Understanding embolus transport and source to destination mapping of thromboemboli in hemodynamics driven by left ventricular assist device

Abstract

Left Ventricular Assist Devices (LVADs) are a key treatment option for patients with advanced heart failure, but they carry a significant risk of thromboembolic complications. While improved LVAD design, and systemic anticoagulation regimen, have helped mitigate thromboembolic risks, ischemic stroke due to adverse thromboembolic events remains a major concern with current LVAD therapies. Improved understanding of embolic events, and embolus movement to the brain, is critical to develop techniques to minimize risks of occlusive embolic events such as a stroke after LVAD implantation. Here, we address this need, and devise a quantitative in silico framework to characterize thromboembolus transport and distrbution in hemodynamics driven by an operating LVAD. We conduct systematic numerical experiments to establish that our framework can quantify the source-to-destination transport patterns of thromboemboli as a function of: LVAD outflow graft anastomosis, LVAD operating pulse modulation, thromboembolus sizes, and origin locations of emboli. Additionally, we demonstrate how the resulting embolus distribution patterns compare and correlate with descriptors based solely on hemodynamic patterns such as helicity, vorticity, and wall shear stress. Using the concepts of size-dependent embolus-hemodynamics interactions, and jet impingement driven flow for hemodynamics under LVAD operation as established in our prior works, we gain valuable insights on departure of thromboembolus distribution from flow distribution, and establish that our in silico model can generate deep insights into embolus dynamics which is not otherwise available from standard of care imaging and clinical data.

Introduction

Heart failure constitutes a major global health concern, affecting at least 26 million individuals worldwide^1,2,3. The prevalence of heart failure continues to rise over time with the aging population. According to latest statistics compiled by the American Heart Association (AHA) and the National Health and Nutrition Examination Survey (NHANES), an estimated 6.7 million American adults above the age of 20 years (2.2%) had advanced heart failure between 2017 and 2020⁴. Left ventricular assist devices (LVADs) are implantable pumps that provide mechanical circulatory support and have emerged as the standard of care for bridge-to-transplant as well as destination therapy in advanced heart failure patients^5,6,7,8. Although there have been significant advancements in LVAD therapy over the past several decades, ischemic stroke remains a significant cause of morbidity and mortality in patients after LVAD implantation^9,10. Stroke caused after LVAD implantation have been reported in multiple studies with a rate in the range of 11-47%^11,12,13,14. The most recent report of the Interagency Registry of Mechanical Circulatory Support (INTERMACS), which included the least thrombogenic LVADs currently available (HeartMate3) the stroke rate was still noted at 6-8%¹⁵. Progress in understanding and reducing the risks of post-implant strokes can have a profound effect on the overall success of treatments. However, a significant obstacle lies in the limited understanding of the factors that contribute to post-implant stroke risks in individuals supported by LVAD. For increased surgical treatment efficacy, understanding and considering these factors prior to the surgical implantation is advantageous.

Thrombotic complications in LVADs can be attributed to various factors, including the activation of the extrinsic coagulation pathway due to foreign materials used in the pump (hemocompatibility), shear stress, flow stasis in the ventricle due to ventricular dysfunction, stasis in the pump body, or the outflow graft¹⁶. Concurrent inflammation and infection can also promote coagulation^17,18. Shear-induced hemolysis leads to the release of ADP from red blood cells, subsequently triggering platelet activation¹⁷. Additionally, altered flow patterns resulting from LVAD operation can contribute to endothelial injury within blood vessels, potentially accelerating the development of thrombus in the LVAD graft^19,20. Consequently, the LVAD outflow graft represents a major source of thromboemboli that can lead to cerebrovascular accidents and embolic strokes. Furthermore, flow stasis observed in the aortic arch root due to altered hemodynamics²¹ after LVAD implantation can lead to thrombosis in the aorta. Intermittent aortic valve opening from ventricular contractions can then propel thromboembolic particles in the aortic root towards the cervical vessels. Improved understanding of stroke risks in patients in LVAD support, therefore, will require understanding how thromboemboli originating from these different embolization sites can distribute towards the brain.

Such insights on stroke post-LVAD will require quantitative characterization of post-implant hemodynamics, as well as thromboembolic events. Thrombotic events, risks of embolization, and embolus distribution to the brain, are not just a function of patient vascular anatomy and physiological variables, but also intimately depends upon hemodynamics and embolus-hemodynamics interactions. However, standard imaging and clinical workup, as well as in vivo investigations using animal models do not always provide these information in sufficient resolution. In silico advances have enabled a viable avenue for studying such phenomena in a patient-specific manner. Extensive in silico investigations have been reported on investigating the impact of the surgical attachment angle of the LVAD outflow graft on hemodynamics within the aortic arch and its potential for thrombosis^{22,23,24,25,26}. Computational research has delved into various specific factors, including but not limited to: examining the impact of pulse modulation on LVAD flow in both adult and pediatric populations^27,28,29, exploring additional surgical attachment parameters for VADs³⁰, investigating the influence of viscoelastic hemorheology on VAD-powered circulation³¹, assessing cerebral embolism risks³², and assessing the consequences of intermittent reopening of the aortic valve³³. In a series of prior works, we have developed a computational framework to quantitatively assess a range of hemodynamic descriptors such as helicity, vorticity, wall shear, and viscous energy dissipation as function of LVAD outflow graft anastomosis and pulse flow modulation^21,34. However, detailed in silico quantification of spatiotemporally varying embolus-hemodynamics interactions and a quantitative source-to-destination mapping of thromboembolus transport towards the brain via the cervical vessels has not been studied for LVAD-driven circulation. Motivated by this knowledge gap, here we demonstrate a patient-specific in silico embolus-hemodynamics model, established extensively in our prior works for stroke^35,36,37,38, for quantitative characterization of embolus distribution towards the cervical vessels post-LVAD implantation. Our goal is to demonstrate key features of thromboembolus source to destination transport trends as function of surgical variables such as varying graft anastomosis and pulse flow modulation, and embolus properties such as size and release locations.

