Biomechanical assessment of aortic valve stenosis: Advantages and limitations

Journal Pre-proof Biomechanical Assessment of Aortic Valve Stenosis: Advantages and Limitations Parnia Zakikhani, Raymond Ho, William Wang, Zhiyong Li PII:

S2590-0935(19)30009-8

DOI:

https://doi.org/10.1016/j.medntd.2019.100009

Reference:

MEDNTD 100009

To appear in:

Medicine in Novel Technology and Devices

Received Date: 21 September 2019 Accepted Date: 30 September 2019

Please cite this article as: Zakikhani P, Ho R, Wang W, Li Z, Biomechanical Assessment of Aortic Valve Stenosis: Advantages and Limitations, Medicine in Novel Technology and Devices, https:// doi.org/10.1016/j.medntd.2019.100009. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Biomechanical Assessment of Aortic Valve Stenosis: Advantages and Limitations Parnia Zakikhani1, Raymond Ho1, William Wang2, Zhiyong Li1,3,4 1

School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology (QUT), Brisbane, Australia 2

3

Department of Cardiology, Princess Alexandra Hospital，Brisbane, Australia

School of Biological Science and Medical Engineering, Southeast University, Nanjing, China 4

School of Pharmacology, University of Queensland, Brisbane, Australia

Corresponding author: Professor Zhiyong Li School of Biological Science and Medical Engineering, Southeast University, Nanjing, China Email: [email protected] Abstract Aortic valve stenosis (AS) is a common and potentially severe disease of the heart. Accurate assessment of AS is a critical factor in determining prognosis and management. This paper describes the advantages and limitations of AS assessment from a biomechanical engineering perspective, by contrasting the non-invasive AS diagnostic methods of echocardiography (Echo), computed tomography (CT), magnetic resonance imaging (MRI), computational analysis (CA) including the invasive technique of cardiac catheterisation. The findings illustrated that current methods of AS evaluation, with assumptions of an ideal fluid, geometry and governing equations may not apply well to the aortic valve pathology and could increase the uncertainty of the degree of stenosis and valve area. This review suggests an alternative method using CA, which could potentially overcome the pitfalls of other AS assessments that incorporate geometry, pressure recovery and aorta wall compliance, based on the accurate conversion of AS imaging to the numerical modelling. Further, this review highlights the importance of boundary conditions, and the role of verification and validation to produce reliable computational results. Keywords: aortic valve stenosis; echocardiography; computed tomography; magnetic resonance imaging, computational analysis; fluid dynamics 1. Introduction Aortic Stenosis (AS) is the disease in which the aortic valve (AV) orifice becomes narrow and restricts the blood flow from passing through the left ventricle (LV) into the ascending aorta. Progressive AS results in an increasing pressure gradient across the LV and aorta, where a higher LV systolic pressure is required to maintain cardiac output [1] and increases cardiac afterload [2, 3]. Untreated severe symptomatic AS is associated with a poor prognosis towards heart failure, coronary insufficiencies, syncope or sudden death. A common risk factor of AS is age-related degeneration and calcification of the AV. Due to the aging population in developed countries, AS has become one of the most severe valvular heart diseases. The standard treatment for AS is valve replacement surgery, and the number of cases has been predicted to increase from 290,000 each year to 850,000 by 2050 [4]. Also, other factors, including congenital bicuspid valves and rheumatic heart disease, contribute to AS [5, 6]. In contrast to normally formed tricuspid AV, a congenital malformation is the bicuspid aortic valve (BAV) [7]. A combination of AS and BAV occurs at a much earlier age compared to the general population [8], possibly due to an abnormality in blood fluid flow, affecting the inner aortic wall surface and stress distribution on AV

