Predictive Model for Thrombus Formation After Transcatheter Valve Replacement

Abstract

Purpose—

Leaflet thrombosis is a significant adverse event after transcatheter aortic valve (TAV) replacement (TAVR). The purpose of our study was to present a semi-empirical, mathematical model that links patient-specific anatomic, valve, and flow parameters to predict likelihood of leaflet thrombosis.

Methods—

The two main energy sources of neo-sinus (NS) washout after TAVR include the jet flow downstream of the TAV and NS geometric change in volume due to the leaflets opening and closing. Both are highly dependent on patient anatomic and hemodynamic factors. As rotation of blood flow is prevalent in both the sinus of Valsalva and then the NS, we adopted the vorticity flux or circulation (Γ) as a metric quantifying overall washout. Leaflet thrombus volumes were segmented based on hypo-attenuating leaflet thickening (HALT) in post-TAVR patient’s gated computed tomography. Γ was assessed using dimensional scaling as well as computational fluid dynamics (CFD) respectively and correlated to the thrombosis volumes using sensitivity and specificity analysis.

Results—

Γ in the NS, that accounted for patient flow and anatomic conditions derived from scaling arguments significantly better predicted the occurrence of leaflet thrombus than CFD derived measures such as stasis volumes or wall shear stress. Given results from the six patient datasets considered herein, a threshold Γ value of 28.0 yielded a sensitivity and specificity of 100% where patients with Gamma < 28 developed valve thrombosis. A 10% error in measurements of all variables can bring the sensitivity specificity down to 87%.

Conclusion—

A predictive model relating likelihood of valve thrombosis using Γ in the NS was developed with promising sensitivity and specificity. With further studies and improvements, this predictive technology may lead to alerting physicians on the risk for thrombus formation following TAVR.

INTRODUCTION

Transcatheter aortic valve (TAV) replacement (TAVR) originally emerged as an alternative in extreme risk patients undergoing surgical aortic valve (SAV) replacement (SAVR) procedures,^36,50 and is now approved in all risk categories.³³ Several adverse effects were shown to accompany TAVR, namely elevated pressure gradients mostly due to patient-prosthesis mismatch,^47,48 valvular leakage,^48,64 early leaflet degeneration,^2,54 coronary obstruction,^22,26 left bundle branch block and conduction abnormalities,^63,48,61 TAV migration or embolization,^27,48,59 and aortic annulus injury or rupture.^29,46,48 Most recently, valve thrombosis, whether clinical or sub-clinical (as evidenced by hypo-attenuating leaflet thickening or HALT),^{5,37,38,40,48,57} has been shown to increase early structural valve deterioration (SVD) and the risk for cerebro-embolic events.^1,3

Valvular leaflet thrombosis can reduce the aortic valve leaflet mobility,⁵⁷ potentially resulting in increased transvalvular gradients,⁴ It can compromise the durability of the valve leaflets,^43,65 and also lead to elevated incidence of embolization and strokes.^4,9 The bioprosthetic leaflets of bioprosthetic SAVs and TAVs make them prone to deterioration, whether structural or non-structural. Structural valve degeneration involves an intrinsic pathology of the leaflets or stent structure (leaflet tear, calcification, stent fracture, etc.); however, non-SVD processes involve valve thrombosis, infective endocarditis and patient prosthesis mismatch²⁵ which is usually after TAVR.