Methods

Image-based modeling of vascular anatomy

For this study, we selected a patient-specific vascular network used extensively in our prior works for quantitative assessment of hemodynamics driven by LVADs^21,34, adapted from the open source SimVascular model repository³⁹. The native vascular anatomy for the model considered here includes the aortic arch and branch arteries extending up to the iliofemoral arteries. Computed Tomography (CT) images of the selected vascular network were segmented using a 2D lofted image segmentation technique, which were subsequently used to generate a patient-specific 3D model using the open source software tool SimVascular⁴⁰. An LVAD outflow graft was then surgically placed along the aortic arch of the patient-specific model, using an image-based virtual surgical anastomosis workflow as detailed in our prior study²¹. The LVAD outflow graft was virtually attached such that the resulting graft does not intersect nearby organ (that is, heart, lungs etc.) or bone (that is, sternum, ribs etc.) boundaries. This ensured generating realistically achievable surgical LVAD outflow graft anastomoses. Using this approach, we generated a set of 9 different parametric graft anastomoses, based on 3 combinations of orientation angles measured towards or away from the aortic valve (labelled with an Inc tag), and 3 combinations of orientation angles measured towards left or right of the heart across the coronal plane (labelled with an Azi tag). The model generation, and the varying anastomosis angles, are illustrated in Fig. 1 (a) and (b). Specifically, the graft anastomosis angles for inclination angles are as follows: (1) perpendicular to the aorta (Inc90); (2) 45$^{\circ }$ towards the aortic valve (Inc45); and (3) 45$^{\circ }$ towards the aortic arch (Inc135). The graft anastomosis angles for azimuthal angles are as follows: (1) 45$^{\circ }$ right of the heart (AziNeg45); (2) perpendicular to the coronal plane (Azi0); and (3) 45$^{\circ }$ left of the heart (Azi45). Furthermore, in this study, we assumed that the aortic valve was sealed throughout and has no aortic valve opening. This assumption, as well as additional intricacies of the image-based workflow, has been discussed at length in our prior works^21,34.

Patient-specific hemodynamics modeling

The overall workflow starting from image data to embolus transport model has been illustrated in Figure 1(a). Three-dimensional simulations of blood flow was conducted for each of the 9 models, assuming blood to be a homogeneous Newtonian fluid⁴¹ of effective density ($\rho$) 1060 kg/m³ and dynamic viscosity ($\mu$) 4.0 cP. The flow domain comprising the vessel lumen and the LVAD outflow graft for each of the 9 models were discretized into a computational grid comprising linear tetrahedral elements with a maximum edge size of $\approx$ 0.67 mm, with resulting meshes comprising $\approx$ 4 million tetrahedral cells. These choices were guided based on prior mesh refinement and convergence studies based on the underlying SimVascular solver as noted in previous works^37,42. For each model, blood flow velocity and pressure was computed by solving the incompressible Navier-Stokes equations for momentum balance and the continuity equation for mass balance. A Petrov-Galerkin stabilized finite element method^43,44,45,46 implemented in the open source SimVascular package⁴⁰, was used to solve these equations, using a numerical integration time-step of 0.001 sec. Flow was driven from the LVAD outflow graft inlet, and the aortic valve was assumed to remain shut for all simulations presented here. As described in detail in our prior works^21,34, a set of three different scenarios of pulse modulation were considered for the inlet flow from the LVAD outflow graft: (a) a constant uniform flow over time (referred to as constant or C); (b) flow with a low extent of pulse modulation (referred to as Low modulation or L); and (c) flow with a high extent of pulse modulation (referred to as High modulation or H); with the pulse modulated flow profiles adapted from prior studies⁴⁷. The time-averaged inlet flow was fixed at 4.9 L/min for all the models, mapped spatially across the outflow graft inlet geometry in form of a Womersley-type flow profile. The pulsatility index (PI) is defined as $PI=(Q_{max}-Q_{min})/Q_{avg}$ with $Q_{max}$ being the maximum flow rate; $Q_{min}$ being the minimum flow rate; and $Q_{avg}$ the average flow rate for the LVAD. The value of PI for low modulation flow and high modulation flows are 0.81 and 1.82 respectively. Three-element Windkessel boundary conditions with parameters: proximal resistance ($R_p$); distal resistance ($R_d$); and compliance (C); were used to consider the effect of the truncated downstream vasculature on the flow. Quantitative details of the three inflow profiles with their pulsatility index (PI), and the individual Windkessel parameters $R_P$, $R_d$, and C have been specified in our prior work^21,34 and are not reproduced here for brevity. However, the different flow profiles, and the Windkessel boundary condition parameters, are enumerated in the Supplementary Material for handy reference. The numerical simulation was implemented using the built-in stabilized finite element solver in SimVascular. Blood flow was simulated for a total of 9 different anastomosis models, with 3 different inflow patterns, leading to 27 different CFD models, each simulated for a duration of 3 seconds. An additional simulation was conducted to estimate the baseline physiological flow without the presence of an LVAD, driven by a pulsatile flow profile as outlined in^21,34. The results from the third second of the total simulation duration was further used for embolus transport calculations outlined next.

Modeling the movement of thromboemboli

Transport of thromboemboli across the arteries was modelled, by assuming each embolus to be a spherical particle, and modeling their dynamics in the simulated blood flow using a custom modified form of the Maxey-Riley equation⁴⁸, that we have developed extensively in a series of prior works^35,36,37,38. Briefly, this equation incorporates the effects of the drag force, shear-gradient-driven lift forces, fluid stresses for undisturbed flow, added mass and buoyancy forces, alongwith a soft particle-wall collision model to account for embolus interactions with vessel wall. The final form of this equation is stated as follows:

