Mathematical Study of the Pulmonary Gas Exchange for the Respiratory System under Normal and Abnormal Conditions

Nirali Patel; Kaushal Patel

doi:10.17485/IJST/v16iSP4.ICAMS10

Article

Mathematical Study of the Pulmonary Gas Exchange for the Respiratory System under Normal and Abnormal Conditions

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16iSP4.ICAMS10

Year: 2023, Volume: 16, Issue: Special Issue 4, Pages: 1-7

Original Article

Mathematical Study of the Pulmonary Gas Exchange for the Respiratory System under Normal and Abnormal Conditions

Nirali Patel^1*, Kaushal Patel²

¹Department of Mathematics, Veer Narmad South Gujarat University, Surat, Gujarat, India
²Associate Professor, Department of Mathematics, Veer Narmad South Gujarat University, Surat, Gujarat, India

*Corresponding Author
Email: [email protected]

Received Date:12 October 2023, Accepted Date:22 November 2023, Published Date:25 December 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: To find the relationship of the concentration of Oxygen and Carbon dioxide in the respiratory system. Our objective is to establish the relationship between partial pressure and saturation of oxygen. Also, to evaluate the Oxygen diffusion capacity into the capillary at different levels of hemoglobin. Methods: We follow the classical equations solved using analytic and numerical techniques for evaluating the diffusion capacity of oxygen from the alveolus to the pulmonary capillary by MATLAB software simulation. Findings: Establish the relationship between partial pressure and saturation of oxygen at various situations. Evaluate the diffusion capacity behaviour of the Oxygen into the capillary by different levels of hemoglobin. Novelty: This study presents a parametric model of the concentration of Oxygen and Carbon dioxide in the respiratory system that incorporates partial pressure and saturation relation concerning the exchange of gases. We also solved the classical relationship numerically.

Keywords: Oxygen concentration, Gas exchange, Partial Pressure, Saturation of gases, Mathematical model and simulation

References

Raffe MR. Respiratory gas transport. In: The Veterinary ICU Book. (pp. 15-23) CRC Press. 2020.
Stickland MK, Tedjasaputra V, Seaman C, Fuhr DP, Collins SÉ, Wagner H, et al. Intra‐pulmonary arteriovenous anastomoses and pulmonary gas exchange: evaluation by microspheres, contrast echocardiography and inert gas elimination. The Journal of Physiology. 2019;597(22):5365–5384. Available from: https://physoc.onlinelibrary.wiley.com/doi/epdf/10.1113/JP277695
Semchyk T, Korniush I, Hovorukha V, Tashyrev O. The study of the gas exchange function of lungs via the mathematical model of the functional respiratory system. Ecological Engineering and Environment Protection. 2021;3:17–23. Available from: https://ecoleng.org/archive/2021/3/17-23.pdf
Sapoval B, Kang M, Dinh‐xuan AT, Kang M, Dinh‐xuan AT. Modeling of Gas Exchange in the Lungs. Comprehensive Physiology. 2021;11(1):1289–1314. Available from: https://doi.org/10.1002/cphy.c190019
Si XA, Xi J. Pulmonary Oxygen Exchange in a Rhythmically Expanding–Contracting Alveolus–Capillary Model. Journal of Respiration. 2022;2(4):159–173. Available from: https://doi.org/10.3390/jor2040015
Hung A, Koch S, Bougault V, Gee CM, Bertuzzi R, Elmore M, et al. Personal strategies to mitigate the effects of air pollution exposure during sport and exercise: a narrative review and position statement by the Canadian Academy of Sport and Exercise Medicine and the Canadian Society for Exercise Physiology. British Journal of Sports Medicine. 2023;57(4):193–202. Available from: http://dx.doi.org/10.1136/bjsports-2022-106161
Patel N, Patel K. Estimation of Pulmonary Gas Exchange in the Human Respiratory System Under Normal and Abnormal Conditions. Biosciences Biotechnology Research Asia. 2023;20(1):255–262. Available from: http://dx.doi.org/10.13005/bbra/3086
Jaeger JM, Titus BJ, Blank RS. Essential Anatomy and Physiology of the Respiratory System and the Pulmonary Circulation. In: Slinger P., ed. Principles and Practice of Anesthesia for Thoracic Surgery. (pp. 65-92) Springer Cham. 2019.
Wittenstein J, Scharffenberg M, Ran X, Keller D, Michler P, Tauer S, et al. Comparative effects of flow vs. volume-controlled one-lung ventilation on gas exchange and respiratory system mechanics in pigs. Intensive Care Medicine Experimental. 2020;8(S1):1–16. Available from: https://doi.org/10.1186/s40635-020-00308-0
Lone AUH, Khanday MA. Mathematical analysis of oxygen and carbon dioxide exchange in the human capillary and tissue system. Computer Methods in Biomechanics and Biomedical Engineering. 2023;26(2):199–208. Available from: https://doi.org/10.1080/10255842.2022.2053115
Stewart GM, Cross TJ, Joyner MJ, Chase SC, Curry T, Lehrer-Graiwer J, et al. Impact of Pharmacologically Left Shifting the Oxygen–Hemoglobin Dissociation Curve on Arterial Blood Gases and Pulmonary Gas Exchange During Maximal Exercise in Hypoxia. High Altitude Medicine & Biology. 2021;22(3):249–262. Available from: https://doi.org/10.1089/ham.2020.0159
Jiang S, Fu Z, Li P, Shen Y, Su Q, Cai G, et al. A model of the pulmonary acinar circulatory system with gas exchange function to explore the influence of alveolar diameter. Respiratory Physiology & Neurobiology. 2022;300:103883. Available from: https://doi.org/10.1016/j.resp.2022.103883
Hennigs C, Becher T, Rostalski P. Mathematical lung model for local gas exchange based on EIT-measurements. Current Directions in Biomedical Engineering. 2022;8(2):376–379. Available from: https://doi.org/10.1515/cdbme-2022-1096
Hall JE, Guyton AC. Diffusion of Gases Through the Respiratory Membrane. In: Guyton and Hall Textbook of Medical Physiology (12). (pp. 489-492) Saunders/Elsevier. 2010.
Ushamohan BP, Rajasekaran AK, Belur YK, Ilavarasu J, Srinivasan TM. Nitric Oxide, Humming and Bhramari Pranayama. Indian Journal Of Science And Technology. 2023;16(5):377–384. Available from: https://doi.org/10.17485/IJST/v16i5.1212
Gupta N, Kumar P, Mehta T. Physical Activity, Yoga and Meditation in Improving Immunity and Fighting Against Viral Respiratory Infections - A Systematic Review . (An Aid to COVID-19 and such Pandemics) Indian Journal Of Science And Technology. 2022;15(38):1923–1931. Available from: https://doi.org/10.17485/IJST/v15i38.934

Copyright

© 2023 Patel & Patel. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)