SAVs are characterized by long-term durability.²⁵ In a study on a large cohort of 12,569 patients with Carpentier-Edwards valve, re-operation rate was 1.9% and 15% at 10 and 20 years, respectively.²⁵ In another study with a total of 672 patients, the 10-year mortality rate in elderly SAVR recipients of a bioprosthetic valve was determined by their older age and the presence of comorbidities.⁵¹ In that same study, 30.1% of patients had subclinical SVD defined as an increase of more than 10 mm Hg in mean transvalvular gradient combined with a decrease to less than 0.3 cm² in valve area and/or new-onset mild or moderate aortic regurgitation,⁵¹ whether caused by thrombus or not. Generally, thrombus forms more frequently with TAVs than SAVs as per the SAVORY/RESOLVE registry.⁴ However, the PARTNER 3 sub-study data showed that at 30 days, the incidence of HALT was significantly higher among patients treated with TAVR than among those treated with surgery (13.3% vs 5.0%; p = 0.03), but the incidence at 1 year (27.5% with TAVR vs 20.2% with surgery; p = 0.19) was similar.³⁹ A study involving multicenter data on 4266 patients who underwent TAVR showed elevated transvalvular pressure gradient accompanying TAV thrombosis.³⁰ While elevated pressure gradients constitute an indicator on overall valve performance and may give an insight on long-term durability,^25,44 leaflet thrombosis may not be always accompanied by elevated pressure gradients (i.e. subclinical). A study by Hansson et al. showed that thrombosis was detected with 7% of the patients enrolled in the study, of which only 18% showed symptoms.¹⁰ In patients presenting with elevated gradients, anti-coagulation therapy was found to normalize hemodynamics.⁵³ However, it was shown that after discontinuation of therapy, leaflet disease and pathology relapsed.⁵³ This has placed leaflet thrombosis in the category of pathologic processes that lead to valve deterioration.⁷ Thus, recognition and reduction of thrombus formation may result in safer and more durable bioprosthetic valves.²³ Currently, anti-coagulation regimen with Vitamin-K antagonists for 3–6 months are considered the primary therapy to treat, prevent, and resolve thrombosis.⁵⁵

In the literature, thrombosis is associated with blood stasis.^31,32,42 Areas of recirculating blood flow under low shear stresses are predisposed to thrombus formation and thrombo-embolism.³² Several recent studies have shown the importance of blood stasis in the sinus^{19,20,11,12,16–17} and the neo-sinus (NS)—a region formed between the TAV leaflet and the native valve leaflet—and its correlation with potential thrombus formation.^{13,14,16,34,41,56,60} In particular, two of these studies now show an explicit relationship between the percentage of blood stasis in the NS and the volume of thrombus.^56,60 Zones of blood stasis promote elevated transport and adhesion of blood components such as platelets on the biomaterial surface.^8,62 This leads to having the platelets accumulate which leads to thrombus formation. It is important to note that the size and shape of the sinus and the neo-sinus after TAVR vary within a single patient, corresponding to each NS, as well as across patients with large patient to patient anatomic variability. This also influences the resulting hemodynamics and therefore the degree of blood stasis^15,35,41 at the individual NS level. Thus, idealized studies involving generic sinus, neo-sinus and aortic root models fail to capture essential flow characteristics and make drawing disease-related conclusions or planning to mitigate leaflet thrombosis difficult.

While computational modelling can be used in conjunction with experimental techniques to provide insights into the underlying fluid mechanics, its use is challenged by large deformation of the valve leaflets, simplifications and assumptions needed to model the fluid–structure interaction (FSI), and subsequent validation. Computational frameworks involve a translation of mathematical descriptions of partial differential equations to numerical schemes and algorithms. In the absence of a full characterization of the properties needed to simulate valve flow, for instance, the results of computational simulations may not be completely representative.⁵⁸ Zakerzadeh et al.⁶⁶ summarized improvements in methods for coupling blood flow with valve dynamics. Despite many improvements on the algorithms utilized, these simulations require sophisticated high-performance computing (HPC) facilities with hundreds of cores and nodes. The more accurate the information that is demanded of these models, the more expensive the computing requirements become.²⁴

Therefore, there is clearly a motivation to (a) personalize TAVR such that each patient is matched with an optimal valve selection and deployment plan to minimize the likelihood of thrombosis and (b) use rapid algorithms that do not rely on expensive numerical approaches, but rather quickly predict hemodynamic parameters such as predicting flow stasis (or any other known correlate or surrogate for thrombosis likelihood), using empirical, semi-empirical reduced order model approaches based on critical anatomical and valve implantation parameters of the patient and the valve.

