Multi-Scale, Patient-Specific Computational Flow Dynamics Models Predict Formation of Neointimal Hyperplasia in Saphenous Vein Grafts

Bypass occlusion due to neointimal hyperplasia (NIH) is among the major causes of peripheral graft failure. Its link to abnormal hemodynamics in the graft is complex, and isolated use of hemodynamic markers insufficient to fully capture its progression. Here, a computational model of NIH growth is presented, establishing a link between computational fluid dynamics (CFD) simulations of flow in the lumen, with a biochemical model representing NIH growth mechanisms inside the vessel wall. For all 3 patients analyzed, NIH at proximal and distal anastomoses was simulated by the model, with values of stenosis comparable to the computed tomography (CT) scans.


Introduction
Autogenous vein bypass is the most common technique for peripheral arterial revascularization for severe peripheral arterial diseases but is prone to develop neointimal hyperplasia (NIH), a leading cause of bypass failure. 1 Both experimental studies and clinical observations suggest that one of the factors destabilizing the remodeling process is a lower level of wall shear stress on the arterial wall, 2 Table I). 3,4 We hypothesized that both low and oscillatory levels of shear stress should be considered simultaneously when assessing the proclivity of a certain region in bypass grafts to develop NIH, 5,6 and we simulated NIH progression using a multi-scale computational framework that we previously developed, 7 comparing our results to a patient-specific clinical dataset (obtained with the patients' informed consent for research and publication).

Methods
The computational framework was informed by patient-specific imaging data, including anatomical images and hemodynamic markers. Doppler scans immediately after surgery and CT scans at 8, 19 and 24 months after surgery (for patients 1-3, respectively) were obtained from routine clinical studies after approval from the institutional review board (IRB) (approval number AD0009, Veteran Affairs Connecticut Healthcare System, West Haven, CT, USA).
CT scans immediately after surgery were not available, as the data was acquired retrospectively from selected patients that received standard of care with regular postoperative surveillance.
Postoperative surveillance, at the institution where data was collected, is only performed via duplex ultrasound, as it is noninvasive, does not require nephrotoxic dye, is reproducible, and correlates with outcomes as documented with extensive literature, and as such, CT scans are only obtained when the duplex ultrasound suggested an abnormality and additional anatomic information is required. In order to overcome these limitations, a 'baseline' configuration (representing the vein-graft conditions right after implantation) was obtained by processing the images and 'virtually removing' regions of NIH growth, well in line with other work in the literature. [8][9][10][11][12][13][14][15] Data required deidentification despite IRB approval in compliance to VA requirements for patients' privacy.
CFD analyses were performed as described in a previous publication. 7 A non-Newtonian Carreau-Yasuda model was used for blood viscosity, with parameters reported in previous studies. 16 For comparison, simulations were also run with a Newtonian model (viscosity of 0.035 dynes•s /cm 2 ). Inflow conditions were described by flow curves obtained from Doppler scans. These were applied first with a flat profile, and with a parabolic profile in a different set of simulations for comparison. Boundary conditions at the outlets were implemented via twoelement Windkessel models of the external vasculature (Supplementary Figure 1), tuned to patient-specific data on a 0D model (Supplementary Table II).
Simulation results were processed using ANSYS CFD Post (Ansys, Inc.). Hemodynamic stress indices linked to vascular remodeling, specifically TAWSS and a term encompassing low shear together with oscillations -the highly oscillatory, low magnitude shear (HOLMES) - Table I) were extracted at each node and imported into a mathematical model of NIH progression, described in Supplementary Figure 2. The output of the simulation model for each patient is the predicted (calculated) values of NIH growth along the graft, following the same blueprint described in our previous work, 7 and summarized in Supplementary Table   III. In a nutshell, based on the 'base' configuration for each patient (a vein-graft free of NIH, representing conditions just after implantation), CFD analyses are coupled to a mathematical (time-dependent) model of NIH growth that takes into account smooth muscle cells and 5 collagen turnover, growth factors and NO production. This is a dynamic simulation process that captures the transformation of the vein-graft due to NIH and mimics the evolution of the disease for each patient, in time. A diagram of the different cases is presented in

Results
Hemodynamic analyses were performed on all three bypass geometries (Figure 1)

Discussion
These results highlight the impact of two different measures of wall shear stress, TAWSS and HOLMES, and the importance of the interaction between TAWSS and OSI in NIH progression (Supplementary Figure 6). In all cases, the simulation model correctly predicted areas of NIH growth, with values that were similar to the stenoses observed in the CT scans when using the HOLMES index, with a maximum discrepancy (presented as % area) of 8% between stenosis values observed in patients 1-3 when compared to CT scans (Figure 3). When using TAWSS, not all NIH-stenotic regions are predicted and for those that are, the amount of luminal narrowing is consistently underestimated and sometimes by a significant amount -as in the case of patient 3 -with a reported difference in terms of NIH growth area of 41% (Figure 3).
This suggests that TAWSS is an unreliable metric to estimate both plaque location and the degree of stenosis in vein-grafts.
CFD has been used to analyze the hemodynamics of grafts for multiple cardiovascular procedures, such as endovascular repair, 21 coronary stenting 22 and AVF. 23 Much less research has been reported on mechanisms of failure of peripheral bypasses, with most reported work focused on design optimization. 24 This preliminary study of 3 patients couples CFD analyses with a model of smooth muscle cells and collagen turnover, including growth factor and NO production. 7 The results show a change from an initial, predominantly homogeneous distribution of smooth muscle cells and collagen at day 146 to a localized area of growth corresponding to areas in which the graft experienced low shear and oscillations ( Supplementary Figure 4 and 5). In addition, our analysis shows that morphometric indicators alone might not be enough to identify successful grafts. For instance, torsion has been observed to be one of the key factors affecting large vessel hemodynamics, 25

Conclusions
In the application of a multi-scale model of NIH on three different patient-specific cases, the HOLMES index was the best predictor for the location of NIH progression that corresponded to developing stenoses identifiable in CT scans. Results also suggest that TAWSS is an unreliable predictor of NIH growth. The analysis demonstrated how multiscale modeling may play an important role in the post-revascularization management of PAD patients, and specifically, in delineating those at risk of developing NIH.

Acknowledgements
The authors gratefully acknowledge support by the Leverhulme Trust Senior Research