Performance assessment of an electrostatic filter-diverter stent cerebrovascular protection device. Is it possible not to use anticoagulants in atrial fibrilation elderly patients?

Stroke is the second leading cause of death worldwide. Nearly two-thirds of strokes are produced by cardioembolisms, and half of cardioembolic strokes are triggered by Atrial Fibrillation (AF), the most common type of arrhythmia. A more recent cause of cardioembolisms is Transcatheter Aortic Valve Replacements (TAVRs), which may onset post-procedural adverse events such as stroke and Silent Brain Infarcts (SBIs), for which no definitive treatment exists, and which will only get worse as TAVRs are implanted in younger and lower risk patients. It is well known that some specific characteristics of elderly patients may lower the safety and efficacy of anticoagulation therapy, making it a real urgency to find alternative therapies. We propose a device consisting of a strut structure placed at the base of the treated artery to model the potential risk of cerebral embolisms caused by dislodged debris of varying sizes. This work analyzes a design based on a patented medical device, intended to block cardioembolisms from entering the cerebrovascular system, with a particular focus on AF, and potentially TAVR patients. The study has been carried out in two stages. Both of them based on computational fluid dynamics (CFD) coupled with Lagrangian particle tracking method. The first stage of the work evaluates a variety of strut thicknesses and inter-strut spacings, contrasting with the device-free baseline geometry. The analysis is carried out by imposing flowrate waveforms characteristic of both healthy and AF patients. Boundary conditions are calibrated to reproduce physiological flowrates and pressures in a patient's aortic arch. In the second stage, the optimal geometric design from the first stage was employed, with the addition of lateral struts to prevent the filtration of particles and electronegatively charged strut surfaces, studying the effect of electrical forces on the clots if they are considered charged. Flowrate boundary conditions were used to emulate both healthy and AF conditions. Results from numerical simulations coming form the first stage indicate that the device blocks particles of sizes larger than the inter-strut spacing. It was found that lateral strut space had the highest impact on efficacy. Based on the results of the second stage, deploying the electronegatively charged device in all three aortic arch arteries, the number of particles entering these arteries was reduced on average by 62.6% and 51.2%, for the healthy and diseased models respectively, matching or surpassing current oral anticoagulant efficacy. In conclusion, the device demonstrated a two-fold mechanism for filtering emboli: while the smallest particles are deflected by electrostatic repulsion, avoiding microembolisms, which could lead to cognitive impairment, the largest ones are mechanically filtered since they cannot fit in between the struts, effectively blocking the full range of particle sizes analyzed in this study. The device presented in this manuscript offers an anticoagulant-free method to prevent stroke and SBIs, imperative given the growing population of AF and elderly patients.

Incompressible flow Blood was modeled as a Newtonian incompressible viscous fluid.The Newtonian approximation is an acceptable assumption and not far from reality in a significant part of the circulatory system under normal conditions.This is especially true in large blood vessels where red blood cells are well below the characteristic sizes of the vessels [1].The velocity and pressure fields in the aortic arch, u and p respectively, have thus been obtained by solving the incompressible Navier-Stokes momentum and continuity equations: where ρ = 1.106 g cm 3 and ν = 0.035 g cms are the blood density and kinematic viscosity respectively.The corresponding boundary conditions are specified in section Aortic arch geometry from the main document.
Boundary conditions for the flow: healthy and atrial fibrillation conditions In order to set up the computational simulations, physical governing equations must be complemented by boundary conditions for both the fluid and particle dynamics as well as the electric field.For the fluid, the following boundary conditions are prescribed at the boundaries: • Inlet: velocity Dirichlet boundary condition.
• Outlets: reduced-order (3-element Windkessel) model, imposed as a traction boundary condition, in which distal resistances and capacitances are modelled for a more accurate boundary conditions.In particular, the values for the present work are a 0 Pa for imposed pressure in the outlets, a resistive term equal to 100.0 and a scaling coefficient of 0.5.
• Arterial walls and deflector: no-slip Dirichlet boundary conditions.
It is noted that each one of the Windkessel boundary conditions were calibrated for the flow rates and pressures to fit the experimental results from [2] for the healthy patient case.The flowrate waveforms imposed at the inlet are representative of a healthy patient and an AF patient.In Figure 1 these two inflows used in the first stage are shown.The second stage modifies the AF inflow to adjust the physiology of a real patient in a more accurate way. Figure 1a the new inflow for AF is compared with the healthy patient.The healthy patient has a heart rate of 70 bpm and a cardiac output of 4.286 L min −1 .In contrast, the AF patient has a higher heart rate, of 150 bpm, and a lower cardiac output, of 3.429 L min −1 , a 20% decrease with respect to the healthy patient, as reported in [3].These flowrates were used for the second phase addapted to this specific geometry.

