Hemoglobin is the red component of the red blood cell, it combines with oxygen to keep the body functional. The fractional saturation of hemoglobin is usually computed graphically but the hill equation gives a more specific value.

Calculations:

The hill equation can be expressed as;

$Y_{O_{2} } =\frac{(P_{O_{2} })^{h}}{(P_{_{50} })^{h}+(P_{O_{2} })^{h}}$

Where $Y_{O_{2} }$ is the fractional saturation of oxygen =?;

$P_{O_{2} }$ is the partial pressure of oxygen = 72 mm Hg;

$P_{_{50}$ is the partial pressure of oxygen when the hemoglobin is 50%

saturated = 24 mm Hg and;

h is the Hill coefficient = 3.

Substituting the values into the expression above we have;

$Y_{O_{2} } =\frac{(72 mm Hg_{_{} })^{3}}{(24 mm Hg_{_{} })^{3}+(72 mm Hg_{_{} })^{3}}$

$Y_{O_{2} }$ = $\frac{373248}{13824 + 373248}$

$Y_{O_{2} }$ = $\frac{373248}{387072}$

$Y_{O_{2} }$ = 0.964

Therefore the fractional saturation is 0.964 or 96.4 %(multiply by 100)

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