Abstract

Computational fluid dynamics (CFD), alone or coupled with the most advanced imaging tools, allows for the assessment of blood flow patterns in cardiovascular disease to both understand their pathophysiology and anticipate the results of their surgical or interventional repair. CFD is a mathematical technique that characterizes fluid flow using the laws of physics. Through the utilization of specific software and numerical procedures based on virtual simulation and/or patient data from computed tomography, resonance imaging, and 3D/4D ultrasound, models of circulation for most CHDs can be reconstructed. CFD can provide insight into the pathophysiology of coronary artery anomalies, interatrial shunts, coarctation of the aorta and bicuspid aortic valve, tetralogy of Fallot and univentricular heart, valvular heart disease, and aortic disease. In some cases, CFD may be able to simulate different types of surgical or interventional repairs, allowing for the tailoring of treatment accordingly.

Introduction

Computational fluid dynamics (CFD) is a well-established technique used in many fields of engineering design and analysis [1].. Notably, bioengineers have adopted CFD for studying complex physiological flows [2]. There is an increasing interest in applying these methods to cardiovascular medicine, and CFD-based techniques are increasingly used to build computer representations of the cardiovascular system in both healthy and pathological conditions [3]. The aim of the present review is to outline the findings of CFD in the study of cardiovascular pathophysiology, as well as CFD's applications in endovascular and surgical repair planning.

Computational Fluid Dynamics

Definition

CFD is a technique that uses computer simulations to analyze systems involving fluid flow, heat transfer, and associated phenomena (e.g., chemical reactions) [4]. CFD is suitable for a wide range of industrial and non-industrial applications, including aircraft and automotive aerodynamics, ship hydrodynamics, turbomachinery, meteorology, and biomedical engineering, among others [5]. In cardiovascular hemodynamics, CFD is usually utilized to analyze blood flow patterns within the heart and vessels by considering physical laws governing fluids. Biological effects, such as auto-regulation, healing, and growth, are seldom modeled. Specifically, the governing equations of fluid motion are the continuity equation (eq. 1), which is derived from mass conservation, and the Navier-Stokes equations (eq. 2), which are derived from momentum conservation, and which can be expressed in the case of an incompressible and Newtonian fluid as follows: ∇.v=0      (1)
ρ[∂v/∂t + v·∇v]= −∇p + μ∇²v + ρg       (2)
where ∇ is the nabla operator, v the velocity vector, ρ is the blood density, t is the time, p is the pressure, and g is the gravity. . These non-linear, partial differential equations cannot be solved analytically in the case of complex three-dimensional geometries. Thus, numerical techniques, usually based on the finite volume or finite element method, are adopted to solve the discretized form of the equations within CFD software packages [5]. First, by means of the meshing process, the fluid domain (i.e., continuum of interest) is subdivided into smaller, non-overlapping sub-domains called elements. Secondly, the governing equations are integrated over all the elements of the domain and then converted into a system of non-linear algebraic equations. Lastly, the resulting set of algebraic equations (often in the order of millions of equations) is solved iteratively using computer workstations or high-performance computing clusters. Nowadays, advancements in parallel computer processing have allowed for solutions to the governing equations of fluid motion to be calculated under non-steady conditions in complex anatomies within a reasonable computational timeframe. Typically, resolving a time-accurate expression can require one or more days of computations, considering a fluid domain discretized into one million elements (or more) and multiple cardiac cycles, which are each subdivided into hundreds of time steps [6].

CFD analysis: workflow

The main steps of a patient-specific CFD analysis are summarized in Figure 1. First, the three-dimensional geometrical model of the vascular region of interest is reconstructed from non-invasive or invasive images. Specifically, vessels and cardiac chambers are virtually reconstructed based on the measurements of vessel diameters and lengths obtained by quantitative coronary angiography, computed tomography, MRI analyses, or by processing intravascular images (i.e., intravascular ultrasound or optical coherence tomography) [7-8]. Manual or semi-automatic segmentation algorithms, which are included in commercially available software, are used to identify the region of interest. As a result of the segmentation process, a preliminary, triangulated mesh surface representing the vessel or cardiac chamber wall is obtained. The model is subsequently optimized by applying refinement processes such as triangle reduction and smoothing operations [5]. Secondly, the obtained geometrical model is discretized (meshing process) [5]. Typically, the computational grid is characterized by tetrahedral (or hexahedral) elements within the fluid domain and a prism layer close to the wall, which is introduced to better capture the high-velocity gradients at this location. Thirdly, the set-up of the CFD simulation is defined. In particular, the physical model (e.g., unsteady flow with or without the inclusion of a turbulent model), blood properties (i.e., blood density and viscosity), initial conditions, boundary conditions, and solver settings are set. Delimiting the initial and boundary conditions, which are prescribed values of the calculated quantities (i.e., velocity and pressure) at certain times and locations, is mandatory for the resolution of the governing equations. These conditions can be derived from imaging data or experimental measurements, such as MRI data, Doppler ultrasound, catheter-based pressure, and velocity measurements, or transesophageal echocardiography. Fourth, the CFD simulation is run on a computer workstation or high-performance computing cluster by taking advantage of their parallel computing features. Lastly, once the solution of the CFD analysis is obtained, the results are post-processed in order to extract the hemodynamic quantities of interest, which are detailed in the following sub-section.

