Pressure distribution in normal, stenotic, and stented transplant renal arteries
The pressure distribution of TRA is shown in Figure 1. Pressure was uniform in the normal and stented TRA but changed abruptly in the stenotic TRA. In the stenotic TRA, pressure reached to a high level ahead the stenosis, promptly decreased to the trough level at the stenosis throat, and then slightly increased at downstream stenosis leading to an adverse pressure gradient. Similar phenomena were observed at both diastole and systole phases.
Velocity in normal, stenotic, and stented transplant renal arteries
Velocity streamline of TRA is shown in Figure 2. The streamlines at the upstream of stenosis were no intersection indicating a laminar flow pattern. However, a mere elliptic-shaped vortex near the inner wall and a separation zone developed at downstream stenosis [Figure 2a and 2c]. The maximal velocity of stenotic TRA significantly increased as compared to normal TRA at both end diastole phase (2.94 [2.14, 3.30] m/s vs. 1.06 [0.89, 1.15] m/s, Z = −3.372, P = 0.001) and peak systole phase (3.25 [2.67, 3.56] m/s vs. 1.65 [1.18, 1.72] m/s, Z = −3.373 P = 0.001) [Figure 2b and 2d]. As expected, the vortex and separation zone were ameliorated when stent was implanted [Figure 2a and 2c], and the maximal velocity decreased to 0.94 (0.84, 1.02) (Z = −3.372, P = 0.001) at end diastole phase and 1.24 (1.12, 1.35) m/s (Z = −3.373, P = 0.001) at peak systole phase [Figure 2b and 2d].
Wall shear stress in normal, stenotic, and stented transplant renal arteries
Wall shear stress (WSS) is a function of the velocity gradient of blood flow adjacent vascular endothelium, which is proportional to volume flow rate and inversely proportional to the cube of the lumen radius. The formula is
, where τ is the WSS, µ is the blood viscosity, and r is lumen radius. The WSS of TRA is shown in Figure 3. A remarkable high WSS was observed mainly at stenosis throat indicated as red zone, and a low WSS was indicated as blue zone at downstream stenosis [Figure 3a and 3e]. Compared to normal TRA, maximal WSS of stenotic TRA significantly increased at both end diastole phase (256.5 [149.8, 349.4] Pa vs. 41.7 [37.8, 45.3] Pa, Z = −3.372, P = 0.001) and peak systole phase (281.3 [184.3, 364.7] Pa vs. 65.8 (61.2, 71.9) Pa, Z = −3.372, P = 0.001) [Figure 3b and 3f]. Reversely, minimal WSS of stenotic TRA significantly decreased when compared to normal TRA at both end diastole phase (0.07 [0.03, 0.13] Pa vs. 0.52 [0.45, 0.67] Pa, Z = −3.382, P = 0.001) and peak systole phase (0.08 [0.03, 0.19] Pa vs. 0.70 [0.60, 0.81] Pa, Z = −2.952, P = 0.001) [Figure 3d and 3h]. The maximal WSS significantly decreased to 118.6 (113.2, 125.1) Pa (Z = −2.810, P = 0.001) at end diastole phase and 180.3 (163.9, 193.4) Pa (Z = −2.154, P = 0.001) at peak systole phase after stent implantation [Figure 3b and 3f].
To accurately compare low WSS region in individual TRAs, the low-WSS region ratio (arealow WSS/areatotal) was introduced to neutralize the variation of vascular or stent area. Arealow WSS referred to dark blue zone and area total meant target vascular or stent area, as shown in Figure 4a and 4c. When compared to normal TRA, low-WSS region ratio significantly increased in stenotic TRA at end diastole phase (0.84 [0.72, 0.93] vs. 0.14 [0.11, 0.16], Z = −3.380, P = 0.001) or at peak systole phase (0.81 [0.74, 0.91] vs. 0.14 [0.13, 0.15], Z = −3.379, P = 0.001) [Figure 4b and 4d]. Notably, low-WSS region ratio did not decrease after stenting either at end diastole phase (0.84 [0.78, 0.91], Z = −0.423, P = 0.672) or at peak systole phase (0.84 [0.78, 0.90], Z = −0.469, P = 0.639) [Figure 4b and 4d].
