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Cardiac Output

Dye Dilution Method

The dye dilution method is done by rapidly injecting a dye, indocyanine green, into the right atrium of the heart. The dye flows with the blood into the aorta. A probe is inserted into the aorta to measure the concentration of the dye leaving the heart at equal time intervals [0, T] until the dye has cleared. Let c(t) be the concentration of the dye at time t. By dividing the time intervals from [0, T] into subintervals Δt, the amount of dye that flows past the measuring point during the subinterval from $t=t_{i-1}$ to $t=t_{i}$ is:

$(concentration)(volume)=c(t_{i})(F\Delta t)$

where $F$ is the rate of flow that is being calculated. The total amount of dye is:

$\sum _{i=1}^{n}c(t_{i})(F\Delta t)=F\sum _{i=1}^{n}c(t_{i})(\Delta t)$

and, letting $n\rightarrow \infty$, the amount of dye is:

$A=F\int _{0}^{T}c(t)dt$

Thus, the cardiac output is given by:

$F={\frac {A}{\int _{0}^{T}c(t)dt}}$

where the amount of dye $A$ is known, and the integral can be determined using the concentration readings.

The dye dilution method is one of the most accurate methods of determining cardiac output during exercise. The error of a single calculation of cardiac output values at rest and during exercise is less than 5%. This method does not allow measurement of 'beat to beat' changes, and requires a cardiac output that is stable for approximately 10 s during exercise and 30 s at rest.