Thrombus model: particle transport
Particle transport was simulated in a Lagrangian frame of reference, following each individual particle.The main assumptions of the model were: • particles were sufficiently small and the suspension sufficiently diluted to neglect their effect on blood-flow: i.e. one way coupling; • particles were spherical and did not interact with each other; • particle rotation was negligible;  • thermophoretic forces were negligible; and • the forces considered were drag F d , gravitational F g , buoyancy F b , and, for the second stage, electric force F e is also considered.
Particles are injected assuming a circumferential distribution at a radial distance of 40% of the aortic radius [4], as observed in Figure 2. Clot injections are conducted at three different cardiac cycle moments assumed which correspond to a beginning of systolic (S), accelerating (A), and peak stage of the cardiac cycle (P) as in [4], illustrated in Figure 1 .
In order to properly define the deflection/blocking capacity of the device, different particle types, corresponding to different particle models defined by forces considered and the diameter and density properties for each type.These different particles were used as shown in Table 1.In particular all 7 were used in the first stage and only the first 5 (from 1st to 5th of the Table 1) in the second one.Force models are applied to the particles with types 1 to 6, which have a density of 1.08g cm −3 and different diameters, ranging from d p 10 µm to 2mm.Particles of types 1 to 3 (d p ∈ [10, 100]µm) are of importance for evaluating the efficacy of the device in avoiding micro-embolisms and associated SBI.Larger particles of types 4 to 6 (d p ∈ [0.5, 2]mm) represent larger embolisms, which may produce cerebral strokes.
The trajectory of these particles can be obtained by using Newton's Second Law, F = ma, where the force F is the sum of the different forces exerted on the particle, m is the particle mass and a is the particle acceleration.In this case the forces applied on the particles are: • Gravity: F g = m p g, where m p and g corresponds to particle mass and gravitational acceleration.
• Buoyancy: ρp , where ρ f and ρ p corresponds to the fluid and particle densities respectively.
• Drag: F d the force acting in the opposite direction to the relative motion of an object moving with respect to a surrounding fluid.The equation for the drag force assumed the particle reached its terminal velocity and is given by: being µ the dynamic flow viscosity, d p particle density and Re the particle Reynolds number, calculated from its relative velocity with the fluid: Re = |u p − u f |d p /ν with u p and u f corresponding to particle and fluid velocity.C d is the drag coefficient given by Chen model described in [5] • Electric force: F e electrically charged deflector created an electric field which exerts a repulsive force through the electrical charged blood clots and described mathematically in the next section .
Particle transport was modelled by considering the above described forces, and solving Newton's second law to obtain particle accelerations: where a p and m p correspond to particle acceleration and particle mass.
For the case of type 7 particles, their trajectory is obtained by computing the velocity integral, meaning that these particles act like tracers, without considering any force acting on them and they move following the flow.All particles injected in the geometry are considered spheres with their diameters described in Table 1.
It is important to remark that in vivo studies are more likely to show larger clot diameters [6] than those specified in the table 1.However, those large clots were not considered in our analysis as they will simply not fit between the struts.Moreover, it is important to emphasise that as indicated in Table 1, for some deflector geometries, particles of types 4, 5 and 6 have a diameter larger than or equal to the inter-strut spacing (geometries 1, 2 & 3) and thus cannot enter the LCCA through this space. .
Boundary conditions thrombus model For the particles injected into the flow, the following boundary conditions are prescribed: • inlet & outlets: absorbing boundary condition, which means particles passing through such surfaces.
• arterial walls: slip boundary condition, which allows tangential velocities and removes the normal one and • deflector: elastic bounce boundary condition, which implies imposing normal velocity with opposite sense removing the tangential momentum.

Electrostatic field
The resulting electric field is obtained by solving the potential Poisson equation: where Q d is the total charge distributed superficially on the struts of the devices present in each configuration, ϵ 0 and ϵ r are the electrical permittivity for the vacuum and relative permittivity of blood.Finally, we use the relation between potential and electric field: E = −∇V .The electric field generated by the superposition of the three devices deployed in the three arteries is illustrated in Figure 3.  Boundary conditions electric potential The boundary conditions of the Poisson equation are −1.3mV in the intima or internal aortic walls and free in the inlet and outlet surfaces.

