The coil intervention is a common aneurysm treatment strategy, but the effect of coil size on aneurysm hemodynamics and mechanics is not fully understood. In this paper, how different sizes of coils affect the hemodynamic and mechanical properties of a real internal carotid artery (ICA) aneurysm was investigated. A fluid-structure interaction (FSI) method based on the Arbitrary Lagrangian-Eulerian (ALE) approach was used to consider non-Newtonian blood flow, linear elastic arterial wall and simulations. It is indicated that with the increase of coil size, the hemodynamic parameters related to aneurysm such as wall shear stress (WSS), time-averaged WSS (TAWSS) and oscillatory shear index (OSI) decreased significantly. However, too large coils will compress the parent artery, produce high TAWSS areas in adjacent branches, and cause stress concentration on the aneurysm wall. Moreover, both the average displacement and von Mises stress of the aneurysm dome initially decrease and then increase with coil size. The appropriate size of the coil is beneficial to minimize displacement and stress by reducing blood flow velocity and vortices. The effects of different coil sizes were predicted by computational fluid dynamics (CFD), and the individualized treatment plan was adjusted according to the aneurysm morphology and hemodynamic characteristics. Our results provide a new theoretical basis for interventional therapy and help to promote the transformation of coil intervention from empirical filling to mechanics-oriented precision treatment.
Atherosclerotic plaque formation alters local vascular geometry, leading to disturbed blood flow patterns. These geometric irregularities produce spatial heterogeneity in wall shear stress (WSS), which plays a critical role in endothelial dysfunction and early immune cell recruitment during atherogenesis. However, the dynamic effect of spatial heterogeneity of wall shear stress on endothelial-immune interactions remains unclear. A multiscale computational model that integrates hemodynamics, endothelial cell phenotype transitions, and immune responses was developed. The model is used to investigate endothelial cell (EC) phenotype transitions and immune cell dynamics under varying damage threshold (DNO) conditions. Low-shear stress regions were found to expand with increasing DNO. Nitric oxide (NO) production was decreased, leading to accelerated EC activation and death. Monocyte Chemoattractant Protein-1 (MCP-1) expression was elevated, and monocyte recruitment and differentiation were enhanced, resulting in a higher proportion of pro-inflammatory M1 macrophages. The model reproduced experimental observations and provided robust predictions under different DNO scenarios. These results indicate that dynamic WSS drives EC state transitions and regulates immune cell recruitment and differentiation, providing a framework for studying vascular inflammation. Spatially heterogeneous WSS induces local NO depletion, which accelerates EC activation and death in low-shear stress regions, explaining focal endothelial dysfunction. EC injury further increases MCP-1 production, enhances monocyte recruitment, and promotes macrophage polarization toward a pro-inflammatory phenotype, demonstrating the ability of the model to capture flow-dependent vascular immune dynamics and inflammatory lesion development. This work provides mechanistic insight into the interplay between mechanical forces and vascular immune responses and may guide strategies for preventing endothelial injury and promoting anti-inflammatory therapy.
Bone remodeling refers to the physiological behavior of bone tissue changes with changes in the biomechanical environment. Researches of bone remodeling process are significant for bone tissue engineering. The use of numerical simulation technology is an important means to analyze the bone remodeling process. The research of computational methods can deeply reveal the growth law of bone tissue under external load and environmental effects. This work aims to develop the computational model using a meshless method, and simulate an evolution of the porous structure of trabecular bone. The main research objectives include: (1) proposing a novel bone remodeling model based on the radial point interpolation method (RPIM), which integrates the mechanical and biological aspects of bone remodeling; (2) analyzing the theoretical foundations of the meshless method, including the mechanical model driven by strain energy stimulation and the biological model regulated by cell growth, death, and proliferation. This work and the presented cases are limited to two-dimensional areas. The results demonstrate that the proposed bone remodeling model can reflect the bone remodeling process and reflect the dynamic changes inside the bone throughout its life cycle. The developed computational algorithm is highly efficient, and can form the porous structure of trabecular bone through image fitting.
