Mathematical and Computational Modeling of Device-Induced Thrombosis

Abstract

Given the extensive and routine use of cardiovascular devices, a major limiting factor to their success is the thrombotic rate that occurs. This both poses direct risk to the patient and requires counterbalancing with anticoagulation and other treatment strategies, contributing additional risks. Developing a better understanding of the mechanisms of device-induced thrombosis to aid in device design and medical management of patients is critical to advance the ubiquitous use and durability. Thus, mathematical and computational modelling of device-induced thrombosis has received significant attention recently, but challenges remain. Additional areas that need to be explored include microscopic/macroscopic approaches, reconciling physical and numerical timescales, immune/inflammatory responses, experimental validation, and incorporating pathologies and blood conditions. Addressing these areas will provide engineers and clinicians the tools to provide safe and effective cardiovascular devices.

1. Introduction

Blood-contacting medical devices are used to treat a variety of cardiovascular (CV) and cardiopulmonary diseases. These devices perturb hemostasis, resulting in complications that manifest in the patient as thrombosis and hemorrhage. Thrombosis is not only a frequent source of device failure [1], but excessive clotting and/or bleeding may also pose direct risks to the patient [2].

Nevertheless, devices have emerged as the standard-of-care for many cardiovascular disease conditions [3]. Current device use, incidence of adverse events, and material surfaces, and upcoming and novel/controversial devices, are summarized in Table 1.

Table 1.

Overview of blood-contacting medical devices

Device	Refs	Clinical Indication for Use	Rate of Failure or Adverse Events	Material Surface(s)	Notes
Stents	[69,70]	Arterial Obstructions	Thrombosis <1%; restenosis 10%	metal (e.g. nitinol, stainless steel) ± coatings (e.g. carbon)
Grafts	[71]	Vascular Repair or Bypass	20-40% not patent at 5 years	saphenous vein, polymer (e.g. nylon, PTFE)
Catheters	[72]		Central venous catheters 14-18%; peripherally-inserted central catheters 5-15% in-hospital	silicone rubber, polyurethane
Heart Valves		Valvular Heart Disease
Bioprostethic Valves	[73]		Thrombosis ≤2-3%/year	fixed biologic tissues, can be on stent/graft scaffold
Mechanical Valves	[74]		Thrombosis ≤2-3%/year, up to 6%/year if insufficient anticoagulation		Requires lifelong anticoagulation
Transcatheter Aortic Valve Replacement (TAVR)	[75]	Aortic Stenosis	Thrombosis 16.9%	fixed biologic tissues on stent/graft scaffold	Increasing in use
Mechanical Circulatory Support (MCS)		Heart Failure
Ventricular Assist Devices (VADs)	[76-78]		Thromboembolic events as high as 30% in HeartMate II (adult) and Berlin Heart EXCOR (pediatrics)	metals, ceramics, plastics	Decreases over time
Intra-Aortic Pumps	[79]		1% thrombosis, 27% bleeding	polyethylene, polyurethane
Cardiopulmonary Bypass	[80]	Cardiac Surgery	2-10% myocardial infarction, 3% stroke	plastics	Many other complex complications, both surgical and related to critical illness
Total Artifical Hearts (TAHs)	[81,82]		20% bleeding, 1.6% embolus, 2% stroke	polyurethane
Extracorporeal Membrane Oxygenation (ECMO)	[19,83]	Heart and/or Lung Failure	≥90% some clot formation in circuitry; balance of bleeding risk with anticoagulation level	mainly plastics, metals	Notable pediatric patient population; encompasses many devices assembled into circuitry
Inferior Vena Cava (IVC) Filters	[84]	Pulmonary Embolism Risk	≤30% thrombosis, DVT as high as 43%	metals (e.g. nitinol, stainless steel)	Intended to cause obstruction; reports of incidence vary widely
Endovascular Coils	[85]	Cerebral Aneurysm	9.1% total complication rate, including rebleeding, ischemia, and rupture	metals (e.g. platinum alloy)	Intended to cause thrombosis
Resuscitative Endovascular Balloon Occlusion of the Aorta (REBOA)	[86]	Hemorrhage	Unclear; may increase mortality	plastics, employed by catheter/guidewire	Use still controversial
Dialysis	[87]	Kidney Disease	<1%/year	plastics
Micro- and Nanoparticles	[88,89]	Thrombosis	n/a	charged polymers	Novel

