= Coronary oxygen uptake
{title2=$\dot V_{\mathrm O_2}$}
\b[Coronary oxygen uptake] is the net rate at which a specified myocardial region removes oxygen from its supplying blood. For matched inflow and outflow with negligible oxygen storage change, the regional <Fick principle> balance is
$$
\dot V_{\mathrm O_2}=Q(C_a-C_v).
$$
Here $Q$ is volume flow, $C_a$ <arterial oxygen content> and $C_v$ <venous oxygen content>. The <arteriovenous oxygen content difference> measures removal per blood volume; multiplying by flow gives removal per time.
In an original example, $Q=250\,\mathrm{mL\,min^{-1}}$, $C_a=0.20$ and $C_v=0.08\,\mathrm{mL\ O_2\,mL^{-1}}$ give uptake $30\,\mathrm{mL\ O_2\,min^{-1}}$. <Coronary oxygen delivery> is instead $QC_a=50$ in the same amount-per-time units. The remaining oxygen leaves in the venous outflow.
The complete control-volume statement makes the assumptions explicit:
$$
\dot V_{\mathrm O_2}=Q_{\rm in}C_a-Q_{\rm out}C_v-\frac{\mathrm dM_{\mathrm O_2}}{\mathrm dt},
$$
where $M_{\mathrm O_2}$ is stored oxygen in the represented region. If input and output carry $50$ and $20\,\mathrm{mL\ O_2\,min^{-1}}$, while storage increases at $5$, tissue uptake is $25$, not $30$. Thus an inflow–outflow difference during accumulation is not automatically a steady metabolic rate.
The required quantities also come from different observations. The primary coronary thermodilution study estimated volumetric flow using saline infusion and pressure/temperature sensing.<Direct volumetric blood flow measurement in coronary arteries by thermodilution by Wilbert Aarnoudse and others>[Abstract, Methods]{ref} A separate primary whole-blood oximeter used red and infrared illumination, a photodetector and computation to obtain hemoglobin concentration and saturation.<An oximeter for measuring hemoglobin concentration and oxygen content by A. P. Shepherd and others>[Abstract, optical apparatus and separate computed quantities]{ref} Neither instrument alone supplies every term of the balance.
Territory matching is essential. A flow measured in one coronary branch and a venous mixture draining a different region need not define that branch's oxygen uptake. Sampling time, represented tissue, measurement units and storage assumptions must accompany the numerical result.
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