Computational Simulations of Provisional Stenting of a Diseased Coronary Artery Bifurcation Model

Although stenting of non-branched arterial segments has acceptable clinical outcomes, in-stent restenosis (ISR) and stent thrombosis remain clinically significant issues for vascular bifurcations (15–28% restenosis). Local fluid and solid stresses appear to play an important role in restenosis and thrombosis. The combined role of wall shear stress (WSS) and circumferential wall stresses (CWS) is unclear in the case of stenting at vascular bifurcations. Using numerical simulations, we computed the fluid shear, solid stresses and the stress ratio at the the bifurcation region. Stenting of main vessel increased the maximum CWS in the the side branch (SB), resulting in a nearly two-fold increase of stress ratio in the SB compared to the MB (5.1 × 105 vs. 9.2 × 105). The existence of plaque decreased WSS and increased CWS near the carina, increasing the stress ratio at the SB. The changes of stress ratio were highly consistent with clinical data on bifurcation stenting. Fluid dynamics and solids mechanics should be considered in planning of stenting for a specific bifurcation, as their combined biomechanical effect may play an important role in stent restenosis and thrombosis.

www.nature.com/scientificreports www.nature.com/scientificreports/ ρ η ρ where V is fluid velocity, P is fluid pressure, ρ is fluid mass density, η is fluid dynamic viscosity, ∇ → is the gradient operator. D is the fluid rate of deformation tensor.
The governing equations for the solids were the Momentum and Equilibrium equations; i.e., Newton's laws of Mechanics: i i j j i s ,  www.nature.com/scientificreports www.nature.com/scientificreports/ where a i is acceleration, f i is force per unit mass, s Ω(t) is the vessel domain at time t, n j is normal vector, t i is surface traction vector, and σ ij is stress. The stent struts interact with the vessel wall by the Augmented Lagrangian contact algorithm. To model the interactions, contact surfaces were defined. The vessel wall was constrained in the proximal and distal sections to prevent free body movement. flow simulations. The blood was modeled with flow based on human coronary artery velocity measurements applied at the inlet of artery 13,14 . For the outlet, a traction free boundary condition was imposed 5 . The flow was assumed to be non-turbulent. To evaluate the effects of both the solid and fluid mechanics, we introduced a stress ratio as Solid CWS/Fluid WSS. This stress ratio was previously validated for investigation of mechanical disturbances within blood vessels 5 .  (C) The simulations found that stenting of bifurcation with plaque resulted in higher stress ratio than that of without plaque (4.7 × 10 5 vs. 7.9 × 10 5 ).

Results
The Reynolds numbers in the current study was an order of magnitude smaller than the Reynolds number for transition to turbulence (>2,300). Therefore, the current non-turbulent models were appropariate.
For provisional stenting with bifurcation plaque, the stress distribution shows stress concentration at the SB, at interface with plaque near the carina ( Fig. 2A). Stenting of bifurcation with plaque resulted in higher mean stresses than that of without plaque (270 KPa vs. 220 KPa) (Fig. 2B). The fluid WSS distribution in stenting of bifurcation with plaque is shown in Fig. 3. The areas around the plaque and carina had lower WSS. Stenting of bifurcation with plaque resulted in lower WSS than that of without plaque (0.46 Pa vs. 0.34 Pa) (Fig. 3). The simulations found that stenting of bifurcation with plaque resulted in higher stress ratio than that of without plaque (4.7 × 10 5 vs. 7.9 × 10 5 ) (Fig. 3C).
Stenting of bifurcation with plaque resulted in higher mean CWS in SB than MB (290 KPa vs. 230 KPa) (Fig. 4A). Stenting of bifurcation resulted in lower WSS in SB than MB (0.47 Pa vs. 0.32 Pa) (Fig. 4B). The simulations predict the SB to have a nearly twice as large stress ratio as the MB (5.1 × 10 5 vs. 9.2 × 10 5 ) (Fig. 4C). The simulations further predicted that the carina has a much larger stress ratio than the vessel average, due to higher CWS and lower WSS (Fig. 5).

Discussion
Treatment of coronary bifurcation lesions is still one of the most demanding procedures of interventional cardiology. The optimal technique for a particular bifurcation remains unclear due to the wide range of bifurcation anatomy. Numerical simulations is a powerful tool to model a variety of bifurcation geometries and quantify the effects of various stenting techniques on the vessel biomechanics. The major findings of this simulation study are that the decrease of WSS and increase in CWS are greater at SB than MB during provisional stenting. The results show the SB has a larger stress ratio than the MB. Higher re-stenosis rate at SB have been found clinically. The www.nature.com/scientificreports www.nature.com/scientificreports/ restenosis rate at SB was 14.7%, while much lower at 6.7% for the MB 4,7 . This is consistent with simulation findings that the SB to have a larger stress ratio than the MB (Fig. 4).
Intramural stresses are known to be stimuli for tissue remodeling, i.e., vessels develop hyperplasia to reduce intramural stresses. Additionally, low fluid WSS enhances inflammatory processes and promote thrombosis 10,12,14 . Higher restenosis rates of 15% and 28% in the SB were reported in clinical trials (CACTUS and Nordic bifurcation study) using DES 4,15 . In a study of patients with severe coronary disease, Nakazawa et al. found that late stent thrombosis was more prevalent near the carina region 16,17 . The simulations predicted that the carina has a much larger stress ratio than the center of plaque, due to higher CWS and lower WSS (Fig. 5).
It is worth noting that the SB ISR rate (15% to 28%) 4 ) and thrombosis remain high for DES. The lack of hyperplasia on the struts of DES can cause persistent low fluid shear stress which may lead to stent thrombosis. Higher intramural stresses in the vessel wall are stimuli for inflammatory responses such as smooth muscle cell proliferation 10 . Additionally, the higher stresses can potentially cause stent and plaque fracture, leading to acute thrombosis. The frequency of late stent thrombosis was greater in the DES group (75%) than in the BMS group (36%) 16 .
Limitations. This simulation study has the following limitations. First, the kissing-balloon technique was not simulated after provisional stenting of the MB. Kissing balloon is expected to open up the stenosis and struts in the SB near the carina, and normalize the WSS in SB. The simulation of strut interactions with plaque and balloon is beyond the scope of the current study. Second, the typical 60-degree angle was tested between the MB and the SB 18 . For the case of dedicated bifurcation stents, it may be helpful to evaluate the optimal angle as the angle can be adjusted in the device design. This issue may be investigated in future studies. Finally, for the outlet of the vessels, a traction free boundary condition was imposed in the current study. More severe stenosis (e.g., 90%) may affect the outlet traction significantly. Figure 5. The simulations predict that the carina to have a much larger stress ratio as the vessel average, due to higher CWS and lower WSS at carina. The carina region is known to have higher incidences of stent thrombosis [Nakazawa et al., 2010].