In this study, we present a new method that can serve as an effective basis towards rapid schemes to stratify the risk of leaflet thrombosis based on the valve geometric, anatomical, and flow related (hemodynamic) parameters. This work will introduce future work to optimize valve selection and deployment strategy for individualizing TAVR with respect to minimizing the likelihood of leaflet thrombosis and its downstream impacts such as cerebral and other systemic embolizations, early structural valve degenerations, and any future need for anticoagulant therapies.

Semi-Empirical Leaflet Thrombosis Predictive Model Development

Dimensional Analysis

Arguments for Circulation as the Parameter of interest

The approach to develop the model relies on the basic understanding that two main energy sources that drive the NS flow after TAVR. The first one is the energy from the forward flow jet that cascades down into the NS through vortices, and the second is the energy from the moving leaflet that directly changes the volume of the neo-sinus each time the leaflet opens and closes—each time ejecting a fraction of the neo-sinus volume and then refilling again.

The cascade of kinetic energy from the main jet into the sinus and neo-sinus, as shown in Fig. 1, has been demonstrated in several studies.^{13,15,16,56,60} As the valve begins to open, a starting vortex forms at the edge of the leaflets leading to the propagation of flow into the neo-sinus and sinus regions. As the velocity increases towards peak systole, the neo-sinus reaches its minimal volume with only a few vortices existing. In contrast, the sinus experiences a resulting flow induced by the aortic sinus vortex that gets entrapped during this period and the vorticity is fed from the free shear layers that surround the main jet. Beyond peak systole, flow deceleration and adverse pressure gradient facilitate leaflet closure and further entrainment into the sinus. During this period, the sinuses experience more chaotic flow characterized by smaller multi-directional vortices compared to those observed between acceleration and peak systole, whereas the neo-sinus region starts increasing in volume allowing backwards flow in the NS cavity, which are further broken up into several smaller vortices.¹⁸

FIGURE 1.

Schematic representation of the evolution of the flow in the sinus and the neo-sinus as the aortic valve opens and closes.

The intensity of the forward flow at peak systole and the ensuing interaction with the sinus and ascending aorta therefore dictates the strength (and the patterns) of the resulting flow in both the sinus and neo-sinus cavities.²¹ The complexity and multi-directionality of the structures formed in the sinus and neo-sinus necessitate the consideration of vorticity and circulation as major fluid dynamic parameters that facilitate energy transfer between the main jet and the sinuses. While vorticity is a point measure of local rotation computed as the curl of the velocity field, circulation is the net flux of vorticity existing in all vortex tubes in a domain. Circulation may be computed either as an area integral of vorticity or as closed loop integrals of velocity along a 3D curve that forms a loop. Although vorticity and circulation are instantaneous Eulerian measures and may have some limitations from the standpoint of not capturing true Lagrangian properties such as particle residence time etc., recent transport-related work seems to show a correlation between vorticity and flow stagnation.⁵² For a more rigorous description of these key fluid dynamic concepts the reader is directed to Chapter 5 of Fluid Mechanics by Kundu and Cohen (second edition).²⁸

As the problem of flow stasis in the vicinity of heart valves is about two relatively “enclosed” cavities of different geometries, one relatively constant (sinus) and another more dynamic (neo-sinus), circulation as described above is a natural flow dynamic parameter to measure or quantify how energetic the recirculation and vortices are in these enclosed regions. Therefore, the above arguments follow that magnitude of circulation entering into the neo-sinus must correlate (at least macroscopically) with how energetic the flow is in the neo-sinus and hence likelihood of thrombus occurrence. The higher the circulation entering the neo-sinus, the less likely is thrombus formation within the neo-sinus.

