Center for Integrative Biomedical Computing

2007

S.E. Geneser, R.M. Kirby, D. Xiu, F.B. Sachse.
**“Stochastic Markovian Modeling of Electrophysiology of Ion Channels: Reconstruction of Standard Deviations in Macroscopic Currents,”** In *Journal of Theoretical Biology*, Vol. 245, No. 4, pp. 627--637. 2007.

DOI: 10.1016/j.jtbi.2006.10.016

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

M. Jolley, J.G. Stinstra, D.M. Weinstein, S. Pieper, R.S.J. Estepar, G. Kindlmann, R.S. MacLeod, D.H. Brooks, J.K. Triedman.
**“Open-Source Environment for Interactive Finite Element Modeling of Optimal ICD Electrode Placement,”** In *Functional Imaging and Modeling of the Heart*, Lecture Notes in Computer Science (LCNS), Vol. 4466/2007, pp. 373--382. 2007.

ISBN: 978-3-540-72906-8

G. Kindlmann, D.B. Ennis, R.T. Whitaker, C.-F. Westin.
**“Diffusion Tensor Analysis With Invariant Gradients and Rotation Tangents,”** In *IEEE Transactions on Medical Imaging*, Vol. 26, No. 11, pp. 1483--1499. 2007.

S. Lew, C. Wolters, A. Anwander, S. Makeig, R.S. MacLeod.
**“Low Resolution Conductivity Estimation to Improve Source Localization,”** In *New Frontiers in Biomagnetism. Proceedings of the 15th International Conference on Biomagnetism, Vancouver, BC, Canada, August 21-25, 2006.*, International Congress Series, Vol. 1300, pp. 149--152. June, 2007.

M. Malik, Y. Birnbaum, R.S. MacLeod, V. Shusterman.
**“Markers of impaired repolarization,”** In *Journal of Electrocardiology*, Vol. 40, No. 1, pp. S54--S57. January, 2007.

M.D. Meyer, R.M. Kirby, R.T. Whitaker.
**“Topology, Accuracy, and Quality of Isosurface Meshes Using Dynamic Particles,”** In *IEEE Transactions on Visualization and Computer Graphics*, Vol. 13, No. 6, IEEE, pp. 1704--1711. Nov, 2007.

J.F. Shepherd, C.R. Johnson.
**“Hexahedral Mesh Generation for Biomedical Models in SCIRun,”** SCI Institute Technical Report, No. UUSCI-2007-008, *University of Utah*, 2007.

S. Shome, R.L. Lux, B.B. Punske, R.S. MacLeod.
**“Ischemic Preconditioning Protects Against Arrhythmogenesis Through Maintenance of Both Active as well as Passive Electrical Properties in Ischemic Canine Hearts,”** In *Journal of Electrocardiology*, Vol. 40, No. 6 supp, pp. S150--S159. Nov-Dec, 2007.

S. Shome, J.G. Stinstra, C Henriquez, R.S. Macleod.
**“Influence of Extracellular Potassium and Reduced Extracellular Space on Conduction Velocity During Acute Ischemia: A Simulation Study,”** In *Journal of Electrocardiology*, Vol. 40, No. 4, pp. S5--S6. 2007.

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. 2007.

J.K. Triedman, M. Jolley, R.S. MacLeod, J.G. Stinstra, D.H. Brooks, S. Pieper.
**“A System for Image Based Finite Element Modeling of Novel Defibrillation Strategies,”** In *Life Science Systems and Applications Workshop, 2007. LISA 2007*, pp. 63--66. 2007.

J.K. Triedman, M. Jolley, R.S. MacLeod, J. Stinstra, D.H. Brooks, S. Pieper.
**“Finite Element Modeling of Novel Defibrillation Approaches in Children and Adults,”** In *Proc. LISSA Conf.*, Bethesda, MD, November, 2007.

S.X. Vasquez, A.N. Bahadur, J.T. Johnson III, D.R. Rodriguez, C. Keller.
**“Severe Runting of a Laboratory Mouse (Mus musculus),”** In *Lab Animal*, Vol. 36, No. 1, pp. 19, 22--23. January, 2007.

C.H. Wolters, H. Köstler, C. Möller, J. Härtlein, L. Grasedyck, W. Hackbusch.
**“Numerical Mathematics of the Subtraction Method for the Modeling of a Current Dipole in EEG Source Reconstruction Using Finite Element Head Models,”** In *SIAM J. on Scientific Computing*, Vol. 30, No. 1, pp. 24--45. 2007.

C.H. Wolters, H. Köstler, C. Möller, J. Härdtlein, A. Anwander.
**“Numerical Approaches for Dipole Modeling in Finite Element Method Based Source Analysis,”** In *New Frontiers in Biomagnetism. Proceedings of the 15th International Conference on Biomagnetism, Vancouver, BC, Canada, August 21-25, 2006.*, International Congress Series, Vol. 1300, pp. 189--192. June, 2007.

B. Yihnaz, R.S. MacLeod, B.B. Punske, B. Taccardi, and D.H. Brooks.
**“Generalized training subset selection for statistical estimation of epicardial activation maps from intravenous catheter measurements,”** In *Compo in BioI. and Med.*, In *Compo in BioI. and Med.*, Vol. 37, No. 3, pp. 328--336. 2007.

B. Yilmaz, R.S. MacLeod.
**“Generalized Training Subset Selection for Statistical Estimation of Epicardial Activation Maps from Intravenous Catheter Measurements,”** In *Computers in Biology and Medicine*, Vol. 37, No. 9, pp. 328--336. March, 2007.

2006

G. Adluru, E.V.R. DiBella, R.T. Whitaker.
**“Automatic Segmentation of Cardiac Short Axis Slices in Perfusion MRI,”** In *Proceedings of The 2006 IEEE International Symposium on Biomedical Imaging*, pp. 133--136. 2006.

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