$$\begin{aligned}&m_p \frac{d \vec {v}_p}{d t}=\underbrace{\frac{1}{2} \rho _f C_D\left( \pi R_p^2\right) \left\| \vec {u}-\vec {v}_p\right\| \left( \vec {u} - \vec {v}_p\right) }_{\text{ drag } \text{ force } } +\underbrace{C_{s l} \rho _f R_p^2 \frac{\sqrt{\mu _f}}{\sqrt{\rho _f\Vert \vec {\omega }\Vert }}\left[ \left( \vec {u}-\vec {v}_p\right) \times \vec {\omega } \right] }_{\text{ lift } \text{ force } \text{(shear-gradient) } } \nonumber \\&+\underbrace{\mathcal {V}_p(-\nabla p+\nabla \cdot \underline{\underline{\varvec{\tau }}})}_{\text{ fluid } \text{ stresses, } \text{ undisturbed } \text{ flow } } +\underbrace{C_{\textrm{am}} \frac{\rho _f \mathcal {V}_p}{2}\left[ \frac{D \vec {u}}{D t}-\frac{d \vec {v}_p}{d t}\right] }_{\text{ added } \text{ mass }}+\underbrace{\left( m_p-\rho _f \mathcal {V}_p\right) \vec {g}}_{\text {buoyancy }} +\underbrace{\mathcal {I}(\mathcal {P}, \mathcal {W})\left[ \Delta \vec {v}_p\left( e_{\text{ lub } }\right) \right] }_{\text{ elastohydrodynamic } \text{ wall-collisions } } \end{aligned}$$

(1)

In the above equation, $m_p$ denotes the particle mass, $R_p$ is the particle radius, $\mathcal {V}_p$ is the particle volume (which in this case will be $4/3 \pi R_p^3$ with the spherical shape assumption), $\tau$ denotes the stress tensor from undisturbed forces (obtained from CFD simulations), $\vec {u}$ is the simulated blood flow velocity output from CFD simulations, and v$_p$ is the translational particle velocity. $\hbox {C}_{am}$ is the added mass coefficient (which has a fixed value of 0.5 for spherical particle shape), $C_D$ is the drag coefficient, and $C_{sl}$ denotes the shear-gradient lift force coefficient adopted from prior works^49,50. $\vec {\omega }$ = $\nabla \times \vec {u}$ is the vortcity of the flow where the particle is located. $\mathcal {I}$($\mathcal {P}$,$\mathcal {W}$) is an indicator that has a value of 1 when a particle $\mathcal {P}$ comes into contact with the artery wall, and the value of this function is 0 otherwise. Next, the contribution of the momentum changed created by the elastohydrodynamic lubrication and particle-wall collisions is denoted by the term [$\delta$ v$_p$($\hbox {e}_{\text {lub}}$)] where $\hbox {e}_{\text {lub}}$ is the restitution coefficient. For the embolus transport modeling in LVAD driven flows, precise resolution of the embolus interactions with the vessel walls is especially critical in the regions at and around the LVAD outflow jet impingement on the aorta wall. To address this, we modified the particle-wall contact resolution method from our prior works³⁶ into one that relies on computed Signed Distance Fields (SDF) of the vascular geometry. Specifically, we use a fast voxel-based interpolation method⁵¹ to compute the SDF based on the 3D model created from image-segmentation; interpolate the computed SDF back on to the CFD grid over which flow and particle dynamics computations occur; and resolve particle-wall contact by interpolating the computed SDF at particle locations and checking if computed SDF is less than particle radius $R_p$. Each thromboembolus particle is released individually from a specified source or release location, making this a Monte Carlo type sampling based simulation; and hence, no contact mechanics interactions between individual thromboemboli were considered.

Design of in-silico experiments

Using the underlying image-based modeling, hemodynamics simulation, and embolus transport simulation techniques as identified in Sections Image-based modeling of vascular anatomy, Patient-specific hemodynamics modeling, and Modeling the movement of thromboemboli respectively; we setup a parametric design for in silico experiments to understand embolus dynamics patterns in LVAD driven flows. For a source-to-destination transport analysis, the choice of embolus source and destination is crucial. To substantiate our choice, we note that when compared against flow driven by the opening of the aortic valve in normal scenario (the Aortic Outflow (AO) jet); hemodynamics driven by the LVAD outflow (LO) jet leads to significantly differing flow patterns owing to the jet traversing across the aorta centerline, impinging with the aorta wall, and leading to regions of stasis in the aortic root, especially for cases where the outflow graft angles away from the aortic valve (indicated in detail in parametric analysis showed in ²¹). Distinction between these two different jet flows was explained using a conceptual framework of two jet flow model outlined in our prior works^21,34 (see also discussion in Section 4.1). We account for these hemodynamic features and their connection to thromboembolic events explicitly in the source-destination mapping analysis by specifically considering the following scenarios in our design of experiments. First: as jet flow enters the aorta from the LVAD, thromboemboli, originating from device-hemodynamics interactions or ingested from the ventricle, can enter the flow direcctly via the LVAD outflow graft inlet. Some of these emboli can travel directly towards the brain via cervical vessels, while some may reach the aortic root region and remain accumulated there. Second: thrombogenicity induced by flow stasis in the aortic root can lead to additional thromboemboli in the aortic root. Third: the accumulated emboli from the first and second factors above can get re-entrained in blood flow in case of intermittent aortic valve opening, and subsequently reach the brain via the cervical vessels. While under high LVAD support, we assume that the the valve remains closed (see also our discussion in Section 4.1), this risk of embolic events need to be nevertheless included in the analysis. Accounting for these arguments, we consider two thromboembolus sources: LVAD outflow graft inlet, and the aortic root region; and two destinations of relevance for stroke: the branching arteries into the cervical vessels, and the aortic root region. For each source-destination combination, we conduct thromboembolus transport for each of the 9 different anastomosis, for each of the 3 pulse modulation scenarios. We consider a set of 8 different thromboembolus sizes ranging from 0.5 mm to 4.0 mm in diameter, mimicking a range of stroke scenarios. The outline of this parametric design of experiments is presented in Figure 2. Across all parameter combinations, this led to a total of 432 simulations, for each of which 5,000 thromboembolus samples were tracked. This sample size of 5,000 per simulation has been based on sample statistics studies as reported in multiple of our prior works^{35,36,37,38,52}, wherein the distribution statistics were found to be robust at this sample size regime, with each embolus independently chosen or seeded. In total, this design led to source to destination distribution data spanning a total of 2.16 million embolus sample experiments. Each thromboembolus was modeled as an idealized sphere with material properties assigned based on measured thrombus properties available in the literature^36,53,54: material density 1.11 g/cm³; elasticity 1667.64 Pa; Poisson ratio 0.30; and viscosity 0.42 Pa.s. For each of the 27 models, flow velocity data from the third second of simulated hemodynamics was stitched together 4 times to create a representative flow-field spanning 4 cardiac cycles that has no cycle-to-cycle flow variations. For each of these 432 simulations, the computational endpoint comprised a number fraction defined as $N_k$/$N_{res}$ where $N_k$ is the number of emboli that reached the cervical vessels or accumulated in the aortic root from the LVAD graft or aortic root source and $N_{res}$ is the total number of emboli that is resolved in each variation of the 3D LVAD model after 4 cardiac cycles.