leaflets [9]. This disease destroys the collagen fibres in the AV cusps of affected patients and eventually results in the formation of calcium deposits on the leaflets of the AV[10, 11]. The AV is located between the LV outflow tract and ascending aorta with three cusps. The microstructure of AV leaflets consists of three layers, fibrosa, spongiosa, and ventricularis. The fibrosa comprises of collagen fibres type-I which formed in a radial direction parallel to the free edge of the leaflet and transfer the leaflets load to the aortic root’s wall [12]. The spongiosa layer between fibrosa and ventricularis act as a lubricant when they deform and shear due to pressurisation and bending of the leaflets [13]. During the systole, when the AV is fully opened the ventricularies reduce the radial strain [4] (Fig 1). The changes in the leaflets morphology with age influences the geometry of the orifice area, lessens the valve durability and increases the valve stress [14]. The noncoronary cusp is frequently affected ahead of the left and right coronary cusps because of the highest mechanical forces and the low shear stress amongst the noncoronary cusp endothelium induced by diastole flow [15]. Accurate assessment of AS severity is vital to identify the high-risk patients, and to predict those who need treatment. The severity of AS based on hemodynamic parameters has been classified into three categories: mild, moderate and severe [16]. The parameters include AV flow velocity, mean transvalvular gradient and AV area (Table 1). With the effect of AS altering blood flow in the LV and ascending aorta, it is essential to analyse the orifice area and leaflet stress distribution. Finite element analysis (FEA) combined with computational fluid dynamics (CFD) has been shown to evaluate the dynamics of blood flow and mechanical strength effectively. This review aims to provide a summary of the current AS assessment from the perspective of engineering analysis and highlights the potential use of CA as an alternative assessment with validation as a critical process to determine a level of acceptance. .

A

B

Figure 1 a) the cross-section of an aortic valve leaflet, b) microstructure of the valve leaflet [4].

2.

The clinical issues and current diagnosis methods

The accurate measurement method of the AS severity is to ensure that the treatment is performed only on the appropriate patients [17]. The severity of AS can be assessed clinically, with both invasive and non-invasive techniques. The invasive assessment of cardiac catheterisation obtains the transvalvular gradient, evaluates cardiac output and estimates the valve area, but carries procedural risks [18]. Non-invasive techniques have advantages over the invasive methods of low cost, less risk and discomfort to patients. Although non-invasive methods have a limitation in the accuracy of the hemodynamic parameter measurements, due to technical and theoretical assumptions[19]. The current diagnostic techniques are dependent on blood flow with the invasive method assesses the disease using the Gorlin equation. In contrast, the non-invasive method estimates the area of the valve based on the Continuity equation and the Navier-Stokes equation with its derivative, the Bernoulli equation for ideal fluids to describe the behaviour of blood flow. 2.1 Invasive 2.1.1 Cardiac catheterisation & pressure recovery phenomenon Cardiac catheterisation is an invasive method to assess the severity of AS with pressure gradient measurement or AV area calculation. Maximal transvalvular pressure gradient (TPGmax) and mean transvalvular pressure

gradient (TPGnet) are measured using cardiac catheters. Using the thermodilution technique to obtain flow rate [21], the Gorlin formula is used to calculate the effective orifice area (EOA). When the computed Gorlin EOA was compared with the calculated EOA (using the Continuity equation and ultrasound Doppler for velocity), the EOA (by catheter) was higher than the EOA (calculated Doppler). The severity of stenosis and the size of the ascending aorta causes pressure recovery. Using multi-tip micromanometer pigtail catheter with the cross-sectional area of 0.05 cm2 [22], the pressure at vena contracta, within the left ventricular and the aorta, the pressure recovery had been completed and recorded to calculate the effective AV area with the Gorlin formula. The results indicated that the differences in the measurement were induced by pressure recovery. Subtraction of the measured pressure gives the value of pressure recovery at vena contracta from net pressure and after vena contracta by Doppler echocardiography and catheterisation respectively. The effect of this phenomenon on the measurement of the valve EOA and the pressure gradient by Doppler and catheter was investigated [21, 23]. The results showed significant differences between two types of measurement of similar parameters. These discrepancies were caused by pressure recovery on the AV with stenosis. The magnitude of the pressure recovery depends on the severity of the AV stenosis. Although catheterisation technique has been used to measure pressure gradient, there is a limitation in the accurate placement of catheter from the AV stenosis [25, 26]. 2.2 Non-invasive 2.2.1 Echocardiography Echocardiography is the most commonly used method to assess and diagnose the severity of AS. Based on transmitting ultrasonic waves, the size and motion of the heart chamber is visualised with M-mode and 2D echocardiography. The hemodynamic measurement of blood flow to evaluate and classify the AV severity can be provided by Doppler-echocardiography [16]. Echocardiography has limitations in the assessment of AS severity, which is listed in Table 1. Doppler-echocardiography is used to calculate the pressure gradient across the AV which is derived from the simplified Bernoulli equation, with an assumption of low proximal velocity to the aortic stenosis, where only the maximum velocity is required [27, 28]. Another assumption is the deceleration/acceleration of the flow, caused by the total pressure drop without considering the effect of viscous and unsteady fluid components [29]. The application of the Bernoulli equation to describe the drop pressure during the distal and proximal is given as: p2-p1= 1/2ρ(v22-v12) + ρ(dv/dt)dx + R(v)