While disease etiologies and patient populations vary among blood-contacting devices and their applications, they all share the same overarching challenges: (1) device-induced thrombosis is not fully understood, and therefore is clinically unpredictable, and (2) clinical trials can be extremely difficult and risky in these patient populations, sometimes to the point of being prohibitively so. Therefore, in silico studies are a critical tool to complement in vitro, ex vivo, and in vivo studies to contribute to overcoming these challenges. Device thrombosis modelling can be used to inform on device design in the preclinical stage, and to inform on treatment and clinical handling of current patients, by developing guidelines and on demand treatments.

In this review, the initial focus is a discussion on the pathophysiology of device thrombosis. We then assess modelling efforts posterior to Fogelson and Neeves’ 2015 review [4], with a focus on model assumptions to facilitate discourse on the physiological relevance of different mathematical and computational approaches.

2. Device Perturbation of Hemostasis: Virchow’s Triad

As is widely appreciated, Virchow theorized, rather correctly, that hemostasis is a delicate balance between the blood state, surface, and flow [5]. The original Virchow’s Triad comprised stasis, vessel injury, and hypercoagulability. While there have been recent adaptations to his theory, the basic concept remains applicable to devices via a more liberal interpretation of the original construct, which we have summarized in Figure 1.

Figure 1. Virchow’s Triad for Device Thrombosis.

The driving mechanisms of device thrombosis can be viewed through the lense of Virchow’s Triad. The blood state, device surface, and device flow patterns have concomitant effects that ultimately result in thrombosis.

2.1. Blood state

Blood is a suspension containing erythrocytes, leukocytes, platelets, factors, ions, and glycoproteins, which all have critical roles to maintain hemostasis and perform other physiological functions [6]. Coagulation, a critical physiological function, occurs by initiation via either vascular-injury or foreign-body contact and is comprised of dozens of cellular species and nearly 100 reactions to form a stable thrombus [7]. With the introduction of a device in the CV system, the surface-mediated pathway (foreign-body) is stimulated along with the activation of the tissue-mediated pathway (vascular injury) as the endothelium is disrupted by the device during implantation. Whether these events are separate or simultaneous remains unknown, and while the question may be moot since both lead to thrombosis, elucidation of the interactions and timeline could inform therapeutic inhibition of either or both pathways.

In addition to coagulation, platelets are significant contributors to clotting and interface with other cellular components such as von Willebrand Factor (VWF) and fibrin(ogen).Their impact on devices can be substantial, including total device failure. Given the mechanical and chemical sensitivities of platelets, their response is critical to gauge device thrombogenicity. Platelets can be stimulated by high shear, the surface-mediated pathway, and activated by biochemical means [8]. For example, when platelets attach to VWF adsorbed to the device surface, this creates a foundational support for the clot (along with contributions from other clotting factors). VWF can also be compromised due to degradation, as has been shown in ECMO and VAD patients that develop bleeding events [9].

These cellular components are currently thought to have the most significant impact on devices, but as this area continues to be studied, more may be revealed. Thus the blood state, which includes its constituents, is quite integral to determining device success. However, the device surface itself can dramatically influence clotting.

2.2. Surface

When blood contacts a biomaterial surface, a series of complex systems initiate that potentiate thrombosis via the pathways described in 2.1. Proteins are adsorbed immediately to the surface [1,10,11], a process which is controlled initially by diffusion but dominated by protein-surface affinity over time (Vroman Effect, [12]). Device materials are typically hydrophobic, and have affinity with many proteins [13]. The most commonly adsorbed plasma proteins are albumin, fibrinogen, immunoglobulin G (IgG), fibronectin, and VWF. As mentioned previously, VWF and fibrinogen appear to be the most critical for platelet activity [14]. In the adsorption process, proteins undergo conformational changes to expose hydrophobic domains, which results in expression of receptor sites, causing subsequent immune crosstalk, and further potentiating thrombosis [15-17]. The phenotype of the end surface is dependent on the biomaterial, thus a multitude of unique surfaces exists.