Results

Thromboembolus distribution from LVAD outflow graft

Here we discuss simulated thromboembolus distribution from the LVAD outflow graft as the source, as function of varying outflow graft anastomosis and pulse modulation of the LVAD. Figure 3(a) depicts the distribution of thromboemboli from outflow graft moving into the cervical vessels towards the brain across all 27 flow scenarios, combining all thromboembolus particle sizes. The corresponding thromboembolus distribution from LVAD outflow graft towards the aortic root is presented in Figure 3(b). Based on these simulated data, we note that when emboli entering from the LVAD outflow graft are considered, the distribution of thromboemboli towards the cervical vessels is significantly greater than that of accumulation in the aortic root (p-value $<<$ 0.01 using non-parametric Mann-Whitney U test, see also Supplementary Material). The data also indicate that both the anastomosis angles, as well as the pulse modulation, influences the distribution of thromboemboli coming in through the outflow graft. Across the Inc anastomosis angles considered, for all combinations and across all particle sizes, the Inc135 case - that is, angled away from the aortic valve at 45$^{\circ }$ towards the aortic arch - has the least extent of emboli distributing towards the cervical vessels, across all sizes considered. The combination with the highest extent of thromboembolus distribution towards the cervical vessels is the Inc45AziNeg45 anastomosis with low pulse modulation; while that with the least extent of distribution towards the cervical vessels is Inc135Azi-45 anastomosis with low pulse modulation. While accumulation in the aortic root is significantly lesser, it is relevant to note that Inc135 anastomoses with graft angled away from the aortic valve leads to higher extent of accumulation compared to other anastomoses, across all pulse modulation and particle sizes considered.

Thromboembolus distribution from aortic root

Similar to Section Thromboembolus distribution from aortic root, the simulated thromboembolus distribution from the aortic root region as the source is presented in Figure 4, illustrated as function of varying outflow graft anastomoses and pulse modulation of the LVAD. Similar to the trends observed in Section Thromboembolus distribution from LVAD outflow graft, we note that the distribution of thromboemboli from aortic root region as the source is influenced by both anastomosis angles, as well as extent of pulse modulation. The distribution of thromboemboli into the cervical vessels towards the brain is presented in Figure 4(a), while the acccumulation of thromboemboli in the root region (those that remain entrained at the source) is presented in Figure 4(b). We note that thromboembolus accumulation at the root is significantly higher for emboli originating at the root, compared to those entering from the LVAD outflow graft (p-value $<<$ 0.01 using non-parametric Mann Whitney U test, see also Supplementary Material). The extent of accumulation is also markedly higher for the Inc135 anastomoses, with the LVAD outflow graft angled away from the aortic root. Conversely, for these Inc135 anastomoses, the extent of distribution towards the cervical vessels is notably lower, with the least extent of thrombembolus distribution towards the cervical vessels noted for the Inc135Azi0 anastomosis with low pulse modulation. The Inc45Azi-45 and the Inc90Azi-45 anastomoses led to the highest extents of thromboemboli moving potentially towards the brain, with the low pulse modulation scenario for both cases having a distribution fraction of 0.47 - the maximum distribution fraction towards the cervical vessels from the aortic root. Likewise, the case with highest embolus accumulation is the Inc135Azi0 low pulse modulation scenario with a computed fraction of 0.62 across all thromboembolus sizes.

Combined thromboembolus distribution governing stroke risk

Here we illustrate the overall source to destination distribution across both thromboembolus destinations (cervical vessels and aortic root), when both sources (LVAD outflow graft and aortic root) are considered together as embolus origin sites. These are computed as the fraction of emboli that reach the cervical vessels or the aortic root originating from both sources considered in our simulations. This combined distribution is illustrated in Figure 5 as function of varying outflow graft anastomosis and pulse modulation of the LVAD. Figure 5 (a) presents combined thromboembolus distribution towards the cervical vessels, across all of the 27 flow scenarios considered here and combining all thromboembolus particle sizes. The corresponding combined accumulation in the aortic root is presented in Figure 5 (b). We observe that outflow graft anastomoses with angle Azi-45 have greater extent of embolus distribution to the cervical vessels from both sources, across all thromboembolus sizes combined. Additionally, while the anastomosis angled 45$^{\circ }$ towards the aortic arch (that is Inc135 models) altogether have the least extent of thromboembolus distribution directly towards the arch, they have the greatest extent of thromboembolus accumulation at the aortic root. This indicates that expectations based on anastomosis angles alone can lead to competing trends in embolus transport patterns when direct traversal towards the cervical vessels and accumulation in the aortic root region are simultaneously considered. The maximum distribution of thromboemboli from both sources combined, towards the cervical vessels, is observed for the Inc45AziNeg45 model with low pulse modulation. The maximum accumulation of thromboemboli at the aortic root, from both sources combined, is observed for the Inc135Azi0 model with low pulse modulation.