CFD analysis: quantities of interest

The main flow phenomena that can be characterized by CFD by corresponding hemodynamic quantities of interest are reported in Table 1. The hemodynamic quantities derived from both pressure and velocity fields are analyzed. The pressure in the vessels and chambers is expressed in pascal (Pa), as per the International System of Units. The vorticity magnitude (expressed in 1/s) is defined as the magnitude of the vorticity vector; the vorticity vector expresses the rotation of a fluid element as it moves through the domain, and it may be representative of pathological conditions when substantially removed from baseline [9]. The wall shear stress (WSS) (expressed in Pa) is defined as the frictional force of flowing blood along the wall surface per unit area. WSS values deviating from baseline are indexes of abnormalities leading to thrombus formation, abnormal vessel modeling and remodeling, and arterial damage [10]. Another important quantity to be evaluated is the power (energy per unit time, measured in watts) dissipated when the blood flows through arteries. Minimizing this loss of energy when designing or re-routing blood in surgical connections is desirable, and such an index thus may be used to predict the successful streamlining of blood flow.

CFD applications for congenital heart disease

CFD is currently applied to a variety of CHDs in order to both pathophysiology evaluation and surgical or interventional procedures planning.

Embryonic heart development

Hemodynamic processes begin shaping the growth of the developing heart from the early embryonic stages. Blood circulation starts with the beating primitive tubular heart (around the beginning of the fourth gestational week in human development) [11]. From this time on, the dynamics of blood flow determine many aspects of cardiovascular development. For instance, the formation of vessels and capillaries, and even the differences between arterial and venous phenotypes, are determined by blood flow characteristics [7]. In the heart, the relationships between blood flow and cardiac tissues also determine how the heart continues to develop [12-13]. Understanding blood flow mechanics ultimately helps researchers to identifying the causes of congenital heart malformations. Detailed CFD models of both the developing vasculature and the heart, together with experimental data on adaptations to blood flow, are starting to elucidate important aspects of the complex mechanisms by which blood flow dynamics regulate cardiovascular growth and development. In this respect, WSS plays an important role in cardiovascular adaptations to flow. CFD simulations of the fetal heart, imaged by an echocardiogram, reveal complex flow patterns and the presence of flow vortex rings in both the left and right ventricles. These flow vortex rings generate significant WSS on the endocardium, potentially playing an important role in cardiac efficiency [14]. Indeed, CFD allows for the quantification of WSS, which is otherwise extremely difficult using only flow data measured in vivo.

Congenital coronary artery anomalies

Coronary artery anomalies (CAAs) accounts for 0.64% to 5.60% of patients undergoing coronary angiography [15-16]. The pathophysiology and clinical history of the majority of CAAs have been fully clarified in the past 30 years. Myocardial bridges and anomalous origin from the opposite sinus (ACAOS) constitute the most clinically investigated pathologies among the wide spectrum of coronary artery anomalies, as they have been associated with myocardial infarction and sudden cardiac death [17].
Myocardial bridges (MB) were assessed by Javadzadegan et al. [18] using CFD by dividing patient-specific myocardial bridge models (n=10) by length. A direct relationship between myocardial bridge length and hemodynamic perturbations emerged in this study. Specifically, long myocardial bridge length seemed to be associated with lower WSS and higher residence time in the segment proximal to the bridge and a higher WSS and shorter residence time within the bridge, as compared to short length. More recently, Sharzehee M et al. [19] demonstrated that increasing the MB length (by 140%) only had a significant impact on the pressure drop in a severe MB (39% increase during exercise). However, increasing the stenosis length dramatically increased the pressure drop in both moderate and severe stenoses at all flow rates (31% and 93% increase during exercise, respectively). Both CFD and experimental results confirmed that the MB had a higher maximum and a lower mean pressure drop when compared to the stenosis, regardless of MB/stenosis severity. The description of ACAOS is currently based on the terminology introduced by Angelini et al. [20], including an L or R prefix to indicate the (Right or Left) coronary artery involved and a suffix to indicate the proximal course: intramural (IM), pre-pulmonic (PP), subpulmonic (SP), retro-aortic (RA), retrocardiac (RC) and wrapped around the apex (WA). Rigatelli et al. computationally investigated the pathophysiology of Left ACAOS with and without an IM course [21]. After reviewing both the angiographic and computed tomography findings of 13 athletes, CFD models were created to simulate conditions reflecting extreme effort. In particular, vorticity magnitude, static pressure, and WSS were analyzed in models of L-ACAOS with no IM course and L-ACAOS-IM at rest and during exercise. The mean vorticity magnitude and WSS significantly increased from rest to exercise in both models in all the major coronary arteries. The mean static pressure (1.118e+004 vs 1.164e+004 Pa, p < 0.001), as well as the mean vorticity magnitude and mean WSS (7012.78 1/s vs 9019.56 1/s, p < 0.001, Δ=2006.78 1/s and 3.02 Pa vs 2.11 Pa, p < 0.001, Δ=0.91 Pa), significantly increased with exercise in the L-ACAOS-IM model. This net increment was transmitted to the entire left coronary system in the L-ACAOS-IM model but not in the L-ACAOS model with no IM. More recently, we analyzed the pathophysiology of L- and R- ACAOS with the IM course in relation to the eventual stenting of the IM course [22]. We theorized that the phasic squeezing phenomena inside IM could be produced by a combined mechanism of compression and twisting, which causes a net pressure drop leading to myocardial ischemia. This hypothesis seems to be confirmed in part by the study by Razavi et al. [23], which showed that different flow patterns exist natively between right and left anomalous coronary arteries. Unroofing may normalize time-averaged WSS, but with some differences related to the AO.