Model Derivation to estimate Circulation entering in Neo-Sinus

The parameters that dictate, and therefore predict, the macroscopic properties derived from the neo-sinus flow over the cardiac cycle can be categorized into two groups: (1) fluid flow parameters and (2) geometric/anatomic parameters, as defined in Table 1 and highlighted in Fig. 2.

TABLE 1.

Parameters dimensions for dimensional analysis.

Parameters	Time (T)	Length (L)	Mass (M)
Stasis volume, SV	–	3	–
Neo-sinus volume, NSV	–	3	–
Kinematic viscosity, γ	− 1	2	–
Dynamic viscosity, μ	− 1	− 1	1
Heart rate, HR	− 1	–	–
Circulation, Γ	− 1	2	–
Ejection time, Tej	1	–	–
Velocity of main jet, V	− 1	1	–
Width of neo-sinus, w	–	1	–
Height/depth of neo-sinus, h	–	1	–
Angle between velocity direction and stent, θ	–	–	–
Distance from leaflet tip and sinotubular junction, d	–	1	–
Cross-sectional area of neo-sinus, Ac	–	2	–
Wall shear stress, WSS	− 2	− 1	1
Kinetic energy, KE	− 2	2	1

FIGURE 2.

Fluid flow and geometric parameters governing neo-sinus flow.

1. Fluid flow parameters: Stasis volume (SV), neo-sinus volume (NSV), kinematic viscosity (γ), dynamic viscosity (μ), heart rate (HR), the circulation (Γ), ejection time (T_ej) and velocity of the main jet (V) as shown in Fig. 2. In addition, other parameters can represent the state of flow in the neo-sinus such as wall shear stress (WSS) and total kinetic energy (KE) in the neo sinus volume.

2. Geometric parameters: width of the neo-sinus w, height or depth of the neo-sinus h, the angle between the velocity direction and the stent of the transcatheter valve θ and the distance from the tip of the leaflet perpendicular to the leaflet edge and intersecting the sinotubular (STJ) junction d as shown in Fig. 2. The cross-sectional area A_c of the neo-sinus taken from a longitudinal or axial perspective was also considered as shown in Fig. 2.

SV is defined as the neo-sinus stasis volume where velocities are below 0.05 m/s, consistent with Singh-Gryzbon et al.⁵⁶ and NSV is the total volume of the neo-sinus obtained from 3D reconstruction. SV and Γ are considered dependent as they can be expressed in terms of other parameters. The geometric parameters on the other hand are independent parameters.

Applying the Buckingham PI theorem, a dimensional analysis is performed. The dimensions are listed in Table 1.

The analysis below is divided into two steps: (1) derivation of a scaling relationship for neo-sinus stasis volume, given the influx of circulation into the neo sinus is known, and (2) derivation of a relationship for circulation influx into the neo-sinus, given global variables including valve jet velocity and geometric information including the relative orientation of the jet within the anatomy.

Step 1: Connecting Stasis Volume (SV) to Circulation Influx (Γ)

Taking the neo-sinus as the volume of interest, and defined in Fig. 2, the parameters that scale the SV can be listed as follows: h, w, HR, γ and Γ. These selected parameters are NS-specific, and intentionally exclude global geometric variables from the anatomy or the main flow characteristics. It was implicitly assumed that those dependencies indirectly influence the Γ alone and it is Γ that then dictates the stasis volume or any other global flow property of the neo-sinus. Using the Buckingham PI group analysis and writing dimensionless PI groups as:

$${\pi }_1=f\left({\pi }_2,{\pi }_3,{\pi }_4\dots {\pi }_n\right)$$

Using HR and w as repeating variables, SV, h and γ can be normalized as follows:

$${\pi }_1=\frac{\text{SV}}{w^3}=\frac{\text{SV}}{\text{NSV}}$$ (1)

with w³ being scaled as a volumetric measure such as NSV.

