Patient-specific simulation of coronary artery pressure measurements: an in vivo three-dimensional validation study in humans

Computational fluid dynamics modeling of coronary artery blood flow using OpenFOAM: Validation with the food and drug administration benchmark nozzle model

Cardiovascular disease (CVD), a global health concern, particularly coronary artery disease (CAD), poses a significant threat to well-being. Seeking safer and cost-effective diagnostic alternatives to invasive coronary angiography, noninvasive coronary computed tomography angiography (CCTA) gains prominence. This study employed OpenFOAM, an open-source Computational Fluid Dynamics (CFD) software, to analyze hemodynamic parameters in coronary arteries with serial stenoses. Patient-specific three-dimensional (3D) models from CCTA images offer insights into hemodynamic changes. OpenFOAM breaks away from traditional commercial software, validated against the FDA benchmark nozzle model for reliability. Applying this refined methodology to seventeen coronary arteries across nine patients, the study evaluates parameters like fractional flow reserve computed tomography simulation (FFRCTS), fluid velocity, and wall shear stress (WSS) over time. Findings include FFRCTS values exceeding 0.8 for grade 0 stenosis and falling below 0.5 for grade 5 stenosis. Central velocity remains nearly constant for grade 1 stenosis but increases 3.4-fold for grade 5 stenosis. This research innovates by utilizing OpenFOAM, departing from previous reliance on commercial software. Combining qualitative stenosis grading with quantitative FFRCTS and velocity measurements offers a more comprehensive assessment of coronary artery conditions. The study introduces 3D renderings of wall shear stress distribution across stenosis grades, providing an intuitive visualization of hemodynamic changes for valuable insights into coronary stenosis diagnosis.

Patient-Specific Numerical Simulations of Coronary Artery Hemodynamics and Biomechanics: A Pathway to Clinical Use

PURPOSE

Numerical models that simulate the behaviors of the coronary arteries have been greatly improved by the addition of fluid-structure interaction (FSI) methods. Although computationally demanding, FSI models account for the movement of the arterial wall and more adequately describe the biomechanical conditions at and within the arterial wall. This offers greater physiological relevance over Computational Fluid Dynamics (CFD) models, which assume the walls do not move or deform. Numerical simulations of patient-specific cases have been greatly bolstered by the use of imaging modalities such as Computed Tomography Angiography (CTA), Magnetic Resonance Imaging (MRI), Optical Coherence Tomography (OCT), and Intravascular Ultrasound (IVUS) to reconstruct accurate 2D and 3D representations of artery geometries. The goal of this study was to conduct a comprehensive review on CFD and FSI models on coronary arteries, and evaluate their translational potential.

METHODS

This paper reviewed recent work on patient-specific numerical simulations of coronary arteries that describe the biomechanical conditions associated with atherosclerosis using CFD and FSI models. Imaging modality for geometry collection and clinical applications were also discussed.

RESULTS

Numerical models using CFD and FSI approaches are commonly used to study biomechanics within the vasculature. At high temporal and spatial resolution (compared to most cardiac imaging modalities), these numerical models can generate large amount of biomechanics data.

CONCLUSIONS

Physiologically relevant FSI models can more accurately describe atherosclerosis pathogenesis, and help to translate biomechanical assessment to clinical evaluation.

Coronary computed tomography angiography-based endothelial wall shear stress in normal coronary arteries

