The effect of subbranch for the quantification of local hemodynamic environment in the coronary artery: a computed tomography angiography–based computational fluid dynamic analysis : Emergency and Critical Care Medicine

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The effect of subbranch for the quantification of local hemodynamic environment in the coronary artery: a computed tomography angiography–based computational fluid dynamic analysis

Shi, Yibinga; Zheng, Jinb; Yang, Ninga; Chen, Yangc; Sun, Jingxia; Zhang, Yinga; Zhou, Xuanxuana; Gao, Yongguanga; Li, Suqinga; Zhu, Haijingd; Acosta-Cabronero, Julioe; Xia, Pinga,∗; Teng, Zhongzhaob,c,e,∗

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Emergency and Critical Care Medicine 2(4):p 181-190, December 2022. | DOI: 10.1097/EC9.0000000000000062
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Cardiovascular diseases are the no. 1 killer globally.[1,2] Rupture of atherosclerotic plaques is the main cause of ischemic cardiovascular diseases. Atherosclerosis is commonly referred to as the accumulation of fatty and/or fibrous material in the intima.[2,3] Imaging-defined luminal stenosis is currently the only validated diagnostic criterion for clinical decision-making with a threshold of 70%.[4] However, serious limitations exist. It has been observed that approximately only 15% of patients with acute coronary syndrome have luminal stenosis of greater than 70%.[5] However, it has been accepted for many decades that most acute coronary events arise from the rupture of mildly to moderately stenotic plaques.[5] Detailed lesion morphologic and compositional features are more relevant to patients’ clinical presentations and subsequent ischemic events.[6–8] Postmortem studies showed that most victims with cardiac arrests were caused by high-risk plaques characterized by large lipid cores and thin fibrous caps.[9] These features can be captured by minimally invasive imaging modalities, including virtual histology intravascular ultrasound[7,8] and optical coherence tomography,[6] and provide incremental prognostic value for significant coronary artery stenosis.[10] However, prospective studies have shown that future clinical event rates attributable to high-risk plaques were <10% for 3 years.[6,7] Therefore, additional biomarkers are needed to improve the prediction power for subsequent ischemic events.

Under physiological conditions, atherosclerotic plaques are subject to mechanical loading induced by dynamic blood pressure, blood flow, and heartbeat. The growth and rupture of a plaque are affected by the local hemodynamic environment.[11,12] Mechanical stimuli induced by blood flow are to be physiologically, pathologically, and clinically relevant. For example, low and oscillatory wall shear stresses (WSSs) contribute to the initialization and development of coronary atherosclerosis. The cross-lesion fractional flow reserve (FFR) is associated with downstream perfusion and is used to guide stenting. Computed tomography angiography (CTA)–based computational fluid dynamics (CFD) modeling is a popular noninvasive approach that quantifies the local hemodynamic environment and calculates the above parameters.[12,13]

Despite the growing popularity of CTA-based CFD analysis, the accuracy of hemodynamic parameter calculation has not been assessed comprehensively. The results of the CTA-based CFD analysis largely depend on the model geometry, which includes the configuration of the arteries and subbranches, and loading conditions, which are the flow rates at the inlet and outlets. CTA can visualize small distal branches with a dimension of approximately 0.5 mm, but it is difficult for smaller subbranches. Although it is nontrivial when small distal branches are considered, not all branches can be considered in practice because of their resolution and the limitation of image processing algorithm. A common way is to remove branches that are not of interest. However, the impact of such removal has not been comprehensively quantified. Previous studies have emphasized the importance of side branches in estimating the WSS, although there are inconsistencies in the influence of pressure-related parameters, such as CTA-derived FFR.[14–18]

This study was designed to investigate whether there was a possibility to remove branch segments to reduce preprocessing time and computational cost and to quantify the changes induced by the removal. A patient-specific model developed from CTA images was used to assess the effects of branch removal. CFD–related parameters, including time-averaged pressure (TAP), time-averaged WSS (TAWSS), oscillatory shear index (OSI), and relative residence time (RRT), were compared with the changes in boundary conditions from removing branch segments in regions around the stenosis. The effect of branch removal on the hemodynamic environment upstream along the arterial centerline was also examined.