Bicuspid aortic valve

Interatrial shunts include patent foramen ovale (PFO), secundum atrial septal defect (secundum ASD), sinus venosus ASD, and ostium primum ASD [24]. There are very few studies applying CFD to interatrial shunts. Our group investigated the pathophysiology of right-to-left shunting in patients with PFO with CFD [25]. In this study, we reconstructed the connection between the right and left atria using MRI data from a pool of patients with mild or permanent right-to-left shunting. In the CFD simulations, higher vorticity was observed in the case of permanent R-L shunt involving the wall of the left atrium (LA), especially at the left atrial appendage (LAA, Figure 2). On the contrary, when the severity of the shunt decreases, the vorticity in the same area is resultantly lower. Moreover, a marked gradient in total pressure (defined as the sum of static and dynamic pressures, measured in pascal (Pa)) was found across the PFO. A higher vorticity magnitude was observed in the permanent shunt both in the (117.32 vs 110.25, p=0.001) and at the LAA (33.29 vs 21.25, p=0.001) when compared to mild shunt.

Interatrial shunts

Bicuspid aortic valve (BAV), usually associated with both valve dysfunction and aortic pathologies such as aortic dilatation and dissection, represents the most common CHD [26]. The abnormal arrangement of the aortic valve leaflets in BAV generates an abnormal flow pattern in the ascending aorta, depending on the type of leaflet fusion [27-28]. Emendi et al. [29] demonstrated that fluid-structure interaction derived from MRI predicted the direction and magnitude of the flow jet impinging onto the aortic wall, as well as the location and extension of secondary flows and vortices developing at systole.
Rigatelli et al. suggested that such abnormal flow patterns, as evaluated by CFD, may be worsened by a concomitant coronary artery disease of proximal major coronary arteries, such as the left main stem, due to aberrant distribution of aortic WSS [30]. Some authors comparing the blood flow in BAV to that in normal (non-dilated) aortas with tricuspid aortic valves showed an altered WSS distribution in all different BAV fusion types [31-32]. Both 4D-flow cardiovascular MRI and CFD analyses showed abnormal WSS distribution in patients with BAV even before aortic dilation occurred, suggesting that abnormal WSS could precede anatomical remodeling of the aorta. Thus, the monitoring of both WSS and aortic diameters has the potential to allow early identification of young, asymptomatic patients at risk for progression of aortopathy [33], guiding surgeons to reinforce the aortic sites at increased risk [34].

Coarctation of the aorta

Coarctation of the aorta (CoA) is a narrowing of the upper descending thoracic aorta, generally distal to the origin of the left subclavian artery and near the insertion of the ligamentum arteriosum. CoA accounts for approximately 5%–8% of all CHDs [35]. The available diagnostic imaging tools provide dimensions, velocities, and pressure gradients but cannot characterize aortic blood flow and its effects on the aortic wall. CFD, coupled with cardiac MRI, can offer a more comprehensive evaluation of the transaortic gradient, which is frequently uncorrected in sedated patients. Additionally, it may allow for the evaluation of blood flow patterns inside the aorta, as well as the potential effects of stenting or surgical repair [36]. CFD has been used for surgical planning in clinical settings to aid surgeons and physicians in decision-making [37-39]. Models of each patient's anatomy after various types of surgery or stenting procedures can be generated, and CFD analyses based on patient-specific boundary conditions can assess the expected hemodynamics after intervention (Figure 4). Capelli et al. [40] used CFD to identify the maximum expansion diameter that would allow for effectively covered stent placement at the level of the narrowing while avoiding obstruction of the aberrant right subclavian artery and bronchial compression of the. The CFD analyses are able to quantify the decrease in the peak velocity and pressure gradient, which in all the virtually-treated CoA patients dropped from an average of 15.5 mmHg pre-implant to 1.9 mmHg after stenting, predicting the results observed in real patients in the cath lab.

Tetralogy of Fallot

Tetralogy of Fallot (ToF) is a major congenital cardiac disease characterized by pulmonary stenosis, ventricular septal defect, over-riding aorta, and right ventricle (RV) hypertrophy; ToF results in cyanosis and accounts for 7%–10% of all CHDs [41]. The surgical widening of the right ventricular outflow tract usually produces a certain degree of pulmonary valve regurgitation (PR), which can result in RV volume and pressure overload over time. PR could also play a role in the formation of vortex flow in PAs, although the aetiology is still poorly understood. In general, flow vortices are associated with alterations in WSS and affect endothelial function [42]. CFD could potentially identify parameters suitable for the prediction of outcomes in patients with repaired ToF and can define the timing for pulmonary valve replacement. Moreover, the coupling of CFD with virtual procedure simulation may be used to tailor possible percutaneous pulmonary valve implantation according to each patient's anatomy and flow patterns, as already demonstrated by Capelli et al. [42].

