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Blood Flow Quantification with Contrast-enhanced US: "Entrance in the Section" Phenomenon—Phantom and Rabbit Study¹

¹ From the Parametric Imaging Laboratory, UMR 7623 CNRS and Paris University VI, 15 rue de l’École de Médecine, 75006 Paris, France (O.L., S.F.A., J.M.C., S.L.B., E.K., G.B.); Department of Radiology, Necker Hospital, AP-HP, Paris, France (O.L., S.F.A., J.M.C.); and Department of Radiology, Pitié-Salpêtrière Hospital, AP-HP, Paris, France (O.L.). Received June 13, 2002; revision requested August 8; revision received October 17; accepted December 10. Address correspondence to S.L.B. (e-mail: bridal@lip.bhdc.jussieu.fr).

View larger version (19K): [in a new window]   Figure 1. Diagram of flow phantom. Dialysis filter and tubing were positioned so that the solution was pumped up a vertical segment of tubing at the measurement sites. Parts of phantom are reservoir located 2 m above the dialysis cartridge (1), automatic injector filled with US contrast agent (2), continuous wave (CW) Doppler measurement system (3), dialysis cartridge with 9,000 200-µm-diameter hollow fibers (4), US machine with a sector transducer (5), and peristaltic pump (6).

View larger version (159K): [in a new window]   Figure 2. Coronal US scan in left kidney of rabbit 2 shows positions of the large cortex ROI (ROI Large), the three groups of four ROIs positioned on a segmental artery (ROIs Seg), the corresponding interlobar artery ROI (ROIs Ila), and the cortex ROI (ROIs Cort) fed by this artery.

View larger version (40K): [in a new window]   Figure 3a. Scatterplots for the (a) proximal and (b) distal ROIs depict signal intensities in the dialysis cartridge as a function of time and flow rate. (c, d) Scatterplots depict the corresponding value calculated for the concentration of microbubbles as a function of time as given by the model in the first (c) and third (d) subvolumes. Destruction coefficient was fixed arbitrarily at 0.5, with three values of (related with the flow rate by the relation 1/ = F/Vb) (Appendix). Values of were decreased each time by a factor of 2 to simulate a doubling of the flow rate. Calculated destruction-reperfusion curves in c and d depict results that correspond well to the experimental flows in a and b, respectively.

View larger version (46K): [in a new window]   Figure 3b. Scatterplots for the (a) proximal and (b) distal ROIs depict signal intensities in the dialysis cartridge as a function of time and flow rate. (c, d) Scatterplots depict the corresponding value calculated for the concentration of microbubbles as a function of time as given by the model in the first (c) and third (d) subvolumes. Destruction coefficient was fixed arbitrarily at 0.5, with three values of (related with the flow rate by the relation 1/ = F/Vb) (Appendix). Values of were decreased each time by a factor of 2 to simulate a doubling of the flow rate. Calculated destruction-reperfusion curves in c and d depict results that correspond well to the experimental flows in a and b, respectively.

View larger version (22K): [in a new window]   Figure 3c. Scatterplots for the (a) proximal and (b) distal ROIs depict signal intensities in the dialysis cartridge as a function of time and flow rate. (c, d) Scatterplots depict the corresponding value calculated for the concentration of microbubbles as a function of time as given by the model in the first (c) and third (d) subvolumes. Destruction coefficient was fixed arbitrarily at 0.5, with three values of (related with the flow rate by the relation 1/ = F/Vb) (Appendix). Values of were decreased each time by a factor of 2 to simulate a doubling of the flow rate. Calculated destruction-reperfusion curves in c and d depict results that correspond well to the experimental flows in a and b, respectively.

View larger version (22K): [in a new window]   Figure 3d. Scatterplots for the (a) proximal and (b) distal ROIs depict signal intensities in the dialysis cartridge as a function of time and flow rate. (c, d) Scatterplots depict the corresponding value calculated for the concentration of microbubbles as a function of time as given by the model in the first (c) and third (d) subvolumes. Destruction coefficient was fixed arbitrarily at 0.5, with three values of (related with the flow rate by the relation 1/ = F/Vb) (Appendix). Values of were decreased each time by a factor of 2 to simulate a doubling of the flow rate. Calculated destruction-reperfusion curves in c and d depict results that correspond well to the experimental flows in a and b, respectively.

View larger version (34K): [in a new window]   Figure 4a. Mean destruction-reperfusion curves in the left kidney of (a) rabbit 1 and (b) rabbit 2 were obtained for segmental artery ROIs (top), the corresponding interlobar artery ROIs (middle), and the cortex ROIs (bottom). Replenishment curves begin with a lower slope than would be described by the exponential form A(1 - e-t). This sigmoid aspect is weakest for the segmental artery ROIs and strongest for the cortex ROIs.

View larger version (37K): [in a new window]   Figure 4b. Mean destruction-reperfusion curves in the left kidney of (a) rabbit 1 and (b) rabbit 2 were obtained for segmental artery ROIs (top), the corresponding interlobar artery ROIs (middle), and the cortex ROIs (bottom). Replenishment curves begin with a lower slope than would be described by the exponential form A(1 - e-t). This sigmoid aspect is weakest for the segmental artery ROIs and strongest for the cortex ROIs.

View larger version (22K): [in a new window]   Figure 5. Destruction-reperfusion curves obtained in the large cortex ROIs in rabbit 1 () and rabbit 2 (). Averaging of the data from all pixels in these ROIs leads to smoothing of the curves, which emphasizes the sigmoid aspect of the initial portion of the replenishment curves obtained in the parenchyma when the imaging plane intersects the feeding arteries.

View larger version (6K): [in a new window]   Figure A1a. (a) Diagram of three subvolumes in the ultrasound field placed serially with respect to the flow direction. Cbo represents the constant blood concentration of the microbubbles in the equilibrium phase that enter the first subvolume. Cn(t) is the time-varying concentration of the microbubbles in the subvolume n. Vb is the volume of blood in each subvolume. (b) Theoretic curves derived from our mathematical model describe the evolution of the microbubble concentration Cbn(t) in the first subvolume (n = 1, top solid and dashed-dotted lines) and third subvolume (n = 3, bottom dashed and dashed-dotted lines). Solid and dashed lines represent the cases where destruction of the microbubbles induced by the observation ultrasound field is null. The dashed-dotted lines show the results when the destruction coefficient is 0.25. Other parameters used for calculation were C0 = 500 microbubbles per milliliter, inflow = outflow = 1 mL/sec, and Vb = 1 mL.

View larger version (16K): [in a new window]   Figure A1b. (a) Diagram of three subvolumes in the ultrasound field placed serially with respect to the flow direction. Cbo represents the constant blood concentration of the microbubbles in the equilibrium phase that enter the first subvolume. Cn(t) is the time-varying concentration of the microbubbles in the subvolume n. Vb is the volume of blood in each subvolume. (b) Theoretic curves derived from our mathematical model describe the evolution of the microbubble concentration Cbn(t) in the first subvolume (n = 1, top solid and dashed-dotted lines) and third subvolume (n = 3, bottom dashed and dashed-dotted lines). Solid and dashed lines represent the cases where destruction of the microbubbles induced by the observation ultrasound field is null. The dashed-dotted lines show the results when the destruction coefficient is 0.25. Other parameters used for calculation were C0 = 500 microbubbles per milliliter, inflow = outflow = 1 mL/sec, and Vb = 1 mL.