Materials and methods

Patient-specific model reconstruction

CTA images were obtained from a 69-year-old man. A calcified stenosis, approximately 50%, was present at the proximal left anterior descending (LAD) artery (Fig. 1A). The resolution of the CTA images was 0.383 × 0.383 × 0.5 mm3. The patient’s luminal segmentation was automatically generated by Aladdin CT-VascularView (Nanjing Jingsan Medical Science and Technology, Ltd, Nanjing, China). A total of 22 coronary segments were classified into 4 levels in the left coronary artery (LCA) branches (Supplementary Fig. 1, Level 0 was defined as the segment directly coming out of the aorta. Levels 1 to 3 branch segments were the child branch segments that were 1 level higher than their parent branch segments. The coronary segments were further corrected along each segment’s centerline to generate a smooth surface mesh (Fig. 1B). To create a smooth surface mesh, the CTA image and segmentation were straightened and resampled to 0.5 × 0.5 × 0.5 mm3 along the branch centerline. Threshold and active contours without border algorithms were used to improve the straightened luminal segmentation.[19,20] The surface mesh was smoothed using Taubin’s algorithm.[21] All coronary artery outlets were clipped and extended with a length of 10 times of the local diameter to eliminate the outlet effects. There were a total of 230,036 tetrahedral elements and 199,599 prismatic elements in the model with all 22 LCA segments as shown by Model 0 in Fig. 1C. This model was used as a baseline to compare the effects of branch removal. The mesh-dependency analyses and an example of the complete model used for CFD simulation were provided in the Supplementary Figures 6 and 7 (,

Figure 1:
Overview of the analysis process. (A) On the left-hand side, a curved multiplanar reconstruction of the LAD artery from the patient’s CTA. Focal stenosis approximately 50% was present at the pLAD artery section. The middle section shows a zoom-in view of the plaque and the anterior and posterior regions of the calcified plaque. Four ROIs were longitudinally assigned at and around the plaque, as shown by ROIs 1 to 4 in the middle section. ROIs 2 and 3 were the anterior and posterior half of the plaque with half the plaque length. ROIs 1 and 4 were the anterior and posterior regions of the plaque with the same plaque length. Four points, a, b, c, and d, of interest were chosen to observe the parameter variation among different models. Points a and d were the longitudinal shoulder points between ROIs 1 and 2, and 3 and 4. Points b and c were the circumferential points at the plaque cap and shoulder at the maximal stenosis. (B) The smoothed surface mesh of the complete model with all LCA, aortic root, and RCA segments generated from the CTA segmentation. (C–F) TAP, TAWSS, OSI, and RRT computed from the fluid dynamics (CFD) simulation of the complete LCA tree. CFD, computational fluid dynamics; CTA, computed tomography angiography; LAD, left anterior descending; LCA, left coronary artery; OSI, oscillatory shear index; pLAD, proximal LAD; RCA, right coronary artery; ROIs, regions of interest; RRT, relative residence time; TAP, time-averaged pressure; TAWSS, TAWSS, time-averaged wall shear stress.

Computational fluid dynamic simulation

The CFD simulation was performed on ADINDA 9.6 (ADINA R&D Inc, MA, USA). The blood flow was assumed to be incompressible, transient-laminar, viscous, and Newtonian. The blood density was 1.06 g/cm3 with a viscosity of 0.035 poise. The governing equation was the incompressible Navier-Stokes equation,

ρvt+ρv·v=p+μ2v Eq. 1

where v is the flow velocity, p is the pressure, and μ and ρ are blood viscosity and density, respectively. The no-slip boundary condition was applied at the luminal surface.

Time-dependent pressure loading was applied at the aortic inlet with time-dependent blood flows at the outlets of the aorta and coronary arteries. The pressure waveform and flow waveforms were adapted from a previous study,[22] and the average amount of blood inflow was determined from the reference.[23] Four percent of the total inflow was assumed to be distributed between coronary arteries.[24] Blood flow distribution among coronary arteries obeyed Murray’s[25] law as follows:

QDδAδ/2 Eq. 2

QbranchQmain=AbranchAmainδ/2 Eq. 3

in which Q is the blood flow, D is the diameter, and A is the average area. The empirical constant δ was set to be 2.6. The simulation was run over 5 cardiac cycles, and results from the last cardiac cycle were extracted for analysis.