Mass flow rate in normal, stenotic, and stented transplant renal arteries
Mass flow rate (MFR) of TRA represents blood flow into renal grafts per unit time. The MFR of TRA is shown in Figure 5. Compared to normal TRA, MFR of stenotic TRA significantly decreased at either end diastole phase (1.5 [1.0, 3.0] g/s vs. 11.0 [8.0, 11.3] g/s, Z = −3.420, P = 0.001) or peak systole phase (2.0 [1.3, 3.3] g/s vs. 16.5 [13.0, 20.3] g/s, Z = −3.395, P = 0.001) [Figure 5a and 5c]. When stent was implanted, MFR increased to 8.0 (6.0, 15.5) g/s (Z = −3.414, P = 0.001) at end diastole and 10.0 (9.5, 21.0) g/s (Z = −3.356, P = 0.001) at peak systole [Figure 5a and 5c]. To accurately evaluate blood flow distribution in individual TRAs, MFR ratio (MFRoutlet/MFRinlet) was introduced to neutralize the variation of individuals. The proximal end of iliac artery was defined as the inlet, and the TRA and distal end of iliac artery were defined as the outlets in the present study. Hence, TRA MFR ratio could be expressed as MFRTRA/MFRinlet. When compared to normal TRA, TRA MFR ratio significantly decreased in stenotic TRA at end diastole phase (0.03 [0.02, 0.05] vs. 0.19 [0.15, 0.25], Z = −3.375, P = 0.001) or at peak systole phase (0.04 [0.02, 0.05] vs. 0.20 [0.18, 0.25], Z = −3.375, P = 0.001) [Figure 5b and 5d]. The TRA MFR ratio significantly increased to 0.19 (0.17, 0.21) (Z = −3.375, P = 0.001) at end diastole phase and 0.20 (0.18, 0.21) (Z = −3.373, P = 0.001) at peak systole phase after stent implantation [Figure 5b and 5d].
This study demonstrated the hemodynamic characteristics of TRAS and its alteration after stent treatment using a patient-specific CFD model. Maximal velocity increased by 2 times, maximal WSS increased by 4–6 times, and MFR decreased by 80% when comparing TRAS to normal TRA. Stent implantation restored or ameliorated the alterations of the above hemodynamic factors. Low-WSS region ratio significantly increased in TRAS by 8 times and remained unchanged after stent implantation.
As observed, pressure significantly dropped across stenosis throat and produced an adverse pressure gradient, which is prone to destabilize the blood flow. Meanwhile, retardation of flow velocity led to a separation of adjacent vessel blood from the inner mainstream, and thus caused the formation of downstream separation zone. The separation zone is considered to be harmful since it may prolong the resident time of blood at poststenosis area. A remarkable increased WSS at stenosis throat was observed. It is of note that the maximum WSS was approximately 412 Pa and 370 Pa at peak systole and end diastole phase, respectively, which is much higher than the published data in artery stenosis. According to the formula of WSS, changes in lumen radius might result in significant changes of WSS. Hence, one possible explanation for our results is the significantly narrow lumen radius in the present study. The degree of all stenosis enrolled in this study was over 70% and even up to 90% in some TRAS.
Large low WSS area was observed at the downstream of stenosis in this study. The large low WSS area may accelerate stenosis progression or lead to secondary stenosis unless timely treatment is implemented. It is reported that distal region of stenotic artery is more prone to develop atherosclerosis. Multiple stenosis usually occurred at the downstream of a diseased vascular bed due to low WSS area distal to the primary stenosis. The possible mechanism is that low WSS can influence the development of neointimal hyperplasia and lead to stenosis by triggering inflammatory cell-mediated destructive remodeling. MFR dramatically decreased in stenotic TRA, which is in accordance with the finding that MFR appeared with apparent reduction when stenosis degree was over 50%.
It is not surprising to find that hemodynamics of TRAS was significantly improved by stent implantation in the aspects of uniform pressure distribution, ameliorated vortex and separation zone, corrected abnormal velocity, decreased maximal WSS, and increased MFR. However, it is of note that large low WSS area was found at stent region, and low-WSS region ratio remained unchanged after stent implantation. This is in accordance with findings from published studies on stented coronary and vertebral arteries. The influence of stent on geometry of vessel wall has not been fully understood. Nevertheless, alteration in cross-sectional geometry after stent implantation exerts an important impact on WSS distributions, which may play roles in subsequent restenosis. Low WSS is reported to be related to endothelial cell proliferation and formation of in-stent neointima.
Our study has several limitations that deserve to mention. First, although CFD can provide clinically relevant hemodynamic information, more clinical studies and analyses should be carried out to prove the accuracy and validity. Second, the basis of CFD methodology is governed by the transient Navier–Stokes equations with the fluid assumed as an incompressible non-Newtonian, laminar fluid. The effect of artery compliance and blood flow waveform was not considered in the present study. The biological response of the vascular wall was not considered here, and merely hemodynamic effects were investigated.
In conclusion, our study revealed that the hemodynamics including pressure distribution, velocity, WSS, and MFR changed significantly when TRAS occurred by CFD based on a patient-specific model. Moreover, stent implantation may leave an intrinsic risk factor for restenosis of TRAS. Further studies are needed to determine its effect on clinical outcome.
