MODELING ACUTE ISCHEMIC STROKE RECANALIZATION THROUGH CYCLIC ASPIRATION

Abstract

We model the deformation of a thromboembolus lodged in a cerebral artery under the application of aspiration pressure as it would be provided by an aspiration catheter during a mechanical thrombectomy procedure. The system considered consists of (i) a clot modeled as a viscoelastic solid; (ii) an artery modeled as a hyperelastic solid; and (iii) a viscoelastic cohesive interface between the clot and the artery. For the chosen system and geometry, we show that the application of aspiration pressure results in the impingement of the thrombus against the inner arterial wall near the aspiration location. Conditions leading to interfacial failure are nucleated at the distal end of the clot and, depending on the details of the loading conditions, propagate toward the proximal end. The results provide useful information in identifying the circumstances that play a decisive role for clot removal by aspiration alone.

Introduction

Stroke is the second leading cause of death worldwide (over 6.5 million deaths/year) (Benjamin et al., 2017), with acute ischemic stroke (AIS) accounting for 87% of these (Go et al., 2014). AIS results from a cerebral arterial occlusion by a thromboembolus and, especially in larger vessels, mechanical thrombectomy might remove the occlusion (Nogueira et al., 2018). Current thrombectomy devices are typically of two types: stent retrievers (e.g. the Medtronic’s Solitaire and Stryker’s Trevo) and suction systems (Penumbra). These technologies can improve AIS outcomes either alone or in combination (Saver et al., 2012; Jansen et al. 2013; Lapergue et al., 2017). However, recanalization is achieved only in approximately 85% of patients (Grech et al., 2015) and 17% of these still die within 90 days (Grech et al., 2015). Additional postsurgical distal embolization is a complication affecting approximately 13% of mechanical thrombectomies (Gascou et al., 2014). Data show that with current technology, about 80% of eligible stroke patients will either die or suffer a major disability following a mechanical thrombectomy. These facts provide a strong motivation to improve current mechanical thrombectomy techniques. However, given the critical nature of the procedure, large clinical studies cannot be performed thus leaving modeling as one of the few tools with which to systematically investigate the various factors that play a role in successfully achieving recanalization.

To investigate improvements to mechanical thrombectomies, our group formulated a benchtop experimental model of the deformation of a clot analog subjected to cyclic aspiration (Good et al., 2020a,b). We also formulated a computational model to predict clot deformation and to study failure of the clot-artery interface. In Good et al. (2020b), our model consisted of a lodged thromboembolus and the cohesive interface between it and the arterial wall, the latter assumed rigid (Fig. 1). We modeled the clot as a nonlinear viscoelastic body with either Kelvin-Voigt or Oldroyd-B rheological response (cf. Rajagopal and Srinivasa, 2000). The clot-artery interface was modeled as a cohesive zone (CZ), also with a Kelvin-Voigt or Oldroyd-B rheological behavior. We included a failure model in which damage accumulation causes the degradation of the CZ load bearing capability. We showed that the computational models allowed us to match experimental measurements. We then conducted a parametric study of the clot deformation and interfacial failure to elucidate the role of the various constitutive properties in leading to clot removal under cyclic aspiration. We considered a neoprene clot analog and the case of a porcine clot. In either case, we assumed that the aspiration pressure was applied uniformly over the entire proximal clot surface. We observed that interfacial damage was nucleated at both ends. However, the distal end experienced a more pronounced damage growth and was the location of failure initiation.

Figure 1:

a Model consisting of a lodged thromboembolus in a cerebral artery exposed to aspiration from an upstream catheter. b Diagram of the CZ model as the thromboembolus is pulled away from the arterial wall.

Here, we improve on Good et al. (2020b) by accounting for the artery’s deformability and limiting the application of the aspiration pressure over the area of the clot facing the catheter’s inner lumen. We choose dimensions typical of the M1 segment of the middle cerebral artery (MCA) and a clot with thickness equal to its radius. We choose constitutive properties for the MCA and for the clot that can be considered physiologically relevant. The chosen CZ properties are meant as a numerical experiment to assess deformation and CZ failure scenarios. We show that the clot tends to become impinged against the arterial wall. This new finding has significant implications for the development of cyclic aspiration thrombectomy devices.

