Figure 1 shows the workflow of the study. Briefly, starting from CT and Doppler ultrasound (DUS) data of human stented femoral arteries, three-dimensional (3D) patient-specific geometrical models of SFAs were reconstructed at multiple follow-ups and used to perform CFD simulations. A morphological analysis quantified the lumen remodeling over time in terms of lumen area change between consecutive follow-ups. Hemodynamics was investigated in terms of WSS-based descriptors. After a preliminary spatial decorrelation analysis, the hemodynamic results were combined with the morphological data to investigate the link between hemodynamics and ISR development. Finally, clinical information, such as age, diabetes, stent length and presence of stent overlapping were included in the statistical analysis.
Clinical Dataset
Patients suffering from peripheral artery disease were screened at Malcom Randall VAMC (Gainesville, FL, USA) between 2007 and 2012 to identify those who were treated with self-expanding stents and consented to post-operative CT scan protocol (Fig. 2). Seven individuals (for a total of ten lesions, A-K, Table 1), treated with the EverFlex stent (EV3, Medtronic, Dublin, Ireland), presented the necessary CT and DUS data. Specifically, the CT and DUS data were gathered at 1-week (1W), 1-month (1M), 6-month (6M, except for one patient without usable CT data), and 1-year (1Y) post-operative follow-ups. The study was conducted in accordance with the principles of the Declaration of Helsinki and met the requirement of medical ethics. The study protocol was approved by the institutional review board at University of Florida and each participant provided the written consent.
The baseline demographics and medical history (diabetes and coronary artery disease) of the selected patients are provided in Table 1, along with the intervention outcome (failure/success at post-operative 2-year), the stent length and the presence of stent overlapping (observed by visual inspection of CT images). The patients were all male, with an average age of 63.6±7.3 years (mean ± standard deviation).
3D Reconstruction and Hemodynamic Analysis
Patient-specific SFA geometrical models (Fig. 3) were reconstructed from CT using a previously developed reconstruction method.10 In detail, a first raw 3D vessel reconstruction, including the common femoral artery bifurcation, was obtained by applying an active contour method, based on a level set algorithm.10 Then, the obtained geometrical model was automatically corrected in both the stented and non-stented regions through calibrated thresholds and freed from metallic artifacts and calcifications.10
The SFA models were used for both the morphological analysis (all the follow-ups) and the computation of hemodynamics (1W, 1M and 6M follow-ups). Regarding the CFD simulations, the models were discretized into tetrahedral elements considering curvature-based refinement and a prismatic boundary layer using ICEM CFD (v.18.2, Ansys Inc., Canonsburg, PA, USA). The element size was based on a previously performed mesh-independence study,10 resulting in a mesh cardinality ranging from 2,013,029 to 8,535,680 elements in the models A at 6M and K at 1W follow-up, respectively. Transient CFD simulations (n = 23) were performed using the commercial software Fluent (v.18.2, Ansys Inc.), based on the finite volume method. A patient-specific pulsatile flow waveform, derived from the patient’s DUS images, was applied to the inlet of the common femoral artery as a parabolic velocity profile. The sequence of peak velocities from the Doppler spectrum at the level of the common femoral artery was elaborated by applying a previously proposed algorithm29 that enabled the estimation of the patient-specific flow-rate. A flow-split of 0.67:0.33 was applied to the SFA and the profunda femoral artery, respectively.20 The no-slip condition was prescribed at the vessel walls, assumed as rigid. The blood was considered as an incompressible, homogeneous, non-Newtonian fluid with density of 1060 kg/m3 and viscosity described by the Carreau model. Regarding the solver settings, a pressure-based solver with a full implicit coupled scheme for the velocity-pressure coupling was adopted. Second order accuracy was chosen for pressure and momentum spatial discretization, and for time integration. Following a sensitivity analysis,10 the convergence for the continuity and momentum residuals was set to 5·10−5, and the cardiac cycle was discretized into 100 time steps (with time-step size in the range of [0.0061 - 0.0110] seconds, according to the patient-specific case). Further details about the CFD simulations are reported elsewhere.10
Morphological and Hemodynamic Quantities of Interest
Lumen remodeling was quantified by calculating the lumen area change in the stented region (i.e. region of interest) as follows:
$$\Delta A_{i:i + 1} = \, A_{i} - A_{i + 1}$$
(1)
where A is the lumen area, and i is the specific follow-up. Accordingly, a positive lumen area change corresponds to inward remodeling (i.e. lumen reduction), whereas a negative lumen area change to outward remodeling (i.e. lumen enlargement). The fractional rate of lumen area change, normalized by the number of weeks occurred between two consecutive follow-ups, was computed for each time interval (i.e. first, 1W-1M; intermediate, 1M-6M; last, 6M-1Y).
Hemodynamics was investigated by analyzing the WSS vector field along the stented region. In addition to three well-known WSS-based descriptors, namely the time-averaged WSS (TAWSS), oscillatory shear index (OSI), and relative residence time (RRT), the following descriptors of WSS multidirectionality were quantified (Table 2, Fig. Suppl-1): transverse WSS (transWSS),23 i.e. the average of the WSS component perpendicular to the direction of the time-averaged WSS; cross flow index (CFI),23 i.e. the normalized transWSS; time-averaged axial WSS (TAWSSax),24 i.e. the average of the WSS component aligned with the tangent to the vessel centerline; time-averaged secondary WSS (TAWSSsc),24 i.e. the average of the WSS component along the secondary direction; and WSSratio,24 i.e. the ratio between the cycle-averaged magnitude of the secondary and the axial WSS components.
