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New mathematical models of inert gas transport through biological tissue in hyperbaric environments
The thesis is concerned with a fundamental mathematical analysis of inert gas transport through biological tissue at a raised ambient partial pressure. Three basic time-scales of transport in tissue are defined and their relationship examined and compared with existing models, which e.re shown to be...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613142729621504 |
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| access_status_str | Open Access |
| author | Hennessy, Thomas Richard |
| author2 | Brundrit, Geoff |
| author_browse | Brundrit, Geoff Hennessy, Thomas Richard |
| author_facet | Brundrit, Geoff Hennessy, Thomas Richard |
| author_sort | Hennessy, Thomas Richard |
| collection | Thesis |
| description | The thesis is concerned with a fundamental mathematical analysis of inert gas transport through biological tissue at a raised ambient partial pressure. Three basic time-scales of transport in tissue are defined and their relationship examined and compared with existing models, which e.re shown to be usually inadequate in one or more ways. As a result three new mathematical models are proposed and solved both asymptotically and numerically. The first is applied to experimental data for non-perfused tissue which yields an improved value of the intracellular diffusion coefficient for nitrogen. An expression is also derived which should be useful in evaluating this constant and the volume fraction of extracellular fluid. The second embraces a number of current models and is applicable to perfused tissue. It should be useful in interpreting inert gas uptake curves. The model is applied to experimental data, and a source of possible error is discovered in using experimental non-asymptotic time constants. The third is a model which claims to resolve the controversy between the diffusion and perfusion theories of gas transport in tissue. The result is that in the large, diffusion is more important than perfusion, except in muscle tissue where they interact. Three different methods of numerical inversion of the Laplace Transform are compared and one is shown to be the most useful for solving gas uptake problems. The main result of the thesis is a contribution to the establishment of a mathematical basis for gas transport in various situations in the biological sphere. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/17678 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:26.417Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/17678 New mathematical models of inert gas transport through biological tissue in hyperbaric environments Hennessy, Thomas Richard Brundrit, Geoff Van Zyl, J J W Mathematics The thesis is concerned with a fundamental mathematical analysis of inert gas transport through biological tissue at a raised ambient partial pressure. Three basic time-scales of transport in tissue are defined and their relationship examined and compared with existing models, which e.re shown to be usually inadequate in one or more ways. As a result three new mathematical models are proposed and solved both asymptotically and numerically. The first is applied to experimental data for non-perfused tissue which yields an improved value of the intracellular diffusion coefficient for nitrogen. An expression is also derived which should be useful in evaluating this constant and the volume fraction of extracellular fluid. The second embraces a number of current models and is applicable to perfused tissue. It should be useful in interpreting inert gas uptake curves. The model is applied to experimental data, and a source of possible error is discovered in using experimental non-asymptotic time constants. The third is a model which claims to resolve the controversy between the diffusion and perfusion theories of gas transport in tissue. The result is that in the large, diffusion is more important than perfusion, except in muscle tissue where they interact. Three different methods of numerical inversion of the Laplace Transform are compared and one is shown to be the most useful for solving gas uptake problems. The main result of the thesis is a contribution to the establishment of a mathematical basis for gas transport in various situations in the biological sphere. 2016-03-14T07:03:52Z 2016-03-14T07:03:52Z 1973 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/17678 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Hennessy, Thomas Richard New mathematical models of inert gas transport through biological tissue in hyperbaric environments |
| thesis_degree_str | Doctoral |
| title | New mathematical models of inert gas transport through biological tissue in hyperbaric environments |
| title_full | New mathematical models of inert gas transport through biological tissue in hyperbaric environments |
| title_fullStr | New mathematical models of inert gas transport through biological tissue in hyperbaric environments |
| title_full_unstemmed | New mathematical models of inert gas transport through biological tissue in hyperbaric environments |
| title_short | New mathematical models of inert gas transport through biological tissue in hyperbaric environments |
| title_sort | new mathematical models of inert gas transport through biological tissue in hyperbaric environments |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/17678 |
| work_keys_str_mv | AT hennessythomasrichard newmathematicalmodelsofinertgastransportthroughbiologicaltissueinhyperbaricenvironments |