A data-motivated density-dependent diffusion model of in vitro glioblastoma growth
Glioblastoma multiforme is an aggressive brain cancer that is extremely fatal. It is characterized by both proliferation and large amounts of migration, which contributes to the difficulty of treatment. Previous models of this type of cancer growth often include two separate equations to model proli...
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| Format: | Article |
| Language: | English |
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AIMS Press
2015-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1157 |
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| author | Tracy L. Stepien Erica M. Rutter Yang Kuang |
| author_facet | Tracy L. Stepien Erica M. Rutter Yang Kuang |
| author_sort | Tracy L. Stepien |
| collection | DOAJ |
| description | Glioblastoma multiforme is an aggressive brain cancer that is extremely fatal. It is characterized by both proliferation and large amounts of migration, which contributes to the difficulty of treatment. Previous models of this type of cancer growth often include two separate equations to model proliferation or migration. We propose a single equation which uses density-dependent diffusion to capture the behavior of both proliferation and migration. We analyze the model to determine the existence of traveling wave solutions. To prove the viability of the density-dependent diffusion function chosen, we compare our model with well-known in vitro experimental data. |
| format | Article |
| id | doaj-art-5f57c4ba9a2341f8b43a0366edcbed7f |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-5f57c4ba9a2341f8b43a0366edcbed7f2025-01-24T02:33:57ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-07-011261157117210.3934/mbe.2015.12.1157A data-motivated density-dependent diffusion model of in vitro glioblastoma growthTracy L. Stepien0Erica M. Rutter1Yang Kuang2School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281Glioblastoma multiforme is an aggressive brain cancer that is extremely fatal. It is characterized by both proliferation and large amounts of migration, which contributes to the difficulty of treatment. Previous models of this type of cancer growth often include two separate equations to model proliferation or migration. We propose a single equation which uses density-dependent diffusion to capture the behavior of both proliferation and migration. We analyze the model to determine the existence of traveling wave solutions. To prove the viability of the density-dependent diffusion function chosen, we compare our model with well-known in vitro experimental data.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1157traveling wavesglioblastomabiomathematical modelingtumor growth simulation. |
| spellingShingle | Tracy L. Stepien Erica M. Rutter Yang Kuang A data-motivated density-dependent diffusion model of in vitro glioblastoma growth Mathematical Biosciences and Engineering traveling waves glioblastoma biomathematical modeling tumor growth simulation. |
| title | A data-motivated density-dependent diffusion model of in vitro glioblastoma growth |
| title_full | A data-motivated density-dependent diffusion model of in vitro glioblastoma growth |
| title_fullStr | A data-motivated density-dependent diffusion model of in vitro glioblastoma growth |
| title_full_unstemmed | A data-motivated density-dependent diffusion model of in vitro glioblastoma growth |
| title_short | A data-motivated density-dependent diffusion model of in vitro glioblastoma growth |
| title_sort | data motivated density dependent diffusion model of in vitro glioblastoma growth |
| topic | traveling waves glioblastoma biomathematical modeling tumor growth simulation. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1157 |
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