Financial support and sponsorship
This study was supported by grants from the Science and Technology Planning Project of Guangdong Province (No. 2014B020212006), the Science and Technology Program of Guangzhou (No. 2014Y2-00114), and the Guangdong Provincial Key Laboratory on Organ Donation and Transplant Immunology (No. 2013A 061401007).
Conflicts of interest
There are no conflicts of interest.
We thank Dr. Dicken S. Ko from Massachusetts General Hospital of Harvard Medical School for his critical comments and polishing work on the manuscript.
1. Willicombe M, Sandhu B, Brookes P, Gedroyc W, Hakim N, Hamady M, et al Postanastomotic transplant renal artery stenosis: Association with de novo
class II donor-specific antibodies Am J Transplant. 2014;14:133–43 doi: 10.1111/ajt.12531
2. Chen W, Kayler LK, Zand MS, Muttana R, Chernyak V, DeBoccardo GO. Transplant renal artery stenosis: Clinical manifestations, diagnosis and therapy Clin Kidney J. 2015;8:71–8 doi: 10.1093/ckj/sfu132
3. Franco D, Milde F, Klingauf M, Orsenigo F, Dejana E, Poulikakos D, et al Accelerated endothelial wound healing on microstructured substrates under flow Biomaterials. 2013;34:1488–97 doi: 10.1016/j.biomaterials.2012.10.007
4. Samady H, Eshtehardi P, McDaniel MC, Suo J, Dhawan SS, Maynard C, et al Coronary artery wall shear stress is associated with progression and transformation of atherosclerotic plaque and arterial remodeling in patients with coronary artery disease Circulation. 2011;124:779–88 doi: 10.1161/CIRCULATIONAHA.111.021824
5. Stone PH, Coskun AU, Kinlay S, Clark ME, Sonka M, Wahle A, et al Effect of endothelial shear stress on the progression of coronary artery disease, vascular remodeling, and in-stent restenosis in humans In vivo
6-month follow-up study Circulation. 2003;108:438–44 doi: 10.1161/01.CIR.0000080882.35274.AD
6. Tse KM, Chang R, Lee HP, Lim SP, Venkatesh SK, Ho P. A computational fluid dynamics study on geometrical influence of the aorta on haemodynamics Eur J Cardiothorac Surg. 2013;43:829–38 doi: 10.1093/ejcts/ezs388
7. Chaichana T, Sun Z, Jewkes J. Computational fluid dynamics analysis of the effect of plaques in the left coronary artery Comput Math Methods Med 2012. 2012:504367 doi: 10.1155/2012/504367
8. Schneiders JJ, Marquering HA, Antiga L, van den Berg R, VanBavel E, Majoie CB. Intracranial aneurysm neck size overestimation with 3D rotational angiography: The impact on intra-aneurysmal hemodynamics
simulated with computational fluid dynamics AJNR Am J Neuroradiol. 2013;34:121–8 doi: 10.3174/ajnr.A3179
9. Qiao A, Dai X, Niu J, Jiao L. Hemodynamics
in stented vertebral artery ostial stenosis based on computational fluid dynamics simulations Comput Methods Biomech Biomed Eng. 2016;19:1190–200 doi: 10.1080/10255842.2015.1123253
10. Piskin S, Serdar Celebi M. Analysis of the effects of different pulsatile inlet profiles on the hemodynamical properties of blood flow in patient specific carotid artery with stenosis Comput Biol Med. 2013;43:717–28 doi: 10.1016/j.compbiomed.2013.02.014
11. Sinha Roy A, Back LH, Banerjee RK. Guidewire flow obstruction effect on pressure drop-flow relationship in moderate coronary artery stenosis J Biomech. 2006;39:853–64 doi: 10.1016/j.jbiomech.2005.01.020
12. Zhang W, Qian Y, Lin J, Lv P, Karunanithi K, Zeng M. Hemodynamic analysis of renal artery stenosis using computational fluid dynamics technology based on unenhanced steady-state free precession magnetic resonance angiography: Preliminary results Int J Cardiovasc Imaging. 2014;30:367–75 doi: 10.1007/s10554-013-0345-0
13. Kagadis GC, Skouras ED, Bourantas GC, Paraskeva CA, Katsanos K, Karnabatidis D, et al Computational representation and hemodynamic characterization of in vivo
acquired severe stenotic renal artery geometries using turbulence modeling Med Eng Phys. 2008;30:647–60 doi: 10.1016/j.medengphy.2007.07.005
