Coronary oxygen delivery (source code)

= Coronary oxygen delivery

\b[Coronary oxygen delivery] is the rate at which oxygen is brought to a specified myocardial territory in its arterial blood supply. If volume flow is $Q$ and <arterial oxygen content> is $C_a$, then
$$
D_{\mathrm O_2}=QC_a.
$$
Flow and content must use compatible volume units and refer to the same territory and interval. Delivery is an inflow quantity; <coronary oxygen uptake> is the net amount removed from the blood by the represented tissue.

For an original example, $Q=250\,\mathrm{mL\,min^{-1}}$ and $C_a=0.20\,\mathrm{mL\ O_2\,mL^{-1}}$ give $D_{\mathrm O_2}=50\,\mathrm{mL\ O_2\,min^{-1}}$. The same delivery can arise from $Q=200$ with $C_a=0.20$, or $Q=250$ with $C_a=0.16$: both give $40\,\mathrm{mL\ O_2\,min^{-1}}$. Delivery alone cannot identify which factor changed.

Oxygen content is not the same observable as oxygen <partial pressure> or <oxygen saturation>. Much of blood's oxygen is carried by <hemoglobin>; the amount of carrier therefore matters as well as its saturation.<Anatomy and Physiology 2e by J. Gordon Betts and others>[Section 22.5, Oxygen Transport]{ref} Substituting a pressure value for $C_a$ would also fail dimensionally.

An original independent-error approximation gives
$$
\frac{u_D^2}{D^2}\simeq\frac{u_Q^2}{Q^2}+\frac{u_C^2}{C_a^2}.
$$
Relative standard uncertainties $5\%$ and $2\%$ combine to about $5.39\%$ under the stated assumptions. A covariance term is required when the input errors are correlated.<Evaluation of measurement data — Guide to the expression of uncertainty in measurement by JCGM>[Sections 5.1–5.2, propagation with independent and correlated inputs]{ref}

The measurement apparatus determines which input is actually observed. A primary coronary-flow study used continuous saline infusion and a pressure/temperature-sensing guidewire, testing volumetric flow estimation in five dogs and 35 patients.<Direct volumetric blood flow measurement in coronary arteries by thermodilution by Wilbert Aarnoudse and others>[Abstract, Methods]{ref} Such a temperature-dilution observation does not itself measure oxygen content; a delivery estimate must obtain that input separately.

<Mass-specific myocardial oxygen delivery> adds a tissue-mass denominator. Total delivery $40\,\mathrm{mL\ O_2\,min^{-1}}$ to $200\,\mathrm g$ corresponds to $20\,\mathrm{mL\ O_2\,min^{-1}}$ per $100\,\mathrm g$. A bulk value, a mass-normalized value and a regional value answer different questions, and normalizing a total does not reveal uneven distribution within the territory.