Indicator dilution ($Q=M/\int C(t)dt$)

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,For $M=4.00$ mg and curve area $0.800\mathrm{mg}\min {\mathrm{L}}^{-1}$, flow is $5.00\mathrm{L}\mathrm{mi}{\mathrm{n}}^{-1}$. 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 $4/0.960\approx 4.17$ 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.^[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.