Electrical parameters of model
Blood flow model parameters Blood viscosity, or the thickness of blood, is generally considered to be normal when it falls within a range of 3.5 to 5.5 cP.However, it is important to note that blood viscosity is not a constant value and can vary significantly depending on the specific conditions in which it is being measured.For example, the viscosity of blood can change based on the shear rate, or the speed at which the blood is flowing.At a shear rate of 0.1 s −1 , the viscosity of the same blood sample may be as high as 60 cP.However, at a shear rate of 200 s −1 , the viscosity would be much lower, at around 5 or 6 cP.This means that the viscosity of blood can differ in different parts of the circulatory system, such as the large arteries, veins, and microcirculation, where shear rates can range from a few s −1 to over 1000 s −1 .Blood viscosity is influenced by several factors, including the concentration of red blood cells, the thickness of plasma, the ability of red blood cells to deform under flow, and their tendency to clump together [7], and therefore we considered blood visocisity value of 0.035 g cs Thrombus model parameters The charge of the simulated blood clots was determined following [8], where the authors study electrophoretic mobility of electrically charged particles.Electrophoresis involves the separation of charged clots under the influence of an electric field.In fact, this mechanism is the result of the combination of two different processes, intrinsic electrophoretic mobility and electroosmotic flow.The first one can be expressed as: where µ is the electrophoretic mobility, q is the charge of the particle that we are interested in, ν the viscosity of the medium, and r s the hydrodynamic radius.The electrophoretic mobility was taken as µ = −0.0336cm 2 statV −1 s −1 = −1.12µm s V −1 cm −1 [9].The densities assigned to blood clots were 1.08 g cm −3 [10].By expressing the charge as a function of the remaining parameters in (6), electrical charges were obtained for each diameter, and summarized in Table 2.
Device model parameters As described in Section ??, the surface charge on the graphene oxide in 0.001M N aCl was determined approximately as −75 mC m −2 in good agreement with the previous work [11] where the value was equal −80 mC m −2 , at pH 6.5 extracted from a zeta potential measurement, albeit in NaCl.In CGS units, these two values correspond to −22, 484.43 statC cm −2 and −23, 983.39 statC cm −2 .Based on these results, we have considered a surface charge of the device corresponding to −24, 000 statC cm −2 .This value needs to be integrated for all the surfaces of the devices placed in the domain producing the total charge Q d in (5), responsible for the electric field, which exerts the repulsive force on blood clots.

Quantities of interest
The following quantities of interest are used for both particle statistics and flow dynamics: • The particle deflecting efficacy at the arterial outlets where the device is deployed, with and without considering electric charge.This metric provides a means of computing the efficacy of the device CEPD.
• The maximum ejected flowrate in the treated artery.This value can be used to determine the variation in flowrate ejected to the arteries with respect to the case without deflector.It thus enables computing what will be the effect on oxygen delivery to the cerebrovascular system.
• Volume-averaged metrics have also been computed in order to evaluate the risk of thrombus formation due to the presence of the medical device.The region of interest considered is the volume encapsulated by the deflector as shown in Figure 4.The quantities of interest evaluated are: -The average kinetic energy, associated to washout.
-The average second invariant of the velocity gradient ∇u, that is, , where S is the symmetric part of the velocity gradient known as the rate of strain, and Ω is the antisymmetric part known as the vorticity tensor.This invariant, is also used in the Q-criterion that quantifies the level of vorticity in the flow by defining vortices as volumes where Q > 0 (where the vorticity magnitude is greater than the magnitude of the rate of strain).
-∆Q:the drop in ejected flowrate at the arterial outlets where the device is deployed, relative to the untreated case.

Hydrodynamic quantities of interest
The first stage of the present work is focused on the analysis of the hydrodynamics effects of the deflector placed at the base of the arteries and how these hydrodynamics effects affect the trajectories of the potential clots travelling through the aortic arch.To that end, different configurations of the struts forming the presented device are analysed.
The presence of the deflector influences the haemodynamic flow locally.Figure 5 qualitatively depicts the fluid velocity field around the LCCA base where the deflector is deployed in this first study.Different instants of a single cycle are shown corresponding approximately to the peak stage (Figure 5a), the midterm of the deceleration phase (Figure 5b) and the plateau stage (Figure 5c).To quantitatively analyse the effect of the deflector on the flow, different hydrodynamic metrics were computed.
Considering the results of the second of the cited metrics in the supplementary appendix section 1.2, the maximun flowrate, we could observe that the mean value all the configurations is 68,91 with a standard deviation of 1.019.So no significant reduction in flowrate is obtained in either case for the different configurations represented in the table presented in section Device design from the main document.
The kinetic energy quantity of interest evaluated in the region of interest considered in Figure 4 is reduced comparing the non-device configuration for all the analyzed configuration, obtaining a maximum value of 20% for the Geometry-4 case represented in the table presented in section Device design from the main document.Although the results indicates that the presence of the deflector reduces the velocity downstream of the deflector, the Geometry-2 configuration is the one that mantain higher kinetic energy with a reduction of less that 10 % .
In order to quantify the degree of vortices generated by the deflector, the Q-invariant (second invariant of velocity gradient) is computed.Based on the results obtained, again we see that the deflector presenting a lowest Q value (i.e., presenting similar results to the case with no deflector     implanted) is the one with dimensions L si = 0.75 mm and L st = 0.75 mm, being the design which produces less vortices in the evaluated region.Figure 6 shows results for the particles effectively passing through the deflector device (in between struts) deployed at the base of the LCCA.Particle counts are normalised by the total number of particles reaching the LCCA outflow in the no-deflector case, obtaining our quantity of interest called ϵ.It can be seen that particle counts there are only reduced for particles above or equal to 0.5 mm for the healthy patient case (Figure 6a).These sizes correspond to the minimum interstrut spacings of the analysed designs.As should occur, particles above the inter-strut spacing are 100% blocked, while when slightly below the inter-strut spacing (e.g., see Figure 6a: d p 0.5 mm, L si = 0.75 mm where particle deposition is reduced by 38%), a moderate reduction is observed.For particles well below the inter-strut spacing (d p ≪ L st ) no significant reduction is observed.In fact, for some of these particle-strut combinations an increased number of particles are detected in the LCCA.It is remarkable that reductions in particles passing through the device are observed for particles with diameters below L si in the L si = 0.75 mm in the healthy case (Figure 6a).