$${\pi }_2=\frac{h}{w}\left(\text{representing the aspect ratio of the neo-sinus}\right)$$ (2)

$$\begin{gathered} {\pi }_3=w\sqrt{\frac{2\pi \text{HR}}{\gamma }} \\ ={\alpha }_{\text{NS}}\left(\text{representing a Womersley number of the neo-sinus}\right) \end{gathered}$$ (3)

$${\pi }_4=\Gamma /\left(\text{HR}\cdot w^2\right)$$ (4)

In the π group given in Equation 4, the normalization of Γ can be alternatively expressed in terms of a characteristic circulation defined by the ejection time T_ej which is related to HR, and cross-sectional area of the neo-sinus A_c (related to w²):

$${\pi }_4=\frac{\Gamma \cdot T_{\text{ej}}}{A_{\text{c}}}$$ (5)

Intuitively, Eq. (5) represents the non-dimensionalization of Γ with a natural circulation scale defined over the neo-sinus cross-section given by A_c/T_ej. A larger π₄ indicates a stronger “stirring”of the neo-sinus.

The resulting overall equation connecting the different parameters becomes:

$$\frac{\text{SV}}{\text{NSV}}=f\left(\frac{h}{w},\frac{\Gamma \cdot T_{\text{ej}}}{A_{\text{c}}},{\alpha }_{\text{NS}}\right)$$ (6)

where f is a model function that Buckingham PI theorem says must exist relating the four distinct π groups and can be empirically estimated using in-vivo, in-vitro or in-silico data.

Step 2: Connecting Circulation Influx to Global Parameters

To derive a relationship between circulation entering the neo-sinus and global parameters such as jet velocity, its orientation and relative positioning of the neo-sinus entrance, the large-scale flow phenomena can be considered. In the process of aortic valve opening, net transport of circulation or advection of circulation occurs from and by the accelerating main jet exiting the leaflets leading to entrapment of some of this circulation in the nearest cavity that is the neo-sinus. Using scaling arguments, the circulation generated by the main jet that hovers over the neo-sinus is largely dictated by the distance between the sinotubular junction (STJ) and the main jet. Thus, the magnitude of this circulation can be estimated using the velocity of the main jet (V), the shortest distance from the line through the tip of the leaflet along the direction of the TAV stent and the STJ junction (d). This distance is dependent on the angle between the velocity direction and the stent of the transcatheter valve. The circulation influx into the neo-sinus, Γ, must then be given by some fraction of V · d · cos θ. As the flow crosses the aortic valve with a velocity V, what determines the fraction of the flow that would be going into one neo-sinus depends on the velocity of the main flow crossing the aortic valve and the distance d. This fraction can be modeled as the ratio of the area of the neo-sinus opening, A_NS, to the “flow separated area” as defined in Fig. 3 and shown in Equation 7 below.

FIGURE 3.

Visualization of the separated area (left) and neo-sinus area (right), used to evaluate the fraction of circulation influx into the neo-sinus.

$$\Gamma \approx V\cdot d\cdot \text{cos }\theta \cdot \text{Ratio}\approx \frac{V\cdot d\cdot \text{cos }\theta \cdot A_{\text{NS}}}{A_{\text{separated}}}$$ (7)

Combining the results of the above two steps, the normalized circulation term is given by the relationship:

$${\Gamma }_{\text{norm}}\approx \frac{V\cdot d\cdot \text{cos }\theta \cdot A_{\text{NS}}\cdot T_{\text{ej}}}{A_{\text{separated}}\cdot A_{\text{c}}}$$ (8)

