## Chris JohnsonInverse ProblemsComputational Electrophysiology |
## Rob MacLeodECG ImagingCardiac Disease Computational Electrophysiology |
## Jeff WeissComputational Biomechanics |
## Orly AlterComputational Biology |

## Chris ButsonNeuromodulation |
## Tamara BidoneComputational Models |

- Center for Integrative Biomedical Computing
- Muskuloskeletal Research Laboratory
- Genomic Signal Processing Lab

Tensor Decomposition Reveals Concurrent Evolutionary Convergences and Divergences and Correlations with Structural Motifs in Ribosomal RNAC. Muralidhara, A.M. Gross, R.R. Gutell, O. Alter. In PLoS ONE, Vol. 6, No. 4, Public Library of Science, pp. e18768. April, 2011. DOI: 10.1371/journal.pone.0018768 Evolutionary relationships among organisms are commonly described by using a hierarchy derived from comparisons of ribosomal RNA (rRNA) sequences. We propose that even on the level of a single rRNA molecule, an organism's evolution is composed of multiple pathways due to concurrent forces that act independently upon different rRNA degrees of freedom. Relationships among organisms are then compositions of coexisting pathway-dependent similarities and dissimilarities, which cannot be described by a single hierarchy. We computationally test this hypothesis in comparative analyses of 16S and 23S rRNA sequence alignments by using a tensor decomposition, i.e., a framework for modeling composite data. Each alignment is encoded in a cuboid, i.e., a third-order tensor, where nucleotides, positions and organisms, each represent a degree of freedom. A tensor mode-1 higher-order singular value decomposition (HOSVD) is formulated such that it separates each cuboid into combinations of patterns of nucleotide frequency variation across organisms and positions, i.e., \"eigenpositions\" and corresponding nucleotide-specific segments of \"eigenorganisms,\" respectively, independent of a-priori knowledge of the taxonomic groups or rRNA structures. We find, in support of our hypothesis that, first, the significant eigenpositions reveal multiple similarities and dissimilarities among the taxonomic groups. Second, the corresponding eigenorganisms identify insertions or deletions of nucleotides exclusively conserved within the corresponding groups, that map out entire substructures and are enriched in adenosines, unpaired in the rRNA secondary structure, that participate in tertiary structure interactions. This demonstrates that structural motifs involved in rRNA folding and function are evolutionary degrees of freedom. Third, two previously unknown coexisting subgenic relationships between Microsporidia and Archaea are revealed in both the 16S and 23S rRNA alignments, a convergence and a divergence, conferred by insertions and deletions of these motifs, which cannot be described by a single hierarchy. This shows that mode-1 HOSVD modeling of rRNA alignments might be used to computationally predict evolutionary mechanisms. |

Finite Element Based Discretization and Regularization Strategies for 3D Inverse ElectrocardiographyD. Wang, R.M. Kirby, C.R. Johnson. 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 |

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

Global Effects of DNA Replication and DNA Replication Origin Activity on Eukaryotic Gene Expression,L. Omberg, J.R. Meyerson, K. Kobayashi, L.S. Drury, J.F.X. Diffley, O. Alter. In Nature Molecular Systems Biology, Vol. 5, No. 312, pp. (published online). October, 2009. DOI: 10.1038/msb.2009.70 |

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

Visual Analysis of Bioelectric FieldsX. Tricoche, R.S. MacLeod, C.R. Johnson. In Visualization in Medicine and Life Sciences, Mathematics and Visualization, Springer-Verlag, pp. 205--220. 2008. |

CRA-NIH Computing Research Challenges in Biomedicine Workshop RecommendationsD. Reed, C.R. Johnson. Note: Computing Research Association (CRA), 2007. |

A Tensor Higher-Order Singular Value Decomposition for Integrative Analysis of DNA Microarray Data From Different Studies,L. Omberg, G.H. Golub, O. Alter. In Proceedings of the National Academy of Sciences, Vol. 104, No. 47, Proceedings of the National Academy of Sciences, pp. 18371–-18376. November, 2007. DOI: 10.1073/pnas.0709146104 |

Genomic Signal Processing: From Matrix Algebra to Genetic NetworksO. Alter. In Microarray Data Analysis: Methods in Molecular Biology, Vol. 377, Edited by M.J. Korenberg, Humana Press, Totowa, pp. 17--59. 2007. DOI: 10.1007/978-1-59745-390-5_2 |

BioMesh3D: A Meshing Pipeline for Biomedical ModelsSCI Institute Technical Report, M. Callahan, M.J. Cole, J.F. Shepherd, J.G. Stinstra, C.R. Johnson. No. UUSCI-2007-009, University of Utah, 2007. |

Hexahedral Mesh Generation for Biomedical Models in SCIRunSCI Institute Technical Report, J.F. Shepherd, C.R. Johnson. No. UUSCI-2007-008, University of Utah, 2007. |

Discovery of Principles of Nature from Mathematical Modeling of DNA Microarray DataO. Alter. In Proceedings of the National Academy of Sciences, Vol. 103, No. 44, Proceedings of the National Academy of Sciences, pp. 16063--16064. October, 2006. DOI: 10.1073/pnas.0607650103 |