Advances in the application of computational fluid dynamics in cardiovascular flow

Abstract Computational Fluid Dynamics (CFD) plays an important role in assessment of genesis and prognosis of atherosclerosis and as a promising tool for risk stratification. CFD is widely used by a majority of the researchers, although, many experimental studies show that the results obtained by CFD are inconsistent with the physio-pathological manifestations, which is mainly due to inconsistent definition of parameters, limited data availability and extreme complexity and heterogeneous behavior of plaque growth and its rupture. In this review, the results obtained by Computational Fluid Dynamics are summarized and an attempt is made to deduce the broad causes of various errors and possible solutions.


Introduction
Computational Fluid Dynamics (CFD) has been an established tool since many decades to solve and visualize complex flow problems in biomedical applications.A combination of medical image processing, reconstruction of vasculature, and technology to generate computational mesh to calculate hemodynamic parameters can yield temporal and spatial distributions of blood flow (Fujimura et al., 2018).Flow of blood is a critical parameter in formation of arterial stenosis .It plays an important role in stimulation of endothelium and development of inflammatory cells and the corresponding response of the endothelium.Healthy endothelial layer makes sure that the vascular lumen is stable and controls the distribution of anti-inflammatory factors.Imbalance between the flow conditions and endothelium alters the physiological factors of the vessel and initiates the development of atherosclerosis (Gimbrone & Garcia-Cardeña, 2016;, Rafieian-Kopaei et al., 2014).
Hemodynamic shear stress is constantly applied to the blood vessel's luminal and endothelial surfaces (Urschel et al., 2021;Davies, 2009).It has been shown experimentally that shear stress will actively influence the vessel wall remodelling (Krishnan et al., 2021), (Blum et al., 2022).Atherosclerosis is still a geometrically localised disease that affects the artery bifurcations' outer borders.Hemodynamic indices such as wall shear stress, velocity, and pressure acting on the endothelium surface as a result of blood flow are weaker in these areas than in protected areas (Olender, 2021), (Saveljic & Filipovic, 2021), (Gasser et al., 2021).Although the severity of carotid stenosis is widely used to determine the risk of stroke, the majority of people with severe stenotic arteries do not have a stroke; however, stroke can occur in people with moderate stenosis.This demonstrates that local hemodynamic variables have a significant role as a stroke indication (Xu et al., 2021), (Dalby et al., 2021).The identification of such sensitive atherogenic locations has benefited greatly from computational fluid dynamics simulations (Williamson et al., 2022).CFD is a useful tool for figuring out how atherosclerosis works.The function of hemodynamics and plaque development and progression in arteries is explained using anatomically realistic CFD models and boundary conditions obtained from in vivo imaging techniques (Starodumov et al., 2022), (KA Smith et al., 2021).Earlier image based CFD was used for qualitative validation which has moved on towards quantitative validation and has gained acceptance for applied vascular research.Recent trend in CFD is to use realistic models which is extracted from ex vivo or in vivo imaging techniques which produces a set of images using which the lumen of the arteries are extracted and reconstructed to produce a 3D lumen geometry Gamage et al., 2021), (Warey et al., 2021), (Settecase & Rayz, 2021).
Image-based CFD was used to study the hemodynamics of patient-specific models to prove the suitability of CFD to study the flow field.Navier Stokes equation is used to study the time varying flow in common carotid artery bifurcation in combination with medical imaging which is vital in future risk assessment with carotid diseases (Nannini et al., 2021), (Hossain et al., 2021), (Abazari et al., 2021).The combination of CFD and MR imaging can be used to investigate the flow patterns and the relationship between hemodynamic factors and atherosclerosis can be quantified (Andelovic et al., 2021), (Chen et al., 2021) .Recent trend in computational hemodynamics is to use realistic models in the study obtained from medical imaging technology like CT (Computed Tomography) and MRI (Kadem et al., 2022).This paper reviews the advances in application of CFD mainly in the stenosed carotid arteries.We enumerate the technical aspects of image based modelling by using CT and MRI and review the methods used to create patient-specific stenosis models and boundary conditions for simulation.The original research publications were examined by comparing the amount of WSS using 4D flow MRI and CFD.The following requirements were considered in the study.Studies that used a MRI acquisition approach and a CFD method must have evaluated the WSS within an arterial bifurcation.The degree of concordance between the WSS magnitudes achieved by the two approaches must have been quantitatively compared in studies.Included were both unhealthy and healthy arteries.Studies both in vivo and in vitro were included; the former examined the hemodynamics of actual patients, while the latter examined replicas of human arteries.The analysis disregarded animal research and any studies considering surgical intervention.

