Computational Models
Simulations of Biological Systems
Multi-Physics Models of Cancer Cells
![]() ![]() Finite Element Based Discretization and Regularization Strategies for 3D Inverse Electrocardiography D. 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 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. |
![]() ![]() Using the stochastic collocation method for the uncertainty quantification of drug concentration due to depot shape variability J.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 therapy S.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 Fields X. 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 Recommendations D. 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 Networks O. 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 Models SCI 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 SCIRun SCI 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 Data O. 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 |
![]() ![]() Singular Value Decomposition of Genome-Scale mRNA Lengths Distribution Reveals Asymmetry in RNA Gel Electrophoresis Band Broadening, O. Alter, G. H. Golub. In Proceedings of the National Academy of Sciences, Vol. 103, No. 32, Proceedings of the National Academy of Sciences, pp. 11828--11833. July, 2006. DOI: 10.1073/pnas.0604756103 |