(1)

Where p2-p1 is the pressure drop (or ∆P), 1/2ρ (v22-v12) represents the convective acceleration and v2 is the systole velocity, and v1 is the diastole velocity at the AV, ρ is the blood density, ρ (dv/dt)dx is the blood flow acceleration and R(v) is the viscous friction. In this equation, the viscous friction and blood flow acceleration are ignored. The area of the AV is significantly greater because of the valve stenosis. Therefore, v1 can be ignored, and the change in the convective acceleration component is simplified to v22. The Bernoulli equation is now reduced to ∆P=1/2ρv22, and the simplified Bernoulli equation for pressure drop is ∆P=4v2 [27, 30]. Therefore, the simplification process develops an insufficiency in describing the effects of viscous dissipation during fluid flow [31]. Additionally, the aortic valve area (AVA) has been calculated with the use of the continuity equation (eq. 2) [32], AVA= (CSALV × VLVOT)/ VAV

(2)

CSALV: the cross-sectional area of the left ventricle VLVOT: velocity at the left ventricular outflow tract VAV: velocity at the aortic valve However, further inaccuracies are found when the LV CSA, from the echocardiography, is calculated with circle area formula (π (D/2)2) where the diameter is based on an ideal circular CSA [33], while the actual CSA images are not geometrically circular.

Table 1. Classification of AS severity and limitations of hemodynamic parameters measurement by Doppler-echo [16, 26, 34] Normal

Mild

Moderate

Severe

-

<25

25-40

40 or 50

Aortic stenosis jet velocity (m/s)

<2.5

2.5-2.9

3-4

>4

Aortic valve area (cm2)

3-4

1.5-2

1-1.5

<1

Mean gradient (mm Hg)

Limitations • Calculation of an accurate mean gradient is dependent on precise velocity measurement. • It is dependent on blood flow. • Parallel alignment of the ultrasonic transducer is required for measuring the velocity correctly. • It is dependent on blood flow. • To solve the continuity equation, three parameters are required, such as the diameter of the left ventricular outflow tract, flow velocity and aortic velocity. Error in this measurement may occur.

2.2.2 Computed Tomography (CT) Computed tomography (CT) provides a high-resolution anatomic measurement and assesses AV calcification (AVC), which can be correlated with the severity of AS at baseline and progression of disease with serial scanning [35]. In assessing the overall calcified volume, a combination of multislice CT with ECG gating in comparison with electron beam CT and prospectively triggered multislice may decrease the interscan variability[36, 37]. Multislice CTs can identify a much smaller volume of calcified AV compared to the amount detected by echocardiography. For instance, the growth and initiation of AV calcification of 12 patients were evaluated by CT scans with the method of reverse calcification technique (RCT) [38]. The geometry model of a normal AV was based on mathematical equations used to provide three-dimensional (3D) AV geometry. The model was imported in Abaqus software to reproduce the leaflets with a thickness of 0.3mm as a shell type; the model was assumed as a heterogeneous body, consisting of collagen fibres in the elastin layers. Both collagen fibres and elastin layers were assumed to have hyperplastic mechanical behaviour, and the calcification was projected on the leaflet’s surface. The researchers found that the denser region in the cusps are induced by older calcification, and the highest concentration was close to the geometric centre of the calcification volume. 2.2.3 Magnetic resonance imaging (MRI) MRI is a versatile technique and could evaluate 2D and 3D anatomical structures, as well as flow velocities. The diagnosis techniques of AV stenosis are compared and shown in Table 2. Using chamber and volume quantifications and flow velocities, MRI assesses AS and has been compared with echocardiography [39]. The MRI had issues of lower temporal and spatial resolution compared with echocardiography. Different types of advanced flow MRI methods have been used by researchers to study the blood flow specification such as 4D flow MRI, real-time PC-MRI, Fourier velocity encoding or Bayesian multipoint velocity encoding [40-42]. The

4D flow MRI in comparison with other advanced methods, enables the evaluation of blood flow in three directions within the 3D vascular structure [43]. It also can visualise and measure the temporal evolution of the intricate blood flow patterns in the aorta. The 4D flow was used in a study to investigate the effect of BAV on wall shear stress (WSS) and distribution of WSS on thoracic aorta [44]. The MRI used a 3T MR system, and the data obtained with ECG-gating cycle, comprised of echo time, repetition time, flip angle, voxel size, temporal resolution and velocity encoding. The acquired data were analysed and visualised with CFD. The results showed that changes in WSS could cause aortopathy. In another study, the collected data were simulated and visualized in EnSight software to assess the blood flow in the ascending aorta [45] illustrating secondary blood flow features for BAV.