Univentricular heart

Norwood circulation

Migliavacca et al. [45] utilized CFD to investigate the Norwood circulation, evaluating the shunt pressure drop–flow relationships, as well as varying shunt implantation angles, diameters, curvatures, and input pulsatility values, and found that shunt diameter was the main determinant of graft flow (as expected). They demonstrated that most pressure drops occurred near the proximal anastomosis, and curved grafts resulted in a lower pressure drop compared to straight grafts, due to reduced flow-line skewness towards the lateral graft wall near the proximal anastomosis. Subsequently, the same research group compared variants of the Norwood reconstructive surgeries with post-operative catheterization and Doppler data by carrying out a multi-scale CFD analysis [46]. A variation of the Norwood operation that utilized a modified Blalock–Taussig shunt was compared with the right ventricle-to-pulmonary artery shunt modification. The model predicted that the right ventricle shunt would result in higher aortic diastolic pressure, decreased pulmonary arterial pressure, lower pulmonary to systemic flow, and higher coronary perfusion relative to the innominate artery-to-right pulmonary artery shunt.

Fontan circulation

Assessment of the hemodynamic processes in Fontan circulation is difficult due to the abnormal position and geometry of the systemic ventricle, the extent of the Fontan circuit, and the passive nature of flow to pulmonary circulation. Blood flow to pulmonary circulation in Fontan patients is subjected to the peripheral muscle pump, systemic venous pressure, the systolic and diastolic performance of the systemic ventricle, and intrathoracic pressure changes during respiration. Recent research suggested that energy loss within the TCPC is an important factor in Fontan hemodynamics and should be decreased as much as possible via changes in vessel size, anastomosis shape, total blood flow, and pulmonary/caval flow distribution [47].
Haggerty et al. [48] used CMR-based CFD to evaluate the hemodynamics in 100 Fontan patients, with a focus on power loss within the Fontan circuit and demonstrated that Fontan tunnel stenosis and undersized pulmonary arteries are associated with increased power loss having a clear negative effect on Fontan hemodynamics.
CFD has been used to aid surgeons and physicians in clinical decision-making [49], providing insight into the preoperative blood flow. Models of each patient's anatomy after several different types of surgery can be virtually created, and patient-specific boundary conditions can be used to assess the expected hemodynamics after surgery.

Coronary artery physiology

Stent rheology

CFD is currently being utilized to understand the impact of stent structure on coronary blood flow parameters. Several recent studies have suggested that the local geometric environment created by a deployed stent may influence regional blood flow characteristics and alter distributions of wall shear stress (WSS) after implantation, thereby creating the conditions by which some specific areas of the vessel wall can be more susceptible to neointimal hyperplasia and restenosis [50]. Stents are most frequently implanted in curved vessels such as the coronary arteries, but most computational studies examining blood flow patterns through stented vessels use linear, cylindrical geometric models (Figure 3). It is likely that restenosis after stent implantation in curved arteries also occurs as a consequence of changes in fluid dynamics that are created after stent implantation. Ladisa et al. [51] found that the time-averaged WSS in the proximal portion of the stent ranged from 8.91 to 11.7 dynes/cm² along the pericardial luminal surface and 4.26 to 4.88 dynes/cm² along the myocardial luminal surface of curved coronary arteries, compared to 8.31 dynes/cm² observed throughout the stented region of a straight vessel implanted with an equivalent stent. The same group hypothesized that channeling of adjacent blood layers would have a profound effect on wall shear stress due to stent geometry [52]. Stagnation zones are usually localized in the proximity of stent struts. Minimum WSS decreased by 77% in stented compared to unstented vessels. Regions of low WSS were extended at the stent outlet and localized to regions where adjacent axial strut spacing was minimized, and the circumferential distance between struts was huge. These preliminary results have been confirmed by different authors [53-54], who also suggested that stents with a helical configuration generated an extra swirling component of the flow in a helical direction without significant changes to the distribution of WSS.

Coronary bifurcation

One of the most valuable applications of CFD in coronary artery research is in the study of coronary artery bifurcations, particularly that of the left main bifurcation. CFD was used to anticipate the results of complex bifurcation stenting and to understand how bifurcation rheology changes following stenting with various devices and techniques. Chen et al. [55] showed that stenting of the main vessel increased the maximum CWS in the side branch (SB), resulting in a nearly two-fold increase in the stress ratio in the SB compared to the MB (5.1 × 105 vs. 9.2 × 105). The existence of plaque decreased WSS and increased CWS near the carina, increasing the stress ratio at the SB. The changes in the stress ratio were highly consistent with clinical data on bifurcation stenting. Similarly, other investigations have suggested that angles of bifurcation [56] and stenting technique may differently impact stent rheology, potentially influencing the risk of restenosis and thrombosis based on the amount of metal struts placed into the carina [57-58] (Figure 4). Another variable considered was the site for the proximal optimization technique, which has a major role in determining the surface of the area corresponding with lower WSS. CFD has also been used to determine the risk of occlusion in patients with subclinical disease of the Left main or other bifurcation sites, suggesting a correlation between WSS in pre-existing coronary disease and the risk of acute closure of the vessel [59].