Endothelial wall shear stress (ESS) is a biomechanical force which plays a role in the formation and evolution of atherosclerotic lesions. The purpose of this study is to evaluate coronary computed tomography angiography (CCTA)-based ESS in coronary arteries without atherosclerosis, and to assess factors affecting ESS values. CCTA images from patients with suspected coronary artery disease were analyzed to identify coronary arteries without atherosclerosis. Minimal and maximal ESS values were calculated for 3-mm segments. Factors potentially affecting ESS values were examined, including sex, lumen diameter and distance from the ostium. Segments were categorized according to lumen diameter tertiles into small (< 2.6 mm), intermediate (2.6-3.2 mm) or large (≥ 3.2 mm) segments. A total of 349 normal vessels from 168 patients (mean age 59 ± 9 years, 39% men) were included. ESS was highest in the left anterior descending artery compared to the left circumflex artery and right coronary artery (minimal ESS 2.3 Pa vs. 1.9 Pa vs. 1.6 Pa, p < 0.001 and maximal ESS 3.7 Pa vs. 3.0 Pa vs. 2.5 Pa, p < 0.001). Men had lower ESS values than women, also after adjusting for lumen diameter (p < 0.001). ESS values were highest in small segments compared to intermediate or large segments (minimal ESS 3.8 Pa vs. 1.7 Pa vs. 1.2 Pa, p < 0.001 and maximal ESS 6.0 Pa vs. 2.6 Pa vs. 2.0 Pa, p < 0.001). A weak to strong correlation was found between ESS and distance from the ostium (ρ = 0.22-0.62, p < 0.001). CCTA-based ESS values increase rapidly and become widely scattered with decreasing lumen diameter. This needs to be taken into account when assessing the added value of ESS beyond lumen diameter in highly stenotic lesions.

Detailed behaviour of endothelial wall shear stress across coronary lesions from non-invasive imaging with coronary computed tomography angiography

AIMS

Evolving evidence suggests that endothelial wall shear stress (ESS) plays a crucial role in the rupture and progression of coronary plaques by triggering biological signalling pathways. We aimed to investigate the patterns of ESS across coronary lesions from non-invasive imaging with coronary computed tomography angiography (CCTA), and to define plaque-associated ESS values in patients with coronary artery disease (CAD).

METHODS AND RESULTS

Symptomatic patients with CAD who underwent a clinically indicated CCTA scan were identified. Separate core laboratories performed blinded analysis of CCTA for anatomical and ESS features of coronary atherosclerosis. ESS was assessed using dedicated software, providing minimal and maximal ESS values for each 3 mm segment. Each coronary lesion was divided into upstream, start, minimal luminal area (MLA), end and downstream segments. Also, ESS ratios were calculated using the upstream segment as a reference. From 122 patients (mean age 64 ± 7 years, 57% men), a total of 237 lesions were analyzed. Minimal and maximal ESS values varied across the lesions with the highest values at the MLA segment [minimal ESS 3.97 Pa (IQR 1.93-8.92 Pa) and maximal ESS 5.64 Pa (IQR 3.13-11.21 Pa), respectively]. Furthermore, minimal and maximal ESS values were positively associated with stenosis severity (P < 0.001), percent atheroma volume (P < 0.001), and lesion length (P ≤ 0.023) at the MLA segment. Using ESS ratios, similar associations were observed for stenosis severity and lesion length.

CONCLUSIONS

Detailed behaviour of ESS across coronary lesions can be derived from routine non-invasive CCTA imaging. This may further improve risk stratification.

Transient wall shear stress estimation in coronary bifurcations using convolutional neural networks

BACKGROUND AND OBJECTIVE

Haemodynamic metrics, such as blood flow induced shear stresses at the inner vessel lumen, are associated with the development and progression of coronary artery disease. Understanding these metrics may therefore improve the assessment of an individual's coronary disease risk. However, the calculation of such luminal Wall Shear Stress (WSS) using traditional Computational Fluid Dynamics (CFD) methods is relatively slow and computationally expensive. As a result, CFD based haemodynamic computation is not suitable for integrated and large-scale use in clinical settings.

METHODS

In this work, deep learning techniques are proposed as an alternative method to CFD, whereby luminal WSS magnitude can be predicted in coronary bifurcations throughout the cardiac cycle based on the steady state solution (which takes <120 seconds to calculate including preprocessing), vessel geometry and additional global features. The deep learning model is trained on a dataset of 101 patient-specific and 2626 synthetic left main bifurcation models with 26 separate patient-specific cases used as the test set.