Effect of pulse modulation on thromboembolus fate

As outlined in Patient-specific hemodynamics modeling, three different LVAD pulse modulations were considered for the simulations, to quantify differences in thromboembolus transport to the cervical vessels due to extent of pulse modulation. The results presented in Figures 3, 4, and 5 together indicate that varying extent of pulse modulation, for the different anastomoses considered, can lead to significant variabilities in embolus source to destination transport. Specifically, for thromboembolus distribution from LVAD outflow graft to the cervical vessels, high pulse modulation was associated with higher distribution fractions (compared to constant and low pulse modulation) for 6 out of the 9 anastomoses considered. Likewise, for thromboembolus distribution from aortic root to the cervical vessels, constant (no pulse modulation) was associated with higher distribution fractions (compared to high and low modulation) for 6 out of the 9 anastomoses considered. In both of these cases, the highest distribution of thromboemboli to the cervical vessels were associated with low pulse modulation cases - Inc45AziNeg45 for thromboemboli from LVAD outflow graft, and Inc90AziNeg45 for thromboemboli from aortic root. While these observations indicate that pulse modulation influences extent of embolus movement towards the brain in LVAD flows, there are no consistent trends or dependency on the extent of pulse modulation that can be inferred, warranting further detailed investigations.

Effect of thromboembolus size on thromboembolus distribution

The simulated thromboembolus distribution shows a strong dependence on embolus size, which is in agreement with observations on embolus transport in arterial flows as indicated in several prior works^35,38,55. Figure 6 illustrates the variation of thromboembolus distribution towards the cervical vessels from LVAD outflow graft, aortic root, and both sources combined. Figure 7 illustrates the same for thromboembolus accumulation at the aortic root. The trends are presented as function of the outflow graft angle towards/away from the aortic valve, that is Inc angles. In both figures, the averaged trendlines across Azi0, Azi45, and AziNeg45 anastomosis are presented in black, blue, and red solid lines respectively, while the aggregate average trends across all 27 anastomosis-pulsatility combination is presented in green dashed line. When thromboembolus distribution into the cervical vessels is considered, the average trend across all anastomoses and pulse modulation combinations indicates a decrease in distribution with increasing embolus size. When individual anastomoses are considered, we observe that for the Inc90 cases, the thromboembolus distribution with size departs from this average trend, and for the size ranges considered here, thromboembolus movement into the cervical vessels increases with size - for both LVAD outflow graft, aortic root, as well as both sources combined. An increase in size dependent distribution towards the cervical vessels for small emboli is also observed for the Inc45 anastomoses. Conversely, thromboembolus distribution to the cervical vessels for all Inc135 configurations consistently reduce with increasing size. On the other hand, considering thromboembolus accumulation at the aortic root illustrated in Figure 7, we observe that the average trend across all anastomoses and pulse modulation combinations indicates an increase in accumulation with increasing embolus size. Cases with Inc135 anastomoses, as noted in Section Thromboembolus distribution from LVAD outflow graft and Thromboembolus distribution from aortic root, have low extents of accumulation at the root overall. Together, these observations on embolus source-to-destination distribution shows a strong size-dependence for both movement into the cervical vessels, and accumulation at the aortic root. Additional detailed data visualization for all anastomosis combinations is provided in the Supplementary Material, further substantiating the evidence for this noted size-dependent distribution trend.

Correlation of embolus distribution with hemodynamic alteration

In a prior work²¹, we have focused exclusively on hemodynamic descriptors for varying outflow graft angles and pulse modulation, devising descriptors for the extent of hemodynamic alteration post-LVAD (driven by LVAD outflow jet) when compared against pre-implantation physiological flow (driven by the aortic outflow jet). With the extensive in silico analysis of thromboembolus distribution as conducted here, we can now further analyze the correlation between embolus distribution and hemodynamic descriptors for altered state of flow in aorta post LVAD implantation. Specifically, we computed correlation coefficients between the simulated thromboembolus distribution, and the hemodynamic descriptors as defined in our prior work²¹. These descriptors quantified the extent of vorticity using Q-criteria, positive and negative helicity using LNH, and wall shear stress using TAWSS, each compared between LVAD-driven flow and baseline flow without LVAD. The computed Pearson correlation coefficients between these descriptors and source-to-destination thromboembolus distribution aggregated across all embolus sizes are listed out in Table 1. We observe that, based on the simulation data, thromboembolus distribution shows weak to no correlation with vorticity descriptor; while showing some of the strongest correlation with wall shear stress descriptor. Thromboembolus accumulation at the aortic root shows moderate correlation with positive helicity, while negative helicity descriptors are more correlated with thromboembolus distribution to the cervical vessels. We further note that these correlations also present with strong thromboembolus size dependency, which is illustrated in Figure 8 and Figure 9. This illustration affirms the strong negative correlation with wall shear descriptors, and overall negative levels of correlation with negative helical flow, with variations in thromboembolus size.

