Mathematical Biosciences and Engineering, 2011, 8(2): 239-252. doi: 10.3934/mbe.2011.8.239.

Primary: 92C50; Secondary: 92C17, 76D27, 35R35.

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Investigating the steady state of multicellular spheroids by revisiting the two-fluid model

1. Dipartimento di Matematica "U. Dini", Università di Firenze, Viale Morgagni 67/A, 50134 Firenze
2. Dipartimento di Matematica "U. Dini", Universita' di Firenze, Viale Morgagni 67/A, 50134 Firenze
3. Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti" - CNR, Viale Manzoni 30, 00185 Roma

In this paper we examine the steady state of tumour spheroids considering a structure in which the central necrotic region contains an inner liquid core surrounded by dead cells that keep some mechanical integrity. This partition is a consequence of assuming that a finite delay is required for the degradation of dead cells into liquid. The phenomenological assumption of constant local volume fraction of cells is also made. The above structure is coupled with a simple mechanical model that views the cell component as a viscous fluid and the extracellular liquid as an inviscid fluid. By imposing the continuity of the normal stress throughout the whole spheroid, we show that a steady state can exist only if the forces on cells at the outer boundary (provided e.g. by a surface tension) are intense enough, and in such a case we can compute the stationary radius. By giving reasonable values to the parameters, the model predicts that the stationary radius decreases with the external oxygen concentration, as expected from experimental observations.
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Keywords Cancer modelling; flow of fluid mixtures; avascular tumours; free boundary problems.

Citation: Antonio Fasano, Marco Gabrielli, Alberto Gandolfi. Investigating the steady state of multicellular spheroids by revisiting the two-fluid model. Mathematical Biosciences and Engineering, 2011, 8(2): 239-252. doi: 10.3934/mbe.2011.8.239

 

This article has been cited by

  • 1. ALESSANDRO BERTUZZI, ANTONIO FASANO, ALBERTO GANDOLFI, CARMELA SINISGALLI, MODELING THE EVOLUTION OF A TUMORAL MULTICELLULAR SPHEROID AS A TWO-FLUID BINGHAM-LIKE SYSTEM, Mathematical Models and Methods in Applied Sciences, 2013, 23, 14, 2561, 10.1142/S0218202513500401
  • 2. Alberto Gandolfi, Marco Gabrielli, Antonio Fasano, Erratum to: Investigating the steady state of multicellular sheroids by revisiting the two-fluid model, Mathematical Biosciences and Engineering, 2012, 9, 3, 697, 10.3934/mbe.2012.9.697
  • 3. Antonio Fasano, Alberto Gandolfi, , Mathematical Methods and Models in Biomedicine, 2013, Chapter 7, 179, 10.1007/978-1-4614-4178-6_7
  • 4. Antonio Fasano, Alessandro Bertuzzi, Carmela Sinisgalli, , Mathematical Oncology 2013, 2014, Chapter 2, 27, 10.1007/978-1-4939-0458-7_2

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