However, the device surface is absorbed in its entirety, yet thrombosis tends to be localized [18,19]. Flow is thus the final key mechanistic driver.

2.3. Flow

Flow and its characteristics have been demonstrated to be quite potent in determining the effectiveness and long-term viability of a device. Fundamentally, flow regimes (i.e. laminar, transitional, and turbulent) can affect cellular responses by creating pathologically low and high stress regions, whereby shear stress can induce platelet activation [3,20], the combination of shear stress and its exposure time can induce hemolysis and thus potentiate coagulation [21], and recirculating flows and wakes can facilitate clotting [22,23]. Hemostatic and thrombotic mechanisms in vivo proceed via mechanisms that are flow dependent, resulting in gel-like coagulation “red” clots at low shear, and brittle platelet-rich “white” clots at high shear [24,25]. Experimental studies have demonstrated the impact of shear stress on platelet activation/aggregation [26-28] and thrombosis [29]. Pathologic flows created by the presence of devices and actions associated with them can influence hemostasis with examples of recirculating flows/wakes in ECMO circuitry and IVC filters, and extremely high shear stress associated with prosthetic heart valves and VADs (examples found in Table 1). Residence time of platelets and factors is another crucial factor that may enhance clotting [26].

Flow, the blood state, the biomaterial surface, and their concomitant effects are thus the essential elements to understanding the unique qualities of device thrombosis (Figure 1), and therefore determine their ultimate success.

3. Modelling Approaches Available

Despite much effort and tremendous progress, device thrombosis modelling remains extremely challenging due to the variety and complexity of the phenomena. Recently, comprehensive modelling studies (Table 2) have extensively covered hemostasis and thrombosis in the setting of the vasculature, and in the context of natural physiology and pathology [30]. In fact, some studies have demonstrated highly fidelic models of thrombosis in the setting of high shear [31]. However, as detailed in Section 2, device thrombosis has additional mechanisms which must be considered in the modelling effort, making the challenge even greater. Device modelling and understanding remains less elucidated than in vivo hemostasis and thrombosis.

Table 2.

Summary of recent approaches and assumptions

	Refs	Flow domain	Coagulat ion	Platelets	Clot	Contact system	Injury site	Gap to device
High shear	[50]	3D NS 10−3 m	none	Particles	no	no	yes	Domain size // biochemistry // contact //clot
	[20]	3D DPD 10−5 m	none	CGMD	no	no	yes	Domain size // biochemistry // contact // clot
	[51]	3D DPD 10−4 m	none	Particles	yes	no	yes	Domain size // biochemistry // contact // Ventricular assist devices
	[60]	3D NS 10−2 - 10−1 m	none	Pseudo particles	yes	no	yes	Biochemistry // contact
Low shear	[47,48]	2D DPD 10−4 m	8 species	none	yes	no	yes	3D // domain size // contact system // platelets
	[49]	2D NS 10−2 m	20 species	none	no	yes	no	3D // platelets // clot // Generally device related
All flow regimes	[55]	2D NS 10−2 m	1 species	2 scalar quantities	yes	no	no	3D // biochemistry // clot retraction on flow // Generally device related
	[90]	2D DPD 10−4 m	3 species	Particles	yes	no	yes	3D // domain size // contact // platelet-protein coupling
	[18,56,57]	3D NS 10−1 m	5 species	5 scalar quantities	yes	no	no	Contact // Ventricular assist devices
	[54]	3D NS 10−2 - 10−1 m	1 species	3 scalar quantities	no	no	no	Biochemistry // clot retraction
	[52]	3D NS 10−4 m	20 species	Particles	yes	yes w/o XII	yes	Domain size // FXII
	[91]	2D NS 10−4 m	8 species	Particles	yes	no	yes	3D // domain size // contact
	[58]	3D NS 10−2 - 10−1 m	5 species	3 scalar quantities	yes	no	no	Contact // Flow diverters
	[59]	3D NS 10−2 m	5 species	2 scalar quantities	yes	no	no	Specific to stenosis geometries // contact

