Accurate numerical simulation of electrodiffusion and water movement in brain tissue
Mathematical modelling of ionic electrodiffusion and water movement is emerging as a powerful avenue of investigation to provide new physiological insight into brain homeostasis. However, in order to provide solid answers and resolve controversies, the accuracy of the predictions is essential. Ionic...
| Үндсэн зохиолчид: | , , , |
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| Формат: | Journal article |
| Хэл сонгох: | English |
| Хэвлэсэн: |
Institute of Mathematics and its Applications
2021
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| _version_ | 1826307787077976064 |
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| author | Ellingsrud, AJ Boullé, N Farrell, PE Rognes, ME |
| author_facet | Ellingsrud, AJ Boullé, N Farrell, PE Rognes, ME |
| author_sort | Ellingsrud, AJ |
| collection | OXFORD |
| description | Mathematical modelling of ionic electrodiffusion and water movement is emerging as a powerful avenue of investigation to provide new physiological insight into brain homeostasis. However, in order to provide solid answers and resolve controversies, the accuracy of the predictions is essential. Ionic electrodiffusion models typically comprise non-trivial systems of non-linear and highly coupled partial and ordinary differential equations that govern phenomena on disparate time scales. Here, we study numerical challenges related to approximating these systems. We consider a homogenized model for electrodiffusion and osmosis in brain tissue and present and evaluate different associated finite element-based splitting schemes in terms of their numerical properties, including accuracy, convergence, and computational efficiency for both idealized scenarios and for the physiologically relevant setting of cortical spreading depression
(CSD). We find that the schemes display optimal convergence rates in space for problems with smooth manufactured solutions. However, the physiological CSD setting is challenging: we find that the accurate
computation of CSD wave characteristics (wave speed and wave width) requires a very fine spatial and fine temporal resolution. |
| first_indexed | 2024-03-07T07:08:19Z |
| format | Journal article |
| id | oxford-uuid:c55ef2fc-7def-4111-a63c-a37f356bb29b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:08:19Z |
| publishDate | 2021 |
| publisher | Institute of Mathematics and its Applications |
| record_format | dspace |
| spelling | oxford-uuid:c55ef2fc-7def-4111-a63c-a37f356bb29b2022-05-23T09:21:57ZAccurate numerical simulation of electrodiffusion and water movement in brain tissueJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c55ef2fc-7def-4111-a63c-a37f356bb29bEnglishSymplectic ElementsInstitute of Mathematics and its Applications2021Ellingsrud, AJBoullé, NFarrell, PERognes, MEMathematical modelling of ionic electrodiffusion and water movement is emerging as a powerful avenue of investigation to provide new physiological insight into brain homeostasis. However, in order to provide solid answers and resolve controversies, the accuracy of the predictions is essential. Ionic electrodiffusion models typically comprise non-trivial systems of non-linear and highly coupled partial and ordinary differential equations that govern phenomena on disparate time scales. Here, we study numerical challenges related to approximating these systems. We consider a homogenized model for electrodiffusion and osmosis in brain tissue and present and evaluate different associated finite element-based splitting schemes in terms of their numerical properties, including accuracy, convergence, and computational efficiency for both idealized scenarios and for the physiologically relevant setting of cortical spreading depression (CSD). We find that the schemes display optimal convergence rates in space for problems with smooth manufactured solutions. However, the physiological CSD setting is challenging: we find that the accurate computation of CSD wave characteristics (wave speed and wave width) requires a very fine spatial and fine temporal resolution. |
| spellingShingle | Ellingsrud, AJ Boullé, N Farrell, PE Rognes, ME Accurate numerical simulation of electrodiffusion and water movement in brain tissue |
| title | Accurate numerical simulation of electrodiffusion and water movement in brain tissue |
| title_full | Accurate numerical simulation of electrodiffusion and water movement in brain tissue |
| title_fullStr | Accurate numerical simulation of electrodiffusion and water movement in brain tissue |
| title_full_unstemmed | Accurate numerical simulation of electrodiffusion and water movement in brain tissue |
| title_short | Accurate numerical simulation of electrodiffusion and water movement in brain tissue |
| title_sort | accurate numerical simulation of electrodiffusion and water movement in brain tissue |
| work_keys_str_mv | AT ellingsrudaj accuratenumericalsimulationofelectrodiffusionandwatermovementinbraintissue AT boullen accuratenumericalsimulationofelectrodiffusionandwatermovementinbraintissue AT farrellpe accuratenumericalsimulationofelectrodiffusionandwatermovementinbraintissue AT rognesme accuratenumericalsimulationofelectrodiffusionandwatermovementinbraintissue |