Mathematical modelling of oxygen transport to tissue.
The equations governing oxygen transport from blood to tissue are presented for a cylindrical tissue compartment, with blood flowing along a co-axial cylindrical capillary inside the tissue. These governing equations take account of: (i) the non-linear reactions between oxygen and haemoglobin in blo...
| Main Authors: | , , |
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| Formato: | Journal article |
| Idioma: | English |
| Publicado em: |
2002
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| _version_ | 1826280547016507392 |
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| author | Whiteley, J Gavaghan, D Hahn, C |
| author_facet | Whiteley, J Gavaghan, D Hahn, C |
| author_sort | Whiteley, J |
| collection | OXFORD |
| description | The equations governing oxygen transport from blood to tissue are presented for a cylindrical tissue compartment, with blood flowing along a co-axial cylindrical capillary inside the tissue. These governing equations take account of: (i) the non-linear reactions between oxygen and haemoglobin in blood and between oxygen and myoglobin in tissue; (ii) diffusion of oxygen in both the axial and radial directions; and (iii) convection of haemoglobin and plasma in the capillary. A non-dimensional analysis is carried out to assess some assumptions made in previous studies. It is predicted that: (i) there is a boundary layer for oxygen partial pressure but not for haemoglobin or myoglobin oxygen saturation close to the inflow boundary in the capillary; (ii) axial diffusion may not be neglected everywhere in the model; (iii) the reaction between oxygen and both haemoglobin and myoglobin may be assumed to be instantaneous in nearly all cases; and (iv) the effect of myoglobin is only significant for tissue with a low oxygen partial pressure. These predictions are validated by solving the full equations numerically and are then interpreted physically. |
| first_indexed | 2024-03-07T00:15:19Z |
| format | Journal article |
| id | oxford-uuid:7aa3a9df-57d8-49a8-a76b-9be45b411415 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:15:19Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | oxford-uuid:7aa3a9df-57d8-49a8-a76b-9be45b4114152022-03-26T20:45:20ZMathematical modelling of oxygen transport to tissue.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7aa3a9df-57d8-49a8-a76b-9be45b411415EnglishSymplectic Elements at Oxford2002Whiteley, JGavaghan, DHahn, CThe equations governing oxygen transport from blood to tissue are presented for a cylindrical tissue compartment, with blood flowing along a co-axial cylindrical capillary inside the tissue. These governing equations take account of: (i) the non-linear reactions between oxygen and haemoglobin in blood and between oxygen and myoglobin in tissue; (ii) diffusion of oxygen in both the axial and radial directions; and (iii) convection of haemoglobin and plasma in the capillary. A non-dimensional analysis is carried out to assess some assumptions made in previous studies. It is predicted that: (i) there is a boundary layer for oxygen partial pressure but not for haemoglobin or myoglobin oxygen saturation close to the inflow boundary in the capillary; (ii) axial diffusion may not be neglected everywhere in the model; (iii) the reaction between oxygen and both haemoglobin and myoglobin may be assumed to be instantaneous in nearly all cases; and (iv) the effect of myoglobin is only significant for tissue with a low oxygen partial pressure. These predictions are validated by solving the full equations numerically and are then interpreted physically. |
| spellingShingle | Whiteley, J Gavaghan, D Hahn, C Mathematical modelling of oxygen transport to tissue. |
| title | Mathematical modelling of oxygen transport to tissue. |
| title_full | Mathematical modelling of oxygen transport to tissue. |
| title_fullStr | Mathematical modelling of oxygen transport to tissue. |
| title_full_unstemmed | Mathematical modelling of oxygen transport to tissue. |
| title_short | Mathematical modelling of oxygen transport to tissue. |
| title_sort | mathematical modelling of oxygen transport to tissue |
| work_keys_str_mv | AT whiteleyj mathematicalmodellingofoxygentransporttotissue AT gavaghand mathematicalmodellingofoxygentransporttotissue AT hahnc mathematicalmodellingofoxygentransporttotissue |