The One-Dimensional (1D) Numerical Model: An Application to Oxygen Diffusion in Mitochondria Cell
DOI:
https://doi.org/10.21512/comtech.v14i2.9705Keywords:
mitochondria cell, One-Dimensional (1D) numerical model, oxygen diffusionAbstract
The first model of oxygen transport was formulated by August Krogh. However, the investigations conducted have yet to yield a complete analytical model and a widely applicable solution for One-Dimensional (1D) network construction. The research sought to provide numerical and analytical solutions for the oxygen transfer model in mitochondrial cells to enable researchers to estimate the molecular dynamics and diffusion characteristics in mitochondrial cells. The oxygen diffusion process in mitochondria was modeled with ID numerical models. The numerical models used to solve the equations were explicit and implicit. The explicit model consisted of Forward Time Center Space (FTCS) and DuFort-Frankel. Meanwhile, the implicit model had Crank-Nicholson and Laasonen. The numerical solutions of the explicit and implicit were divided into four scenarios with a variation of Δt and compared with the analytical solutions. The results show that the Laasonen method is the best in describing the diffusion process. The best scenario with the lowest slope value and small Root Mean Square Error (RMSE) value is scenario 2 (Δt = 3,33E-4 s and Δx = 2,00E-5 cm). The numerical model and analytical solution show that the time required to reach a steady state is 0,7 s. It indicates oxygen exchange in two sides of the mitochondrial cell after 0,7 s.
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References
Al Mamun, A., Ali, M. S., & Miah, M. M. (2018). A study on an analytic solution 1D heat equation of a parabolic partial differential equation and implement in computer programming. International Journal of Scientific & Engineering Research, 9(9), 913–921.
Bailey, D. F. (1977). Review of elementary differential equations and boundary value problems; Differential equations and their applications, an introduction to applied mathematics, by W. E. Boyce, R. C. DiPrima, & M. Braun. The American Mathematical Monthly, 84(8), 664–665. https://doi.org/10.2307/2321040
Berry, F. S., & Berry, W. D. (2018). Innovation and diffusion models in policy research. In Theories of the policy process. Routledge. https://doi.org/10.4324/9780429494284-8
Damsgaard, C., Lauridsen, H., Harter, T. S., Kwan, G. T., Thomsen, J. S., Funder, A. M., ... & Brauner, C. J. (2020). A novel acidification mechanism for greatly enhanced oxygen supply to the fish retina. eLife, 9, 1–20. https://doi.org/10.7554/ELIFE.58995
Fathollahipour, S., Patil, P. S., & Leipzig, N. D. (2019). Oxygen regulation in development: Lessons from embryogenesis towards tissue engineering. Cells Tissues Organs, 205 (5–6), 350–371. https://doi.org/10.1159/000493162
Figueiredo, L., Pace, R., D’Arros, C., Réthoré, G., Guicheux, J., Le Visage, C., & Weiss, P. (2018). Assessing glucose and oxygen diffusion in hydrogels for the rational design of 3D stem cell scaffolds in regenerative medicine. Journal of Tissue Engineering and Regenerative Medicine, 12(5). https://doi.org/10.1002/term.2656
Joyce, W., & Wang, T. (2021). How cardiac output is regulated: August Krogh’s proto-Guytonian understanding of the importance of venous return. Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology, 253. https://doi.org/10.1016/j.cbpa.2020.110861
Juttukonda, M. R., Donahue, M. J., Waddle, S. L., Davis, L. T., Lee, C. A., Patel, N. J., ... & Jordan, L. C. (2021). Reduced oxygen extraction efficiency in sickle cell anemia patients with evidence of cerebral capillary shunting. Journal of Cerebral Blood Flow & Metabolism, 41(3), 546–560. https://doi.org/10.1177/0271678X20913123
Koeppen, B. M., & Stanton, B. A. (2023). Berne and Levy physiology e-book. Elsevier Health Sciences.