Branch removal

Levels 1 to 3 of LCA branch segments were removed sequentially to investigate the effect of branch removal (Fig. 2). Only branch segments from LAD artery and left circumflex artery were removed. The branch removal strategies included removing a pair of Level 3, Level 2, or Level 2 and Level 1 child branches of the same parent branch (Models 5, 6, 10–12, and 15–17). For instance, Model 6 removes the distal LAD (dLAD) artery and the second diagonal branch (D2) from mid LAD artery. The other 2 branch removal strategies were to remove all branch segments of the same level (Models 1–4, 13, and 14) and to remove only a single branch segment (Models 7–9, 18, and 19).

Figure 2:
All models used in this study. Model 0 (baseline model): all LCA segments. Model 1: no Level 2 (L2) branch. Model 2: no Level 3 (L3) branches. Model 3: LAD artery without L2 branches and LCX without L3 branches. Model 4: LAD artery without L3 branches. Model 5: LAD artery without mLAD artery and D1. Model 6: LAD artery without dLAD artery and D2. Model 7: LAD artery without zeroth diagonal branch (D0) and D1. Model 8: LAD artery without D0. Model 9: LAD artery without D1. Model 10: LAD artery without the pair of branches of D1 (D1x). Model 11: LAD artery without the pair of branches of D2 (D2x). Model 12: LAD artery without the pair of branches of dLAD (dLADx) artery. Model 13: LCX without L2 and LAD artery without L3. Model 14: LCX without L3. Model 15: LCX without mLCX and zeroth obtuse marginal branch (OM0). Model 16: LCX without mLCX and OM1. Model 17: LCX without dLCX and OM2. Model 18: LCX without OM0. Model 19: LCX without OM1. D1, first diagonal branch; D2, second diagonal branch; dLAD, distal LAD; dLCX, distal LCX; LAD, left anterior descending; LCA, left coronary artery; LCX, left circumflex artery; mLCX, mid LCX; OM1, first obtuse marginal branch; OM2, second obtuse marginal branch.

The change in outlet branches affected the total outflow of not only the whole artery tree, the LCA artery tree, and the corresponding artery tree, such as the LAD artery tree. The outflow measurements and differences were derived from Eq. 3,

QCA,out=QCA,branch=AbranchAmainδ/2QCA,in Eq. 4

Outflow difference=QCA,inQCA,outQCA,in×100% Eq. 5

where QCA,out and QCA,in are the total blood outflow and inflow of a coronary artery tree. QCA,branch is the blood outflow of each distal coronary artery segment of the corresponding coronary artery tree. For example, QCA,branch is the blood outflow of the 7 coronary segments, which are the 3 child branch pairs of dLAD artery, first diagonal branch (D1), D2, and the single zeroth diagonal branch (D0) in the LAD artery tree (Supplementary Fig. 1, in the complete Model 0 in Fig. 1C.

Postprocessing and analysis

Four parameters, TAP, TAWSS, OSI, and RRT, were calculated based on the simulation results extracted from the last cardiac cycle.[26] TAP is the distribution of average force per unit area, pressure (p), over the whole cardiac cycle (Tc) on the artery wall surface,[26]

TAP=1Tc0Tcpdt Eq. 6

Time-averaged WSS is the temporal average of the WSS (τw) over the entire cardiac cycle (Tc). A low TAWSS could be related to atherogenesis,[26]

TAWSS=1Tc0Tcτwdt Eq. 7

OSI measures the change in WSS direction and magnitude during a cardiac cycle. A high OSI indicates the region of recirculating blood flow,[26]

OSI=1210Tcτwdt0Tcτwdt Eq. 8

RRT is the relative residual time of a particle that is inversely proportional to the traveled distance of the particle during a cardiac cycle,[26]

RRT = [(1 − 2 × OSI) × TAWSS]−1 Eq. 9

TAP, TAWSS, OSI, and RRT at 4 points (a, b, c, and d in Fig. 1A) were extracted from the 20 models for the location-matched comparison. Points a and b are at the beginning and finishing locations, the longitudinal shoulder region, of the plaque in the proximal LAD artery. Points c and d are at the circumferential shoulder and middle of cap regions of the plaque.