Sacroiliac joints (SIJ) injury has been recognised as a crucial cause of low back pain (LBP), but investigations on SIJ are insufficient. The aim of this study was to reveal the mechanism of SIJ injury induced by different vibration conditions and body inclinations and thus to analyse the relationship between vibration and LBP. Based on whole-body finite element models, eight load cases were analysed, where the multi-axis vibration loading cases were closer to the typical vehicle environment. In addition, three different body inclinations were involved to analyse the effect of body inclinations on vibration transmission of SIJ. The results showed that the vertical vibration would induce larger loads on SIJ than the fore-and-aft vibration. Single-axis vibrations tended to cause large fore-and-aft loads of SIJ, and multi-axis vibrations tended to cause large vertical loads. For the three body inclinations, static loads on SIJ were minimal at 100° and dynamic loads were minimal at 110°, which indicated that the 100° inclination was a recommended sitting posture for occupational drivers to reduce their incidence of LBP. These findings might be helpful for understanding the association between different vibration conditions and LBP, and provide reasonable ergonomics recommendations for occupational drivers to reduce the incidence of LBP.
We present a comprehensive computational model to simulate the coupled dynamics of aqueous humor flow and heat transfer in the human eye. To manage the complexity of the model, we make significant efforts in meshing and efficient solution of the discrete problem using high-performance resources. The model accurately describes the dynamics of the aqueous humor in the anterior and posterior chambers and accounts for convective effects due to temperature variations. Results for fluid velocity, pressure, and temperature distribution are in good agreement with existing numerical results in the literature. Furthermore, the effects of postural changes and wall shear stress behavior are analyzed, providing new insights into the mechanical forces acting on ocular tissues. Overall, the present contribution provides a detailed three-dimensional simulation that enhances the understanding of ocular physiology and may contribute to further progress in clinical research and treatment optimization in ophthalmology.
Fontan-associated liver disease (FALD) is a disorder arising from hemodynamic changes and venous congestion in the liver. This disease is prominent in patients with hypoplastic left heart syndrome (HLHS). Although HLHS patients typically survive into adulthood, they have reduced cardiac output due to their univentricular physiology (i.e., a Fontan circuit). As a result, they have insufficient blood delivery to the liver. In comparison, patients with double outlet right ventricle (DORV), also having a univentricular circuit, have a lower incidence of FALD. In this study, we use a patient-specific, one-dimensional computational fluid dynamics (1D-CFD) model to predict hemodynamics in the liver of an HLHS patient and compare the predictions with an age- and size-matched single-ventricle Fontan DORV control patient. Additionally, we simulate FALD conditions in the HLHS patient to predict hemodynamic changes across various stages of disease progression. Our results show that the HLHS patient has higher hepatic arterial pressure compared to the DORV patient. This difference is exacerbated as FALD conditions progress. HLHS patients also have higher average portal pressures than DORV patients. The wall shear stress (WSS) is higher in the hepatic network for the simulated FALD patients. WSS is slightly decreased in the portal network for the HLHS patients, consistent with the development of portal hypertension. Perfusion analysis gives insight into regions of liver tissue at risk for fibrosis development, showing increasing pressures and reduced flow throughout the liver tissue fed by the portal vein under FALD conditions. Our results provide insight into the specific hemodynamic changes in Fontan circulation that can cause FALD.
Research in the dynamics of blood flow is essential to the understanding of one of the major driving forces of human physiology. The hemodynamic conditions experienced within the cardiovascular system generate a highly variable mechanical environment that propels its function. Modeling this system is a challenging problem that must be addressed at the systemic scale to gain insight into the interplay between the different time and spatial scales of cardiovascular physiology processes. The vast majority of scientific contributions on systemic-scale distributed parameter-based blood flow modeling have approached the topic under relatively simple scenarios, defined by the resting state, the supine position, and, in some cases, by disease. However, the physiological states experienced by the cardiovascular system considerably deviate from such conditions throughout a significant part of our life. Moreover, these deviations are, in many cases, extremely beneficial for sustaining a healthy life. On top of this, inter-individual variability carries intrinsic complexities, requiring the modeling of patient-specific physiology. The impact of modeling hypotheses such as the effect of respiration, control mechanisms, and gravity, the consideration of other-than-resting physiological conditions, such as those encountered in exercise and sleeping, and the incorporation of organ-specific physiology and disease have been cursorily addressed in the specialized literature. In turn, patient-specific characterization of cardiovascular system models is in its early stages. As for models and methods, these conditions pose challenges regarding modeling the underlying phenomena and developing methodological tools to solve the associated equations. In fact, under certain conditions, the mathematical formulation becomes more intricate, model parameters suffer greater variability, and the overall uncertainty about the system's working point increases. This paper reviews current advances and opportunities to model and simulate blood flow in the cardiovascular system at the systemic scale in both the conventional resting setting and in situations experienced in everyday life.
