Optimal Renal Artery-Aorta Angulation Revealed by Flow Simulation

Abstract

Introduction: In the circulatory system, the vessel branching angle may have hemodynamic consequences. We hypothesized that there is a hemodynamically optimal range for the renal artery's branching angle.

Methods: Data on the posttransplant kinetics of estimated glomerular filtration rate (eGFR) were analyzed according to the donor and implant sides (right-to-right and left-to-right position; n = 46). The renal artery branching angle from the aorta of a randomly selected population was measured using an X-ray angiogram (n = 44). Computational fluid dynamics simulation was used to elucidate the hemodynamic effects of angulation.

Results and discussion: Renal transplant patients receiving a right donor kidney to the right side showed faster adaptation and higher eGFR values than those receiving a left donor kidney to the right side (eGFR: 65 ± 7 vs. 56 ± 6 mL/min/1.73 m2; p < 0.01). The average branching angle on the left side was 78° and that on the right side was 66°. Simulation results showed that the pressure, volume flow, and velocity were relatively constant between 58° and 88°, indicating that this range is optimal for the kidneys. The turbulent kinetic energy does not change significantly between 58° and 78°.

Conclusion: The results suggest that there is an optimal range for the renal artery's branching angle from the aorta where hemodynamic vulnerability caused by the degree of angulation is the lowest, which should be considered during kidney transplantations.

Keywords: Flow simulation; Hemodynamics; Renal artery branching angle; Single kidney; Transplantation.

Fig. 1.

Image of the sectioned model with average renal artery branching angles on both sides, showing the finite-element mesh demonstrating the inflation layers and the mesh refinement. Image exported from Ansys Academic 2020 R2.

Fig. 2.

Comparison of eGFRs of kidney transplant patients receiving right-to-right- or left-to-right-side donor kidneys as a function of time. Mean ± SEM, * statistically significant differences per the χ² test and t test using IBM SPSS Statistics 25. The graph image was created using GraphPad Prism 8. eGFR, estimated glomerular filtration rate.

Fig. 3.

Scatter diagram of the measurement points of the RBA from the aorta in the left and right positions. The dashed line represents the mean values on each side. The graph image was created using GraphPad Prism 8. RBA, renal artery branching angle; ∎, right-side values of angulation measurement; ▲, left-side values of angulation measurement.

Fig. 4.

Computational fluid dynamics-simulated area-weighted average turbulent kinetic energy (TKE) as a function of time in the renal arteries during a cardiac cycle in an idealized model with a statistical average angulation on both sides. Graphs were created using GraphPad Prism 8. The model image was created, and the figure was composed using Gimp 2.10.22. ─────, left-side artery; ─ ─ ─ ─, right-side artery; Sys, systolic peak; Dia, diastolic peak; TKE, area-weighted average turbulent kinetic energy.

Fig. 5.

Computational fluid dynamics-simulated area-weighted average total pressure (a, b, c) and turbulent kinetic energy (d, e, f) as a function of time in the renal arteries during a cardiac cycle in idealized models with a statistical average, maximum left-side angulation, and minimum left-side angulation with and without a right-side artery. a L-avg: pressure values of the left renal artery at average left-side angulation; R-avg: pressure values of the right renal artery at average left-side angulation; L-avg-single: pressure values of the left renal artery at average left-side angulation and a single left-side kidney. b L-Lmax: pressure values of the left renal artery at maximum left-side angulation; R-Lmax: pressure values of the right renal artery at maximum left-side angulation; L-Lmax-single: pressure values of the left renal artery at maximum left-side angulation and a single left-side kidney. c L-Lmin: pressure values of the left renal artery at minimum left-side angulation; R-Lmin: pressure values of the right renal artery at minimum left-side angulation; L-Lmin-single: pressure values of the left renal artery at minimum left-side angulation and a single left-side kidney. d L-avg: turbulent kinetic energy values of the left renal artery at average left-side angulation; R-avg: turbulent kinetic energy values of the right renal artery at average left-side angulation; L-avg-single: turbulent kinetic energy values of the left renal artery at average left-side angulation and a single left-side kidney. e L-Lmax: turbulent kinetic energy values of the left renal artery at maximum left-side angulation; R-Lmax: turbulent kinetic energy values of the right renal artery at maximum left-side angulation; L-Lmax-single: turbulent kinetic energy values of the left renal artery at maximum left-side angulation and a single left-side kidney. f L-Lmin: turbulent kinetic energy values of the left renal artery at minimum left-side angulation; R-Lmin: turbulent kinetic energy values of the right renal artery at minimum left-side angulation; L-Lmin-single: turbulent kinetic energy values of the left renal artery at minimum left-side angulation and a single left-side kidney. The graph image was created using GraphPad Prism 8.

Fig. 6.

Computational fluid dynamics-simulated maximum values as a function of left-side renal artery angulation. a Maximum pressure. b Maximum velocity magnitude. c Maximum volume flow. d Maximum turbulent kinetic energy. The vertical lines enclose the optimal angulation range, which is 58°–88° in the a–c cases and 58°–78° in the d case. The right-side renal artery angle is the average value at all points. All values are calculated as area-weighted averages on the cross section of the renal arteries. The graph image was created using GraphPad Prism 8. ─ ─ ─ ─, right side; ─────, left side.

Fig. 7.

Suboptimal and optimal renal artery angulation ranges. The figure was created using Gimp 2.10.22. Pressure, area-weighted average pressure; velocity, area-weighted average velocity magnitude; flow, area-weighted average volume flow; turbulence, area-weighted average turbulent kinetic energy.