Four luminal regions of interest (ROIs) were assigned to investigate the branch removal effect at and around the plaque in the proximal LAD artery, as shown in Fig. 1A. Regions of interest 2 and 3 are the anterior and posterior halves of the plaque lumen. Regions of interest 1 and 4 are the anterior and posterior luminal regions in front of and after the plaque with the same length as the plaque length. Moreover, luminal regions up to 5-diameter length upstream from the branch cutoff position were used to compare the branch removal effect on the 4 parameters. The relative difference at each node and in each ROI or luminal region was assessed by referring to values in the baseline Model 0,

mk=kbaselinekmodelkbaseline×100%,k=TAPTAWSSOSIRRT Eq. 10

and the absolute values of minima, mean, and maxima of mk were reported to assess the effect of the branch removal.


General description of computational fluid dynamic results

The computed TAP, TAWSS, OSI, and RRT of the baseline model are shown in Fig. 1C–F. There was not a significant drop in the TAP, from 91.40 mmHg to approximately 91.12 mmHg, across the stenosis. The TAWSS was high (2.50–3.50 Pa) at the stenosis and at bending and narrowing distal branches. The low TAWSS positions correspondingly had a high OSI and RRT, and vice versa. In particular, the posterior region of the plaque, around ROI 4, showed a minor drop in TAP (0.28 mmHg), low TAWSS (0.25 Pa), and high OSI (0.17) and RRT (5.98). Results of TAP, TAWSS, OSI, and RRT of the rest 19 models are provided in Supplementary Figures 2–5 (,,,, respectively.

Effect of the branch removal

The effect in the stenotic region

Fig. 3 illustrates the comparison of TAP, TAWSS, OSI, and RRT at the 4 locations (points a, b, c, and d in Fig. 1A) around the stenosis among the 20 models. There were generally negligible changes in TAP of all points a to d among the total 19 models relative to the baseline results, with maximum mTAP being approximately 0.17%. In contrast, the fluctuations in TAWSS, OSI, and RRT were considerable at all 4 points. The maximal absolute mTAWSS, mOSI, and mRRT all occurred at point d with approximately 50% reduction in TAWSS from 0.25 Pa to 0.13 Pa; 150% increase in OSI from 0.17 Pa to 0.43 Pa; and 750% increase in RRT from 5.98 Pa to 50.08 Pa.

Figure 3:
Visualization of parameters from computational fluid dynamics simulation of 20 LCA models at the 4 points in Figure 1A. For OSI and RRT, there are secondary axes for point d whose variation is larger than the other 3 points on the primary axes. OSI, oscillatory shear index; RRT, relative residence time; TAP, time-averaged pressure; TAWSS, time-averaged wall shear stress.

The maximal change in TAWSS occurred in Model 9 without the D1 branch. The maximal changes in OSI and RRT were in Model 1 without Level 2 branches. For points a and c, the maximal absolute mTAWSS, mOSI, and mRRT occurred in Model 7 without the D0 and D1 branches. The differences were approximately 40%, 20%, and 65% in TAWSS, OSI, and RRT for point a, and 40%, 19%, and 66% for point c, respectively. For point b, maxima were 36%, 8%, and 59% in TAWSS, OSI, and RRT in Model 9.

The boxplots in Fig. 4 show the effect in the 4 ROIs of removing different branches at different levels. The lowest level removed from the LCA artery tree was used to cluster models for the comparison (no Level 1: Models 5, 15, and 16; no Level 2: Models 1, 3, 6–9, 13, and 17–19; no Level 3: Models 2, 4, 10–12, and 14). The boxplots of absolute maxima, minima, and mean of mTAP, mTAWSS, mOSI, and mRRT in the 4 ROIs showed that the maximum-minimum ranges of the boxplots of no Level 3 and points of no Level 1 were within the maximum-minimum range of the boxplot of no Level 2. There was little variation of medians between boxplots of no Levels 2 and 3.