The next section describes the models for the system’s components. Various deformation scenarios are then considered. For simplicity, we select a single set of constitutive parameters for the clot and artery while considering a range of CZ parameter values.

Methods

Basic kinematics and constitutive modeling

Subscripts a, c, and cz are used to distinguish between the artery, clot, and cohesive interface, respectively. X and x denote position in the reference and deformed configurations, respectively, with corresponding gradient operators ∇_X and ∇_x. w = x — X is the displacement, v = w is the material velocity. The CZ opening displacement (CZOD) is δ = w_a — w_c + θ ν where θ is the CZ’s nominal thickness, and ν is the CZ’s referential orientation unit vector. We write δ for the magnitude of δ. As the CZ embodies the behavior of the blood between artery and clot as well as the artery’s intima layer, θ is representative of the thickness of these layers. Numerically, θ allows for a convenient computation of δ/δ (needed to describe CZ tractions) and handling of clot-artery interpenetration.

We model the thrombus as an incompressible viscoelastic Kelvin-Voigt solid (cf. van Kempen et al., 2016) with Cauchy stress

$${\mathbf{\sigma }}_c=p_{c}I+{\mu }_c(B-I)+2{\eta }_{c}D,$$ (1)

where p_c is a multiplier to enforce incompressibility, I is the identity tensor, μ_c is the clot’s shear elastic modulus, B = FF^T is the left Cauchy-Green strain, F = I + ∇_Xw is the deformation gradient (the superscript T indicates transpose), and where η_c is the dynamic viscosity of the clot with D = (L + L^T)/2 and L = ∇_xv. As in Good at al. (2020b), we choose μ_c = 1060 Pa and η_c = 8.33 Pa · s (cf. porcine clot in van Kempen et al., 2016). Modeling the thrombus as a solid is appropriate for mature clots. We will investigate coarsely ligated clots in future work.

We model the artery as an incompressible hyperelastic solid with Cauchy stress

$${\mathbf{\sigma }}_a=p_{a}I+2F\frac{\partial \mathrm{\Psi }}{\partial C}{F}^T,$$ (2)

where p_a is a multiplier to enforce incompressibility, C = F^TF is the right Cauchy-Green strain, and Ψ is the strain energy per unit referential volume. To tailor our model toward the M1 segment of the MCA, we base our Ψ on that by Eriksson et al. (2009):

$$\mathrm{\Psi }=\frac{{\mathrm{\mu }}_a}{2}\left({\text{I}}_1-3\right)+\frac{k_{1,\text{med}}}{2k_{2,\mathrm{med}}}\sum _{\text{i}=4,6}\left({\text{e}}^{{\text{k}}_{2,\mathrm{med}}{\left({\text{I}}_{\text{i}}-1\right)}^2}-1\right),$$ (3)

where ‘med’ stands for media, μ_a = 0.3 MPa, k_1,med = 0.24 MPa, k_2,med = 0.8393, and where I₁ = tr(C), I₄ = m₁ · Cm₁, I₆ = m₂ · Cm₂, with the unit vectors m₁ and m₂, taken at ± 85 ° relative to the artery’s axis, describing the media’s fiber families. We omitted the adventitia’s contribution to the strain energy. This choice is motivated by our interest in the system’s response to the application of aspiration within the vessel’s lumen, i.e., a loading scenario somewhat opposite to distension, which is essential in aneurysm modeling. We note that μ_a is much larger than μ_c. Our results show that even with the chosen strain energy the strong difference between μ_c and μ_a makes the artery appear almost rigid.