Noninvasive prediction of Fractional Flow Reserve (FFR) from imaging data through computational modeling has emerged as a promising alternative to invasive pressure measurements. Simulating coronary physiology, specifically coronary stenosis, poses a significant challenge due to the complex geometries of stenotic lesions and the need for physiologically realistic boundary conditions. Coupled 1D-3D modeling frameworks integrate a global one-dimensional (1D) circulation model with localized three-dimensional (3D) Computational Fluid Dynamics (CFD), enabling dynamic updates of boundary conditions and more accurate hemodynamic simulation. In this study, we couple a global 1D model of the coronary tree and partial systemic circulation with 3D CFD simulations using synthetically generated coronary stenosis geometries. We created three lesion types-symmetric, eccentric, and irregular-at severities of 50%, 70%, and 80%, to evaluate explicit coupling strategies for FFR prediction. We compare a steady-state 3D simulation driven by mean flow from the transient 1D model with transient 3D simulations that exchange data continuously at every step or only at the end of the converged cardiac cycle. Applied to the synthetic stenotic geometries, all approaches predicted similar FFR values, while the steady-state strategy achieved a significant reduction in computational cost, rendering it the most efficient for FFR prediction. Moreover, for irregular lesion geometries, localized 3D modeling revealed discrepancies in pressure loss compared to a simplified lumped model, demonstrating the added value of high-fidelity 3D simulations in complex cases.
Patients with lower limb lymphedema experience lymphatic fluid accumulation and swelling, which can progress to fibrosis and fat deposition in the soft tissues, impacting patients physically, socially, and psychologically. Compression therapy is one of the main treatments for lymphedema, but its effects on lymphedematous soft tissues are not yet fully understood. In this study, we developed a finite element model of a lymphedematous leg including subcutaneous and muscle tissues, as well as skin and fascia cruris, to investigate the hydrostatic pressure distribution resulting from the interface pressure applied by a compression stocking. The results highlight the significant influence of the leg's external geometry on the interface pressure, and demonstrate the importance of modeling skin to accurately predict hydrostatic pressure distribution in the subcutaneous tissue, with a 3.5% reduction in leg volume observed after compression. The outcomes improve the understanding of the effects of compression therapy on lower limbs affected by lymphedema and support the development of adapted treatment strategies for patients.
Machine learning (ML) models are becoming increasingly valuable for cardiovascular prediction and simulation, offering critical support for medical decision-making. These models are particularly useful for predicting disease progression and evaluating potential treatments. A major challenge in these models is to preserve the geometric fidelity of meshes while optimizing parameter efficiency to reduce memory usage, computational resources and execution time. In this paper, we present innovative approaches to abdominal aortic aneurysm (AAA) mesh compression, utilizing both statistical and deep learning models, with a focus on unsupervised learning techniques. We explore principal component analysis (PCA) as a statistical method and compare it with several deep learning models, including a simple autoencoder, an enhanced autoencoder based on PCA, a convolutional neural network (CNN), and a graph neural network (GNN). Human aortas are compressed using different statistical and deep learning methods to get the most relevant features. The mesh is reconstructed using the computed features and the error of the reconstructed meshes is compared. Our results indicate that PCA, using 64 principal components, outperforms deep learning models with a comparable latent space of 64, achieving the best overall performance. Among the deep learning approaches, the PCA-based autoencoder demonstrates the highest effectiveness.
Recently, researchers have explored the wall shear stress (WSS) obtained from medical images and computational fluid dynamics (CFD) to provide medical support. However, low-frequency noise caused by the resolution of the medical images increases the surface roughness of the geometry, thereby reducing the calculation accuracy of WSS. To reduce the surface roughness, regular smoothing methods are applied to geometries obtained from low-resolution medical images; however volume changes are a problem. In this study, we developed a method to obtain geometries with reduced surface roughness and minimal volume changes from medical images used in checkups, which have low resolution. Our approach combines interpolation of coordinate points with selective removal of low-frequency noise. This method was applied to 12 carotid artery geometries and one cerebral artery geometry obtained from medical images during the medical checkups; the changes in surface roughness, volume, and WSS in the CFD were compared with before and after smoothing. As a result, we found that the surface roughness of the carotid artery geometries after applying the developed method was approximately 27%-32% smaller than the original geometries, with the volume change remaining minimal, approximately a few percent. The WSS in CFD was found to be approximately 4.2% lower than that of the original geometries. These results demonstrate that our approach improves CFD accuracy for carotid and cerebral arteries, making it useful for medical support based on low-resolution medical images.
