= Hemoglobin-concentration and saturation separation
\b[Hemoglobin-concentration and saturation separation] is the distinction between how much <hemoglobin> a volume of <blood> contains and what fraction of its available oxygen-binding capacity is occupied. <Oxygen saturation> is a <ratio>; <hemoglobin> concentration is an amount per volume. Neither quantity alone specifies <arterial oxygen content>.
Let $H$ be total <hemoglobin> concentration, $F$ the <fractional oxyhemoglobin> and $\beta$ a chosen oxygen capacity per unit <hemoglobin> mass. A simple content model is
$$
C_{\mathrm O_2}=\beta HF+\alpha p_{\mathrm O_2},
$$
where the final term represents dissolved <oxygen> using a solubility coefficient $\alpha$ and oxygen <partial pressure> $p_{\mathrm O_2}$. The model separates carrier amount, carrier occupancy and dissolved gas. <Functional oxygen saturation> can replace $F$ only when the excluded <hemoglobin> species are negligible or separately accounted for.<Hemoglobin by Radiometer>[Total hemoglobin and oxygen-binding capacity]{ref}<Oxyhemoglobin by Radiometer>[FO2Hb versus oxygen saturation]{ref}
For an original comparison, neglect dissolved <oxygen> and stipulate $\beta=1.34$ mL/g and $F=0.98$. Samples with $H=15$ and $H=8$ g/dL then carry about $19.70$ and $10.51$ mL of bound <oxygen> per dL, respectively. The equal <oxygen saturation> does not imply equal oxygen content. Conversely, halving $H$ and doubling $F$ preserves the product $HF$ only while the new <fraction> remains physically attainable.
A primary instrument illustrates how the distinction can be measured rather than merely defined. In 1989, a capillary-tube oximeter used red and infrared light, a detector and digitized processing to derive <hemoglobin> concentration and <oxygen saturation> separately.<An oximeter for measuring hemoglobin concentration and oxygen content by A. P. Shepherd and others>[Abstract, instrument and separate concentration/saturation calculations]{ref} Measurements sensitive to different optical features supply information that one saturation number cannot contain. At fixed <blood flow>, oxygen delivery scales with content; equal saturation readings alone cannot establish equal delivery.
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