Boundary conditions
The region of interest is always condensed in image-based models.This implies that inflow and outflow boundary conditions be used to analyse stiff walls.At the inlet, a velocity profile is usually prescribed with a specified shape, but it can also be based on recorded time variable velocity profiles (König et al., 2021), (Yao et al., 2021).There is always debate regarding using a fully developed flow profile at the inlet because the upstream segments, which are normally straight, are bifurcated distally, resulting in undeveloped profiles (Carvalho, Carneiro et al., 2021), (Watson), (Fan et al., 2021), (Soares et al., 2021).However, if the domain is truncated far enough from the region of interest where the inlet is considered, the negative effects of the downstream arterial network can be avoided (Bodlak, 2021), (Papamanolis et al., 2021).
The outflow conditions will be determined by the dimensions of the outflow tract, assuming mass conservation and any of the specified scaling rules (Vixège et al., 2021), (Hameed et al., 2021).By scaling the shape of a canonical flow waveform, the same scaling laws can be utilised to determine discrete inflow conditions.Although applying particular inflow and outflow boundary conditions based on MRI or Ultrasound measurements may be preferable, phase shifts and a reduction in outflow vs. inflow rates at a distance from the inlet must be addressed for hard walls (Vixège et al., 2021), (Hameed et al., 2021), (Thirugnanasambandam et al., 2021), (Johnston et al., 2021).Because uncorrected flow wave forms diverge from genuine in vivo values, they can be used to distensible models.However, applying flow wave forms to distensible models becomes problematic (Mahutga, 2021).Data on flow waveform reductions or phase shifts could be beneficial for assuming bulk compliance of arteries and assigning attributes to deformable arterial walls.Ultrasound and MRI can be utilised to get direct measurements of the lumen's nonlinear dimensions, which can then be scaled to account for a time-varying pressure waveform (Feiger et al., 2021), (Garber et al., 2021), (Taylor & Steinman, 2010).Inlet and exit profiles, as well as zero traction, were proposed by the majority of 3D blood flow models (Arzani, 2018), (Mukherjee et al., 2018), (Habibi et al., 2020).Because measured and prescribed flow measurements were used, vessel compliance was ignored, and the goal was to compute velocity, field, and WSS, this was sufficient for the majority of simulations.However, in some circumstances, such as forecasting the results of treatments, the limitations of the supplied boundary conditions were obvious (Deng et al., 2021), (Modi et al., 2019), (Shankar et al., 2022).The requirement for presuming realistic boundary conditions became important with the introduction of methodologies to include vessel compliance and the rising importance of developing more extensive models and predictive applications (Ninos et al., 2021), (Jones et al., 2022), (Singh et al., 2020).The development of multi-scale and multi-domain models in which the inflow and flow rate of an imagebased 3D numerical domain is coupled to the inflow or outflow of a reduced order model has made significant progress (1D network or lumped model; Tran, 2018), (Colebank, 2021), (Fleeter et al., 2020).A coupled multi domain method for a 3D FEA (Finite element analysis) of blood flow was presented where the domain was constrained to the major arteries and the downstream models were represented by simpler models (Spilker et al., 2006), (Vignon-Clementel et al., 2006).The image-based 3D models and reduced order 1D or zero-dimensional models were linked using both staggered and completely coupled techniques.For 1D network models, geometrical and material properties should be assigned using fractal or morphometrical methods (Esmaily Moghadam et al., 2013).Numerically optimised methods are utilised to prevent the values of lower order model parameters from matching the flow distribution or pressure in anatomical models (Fossan et al., 2018), (Mirramezani & Shadden, 2020), (Safikhani et al., 2021), (Alimohammadi, 2018), (Windisch et al., 2020), (Tomasina et al., 2019).