Figure 4:
Boxplots and point plotting of difference in the CFD parameters between modified models and the baseline model with 3 branch removing levels. The baseline model is Model 0, and the modified models are Models 1 to 19 in Figure 2. The definitions of levels are shown in Supplementary Figure 1 ( Only 3 models, Model 3, 15, and 16, have Level 1 branch segments removed, so their corresponding points were directly plotted next to boxplots of the other 2 levels. Modified models without Level 2 are Models 1, 3, 6 to 9, 13, and 17 to 19 and without Level 3 are Models 2, 4, 10 to 12, and 14. Outliers of the boxplots are excluded. CFD, computational fluid dynamics; OSI, oscillatory shear index; ROI, region of interest; RRT, relative residence time; TAP, time-averaged pressure; TAWSS, time-averaged wall shear stress.

The effect near the location where the branch was removed

Three models from the LAD artery tree were chosen with the outflow differences <5% (Fig. 5) to assess the upstream propagation of the effect due to the branch removal. The 3 chosen models were 6 (without D2 and dLAD artery), 8 (without D0), and 12 (without dLADx [without the pair of branches of dLAD artery]). In general, the absolute maxima, minima, and mean of mTAP, mTAWSS, mOSI, and mRRT did not significantly vary from each other in the 3- to 5-diameter regions. In particular, the maximum and minimum of mTAP were negligible (<0.05%) across the entire 5-diameter length along the centerline. However, the branch removal had a significant impact on the absolute minimum mTAWSS, which could be as high as 1169% in Model 12 in the region within 1- to 2-diameter length.

Figure 5:
Upstream effect on CFD parameters from branch removal in Models 6, 8, and 12. For Models 6 and 12, there are secondary axes for the 1D difference of which the variation was larger than the other 2 to 5D difference on the primary axes. Models 6, 8, and 12 had outflow differences <5% in the LAD artery. CFD, computational fluid dynamics; D, diameter; LAD, left anterior descending; OSI, oscillatory shear index; RRT, relative residence time; TAP, time-averaged pressure; TAWSS, time-averaged wall shear stress.

Effect of the outflow rate on the stenotic region

The flow rate is one of the key factors affecting the calculation of flow parameters. Nevertheless, it is challenging to quantify flow rate and flow parameters using current noninvasive imaging technologies. The removal of branches led to changes in flow rate and was determined by Equation 3. According to the outflow difference (Eq. 5), the 19 modified models were grouped into 3 clusters, >30% (Models 1, 3, 7, and 9), 5% to 10% (Models 2, 4, 8, 11, and 13), and <5% (Models 5, 6 10, 12, and 14–19). The boxplots in Fig. 6 show how the absolute minimum, maximum, and mean of mk(k = TAP, TAWSS, OSI, RRT) (Eq. 10) vary with the flow rate difference. There was an overall decrease in all characteristics’ differences with the decrease in LAD artery outflow. The maximum was only 0.25% for mTAP, but could reach greater than 50% for mTAWSS, mOSI, and mRRT.

Figure 6:
Boxplots of difference in the CFD parameters between modified models and the baseline model with 3 outflow difference ratios in the LAD artery. The baseline model is Model 0, and the modified models are Models 1 to 19 in Figure 2. Outflow difference ratios are the changes in flow in the LAD artery in the modified model with respect to the baseline model. The outflow difference ratios of 19 modified models were grouped into 3 clusters, >30% (Models 1, 3, 7, and 9), 5% to 10% (Models 2, 4, 8, 11, and 13), and <5% (Models 5, 6, 10, 12, and 14–19). Outliers of the boxplots are excluded. CFD, computational fluid dynamics; LAD, left anterior descending; OSI, oscillatory shear index; ROI, region of interest; RRT, relative residence time; TAP, time-averaged pressure; TAWSS, time-averaged wall shear stress.