RESULTS

The model showed high fidelity predictions with <5% (normalised against mean WSS magnitude) deviation to CFD derived values as the gold-standard method, while being orders of magnitude faster with on average <2 minutes versus 3 hours computation for transient CFD.

CONCLUSIONS

This method therefore offers a new approach to substantially reduce the computational cost involved in, for example, large-scale population studies of coronary haemodynamic metrics, and may therefore open the pathway for future clinical integration.

Investigating the effects of external pressure on coronary arteries with plaques and its role in coronary artery disease

The risk of an acute coronary event stems from the amount and type of plaque present, as well as the fluid and structural dynamics in the coronary artery. If the plaque's structural stress exceeds the mechanical strength, the fibrous cap may rupture and lead to thrombosis. The patient is then likely to face a sudden myocardial infarction. An association between Coronary Heart Disease (CHD) and Sudden Cardiac Death (SCD) has been long recognised. For the first time, we are reporting a correlation between applied external pressure, such as Cardiopulmonary Resuscitation (CPR), coughing, sneezing, blowing one's nose, etc., and diseased coronary artery plaque via 3 D coronary artery models and two-way Fluid-Solid Interaction (FSI) models. Shear and von Mises stresses inside arteries and plaques have been shown to play a major role in plaque development, progression of disease, and the likelihood of plaque rupture. Our results show a drastic change in maximum shear (300%) and von Mises stresses (500%) with increasing external pressure. This change may indicate an onset of imminent plaque rupture. Furthermore, FSI modelling indicates a strong correlation between plaque thickness, location, and external pressure. With further clinical and simulation studies, this information could be helpful in understanding potential limit pressure in the CPR process for patients with CHD.

Non-Invasive Flow Ratio (NiFR) Measurement based on Angiography Images

Background:

Fractional flow reserve (FFR) is a gold standard to assess the impact of stenosis on the blood flow. The FFR method enhances diagnostic accuracy, lessens the need for stenting, and reduces costs. However, FFR is used in less than 10% of percutaneous coronary intervention (PCI) procedures because it needs pressure wires to measure the distal and proximal pressures and adenosine to create hyperemic conditions. Pressure-wire-based FFR measurement is, therefore, expensive and invasive.

Objective:

This study aims to introduce a new approach on the basis of 3D coronary angiography and the Thrombolysis in Myocardial Infarction (TIMI) frame count for fast computation of FFR in patients with coronary artery disease.

Material and Methods:

In this simulation study, we herein introduce Non-Invasive Flow Ratio drawing upon CFD to measure FFR based on coronary angiography images with less run time. In this study, 3D geometry was created based on coronary angiography images. The mean volumetric flow rate was calculated using the TIMI frame count. FFR calculated based on CFD was compared with pressure-wire-based FFR and NiFR was calculated in 85 patients.

Results:

The NiFR (r = 0.738, P< 0.001) exhibited a strong correlation with pressure-wire-based FFR. The result indicated that FFR was higher than 0.8 in the arteries with non-signif­icant stenosis and lower than 0.8 in the arter­ies with significant stenosis.

Conclusion:

The computational simulation of FFR and hemodynamic parameters such as pressure drop is a safe, efficient, and cost-effective method to evaluate the severity of coronary stenosis.

CT-based fractional flow reserve: development and expanded application

Computations of fractional flow reserve, based on CT coronary angiography and computational fluid dynamics (CT-based FFR) to assess the severity of coronary artery stenosis, was introduced around a decade ago and is now one of the most successful applications of computational fluid dynamic modelling in clinical practice. Although the mathematical modelling framework behind this approach and the clinical operational model vary, its clinical efficacy has been demonstrated well in general. In this review, technical elements behind CT-based FFR computation are summarised with some key assumptions and challenges. Examples of these challenges include the complexity of the model (such as blood viscosity and vessel wall compliance modelling), whose impact has been debated in the research. Efforts made to address the practical challenge of processing time are also reviewed. Then, further application areas—myocardial bridge, renal stenosis and lower limb stenosis—are discussed along with specific challenges expected in these areas.