We choose a CZ model rheologically analogous to an Oldroyd-B fluid: the tractions acting on the clot (opposite to those on the artery, cf. Fig. 1b) are

$${\mathit{s}}_{cz}=\left({\mathrm{\eta }}_{cz}\dot{\mathrm{\delta }}+k_{cz}{\mathrm{\delta }}_e\right){\mathit{e}}_{cz},{\dot{\mathrm{\delta }}}_e=\dot{\mathrm{\delta }}-{\mathrm{\delta }}_e/{\tau }_{cz},$$ (4)

where η_cz is the CZ viscosity (SI units: Pa · s/m), k_cz is the CZ stiffness (SI units: Pa/m), e_cz = δ/δ, and τ_cz is the CZ relaxation time. To prevent clot-artery interpenetration, we add to the CZ tractions an elastic contribution perpendicular to the interface and proportional to log [1 + (δ · ν/θ)] for δ · ν < 0 and zero otherwise.

The mass densities for the clot and artery are ρ_c = 1080 kg/m³ (cf. van Kempen et al., 2016) and ρ_a = 1000 kg/m³ (MCA specific values could not be found in the literature). Finally, we assume that both clot and artery are initially stress free as is the CZ, which is dictated by convenience rather than realistic expectations. The system’s residual stress is likely to play a significant role when considering greater aspiration pressures and larger clots. The present analysis is only groundwork to obtain some initial understanding of the system’s deformation and failure modes.

Geometry and loading conditions

We consider the simple geometry in Fig. 2, with dimensions typical of the MCA M1 segment and axial dimensions meant to limit the size of our computational domain. The clot diameter D_c = 2.85 mm is equal to the artery inner diameter (Han et al., 2014) whereas the outer diameter of the artery is D_a = 3.4 mm (Vuillier et al., 2008). The axial lengths of the clot and artery are equal to their respective (outer) radii, with the clot centered relative to the artery. The lower end of the domain is exposed to the aspiration pressure provided by the catheter over a circular area of diameter D_cat = 1.8288 mm, which is the inner lumen diameter of the Navien 072 (072) catheter, this being the largest among those in Good et al. (2020a). The aspiration pressure is p_asp = p₀sin (2πft + π/2), where f is the aspiration frequency and the amplitude p₀ is half of the maximum applied aspiration pressure. While Fig. 2 shows the aspiration pressure in the axial direction, the resulting tractions are perpendicular to the deformed configuration of the clot’s lower surface. The only additional boundary condition was the suppression of axial motion for the proximal end of the arterial wall (cf. Fig. 2). As the geometry, loading, constitutive properties, and boundary conditions satisfy axisymmetry conditions, results were computed using an axisymmetric formulation.

Figure 2:

System’s geometry and loading. The z-axis is the system’s axis of axial symmetry. The zone with diameter D_cat denotes the area over which a time-periodic and spatially uniform aspiration pressure p_asp, is assumed to be applied by the catheter. The traction distribution induced by p_asp remains perpendicular to the deformed configuration of the lower clot surface. The axial displacement of the arterial wall’s lower surface is suppressed.

Numerical implementation

Simulations were performed with our custom finite element formulation implemented in COMSOL Multiphysics® (COMSOL, 2020). The artery’s hyperelasticity was implemented using a variant of the stabilized formulation by Masud and Truster (2013). The nonlinear solver for the clot was based on an arbitrary Lagrangian–Eulerian scheme following Hron et al. (2014). The CZ evolution was coded as ordinary differential equations at (surface) Gauss quadrature points. We performed code verification following the method of manufactured solutions (Salari and Knupp, 2000). The solution domain was discretized using quadrilateral elements and, after a mesh sensitivity study, we used a linear Lagrange polynomial interpolation for the displacement fields and a discontinuous piece-wise constant interpolation for p_c and p_a. The mesh size was uniform with diameter 0.01718 mm. The nonlinear solver was IDAS (Hindmarsh et al., 2005) with second-order variable-step-size backward differentiation formula (Quarteroni et al., 2000). The time step had a maximum value of 0.001 s. While error measures depend on all the parameters of a calculation, as an example, for the results in Fig. 6, the relative L₂ error norm of the clot’s displacement with respect to a spatial discretization twice as coarse as that indicated was 0.0082: an accuracy more than sufficient for our purposes. The linear solver within IDAS was selected to be a two-step segregated solver (the stabilization field for the hyperelastic formulation was determined separately from the rest), each step using MUPMS (Amestoy et al., 2000). For damage progression, the solver had an additional staggered step for the determination of the maximum CZOD on a point-by-point basis and up to the current time. To preserve stability, damage growth was estimated at the previous time step.