During a large vessel occlusion, the survivability of the affected brain tissue depends on the ability of blood to reach the compromised territory. Consequently, the severity of ischemic strokes and the outcome of interventional treatments like thrombectomy are strongly influenced by individual anatomical features of the brain's vascular network, particularly its collateralization. However, analyzing the role of collateral circulation has proven particularly challenging, as it requires highly detailed models of arterial networks that include very small collateral vessels (~50 μm diameter). This article presents a computational framework for constructing realistic brain vascular models that capture the anatomical variability of both the circle of Willis and the pial collateral network. The methodology integrates image-based vascular reconstruction, arterial tree extension via constrained constructive optimization, and generation of leptomeningeal collateral vessels. Blood flow simulations are performed using lumped parameter models, while virtual angiograms are generated through distributed compartment modeling of transport. A virtual patient population with variable collateralization is used to study the impact of anatomical differences on collateral flow and angiographic signatures in the presence of large vessel occlusions. The results show good agreement with in vivo data and highlight features that could help infer the level of collateralization from clinical angiograms. This framework offers a foundation for improving patient-specific stroke treatment planning and understanding the hemodynamic implications of vascular variability.
Residual thoracic aortic dissection (RTAD) is a pathology whose patient-dependent evolution is an important clinical issue, and for which numerical fluid-structure interaction (FSI) models can be helpful. However, the proposal of an ad hoc mechanical wall and flap model remains a challenge. To make progress on this issue, we seek to understand the respective influence of the flap and the wall in interaction with the flow in RTAD. Based on a patient's RTAD geometry, we established different FSI models to simulate the mechanical behaviour of the wall and flap. We varied the Young's modulus of the wall between 1.2 MPa (W12) and 2.7 MPa (W27) and the Young's modulus of the flap between 0.6 MPa (F06) and 1.2 MPa (F12), resulting in 3 different cases to study (F06W12, F12W12 and F06W27) and allowing a relative comparison. Structural displacements and stresses are equivalent in F06W12 and F12W12, resulting in equivalent flow characteristics. When comparing F06W12 with F06W27, we show that a stiffer wall reduces flap motion by 49.8%, 51% and 52% respectively, around the first entry tear, second and third one respectively. The difference in flow pressure between channels, which reflects the resistance to flow, is very small (about 1-2 mmHg) and similar for all 3 cases. This result seems to be highly related to the current geometry with one entry and two re-entry tears. Our results show that the wall is the main driver of the overall mechanical behaviour of the RTAD. We demonstrated that a stiffer pathological wall leads to smaller flap displacements, which is consistent with clinical observations in the chronic phase.
In this study, the biomechanical performance of four different coating materials applied on 316L stainless steel Schanz screws used in the treatment of intertrochanteric fractures (ITF) was examined by finite element analysis (FEA). Coatings: hydroxyapatite (hA), hexagonal boron nitride (hBN), zirconium dioxide (ZrO2), and aluminum oxide (Al2O3). How these coatings affect the mechanical properties, durability, and biocompatibility of screws reveals the potential to increase the effectiveness of external fixators. Analyses aim to make recommendations for safer and more effective applications during the treatment process by examining the effects of each coating on stress distribution, deformation and stress parameters. Ultimately, the most suitable material selection for fracture healing depends on clinical needs and the patient's condition. If high stress transmission is required, 316L or 316L-hA may be preferred. If more stable and low shear performance is desired, 316L-ZrO2 or 316L-Al2O3 coatings might be considered. In any case, it is essential to take all parameters into account when choosing the material.
