Early Atherosclerotic Changes in Coronary Arteries are Associated with Endothelium Shear Stress Contraction/Expansion Variability

Although unphysiological wall shear stress (WSS) has become the consensus hemodynamic mechanism for coronary atherosclerosis, the complex biomechanical stimulus affecting atherosclerosis evolution is still undetermined. This has motivated the interest on the contraction/expansion action exerted by WSS on the endothelium, obtained through the WSS topological skeleton analysis. This study tests the ability of this WSS feature, alone or combined with WSS magnitude, to predict coronary wall thickness (WT) longitudinal changes. Nine coronary arteries of hypercholesterolemic minipigs underwent imaging with local WT measurement at three time points: baseline (T1), after 5.6 ± 0.9 (T2), and 7.6 ± 2.5 (T3) months. Individualized computational hemodynamic simulations were performed at T1 and T2. The variability of the WSS contraction/expansion action along the cardiac cycle was quantified using the WSS topological shear variation index (TSVI). Alone or combined, high TSVI and low WSS significantly co-localized with high WT at the same time points and were significant predictors of thickening at later time points. TSVI and WSS magnitude values in a physiological range appeared to play an atheroprotective role. Both the variability of the WSS contraction/expansion action and WSS magnitude, accounting for different hemodynamic effects on the endothelium, (1) are linked to WT changes and (2) concur to identify WSS features leading to coronary atherosclerosis. Supplementary Information The online version contains supplementary material available at 10.1007/s10439-021-02829-5.

images were triggered in diastole. Both IVUS and CCTA images were then used to reconstruct the pig-specific coronary artery geometries at T1 and T2. In detail, at each time point IVUS images were segmented into lumen contours with QCU-CMS software (Leiden, The Netherlands), and then aligned along the 3D centerline extracted from CCTA images using the MeVisLab software (MeVis Medical Solutions AG, Bremen, Germany). As previously reported 2 , IVUS and CCTA images were matched using side branches as anatomical landmarks. The resulting geometries are displayed in Figure S1. Finally, the geometrical dimensions of each swine-specific coronary artery at time points T1 and T2 of the study are reported in Table S1 in terms of mean radius section and main vessel length.

Numerical Settings
Individual in vivo ComboWire Doppler velocity measurements were used to derive individualized boundary conditions according to the following strategy: (1) the inlet flow rate was estimated from the most proximal Doppler velocity measurement, and prescribed as inlet boundary condition in terms of time-dependent flat velocity profile; (2) the perfusion of side branches was quantified as the difference between Doppler velocity-based flow rate measurements taken upstream and downstream from each side branch and applied as outflow condition in terms of measured flow ratio. If velocity-based flow measurements were inaccurate or not available, a diameter-based scaling law 4 was applied to estimate the flow ratio at the outflow section 3,6 . No-slip condition was assumed at the arterial wall.
The computational fluid dynamics (CFD) code Fluent (ANSYS Inc., Canonsburg, PA, USA) was used on fluid domains discretized in ICEM CFD (ANSYS Inc., USA), by means of tetrahedrons and a 5-layers prismatic boundary layer. Blood was modelled as an incompressible (with density equal to 1060 kg/m 3 ), non-Newtonian fluid using the Carreau model, belonging to the family of the generalized Newtonian fluids, whose dynamic viscosity is defined as: where, is the shear rate, and = 0.0035 kg m -1 s -1 , = m -1 s -1 , = 25 s, = 0.25 1 .
Second order accuracy was prescribed to solve both the momentum equation and pressure with the COUPLED pressure-velocity coupling scheme. The backward Euler implicit scheme was adopted for time integration, with a fixed time increment defined as the measured swine-specific cardiac period divided by 100 3,5,6 . Convergence was achieved when the maximum mass and momentum residuals fell below 10 -5 . All CFD setting (including mesh element size) were based on a sensitivity analysis 6 , allowing only differences in terms of WSS lower than 1%.

Supplemental Results
The number and nature of instantaneous WSS fixed points at the coronary luminal surface was analysed and compared at time points T1 and T2. Their distribution, median and quartile range is presented in Figure S2. As expected, at T1 and T2 the number of WSS saddle points was higher than the number of WSS sinks and sources. Moreover, the occurrence of instantaneous WSS saddle points, sinks and sources was differently distributed at both time points T1 and T2, with saddle points distribution differing significantly from those of sinks (p=0.04 at T1 and p=0.0073 at T2, respectively; Figure S2) and sources (p=0.032 at T1 and p=0.0053 at T2; Figure S2). Conversely, no significant differences emerged between sink and source occurrence (p=0.67 at T1 and p=0.93 at T2, respectively; Figure S2). Figure S3 reports the luminal distribution of TSVI (quantifying the variation of WSS contraction/expansion action along the cardiac cycle) at T1 and T2, together with the distribution of measured WT at time points T1, T2 and T3 along the follow-up study, for all the investigated coronary models. By visual inspection it emerged that, in general, regions exhibiting high WT values markedly co-localized with luminal surface areas interested by a greater variation of WSS contraction/expansion action along the cardiac cycle ( Figure S3). In detail, it resulted that ( Figure   S3): (1) Figure S3); (4) the decrease in TSVI from T1 to T2 corresponded to luminal surface areas of WT regression from T2 to T3 (luminal regions highlighted by dashed black circles in Figure S3).
Tables S2 reports the odds ratios with associated confidence intervals quantifying the strength of the association between the luminal exposure to WSS-based quantities and high WT outcomes, as already displayed in Figure 5 of the main text.
Tables S3 reports the odds ratios with associated confidence intervals quantifying the strength of the association between the luminal exposure to WSS-based quantities and low WT outcomes, as already displayed in Figure 6 of the main text. Figure S1. Geometry of the 9 swine coronary artery models at T1 and T2 of the follow-up time. Labels from A to C identify a single swine. For each swine, LAD, LCX and RCA geometries were reconstructed.