Discussion

Insights on hemodynamics and the two jet flow model

We present thromboembolus transport simulations in a patient-specific vascular network comprising the aortic arch and branching arteries with a virtually attached LVAD outflow graft. The results shed several insights into embolus transport and source to destination distribution patterns when the flow is driven by an operating LVAD for varying extent of pulse modulation, and varying thromboembolus sizes. As noted in several of our prior works^36,37,38, the transport of emboli from a source to a destination site is intimately related to the overall state of hemodynamics in the vessels that the emboli travel through. In our previous contributions^21,34 we have described a conceptual model for hemodynamic understanding of LVAD-driven flows, referred to as two jet flow model, based on the fundamental role of jet-driven flows and jet impingement in LVAD-driven flows. Specifically, unlike in physiological flow without LVAD which is driven by the aortic outflow jet traversing along the aortic centerline or curvature only during cardiac systole, flow due to operating LVAD is driven by a continuously flowing jet (with some pulse modulations) traversing across the aorta centerline and impinging directly on the aorta wall. We have shown in prior works^21,34 that differences in the way the LVAD outflow jet (for post-implant flow) and the aortic jet (for physiological non-LVAD pre-implant flow estimate) enter and traverse the aortic arch determines the state of hemodynamic alterations post-implantation. Here, we demonstrate how the LVAD outflow jet dynamics, its impingement on the aortic wall, and subsequent flow roll up and secondary vortices ultimately determine embolus source-to-destination transport. The LVAD outflow graft anastomosis angle determines the angle and location of the LVAD outflow jet entry and its impingement on the aorta wall; while the extent of pulse modulation will influence the temporal intensity of the impingement flow. Consequently, as a thromboembolus enters the aortic arch through the LVAD graft, it can get entrained in the post-impingement flow patterns of the aortic arch and ultimately travel to a destination site such as the cervical vessels. These factors explain the strong dependence of embolus source to destination distribution on both anastomosis angles and pulse modulation as observed in our simulation case study. Additionally, as the LVAD outflow jet traverses across the aorta centerline and impinges directly on the aorta wall closer to the aortic valve, prominent stasis regions are formed near the aortic root, which can lead to embolus formation and accumulation. We showed that this needs to be accounted for to rigorously estimate of thromboembolus transport propensity towards the brain (that is, for our analysis we have the LVAD outflow graft as well as the aortic root as source for thromboemboli, as explained in Section 2.4, and Sections 3.1-3.3). This accumulation at the root is a feature of LVAD-driven flows, and is not generally the case for modeling stroke in patients without an LVAD (as shown in our multiple prior works on cardioembolic strokes^35,36,38). We note the additional scenario of intermittent valve opening during LVAD operation where the dominant LVAD outflow jet and a weaker aortic outflow jet are operational simultaneously. We have not considered this case in our simulations, and instead focused on the majority of operational scenarios which involves only the LO jet. This assumption of ours is backed by several studies. Specifically, it is regarded that the aortic valve remains continuously closed during periods of high LVAD support^56,57. Furthermore, with continuous VAD support over time, the valve may degrade or undergo fusion⁵⁸. In case valve opening occurs, it is intermittent, and generally contributes to a lower level of trans-valvular flow compared to the extent of flow emanating from the LVAD outflow jet. We have indirectly accounted for these low flow effects via potential re-entrainment of emboli from the aortic root in our simulation studies. Finally, correct modeling of the intermittent opening of valves is also a sufficiently complex computational feature of its own beyond the scope of the present study, as the regulation of trans-valvular pressure that contributes to the opening of the valve is in turn related to factors such as VAD speed^59,60 which must be carefully accounted for. Therefore, within the scope of this work, we have chosen to focus on the more common case of the aortic valve remaining closed during VAD supported flow. As a final remark, we note that there is nothing fundamental to our method that will prevent us from adding the effect of the intermittent flow from the aortic valve in future studies focusing on device specific operational trans-valvular pressures and intermittent opening.

Insights on embolus-hemodynamics interactions

Finite-sized embolus particles interact with local blood flow features as a function of their size and inertia, and this embolus-hemodynamics interaction mechanics determines embolus fate. We have characterized the complexity of these interaction mechanics for embolus transport in pulsatile arterial hemodynamics in multiple prior studies^36,36,38. The momentum response time is a key physical variable that determines this embolus-hemodynamics interaction mechanics. Momentum response time represents the time taken by a finite-sized inertial particle (such as an embolus) immersed in a fluid (blood) to respond to local changes in background fluid flow (in this case, blood flow). For this study, we considered thromboemboli in the diameter range of 0.5 mm - 4.0 mm, which leads to an estimated range of 0.004 sec - 0.24 sec for thromboembolus momentum response time (refer to our prior work ³⁸, for instance, for further details). Smaller emboli will have lower inertia and a smaller momentum response time, and can respond to and get entrained by the background blood flow faster. Conversely, larger emboli will have greater momentum response time, and will respond to hemodynamic forces slower, thereby deviating significantly from flow path. Consequently, embolus distribution under the LVAD driven jet flow presents with a strong size-dependency as observed from our analysis. This also explains the size-dependence in correlation coefficients with hemodynamic descriptors as noted in Section Correlation of embolus distribution with hemodynamic alteration. We further note that this size-dependent dynamics; the complexity of the aortic flow with jet impingement, secondary circulation, vortex formation and helical flow; and the non-linear nature of the underlying hemodynamic forces on the emboli, lead to high variability in embolus distribution patterns and their departure from expectations based on flow distribution alone. This renders a major challenge to the understanding of embolic stroke or other cerebrovascular embolic events for patients on LVAD circulatory support. We have previously demonstrated the importance of understanding embolus-hemodynamics interactions to elucidate embolus distribution patterns across the Circle of Willis in the brain^37,38. The observations from this study further advance this argument for embolic events in patients on LVAD circulatory support, that embolus distribution across bifurcating vessel networks cannot be inferred solely based on vessel geometry and/or expected flow distribution.

Interplay of flow and graft anastomosis as a determinant for embolus destination

Multiple existing studies have characterized LVAD-driven flow using bulk hemodynamic descriptors such as wall shear, pressure, and residence time^{22,23,24,25,26,30} obtained from estimated hemodynamics after LVAD implantation. In prior works^21,34, we introduced the alternative idea of descriptors based on extent of post-implantation hemodynamic alteration with reference to a baseline physiological flow pre-implantation. The direct comparison of thromboembolus distribution trends against variations in hemodynamic descriptors for extent of alteration, with varying anastomosis angles and LVAD pulse modulation, offers a novel perspective on hemodynamic underpinnings of stroke and thromboembolic events in LVAD circulatory support. Specifically from the simulations presented here, when compared against thromboembolus distribution trends, we observed a strong negative correlation for wall shear stress descriptors (against baseline flow). From the hemodynamics analysis presented in²¹, the wall shear descriptor was the highest for Inc135 outflow graft anastomoses, where the graft inlet is directed away from the aortic valve. The LVAD outflow jet, therefore, is directed towards the distal aortic arch, and the jet impingement and post-impingement flow is less arrested compared to the other two Inc angle anastomoses. This increases the area over which the flow develops post-impingement, consequently increasing the average wall shear stress integrated over the aortic arch surface, as detailed in our prior work²¹. Concurrently, for the Inc135 cases, as the emboli impinge on the distal aortic wall, they spread away from the point of impingement until being entrained in secondary vortices in the arch^61,62. This brings a significant fraction of emboli far downstream of the arch instead of them traveling up the branching vessels into the cervical arteries towards the brain. This provides a hemodynamics based explanation for the strong negative correlation between altered state of wall shear stress due to LVAD flow, and thromboembolus movement towards the cervical vessels. We note that while this discussion addresses the connection between wall shear and embolus transport from the purview of jet impingement fluid flow in the aorta, wall shear stress by itself can have other mechanisms or roles to play in terms of pathological consequences (including disrupted endothelial mechanoregulation and altered endocrine signaling) in patients on LVAD support, which have not been discussed here. Additionally, while thromboembolus distribution towards the cervical vessels is lower for the Inc135 anastomosis, a significant fraction of emboli travel distal to the impingement region down into the aortic root, leading to a higher accumulation of thromboemboli at the root driven by a larger stasis region (as indicated in our prior studies ^21,34). This increased accumulation of emboli at the aortic root consequently also increases the likelihood of thromboemboli traveling towards the cervical vessels in the event of intermittent aortic valve opening, which we have not explicitly modelled here. These dynamic trends are clearly visible in the series of embolus trajectory animations provided in Supplementary Data. We further note that the effect of the anastomosis angle towards/away from the valve (that is, the Inc angle) has been extensively studied^22,23, the effect of the anastomosis angle left/right of the heart (that is, the Azi angle) has been less explored. In our prior works, we presented detailed evidence on how the Azi angle influences aortic hemodynamic features. Here, we further advance that evidence to show how thromboembolus distribution is influenced by the Azi angle. We observe that the AziNeg45 anastomosis generally presents high levels of thromboembolus distribution towards the cervical vessels, and for the Inc45 and Inc90 models, the embolus size dependence manifests differently compared to other Azi angles. One potential explanation for this is that for our model, the AziNeg45 angle shows greater alignment with the centerline of the aortic arch, thereby better aligning the thromboemboli entering the aorta along the curvature of the arch, leading to distinct differences in thromboembolus distribution patterns. A visualization of this geometric alignment, as well as additional data visualization of thromboembolus distribution with respect to Azi angles are included in the Supplementary Material.

