Oxygen transport and release of adenosine triphosphate in micro-channels and arterioles in the human microcirculation
- Published
- Accepted
- Subject Areas
- Biochemistry, Bioengineering, Biophysics, Biotechnology, Mathematical Biology
- Keywords
- Oxygen Transport, Finite Element, ATP, channel/tube flow, Partial Pressure of Oxygen, hemoglobin, Fahraeus Effect, Oxygen Solubility, Hill Equation, Hematocrit
- Copyright
- © 2014 Moschandreou
- Licence
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ PrePrints) and either DOI or URL of the article must be cited.
- Cite this article
- 2014. Oxygen transport and release of adenosine triphosphate in micro-channels and arterioles in the human microcirculation. PeerJ PrePrints 2:e443v2 https://doi.org/10.7287/peerj.preprints.443v2
Abstract
The governing nonlinear equations for oxygen transport and ATP concentration in a microfluidic channel and tube are solved in a novel way with the aid of Maple and COMSOL Multiphysics simulation software. Considering a model which assumes a larger plasma velocity near the wall of a channel/tube in comparison to RBC velocity near the centerline we obtain results showing clearly that there is a significant decrease in oxygen tension in the vicinity of an oxygen permeable membrane placed midway on the upper channel/tube wall and to the right side of it in the downstream field. The purpose of the membrane is to cause a rapid change in oxygen saturation as RBC’s flow through channel/tube. To the right of the membrane downstream the greatest amount of ATP is released. It is shown that for smaller arterioles there is an optimal size for which greater amounts of ATP can be released. Finally the corresponding time-dependent oxygen transport problem for plug flow in a channel, which has not been simulated in previous models in the literature, is analyzed and different starting times are shown for ATP release at different points in the channel. The FE modelling is very accurate: The time evolution problem is modelled and solved in it`s entirety with exact parameters used in the literature for blood flow and oxygen transport in the microcirculation. A comparison is made between the steady state and time dependent solutions in order to validate the results. The implications of the time dependent model for biological systems such as the human microcirculation requires exact information on release of energy as ATP is released from blood cells and the present work is important in providing this information. In particular, the time varying problem for ATP concentration and it’s temporal dynamics, as calculated in this paper is crucial in determining the ADP/ATP concentration pair which is an oscillating pair in the biochemical oscillations that occur in glycolysis in anaerobic yeast cultures.
Author Comment
We improved some parts of the manuscript as follows: (1) Equations 13 and 14, and Figure 4 have been changed. (2) In the Results and Discussion section, number 13145 Pa has been changed to 13345 Pa, and number 98.6 mmHg has been changed to 100 mmHg, at two occurrences in text. (3) In the Time Dependent Equation section, the last sentence has been omitted in the present version.
Supplemental Information
Fig 1
Geometry of mathematical model used for channel flow.
Fig 3-A
ATP concentration in micro-moles versus channel radius in microns(0-100 microns) near permeable membrane.
Fig 3-B
ATP concentration profiles in micro-moles versus channel radius in microns(0-100 microns) far downstream from permeable membrane in channel.
Fig 3-C
Partial pressure of oxygen in pascals versus channel radius in microns(0-100 microns) downstream from permeable membrane in channel.
Fig 5
Oxygen tension( in pascals) distribution in channel of 14700 microns versus 100 microns at time t=5e-5 seconds.
Fig 6
Oxygen tension( in pascals) distribution in channel of 14700 microns versus 100 microns at time t=0.02 seconds.
Fig 7
Oxygen tension( in pascals) distribution in channel of 14700 microns versus 100 microns at time t=0.04 seconds.
Fig 8
Oxygen tension( in pascals) distribution in channel of 14700 microns versus 100 microns at time t=0.07 seconds.
Fig 9
Partial pressure of oxygen in pascals versus tube radius(0-20 microns) near permeable membrane for Poiseuille flow in a tube of radius 20 microns and length 14700 microns.
Fig 10
ATP concentration in micro-moles versus tube radius(0-20 microns) near permeable membrane for Poiseuille flow in a tube of radius 20 microns and length 14700 microns.
Fig 11
Partial pressure of oxygen in pascals versus tube radius(0-20 microns) downstream from permeable membrane for Poiseuille flow in a tube of radius 20 microns and length 14700 microns.
Fig 12
Partial pressure of oxygen in pascals versus tube radius(0-100 microns) downstream from permeable membrane for Plug flow in a tube of radius 100 microns and length 14700 microns.
Fig 13
Partial pressure of oxygen in pascals versus tube radius(0-10 microns) near permeable membrane for Poiseuille flow in a tube of radius 10 microns and length 14700 microns.
Fig 14
Partial pressure of oxygen in pascals versus tube radius(0-10 microns) downstream from permeable membrane for Poiseuille flow in a tube of radius 10 microns and length 14700 microns.
