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Review

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

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Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
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Livestrong Cancer Institutes, Dell Medical School, The University of Texas at Austin, Austin, TX 78712, USA
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Texas Advanced Computing Center, The University of Texas at Austin, Austin, TX 78758, USA
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Department of Civil Engineering and Architecture, University of Pavia, Via Ferrata 3, 27100 Pavia, Italy
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Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712, USA
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Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, TX 78712, USA
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Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, USA
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Department of Computer Science, The University of Texas at Austin, Austin, TX 78712, USA
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Department of Diagnostic Medicine, The University of Texas at Austin, Austin, TX 78712, USA
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Department of Oncology, The University of Texas at Austin, Austin, TX 78712, USA
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Department of Imaging Physics, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, USA
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Author to whom correspondence should be addressed.
Academic Editor: David Wong
Cancers 2021, 13(12), 3008; https://doi.org/10.3390/cancers13123008
Received: 28 April 2021 / Revised: 7 June 2021 / Accepted: 13 June 2021 / Published: 16 June 2021
(This article belongs to the Special Issue Angiogenesis and Anti-angiogenic Therapies)
The recruitment of new vasculature via angiogenesis is a critical component of tumor development, which fundamentally influences tumor growth and response to treatment. The characterization of tumor-induced angiogenesis via mathematical models could enable approaches to forecast tumor response and improve patient care. In this review, we discuss how time-resolved imaging data integrated with mathematical modeling can be used to systematically investigate angiogenesis from the cell to tissue scale and ultimately forecast response to therapy.
Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2–3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions. View Full-Text
Keywords: computational oncology; magnetic resonance imaging; perfusion; partial differential equations; confocal microscopy; systems biology; treatment response; vascular growth; computational fluid dynamics computational oncology; magnetic resonance imaging; perfusion; partial differential equations; confocal microscopy; systems biology; treatment response; vascular growth; computational fluid dynamics
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MDPI and ACS Style

Hormuth, D.A., II; Phillips, C.M.; Wu, C.; Lima, E.A.B.F.; Lorenzo, G.; Jha, P.K.; Jarrett, A.M.; Oden, J.T.; Yankeelov, T.E. Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data. Cancers 2021, 13, 3008. https://doi.org/10.3390/cancers13123008

AMA Style

Hormuth DA II, Phillips CM, Wu C, Lima EABF, Lorenzo G, Jha PK, Jarrett AM, Oden JT, Yankeelov TE. Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data. Cancers. 2021; 13(12):3008. https://doi.org/10.3390/cancers13123008

Chicago/Turabian Style

Hormuth, David A., II, Caleb M. Phillips, Chengyue Wu, Ernesto A.B.F. Lima, Guillermo Lorenzo, Prashant K. Jha, Angela M. Jarrett, J. T. Oden, and Thomas E. Yankeelov 2021. "Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data" Cancers 13, no. 12: 3008. https://doi.org/10.3390/cancers13123008

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