= Indicator dilution
{title2=$Q=M/\int C(t)\,dt$}
\b[<Indicator dilution>] estimates <blood flow> from the transport of an introduced, measurable indicator. A known input is mixed into flowing blood, and a downstream detector records its changing concentration or an analogous calibrated signal. The inference uses a transported-amount balance, rather than merely equating a low peak with a large flow.
For an original first-pass bolus model, let indicator amount $M$ pass a detector in a stream of constant flow $Q$, with background-subtracted concentration $C(t)$. If the full indicator amount crosses that location once, no indicator is lost and mixing makes the measured concentration representative,
$$
M=\int Q C(t)\,dt,
\qquad
\boxed{Q=\frac{M}{\int C(t)\,dt}}.
$$
For $M=4.00$ mg and curve area $0.800\,\mathrm{mg\,min\,L^{-1}}$, flow is $5.00\,\mathrm{L\,min^{-1}}$. Two curves can have different peak heights and widths yet give this same area and flow. A transit time or peak height alone is insufficient.
Missing 20 percent of the area gives an inferred $4/0.640=6.25$ L/min, a 25 percent overestimate. Including an extra 20 percent through recirculation instead gives $4/0.960\approx4.17$ L/min. First-pass isolation, background subtraction and the timing window are therefore parts of the measurement model. Incomplete recovery of the injected indicator can invalidate the assumption that the detected amount equals $M$.
Continuous infusion uses a related steady balance. If indicator enters at known amount rate $\dot M$ and background-corrected downstream concentration is $C$, the simplest negligible-added-volume model gives $Q=\dot M/C$. When infusion volume is appreciable, it contributes to total flow and must be retained.
<Thermodilution> uses a thermal contrast instead of a chemically measured dye concentration. A primary coronary experiment combined continuous saline infusion with an infusion <catheter> and temperature-sensing guidewire.<Direct volumetric blood flow measurement in coronary arteries by thermodilution by Wilbert Aarnoudse and others>[Abstract, Methods]{ref} Thermal capacity, infused-fluid temperature and heat exchange then enter the amount balance. A thermal signal cannot simply be inserted into the dye formula without those conversions.
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