This study quantified the influence of subbranch removal on the calculation of local TAP, TAWSS, OSI, and RRT, as well as the influence of the change in outflow rate estimation induced by subbranch removal. Results showed that TAWSS, OSI, and RRT were more sensitive than TAP to the subbranch removal. TAWSS, OSI, and RRT are computed based on the WSS. They are used to describe the blood flow pattern. A low WSS and oscillatory WSS, low TAWSS and/or high OSI, are closely correlated with endothelial cell dysfunction and atherogenesis.[27] A high RRT means a high residence time of a particle in a certain position. This increases the local attachment and infiltration of harmful substances in the blood.[27]

The TAP showed low sensitivity to subbranch removal with mild stenosis but was still associated with the change in outflow conditions due to the removal. Although the TAP values of the 4 points (a, b, c, and d in Fig. 1A) varied in all models (Fig. 3), the actual variation was very limited (0.28 mmHg in Fig. 3 and 0.25% in Fig. 4). Instead of TAP, a popular way to quantify the effect of the stenosis is the ratio of the TAP proximal and distal to the stenosis, which can be CTA-derived FFR, instantaneous wave-free ratio, and resting distal coronary artery pressure/aortic pressure. Distal coronary artery pressure/aortic pressure takes the ratio of TAP at the resting condition and over the entire cardiac cycle.[28] Computed tomography angiography–derived FFR takes the ratio of TAP at the hyperemia condition, instead of resting, over the whole cardiac cycle.[29] Instantaneous wave-free ratio takes the ratio of TAP at resting only over part of the cardiac cycle that is wave-free.[30] All these ratios are used to estimate the downstream myocardial perfusion or the blood flow after stenosis. The TAP is used because of the proportionality between the change in pressure and the change in the flow rate for the ideal incompressible laminar flow. For this mild stenosis case, the TAP ratio, distal coronary artery pressure/aortic pressure, changed only by 0.26% even with a 30% outflow rate reduction.

The effect of removing various branch segments from different levels did not show a clear relation with the change in TAP, TAWSS, OSI, and RRT (Fig. 5). Apart from the considerable relative differences in all 1-diameter regions of Models 6, 8, and 12 and 2-diameter region in Model 12. For Model 8 with the LAD artery outflow difference of approximately 5%, minimum mTAWSS and maximum mRRT were within 5%, and mean mTAWSS, maximum mTAWSS, and maximum mOSI were within 10%. Model 6 with the LAD artery outflow difference of approximately 3% had mean mTAWSS, maximum mTAWSS within 10%, and minimum mTAWSS, maximum mRRT, and maximum mOSI within 15%. %. Model 6 with the LAD artery outflow difference of approximately 2% had all relative differences within 10% expected maximum mOSI within a smaller range of 5%. Nevertheless, the variation of these 4 parameters was closely associated with the outflow rate (Fig. 6) because the removal of subbranches induced the change in flow rate, governed by Murray’s law (Eqs. 2 and 3) and outflow difference (Eqs. 4 and 5). Therefore, it is critical to consider the outflow rate when medical image–based CFD analysis is performed. Although it is not feasible to segment all subbranches and include them in the simulation, the flow rate must be estimated with sufficient accuracy.

This study showed that the effect of removing branch segments was very localized if the difference in outflow rate was small. The effect was limited to a region less than 5-diameter from the cutting-off position (Fig. 5). The maximal difference occurred in the 1-diameter region directly after the cutting-off position. Such significant differences can be explained considering that the 1-diameter region should experience bifurcation with flow distribution in the baseline model but was still flowing in a single duct in the truncated model. For Model 12 with the removal of dLADx artery, there is a much higher variation in the 2-diameter region. The large bending curvature before the cutting-off position may provide a clue. Therefore, branching and bending should also be considered when deciding the branch removal even with an adequate extension. The difference would decrease below 15% within the 5-diameter range when there was a <5% LAD artery outflow difference. The relatively high differences might come from the points where values at the baseline model were small. Although the difference might not be significant, its division by a relatively small value would still yield a high percentage difference.

Compared with TAP, TAWSS, OSI, and RRT were more sensitive in terms of the changes in models and outflows (Figs. 4 and 6). Time-averaged WSS showed a clear decrease with the decrease in outflows, but this tendency was location-dependent. When the outflow difference was <5%, the relative differences of TAWSS in ROIs 1 and 2 were generally <5% (Fig. 6), and those in ROIs 3 and 4 were greater. The complication of the flow after the stenosis and near the bifurcation might affect the TAWSS characteristics in ROIs 3 and 4. Relative residence time showed a similar trend as the TAWSS characteristics. Maximum mOSI was <10% but without clear variation with LAD artery outflow differences in ROIs 1 and 2, and it was generally >10% in ROIs 3 and 4. These observations may be explained by the fact that the flow was not oscillatory and stable in ROIs 1 and 2.

