A finite element method for growth in biological development
We describe finite element simulations of limb growth based on Stokes flow models witha nonzero divergence representing growth due to nutrients in the early stages of limb bud development.We introduce a ''tissue pressure'' whose spatial derivatives yield the growth velocity in th...
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| Format: | Article |
| Language: | English |
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AIMS Press
2007-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.339 |
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| author | Cornel M. Murea H. G. E. Hentschel |
| author_facet | Cornel M. Murea H. G. E. Hentschel |
| author_sort | Cornel M. Murea |
| collection | DOAJ |
| description | We describe finite element simulations of limb growth based on Stokes flow models witha nonzero divergence representing growth due to nutrients in the early stages of limb bud development.We introduce a ''tissue pressure'' whose spatial derivatives yield the growth velocity in the limband our explicit time advancing algorithm for such tissue flows is described in detail.The limb boundary is approached by spline functions to compute the curvature andthe unit outward normal vector. At each time step, a mixed-hybrid finite element problem is solved,where the condition that the velocity is strictly normal to the limb boundary is treatedby a Lagrange multiplier technique. Numerical results are presented. |
| format | Article |
| id | doaj-art-3118585cf9c34cbfa43b9ea72e461a9e |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-3118585cf9c34cbfa43b9ea72e461a9e2025-01-24T01:53:27ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-01-014233935310.3934/mbe.2007.4.339A finite element method for growth in biological developmentCornel M. Murea0H. G. E. Hentschel1Laboratoire de Mathématiques, Informatique et Applications, Université de Haute-Alsace, 4, rue des Frères Lumière, 68093 MULHOUSE CedexLaboratoire de Mathématiques, Informatique et Applications, Université de Haute-Alsace, 4, rue des Frères Lumière, 68093 MULHOUSE CedexWe describe finite element simulations of limb growth based on Stokes flow models witha nonzero divergence representing growth due to nutrients in the early stages of limb bud development.We introduce a ''tissue pressure'' whose spatial derivatives yield the growth velocity in the limband our explicit time advancing algorithm for such tissue flows is described in detail.The limb boundary is approached by spline functions to compute the curvature andthe unit outward normal vector. At each time step, a mixed-hybrid finite element problem is solved,where the condition that the velocity is strictly normal to the limb boundary is treatedby a Lagrange multiplier technique. Numerical results are presented.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.339finite element algorithms.stokes flow with surface tensionbiological development |
| spellingShingle | Cornel M. Murea H. G. E. Hentschel A finite element method for growth in biological development Mathematical Biosciences and Engineering finite element algorithms. stokes flow with surface tension biological development |
| title | A finite element method for growth in biological development |
| title_full | A finite element method for growth in biological development |
| title_fullStr | A finite element method for growth in biological development |
| title_full_unstemmed | A finite element method for growth in biological development |
| title_short | A finite element method for growth in biological development |
| title_sort | finite element method for growth in biological development |
| topic | finite element algorithms. stokes flow with surface tension biological development |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.339 |
| work_keys_str_mv | AT cornelmmurea afiniteelementmethodforgrowthinbiologicaldevelopment AT hgehentschel afiniteelementmethodforgrowthinbiologicaldevelopment AT cornelmmurea finiteelementmethodforgrowthinbiologicaldevelopment AT hgehentschel finiteelementmethodforgrowthinbiologicaldevelopment |