<P> 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 (\ displaystyle t = t_ (i - 1)) to t = t i (\ displaystyle t = t_ (i)) is: </P> <P> (c o n c e n t r a t i o n) (v o l u m e) = c (t i) (F Δ t) (\ displaystyle (concentration) (volume) = c (t_ (i)) (F \ Delta t)) </P> <P> where F (\ displaystyle F) is the rate of flow that is being calculated . The total amount of dye is: </P> <P> ∑ i = 1 n c (t i) (F Δ t) = F ∑ i = 1 n c (t i) (Δ t) (\ displaystyle \ sum _ (i = 1) ^ (n) c (t_ (i)) (F \ Delta t) = F \ sum _ (i = 1) ^ (n) c (t_ (i)) (\ Delta t)) </P>

Cardiac output (co) is equivalent to heart rate (hr) multiplied by stroke volume (sv)