Modelling of stenosis in the arteries
To predict the behaviour of the arteries under physiological loading conditions it is necessary to model the stenosed region in the artery.Computational techniques were developed to solve reconstruction problems like segmentation, editing etc. and discretization of 3D anatomically realistic models of the vasculature were presented where attention was given to minimize human intervention and maximize reproducibility and produce accurate results and introduction of geometric and fluid dynamics analysis of normal and stenosed arteries (Cebral et al., 2005), (Lee & Xu, 2002).Parallel imaging technique is used to obtain phase locked image which leads to highresolution description of the vessel geometry at one single phase and classical imaging techniques can be applied to this image set to produce corresponding wall surface (Gaidzik et al., 2021).A high-resolution MRI of a stenosed carotid bifurcation was obtained, and an automated detection technique was applied to the images to construct stenosed carotid bifurcation segmentation using a 2D watershed transform form applied to each slice, and a high resolution 3D model was generated (Saxena et al., 2019;Zhu et al., 2021).
The most crucial stage in image-based modelling is the extraction of lumen boundaries from vascular anatomy images (Eslami et al., 2020).Many studies have focused on this process, with studies relying on manual or computer-based picture slice segmentation, which is then paired with a variety of reconstruction methodologies (Zorzal et al., 2019).Performing 3D lumen extraction has become significantly easier with fast and central graphics processing units and large-scale advances in image quality (Duan et al., 2020).Lumen segmentation using a rapid technique and surface reconstruction using MR images reduce the time required to produce finite element meshes.This is accomplished by inflating a computerised virtual balloon inside the lumen geometry generated from MR images to simultaneously segment and reconstruct the lumen, with the lumen's surface being filled with finite elements (Lareyre et al., 2019;Zhang,).3D realistic models were constructed using MR images which are manually segmented and the reconstructed 3D lumen surface was processed using vascular modelling toolkit (Izzo et al., 2018) to smooth and add cylindrical extensions such that fully developed velocity profiles are created and the surface is clipped at particular spots.
Pictures with well-defined vessel wall boundaries, such as those obtained from CT or contrastenhanced MRA, are favoured for segmentation of 3D images (Ghouri et al., 2019;Skopalik et al., 2021).However, because the 3D surface generated by this technique is difficult to alter, 2D segmentation is favoured for low contrast structures such as artery walls, thrombus, or stenosed areas (Youn & From, 2022) especially for IVUS images (Wu et al., 2021).For non-branching segments, lofting the wall rings together is simple, but branches provide a challenge.The availability of open source toolkits for image visualisation, processing, and vascular modelling is a huge step forward in image-based modelling since it allows for the normalisation of vascular model generation (Lesage et al., 2009;Sengupta et al., 2020).Although there are free source scripts available, quality volumetric meshes are generally the domain of commercial mesh producers (Lian, 2010).The meshes are typically over-or under-resolved in comparison to the solution criteria, necessitating the use of an adaptive mesh approach to provide an acceptable forecast of wall shear stress.Because arteries have long tubular shapes and blood velocity is stronger in the radial than in the longitudinal direction, the adaptive mesh technique that produces anisotropic and boundary layer elements is preferred.Shephard et al developed a unique vascular finite element mesh that included anisotropic adaptivity and boundary layer meshing (vmtk. & Accessed February, 2022).When compared to isotropic adaptive mesh refinement techniques, anisotropic meshing can produce mesh independent findings for image-based modelling of blood flow with minimal elements.CT MRI was used taken from volunteers and a 3D artery was generated using the 2D slices obtained from the CT MRI by using a spline curve to connect the slices (Müller et al., 2005).

Application of computational fluid dynamics in blood flow analysis
CFD has emerged as a method for studying and simulating blood flow in a variety of cardiovascular disorders.Using CFD simulations, doctors may forecast illness development and identify risks associated with procedures that might change blood flow in addition to better understanding the underlying biology of diseases.The use of CFD in some of the various disease areas is discussed.Comparing CFD analysis to traditional medical techniques and models has many advantages for cardiovascular applications (Morris et al., 2016).The main benefit of CFD analysis is that it enables the scaling of individualized cardiovascular treatment regimens to broaden patient populations (N Smith et al., 2011).
