# O2 Saturation of Hemoglobin at Varying Altitude

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Hemoglobin (heme) in red blood cells binds to oxygen in the lungs and carries it to all of the tissues of the body. At higher altitudes, the pressure of oxygen in the atmosphere decreases, resulting in less oxygen available to breathe, impacting the fraction of the hemoglobin in the body bound to oxygen. This relationship is complex, depending on a multitude of other factors (e.g., body temperature and pH), yet in general, it can be modeled simply with the Hill equation. This Demonstration shows how the fraction of saturated hemoglobin decreases as the altitude increases. A visual representation of the fraction of saturated hemoglobin is shown with red representing completely saturated hemoglobin and blue representing completely unsaturated hemoglobin.

Contributed by: Shivam Diora, Madeline Durand and Sarah Yee (January 2024)

Open content licensed under CC BY-NC-SA

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## Details

This Demonstration considers the possible factors that can impact hemoglobin binding to oxygen. One of the obvious influences on this relationship is altitude, as people can have trouble breathing at higher altitudes. The relationship between altitude and how hemoglobin binds to oxygen is significant because when people are engaged in activities such as mountain climbing, it is important that they understand how their body will respond to large changes in altitude.

The fraction of saturated hemoglobin in the blood is related to altitude through the partial pressure of oxygen in the atmosphere. With increasing altitude, the partial pressure of oxygen decreases, resulting in less oxygen available for breathing and consequently, a lower amount of saturated hemoglobin.

Use the sliders to see how the fraction of saturated hemoglobin in the blood changes with altitude, body temperature and blood pH. Blood pH is considered because the respiratory rate is related to the blood pH through the bicarbonate buffer system. Additionally, internal temperature is related to rate kinetics and hence would influence heme saturation.

The Hill equation (a simplified mathematical model) is used for these relationships. A visual representation of hemoglobin is displayed that gradually turns from red to blue as heme saturation decreases. Generally, the Hill equation describes dose-dependent relationships by relating the fraction of protein bound to ligand (at constant concentration) to the ligand concentration via the constant (apparent dissociation constant). In this Demonstration, it is used to model the equilibrium between the amount of hemoglobin bound as a function of the partial pressure of oxygen within the atmosphere and p50 (the value of at which Hb is 50 percent saturated by ). P50 depends on a multitude of variables, two of which include internal temperature and blood pH (described by fitted equations derived in [1]). In order to calculate the partial pressure of oxygen as a function of altitude, the equation in [2] was used. Assumptions made for this code include the following: the partial pressure of oxygen within the atmosphere is equal to that within the human body and the amount of heme within the body is at a constant concentration.

References

[1] R. K. Dash, B. Korman and J. B. Bassingthwaighte, "Simple Accurate Mathematical Models of Blood HbO2 and HbCO2 Dissociation Curves at Varied Physiological Conditions: Evaluation and Comparison with Other Models," *European Journal of Applied Physiology*, 116(1), 2016 pp. 97–113. doi:10.1007/s00421-015-3228-3.

[2] Wikipedia. "Barometric Formula." (Nov 21, 2023) en.wikipedia.org/wiki/Barometric_formula.

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