Undoubtedly, the branch removal strategy is beneficial in CFD simulations to reduce workload and save computational power, particularly in cases in which the ROI is focal and does not span the entire arterial segment. Moreover, in all cases, the demands for mesh size and quality are heavy for the distal tiny branches. For example, Model 15 (left circumflex artery without Level 2 branches) with 179,842 tetrahedral elements and 139,207 prismatic elements had the maximal reduction of 110,586 elements compared with the baseline Model 0 in the models with the outflow rate difference <5%. The reduction of elements was approximately a quarter of the total elements in the baseline Model 0, but this did not affect the accuracy of hemodynamic parameters in the ROI. Nevertheless, when removing branches, it is important to keep the outflow difference as little as possible, <5% or less. The branch-removing position should be at least 5 diameters from the ROI. The distance should increase when there are other branches near the ROI and large curvatures near the ROI. Branches close to the ROI should not be removed. Time-averaged pressure is not sensitive to the number of subbranches and boundary condition changes when the stenosis is mild. However, when TAWSS, OSI, and RRT are the parameters of interest, special care should be taken in decision-making to ignore certain subbranches. In short, while keeping the flow rate in the ROI constant, the finding from the current study indicates that the removal of distal branches does not affect the simulation accuracy significantly if there is at least a 5-diameter distance from the cutoff position.

Further studies may compare the other 2 TAP ratios, FFR and instantaneous wave-free ratio, because they are also relevant to the clinical practice. There is also an inconsistency between clear patterns shown of TAP, TAWSS, OSI, and RRT of various points and ambiguous change in the characteristics of these parameters with the changes in outflow, especially for OSI. Moreover, the blood flow is governed by a highly nonlinear equation (Eq. 1), and factors interact with each other nonlinearly. Therefore, a small difference in other loading and boundary conditions might lead to a big difference in the calculation of pressure, WSS, OSI, and RRT. Likely, observations in this study might not be valid in other conditions, for example, arteries with a severe degree of stenosis.


The outflow rate is a dominant factor for the calculation of TAP, TAWSS, OSI, and RRT. Removal of subbranches has a minor effect on the TAP calculation, but its effect is considerable on the TAWSS, OSI, and RRT. The effect of subbranch removal is limited in a region with 5 local diameters.

Conflict of interest statement

Zhongzhao Teng is an Editorial Board member of Emergency and Critical Care Medicine. The article was subject to the journal’s standard procedures, with peer review handled independently of this Editorial Board member and their research groups. Zhongzhao Teng is the Chief Scientist of Tenoke Ltd., UK and Nanjing Jingsan Medical Science & Technology Ltd., China. The other authors have no conflict of interest to disclose.

Author contributions

Shi Y and Yang N provided the patient data, checked the models and revised the manuscript. Zheng J and Chen Y created models, ran CFD simulations, performed the analysis and drafted the manuscript. Sun J and Zhang Y helped to correct the coronary geometry. Zhou X and Gao Y helped in the result extraction. Li S and Zhu H revised the manuscript. Acosta-Cabronero J developed the image processing tool. Teng Z and Xia P designed the study and revised the manuscript significantly.


This research was supported by Bureau of Science and Technology, Xuzhou, People’s Republic of China (KC19176), and the NIHR Cambridge Biomedical Research Centre (BRC-1215-20014).

Ethical approval of studies and informed consent

This study was approved by the ethics Committee of Xuzhou Central Hospital, Jiangsu, People’s Republic of China (Ref: XZXY-LK-20211021-035, October 21, 2021), and written informed consent was obtained from the patient. This manuscript has the consent of the patient for the use of his/her data and for the publication of the data that appear in the article.




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Coronary artery; Hemodynamics; Pressure; Shear stress; Side branch; Stenosis

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