Investigating the steady state of multicellular spheroids by revisiting the two-fluid model
In this paper we examine the steady state of tumour spheroids consideringa structure in which the central necrotic region contains an inner liquidcore surrounded by dead cells that keep some mechanical integrity.This partition is a consequence of assuming that a finite delayis required for the degra...
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AIMS Press
2011-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.239 |
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| author | Antonio Fasano Marco Gabrielli Alberto Gandolfi |
| author_facet | Antonio Fasano Marco Gabrielli Alberto Gandolfi |
| author_sort | Antonio Fasano |
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| description | In this paper we examine the steady state of tumour spheroids consideringa structure in which the central necrotic region contains an inner liquidcore surrounded by dead cells that keep some mechanical integrity.This partition is a consequence of assuming that a finite delayis required for the degradation of dead cells into liquid.The phenomenological assumption of constant local volume fraction ofcells is also made. The above structure iscoupled with a simple mechanical model that views the cell component as aviscous fluid and the extracellular liquid as an inviscid fluid. By imposingthe continuity of the normal stress throughout the whole spheroid, we showthat a steady state can exist only if the forces on cells at the outerboundary (provided e.g. by a surface tension) are intense enough, and in sucha case we can compute the stationary radius. By giving reasonable values tothe parameters, the model predicts that the stationary radius decreases withthe external oxygen concentration, as expected from experimental observations. |
| format | Article |
| id | doaj-art-990d7bbd200142bdaa2b29127d1bcc54 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-990d7bbd200142bdaa2b29127d1bcc542025-01-24T02:01:39ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-03-018223925210.3934/mbe.2011.8.239Investigating the steady state of multicellular spheroids by revisiting the two-fluid modelAntonio Fasano0Marco Gabrielli1Alberto Gandolfi2Dipartimento di Matematica "U. Dini", Università di Firenze, Viale Morgagni 67/A, 50134 FirenzeDipartimento di Matematica "U. Dini", Università di Firenze, Viale Morgagni 67/A, 50134 FirenzeDipartimento di Matematica "U. Dini", Università di Firenze, Viale Morgagni 67/A, 50134 FirenzeIn this paper we examine the steady state of tumour spheroids consideringa structure in which the central necrotic region contains an inner liquidcore surrounded by dead cells that keep some mechanical integrity.This partition is a consequence of assuming that a finite delayis required for the degradation of dead cells into liquid.The phenomenological assumption of constant local volume fraction ofcells is also made. The above structure iscoupled with a simple mechanical model that views the cell component as aviscous fluid and the extracellular liquid as an inviscid fluid. By imposingthe continuity of the normal stress throughout the whole spheroid, we showthat a steady state can exist only if the forces on cells at the outerboundary (provided e.g. by a surface tension) are intense enough, and in sucha case we can compute the stationary radius. By giving reasonable values tothe parameters, the model predicts that the stationary radius decreases withthe external oxygen concentration, as expected from experimental observations.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.239cancer modellingflow of fluid mixturesavascular tumoursfree boundary problems. |
| spellingShingle | Antonio Fasano Marco Gabrielli Alberto Gandolfi Investigating the steady state of multicellular spheroids by revisiting the two-fluid model Mathematical Biosciences and Engineering cancer modelling flow of fluid mixtures avascular tumours free boundary problems. |
| title | Investigating the steady state of multicellular spheroids by revisiting the two-fluid model |
| title_full | Investigating the steady state of multicellular spheroids by revisiting the two-fluid model |
| title_fullStr | Investigating the steady state of multicellular spheroids by revisiting the two-fluid model |
| title_full_unstemmed | Investigating the steady state of multicellular spheroids by revisiting the two-fluid model |
| title_short | Investigating the steady state of multicellular spheroids by revisiting the two-fluid model |
| title_sort | investigating the steady state of multicellular spheroids by revisiting the two fluid model |
| topic | cancer modelling flow of fluid mixtures avascular tumours free boundary problems. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.239 |
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