3.1. Biomarkers Deduced from Pure CFD Results

The device’s presence in the CV system leads to thrombus formation after an unknown delay, which may be hours, days, or even months. Thus, to maximize clinical and/or design utility, a computational tool for device thrombosis should forecast clotting, and predict if, when, and where thrombosis occurs. Because some processes operate at very short time scales (1 ms, say, flow convection or fast biochemical reactions), practical approaches often neglect all the “details” and try to guess the thrombotic response from the analysis of the stationary flow field obtained from classical computational fluid dynamics (CFD). Typical fluid mechanics markers used to predict thrombosis in devices include: low velocity region [32]; residence time [33-38]; flow recirculation [39]; low wall shear stress [34,40,41]; washout [36,37]; kinetic energy density [37]; (platelets) stress accumulation [35,38,42]; (platelets) shear/convection/aggregation [43], and activation indices [44]. These approaches can provide relevant information at low cost about the flow structure and how geometric changes can reduce thrombogenicity [45]. Of course, they do not inform about the size, evolution, thrombus quality, and the clinical result.

An extension of the pure CFD approach was proposed [31,46] in order to predict the time of occlusion in high velocity stenotic channels. In this situation, VWF adsorption on the artificial surface, platelet adhesion via GPIb-VWF, and subsequent activation and aggregation of flowing platelets, lead to thrombus formation. Assuming that these processes can be abstracted by a correlation between the local hemodynamic shear rate and the thrombus growth rate, this approach relies on a set of pure CFD simulations to predict the occlusion time [31,46]. Of course, the approach can only be justified if the shear rate-growth rate correlation indeed exists, and if it can be calibrated in advance.

3.2. Physical-based models

Simulations aiming at describing thrombosis should include models for the coagulation cascade [47-49], and platelet dynamics [20,50,51]. Given the numerous interactions between fibrin formation and platelets during thrombosis, proper in silico models should consider these two ingredients. One of the most advanced formulation to date is likely that of Yazdani et al. [52], where a set of 24 partial differential equations (PDEs) are resolved for fluid flow, 20 biochemical species interacting in the clotting cascade are implemented (following the pattern set forth by Anand et al. [53]) with a set of Lagrangian particles (platelets) that can be chemically activated and produce agonists. The key element that makes this Eulerian-Lagrangian approach capable of representing thrombosis in low and high shear flows is a shear-dependent platelet adhesive model set to correctly reproduce data in vivo and in vitro. Surprisingly, FXII, whose activation on the artificial surface may trigger the intrinsic pathway, was not considered by Yazdani et al. [52]; instead, thrombus formation was triggered by imposing non-zero concentration of the TF-VIIa complex at a site of injury. The initiation of thrombin formation (and therefore fibrin) without explicitly defining an injury site, but rather by relying solely on the activation of factor XII, was made by Méndez Rojano et al. [49], where the backward facing step experiment was computed. A significant concentration of thrombin was present only in the region where thrombus formation had been observed experimentally by Taylor et al. [23], suggesting the flow-contact system interaction is a key element in thrombus location within devices, at least in the low shear regime.

The Eulerian-Lagrangian method developed in [52] is too computationally demanding to be applied to actual devices; the fundamental reason is the tremendous number of particles (1.5 μm each) that must be accumulated to form a thrombus of a typical size of 1 cm. A way to significantly reduce the overall computational load is to represent platelets by Eulerian fields [18,54-59], instead of particles. Wu et al. [18] applied 14 coupled PDEs: 4 for fluid flow, 5 for biochemical species to represent coagulation, and 5 for different platelet types. This approach has shown good potential for complex devices such as the Heartmate II VAD.