ALTERNATIVES TO STASIS VOLUME

In addition to the assessment of likelihood of leaflet thrombosis using stasis volume, other parameters can also be used to assess the state of stasis in the neo-sinus cavity such as the total kinetic energy (KE) or the average wall shear stress (WSS) for near the wall stagnation^49,52 defined over the neo-sinus volume. It is important to note that these equations are not used in the results, they are rather just presented for completion of possible alternative approaches. These alternate parameters, just like stasis volume, are considered dependent parameters whose formulas or expressions are functions of the Circulation combined with the same variables mentioned in the previous section (Γ, h, w, HR, γ). Using dimensional analysis, similar to the previous section, the alternative equations can be expressed as follows:

$$\frac{\text{WSS}\cdot T_{\text{ej}}}{\mu }=\phi \left(\frac{h}{w},\frac{\Gamma \cdot T_{\text{ej}}}{A_{\text{c}}},{\alpha }_{\text{NS}}\right)$$ (9)

$$\frac{\text{KE}\cdot T_{\text{ej}}^2}{\rho \cdot A_{\text{c}}^{2.5}}=h\left(\frac{h}{w},\frac{\Gamma \cdot T_{\text{ej}}}{A_{\text{c}}},{\alpha }_{\text{NS}}\right)$$ (10)

METHODS

Patient Cohort and Model Development

Computational fluid dynamic (CFD) models were developed for six patients who underwent an Edwards SAPIEN 3 (Edwards Lifesciences, CA, USA) valve implantation at the University Heart Center Freiburg-Bad Krozingen. These patients were selected from a cohort⁴⁵ made available through a limited data use agreement between the Freiburg University Hospital and Georgia Institute of Technology (#H17256).

Details of the patient selection criteria as well as development and validation of the CFD models are reported in Singh-Gryzbon et al.⁵⁶ Briefly, computed tomography angiography (CTA) data for the six patients were segmented to obtain 3D models of the post-TAVR aortic root and ascending aorta. Flow waveforms, matched to patient-specific cardiac outputs, were imposed at the aortic inlet while a pressure waveform was imposed at the aortic outlet. Blood was assumed to be Newtonian with a kinematic viscosity and density of 0.0036 Pa·s and 1060 kg/m³, respectively. The continuity equation and Reynolds averaged Navier-Stokes equations with a shear-stress transport transitional model were used to describe 3D incompressible flow and solved using ANSYS CFX 17.1 (ANSYS, Canonsburg, PA, USA). These fluid dynamic simulations were rigid, did not consider FSI effects and were performed at peak systole with the leaflets fully open.

Details of thrombus volume segmentation are described in detail in Singh-Gryzbon et al.⁵⁶

Using the CFD models, comparisons were made between the CFD derived parameters previously described in Singh-Gryzbon et al.⁵⁶ and the calculated normalized circulation described above. The specific CFD derived variables include % stasis volume during diastole, % stasis volume during systole, and average wall shear stress. Furthermore, sensitivity and specificity curves were generated to predict HALT in individual neo sinuses (18 total) and compared to the sensitivity and specificity curves corresponding to that from normalized circulation. Lastly, the uncertainty in sensitivity and specificity curves for the normalized circulation was generated by running 1000 monte-carlo simulations of the calculation of the normalized circulation corresponding to varying % error (standard deviations) in each of the measured variables right hand side of Eq. (8).

RESULTS

Vorticity and Circulation in Patient Specific Models

At peak systole, flow was characterized by a high velocity central jet through the TAV. Flow in and around the sinuses were a result of (i) backflow arising when the central jet impinged on the proximal ascending aorta, due to the curvature, and (ii) indirect filling as a consequence of valve positioning and aortic root shape and size. When the TAV leaflets were fully open, the neo-sinus volume was at its minimum, hence flow in the neo-sinus was characterized by low velocity recirculating regions that came either from the main jet or the sinus. In contrast, during flow deceleration, neo-sinus volumes increased as the leaflets closed. The combination of flow deceleration and aortic curvature resulted in slow recirculating flow or bi-helical patterns in the proximal ascending aorta and aortic root. This facilitated backflow with the formation of small vortices in the neo-sinus and sinus.

The simulation results indicated that patient-specific anatomic and flow conditions accounted for variations in forward flow intensities of the central jet, and flow evolution in and around the sinus and neo-sinus, as indicated in Fig. 4. These variations were observed both across patients and within an individual patient.