Figure 6:

System’s deformed configuration after 10 loading cycles for a case with peak-to-peak aspiration pressure of 10mmHg (1.3332kPa), τ_cz = 0.1s, and CZ thickness of 1μm. The colormap represents the radial displacement in μm. The deformed configuration shown corresponds to the 10s line in the upper left quadrant of Fig. 5. The points in circles a and b have moved downward relative to their initial position, whereas the point in circle c has moved upward.

Results

Deformation with coherent interface

The largest force on the clot results from applying the aspiration pressure over the entirety of the clot’s lower surface. However, the catheter is placed in contact with the thrombus and the aspiration is limited to an area covered by the catheter’s inner lumen. While a realistic loading configuration would account for the contact mechanics between thrombus and catheter, here we consider a simplified loading configuration in which the (deformed) proximal surface of the thrombus is subject to a time dependent and spatially uniform aspiration pressure only over the catheter’s inner lumen.

We first consider the system’s deformation with a perfectly coherent CZ (Fig. 3) in response to a peak-to-peak aspiration pressure of 6 mmHg (800 PA) with 1 Hz frequency. The arrows along the interface depict the tractions that the artery exerts on the clot. These tractions are largest at opposite ends of the interface (with weak stress singularities at said locations, cf., e.g., Weissberg and Arcan, 1992). More interesting is that the tractions are tensile and compressive at the distal and proximal ends, respectively. For the chosen geometry and loading we thus expect interfacial failure to first nucleate at the clot’s distal end. The tractions are consistent with the radial displacement being inward (blue) at the distal end and outward (red) at the proximal end. We observe that there is an “internal island” with inward radial displacement, hovering over the outer edge of the aspiration pressure application area. This zone is accompanied by higher tensile tractions at the interface. This feature is intrinsic to the loading configuration and would persist even when the clot is longer than it is wide. We will consider the effects of varying clot geometries in future work. We point out that while there is enough information to conclude that failure will nucleate at the distal end, it is unclear if it will nucleate at the proximal end or, possibly, somewhere in-between. The subsequent results provide some insight on these issues.

Figure 3:

Deformed configuration at the peak-to-peak value of p_asp during the first loading cycle. Here the peak-to-peak value is 6mmHg = 800Pa, the load frequency is 1Hz, and the CZ is fully coherent, i.e., it acts as a perfect interface. The colormap represents the radial displacement in μm. The arrows represent the traction distribution (per unit area of the reference configuration) exerted on the clot by the arterial wall. Well-known stress singularities exist at both the proximal and distal edges of the CZ (Weissberg and Arcan, 1992). As the clot deforms, its lower end presses against the arterial wall.

Cohesive interface deformation

We now report on CZ deformation but without damage accumulation. We note that, because of the fluid-like CZ rheological response, the CZOD can be arbitrarily large and with components both perpendicular and tangential to the clot-artery interface. The ability to produce such large displacements depends on the aspiration pressure intensity and duration. An increase of applied peak-to-peak pressure while keeping the time form fixed, implies increased loading rates. In turn, as the CZ’s response is time-dependent, this translates into higher cohesive forces in conjunction to high stresses in the interior of the clot. These considerations indicate that fast and high intensity loading configurations need to be examined in conjunction with failure criteria for the interface and the thrombus itself. Here, we focus on relatively low aspiration peak-to-peak values applied cyclically and examine the effect of a CZ failure criterion.