Table 2. The comparison of aortic valve stenosis diagnosis methods [46-49] Methods

Hemodynamic data

Anatomic measurement

Resolution

Risk

Invasive Cardiac catheterisation






-

Damage the endothelium of the artery wall

Non-invasive Magnetic resonance imaging (MRI) Doppler echocardiography









Low Moderate

-






High

Radiation exposure

Computed Tomography (CT)

-

3. Computational analysis (CA) of aortic valve stenosis AS diagnosis with CA requires a basic understanding of fluid dynamics and finite element analysis (FEA). Although an understanding of the theoretical concepts is essential with CA, the geometrical reconstruction, defining realistic boundary conditions and incorporating validation are significant challenges. Generally, the AV has been simulated from two primary methods: geometry-prescribed method to solve the fluid domain and fluidstructure interaction (FSI) to explain the structural reaction imposed by the fluid [50]. 3.1 Fluid dynamics The dynamics of blood fluid flow is an essential principle in the investigation of heart valves mechanics due to the dynamic fluid forces on the valve [51, 52]. With the ejection of blood into the aorta, the sudden expansion of flow from AS causes turbulent flow, associated with dissipating kinetic energy that eventually transforms into heat at a molecular level [53]. The behaviour of the blood flow has been studied and analysed based on different assumptions. In a numerical analysis based on the Navier-Stokes equations, the asymmetric laminar flow was modelled with the premise of incompressible Newtonian viscous fluid, to evaluate the fluid acceleration [54]. The results indicated that viscosity is an essential parameter in the study. It causes vortices in the sinuses of the AV and separates the flow. The Navier-Stokes equation and Poisson equation determines the pressure field from three types of velocity data; fine data, coarse data and data with noise [31]. From these two equations, the mathematical and numerical procedure utilised idealised unsteady flow in both symmetric and non-symmetric geometry derived from physiological data as a basis to conduct a study. The results were compared with the Stokes equation (STE) method and the pressure Poisson equation (PPE), where STE provide better estimations of pressure. The developed mathematical and numerical model was applied to AV stenosis to investigate pressure gradient and energy dissipation of blood flow across the aortic stenosis [18]. The aorta was assumed as a rigid body, and the geometry was oversimplified by removing the valve leaflet. The Navier- Stokes equation for blood fluid is a closer approximation of real fluids, while Bernoulli’s equation is simpler to use, only applies to ideal fluids and is unable to quantify the viscous energy dissipation.

3.2 Geometry reconstruction The location and geometry of the AV are critical in the diagnosis of the AS. The AV geometries are obtained invivo, using MRI, multislice CT images and Echocardiography to perform image processing and combined with ex vivo data reconstructs the physiological geometry [14, 55, 56]. However, identifying the fine free edge of leaflets are often challenging. Capturing accurate details from in-vivo geometries has been performed by manual reconstruction of the valve geometry by selecting points and measurement [57]. The analytical and mathematical formulation was used to build the 3D geometry of the AV [58]. The proposed functions were implemented in TrueGrid software to generate surface and mesh. From two dimensional (2D) images of the IE33 ultrasound system, 298 points were identified at mid-diastole to describe the sinus and the non-coronary cusp. These collected points were tagged on the 3D volumetric images and transformed into Cartesian coordinates. A comparison of the generated surface and measured points were projected onto the valve surfaces and could represent a quantified estimate error of the AV parameters. Similarly, the measured point method was used to reconstruct the aortic root in the mid systole phase of angiographic films [59]. In another study, the geometry of the AV was modelled from CT images [60]. The 3D coordinates of the geometries were digitised manually from 2D images. The generated point cloud was imported in HyperMesh software for creating a surface and finite element meshes on the valve. While another researcher [61] reconstructed the 3D geometry of the aortic root and leaflets in Avizo software. The multislice CT images in systole phase were imported in the Avizo software, and then finite element meshes were generated in the HyperMesh. A few approaches have been performed on the cellular and organ length scales of the AV simulation and studies on the deformation of the valves at tissue and cell levels [62, 63]. The fibrosa and ventricularis of AV tissue were drawn as a separate layer and then connected through the assembly in ADINA software [63]. A single cell of the tissue surrounded by ventricularis or fibrosa as a matrix was created in ADINA and to give an ellipsoidal shape to the cell, the researchers created a sphere within a cube, then the created geometry was 3D scaled. The organ level of the AV was modelled in LS-DYNA and SolidWorks. The developed model was meshed in the HyperMesh, (Fig 2) shows the reconstructed leaflets of the AV.

