical setup is discussed, along with several examples to demonstrate the efficacy of this approach.

Keywords: netl

2010

T. Etiene, L.G. Nonato, C.E. Scheidegger, J. Tierny, T.J. Peters, V. Pascucci, R.M. Kirby, C.T. Silva. “Topology Verification for Isosurface Extraction,” SCI Technical Report, No. UUSCI-2010-003, SCI Institute, University of Utah, 2010.

S.E. Geneser, J.D. Hinkle, R.M. Kirby, Brian Wang, B. Salter, S. Joshi. “Quantifying Variability in Radiation Dose Due to Respiratory-Induced Tumor Motion,” In Medical Image Analysis, Vol. 15, No. 4, pp. 640--649. 2010.
DOI: 10.1016/j.media.2010.07.003

P.K. Jimack, R.M. Kirby. “Towards the Development on an h-p-Refinement Strategy Based Upon Error Estimate Sensitivity,” In Computers and Fluids, Vol. 46, No. 1, pp. 277--281. 2010.
DOI: 10.1016/j.compfluid.2010.08.003

H. Mirzaee, J.K. Ryan, R.M. Kirby. “Quantificiation of Errors Introduced in the Numerical Approximation and Implementation of Smoothness-Increasing Accuracy Conserving (SIAC) Filtering of Discontinuous Galerkin (DG) Fields,” In Journal of Scientific Computing, Vol. 45, pp. 447-470. 2010.

M. Steffen, R.M. Kirby, M. Berzins. “Decoupling and Balancing of Space and Time Errors in the Material Point Method (MPM),” In International Journal for Numerical Methods in Engineering, Vol. 82, No. 10, pp. 1207--1243. 2010.

P.E.J. Vos, S.J. Sherwin, R.M. Kirby. “h-p Efficiently: Implementing Finite and Spectral/hp Element Methods to Achieve Optimal Performance for Low- and High-Order Discretisations,” In Journal of Computational Physics, Vol. 229, No. 13, pp. 5161--5181. 2010.

D.F. Wang, R.M. Kirby, C.R. Johnson. “Resolution Strategies for the Finite-Element-Based Solution of the ECG Inverse Problem,” In IEEE Transactions on Biomedical Engineering, Vol. 57, No. 2, pp. 220--237. February, 2010.

D.F. Wang, R.M. Kirby, R.S. MacLeod, C.R. Johnson. “A New Family of Variational-Form-Based Regularizers for Reconstructing Epicardial Potentials from Body-Surface Mapping,” In Computing in Cardiology, 2010, pp. 93--96. 2010.

2009

S.E. Geneser, R.M. Kirby, Brian Wang, B. Salter, S. Joshi. “Incorporating patient breathing variability into a stochastic model of dose deposition for stereotactic body radiation therapy,” In Information Processing in Medical Imaging, Lecture Notes in Computer Science LNCS, Vol. 5636, pp. 688--700. 2009.
PubMed ID: 19694304

H. Mirzaee, C. Eskilsson, S.J. Sherwin, R.M. Kirby. “Comparison of Consistent Integration Versus Adaptive Quadrature for Taming Aliasing Errors,” SCI Technical Report, No. UUSCI-2009-008, SCI Institute, University of Utah, 2009.

J.S. Preston, T. Tasdizen, C.M. Terry, A.K. Cheung, R.M. Kirby. “Using the stochastic collocation method for the uncertainty quantification of drug concentration due to depot shape variability,” In IEEE Transactions on Biomedical Engineering, Vol. 56, No. 3, Note: Epub 2008 Dec 2, pp. 609--620. 2009.
PubMed ID: 19272865

A.R. Sanderson, M.D. Meyer, R.M. Kirby, C.R. Johnson. “A Framework for Exploring Numerical Solutions of Advection Reaction Diffusion Equations using a GPU Based Approach,” In Journal of Computing and Visualization in Science, Vol. 12, pp. 155--170. 2009.
DOI: 10.1007/s00791-008-0086-0

A. Vo, S. Vakkalanka, M. Delisi, G. Gopalakrishnan, R.M. Kirby, R. Thakur. “Formal Verification of Practical MPI Programs,” In Proceedings of 14th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming (PPoPP), Raleigh, NC, pp. 261--270. February 14-18, 2009.

D.F. Wang, R.M. Kirby, C.R. Johnson. “Finite Element Discretization Strategies for the Inverse Electrocardiographic (ECG) Problem,” In Proceedings of the 11th World Congress on Medical Physics and Biomedical Engineering, Munich, Germany, Vol. 25/2, pp. 729-732. September, 2009.

D.F. Wang, R.M. Kirby, C.R. Johnson. “Finite Element Refinements for Inverse Electrocardiography: Hybrid-Shaped Elements, High-Order Element Truncation and Variational Gradient Operator,” In Proceeding of Computers in Cardiology 2009, Park City, September, 2009.