Red blood cells (RBCs) undergo large structural deformation, including bending, when passing through capillaries. They also exhibit a range of complex shapes such as stomatocytes, discocytes and echinocytes that form due to altered blood pH and salt levels, ingested drugs and adenosine triphosphate depletion. Discrete-spring-network structural models of RBCs employ different numerical treatments of the continuum bending energy. This affects bending accuracy and the prediction of accurate RBC shapes. This research compares three representations called bending energy scheme (BES) A, B and C to evaluate their accuracy in shape predictions. BES A, seen throughout the literature, is based on the formulations of Kantor and Nelson, while BES B and BES C are, respectively, spring-based and node-based curvature calculation methods based on the formulations of Jülicher. Flat and enclosed spring-network membrane test cases are presented, and predictions using the schemes are compared. The flat membrane test cases explored the bending of stiff and soft membranes while the enclosed membrane test cases evaluated equilibrium vesicle and RBC shape prediction, including predictions of the stomatocyte-to-discocyte-to-echinocyte sequence. Predictions showed that BES A and BES B have limitations and can underestimate the true bending deformation. Additionally, BES A and BES B are also unable to capture the necking behaviour critical to the accurate prediction of complex RBC shapes. BES C on the other hand was seen to be accurate and robust and predicted shapes closely matched expected biological shapes. Based on this research, BES C is recommended for all future spring-network RBC structural modelling.
Despite the high mortality rates associated with thromboembolic diseases, computational modeling of the physics of thromboembolism remains underdeveloped in the literature due to the inadequacy of classical finite element methods to accommodate the growth, large deformation, and fracture of blood clots, especially under the influence of fluid dynamic forces. Accordingly, we present a meshless numerical framework, employing peridynamics (PD) that readily captures the constitutive response, damage progression, and eventual failure of a blood clot. The PD framework was validated against three benchmark test cases: tensile loading of a plate with a hole, torsional loading of a column, and tensile loading of thin structural plates both with and without notches. Comparative quantitative and qualitative analysis demonstrated excellent agreement with finite element solutions generated using the commercial software ANSYS. The validated framework was then used to calibrate the peridynamic parameters to accurately reproduce the mechanical response, the cohesive bulk fracture of blood clots under tensile loading, and the debonding of blood clots from artificial surfaces, including titanium (Ti), polyurethane (PU), and polytetrafluoroethylene (PTFE). Force-displacement curves obtained using these calibrated parameters demonstrated a strong correlation with experimental data.
Recently, the concept of a virtual population (Vpop) has attracted attention to provide large-scale, diverse datasets without compromising individual privacy. The development of the Vpop modelling method for the cerebrovasculature shape is necessary to be established with simple parameter tuning and post-processing. This study introduces a multivariate normal distribution (MVND) method to generate a Vpop for the cerebrovasculature shape. We defined an MVND by using the position and inner radius, which represent the vascular shape (centerline), as variables. Patient-specific arteries (basilar artery and internal carotid artery) obtained from MR images were used as a real population (Rpop) to generate an MVND. Then, virtual arteries were sampled from this MVND to generate a Vpop. To evaluate the validity of this method for reproducing shape diversity, we calculated the geometrical features of the centerline in each population. The centerline shows qualitatively similar characteristics between Vpop and Rpop. Geometrical features such as average length calculated from Vpop are in the same range as those of Rpop. Moreover, the distribution of geometrical features exhibits a good degree of fit between Vpop and Rpop. Since MVND considers the correlation among all position and inner radius variables, centerline continuity and anatomical characteristics of cerebrovasculature can be automatically included. Hence, geometric features and their distribution can be reproduced without any parameter tuning. The consistency in geometric parameters between the two populations supports the validity of the MVND method and indicates the potential for generating a Vpop for the cerebrovasculature in a more straightforward and simplified manner.
