= Coronary thermodilution mixing assumptions
\b[Coronary thermodilution mixing assumptions] are the conditions that make a downstream temperature reading representative of the mixture used to infer coronary <blood flow>. They include adequate mixing of infused fluid and <blood>, appropriate <volumetric heat capacity> values, known infusion rate and temperature, and sufficiently small unmodeled <heat transfer> between the fluid and surrounding structures.
The apparatus places these assumptions in a concrete setting. In a primary continuous-infusion study, a <catheter> supplied room-temperature saline while a pressure/temperature guidewire measured distal temperature; the infused-fluid temperature was measured at the <catheter> tip.<Direct volumetric blood flow measurement in coronary arteries by thermodilution by Wilbert Aarnoudse and others>[Abstract, Methods]{ref} Temperature at the tip matters because fluid can exchange heat before entering the measured <blood flow>.
An original two-stream model makes the bookkeeping explicit. Let native <blood flow> be $Q_b$, infusion rate $Q_i$, baseline blood temperature $T_b$, infused-fluid temperature $T_i$ and mixed temperature $T_m$. Assume equal constant <volumetric heat capacity>, no external <heat transfer> and steady complete mixing. <Conservation of energy> gives
$$
Q_bT_b+Q_iT_i=(Q_b+Q_i)T_m,
$$
and hence
$$
Q_b=Q_i\frac{T_m-T_i}{T_b-T_m},\qquad
Q_{\rm mix}=Q_b+Q_i=Q_i\frac{T_b-T_i}{T_b-T_m}.
$$
Native flow and total downstream mixture flow have different numerators. With constructed $Q_i=20$ mL/min, $T_b=37\,{}^{\circ}\mathrm C$, $T_i=27\,{}^{\circ}\mathrm C$ and $T_m=35\,{}^{\circ}\mathrm C$, the model gives $Q_b=80$ mL/min and $Q_{\rm mix}=100$ mL/min. This equal-capacity balance is an explanatory model, not the instrument's full calibration algorithm.
Incomplete mixing changes what the sensor observes. If a sensor sampled an unusually cold filament and read $34\,{}^{\circ}\mathrm C$ for the same other inputs, the formula would return about $46.7$ mL/min instead of 80. Repeating that local reading precisely would not correct its lack of representativeness. More generally, a mixed temperature is weighted by transported heat capacity, rather than being an unweighted spatial mean.
Finally, $Q_b$ becomes sensitive to small temperature errors when $T_b-T_m$ is small. At fixed $Q_i,T_b,T_i$,
$$
\frac{\partial Q_b}{\partial T_m}
=Q_i\frac{T_b-T_i}{(T_b-T_m)^2}.
$$
For the constructed example this is $50$ mL/(min K). The derivative describes local sensitivity within the model; it does not estimate errors from incomplete mixing or heat loss. Those require separate physical evidence.
Back to article page