Atherosclerosis disease progression

CFD has been recently applied to the pathophysiology of atherosclerosis in order to understand the mechanisms underlying plaque progression and rupture. In particular, recent studies have focused on the mechanism referred to as "cavitation." From a physical point of view, cavitation occurs when the pressure (P) in an area of flowing fluid decreases below that of the vapor pressure (Pv). More precisely, cavitation bubbles form immediately below the Pv level, reaching their highest velocity at the lowest pressure level (Pmin), which is also known as the vena contracta point. Subsequently, bubbles increase in size with increasing pressure, leading to bubble collapse above the Pv level. This phenomenon is the result of two separate processes, which represent the essential substrates of cavitation: the former is represented by a large pressure fluctuation (dp/dt), while the latter is due to turbulent flow. CFD studies demonstrated that cavitation is generated by both concentric and eccentric coronary artery stenosis (≥ 75% for the former and ≥ 50% for the latter), which propagates downstream of the vessel, creating microbubbles that ruptured when the fluid pressure is lower than the vapor pressure at a local thermodynamic state [60](Figure 5). Biomechanically, cavitation might damage endothelial surfaces and promote thrombosis. The cavitation phenomenon alone is not sufficient to explain the growth, structural changes, and biochemical modifications in coronary atherosclerotic plaques, but it may act as a concurrent, rather than causal, factor in the precipitation of atherosclerotic disease.

Peripheral Vascular disease

The peripheral vascular disease has begun to become a field of interest for CFD application. CFD has been applied to abdominal aortic aneurysms to predict aneurysm progression and risk of rupture, and it also has been used in the prediction of the putative therapeutic effects of endovascular repair [61-62]. CFD has additionally been utilized to study aortic dissection, where computed pressure and flow conditions can be used to guide (semi-) invasive therapeutic procedure decisions. The physiological effects of therapies can thus be simulated and anticipated [63-64]. CFD has been recently adopted in peripheral artery disease, particularly in femoral and aortoiliac vascular districts, to anticipate the impact on WSS of different stent types and configurations [65] (Figure 6).

Conclusion

Further improvement in the quality of available virtual simulation software and its integration with existing diagnostic tools such as MRI, 3D, and 4D ultrasound, optical coherence tomography, intravascular ultrasound imaging, and angiography are likely to push CFD forward in clinical practice. As a result, the transition from offline assessment and planning to online evaluation and treatment will likely become much more effective.

Funding

This paper was not funded.

Declaration of interest

The authors have no relevant affiliations or financial involvement with any organization or entity with a financial interest or financial conflict with the subject matter or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert testimony, grants or patents received or pending, or royalties.