Relationship of Endothelial Shear Stress with Plaque Features with Coronary CT Angiography and Vasodilating Capability with PET

Background Advances in three-dimensional reconstruction techniques and computational fluid dynamics of coronary CT angiography (CCTA) data sets make feasible evaluation of endothelial shear stress (ESS) in the vessel wall. Purpose To investigate the relationship between CCTA-derived computational fluid dynamics metrics, anatomic and morphologic characteristics of coronary lesions, and their comparative performance in predicting impaired coronary vasodilating capability assessed by using PET myocardial perfusion imaging (MPI). Materials and Methods In this retrospective study, conducted between October 2019 and September 2020, coronary vessels in patients with stable chest pain and with intermediate probability of coronary artery disease who underwent both CCTA and PET MPI with oxygen 15-labeled water or nitrogen 13 ammonia and quantification of myocardial blood flow were analyzed. CCTA images were used in assessing stenosis severity, lesion-specific total plaque volume (PV), noncalcified PV, calcified PV, and plaque phenotype. PET MPI was used in assessing significant coronary stenosis. The predictive performance of the CCTA-derived parameters was evaluated by using area under the receiver operating characteristic curve (AUC) analysis. Results There were 92 coronary vessels evaluated in 53 patients (mean age, 65 years ± 7; 31 men). ESS was higher in lesions with greater than 50% stenosis versus those without significant stenosis (mean, 15.1 Pa ± 30 vs 4.6 Pa ± 4 vs 3.3 Pa ± 3; P = .004). ESS was higher in functionally significant versus nonsignificant lesions (median, 7 Pa [interquartile range, 5-23 Pa] vs 2.6 Pa [interquartile range, 1.8-5 Pa], respectively; P ≤ .001). Adding ESS to stenosis severity improved prediction (change in AUC, 0.10; 95% CI: 0.04, 0.17; P = .002) for functionally significant lesions. Conclusion The combination of endothelial shear stress with coronary CT angiography (CCTA) stenosis severity improved prediction of an abnormal PET myocardial perfusion imaging result versus CCTA stenosis severity alone. © RSNA, 2021 Online supplemental material is available for this article. See also the editorial by Kusmirek and Wieben in this issue.

Blood Flow Modeling in Coronary Arteries: A Review

Atherosclerosis is one of the main causes of cardiovascular events, namely, myocardium infarction and cerebral stroke, responsible for a great number of deaths every year worldwide. This pathology is caused by the progressive accumulation of low-density lipoproteins, cholesterol, and other substances on the arterial wall, narrowing its lumen. To date, many hemodynamic studies have been conducted experimentally and/or numerically; however, this disease is not yet fully understood. For this reason, the research of this pathology is still ongoing, mainly, resorting to computational methods. These have been increasingly used in biomedical research of atherosclerosis because of their high-performance hardware and software. Taking into account the attempts that have been made in computational techniques to simulate realistic conditions of blood flow in both diseased and healthy arteries, the present review aims to give an overview of the most recent numerical studies focused on coronary arteries, by addressing the blood viscosity models, and applied physiological flow conditions. In general, regardless of the boundary conditions, numerical studies have been contributed to a better understanding of the development of this disease, its diagnosis, and its treatment.