FIGURE 4.

Patient-specific q-isosurfaces at mid-acceleration (Mid-acc) and peak systolic flow (Peak) for the six patients (P1–P6).

DERIVED MODELS VS. THROMBUS VOLUME OBTAINED COMPUTATIONALLY

In the following section, the data for the model given by Eq. (6) for both systolic and diastolic phases was obtained from the data of the computational study results by Singh-Gryzbon et al.⁵⁶

Figure 5 shows a plots of thrombus volume vs. three CFD derived variables namely % stasis volume during systole, diastole, the average wall shear stress, and the normalized circulation obtained from the derived model Γ_norm. Included in these plots are data points corresponding to both HALT negative as well as HALT positive cases.

FIGURE 5.

Thrombus volume variation vs. normalized circulation for the six patients (P1–P6), fitted to a power curve. P1, P2 and P3 were positive for leaflet thrombosis whereas P4, P5 and P6 were not.

There is no evidence of any analytical model correlating the thrombus volumes with the CFD derived variables. The linear regression reported in Singh-Gryzbon et al.⁵⁶ with R = 0.821 (R² = 0.67) is shown in Fig. 5B. While this is a strong correlation, it should be noted that it is conditioned on confirmed valve thrombosis. The correlation R² drops to 0.14 when considering the data points for zero thrombus volume.

Neither the normalized circulation nor the CFD derived parameters demonstrate any analytical correlation between the amount of thrombus formed on the leaflets to the flow dynamic variables.

Figure 6 demonstrates the correlation between the three CFD derived variables to the normalized circulation. The % stasis volume during systole shows a negative correlation with normalized circulation with an R² = 0.53. The correlation is poor between % stasis volume during diastole with normalized circulation (R² = 0.094). The averaged wall shear stress correlated positively with normalized circulation with an R² = 0.57.

FIGURE 6.

Percentage of stasis volume in (a) systole and (b) diastole vs. normalized circulation. For the six patients (P1–P6), fitted to a power curve. P1, P2 and P3 were positive for leaflet thrombosis whereas P4, P5 and P6 were not.

Sensitivity and Specificity

Sensitivity and specificity analysis was performed as follows:

$$\text{Sensitivity}=\frac{\text{true positives}}{\text{true positives }+\text{ false negatives}}$$ (11)

$$\text{Specificity}=\frac{\text{true negatives}}{\text{true negatives }+\text{ false positives}}$$ (12)

Sensitivity and specificity analysis (see Fig. 7) showed a cutoff value corresponding to maximum sensitivity and specificity of the three CFD variables and the normalized circulation parameter in predicting leaflet thrombosis. The cutoff value for % stasis volume during systole was 32% for a sensitivity and specificity of 22%. The cutoff value for % stasis volume during diastole was 80% for a sensitivity and specificity of 56%. The cutoff value for average wall shear stress magnitude was 0.93 Pa for a sensitivity and specificity of 77%. The cutoff value for normalized circulation was between 28.5 and 31.0 for a sensitivity and specificity of 100%.

FIGURE 7.

Sensitivity and specificity of the (a) percentage of stasis volume in systole, (b) the percentage of stasis volume in diastole, (c) average Wss and (d) normalized circulation.

Figure 8 shows the uncertainty analysis performed on the sensitivity and specificity of normalized circulation. At 5% error standard deviation in all measured parameters the cutoff is 31.0 with the sensitivity and specificity dropping of 94%. At 10% error the cutoff is at 32.0 with the sensitivity and specificity dropping further to 86%. At 20% error the cutoff is at 33.0 with the sensitivity and specificity dropping to 75%.

FIGURE 8.

Uncertainty analysis performed on the sensitivity and specificity of (a) normalized circulation, and of normalized circulation at (b) 5% error, (c) 10% error, (d) 20% error.