References

1. Taylor CA, Figueroa CA. Patient-specific modeling of cardiovascular mechanics Rev Biomed Eng 2009;11:109–34.
2. Morris PD, Ryan D, Morton AC, et al. Virtual fractional flow reserve from coronary: modeling the significance of coronary lesions: results from the VIRTU-1 (VIRTUal Fractional Flow Reserve From Coronary Angiography) Study. JACC Cardiovasc Interv 2013;6:149–57.
3. Morris PD, Narracott A, von Tengg-Kobligk H, et al. Computational fluid dynamics modelling in cardiovascular medicine. Heart 2016;102:18–28.
4. Theodorakakos A, Gavaises M, Andriotis A, Zifan A, Liatsis P, Pantos I, Efstathopoulos EP, Katritsis D. Simulation of cardiac motion on non-Newtonian, pulsating flow development in the human left anterior descending coronary artery. Phys Med Biol. 2008; 53:4875-9.
5. Cho Y, Kensey KR. Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: steady flows. Biorheology 1991; 8:241–262.
6. Morris PD, Narracott A, von Tengg-Kobligk H, Silva Soto DA, Hsiao S, Lungu A, Evans P, Bressloff NW, Lawford PV, Hose DR, Gunn JP. Computational fluid dynamics modelling in cardiovascular medicine. Heart. 2016 Jan;102(1):18-28. doi: 10.1136/heartjnl-2015-308044.
7. Pennati G, Corsini C, Hsia TY, Migliavacca F; Modeling of Congenital Hearts Alliance (MOCHA) Investigators. Computational fluid dynamics models and congenital heart diseases. Front Pediatr. 2013 Feb 26;1:4. doi: 10.3389/fped.2013.00004. PMID: 24432298; PMCID: PMC3882907.
8. Arbia G,  C, Esmaily Moghadam M, Marsden AL, Migliavacca F, Pennati G, Hsia TY, Vignon-Clementel IE; Modeling Of Congenital Hearts Alliance (MOCHA) Investigators. Numerical blood flow simulation in surgical corrections: what do we need for an accurate analysis? J Surg Res. 2014 Jan;186(1):44-55. doi: 10.1016/j.jss.2013.07.037. Epub 2013 Aug 11.
9. Jamalidinan F, Hassanabad AF, François CJ, Garcia J. Four-dimensional-flow Magnetic Resonance Imaging of the Aortic Valve and Thoracic Aorta. Radiol Clin North Am. 2020 Jul;58(4):753-763. doi: 10.1016/j.rcl.2020.02.008.
10. Morbiducci U, Kok AM, Kwak BR, Stone PH, Steinman DA, Wentzel JJ. Atherosclerosis at arterial bifurcations: evidence for the role of haemodynamics and geometry. Thromb Haemost. 2016 Mar;115(3):484-92. doi: 10.1160/TH15-07-0597.
11. Lindsey SE, Butcher JT, Yalcin HC. Mechanical regulation of cardiac development. Front. Physiol. 2014; 5:318. (doi:10.3389/fphys.2014.00318)
12. Sato Y, Poynter G, Huss D, Filla MB, Czirok A, Rongish BJ, Little CD, Fraser SE, Lansford R. Dynamic analysis of vascular morphogenesis using transgenic quail embryos. PLoS ONE 2010; 5: e12674. (doi:10.1371/journal.pone.0012674)
13. Hierck BP, Van der Heiden K, Poelma C, Westerweel J, Poelmannl RE. Fluid shear stress and inner curvature remodeling of the embryonic heart. Choosing the right lane! Sci. World J. 2008; 8: 212–222. (doi:10.1100/tsw.2008.42)
14. Courchaine K, Rugonyi S. 2018 Quantifying blood flow dynamics during cardiac development: demystifying computational methods. Phil. Trans. R. Soc. B 373: 20170330. http://dx.doi.org/10.1098/rstb.2017.0330
15. Kardos A, Babai L, Rudas L et al. Epidemiology of congenital coronary anomalies: a coronary arteriography study on a central European population. Cathet Cardiovasc Diagn 1997; 42: 270-5.
16. Yamanaka O, Hobbs RE. Coronary artery anomalies in 126,595 patients undergoing coronary arteriography. Cathet Cardiovasc Diagn 1990; 21: 28-40.
17. Rigatelli G, Rigatelli A, Cominato S, Panin S, Nghia NT, Faggian G. A clinical-angiographic risk scoring system for coronary artery anomalies. Asian Cardiovasc Thorac Ann 2012; 20:299-303
18. Javadzadegan A, Moshfegh A, Fulker D, Barber T, Qian Y, Kritharides L, Yong ASC. Development of a Computational Fluid Dynamics Model for Myocardial Bridging. J Biomech Eng. 2018; 140, in press. doi: 10.1115/1.4040127.
19. Sharzehee M, Seddighi Y, Sprague EA, Finol EA, Han HC. A Hemodynamic Comparison of Myocardial Bridging and Coronary Atherosclerotic Stenosis: A Computational Model with Experimental Evaluation. J Biomech Eng. 2020 Dec 3. doi: 10.1115/1.4049221. Epub ahead of print. PMID: 33269788.
20. Angelini P, Uribe C. Anatomic spectrum of left coronary artery anomalies and associated mechanisms of coronary insufficiency. Catheter Cardiovasc Interv. 2018, in press doi: 10.1002/ccd.27656
21. Rigatelli G, Zuin M, Galasso P, Carraro M, D’Elia K, Daniela L, Roncon L, Truyen TTTT, Nguyen T. Mechanisms of Myocardial Ischemia Inducing Sudden Cardiac Death in Athletes with Anomalous Coronary Origin from the Opposite Sinus: Insights from a computational fluid dynamic study. Cardiovasc Revasc Med. 2019 Dec;20(12):1112-1116. doi: 10.1016/j.carrev.2019.01.031.
22. Rigatelli G et al. Computed Tomography-based Patient-specific Biomechanical and Fluid Dynamic Study of Anomalous Coronary Arteries with Origin from the Opposite Sinus and Intramural Course. Heart International In press
23. Razavi A, Sachdeva S, Frommelt PC, LaDisa JF Jr. Patient-Specific Numerical Analysis of Coronary Flow in Children With Intramural Anomalous Aortic Origin of Coronary Arteries. Semin Thorac Cardiovasc Surg. 2020 Aug 26:S1043-0679(20)30271-9. doi: 10.1053/j.semtcvs.2020.08.016. Epub ahead of print. PMID: 32858220.