Computational fluid dynamic-derived wall shear stress of non-significant left main bifurcation disease may predict acute vessel thrombosis at 3-year follow-up

Wall shear stress (WSS) plays a pivotal role on plaque progression in coronary artery disease. We assess the prognostic role of baseline mean WSS in developing a bifurcation-located myocardial infarction (B-MI) over the following 3 years in angiographically non-significant LM bifurcation disease. For this purpose, we retrospectively reviewed the procedural and medical records of consecutive patients evaluated in our center from 1st January 2014 to 1st January 2019 who had a non-significant LM bifurcation disease as evaluated at coronary computed tomography angiography (CCTA) and confirmed by coronary angiography. Each bifurcation model was reconstructed on the patient-specific geometries derived from the CCTA. The population was divided into two groups: patients with (n = 12) and without B-MI (n = 20) over the following 3 years. Both the mean WSSprox of each branch and the WSSentire_lesion of each vessel, adjusted for the respective mean lesions lengths and 3-dimensional percentage of stenosis (DS%), resulted in independent predictors of 3-year B-MI. Multivariate Cox-regression analysis confirmed that a baseline mean WSSentire_model ≥ 5.05 Pa (HR 1.98, 95% CI 1.83-2.10, p = 0.001) was a predictor of 3-year B-MI independently from the entire mean lesions lengths (HR 1.56. 95% CI 1.43.1.68, p = 0.002) and DS% (HR 1.26, 95% CI 1.18-1.37, p = 0.03). In conclusion, in patients with angiographically non-significant LM bifurcation disease, both the mean WSSprox of each branch and WSSentire_lesion of each stenotic vessel predicted the occurrence of B-MI over the following 3 years. Moreover, the WSSentire_bifurcation ≥ 5.05 Pa seems to be a predictor of 3-year B-MI independently from the DS% and lesions lengths.

Optimal Site for Proximal Optimization Technique in Complex Coronary Bifurcation Stenting: A Computational Fluid Dynamics Study

BACKGROUND/PURPOSE

The optimal position of the balloon distal radio-opaque marker during the post optimization technique (POT) remains debated. We analyzed three potential different balloon positions for the final POT in two different two-stenting techniques, to compare the hemodynamic effects in terms of wall shear stress (WSS) in patients with complex left main (LM) coronary bifurcation.

METHODS/MATERIALS

We reconstructed the patient-specific coronary bifurcation anatomy using the coronary computed tomography angiography (CCTA) data of 8 consecutive patients (6 males, mean age 68.2± 18.6 years) affected by complex LM bifurcation disease. Subsequently a virtual bench test was performed in each patient using two different double stenting techniques represented by the DK and Nano crush using the reconstruction of Orsiro stents (Biotronik IC, Bulack, Switzerland).

RESULTS

A significant reduction in the mean WSS values in all the lesion's sites was observed when the final POT was performed 1 mm distally the carina cut plane in both techniques. Moreover, a significant improvement in the mean WSS values of the entire SB (e.g. LCX) was obtained performing the POT 1 mm distally to the carina cut plane. The proximal POT resulted in larger area of lower WSS values at the carina using both the Nano crush and the DK crush techniques.

CONCLUSIONS

In patients with complex LM bifurcation disease the use of a final POT performed 1 mm distally to the carina cut plane might results in more favorable WSS patterns (i.e. higher WSS values) along all stented segments and, especially, along the entire LCX lesions.

Integrating Patient-Specific Electrocardiogram Signals and Image-Based Computational Fluid Dynamics Method to Analyze Coronary Blood Flow in Patients during Cardiac Arrhythmias

Purpose

The aim of this study was to use the computational fluid dynamics (CFD) method, patient-specific electrocardiogram (ECG) signals, and computed tomography three-dimensional image reconstruction technique to investigate the blood flow in coronary arteries during cardiac arrhythmia.

Methods

Two patients with premature ventricular contraction-type cardiac arrhythmia and one with atrial fibrillation-type cardiac arrhythmia were investigated. The inlet velocity of the coronary artery in simulation was applied with the measured velocity profile of the left ventricular outflow tract (LVOT) from the Doppler echocardiography. The measured patient central aortic blood pressure waveform was employed for the coronary artery outlet in simulation. The no-slip boundary condition was applied to the arterial wall.

