Mathematical modelling of tissue-engineering angiogenesis
We present a mathematical model for the vascularisation of a porous scaffold following implantation in vivo. The model is given as a set of coupled non-linear ordinary differential equations (ODEs) which describe the evolution in time of the amounts of the different tissue constituents inside the sc...
| Auteurs principaux: | , , , , , , |
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| Format: | Journal article |
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2009
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| _version_ | 1826307054201995264 |
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| author | Lemon, G Howard, D Tomlinson, M Buttery, L Rose, F Waters, S King, J |
| author_facet | Lemon, G Howard, D Tomlinson, M Buttery, L Rose, F Waters, S King, J |
| author_sort | Lemon, G |
| collection | OXFORD |
| description | We present a mathematical model for the vascularisation of a porous scaffold following implantation in vivo. The model is given as a set of coupled non-linear ordinary differential equations (ODEs) which describe the evolution in time of the amounts of the different tissue constituents inside the scaffold. Bifurcation analyses reveal how the extent of scaffold vascularisation changes as a function of the parameter values. For example, it is shown how the loss of seeded cells arising from slow infiltration of vascular tissue can be overcome using a prevascularisation strategy consisting of seeding the scaffold with vascular cells. Using certain assumptions it is shown how the system can be simplified to one which is partially tractable and for which some analysis is given. Limited comparison is also given of the model solutions with experimental data from the chick chorioallantoic membrane (CAM) assay. |
| first_indexed | 2024-03-07T06:57:14Z |
| format | Journal article |
| id | oxford-uuid:fe88c2e1-a567-4da6-b9c4-a0ff33d7f54c |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:57:14Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:fe88c2e1-a567-4da6-b9c4-a0ff33d7f54c2022-03-27T13:37:26ZMathematical modelling of tissue-engineering angiogenesisJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fe88c2e1-a567-4da6-b9c4-a0ff33d7f54cMathematical Institute - ePrints2009Lemon, GHoward, DTomlinson, MButtery, LRose, FWaters, SKing, JWe present a mathematical model for the vascularisation of a porous scaffold following implantation in vivo. The model is given as a set of coupled non-linear ordinary differential equations (ODEs) which describe the evolution in time of the amounts of the different tissue constituents inside the scaffold. Bifurcation analyses reveal how the extent of scaffold vascularisation changes as a function of the parameter values. For example, it is shown how the loss of seeded cells arising from slow infiltration of vascular tissue can be overcome using a prevascularisation strategy consisting of seeding the scaffold with vascular cells. Using certain assumptions it is shown how the system can be simplified to one which is partially tractable and for which some analysis is given. Limited comparison is also given of the model solutions with experimental data from the chick chorioallantoic membrane (CAM) assay. |
| spellingShingle | Lemon, G Howard, D Tomlinson, M Buttery, L Rose, F Waters, S King, J Mathematical modelling of tissue-engineering angiogenesis |
| title | Mathematical modelling of tissue-engineering angiogenesis |
| title_full | Mathematical modelling of tissue-engineering angiogenesis |
| title_fullStr | Mathematical modelling of tissue-engineering angiogenesis |
| title_full_unstemmed | Mathematical modelling of tissue-engineering angiogenesis |
| title_short | Mathematical modelling of tissue-engineering angiogenesis |
| title_sort | mathematical modelling of tissue engineering angiogenesis |
| work_keys_str_mv | AT lemong mathematicalmodellingoftissueengineeringangiogenesis AT howardd mathematicalmodellingoftissueengineeringangiogenesis AT tomlinsonm mathematicalmodellingoftissueengineeringangiogenesis AT butteryl mathematicalmodellingoftissueengineeringangiogenesis AT rosef mathematicalmodellingoftissueengineeringangiogenesis AT waterss mathematicalmodellingoftissueengineeringangiogenesis AT kingj mathematicalmodellingoftissueengineeringangiogenesis |