SCI Publications

2007


D. Xiu, S.J. Sherwin. “Parametric Uncertainty Analysis of Pulse Wave Propagation in a Model of a Human Arterial Networks,” In Journal of Computational Physics, Vol. 226, No. 2, pp. 1385--1407. 2007.
DOI: 10.1016/j.jcp.2007.05.020

ABSTRACT

Reduced models of human arterial networks are an efficient approach to analyze quantitative macroscopic features of human arterial flows. The justification for such models typically arise due to the significantly long wavelength associated with the system in comparison to the lengths of arteries in the networks. Although these types of models have been employed extensively and many issues associated with their implementations have been widely researched, the issue of data uncertainty has received comparatively little attention. Similar to many biological systems, a large amount of uncertainty exists in the value of the parameters associated with the models. Clearly reliable assessment of the system behaviour cannot be made unless the effect of such data uncertainty is quantified.

In this paper we present a study of parametric data uncertainty in reduced modelling of human arterial networks which is governed by a hyperbolic system. The uncertain parameters are modelled as random variables and the governing equations for the arterial network therefore become stochastic. This type stochastic hyperbolic systems have not been previously systematically studied due to the difficulties introduced by the uncertainty such as a potential change in the mathematical character of the system and imposing boundary conditions. We demonstrate how the application of a high-order stochastic collocation method based on the generalized polynomial chaos expansion, combined with a discontinuous Galerkin spectral/hp element discretization in physical space, can successfully simulate this type of hyperbolic system subject to uncertain inputs with bounds. Building upon a numerical study of propagation of uncertainty and sensitivity in a simplified model with a single bifurcation, a systematical parameter sensitivity analysis is conducted on the wave dynamics in a multiple bifurcating human arterial network. Using the physical understanding of the dynamics of pulse waves in these types of networks we are able to provide an insight into the results of the stochastic simulations, thereby demonstrating the effects of uncertainty in physiologically accurate human arterial networks.

Keywords: Mathematical biology, Hemodynamics, Arterial network, Stochastic modelling, Uncertainty analysis, High-order methods


Y. Yang, X. Chen, G. Gopalakrishnan, R.M. Kirby. “Distributed Dynamic Partial Order Reduction Based Verification of Threaded Software,” In Proceedings of Model Checking Software: 14th International SPIN Workshop, Berlin, Germany, Vol. 4595/2007, pp. 58--75. July, 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.


F. Zhang, C. Goodlett, E. Hancock, G. Gerig. “Probabilistic White Matter Fiber Tracking using Particle Filtering,” In Proceedings of The 10th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI 2007), Lecture Notes in Computer Science, Vol. 4791, pp. 144--151. November, 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.


G. Adluru, E.V.R. DiBella. “Segmentation Based Registration of Myocardium in Cardiac Perfusion Images,” In Proceedings of The 14th Annual Scientific Meeting of The International Society for Magnetic Resonance in Medicine (ISMRM), Vol. 14, pp. 1223. 2006.


G. Adluru, E.V.R. DiBella, M.C. Schabel. “Model-Based Registration for Dynamic Cardiac Perfusion MRI,” In Journal of Magnetic Resonance Imaging, Vol. 24, No. 5, Wiley Subscription Services, Inc., A Wiley Company, pp. 1062--1070. 2006.
DOI: 10.1002/jmri.20756


I. Altintas, O. Barney, Z. Cheng, T. Critchlow, B. Ludaescher, S.G. Parker, A. Shoshani, M. Vouk. “Accelerating the Scientific Exploration Process with Scientific Workflows,” In J. Phys. : Conf. Ser., Vol. 46, pp. 468--478. 2006.


O. Alter. “Discovery of Principles of Nature from Mathematical Modeling of DNA Microarray Data,” 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


O. Alter, G. H. Golub. “Singular Value Decomposition of Genome-Scale mRNA Lengths Distribution Reveals Asymmetry in RNA Gel Electrophoresis Band Broadening,” 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


E.W. Anderson, S.P. Callahan, G.T.Y. Chen, J. Freire, E. Santos, C.E. Scheidegger, C.T. Silva, H.T. Vo. “Visualization in Radiation Oncology: Towards Replacing the Laboratory Notebook,” SCI Institute Technical Report, No. UUSCI-2006-017, University of Utah, 2006.


A.E. Anderson, B.J. Ellis, J.A. Weiss. “Verification, Validation and Sensitivity Studies in Computational Biomechanics,” In Computer Methods in Biomechanics and Biomedical Engineering, pp. (in press). 2006.


R. Armstrong, G. Kumfert, L.C. McInnes, S.G. Parker, B. Allan, M. Sottile, T. Epperly, T. Dahlgren. “The CCA Component Model for High-Performance Scientific Computing,” In Concurrency and Computation: Practice & Experience, Vol. 18, No. 2, John Wiley and Sons Ltd., Chichester, UK pp. 215--229. 2006.
ISSN: 1532-0626


G.A. Ateshian, B.J. Ellis, J.A. Weiss. “Equivalence Between Instantaneous Biphasic and Incompressible Elastic Material Response,” In Journal of Biomechanical Engineering, pp. (in press). November, 2006.


L. Atty, N. Holzschuch, M. Lapierre, J.-M. Hasenfratz, C.D. Hansen, F.X. Sillion. “Soft Shadow Maps: Efficient Sampling of Light Source Visibility,” In Computer Graphics Forum, Vol. 25, No. 4, pp. 725--741. 2006.


S.P. Awate, T. Tasdizen, N. Foster, R.T. Whitaker. “Adaptive, Nonparametric Markov Modeling for Unsupervised, MRI Brain-Tissue Classification,” SCI Institute Technical Report, No. UUSCI-2006-008, University of Utah, 2006.


S.P. Awate, T. Tasdizen, R.T. Whitaker. “Unsupervised Texture Segmentation with Nonparametric Neighborhood Statistics,” In Proceedings of The European Conference on Computer Vision (ECCV) 2006 Springer, Lecture Notes in Computer Science, pp. 494--507. 2006.


S.P. Awate, T. Tasdizen, R.T. Whitaker. “Unsupervised Texture Segmentation with Nonparametric Neighborhood Statistics,” SCI Institute Technical Report, No. UUSCI-2006-011, University of Utah, 2006.


S.P. Awate, R.T. Whitaker. “Unsupervised, Information-Theoretic, Adaptive Image Filtering for Image Restoration,” In IEEE Trans. Pattern Anal. & Mach. Intel., Vol. 28, No. 3, pp. 364--376. March, 2006.
PubMed ID: 16526423