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Modeling Tumor Blood Vessel Dynamics

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Mathematical Methods and Models in Biomedicine

Abstract

Tumor blood vessels are structurally abnormal and functionally inefficient, resulting in incomplete perfusion of tumor vessel networks and nonuniform delivery of chemotherapeutics to the tumor cells. Excessive production of the angiogenic growth factor VEGF (vascular endothelial growth factor) contributes to tumor vessel abnormalities, and many anti-VEGF therapies can cause remodeling or stabilization of tumor blood vessels. This remodeling resembles the process of angioadaptation previously studied in the context of normal physiology and ischemia. During angioadaptation (also know as adaptive remodeling), endothelial cells respond to blood forces to alter blood flow. Some segments dilate, while others contract, eventually producing an efficient network. Although not well understood, it is likely that adaptive remodeling depends on blood shear forces, transvascular pressure, upstream signals transmitted along the endothelium as well as growth factors such as VEGF. To provide an analytical framework for understanding these processes in the context of tumor vasculature, we have developed a mathematical model, supported by multiparameter imaging methodology, which incorporates the necessary elements for predicting the transport of nutrients and drugs throughout tumor vessels and tissue, as well as the adaptive remodeling of the blood vessel network. A better understanding of the mechanisms responsible for the network dynamics may lead to novel approaches for treating tumors or other diseases involving vascular pathologies.

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  1. Massachusetts General Hospital, Harvard Medical School, Boston, MA, 02114, USA

    Lance L. Munn, Christian Kunert & J. Alex Tyrrell

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  1. Lance L. Munn
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  2. Christian Kunert
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Correspondence to Lance L. Munn .

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Editors and Affiliations

  1. , Mathematics and Statistics, Southern Illinois University Edwardsvill, Edwardsville, 62026, Illinois, USA

    Urszula Ledzewicz

  2. , Electrical and Systems Engineering, Washington University, Brookings Drive 1, Saint Louis, 63130, Missouri, USA

    Heinz Schättler

  3. Mathematical Biosciences Institute, Ohio State University, W. 18th Avenue 231, Columbus, 43210-1292, Ohio, USA

    Avner Friedman

  4. Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Eugene Kashdan

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Munn, L.L., Kunert, C., Tyrrell, J.A. (2013). Modeling Tumor Blood Vessel Dynamics. In: Ledzewicz, U., Schättler, H., Friedman, A., Kashdan, E. (eds) Mathematical Methods and Models in Biomedicine. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4178-6_5

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