To demonstrate the usefulness of CFD for studying the flow field, image-based CFD was utilised to examine the hemodynamics of patient-specific models.The findings were experimentally confirmed, and it was shown that wall shear stress (WSS) is a crucial hemodynamic component that causes arterial rupture (Urschel et al., 2021_, (Koseki et al., 2020).The precision of the results is heavily influenced by the boundary condition.Experimental data was used as the inlet condition, and it was discovered that the inlet profile has a significant impact on the properties of blood flow (Feiger et al., 2019), (Bit et al., 2020).The results were compared to other boundary conditions commonly utilised, such as constant external pressure and constant outflow ratio, in a new approach where energy loss minimization at flow bifurcations was used to forecast critical stenosis ratio.The proposed method produced extremely precise results, which were confirmed by clinical measures using colour Doppler ultrasound.CFD and MR imaging can be used together to analyse flow patterns and quantify the link between hemodynamic variables and atherosclerosis (Ngo et al., 2019), (Adib et al., 2020), (Lopes et al., 2021).Pulsatile flow in abdominal aorta model is studied extensively for hemodynamics using an in house developed platform and validated Womerseley solution.The approach was used for predictive computational method into planning vascular surgery (Garber et al., 2021).
Averaged carotid bifurcation models hide intriguing hemodynamic aspects that are apparent in realistic models acquired from non-invasive methods, according to a non-invasive MRI method that gives carotid bifurcation geometry and flow data from which in-vivo hemodynamics may be estimated.The inter-subject variance in the in-vivo wall shear stress pattern significantly supports the assumption that such individual investigations can provide more definitive information about the involvement of hemodynamics in vascular disease.It was also discovered that hemodynamics differ from one subject to the next (Dong et al., 2013).
When an artery has stenosis, it works in the opposite way of a healthy one, causing low and fluctuating WSS during cardiac cycles as well as high shear stress at the throat.The WSS development was predicted using both transient numerical modelling and Ultrasound Doppler experimental approaches, which were both validated (Lopes et al., 2020).Atherosclerosis-prone location is mainly the carotid bulb and the phenomenon is clearly explained which will serve to show its focal nature where it localize in the region of low shear stress in arterial tree (Ooij & Van, Markl, 2020).The application of realistic models in studies gained from medical imaging equipment such as CT and MRI in combination with deep learning and artificial intelligence techniques is a recent trend in computational hemodynamics.Local hemodynamics, particularly shear rate, are the primary cause of thrombus development and plaque rupture, according to advances in stroke research (Kim et al., 2019;Sorin et al., 2020).The presence of high shear rate at partially occluded arteries initiates platelet activation and platelet binding takes place which plays an important role in thrombosis.When there is high speed flow through the stenosis the fibrous cap is subjected to high shear stress which results in plaque rupture (Scharf, 2018).
CFD data may be used in conjunction with MRI and other imaging modalities to provide a clear image of hemodynamics in vessels and to show the risk of embolism and plaque rupture.The experiment was carried out with both steady and unstable pulsatile flow.The hemodynamics are not detailed enough to be determined by an MRI or Doppler Ultrasound.In general, medical diagnostics search for the highest velocity in a volume and presume that velocity is inversely proportional to cross sectional area and hence square of vessel diameter, which is only true when the geometry is smooth and the cross section is circular (Sleight et al., 2021), (Moccia et al., 2018).The shape of the vessels, which is infrequently included in experimental and computational research and rarely observed by diagnostic methods, has a major impact on blood flow.To define and solve equations, the finite volume approach is utilised.Blood also obeys Casson's model only for moderate shear rate flows, demonstrating non-Newtonian behaviour (Pandey et al., 2020).They have discussed the major reasons for plaque rupture and observed that plaque rupture takes place at the upstream of the stenosis.