Figure 4 shows the magnitude of the CZOD at the lower right corner of the thrombus (point B in Fig. 2) as a function of time under cyclic loading with a 1 Hz frequency and peak-to-peak aspiration pressure of 10 mmHg (1.3332 kPa). Three values (0.1, 1.0, and 10 s) of the CZ relaxation time τ_cz were tested, separated by one order of magnitude each. Moreover, four different values (1.0, 2.5, 5.0, and 10 μm) of CZ thickness were tested. Point B is where we expect the smallest CZOD. Indeed, our results confirm this expectation. Overall, these results are consistent with those in Good et al. (2020b), where the more fluid-like is the CZ response, the more rapid is the increase of δ over time. The exception is represented by the case with the thickest cohesive zone (10 μm). In this case it appears that the overall system dynamics under cyclic loading first compresses the CZ and delays its eventual growth. We also note that the thicker the CZ and the more fluid-like its behavior, the greater is the phase difference between the CZOD and the applied loading, noting that, even with the lowest τ_cz, the CZOD rate remains limited. More important is that the increase in CZOD magnitude does not necessarily translate into an overall vertical displacement of the thrombus. This point is illustrated in Fig. 5, which shows the axial displacement of points along the clot’s lateral surface at times an integer number of periods from the initial time. At these time instants, the applied load on the thrombus is zero and the thrombus’s shape is the closest to the initial shape (relative to other time instants along the loading cycle). These plots, which correspond to the lowest value of the CZ relaxation time tested, show that the cyclic load repetition does cause the thrombus to slowly move downward. This conclusion seems to be contradicted by the presence of points that do not move or, worse, move upward (cf. points with positive displacement in the plots with CZ thicknesses from 1 to 5 μm). However, as it can be observed in Fig. 6 depicting the configuration that corresponds to the 10 s line in the upper left quadrant of Fig. 5, this motion is a local phenomenon (circle labeled c in Fig. 6) in what is an otherwise a global downward trend (cf. circles labeled a and b in Fig. 6). Concerning the point in circle c (Fig. 6), it is displaced radially inward by the CZ, which is resisting closure at the instant shown. By contrast, the upward displacement is likely attributable to the overall need for the clot to satisfy volume conservation. Regardless, we note that in the absence of an active damage mechanism, the magnitude of the displacement remains on the order of the CZ thickness even after 10 loading cycles.

Figure 4:

Magnitude of the CZOD (δ) as a function of time measured at the lower right edge of the clot (point B in Fig. 2). The vertical axes report displacement in microns whereas the horizontal axes report time in second. The peak-to-peak applied aspiration pressure was 10mmHg = 1.3332kPa, and the frequency was 1Hz. Each plot reports results for three values of the CZ relaxation time (τ_cz), and the plots differ from each other by the nominal value of the CZ thickness.

Figure 5:

Axial component of the displacement of the thrombus surface facing the artery wall as a function of the axial position along the reference configuration of that surface. The horizontal and vertical axes of each plot are the axial position of the right surface of the clot in millimeters and axial displacement in microns. The four plots are for the same loading conditions described in Fig. 4 and have the same value of the CZ relaxation time, 0.1s

Damage accumulation and CZ failure

The aspiration pressures in current devices are on the order of 85 kPa (Simon et al., 2013) thus four orders of magnitude higher than those in our calculations. Since the clot’s constitutive parameters are in the physiological range, the deformations induced by realistic aspiration pressures would cause interfacial failure and/or clot fragmentation, thus the importance of models that include damage and failure. We adopt the simple damage accumulation model in Good et al. (2020b) based on the idea that the CZ is a coarsely ligated clot film with fibrils providing load-bearing properties. In our model, the CZ fails by a fibril pullout mechanism. Damage accumulation is triggered when a critical value of opening displacement δ_cr is achieved. Damage, here denoted by ϕ, is defined as ϕ = (δ_max — δ_cr)/λ, where λ is the characteristic length of CZ fibrils and δ_max is the pointwise maximum value of δ achieved up to the current time. For simplicity, we assume that δ damage affects the CZ constitutive properties in the same way, so that k_cz = (1 — ϕ)k_cz,i and η_cz = (1 — ϕ)η_cz,i, where k_cz,i and η_cz,i are the undamaged values of the CZ elastic stiffness and viscosity, respectively. Numerically, the damage is computed at the end of each time step taken by the solver.