Organ level

a

b

Tissue level

Cell level

Figure 2. The geometry reconstruction of the aortic leaflets a) selected points from echo images [58], b) reconstructed model [63]

3.3 Loading and boundary conditions The deformation of the AV is dependent on the loading phases induced by flow during pulsation. In FEA, the applied load on the leaflets are based on discrete time steps, which is independent of other factors on the valve such as the viscosity of the blood. Therefore, the interaction of the structure with fluid dynamics simulation may mimic AV movement. The mechanical behaviour of calcification on normal and BAV was simulated in the form of multiscale analysis such as organ-scale, tissue scale and cell scale [62]. To study the enforced dynamic deformation in the calcific aortic stenosis (CAS) on the valvular interstitial cells (VICs). Boundary conditions in this simulation were projected from the organ scale model to tissue scale model and mapped from the tissue scale model to the cell scale model. The deformation of the AV was described by fluid-structure interaction

(FSI) analysis. They modelled the geometry and assumed the aortic root as an isotropic and a single term Mooney-Rivlin material. The solid region was embedded in the fluid domain and to move the sinus radially, the fluid domains were added at the entry region, with the boundary conditions applied. The entry regions and nodes at the junction of both aortic root and entry region were fixed to constrain the axial movement. The obtained results indicated that the difference in the risk of calcification was due to the matrix components throughout the AV where the cells were modelled. The same process was performed on the normal AV and CAS valve to contrast the differences [63]. The investigators found that the abnormal valvular interstitial cells induced by unusual strains in the tissue. The 3D physiological model of BAV and tricuspid AV (TAV) based on MRI in vivo data were modelled in both systole and diastole to analyse the anisotropic and nonlinear response of the tissue [57]. In this analysis, the 80 mmHg of pressure was applied to the FEA model then the time-dependent physiological pressures were added to the substructures of the aortic root and the aortic inner wall. After pressurisation, the maximum stress occurred at the leaflet belly, because of the lower local thickness and distributed collagen fibres all over the tissue [14]. A study of the BAV and TAV were simulated with CFD based on MRI 4D-flow data to capture the timeresolved 3D velocities to assess wall shear stress (WSS) leading to inflammation and changing the adjustment of interstitial cells [9]. The study defined the aortic lumen as a region of interest (ROI), set zero pressure at the outlet and the time-dependent flow for the aorta inlet. The blood fluid was assumed as an incompressible Newtonian. Similarly, the blood was assumed as an incompressible in the aortic root simulation [55]. Due to the presence of collagen fibres in the normal TAV leaflets tissue, the material was assumed as hyper-elastic and transversely isotropic. The rest of the AV tissues were assumed as isotropic, linear and elastic materials with different Young’s modulus at the ascending aorta, interleaflet and Valsalva sinuses. The model was imported in the fluid domain, and inflow and outflow were applied to it. The pressure was set differently on the model as a uniform load distribution on the surface of the inner ascending aorta wall and inner wall of the interleaflet. A consistent transvalvular pressure was superimposed on the ventricular surface. The leaflets in the FSI and structural model were stretched circumferentially during systole while during diastole both sides of the leaflets were stretched. In a subsequent study [3], the structure of normal TAV was modelled in Abaqus software from CT images. The calcification geometry was imported into the model and to reduce the effect of flow boundary conditions on the defined domain, two rigid tubes were added for upstream and downstream of the AV. The flow was assumed as laminar and Newtonian fluid with the assumption of slightly compressible blood. The finite volume method was used for the domain of blood flow. The analysis showed that the geometry of calcification in the sinus area of the cusps change the flow and create asymmetric fluid shear stress on the side of the cusp. The 3-element Windkessel model was connected at the end of the distal on the normal and stenotic TAV model and BAV model separately [64]. The physiologic pressure wave was simulated based on the heart pumping to examine the progress of the disease on the BAV with its morphological characteristics. The structural and fluid meshes were applied to the AV model for FSI analysis. They merged the meshes at the interfaces to give balance to the force traction, and because of large movement of AV and distorting the mesh, an algorithm was developed for reconnecting the meshes automatically. The algorithms were used in an iteration loop to give balance to the system. The analysis indicated that the stress distribution influence on disease progression [3]. As the flow feature changes in the thoracic aorta of the severe AV, the researchers studied the angle of AV flow with low viscosity [65]. They imported the collected phase data form 4D flow MRI into MATLAB software and removed eddy current induced background offset by applying the fitting data in second-order polynomial. Then the outer region of the thoracic area as an ROI was removed. They found that the angle and direction of the AV flow create helical blood flow. It is also induced because of the fusion type of the AV which affects the amount of WSS. Further, another investigation of the BAV orifice and geometry of the thoracic aorta was reconstructed from CT angiography data; the boundary conditions required for blood flow rate were obtained by MRI [66]. These