Lanning, K. M., Erkinaro, T. M., Ohtonen, P. P., Vakkala, M. A., Liisanantti, J. H., Ylikauma, L. A., & Kaakinen, T. I. (2022).
Accuracy, precision, and trending ability of perioperative central venous oxygen saturation compared to mixed venous oxygen saturation in unselected cardiac surgical patients. Journal of Cardiothoracic and Vascular Anesthesia, 36(7), 1995–2001. https://doi.org/10.1053/j.jvca.2021.08.103
Murphy, S. V., De Coppi, P., & Atala, A. (2020). Opportunities and challenges of translational 3D bioprinting. Nature Biomedical Engineering, 4, 370–380. https://doi.org/10.1038/s41551-019-0471-7
Pias, S. C. (2021). How does oxygen diffuse from capillaries to tissue mitochondria? Barriers and pathways. The Journal of Physiology, 599(6), 1769–1782. https://doi.org/10.1113/JP278815
Poole, D. C. (2019). Edward F. Adolph Distinguished Lecture. Contemporary model of muscle microcirculation: Gateway to function and dysfunction. Journal of Applied Physiology, 127(4). 1012–1033. https://doi.org/10.1152/japplphysiol.00013.2019
Poole, D. C., Pittman, R. N., Musch, T. I., & Østergaard, L. (2020). August Krogh’s theory of muscle microvascular control and oxygen delivery: A paradigm shift based on new data. The Journal of Physiology 598(20), 4473–4507. https://doi.org/10.1113/JP279223
Popel, A. S., Goldman, D., & Vadapalli, A. (2003). Modeling of oxygen diffusion from the blood vessels to intracellular organelles. In Oxygen transport to tissue XXIV. Advances in experimental medicine and biology. Springer. https://doi.org/10.1007/978-1-4615-0075-9_46
Saha, B. K., & Chong, W. H. (2021). Diffuse Alveolar Hemorrhage in cardiac diseases. Lung, 199, 103–112. https://doi.org/10.1007/s00408-021-00433-x
Salazar-Noratto, G. E., Luo, G., Denoeud, C., Padrona, M., Moya, A., Bensidhoum, M., ... & Petite, H. (2020). Understanding and leveraging cell metabolism to enhance mesenchymal stem cell transplantation survival in tissue engineering and regenerative medicine applications. Stem Cells, 38(1), 22–33. https://doi.org/10.1002/stem.3079
Shapira, S. N., & Christofk, H. R. (2020). Metabolic regulation of tissue stem cells. Trends in Cell Biology, 30(7), 566–576. https://doi.org/10.1016/j.tcb.2020.04.004
Sikkema, L., Strobl, D. C., Zappia, L., Madissoon, E., Markov, N. S., Zaragosi, L. E., ... & Theis, F. J. (2022). An integrated cell atlas of the human lung in health and disease. bioRxiv.
Vázquez, J. L. (2017). The mathematical theories of diffusion: Nonlinear and fractional diffusion. In M. Bonforte & G. Grillo (Eds.), Nonlocal and nonlinear diffusions and interactions: New methods and directions. Springer. https://doi.org/10.1007/978-3-319-61494-6_5
Wan, X., Liu, Z., & Li, L. (2021). Manipulation of stem cells fates: The master and multifaceted roles of biophysical cues of biomaterials. Advanced Functional Materials, 31(23). https://doi.org/10.1002/adfm.202010626
Wei, P., Dove, K. K., Bensard, C., Schell, J. C., & Rutter, J. (2018). The force is strong with this one: Metabolism (over)powers stem cell fate. Trends in Cell Biology, 28(7), 551–559. https://doi.org/10.1016/j.tcb.2018.02.007
Zhao, W., Cheng, Y., Pan, Z., Wang, K., & Liu, S. (2019). Gas diffusion in coal particles: A review of mathematical models and their applications. Fuel, 252(September), 77–100. https://doi.org/10.1016/j.fuel.2019.04.065
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