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Mathematical Biosciences and Engineering

2005, Volume 2, Issue 3: 445-460. doi: 10.3934/mbe.2005.2.445
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Interstitial Pressure And Fluid Motion In Tumor Cords

  • 1.
    Istituto di Analisi dei Sistemi ed Informatica ''A. Ruberti", CNR, Viale Manzoni 30, 00185 Roma
  • 2.
    Dipartimento di Matematica "U. Dini", Università di Firenze, Viale Morgagni 67/A, 50134 Firenze
  • Received: 01 January 2005 Accepted: 29 June 2018 Published: 01 August 2005

  • MSC : 35R35, 92C37, 92C50.

  • This work illustrates the behavior of the interstitial pressure and of the interstitial fluid motion in tumor cords (cylindrical arrangements of tumor cells growing around blood vessels of the tumor) by means of numerical simulations on the basis of a mathematical model previously developed. The model describes the steady state of a tumor cord surrounded by necrosis and its time evolution following cell killing. The most relevant aspects of the dynamics of extracellular fluid are by computing the longitudinal average of the radial fluid velocity and of the pressure field. In the present paper, the necrotic region is treated as a mixture of degrading dead cells and fluid.

    Citation: Alessandro Bertuzzi, Antonio Fasano, Alberto Gandolfi, Carmela Sinisgalli. Interstitial Pressure And Fluid Motion In Tumor Cords[J]. Mathematical Biosciences and Engineering, 2005, 2(3): 445-460. doi: 10.3934/mbe.2005.2.445

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  • This work illustrates the behavior of the interstitial pressure and of the interstitial fluid motion in tumor cords (cylindrical arrangements of tumor cells growing around blood vessels of the tumor) by means of numerical simulations on the basis of a mathematical model previously developed. The model describes the steady state of a tumor cord surrounded by necrosis and its time evolution following cell killing. The most relevant aspects of the dynamics of extracellular fluid are by computing the longitudinal average of the radial fluid velocity and of the pressure field. In the present paper, the necrotic region is treated as a mixture of degrading dead cells and fluid.


  • This article has been cited by:

    1. Fujun Zhou, Shangbin Cui, Bifurcations for a multidimensional free boundary problem modeling the growth of tumor cord, 2009, 10, 14681218, 2990, 10.1016/j.nonrwa.2008.10.004
    2. Alessandro Bertuzzi, Antonio Fasano, Alberto Gandolfi, Carmela Sinisgalli, 2007, Chapter 13, 978-3-540-44445-9, 151, 10.1007/978-3-540-44446-6_13
    3. Antonio Fasano, Alessandro Bertuzzi, Carmela Sinisgalli, 2014, Chapter 2, 978-1-4939-0457-0, 27, 10.1007/978-1-4939-0458-7_2
    4. M. Scianna, C.G. Bell, L. Preziosi, A review of mathematical models for the formation of vascular networks, 2013, 333, 00225193, 174, 10.1016/j.jtbi.2013.04.037
    5. Andrea Tosin, Initial/boundary-value problems of tumor growth within a host tissue, 2013, 66, 0303-6812, 163, 10.1007/s00285-012-0505-1
    6. Alessandro Bertuzzi, Antonio Fasano, Alberto Gandolfi, Carmela Sinisgalli, 2008, Chapter 7, 978-0-8176-4712-4, 1, 10.1007/978-0-8176-4713-1_7
    7. A. Fasano, A. Bertuzzi, A. Gandolfi, 2006, Chapter 3, 978-88-470-0394-1, 71, 10.1007/88-470-0396-2_3
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  • © 2005 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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