A vascular transport operator.

A pulse or a sharp front in concentration of a tracer or a substrate in the blood within a vessel becomes dispersed while being transported along a vessel. Cross-stream mixing and pulsations in flow with the heartbeat cause the dispersion to be less than would occur with a parabolic velocity profile (Newtonian flow). These characteristics allow intravascular mass transport to be described well by a simple two-parameter differential operator, which is a one-dimensional representation of the rather complex real situation. The operator consists of two components in series, a pure delay and a fourth-order linear differential operator. The latter is merely two underdamped second-order operators in series, with fixed relationships between the natural frequencies and damping coefficients. The operator is useful because it provides a transport function with skewness and kurtosis suitable to intravascular transport where the mean velocity profile is blunter than in Newtonian parabolic flow. The parameters of the operator are its mean transit time, t, and its relative dispersion, RD, which is the standard deviation of the response impulse divided by t. The operator transport function describes blood transport through the human leg arterial system, where the RD values are approximately 15-20%.