Oxygen consumption dynamics in steady-state tumour models
Oxygen levels in cancerous tissue can have a significant effect on treatment response: hypoxic tissue is both more radioresistant and more chemoresistant than well-oxygenated tissue. While recent advances in medical imaging have facilitated real-time observation of macroscopic oxygenation, the under...
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| Format: | Article |
| Language: | English |
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The Royal Society
2014-01-01
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| Series: | Royal Society Open Science |
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| Online Access: | https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.140080 |
| _version_ | 1818340743735934976 |
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| author | David Robert Grimes Alexander G. Fletcher Mike Partridge |
| author_facet | David Robert Grimes Alexander G. Fletcher Mike Partridge |
| author_sort | David Robert Grimes |
| collection | DOAJ |
| description | Oxygen levels in cancerous tissue can have a significant effect on treatment response: hypoxic tissue is both more radioresistant and more chemoresistant than well-oxygenated tissue. While recent advances in medical imaging have facilitated real-time observation of macroscopic oxygenation, the underlying physics limits the resolution to the millimetre domain, whereas oxygen tension varies over a micrometre scale. If the distribution of oxygen in the tumour micro-environment can be accurately estimated, then the effect of potential dose escalation to these hypoxic regions could be better modelled, allowing more realistic simulation of biologically adaptive treatments. Reaction–diffusion models are commonly used for modelling oxygen dynamics, with a variety of functional forms assumed for the dependence of oxygen consumption rate (OCR) on cellular status and local oxygen availability. In this work, we examine reaction–diffusion models of oxygen consumption in spherically and cylindrically symmetric geometries. We consider two different descriptions of oxygen consumption: one in which the rate of consumption is constant and one in which it varies with oxygen tension in a hyperbolic manner. In each case, we derive analytic approximations to the steady-state oxygen distribution, which are shown to closely match the numerical solutions of the equations and accurately predict the extent to which oxygen can diffuse. The derived expressions relate the limit to which oxygen can diffuse into a tissue to the OCR of that tissue. We also demonstrate that differences between these functional forms are likely to be negligible within the range of literature estimates of the hyperbolic oxygen constant, suggesting that the constant consumption rate approximation suffices for modelling oxygen dynamics for most values of OCR. These approximations also allow the rapid identification of situations where hyperbolic consumption forms can result in significant differences from constant consumption rate models, and so can reduce the computational workload associated with numerical solutions, by estimating both the oxygen diffusion distances and resultant oxygen profile. Such analysis may be useful for parameter fitting in large imaging datasets and histological sections, and allows easy quantification of projected differences between functional forms of OCR. |
| first_indexed | 2024-12-13T15:47:45Z |
| format | Article |
| id | doaj.art-526c0a2de5a2437dab9001a1d0ffe403 |
| institution | Directory Open Access Journal |
| issn | 2054-5703 |
| language | English |
| last_indexed | 2024-12-13T15:47:45Z |
| publishDate | 2014-01-01 |
| publisher | The Royal Society |
| record_format | Article |
| series | Royal Society Open Science |
| spelling | doaj.art-526c0a2de5a2437dab9001a1d0ffe4032022-12-21T23:39:38ZengThe Royal SocietyRoyal Society Open Science2054-57032014-01-011110.1098/rsos.140080140080Oxygen consumption dynamics in steady-state tumour modelsDavid Robert GrimesAlexander G. FletcherMike PartridgeOxygen levels in cancerous tissue can have a significant effect on treatment response: hypoxic tissue is both more radioresistant and more chemoresistant than well-oxygenated tissue. While recent advances in medical imaging have facilitated real-time observation of macroscopic oxygenation, the underlying physics limits the resolution to the millimetre domain, whereas oxygen tension varies over a micrometre scale. If the distribution of oxygen in the tumour micro-environment can be accurately estimated, then the effect of potential dose escalation to these hypoxic regions could be better modelled, allowing more realistic simulation of biologically adaptive treatments. Reaction–diffusion models are commonly used for modelling oxygen dynamics, with a variety of functional forms assumed for the dependence of oxygen consumption rate (OCR) on cellular status and local oxygen availability. In this work, we examine reaction–diffusion models of oxygen consumption in spherically and cylindrically symmetric geometries. We consider two different descriptions of oxygen consumption: one in which the rate of consumption is constant and one in which it varies with oxygen tension in a hyperbolic manner. In each case, we derive analytic approximations to the steady-state oxygen distribution, which are shown to closely match the numerical solutions of the equations and accurately predict the extent to which oxygen can diffuse. The derived expressions relate the limit to which oxygen can diffuse into a tissue to the OCR of that tissue. We also demonstrate that differences between these functional forms are likely to be negligible within the range of literature estimates of the hyperbolic oxygen constant, suggesting that the constant consumption rate approximation suffices for modelling oxygen dynamics for most values of OCR. These approximations also allow the rapid identification of situations where hyperbolic consumption forms can result in significant differences from constant consumption rate models, and so can reduce the computational workload associated with numerical solutions, by estimating both the oxygen diffusion distances and resultant oxygen profile. Such analysis may be useful for parameter fitting in large imaging datasets and histological sections, and allows easy quantification of projected differences between functional forms of OCR.https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.140080mathematical modellinghypoxiaoxygen |
| spellingShingle | David Robert Grimes Alexander G. Fletcher Mike Partridge Oxygen consumption dynamics in steady-state tumour models Royal Society Open Science mathematical modelling hypoxia oxygen |
| title | Oxygen consumption dynamics in steady-state tumour models |
| title_full | Oxygen consumption dynamics in steady-state tumour models |
| title_fullStr | Oxygen consumption dynamics in steady-state tumour models |
| title_full_unstemmed | Oxygen consumption dynamics in steady-state tumour models |
| title_short | Oxygen consumption dynamics in steady-state tumour models |
| title_sort | oxygen consumption dynamics in steady state tumour models |
| topic | mathematical modelling hypoxia oxygen |
| url | https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.140080 |
| work_keys_str_mv | AT davidrobertgrimes oxygenconsumptiondynamicsinsteadystatetumourmodels AT alexandergfletcher oxygenconsumptiondynamicsinsteadystatetumourmodels AT mikepartridge oxygenconsumptiondynamicsinsteadystatetumourmodels |