24. Rigatelli G, Zuin M, Nghia NT. Interatrial shunts: technical approaches to percutaneous closure. Expert Rev Med Devices. 2018; 15(10):707-716.
25. Rigatelli G, Zuin M, Fong A. Computational Flow Dynamic Analysis of Right and Left Atria in Patent Foramen Ovale: Potential Links with Atrial Fibrillation. J Atr Fibrillation. 2018; 10(5):1852. doi: 10.4022/jafib.1852.
26. Yener N, Oktar GL, Erer D et al. Bicuspid aortic valve. Ann Thorac Cardiovasc Surg. 2002; 8:264-7.
27. Piatti F, Sturla F, Bissell MM, et al. 4D flow analysis of BAV-Related Fluid-Dynamic alterations: evidences of wall shear stress alterations in absence of Clinically-Relevant aortic anatomical remodeling. Front Physiol 2017; 8:441.
28. Meierhofer C, Schneider EP, Lyko C, et al. Wall shear stress and flow patterns in the ascending aorta in patients with bicuspid aortic valves differ significantly from tricuspid aortic valves: a prospective study. Eur Heart J Cardiovasc Imaging 2013; 14:797–804.
29. Emendi M, Sturla F, Ghosh RP, Bianchi M, Piatti F, Pluchinotta FR, Giese D, Lombardi M, Redaelli A, Bluestein D. Patient-Specific Bicuspid Aortic Valve Biomechanics: A Magnetic Resonance Imaging Integrated Fluid-Structure Interaction Approach. Ann Biomed Eng. 2020 Aug 17. doi: 10.1007/s10439-020-02571-4. Online ahead of print. PMID: 32804291
30. Rigatelli G, Zuin M. Left Main Stenosis Stenting Normalises Wall Shear Stress of Ascending Aorta in Bicuspid Aortic Valve. Heart International In press
31. Cao K, Atkins SK, McNally A, et al. Simulations of morphotype-dependent hemodynamics in non-dilated bicuspid aortic valve aortas. J Biomech 2017; 50:63-70.
32. McNally A, Madan A, Sucosky P. Morphotype-dependent flow characteristics in bicuspid aortic valve ascending aortas: a benchtop particle image velocimetry study. Front Physiol 2017; 8:44.
33. Ando M, Okita Y, Morota T, Takamoto S. Thoracic aortic aneurysm associated with congenital bicuspid aortic valve. Cardiovasc Surg 1998;6:629–34.
34. Piatti F, Sturla F, Bissell MM, Pirola S, Lombardi M, Nesteruk I, Della Corte A, Redaelli ACL, Votta E. 4D Flow Analysis of BAV-Related Fluid-Dynamic Alterations: Evidences of Wall Shear Stress Alterations in Absence of Clinically-Relevant Aortic Anatomical Remodeling. Front. Physiol. 2017; 8:441. doi: 10.3389/fphys.2017.00441
35. Michelena, H. I., Prakash, S. K., Della Corte, A., Bissell, M. M., Anavekar, N., Mathieu, P., et al. (2014). Bicuspid aortic valve identifying knowledge gaps and rising to the challenge from the international bicuspid aortic valve consortium (BAVCON). Circulation 129, 2691-2704. doi: 10.1161/CIRCULATIONAHA.113.007851
36. Riesenkampff E, Fernandes JF, Meier S, et al. Pressure Fields by Flow-Sensitive, 4D, Velocity-Encoded CMR in Patients With Aortic Coarctation. JACC: Cardiovascular Imaging 2014; 7:920–6.
37. Arzani A, Dyverfeldt P, Ebbers T, Shadden SC. In vivo validation of numerical prediction for turbulence intensity in an aortic coarctation. Ann Biomed Eng. 2012 Apr;40(4):860-70. Doi: 10.1007/s10439-011-0447-6. Epub 2011 Oct 21.
38. LaDisa JF Jr, Alberto Figueroa C, Vignon-Clementel IE, Kim HJ, Xiao N, Ellwein LM, Chan FP, Feinstein JA, Taylor CA. Computational simulations for aortic coarctation: representative results from a sampling of patients. J Biomech Eng. 2011 Sep;133(9):091008. doi: 10.1115/1.4004996.
39. LaDisa JF Jr, Dholakia RJ, Figueroa CA, Vignon-Clementel IE, Chan FP, Samyn MM, Cava JR, Taylor CA, Feinstein JA. Computational simulations demonstrate altered wall shear stress in aortic coarctation patients treated by resection with end-to-end anastomosis. Congenit Heart Dis. 2011 Sep-Oct;6(5):432-43. doi: 10.1111/j.1747-0803.2011.00553.x. Epub 2011 Jul 31.
40. Capelli C, Sauvage E, Giusti G, Bosi GM, Ntsinjana H, Carminati M, Derrick G, Marek J, Khambadkone S, Taylor AM, Schievano S. Patient specific simulations for planning treatment in congenital heart disease. Interface Focus 2018; 8: 20170021. doi: 10.1098/rsfs.2017.0021
41. Villafañe J, Feinstein JA, Jenkins KJ, et al. Hot topics in tetralogy of Fallot. J Am Coll Cardiol 2013;62:2155–66.
42. Paszkowiak JJ, Dardik A. Arterial wall shear stress: observations from the bench to the bedside. Vasc Endovascular Surg 2003; 37:47–57.
43. Fontan F, Baudet E. Surgical repair of tricuspid atresia. Thorax 1971; 26:240–8. 44. Galantowicz M,Cheatham JP, Phillips A,Cua CL,Hoffman TM,Hill SL.Hybrid approach for hypoplastic left heart syndrome: intermediate results after the learning curve. Ann Thorac Surg. 2008; 85: 2063–70.
45. Migliavacca F, Pennati G, Dubini G, et al. Modeling of the Norwood circulation: effects of shunt size, vascular resistances, and heart rate. Am J Physiol Heart Circ Physiol 2001; 280: H2076–H2086.
46. Migliavacca F, Balossino R, Pennati G, et al. Multiscale modelling in biofluidynamics: application to reconstructive paediatric cardiac surgery. J Biomech 2006; 39: 1010–1020.