researchers used thermo-fluid software to analyse the model and meshed the geometry in different layers. The prism mesh was generated in five layers near the wall of the vessel, and tetrahedral cells were created for the rest of the geometry with exceptional care at the orifice area of the BAV. The blood flow was assumed as laminar, incompressible Newtonian fluid. Normal density and viscosity values of blood were provided to the CFD model. Boundaries were applied on ascending aorta wall and aortic branches outlets with no pressure condition at the end of the descending aorta. The results demonstrated that jet velocity caused an increase in shear stress distribution on the ascending aortic wall and created an environment for aortopathy. Similarly, other researchers studied the practical factors in flow abnormalities of the AV [67, 68]. The leaflets were assumed as a hyper-elastic material based on incompressible Moony-Rivlin method [68]. They applied the waveform pressure on the fluid domain. The inlet and outlet of the model were free to move in circumferential and radial directions, but in the axial direction, only the aortic wall was constrained. Elastic support was sued for the outer surface of the aortic wall to simulate the generated damping effect from tissue and gave frictionless contact to the leaflets to prevent the leakage through leaflets.

3.4 Verification and validation Verifying and validating (V&V) a computational simulation is essential for creating an accurate analysis to produce reliable and predictive data. Solution verification is the process of determining the numerical accuracy of the mathematical model [69]. Complementing verification is validation, which is a critical method to evaluate how closely a simulation output represents the physical problem. The ASME Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer, states “there can be no validation without experimental data”, and in the context of AS, the data can be derived from in vivo trials or in vitro experiments [70]. The verification process can be broken down into two approaches. The first approach determines how sensitive are the results, on the varying quality level of the elemental meshed domain. This mesh sensitivity test focuses on the magnitudes of residual error and evaluates the adequacy of the number of mesh elements capturing the flow parameters. The second verification approach involves solving the governing equations of the problem. The simulated model can be complicated in its geometry and operating conditions, yet with assumptions, the governing equations may be reduced into a solvable form, to deliver a consistent result for numerical comparison. Within the CFD community, it's usually found, that this first process of mesh sensitivity is a standard requirement and a minimum expectation. Ideally, it’s recommended that both approaches are investigated. The explicit details of CFD verification methods are involved and are not further discussed in this paper, However; the reader is guided to the suggested reading of [70] or the many other available CFD texts to appreciate the technique involved fully. For validating numerical simulations, a standard method is to use existing in vivo information. The benefit of published material is that it is a convenient and low cost to obtain, less time-consuming for conducting specific experiments, no ethics approval usually would be required, and numerous database may be available for crosschecking. The existing in vivo data can either be compared indirectly or directly to the simulation output. The indirect comparison method is either (a) the CFD user modifies the initial boundary conditions and optionally the geometry, to align with the published clinical data [71], or (b) the CFD user compares the published data to the unadjusted simulation results. Approach (a) may provide accurate comparative results since the numerical model is modified until it matches with the clinical data, which is a soft way that reverses engineers the problem to fit the solution. The disadvantage with this approach is that it could increase the distance between the original problem and the numerical model, and thus it may decrease validation relevance. Method (b) is a more straightforward procedure than (a) and does not induce bias into the evaluation. Although, if comparison (b) displays a good agreement between the clinical data and the numerical results, a question of uncertainty creeps in, due to coincidence, which attacks the confidence of a reliable simulation. This coincidence factor may be minimised by increasing the number of compared data samples.