Pelvic organ prolapse (POP) affects many women and involves the displacement of pelvic organs due to weakened support structures. While synthetic meshes are used in surgeries to reinforce these structures, they can lead to complications due to poor biocompatibility and mechanical properties. Biodegradable meshes offer an innovative solution, providing flexible and strong support that enhances tissue reinforcement and reduces the risk of injuries. The main objective of this study is to enhance our understanding and provide valuable insights into the performance of vaginal tissue and mesh implants, which may contribute to the advancement of POP treatment methodologies. This study utilized melt electrowriting to 3D print biodegradable mesh implants with quadratic and cross-shaped geometries, each with a thickness of 240 μm. Uniaxial and ball burst tests were performed on these meshes and sow's vaginal tissue to determine their mechanical properties, and a numerical simulation of the ball burst test was validated, allowing for accurate material representation. The results indicate that the placement of biodegradable PCL meshes in sow's vaginal tissue increases the maximum force by 14% to 20% during ball burst tests. Furthermore, the simulation effectively mimicked the experimental analysis, demonstrating a strong correlation with the experimental data for both the meshes and the tissue. The computational analysis for the quadratic-shaped mesh revealed a maximum difference of 7%, while the vaginal tissue simulation exhibited a difference of approximately 6%. However, discrepancies were observed in the tissue reinforced with the mesh, where the simulation yielded a maximum error of 14%, which may be attributed to the complex interactions between the mesh and the tissue. This multifaceted approach, integrating simulation, material testing, and experimental validation, forms the foundation of in-depth research into the mechanical behavior of vaginal tissue and mesh implants, making significant contributions to the field of POP treatment. Utilizing experimental analysis to validate numerical simulations is essential, as it allows for reducing the need for extensive randomized controlled trials (RCTs) and minimizing the use of animal testing once the simulations are validated.
Aortic dissection (AD), particularly type B aortic dissection (TBAD), is a severe vascular condition with complex biomechanical implications that pose challenges for effective treatment. Thoracic endovascular aortic repair (TEVAR) has emerged as the standard approach for acute complicated TBAD; however, its efficacy in chronic cases remains uncertain due to factors such as fibrotic dissection flap and altered aortic wall properties. Current numerical simulations of TEVAR provide valuable insights into stent-graft behavior but lack comprehensive analyses of the effect of variable thickness distributions in patient-specific aortic anatomies and sensitivity of results to procedural factors such as the guiding catheter position. This study presents a finite element-based simulation pipeline to investigate the impact of (i) thickness variations in the aortic wall and dissection flap and (ii) guiding catheter path on the predictive accuracy of TEVAR outcomes in chronic TBAD. Using a virtual catheter technique implemented in Abaqus/Explicit, stent-graft deployment was simulated in a patient-specific model. The model incorporates hexahedral meshing for wall thickness distribution to improve computational efficiency. Quantitative assessment of the model's predictions reveals strong agreement with post-TEVAR CT data when a uniform aortic wall thickness is assumed and the guiding catheter path is reconstructed based on follow-up CT scan. Specifically, the predictions show radial, longitudinal, transverse, and angular deviations of 4.14% ± $$ \pm $$ 3.25%, 4.75 ± $$ \pm $$ 1.70 mm, 4.29 ± $$ \pm $$ 1.36 mm, and 6.08° ± $$ \pm $$ 4.22°, respectively. Thickness variations in the dissection flap and aortic wall minimally affect stent-graft positional predictions but significantly influence radius expansion and spatial configuration.
Coronary artery disease (CAD) is one of the leading causes of mortality worldwide. Fractional flow reserve (FFR) is a diagnostic metric for evaluating ischemic coronary stenoses, necessitating invasive pressure measurements using a guidewire during maximal hyperemia. The stenosis morphology and the presence of a guidewire influence coronary hemodynamics, warranting further investigation to improve FFR accuracy. This study systematically examines the effect of a pressure guidewire on FFR across different stenosis morphologies under clinically relevant boundary conditions (BCs). Six idealized models of coronary stenosis were developed, representing area stenoses (AS: percentage reduction in the cross-sectional area) of 64%, 75%, 84%, and 91%, based on the dimensions of the left anterior descending (LAD) artery. Computational fluid dynamics (CFD) simulations were conducted using coronary BCs validated against both in vivo and in silico data in the literature. Guidewire-induced FFR deviation (dFFR) exhibited a linear correlation with the blockage ratio-guidewire area relative to minimum lumen area-with deviations exceeding 0.04 for AS greater than 80%. dFFR values were comparable for AS of 64% and 75% across different shapes, but shape-related variation increased (> 0.02) at AS of 84% and 91%. Lesion length (LL) significantly influenced FFR based on morphology: a threefold increase in LL reduced FFR by 0.06 in crescent-shaped stenosis, while having minimal impact in the fully eccentric circular case (AS 84%). However, dFFR remained largely unaffected by LL. Finally, the effects of guidewire malposition on dFFR were negligible in non-circular stenoses (< 0.01) but considerable in circular stenoses (> 0.04 for AS 84%).
