Assessment of a New Mathematical Model for the Computation of Numerical Parameters Related to Renal Cortical Blood Flow and Fractional Blood Volume by Contrast-Enhanced Ultrasound

Abstract

We analyzed the value of a new mathematical model for the quantification of renal cortical blood flow and fractional blood volume by contrast-enhanced ultrasound after the injection of sulfur hexafluoride–filled microbubbles. A vessel-mimicking phantom experiment was preliminarily performed which showed that the effect of microbubble diffusion is negligible compared with the effect of liquid drag. Twelve healthy volunteers (7 male, 5 female; 27 to 48 years [ n = 6; group 1], and 61 to 80 years [ n = 6; group 2], respectively), with normal renal and cardiac function and not undergoing any pharmacologic treatment, were examined. In each volunteer, both kidneys were scanned after intravenous injection of sulfur hexafluoride–filled microbubbles at a slow rate (4.8 mL at a flow of 4.0 mL/min), and the refill kinetics of the renal cortex after microbubble destruction was evaluated by echo-signal intensity quantification. The progressive replenishment of the renal vessels was approximated both by standard negative exponential function and by the piecewise linear function resulting from our mathematical model. A better dataset approximation was provided by piecewise linear versus standard negative exponential function (overall mean square error: 0.44 vs. 0.51; p < 0.05, Wilcoxon test). The piecewise linear function provided a curve composed of four linear tracts ( n = 3 volunteers; 2 from group 1 and 1 from group 2), three linear tracts ( n = 6 volunteers; 3 from group 1 and 3 from group 2) or two linear tracts ( n = 3 volunteers; 1 from group 1 and 2 from group 2). The piecewise linear function versus standard negative exponential function improved data approximation for the computation of numerical values related to renal cortical blood flow velocity and fractional blood volume. (E-mail: quaia@univ.trieste.it)