Table 2 Wall shear stress (WSS)-based hemodynamic descriptors. Post-processing of Morphological and Hemodynamic Results
The morphological and CFD results were processed in order to (i) obtain a spatial match between the morphological and hemodynamic data and (ii) consider them as spatially independent, as described elsewhere.8 Briefly, the lumen area was extracted at 0.2 mm axially-spaced cross-sections and averaged every 1 mm in the axial direction. In this way, one-dimensional (1D) maps of the morphological descriptor were obtained. Similarly, the distributions of WSS-based descriptors were re-organized from three- to two-dimensional (2D) maps, with cells of 1 mm in the axial direction and 1 degree in the circumferential one (Fig. Suppl-2), by using the Vascular Modelling Toolkit (VMTK) (Orobix, Bergamo, Italy, http://www.vmtk.org/). To match the 1D morphological data, the WSS-based 2D maps were circumferentially-averaged, obtaining 1D maps (Fig. Suppl-2). The axial discretization of 1 mm was conservative with respect to the CT axial resolution, in the range of [0.87-0.98] mm.
The 1D maps were subjected to the spatial decorrelation analysis, and made mutually independent through the spatial decorrelation length (Ldecorr).8 Ldecorr indicates the minimal length necessary to consider two data points as independent. Differently from our previous work,8 in which the hemodynamics was solely analyzed at baseline, the decorrelation length was computed here for each follow-up and lesion. Thus, considering separately each lesion, the most conservative Ldecorr (range [2–10] mm) among 1W, 1M and 6M follow-ups was considered. Based on the identified Ldecorr, smaller but independent 1D maps of the morphological and hemodynamic data were obtained for each lesion and used in the subsequent statistical analyses.8
Levels of Analysis
The analysis of results was conducted at two levels,8 namely (i) global level (i.e. between-stent level of analysis), by considering one representative averaged morphological and hemodynamic value for each lesion and each follow-up, and (ii) local level (i.e. within-stent level of analysis) by collecting, for each follow-up, the independent results contained in the lesion-specific arrays into a unique, combined array.
Morphological Progression
The lumen morphology of the entire stented regions was analyzed to investigate the lumen remodeling trajectory (whole-lesion analysis). Furthermore, the following additional investigations were considered:
-
i.
Remodeling trajectory in fringe/mid portions of the lesion (segmental analysis). The stented region was subdivided into three groups: proximal and distal fringes (first and last two decorrelated points of the patient- and time-specific arrays), and the in-between (mid) portion.
-
ii.
Remodeling trajectory in lesions treated with short and long stents. The lesions were subdivided into the following two groups: the lesions treated with short stents (range [40–120] mm, lesions A, B, F and H—Fig. 3, Table 1) and those treated with long stents (≥ 150 mm, considering together the multiple stents).
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iii.
Remodeling trajectory in overlapped/non-overlapped portions of the stents. Five lesions (lesions C-E, J and K—Fig. 3, Table 1) presenting with stent overlapping were analyzed by identifying three groups: the regions upstream or downstream from the overlapping and the region with stent overlapping.
Hemodynamics and ISR Progression
The relationship between hemodynamics and lumen remodeling over time was investigated in the entire stented regions to understand if:
-
i.
the lumen area change ∆Ai: i+1 is associated to the WSS-based descriptors computed at the beginning of the time interval (i);
-
ii.
the WSS-based descriptors at current follow-up (i) affects the lumen area at the subsequent follow-up Ai+1;
-
iii.
the change of WSS-based descriptors in the current time interval (i:i+1) influences the lumen area change in the subsequent time interval ∆Ai+1: i+2.
Statistical Analysis
Data were presented as either mean ± standard deviation or median (interquartile range), depending on the distribution. The normality of the distributions was evaluated using Kolmogorov-Smirnov test.
To examine the lumen remodeling, the comparison of the lumen area distributions at each follow-up and of the fractional rate of lumen area change in the different time intervals was performed. The different groups were compared using analysis of variance or Kruskal-Wallis tests. Then, the individual distributions were tested through Mann-Whitney U or Friedman tests. The linear regression between the lumen area change in each time interval and the lumen area at the beginning of that time interval was also applied.
To measure the direction and strength of the association between WSS-based descriptors and lumen remodeling, the Spearman’s rank-order correlation coefficient was considered. Moreover, to evaluate the probability that luminal surface areas exposed to disturbed shear can successfully identify corresponding regions with large lumen area change, the positive predictive value (PPV) was computed. To do so, objective thresholds of disturbed shear stress were defined by combining the follow-up and lesion-specific WSS-based data.8 The 33th percentile was identified for TAWSS, TAWSSax and TAWSSsc; the 66th percentile was chosen for the other WSS-based descriptors. The percentage of luminal surface area exposed to disturbed shear stress (lower or higher than the given thresholds, depending on the WSS-based descriptor) was computed for each follow-up. The lumen area change was distinguished in low/high according to the 66th distribution percentile.
To integrate the previous investigations, linear mixed models were also built to evaluate the relationship between the lumen area change and one of the WSS-based descriptors, plus clinical data (i.e. patient’s age, presence of comorbidities like diabetes and coronary artery disease, and failure at 2-year post-intervention) and the categorical variable of follow-up time. The analyses were performed by considering the patient as the random factor to account for multiple measures.
The statistical analyses were performed using GraphPrism (v.8.3.1, GraphPad Software) and SAS (v.9.4, SAS Institute). A two-tailed, p-value < 0.05 was considered to be statistically significant.