DISCUSSION

In this study, a reduced model based on dimensional analysis and CFD relating circulation as a surrogate for likelihood of leaflet thrombosis was developed with a promising sensitivity and specificity at 100% and robust performance even at significant errors in measured parameters. This clearly needs to be tested on larger patient cohorts in a prospective manner to be clinically viable. The model was derived and then tested using post-TAVR patient data from the study at Freiburg University Hospital.⁵⁶ The model correlated the flow dynamics in the neo-sinus to the main flow through the TAV and patient specific geometric factors with the key assumption that the transfer of energy into the NS can be captured with a reasonable estimation of the circulation parameter. Therefore, fluid parameters such as velocity magnitude and direction were extracted along with geometric parameters that influenced neo-sinus flow. These geometric parameters included width of the neo-sinus, height or depth of the neo-sinus, the angle between the velocity direction and the stent of the transcatheter valve, the distance from the tip of the leaflet perpendicular to the leaflet edge and intersecting the STJ, and the neo-sinus cross sectional area. It should be noted that the CFD simulations in Singh-Gryzbon et al. were performed at peak systole with the leaflets fully open without accounting for the fluid-structure interaction. Despite that, the peak flow simulations represent an extreme case scenario for the flow in the neo-sinus as the volume of the neo-sinus is the smallest possible.

It is interesting to note that while there is significant correlation between normalized circulation and averaged wall shear stress or % stasis volume during systole, the latter variables do not perform well with respect to predicting leaflet thrombosis as compared to normalized circulation. This demonstrates that more finer flow metrics must exist that would predict leaflet thrombosis better than traditional fluid dynamic parameters such as wall shear stress or the need for full fluid-structure interaction modeling.

While the derived model uses important patient-specific parameters, additional parameters such as annulus diameter, left ventricular outflow tract diameter, sinus diameter, left and right coronary cusps diameters and sinotubular junction height, were potentially related to leaflet thrombosis.⁵⁶ With further studies, these parameters can be included in the model. Additionally, while percentage of circulation in the neo-sinus is one of the predictors of thrombosis, other measurements such as wall shear stress or kinetic energy could also provide insights into the flow in the neo-sinus.

Prediction of outcomes is already in use in medicine particularly the cardiovascular field where for instance the Society of Thoracic Surgeons (STS) predicted risk of mortality (PROM) score is utilized to assess whether a patient is eligible for an invasive procedure. The introduction of computer simulations in the medical field in general during the past decade contributed to improved diagnostics and several companies rely on computer simulations to give real-time feedback to clinicians to get better assessment of a potential diseased state. Using this model, prediction of leaflet thrombosis is possible after valve replacement or for planning purposes prior to implantation.

LIMITATIONS

In this study, we limited our analysis to Eulerian perspectives to model the likelihood of valve thrombosis which inherently involves and depends on the transport of platelets and blood cells (a Lagrangian phenomenon). While we acknowledge that this is not an accurate reflection of biophysics we utilized dimensional analysis as a possible surrogate approach. The sheer strength of dimensional analysis-based parameter construction is evident as demonstrated by the strong predictive power demonstrated by the sensitivity and specificity curve for clinical cases of valve thrombosis. We would also like to iterate that in complex flow aspects such as flow recirculation, separation, and stagnation in the cardiovascular system, Lagrangian analysis may be more appropriate than Eulerian one.⁶ Additionally, this study was based on parameters obtained from rigid CFD simulations that did not account for fluid structure interaction (FSI). Our model is currently derived based on 6 patient data only. The addition of more patients and the implementation of a comprehensive FSI framework will help in refining the model further and in performing a true prospective validation exercise (such as randomized trials) that would ultimately connect to patient outcomes.

CONCLUSION

In this study, patient-specific anatomic, valve, and flow parameters were used to develop a semi-empirical, mathematical model that can be used to predict leaflet thrombosis in TAVR patients with promising sensitivity and specificity. With ongoing improvements to include additional parameters, this work has the potential to inform physicians on thrombus risk before or after TAVR.