Atrial Fibrilation patient: Comparison between all different morphologies over LCCA
In this case, as we can see in Figure 6b, particle counts there are only reduced for particles above or equal to 1.0mm for the AF case.The reductions in particles passing through the device are observed in Figure 6b with diameters below L si = 0.5mm in this AF case.  1. the neutral particles are filtered with an efficacy of 32.0% on average in the artery where the deflector is deployed (26.0% for the healthy patient), 2. this average efficacy increases to 59.6% when the particles are charged (66.5% for the healthy patient), 3. the deflection efficacy of the electrical charge diminishes for larger particle sizes, 4. the number of particle counts of arteries distal to the artery where the deflector is deployed increases by 37.3% on average with respect to the baseline case (38.8% for the healthy patient), and 5. they increase to 41.6% when the particles are electrically charged (46.6% for the healthy patient).
In summary, as for the healthy patient, in the AF patient, the deflector effectively reduces the particle counts in the treated arteries, while producing a slight increase of the particles entering distal arteries left open.

1
Blood flow model: computational fluid dynamics (a) Final flow rate waveforms imposed at the inlet for healthy (red) and AF (blue) patients (b) Flowrate waveform showing particle injection instants in a healthy patient.(c) Flowrate waveform showing particle injection instants in a patient with AF.

Figure 1 :
Figure 1: (a) Improved flowrate in the second stage of the work (above) and instants of particle injection, overlaid with inflow curve (below) (b) from a healthy patient and (c) from a patient with AF.Points in time S, A and P represent the beginning of systolic, accelerating, and peak stage of the cardiac cycle, respectively.

Figure 2 :
Figure 2: Zoomed view of the circumferential distribution (left) and vertical position at the inlet (right).
(a) Side-view of streamlines of the electric field given by the superposition of all three devices.(b) Top-view of streamlines of the electric field given by the superposition of all three devices.

Figure 3 :Table 2 :
Figure 3: Streamlines of electric field generated by superposition of the 3 electrical charged devices placed in the 3 arteries

Figure 4 :
Figure 4: Region of interest where volumetric quantities of interest are integrated.

Figure 5 :
Figure 5: Velocity field around LCCA artery with deployed deflector (top) and without deflector device (bottom) for different instants of a single cycle, from left to right: (a) t = 0.1s, (b) t = 0.27s, and (c) t = 0.54s.

Figure 6 :
Figure 6: Variation in number of particles entering the LCCA for increasing strut thicknesses for the (a) healthy, and AF patient.Particle depositions are normalised by the no-deflector case L si = 0mm.Inter-strut spacings are equal to the strut thickness in each case, as can be seen in the table of section Device design from the main document.

( a )
Particle counts for the healthy patient deploying the device in single arteries (BCT, LCCA, and LSA), and in all at once.

1. 4 . 3
Deflector deployed in a single artery Analogously to previous section, the deflector was deployed individually in each aortic arch artery (BCT, LCCA, or LSA), running separate simulations for each case (see figure representing different device deployment configuration from section Device design from the main document), prescribing the AF flow rate at the inlet.The observations noted in the healthy patient are still observed for the AF patient, with similar particle count differentials when implanting the deflector, and when considering electrical charge: (a) Particle counts for the AF patient deploying the device in single arteries (BCT, LCCA, and LSA), and in all at once.

Table 1 :
Particle types with their corresponding diameters (dp) and comparison with inter-strut spacing of deflector geometries (L si )

Table 4 :
Particle filtering efficacies for the AF patient