The position of particulate buildup on the interior wall curvature, where the WSS is minimal, was predicted, providing insight into the particulate with the walls.The plaque accumulation on the inside curvature of the idealised model was predicted using a multiphase Eularian-Eularian transient non-Newtonian 3D CFD model (Abidi et al., 2021).The flow disruption is due to stenotic shape and height, blood flow recirculation, and downstream of disease in a pulsatile blood flow model involving straight, cylindrical, and rigid tube models, and revealed that peak velocities rely on the shape and height of the stenosis.It can be shown that there is no case to case variation in diastole (Oglat et al., 2018).Two equation turbulent models and transitional variants are used to predict blood flow patterns in a stenosed carotid bifurcation, where plaque growth, progression, and structure at rupture are all linked to low and oscillating shear stress, and it is shown that the transition from laminar to turbulent can change the separation zone length, WSS, and pressure distribution over the plaque (Carvalho, Pinho et al., 2021).In order to do functional imaging for arteries, MRI data is used.The hemodynamic parameters are the results of a blood flow computation that is consistent with the medical data provided.CFD results have been demonstrated to be extremely dependable (Liang et al., 2019).The impact of assumptions about outflow boundary conditions on the solutions of equations governing blood flow in an image-based CFD model of human carotid bifurcation revealed that realistic constraints were required, as applying proper boundary conditions can affect the solutions of equations governing blood flow (Williamson et al., 2022).When hemodynamic measures such as ultrasonography and MR are available, isolated 3D patient specific models can be used.When the goal is to predict the outcomes of alternative therapeutic interventions for individual patients or to test hypotheses about the role of local fluid dynamics and other biomechanical factors in vascular diseases, we should use more realistic constraints like coupling models at different scales (Cai & Li, 2021).
To validate the computational approach, experimental measurements by particle image velocimetry are carried out where main flow characteristics can be easily captured using CFD (Williamson et al., 2022).CFD using patient-specific data is extremely useful for studying the role of blood in disease progression.In this study, the influence of idealised inlet velocity profiles of patient-specific CFD was compared to the true velocity profile of the patient in the carotid bifurcation.Computational simulations of hemodynamics may be used in conjunction with MRI, CT, Doppler, and other invivo diagnostic methods to produce an accurate image of hemdynamics in blood vessels, which can be used to show the danger of embolism or plaque rupture posed by plaque deposits.By detecting WSS distribution in the carotid arteries in conjunction with numerical simulation, it is possible to identify vessel sites where atherosclerotic plaque may grow in different individuals (Ferrarini et al., 2021), (Yang et al., 2018).The pulsatile blood flow distribution within the lumen of arteries was examined using histology images of diseased coronary arteries and computational fluid dynamics.The findings of this investigation revealed that hemodynamics are strongly influenced by the form of the lesion, and that stenosis influences wall shear stress locally.In the stenosis's throat, the maximum wall shear stress is seen.The results reveal that stenosis has an impact on wall shear stress.The plaque forming regions were predicted using computational approaches (Carvalho et al., 2020), (Horn, 2018).
Finding a precise and appropriate set of parameters that may be used to validate numerical modeling and act as initial boundary conditions or material qualities for the simulation is one of the study's challenges (Rayz et al., 2008).Precised reconstruction of the artery and the accompanying flow physiology as input conditions for the simulation are necessary for an accurate characterization of the hemodynamics.Doppler ultrasonography and digital subtraction angiography are all parts of the experimental process (Boutsianis et al., 2004).Many earlier studies used empirical equations like the Womersley model and Hughes model to mimic pulsatile blood flow dynamics in an arterial model due to the complexity of the vasculature and fine control of animal experiments (Yao et al., 2021).In order to determine the practicality of a patient-specific numerical simulation method and to establish the underlying relationship between WSS and stenosis, which may support further medical research, the data measured from the arteries are used to model blood flow.Studying the flow pattern in the artery allows researchers to look into how it relates to vascular problems and subsequent stenosis.This flow pattern includes pressure, WSS, and velocity distribution (Liu., 2007)

Conclusion
To research hemodynamics, image-based modelling of realistic geometry of arteries employing CT, MRI, and CFD investigations of blood is widely used.When compared to idealised models, the use of realistic models aids in a better understanding of hemodynamics.Although MRI provides hemodynamic characteristics based on the geometry of the artery lumen, literature suggests that using CFD in conjunction with CT/MRI data to study blood flow hemodynamics provides better insight.
Precise boundary conditions and other data, including measurements of blood flow velocity and WSS collected from in vivo testing, can be used as the inputs and standards for model evaluation.By comparing the outcomes of simulation and experiment, the modeling can be validated.The use of computational methods to mimic blood flow has been increasingly important in understanding the human circulatory system, particularly the development of stenosis, over the last decade.The use of numerous choices in CFD will assist physicians and technicians in creating patient-specific models and simulating the outcome, planning and predicting treatment for stenosis mitigation, and optimising the necessary devices.You are free to: Share -copy and redistribute the material in any medium or format.Adapt -remix, transform, and build upon the material for any purpose, even commercially.The licensor cannot revoke these freedoms as long as you follow the license terms.
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