Applications of the Lagged Normal Density Curve as a Model for Arterial Dilution Curves

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Abstract
1. Indicator dilution curves (concentration versus time) were recorded from the femoral and dorsalis pedis arteries of normal men after injections of indocyanine green into the superior vena cava or thoracic aorta. A four-parameter mathematical model, the lagged normal density curve, adequately described the form of the portion of these curves representing indicator passing by the sampling site for the first time. 2. The curves were observed to be of constant shape, the spread of the curve being approximately linearly related to the mean transit time t. The spread was dependent on the injection site; dispersion was shown to be greatest in the central circulation, less in the aorta, and still less in the arteries of the leg. For the latter segment, the mean transit time t. The spread was dependent 0.3 t, the square root of the variance was 0.18 t, and the parameters of the lagged normal density curve, σ and τ, were 0.09 t and 0.16 t, respectively. 3. The linear relationships between parameters of the recorded curves and the mean transit times indicate that the effect of rate of flow, over a range from resting values to four to six times above resting values, has almost no influence on the dispersion. This suggests that the flow characteristics are essentially unchanged over this range. Such linear relationships always occur with laminar flow but cannot prove its existence because turbulent flow can also produce this result. The similarity of the linear relationships at low flow rates to those at high flow rates, where turbulence almost certainly is present, suggests that arterial flow is usually turbulent. Turbulence may be expected at relatively low flow rates in nonhomogeneous fluids driven by a pulsatile head of pressure through elastic, branched, tapering, curved tubes.