On the analysis of oxygen diffusion and reaction in biological systems |
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| Affiliation: | 1. Centre for Healthcare Science and Technology, Indian Institute of Engineering Science and Technology Shibpur, Howrah 711103, West Bengal, India;2. Engineering Science and Mechanics Department, Penn State University, University Park, PA 16802, USA;3. The Huck Institutes of the Life Sciences, Penn State University, University Park, PA 16802, USA;4. Biomedical Engineering Department, Penn State University, University Park, PA 16802, USA;5. Materials Research Institute, Penn State University, University Park, PA 16802, USA;1. Department of Genetics, Nicolaus Copernicus University in Toruń, 87–100 Toruń, Poland;2. Centre for Modern Interdisciplinary Technologies, Nicolaus Copernicus University in Toruń, 87–100 Toruń, Poland;3. Department of Plant Physiology, Genetics and Biotechnology, University of Warmia and Mazury, 10–719 Olsztyn, Poland;4. Department of Analytical Chemistry and Applied Spectroscopy, Nicolaus Copernicus University in Toruń, 87–100 Toruń, Poland;5. Department of Agricultural Biotechnology, Bydgoszcz University of Science and Technology, 85–796 Bydgoszcz, Poland;1. Systems Biology of Development Group, Friedrich Miescher Laboratory of the Max Planck Society, 72076, Tübingen, Germany;2. Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, 02143, USA;3. European Molecular Biology Laboratory, Barcelona Outstation, 08003 Barcelona, Spain;4. Modeling Tumorigenesis Group, Translational Oncology Division, Eberhard Karls University Tübingen, 72076, Tübingen, Germany |
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| Abstract: | An analysis of oxygen diffusion and reaction in multiregion biological systems is presented. This analysis considers a time-dependent flux boundary condition and oxygen consumption governed by Michaelis-Menten kinetics. The mathematical problem is developed in a uniform fashion, so as to include both the single cell and anisotropic systems with distinct regions which are characteristic of either a multicell spheroid or a tumor mass. Both transient and steady-state solutions are obtained, based on orthogonal collocation. Literature results on single-cell analysis are corroborated, and detailed transient solutions are presented for the oxygenation of a multicell spheroid, and for systemic oxygenation of both small and large tumors. |
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