14. Bit A, Chattopadhyay H. Numerical investigations of pulsatile flow in stenosed artery Acta Bioeng Biomech. 2014;16:33–44 doi: 10.5277/ABB-00029-2014-05
15. Wolters BJ, Rutten MC, Schurink GW, Kose U, de Hart J, van de Vosse FN. A patient-specific computational model of fluid-structure interaction in abdominal aortic aneurysms Med Eng Phys. 2005;27:871–83 doi: 10.1016/j.medengphy.2005.06.008
16. Piskin S, Serdar CM. Analysis of the effects of different pulsatile inlet profiles on the hemodynamical properties of blood flow in patient specific carotid artery with stenosis Comput Biol Med. 2013;43:717–28 doi: 10.1016/j.compbiomed.2013.02.014
17. Ghirardo G, De Franceschi M, Vidal E, Vidoni A, Ramondo G, Benetti E, et al Transplant renal artery stenosis in children: Risk factors and outcome after endovascular treatment Pediatr Nephrol. 2014;29:461–7 doi: 10.1007/s00467-013-2681-7
18. Becker BN, Odorico JS, Becker YT, Leverson G, McDermott JC, Grist T, et al Peripheral vascular disease and renal transplant artery stenosis: A reappraisal of transplant renovascular disease Clin Transplant. 1999;13:349–55 doi: 10.1034/j.1399-0012.1999.130412.x
19. Messerli FH, Bangalore S, Makani H, Rimoldi SF, Allemann Y, White CJ, et al Flash pulmonary oedema and bilateral renal artery stenosis: The Pickering syndrome Eur Heart J. 2011;32:2231–5 doi: 10.1093/eurheartj/ehr056
20. Chien S, Usami S, Taylor HM, Lundberg JL, Gregersen MI. Effects of hematocrit and plasma proteins on human blood rheology at low shear rates J Appl Physiol. 1966;21:81–7
21. Doyle B, Caplice N. Plaque neovascularization and antiangiogenic therapy for atherosclerosis J Am Coll Cardiol. 2007;49:2073–80 doi: 10.1016/j.jacc.2007.01.089
22. Rikhtegar F, Pacheco F, Wyss C, Stok KS, Ge H, Choo RJ, et al Compound ex vivo
and in silico method for hemodynamic analysis of stented arteries PLoS One. 2013;8:e58147 doi: 10.1371/journal.pone.0058147
23. Chun MS. Electrokinetic secondary-flow behavior in a curved microchannel under dissimilar surface conditions Phys Rev E Stat Nonlin Soft Matter Phys. 2011;83(3 Pt 2):036312 doi: 10.1103/PhysRevE.83.036312
24. Dardik A, Chen L, Frattini J, Asada H, Aziz F, Kudo FA, et al Differential effects of orbital and laminar shear stress on endothelial cells J Vasc Surg. 2005;41:869–80 doi: 10.1016/j.jvs.2005.01.020
25. Li ZY, Tan FP, Soloperto G, Wood NB, Xu XY, Gillard JH. Flow pattern analysis in a highly stenotic patient-specific carotid bifurcation model using a turbulence model Comput Methods Biomech Biomed Engin. 2015;18:1099–107 doi: 10.1080/10255842.2013.873033
26. Filardi V. Carotid artery stenosis near a bifurcation investigated by fluid dynamic analyses Neuroradiol J. 2013;26:439–53 doi: 10.1177/197140091302600409
27. Moore JE Jr, Xu C, Glagov S, Zarins CK, Ku DN. Fluid wall shear stress measurements in a model of the human abdominal aorta: Oscillatory behavior and relationship to atherosclerosis Atherosclerosis. 1994;110:225–40 doi: 10.1016/0021-9150(94)90207-0
28. Malek AM, Alper SL, Izumo S. Hemodynamic shear stress and its role in atherosclerosis JAMA. 1999;282:2035–42 doi: 10.1001/jama. 282.21.2035
29. Rikhtegar F, Wyss C, Stok KS, Poulikakos D, Müller R, Kurtcuoglu V. Hemodynamics
in coronary arteries with overlapping stents J Biomech. 2014;47:505–11 doi: 10.1016/j.jbiomech.2013.10.048
30. Frauenfelder T, Boutsianis E, Schertler T, Husmann L, Leschka S, Poulikakos D, et al In-vivo
flow simulation in coronary arteries based on computed tomography datasets: Feasibility and initial results Eur Radiol. 2007;17:1291–300 doi: 10.1007/s00330-006-0465-1
31. Wentzel JJ, Gijsen FJ, Stergiopulos N, Serruys PW, Slager CJ, Krams R. Shear stress, vascular remodeling and neointimal formation J Biomech. 2003;36:681–8 doi: 10.1016/s0021-9290(02)00446-3
Edited by: Yuan-Yuan Ji
Keywords:© 2017 Chinese Medical Association
Hemodynamics; Kidney Transplantation; Patient-specific Modeling; Renal Artery Obstruction