Clinical implications of findings

The data and insights presented here have multiple broad clinical implications. Thromboembolus source to destination propensity, and its ultimate distribution towards the brain, are direct determinants of stroke and other related cerebrovascular accidents. However, standard-of-care imaging and clinical work-up can not provide sufficient information regarding embolus dynamics and embolus source-destination distribution, driven by embolus-hemodynamics interactions. We have developed an in silico modeling framework that can quantify the thromboembolus transport as a function of LVAD outflow graft anastomosis, pulse modulation, embolus size, and source. Consequently, the underlying in silico framework can provide the basis for pre-surgical analysis of stroke risk post-implantation for individuals on LVAD support, as well as enable avenues for finding optimal patient-specific surgical configurations by analysing a number of virtual “candidate” surgical configurations and identifying ones with minimal predicted embolism risks. This will require further investigations on larger patient cases leveraging the in silico methodology developed here, and remains an area of interest for future developments. Additionally, the findings from the simulations presented in this study provide valuable insights on the mechanisms governing embolic events, highlighting the underlying complex dynamic embolus-hemodynamics interactions. Specifically, the observations indicate the importance of considering both: (a) the direct distribution of emboli entering the aorta towards the cervical vessels; and (b) the accumulation of emboli in the aortic root entrained in stagnated or slow moving flow - for characterizing embolus source-to-destination distribution under LVAD operation. The fact that thromboembolus movement towards the cervical vessels (and subsequently towards the brain) demonstrate a strong size-dependence is of additional clinical relevance. Specifically, smaller and larger emboli have different mechanisms of causing a stroke. Larger emboli get stuck in larger vessels and cause large vessel occlusion (LVO) in M2, A2 and P2 segments of the middle, anterior and posterior cerebral arteries. However, small emboli can perforate the distal beds causing lacunar infarcts^63,64 and cerebral small vessel disease (CSVD)⁶⁵. Our observations from the simulations presented here indicate that smaller thromboemboli entering the aorta from the LVAD outflow graft may have higher probability to transport towards the brain. This small embolus propensity is noteworthy especially considering that small emboli or microemboli are known to cause complications in continuous flow LVADs^66,67, and detection of microembolic siganture using Trans-cranial Doppler is often used as a diagnostic tool for thromboembolic events in patients on LVAD support⁶⁸. Further systematic investigation comparing these predicted source-to-destination embolus transport patterns against noted stroke outcomes and stroke locations will be needed to elucidate these aspects across a larger cohort of patient cases.

Assumptions and limitations

Our in silico study was based on several key assumptions, with some associated limitations, which are noted here. First, we assumed the embolus particle transport from aortic root as a source associated with continuous LO jet flow and did not consider the intermittent flow from AO jet from the aortic valve opening during ventricular systole. Additionally, we assumed that the vessel walls are rigid. Incorporating these additional structural features of intermittent valve opening and vessel wall deformations, within a parametric simulation study such as the one presented here, will be a computationally expensive endeavor and will require efficient numerical models for expanding such in silico approaches to resolve embolus-vessel-hemodynamics three-way interactions. This was not the scope of our study, but remains an area of active interest. However, the overall concept of mapping the source-destination relationship for emboli as outlined here, can be extended to these more resolved models as well. We remark here that, the approach of resolving vessel wall collisions using a Signed Distance Field, and the ability to virtually inject emboli as particles at a chosen source location (and over time) within the vascular model, are both key numerical modeling features presented here that can aid the transition into the aforementioned three-way interaction models. Second, and on a related note to the first assumption, we remark that our goal was to illustrate a framework that enables investigating the parametric influence of variables like outflow graft anastomosis and pulse modulation in general, without making this current study specific to any one device manufacturer. This device-agnostic or manufacturer-agnostic approach was chosen to ensure that the in silico framework described here can be generalized to multiple kinds of devices to look at hemodynamic features downstream from the pump, and embolus-hemodynamics interactions as well as embolus source-to-destination propensities in the aorta (information that are not readily available from standard-of-care imaging). In future clinical comparison studies with larger patient cohorts, our methodology outlined here as well as the fundamental insights on embolus-hemodynamics interactions we have illustrated, can be directly adopted to the particular graft dimensions, anastomoses, and operational details of specific device models such as the Heartware or Heartmate models. Third, we assumed a one-way coupling of the embolic particles with blood flow. This presumes that the blood flow influences the emboli, but the emboli themselves do not significantly alter the flow. This is a reasonable assumption considering that each embolus is modelled individually as a single particle released independently of the others, and that each individual embolus size is small in comparison to the vessel diameters they traverse. The alternative to this is a fully resolved computational model that numerically discretizes each embolus, which will be excessively expensive and prohibit the kind of Monte Carlo sampling study we have presented here. Third, our physics-based embolus-hemodynamics interaction model assumes that the emboli are spherical particles. This is an extensively-adopted modeling choice arising from the fact that presently there is no generalized physics-model for arbitrary non-spherical particle shapes. The derivation of a first-principles physics model of this nature will require significant additional theoretical and computational effort, which is beyond the scope of the study presented here. Moreover, we have not considered the embolus stretching, deformation, and deviation from sphericity governed by the flow-induced forces. Lastly, we have not considered here any modeling of turbulence, which can be of relevance at the impingement site of the LVAD Outflow jet. This remains another area of interest, which will require modifications of the physics-based model for embolus-hemodynamics interactions for turbulence, which have not been explored within the constraints and scope of this study.