An alternative to the indirect method is the direct method (c). The direct comparative method (c) uses the patient’s specific data and boundary conditions for creating a 3D model and pathway to conduct the CFD simulation. The solution is then contrasted back against the initial patient data. This approach provides a high level of validation [72]. The disadvantage of this approach is that it's time-consuming to obtain patient image data, extracting and rebuilding of the data for modelling, gaining ethics approvals and patient permission. A further approach incorporates an in vitro experimental approach (d) which validates the CFD model that includes a physical replica phantom of the 3D model, using flow pattern recognition such as particle image velocimetry (PIV) [73]. This method recreates a component (such as an AV) which is manufactured from a 3D printing system. The 3D printed valve either becomes the tested component or a surrogate disposable and negative mould for the building of a cavity body for testing, as shown in (Fig 3). The benefit of this method is that the 3D phantom is a high-quality copy of the CFD model. The CFD simulation and the PIV flow process and parameters are closely aligned. However, the disadvantage is that the PIV model is a function of the simplified, reduced CFD model and not a direct representation of the physiological problem.

a

b

Figure 3. CFD model flow validation experiment a) 3D aorta model, b) silicon aorta phantom flow experiment

A final check for the CFD user is to compare their modelling results to a specially designed animal pre-clinical or human clinical trial (d). These types of tests are possibly the most challenging of validation experiments. The required organisation of resources is extensive from obtaining ethics approval, surgical staff, operating theatre, the surgical trial can be postponed or cancelled pre and perioperatively. These difficulties are multiplied if numerous tests are required. The preclinical and clinical results would be highly advantageous as a validation approach; however, it will be considered more as part of the end goal of CFD prediction rather than as a validation method. CFD studies must be checked at some level. Prantil et al. in the textbook “Lying by Approximation: The truth about Finite Element Analysis” states that to produce reliable simulation results, we must conduct modelling validation, with theoretical or experimental data [74]. Once this is completed, then we can lower our sceptical lens, yet no texts quantifiably inform the reader of how and to what extent or level of V&V is acceptable. To the authors’ knowledge and at the time of writing, no formal publication of a V &V grading system exists although the American Society of Mechanical Engineers (ASME) has created a detailed a draft standard of V&V for CFD. Therefore, the authors propose to categorise the three methods of indirect, direct and experimental processes (excluding preclinical and clinical trials). These categories are interpreted as a basic level of confidence for the reader to quantify their willingness to trust CFD results. These levels are shown in Table 3, describing each level as it progresses towards V&V. Ideally, each level should build on each other. Table 3: Confidence Hierarchy Level

ali da ti on

V&V

Method B and C

A B

1

Clinical data (Indirect methods)

Remarks High confidence in the results Acceptable confidence in the results, within the context of the specific

Verification

2

Clinical data (Direct methods)

3

Experimental (PIV or similar)

1

Study of mesh insensitivity and convergence of residuals

2

Results satisfy equations

problem

Minimal acceptance of the results

C the

governing

None

D

Cautious of the results

To illustrate Table 3, the hierarchy is applied to six randomly picked, peer-reviewed, published CFD aortic research articles (Table 4), to identify the level of confidence from V&V statements provided in the investigations. The results of the small survey show that a third of the researchers stated that both V&V procedures were carried out. As a standard expectation, most researchers, 5 of the 6, indicated they did verify their modelling. However, only one-third of them validated their results. One researcher did not report any V&V, which is shown as a “No” in Table 4. “No” means that verification and validation were not stated in their reports, although the V&V processes may have occurred. Nevertheless, the lack of ‘A’ level of confidence in the results indicates that the reading audience should knowledge a degree of scepticism or uncertainty. Table 4: Survey of verification and validation stated in research articles Year of Study 2003 [20] 2013 [64] 2016 [75] 2016 [68] 2016 [3] 2017 [72]

