Hydrodynamic aspects of machine perfusion of donor liver and kidneys: the role of computational fluid dynamics

Machine perfusion of donor organs is becoming the standard of preservation in transplantology; however, perfusion parameters — pressure, volumetric flow, and vascular resistance — are still set empirically, without accounting for the hydrodynamic characteristics of the individual organ. Computational fluid dynamics, primarily one-dimensional (1D) and three-dimensional (3D) flow modeling, provides the tools for a physically grounded selection of perfusion regimens.
Aim: to describe the conceptual framework and methodology of 1D modeling of intrahepatic and intrarenal blood flow as applied to machine perfusion of donor liver and kidneys; to present preliminary results of 1D model validation on clinical liver transplantation data; to report the results of 3D CFD modeling of portal vein hemodynamics as a basis for understanding perfusion fluid dynamics; and to propose physically justified perfusion regimens.
Materials and methods. One-dimensional models of hepatic and renal vascular trees were constructed based on the Navier–Stokes equations for tubular structures and Murray's law. Validation of the 1D hepatic arterial tree model was performed in 80 patients who underwent liver transplantation at the N.V. Sklifosovsky Research Institute of Emergency Medicine. To study portal vein hemodynamics, 3D CFD modeling was performed using FlowVision 3.13.01 on two geometric models reconstructed from CT data of real patients; both steady-state and transient simulations were carried out with Doppler-derived pulsatile flow boundary conditions.
Results. The error of the 1D model in calculating pressure at the arterial anastomosis site did not exceed 15%. CFD-guided optimization of reconstruction technique altered surgical strategy in 25% of high-risk patients, yielding a 33.1% increase in wall shear stress and a 64.3% reduction in prothrombotic zones. 3D CFD of the portal vein demonstrated that qualitative differences between Newtonian (Navier–Stokes) and non-Newtonian (Caro) rheological models are negligible, justifying the use of the computationally less demanding Newtonian model; three types of high-risk thrombosis zones were identified — stasis, recirculation, and abrupt flow redirection. With regard to perfusiology: for the liver, the optimal portal flow is 0.25–0.40 ml/min/g at a pressure of 3–6 mmHg; transition to D-HOPE reduces zonal acinar perfusion inhomogeneity from 28–35% to 9–13%; for the kidney — 18–22 mmHg at a flow of 0.8–1.2 ml/min/g.
Conclusion. The combination of 1D modeling (rapid calculation of pressure and flow distribution across the entire organ) and 3D CFD (spatial analysis of local hemodynamic risks) provides the most complete physical basis for machine perfusion parameter selection. The transition from empirical to computationally justified perfusion protocols is feasible on the basis of currently available clinical material.

1. van Rijn R., Schurink I.J., de Vries Y., et al. Hypothermic machine perfusion in liver transplantation — a randomized trial. N Engl J Med. 2021;384(15):1391–1401. doi:10.1056/NEJMoa2031532

2. Czigany Z., Pratschke J., Froněk J., et al. Hypothermic oxygenated machine perfusion reduces early allograft injury and improves posttransplant outcomes in extended criteria donation liver transplantation from donation after brain death. Ann Surg. 2021;274(5):705–712. doi:10.1097/SLA.0000000000005110

3. Nasralla D., Coussios C.C., Mergental H., et al. A randomized trial of normothermic preservation in liver transplantation. Nature. 2018;557(7703):50–56. doi:10.1038/s41586-018-0047-9

4. Moers C., Smits J.M., Maathuis M.H., et al. Machine perfusion or cold storage in deceased-donor kidney transplantation. N Engl J Med. 2009;360(1):7–19. doi:10.1056/NEJMoa0802289

5. Verstraeten L., Jochmans I. Sense and sensibilities of organ perfusion as a kidney and liver viability assessment platform. Transpl Int. 2022;35:10312. doi:10.3389/ti.2022.10312

6. Mynard J.P., Smolich J.J. One-dimensional haemodynamic modeling and wave dynamics in the entire adult circulation. Ann Biomed Eng. 2015;43(6):1443–1460. doi:10.1007/s10439-015-1313-8

7. Morris P.D., Narracott A., von Tengg-Kobligk H., et al. Computational fluid dynamics modelling in cardiovascular medicine. Heart. 2016;102(1):18–28. doi:10.1136/heartjnl-2015-308044

8. Tithof J., Mestre H., Kelley D.H. Lumped parameter liver simulation to predict acute haemodynamic alterations following partial resections. J R Soc Interface. 2023;20(207):20230444. doi:10.1098/rsif.2023.0444

9. Fenton C.G., Pedersen G.B., Li J., et al. A simplified computational liver perfusion model, with applications to organ preservation. Sci Rep. 2025;15:2847. doi:10.1038/s41598-025-85170-4

10. Murray C.D. The physiological principle of minimum work: I. The vascular system and the cost of blood volume. Proc Natl Acad Sci USA. 1926;12(3):207–214. doi:10.1073/pnas.12.3.207

11. Belzer F.O., Southard J.H. Principles of solid-organ preservation by cold storage. Transplantation. 1988;45(4):673–676. doi:10.1097/00007890-198804000-00001

12. Catalano C., Crascì F., Puleo S., et al. Computational fluid dynamics in cardiac surgery and perfusion: a review. Perfusion. 2025;40(2):362–370. doi:10.1177/02676591241239277

13. Schlegel A., Muller X., Kalisvaart M., et al. Outcomes of DCD liver transplantation using organs treated by hypothermic oxygenated perfusion before implantation. J Hepatol. 2019;70(1):50–57. doi:10.1016/j.jhep.2018.10.005

14. van Rijn R., Karimian N., Matton A.P., et al. Dual hypothermic oxygenated machine perfusion in liver transplants donated after circulatory death. Br J Surg. 2017;104(7):907–917. doi:10.1002/bjs.10515

15. Dutkowski P., Schlegel A., de Oliveira M., et al. HOPE for human liver grafts obtained from donors after cardiac death. J Hepatol. 2014;60(4):765–772. doi:10.1016/j.jhep.2013.11.023

16. Chouchani E.T., Pell V.R., Gaude E., et al. Ischaemic accumulation of succinate controls reperfusion injury through mitochondrial ROS. Nature. 2014;515(7527):431–435. doi:10.1038/nature13909

17. Kaminski J., Delpech P.O., Kaaki-Hosni S., et al. Oxygen consumption by warm ischemia-injured porcine kidneys in hypothermic static and machine preservation. J Surg Res. 2019;242:78–86. doi:10.1016/j.jss.2019.04.048

18. Niroomand A., Nita G.E., Lindstedt S. Machine perfusion and bioengineering strategies in transplantation — beyond the emerging concepts. Transpl Int. 2024;37:13215. doi:10.3389/ti.2024.13215