Even with such a simple model, a systematic exploration the problem’s parameter space is outside the scope here. Hence, we focus on a specific choice of CZ failure parameters that is only meant an as illustration of the basic features of damage progression. Specifically, we set δ_cr = 2 μm, λ = 2.5 μm, τ_cz = 0.1s, CZ thickness of 1μm, and a loading frequency of 1Hz.

Figure 7 shows the clot’s final configuration with a fully failed CZ under a peak-to-peak aspiration of 10mmHg (1.3332kPa). The indicated time shows that the CZ failed before the loading cycle ended, as illustrated in Fig. 8 showing the damage distribution along the CZ at various time steps. The most prominent feature of Fig. 8 is that, for the geometry considered, and referring to points A and B in Fig. 2, damage propagates from A to B almost monotonically, as damage at B is nucleated only right before the full CZ failure. This finding is not surprising (cf. results in Fig. 3): the displacement at the clot’s proximal end is radially outward and pushes against the arterial wall thereby hindering separation. However, this conclusion is likely limited to the geometry chosen and will be further investigated in future work.

Figure 7:

System’s deformed configuration following complete interfacial failure for a case with peak-to-peak aspiration pressure of 10mmHg (1.3322kPa), τ_cz = 0.1s, CZ thickness of 1μm, δ_cr = 2μm, and λ = 2.5μm. The colormap represents the radial displacement in μm. The loading frequency was 1Hz, and failure was achieved before the completion of the first loading cycle. As the CZ has failed, the black arrow in the lower right corner of the figure represents the contact force exerted on the thrombus by the artery.

Figure 8:

CZ damage distribution along the CZ at various time instants leading to the configuration in Fig. 7. Again, the simulation had a peak-to-peak aspiration pressure of 10mmHg (1.3332kPa), τ_cz = 0.1s, CZ thickness of 1μm, δ_cr = 2μm, and λ = 2.5μm. The loading frequency was 1Hz, and failure was achieved before the completion of the first loading cycle. Values of damage between 0 and 1 indicate a damaged but not completely failed CZ.

We conclude with a case like the preceding one except for the value of the applied peak pressure, here set to 6mmHg (800Pa). In this case, complete CZ failure is achieved after a few load cycles. The final deformed configuration is like that in Fig. 7. The main difference is the CZ damage progression (Fig. 9). Damage does nucleate at point B in Fig. 2 and progresses upward to join the failure front that had nucleated at the other end and had been traveling toward point B.

Figure 9:

CZ damage distribution along the CZ at various time instants leading to complete CZ failure. The simulation had a peak-to-peak aspiration pressure of 6mmHg (800Pa), τ_cz = 0.1s, CZ thickness of 1μm, δ_cr = 2μm, and λ = 2.5μm. The loading frequency was 1Hz, and failure was achieved after a little more than 2.5 loading cycles. Values of damage between 0 and 1 indicate a damaged but not completely failed CZ.

Summary and conclusions

In this paper we have continued our computational investigation of mechanical thrombectomy in AIS by including the presence of a deformable artery and modeling the application of the aspiration pressure more accurately. For the very low aspiration pressures investigated, the contrast in elastic moduli between artery and clot is such that the artery behaves as though it were rigid, thus validating our modeling assumptions in Good et al. (2020b). One major finding of this work is that for the clot dimensions used, the aspiration pressure causes the clot to push outward against the artery at the end near the catheter. This deformation mode hinders damage nucleation and progression at said location. Both our deformation and damage growth studies confirm that, for the geometry considered, damage nucleates at the end of the interface away from the catheter and then moves toward the catheter leading to complete CZ failure. Extensive additional studies are needed. These studies will focus on elucidating the role of residual stress in the system as well as the details of the aspiration application vis-à-vis the presence of liquid blood around the lodged thromboembolus. In addition, and more importantly, as the damage model seems to be well-suited for studying interfacial degradation, a companion experimental study is needed to identify physiologically relevant CZ parameter values. Finally, to simulate the effects of more realistic values of aspiration pressure, the clot deformation model may need to be completed by a corresponding clot fragmentation model.