Verification Yes No Yes Yes Yes Yes

Validation No No No No Yes Yes

Level of Confidence C D C C A A

Table 4, highlights that not all results can be evenly weighed, and this type of classification assist the readers in their judgement of accepting of simulation results, along with the conclusions that are deduced from those results. 3.5 Limitations Modelling limitations are either (1) inherently built into the CFD solver which become specific to each type of fluid problem, and (2) generalised limitations may restrict an absolute result, which encompasses the CFD simulations. The built-in software limitations are extensive, and the authors invite the readers to consult the various CFD software manufacturer’s user and theory manuals. The manuals will help determine the weaknesses which are primarily based on the suitability of the CFD solver performance, within the expected flow domain. The generalised limitations for the CFD user is a function of their level of skill, project experience and any engineering bias which can affect the simulation output. The areas of concern are reproducing data from patient images, selecting the right regions of interest to build the 3D model, choosing the most appropriate boundary conditions and assumptions. Reconstructing a 3D model from patient images occurs at the beginning of the modelling workflow. Depending on the CFD user’s experience of understanding the physiology and interpreting patient image scans will determine if the critical features are captured within the geometry. (Fig 4) shows the beginning of the workflow to construct a 3D model from imaged data. In this generic example, there are five steps of (A) identifying the parts of interest, and the decisions made to which components are to be included. (B) A ‘rough’ model is created requiring smoothing and repairing the surface; essential details can be accidentally lost or modified. (C) The

CFD user may decide to remove features to increase the focus of the ROI, this also helps in reducing computational complexity and time, although a question of whether that will affect an incorrect response from the system. (D) Usually, a re-faceting of the surface needs to be completed to enable a mesh generation; within this stage, arterial topography may be altered. (E) Finally, a meshed model is created, and the decisions of cell size, quality, near-wall cell inflation, and if spatial areas within the geometry require a higher density of cells to maximise accurate results. All these opportunities to change the original geometry can limit the CFD results as opposed to converging to a realistic simulation.

a

c

b

d

e

Figure 4. The reconstructed geometry of aorta a) segmentation from CT images in 3D slicer software b) 3D modelling in Autodesk Mesh mixer software c) smoothing surface in Autodesk Mesh mixer d) solid modelling in Ansys software e) mesh generation in Ansys

Finally, the use of sophisticated V&V commercial CFD software which is commonly cited as a preferred tool in research studies requires careful management of resources and the possibility of ill-informed choices can limit the output accuracy. However, a careful balance of functional complexity, between the efficiency of simplified practicality and the faithful reproduction of a biological problem can provide meaningful insight to complex physiological issues. 4. Future directions The limitations in cardiac catheterization have interested many researchers developing non-invasive methods in diagnosis the AS. The usage of the invasive process of calculating the AVA through the Gorlin equation has an inaccuracy in evaluating the AVA in low blood flow because the Gorlin constant is dependent on the flow. Also, the AS aorta edge may not be parallel; this causes a false measurement of EOA and pressure recovery [22].

Therefore, the determination of a gold standard in the in vivo measurement of AVA and EOA is highly sought after in the diagnosis of AS [21]. Understanding the flow variation and effect of disease on the leaflets has been performed by different clinical non-invasive techniques. However, the search for an accurate assessment of the level of AS disease is still developing. Doppler echocardiography is the most common technique for evaluating the flow at AVA, yet has the main problem in defining the jet direction of the AS [34]. This method Bernoulli’s equation in the measurement of the pressure drop and ignores the blood flow viscosity. While blood viscosity has a significant influence on the aortic wall in atherosclerosis [76]. MRI in comparison with echocardiography is the newest technique namely 4D flow MRI to study the flow changes in the ascending aorta with indicating different hemodynamic parameters of the flow patterns. However, in the diagnosis of AS knowing the changes in the AV geometry and its influence on EOA is more critical, owing to the anatomical and physiological effects of the leaflets on the flow changes. Therefore, CT images with its higher spatial and temporal resolution define the geometry of the leaflets and orifice area in high detail, is recommended as the image basis for studying the leaflets and geometry with CA. Additionally, the importance of conducting V&V of simulation results should not be underestimated. Determining the level of V&V and applying it to the model should be done before accepting any results. A recommendation of this paper is to strongly suggest to devise a scale of reliability (if no Standards exist) similarly outlined in Table 3. It would also be advantageous if article journals and industrial standards [70] adopt a V&V method to assist the reader or users in interpreting simulation results better. Acknowledgements This work was supported in part by the National Natural Science Foundation of China (NSFC) (No. 11772093, 11972118, 61821002) and ARC (FT140101152). Conflict of Interest statement The authors declare that there are no conflicts of interest. References

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