K. Potter, J. Krüger, C.R. Johnson. Towards the Visualization of Multi-Dimentional Stochastic Distribution Data, In Proceedings of The International Conference on Computer Graphics and Visualization (IADIS) 2008, pp. 191--196. 2008.
J.F. Shepherd, C.R. Johnson. Hexahedral Mesh Generation Constraints, In Journal of Engineering with Computers, Vol. 24, No. 3, pp. 195--213. 2008.
J.G. Stinstra, M.A. Jolley, J.D. Tate, D.H. Brooks, J.K. Triedman, R.S. MacLeod. The Role of Volume Conductivities in Simulation of Implantable Defibrillators, In Computers in Cardiology, Bologna, Italy, 2008.
J.G. Stinstra, M. Jolley, M. Callahan, D.M. Weinstein, M. Cole, D.H. Brooks, J. Triedman, R.S. MacLeod.
Evaluation of Different Meshing Algorithms in the Computation of Defibrillation Thresholds in Children, In Proceedings of the 29th Annual International Conference of the IEEE EMBS, pp. 1422-1425. 2008.
D.R. Sutherland, Q. Ni, R.S. MacLeod, R.L. Lux, B.B. Punske. Experimental Measures of Ventricular Activation and Synchrony, In Pacing and Clinical Electrophysiology, Vol. 31, No. 12, pp. 1560--1570. December, 2008.
X. Tricoche, R.S. MacLeod, C.R. Johnson. Visual Analysis of Bioelectric Fields, In Visualization in Medicine and Life Sciences, Mathematics and Visualization, Springer-Verlag, pp. 205--220. 2008.
J.K. Triedman, M. Jolley, J. Stinstra, D.H. Brooks, R.S. MacLeod. Predictive Modeling of Defibrillation Using Hexahedral and Tetrahedral Finite Element Models: Recent Advances, In Journal of Electrocardiology, Vol. 41, pp. 483--486. 2008.
S.X. Vasquez, M.S. Hansen, A.N. Bahadur, M.F. Hockin, G.L. Kindlmann, L. Nevell, I.Q. Wu, D.J. Grunwald, D.M. Weinstein, G.M. Jones, C.R. Johnson, J.L. Vandeberg, M.R. Capecchi, C. Keller.
Optimization of Volumetric Computed Tomography for Skeletal Analysis of Model Genetic Organisms, In The Anatomical Record: Advances in Integrative Anatomy and Evolutionary Biology, Vol. 291, pp. 475--487. 2008.
PubMed ID: 18286615
G. Adluru, S.P. Awate, T. Tasdizen, R.T. Whitaker, E.V.R. DiBella. Temporally Constrained Reconstruction of Dynamic Cardiac Perfusion MRI, In Magnetic Resonance in Medicine, Vol. 57, pp. 1027--1036. 2007.
G. Adluru, R.T. Whitaker, E.V.R. DiBella. Spatio-Temporal Constrained Reconstruction of Sparse Dynamic Contrast Enhanced Radial MRI Data, In Proceedings of the IEEE International Symposium on Biomedical Imaging, pp. 109--112. 2007.
G. Adluru, E. Hsu, E.V.R. DiBella. Constrained Reconstruction of Sparse Cardiac MR DTI Data, In Proceedings of FIMH 2007, LNCS, No. 4466, pp. 91--99. 2007.
M. Callahan, M.J. Cole, J.F. Shepherd, J.G. Stinstra, C.R. Johnson. BioMesh3D: A Meshing Pipeline for Biomedical Models, SCI Institute Technical Report, No. UUSCI-2007-009, University of Utah, 2007.
M. Callahan, M.J. Cole, J.F. Shepherd, J.G. Stinstra, C.R. Johnson. A Meshing Pipeline for Biomedical Computing, In Engineering with Computers, Special Issue on Computational Bioengineering, pp. (in press). 2007.
J. Cates, P.T. Fletcher, M. Styner, M. Shenton, R.T. Whitaker. Shape Modeling and Analysis with Entropy-Based Particle Systems, In Proceedings of Information Processing in Medical Imaging (IPMI) 2007, LNCS 4584, pp. 333--345. 2007.
Markovian models of ion channels have proven useful in the reconstruction of experimental data and prediction of cellular electrophysiology. We present the stochastic Galerkin method as an alternative to Monte Carlo and other stochastic methods for assessing the impact of uncertain rate coefficients on the predictions of Markovian ion channel models. We extend and study two different ion channel models: a simple model with only a single open and a closed state and a detailed model of the cardiac rapidly activating delayed rectifier potassium current. We demonstrate the efficacy of stochastic Galerkin methods for computing solutions to systems with random model parameters. Our studies illustrate the characteristic changes in distributions of state transitions and electrical currents through ion channels due to random rate coefficients. Furthermore, the studies indicate the applicability of the stochastic Galerkin technique for uncertainty and sensitivity analysis of bio-mathematical models.
Keywords: Stochastic Galerkin, Polynomial chaos, Stochastic processes, Markov modeling, Ion channels
A. Ghodrati, D.H. Brooks, R.S. MacLeod.
Methods of Solving Reduced Lead Systems for Inverse Electrocardiography, In IEEE Trans Biomed Eng, Vol. 54, No. 2, pp. 339--343. February, 2007.
PubMed ID: 17278592
W.-K. Jeong, P.T. Fletcher, R. Tao, R.T. Whitaker.
Interactive Visualization of Volumetric White Matter Connectivity in DT-MRI Using a Parallel-Hardware Hamilton-Jacobi Solver, In IEEE Transactions on Visualization and Computer Graphics, Vol. 13, No. 6, pp. 1480--1487. 2007.
PubMed ID: 17968100