In this study, statistical models are developed for modeling uncertain heterogeneous permeability and porosity in tumors, and the resulting uncertainties in pressure and velocity fields during an intratumoral injection are quantified using a nonintrusive spectral uncertainty quantification (UQ) method. Specifically, the uncertain permeability is modeled as a log-Gaussian random field, represented using a truncated Karhunen–Lòeve (KL) expansion, and the uncertain porosity is modeled as a log-normal random variable. The efficacy of the developed statistical models is validated by simulating the concentration fields with permeability and porosity of different uncertainty levels. The irregularity in the concentration field bears reasonable visual agreement with that in MicroCT images from experiments. The pressure and velocity fields are represented using polynomial chaos (PC) expansions to enable efficient computation of their statistical properties. The coefficients in the PC expansion are computed using a nonintrusive spectral projection method with the Smolyak sparse quadrature. The developed UQ approach is then used to quantify the uncertainties in the random pressure and velocity fields. A global sensitivity analysis is also performed to assess the contribution of individual KL modes of the log-permeability field to the total variance of the pressure field. It is demonstrated that the developed UQ approach can effectively quantify the flow uncertainties induced by uncertain material properties of the tumor.
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September 2017
Research-Article
Investigation of Biotransport in a Tumor With Uncertain Material Properties Using a Nonintrusive Spectral Uncertainty Quantification Method
Alen Alexanderian,
Alen Alexanderian
Department of Mathematics,
North Carolina State University,
Raleigh, NC 27695
e-mail: alexanderian@ncsu.edu
North Carolina State University,
Raleigh, NC 27695
e-mail: alexanderian@ncsu.edu
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Liang Zhu,
Liang Zhu
Department of Mechanical Engineering,
University of Maryland, Baltimore County,
Baltimore, MD 21250
University of Maryland, Baltimore County,
Baltimore, MD 21250
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Maher Salloum,
Maher Salloum
Extreme Scale Data Science and Analytics,
Sandia National Labs,
Livermore, CA 94550
Sandia National Labs,
Livermore, CA 94550
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Ronghui Ma,
Ronghui Ma
Department of Mechanical Engineering,
University of Maryland, Baltimore County,
Baltimore, MD 21250
University of Maryland, Baltimore County,
Baltimore, MD 21250
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Meilin Yu
Meilin Yu
Department of Mechanical Engineering,
University of Maryland, Baltimore County,
Baltimore, MD 21250
e-mail: mlyu@umbc.edu
University of Maryland, Baltimore County,
Baltimore, MD 21250
e-mail: mlyu@umbc.edu
Search for other works by this author on:
Alen Alexanderian
Department of Mathematics,
North Carolina State University,
Raleigh, NC 27695
e-mail: alexanderian@ncsu.edu
North Carolina State University,
Raleigh, NC 27695
e-mail: alexanderian@ncsu.edu
Liang Zhu
Department of Mechanical Engineering,
University of Maryland, Baltimore County,
Baltimore, MD 21250
University of Maryland, Baltimore County,
Baltimore, MD 21250
Maher Salloum
Extreme Scale Data Science and Analytics,
Sandia National Labs,
Livermore, CA 94550
Sandia National Labs,
Livermore, CA 94550
Ronghui Ma
Department of Mechanical Engineering,
University of Maryland, Baltimore County,
Baltimore, MD 21250
University of Maryland, Baltimore County,
Baltimore, MD 21250
Meilin Yu
Department of Mechanical Engineering,
University of Maryland, Baltimore County,
Baltimore, MD 21250
e-mail: mlyu@umbc.edu
University of Maryland, Baltimore County,
Baltimore, MD 21250
e-mail: mlyu@umbc.edu
Manuscript received February 3, 2017; final manuscript received May 16, 2017; published online July 14, 2017. Assoc. Editor: Ram Devireddy.
J Biomech Eng. Sep 2017, 139(9): 091006 (11 pages)
Published Online: July 14, 2017
Article history
Received:
February 3, 2017
Revised:
May 16, 2017
Citation
Alexanderian, A., Zhu, L., Salloum, M., Ma, R., and Yu, M. (July 14, 2017). "Investigation of Biotransport in a Tumor With Uncertain Material Properties Using a Nonintrusive Spectral Uncertainty Quantification Method." ASME. J Biomech Eng. September 2017; 139(9): 091006. https://doi.org/10.1115/1.4037102
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