47. Rijnberg FM, Hazekamp MG, Wentzel JJ, et al. Energetics of blood flow in cardiovascular disease: concept and clinical implications of adverse energetics in patients with a Fontan circulation. Circulation 2018; 137:2393–407.
48. Haggerty CM, Restrepo M, Tang E, et al. Fontan hemodynamics from 100 patient-specific cardiac magnetic resonance studies: a computational fluid dynamics analysis. Thorac Cardiovasc Surg 2014; 148:1481–9.
49. Trusty PM, Restrepo M, Kanter KR, et al. A pulsatile hemodynamic evaluation of the commercially available bifurcated Y-graft Fontan modification and comparison with the lateral tunnel and extracardiac conduits. J Thorac Cardiovasc Surg 2016; 151:1529–36
50. Chen HY, Chatzizisis YS, Louvard Y, Kassab GS. Computational Simulations of Provisional Stenting of a Diseased Coronary Artery Bifurcation. Sci Rep (2020) 10:9667 https://doi.org/10.1038/s41598-020-66777-1
51. Mordellids JF Jr, Olson LE, Douglas HA, Warltier DC, Kersten JR, Pagel PS. Alterations in regional vascular geometry produced by theoretical stent implantation influence distributions of wall shear stress: analysis of a curved coronary artery using 3D computational fluid dynamics modeling. Biomed Eng Online. 2006 Jun 16;5:40. doi: 10.1186/1475-925X-5-40. PMID: 16780592; PMCID: PMC1550410.
52. LaDisa JF Jr, Guler I, Olson LE, Hettrick DA, Kersten JR, Warltier DC, Pagel PS. Three-dimensional computational fluid dynamics modeling of alterations in coronary wall shear stress produced by stent implantation. Ann Biomed Eng. 2003 Sep;31(8):972-80. doi: 10.1114/1.1588654. PMID: 12918912.
53. Martin DM, Murphy EA, Boyle FJ. Computational fluid dynamics analysis of balloon-expandable coronary stents: influence of stent and vessel deformation. Med Eng Phys. 2014 Aug;36(8):1047-56. doi: 10.1016/j.medengphy.2014.05.011. Epub 2014 Jun 20. PMID: 24953569.
54. Chen WX, Poon EK, Hutchins N, Thondapu V, Barlis P, Ooi A. Computational fluid dynamics study of common stent models inside idealised curved coronary arteries. Comput Methods Biomech Biomed Engin. 2017 May;20(6):671-681. doi: 10.1080/10255842.2017.1289374. Epub 2017 Feb 9. PMID: 28349764.
55. Sun Z, Chaichana T. An investigation of correlation between left coronary bifurcation angle and hemodynamic changes in coronary stenosis by coronary computed tomography angiography-derived computational fluid dynamics. Quant Imaging Med Surg. 2017 Oct;7(5):537-548. doi: 10.21037/qims.2017.10.03. PMID: 29184766; PMCID: PMC5682403.
56. Chen HY, Chatzizisis YS, Louvard Y, Kassab GS. Computational Simulations of Provisional Stenting of a Diseased Coronary Artery Bifurcation Model. Sci Rep. 2020 Jun 15;10(1):9667. doi: 10.1038/s41598-020-66777-1. PMID: 32541660; PMCID: PMC7295811.
57. Zuin M, Rigatelli G, Chiastra C. Optimal Site for Proximal Optimization Technique in Complex Coronary Bifurcation Stenting: A Computational Fluid Dynamics Study. Cardiovasc Revasc Med. 2020 Jul;21(7):826-832. doi: 10.1016/j.carrev.2019.12.015. Epub 2019 Dec 11. PMID: 31866275.
58. Rigatelli G, Zuin M, Dell’Avvocata F, Vassilev D, Daggubati R, Nguyen T, Van Viet Thang N, Foin N. Evaluation of coronary flow conditions in complex coronary artery bifurcations stenting using computational fluid dynamics: Impact of final proximal optimization technique on different double-stent techniques. Cardiovasc Revasc Med. 2017 Jun;18(4):233-240. doi: 10.1016/j.carrev.2017.01.002. Epub 2017 Jan 9. PMID: 28108202.
59. Zuin M, Rigatelli G, Vassilev D, Ronco F, Rigatelli A, Roncon L. Computational fluid dynamic-derived wall shear stress of non-significant left main bifurcation disease may predict acute vessel thrombosis at 3-year follow-up. Heart Vessels. 2020 Mar;35(3):297-306. doi: 10.1007/s00380-019-01494-y. Epub 2019 Sep 3. PMID: 31482218.
60. Rigatelli G, Zuin M, Ngo TT, Nguyen HT, Nanjundappa A, Talarico E, Duy LCP, Nguyen T Intracoronary Cavitation as a Cause of Plaque Rupture and Thrombosis Propagation in Patients with Acute Myocardial Infarction: A Computational Study. J Transl Int Med. 2019 Jul 11;7(2):69-75. doi: 10.2478/jtim-2019-0014
61. Georgakarakos E, Ioannou CV, Papaharilaou Y, et al. Computational evaluation of aortic aneurysm rupture risk: what have we learned so far? J Endovasc Ther 2011;18:214–25.
62. Molony DS, Kavanagh EG, Madhavan P, et al. A computational study of the magnitude and direction of migration forces in patient-specific abdominal aortic aneurysm stent-grafts. Eur J Vasc Endovasc Surg 2010;40:332–9.
63. Karmonik C, Müller-Eschner M, Partovi S, et al. Computational fluid dynamics investigation of chronic aortic dissection hemodynamics versus normal aorta. Vasc Endovascular Surg 2013;47:625–31.
64. Chen D, Müller-Eschner M, von Tengg-Kobligk H, et al. A patient-specific study of type-B aortic dissection: evaluation of true-false lumen blood exchange. Biomed Eng Online 2013;12:65.
65. Rigatelli G, Zuin M, Dell’Avvocata F, Nanjundappa A, Daggubati R, Nguyen T. Non-invasive Evaluation of Fluid Dynamic of Aortoiliac Atherosclerotic Disease: Impact of Bifurcation Angle and Different Stent Configurations. J Transl Int Med. 2018 Oct 9;6(3):138-145.