Results

For the patient with irregular cardiac rhythms (Case I), the coronary blood flow rate under the shortened and lengthened cardiac rhythms were 0.66 and 0.96 mL/s, respectively. In Case II, the maximum velocity at the LVOT under a normal heartbeat was found to be 101 cm/s, whereas the average value was 73 cm/s. In Case III, the patient was also diagnosed with a congenital stenosis problem at the myocardial bridge (MCB) at the LAD. The measured blood flow rate at the MCB of the LAD for the three heartbeats in Case III was found to be 0.68, 1.08, and 1.14 mL/s.

Conclusion

The integration of patient-specific ECG signals and image-based CFD methods can clearly analyze hemodynamic information for patients during cardiac arrhythmia. The cardiac arrhythmia can reduce the blood flow in the coronary arteries.

Impact of Inflow Boundary Conditions on the Calculation of CT-Based FFR

Background: Calculation of fractional flow reserve (FFR) using computed tomography (CT)-based 3D anatomical models and computational fluid dynamics (CFD) has become a common method to non-invasively assess the functional severity of atherosclerotic narrowing in coronary arteries. We examined the impact of various inflow boundary conditions on computation of FFR to shed light on the requirements for inflow boundary conditions to ensure model representation. Methods: Three-dimensional anatomical models of coronary arteries for four patients with mild to severe stenosis were reconstructed from CT images. FFR and its commonly-used alternatives were derived using the models and CFD. A combination of four types of inflow boundary conditions (BC) was employed: pulsatile, steady, patient-specific and population average. Results: The maximum difference of FFR between pulsatile and steady inflow conditions was 0.02 (2.4%), approximately at a level similar to a reported uncertainty level of clinical FFR measurement (3–4%). The flow with steady BC appeared to represent well the diastolic phase of pulsatile flow, where FFR is measured. Though the difference between patient-specific and population average BCs affected the flow more, the maximum discrepancy of FFR was 0.07 (8.3%), despite the patient-specific inflow of one patient being nearly twice as the population average. Conclusions: In the patients investigated, the type of inflow boundary condition, especially flow pulsatility, does not have a significant impact on computed FFRs in narrowed coronary arteries.

Optimized Computer-Aided Segmentation and Three-Dimensional Reconstruction Using Intracoronary Optical Coherence Tomography

We present a novel and time-efficient method for intracoronary lumen detection, which produces three-dimensional (3-D) coronary arteries using optical coherence tomographic (OCT) images. OCT images are acquired for multiple patients and longitudinal cross-section (LOCS) images are reconstructed using different acquisition angles. The lumen contours for each LOCS image are extracted and translated to 2-D cross-sectional images. Using two angiographic projections, the centerline of the coronary vessel is reconstructed in 3-D, and the detected 2-D contours are transformed to 3-D and placed perpendicular to the centerline. To validate the proposed method, 613 manual annotations from medical experts were used as gold standard. The 2-D detected contours were compared with the annotated contours, and the 3-D reconstructed models produced using the detected contours were compared to the models produced by the annotated contours. Wall shear stress (WSS), as dominant hemodynamics factor, was calculated using computational fluid dynamics and 844 consecutive 2-mm segments of the 3-D models were extracted and compared with each other. High Pearson's correlation coefficients were obtained for the lumen area (r = 0.98) and local WSS (r = 0.97) measurements, while no significant bias with good limits of agreement was shown in the Bland-Altman analysis. The overlapping and nonoverlapping areas ratio between experts' annotations and presented method was 0.92 and 0.14, respectively. The proposed computer-aided lumen extraction and 3-D vessel reconstruction method is fast, accurate, and likely to assist in a number of research and clinical applications.