Concluding remarks

In summary, we have presented an in silico framework for quantitative investigation of embolus transport, and thromboembolus source-destination mapping, towards characterizing stroke risks in patients on LVAD circulatory support. Through a systematic simulation study, we demonstrated that our in silico framework can quantify embolus dynamics and transport as a function of: (a) varying embolus sizes; (b) varying embolus release locations (sources); (c) varying LVAD outflow graft anastomoses; and (d) varying LVAD flow pulse modulation. The resulting simulations generated high resolution thromboembolus transport and distribution data, that was analyzed in terms of extent of thromboembolus distribution towards the cervical vessels supplying the brain, and extent of thromboembolus accumulation at the aortic root. We identified the importance of considering embolus formation and accumulation at the aortic root for understanding thromboembolic events during LVAD operation. We demonstrated that thromboemboli show a size dependent distribution trend as they travel towards the brain, and indicated how these distribution trends compare and correlate with purely hemodynamics-based descriptors such as wall shear, vorticity, and helicity. Such detailed embolus source-to-destination transport insights can not be obtained from existing imaging and clinical data alone, making this in silico approach highly valuable. Findings from our study also indicate how the in silico quantitative analysis provides insights that can enable future efforts in pre-operative patient-specific planning to determine optimal LVAD graft anastomoses and pulse modulation. The established framework and analyses presented here can be further extended to conduct larger patient cohort studies.

Fig. 1

(a) Schematic overview of the overall computational framework, (b) A virtual family of LVAD models with varying graft anastomosis.

Fig. 2

The structure of the in silico experiments comprising a total of 432 different embolus transport simulations. The parameters include three inc angles, three azi angles, three LVAD pulse modulation, eight embolus sizes, and two release locations

Fig. 3

(a) Total distribution of emboli to cervical vessels across all particle size originating from LVAD graft; (b) Total accumulation distribution of emboli in aortic root across all particle size originating from LVAD graft. The distribution is represented as fraction of emboli that reached the cervical vessels to the total amount of resolved particles at the end of 4 cardiac cycles. The labels C, L and H correspond to constant flow w/o pulse modulation, flow with low pulse modulation, and flow with high pulse modulation respectively (as outlined in Section "Patient-specific hemodynamics modeling").

Fig. 4

(a) Total distribution of emboli to cervical vessels across all particle size originating from Aortic root; (b) Total accumulation distribution of emboli in aortic root across all particle size originating from Aortic root. The distribution is represented as fraction of emboli that reached the cervical vessels to the total amount of resolved particles at the end of 4 cardiac cycles. The labels C, L and H correspond to constant flow w/o pulse modulation, flow with low pulse modulation, and flow with high pulse modulation respectively (as outlined in Section "Patient-specific hemodynamics modeling").

Fig. 5

(a) Total distribution of emboli to cervical vessels across all particle size originating from both source sites (LVAD graft and aortic root) considered together; (b) Total accumulation distribution of emboli in aortic root across all particle size originating from both LVAD graft and aortic root combined. The distribution is represented as fraction of emboli that reached the cervical vessels to the total amount of resolved particles at the end of 4 cardiac cycles. The labels C, L and H correspond to constant flow w/o pulse modulation, flow with low pulse modulation, and flow with high pulse modulation respectively (as outlined in Section "Patient-specific hemodynamics modeling").

Fig. 6

Distribution of embolus particles along with embolus size based on inclination angles for LVAD source, aortic root source and combined source towards cervical vessels. The term combined indicates that both LVAD and aortic sources are considered together. The color black, blue and red represents three different Azi angles: Azi0, Azi45 and Azi-45 respectively. The solid line, dashed line and line with marker represents low pulse modulation, high pulse modulation and constant flow respectively. The mean of the plots in each panel is represented in dashed line with color green.

Fig. 7

Accumulation of embolus particles along with embolus size based on inclination angles for LVAD source, aortic root source and combined source in aortic root. The term combined indicates that both LVAD and aortic sources are considered together. The color black, blue and red represents three different Azi angles: Azi0, Azi45 and Azi-45 respectively. The solid line, dashed line and line with marker represents low pulse modulation, high pulse modulation and constant flow respectively. The mean of the plots in each panel is represented in dashed line with color green.

Fig. 8

Correlation of embolus distribution fraction towards cervical vessels with ratio of hemodynamic descriptors: Q-criteria, Time averaged wall shear stress, positive local normalized helicity and negative local normalized helicity with varying embolus size.

Table 1 Correlation of source to destination distribution of thromboemboli with hemodynamic descriptors for extent of vorticity (ratio of Q-criteria between LVAD driven flow and baseline flow without LVAD), extent of wall shear stress (ratio of TAWSS between LVAD driven flow and baseline flow without LVAD), extent of positive helicity and negative helicity (ratio of +ve/-ve local normalized helicity between LVAD driven flow and baseline flow without LVAD). Thromboembolus distribution is represented here combined across all embolus sizes considered. All correlation estimated using Pearson’s linear correlation coefficients.

Fig. 9

Correlation of embolus accumulation fraction in aortic root with ratio of hemodynamic descriptors: Q-criteria, Time averaged wall shear stress, positive local normalized helicity and negative local normalized helicity with varying embolus size.