Position Paper Computational Cardiology

Computational cardiology is the scientific field devoted to the development of methodologies that enhance our mechanistic understanding, diagnosis and treatment of cardiovascular disease. In this regard, the field embraces the extraordinary pace of discovery in imaging, computational modeling, and cardiovascular informatics at the intersection of atherogenesis and vascular biology. This paper highlights existing methods, practices, and computational models and proposes new strategies to support a multidisciplinary effort in this space. We focus on the means by that to leverage and coalesce these multiple disciplines to advance translational science and computational cardiology. Analyzing the scientific trends and understanding the current needs we present our perspective for the future of cardiovascular treatment.

Behaviour of two typical stents towards a new stent evolution

This study explores the analysis of a new stent geometry from two typical stents used to treat the coronary artery disease. Two different finite element methods are applied with different boundary conditions to investigate the stenosis region. Computational fluid dynamics (CFD) models including fluid-structure interaction are used to assess the haemodynamic impact of two types of coronary stents implantation: (1) type 1-based on a strut-link stent geometry and (2) type 2-a continuous helical stent. Using data from a recent clinical stenosis, flow disturbances and consequent shear stress alterations introduced by the stent treatment are investigated. A relationship between stenosis and the induced flow fields for the two types of stent designs is analysed as well as the correlation between haemodynamics and vessel wall biomechanical factors during the initiation and development of stenosis formation in the coronary artery. Both stents exhibit a good performance in reducing the obstruction artery. However, stent type 1 presents higher radial deformation than the type 2. This deformation can be seen as a limitation with a long-term clinical impact.

Coronary fractional flow reserve measurements of a stenosed side branch: a computational study investigating the influence of the bifurcation angle

Background

Coronary hemodynamics and physiology specific for bifurcation lesions was not well understood. To investigate the influence of the bifurcation angle on the intracoronary hemodynamics of side branch (SB) lesions computational fluid dynamics simulations were performed.

Methods

A parametric model representing a left anterior descending—first diagonal coronary bifurcation lesion was created according to the literature. Diameters obeyed fractal branching laws. Proximal and distal main branch (DMB) stenoses were both set at 60 %. We varied the distal bifurcation angles (40°, 55°, and 70°), the flow splits to the DMB and SB (55 %:45 %, 65 %:35 %, and 75 %:25 %), and the SB stenoses (40, 60, and 80 %), resulting in 27 simulations. Fractional flow reserve, defined as the ratio between the mean distal stenosis and mean aortic pressure during maximal hyperemia, was calculated for the DMB and SB (FFR_SB) for all simulations.

Results

The largest differences in FFR_SB comparing the largest and smallest bifurcation angles were 0.02 (in cases with 40 % SB stenosis, irrespective of the assumed flow split) and 0.05 (in cases with 60 % SB stenosis, flow split 55 %:45 %). When the SB stenosis was 80 %, the difference in FFR_SB between the largest and smallest bifurcation angle was 0.33 (flow split 55 %:45 %). By describing the ΔP_SB−Q_SB relationship using a quadratic curve for cases with 80 % SB stenosis, we found that the curve was steeper (i.e. higher flow resistance) when bifurcation angle increases (ΔP = 0.451*Q + 0.010*Q² and ΔP = 0.687*Q + 0.017*Q² for 40° and 70° bifurcation angle, respectively). Our analyses revealed complex hemodynamics in all cases with evident counter-rotating helical flow structures. Larger bifurcation angles resulted in more pronounced helical flow structures (i.e. higher helicity intensity), when 60 or 80 % SB stenoses were present. A good correlation (R² = 0.80) between the SB pressure drop and helicity intensity was also found.

Conclusions

Our analyses showed that, in bifurcation lesions with 60 % MB stenosis and 80 % SB stenosis, SB pressure drop is higher for larger bifurcation angles suggesting higher flow resistance (i.e. curves describing the ΔP_SB−Q_SB relationship being steeper). When the SB stenosis is mild (40 %) or moderate (60 %), SB resistance is minimally influenced by the bifurcation angle, with differences not being clinically meaningful. Our findings also highlighted the complex interplay between anatomy, pressure drops, and blood flow helicity in bifurcations.