Recently, the concept of pseudo-platelets was introduced [60] to reduce the computational effort while keeping the Lagrangian description of platelets, by far, more realistic than the Eulerian framework. In this view, the spherical particles transported by the flow change their size (from 1.5 to 90 μm) once activated and adhered. This reduces the number of particles required to form the thrombus (by a factor up to (90/1.5)³ = 216000) and significantly reduces the associated computational load. This numerical treatment, although not physically based, produces reasonable thrombus formation according to Zheng et al. [60] and allows increasing size of the affordable computational domains from sub-millimetric, as implemented in [52], to centimetric [60]. In the latter study, a mapping from the particle aggregation step to a phase-field representation of the thrombus material properties and permeability was also first proposed. This methodology opens new perspectives in terms of thromboembolic event prediction, although necessary adaptations to accommodate device thrombosis remain.

4. Future Directions

As efforts continue to develop device-induced models, it should be noted that the U.S. Food and Drug Administration and other regulatory bodies, are keenly interested, and increasingly likely, to accept properly validated models as part of the device approval process. With this context, the future directions to facilitate impactful device modelling is paramount.

4.1. Microscopic vs. Macroscopic Approaches

Currently, there are two modelling approaches to device-induced thrombosis: either considering the individual cells and factors (microscopic) or considering the domain as a continuum and the cells as bulk concentrations (macroscopic). Both approaches have advantages and disadvantages with the associated limitations: the microscopic approach offers a more reliable description of the cell-based phenomena at the cost of (very) large computation load, while the macroscopic view is more efficient but assumes the interactions happen at a “gross” scale, losing the track of the individual interactions. However, developing a synergistic strategy and collaboration between the macroscopic approaches that could implement the microscopic, or even nanoscopic, results could yield significant progress to capture the truly salient features for thrombosis [61]. Within this context, careful consideration of the intent (and setting) of the proposed device is significant, considering endovascular coils aim to clot aneurysms while mechanical circulatory support devices must avoid thrombosis.

4.2. Reconciling Physical and Numerical Timescales

Thrombosis may be visible days, weeks, or months after device implantation, while multiphysics simulations representing flow-coagulation-platelets-surface interactions can only represent fractions of seconds or minutes depending on the model’s spatial scales. On top of purposely increasing reaction rates and/or diffusivity coefficients [18], current efforts to reduce the complexity of kinetics schemes [62,63] or model the near wall transport phenomena [64] may improve the situation, but will most probably be insufficient to fill the gap. A proper way to drastically increase the physical time that a simulation can demonstrate would be to have access to the thrombus growth rate. Then, the entire process could be represented by a set of simulations performed at different stages over the thrombus evolution, using the last computed growth rate to extrapolate from one instant to the following one. This strategy was successfully followed by Mehrabadi et al. [31] in the very simple case where the growth rate can be inferred from the local shear rate issued by pure CFD. This approach could be made more general by leveraging a multiphysics simulation at each step. Thus, future efforts should focus on modelling thrombus growth rate rather than simply their size.

4.3. Immune/Inflammatory

The persistent inflammatory stimuli resulting from blood contact with the device surface induces a perpetual immune response [15]. Adsorbed proteins, in addition to regulating activation of coagulation and platelets, also regulate the activation of complement and immune cells. Fibrinogen on the biomaterial surface can activate circulating monocytes, initiating the inflammatory response [15]. The presence of factors on the membranes of these and other cells can also contribute to activation and propagation of coagulation on the device surfaces. Complement is also activated via binding to the adsorbed surface [17], generating C3a and C5a at the device site [15], and both contribute to further inflammatory activation and stimulate coagulation. Devices can increase circulating platelet-leukocyte aggregates (PLAS, [65]), which are associated with thromboinflammatory diseases [65,66] and linked to cardiovascular events [67]. Including some description of the complement and inflammatory systems, and their crosstalk with thrombosis, should be considered in future modelling efforts.

4.4. Validation

Results from in vitro and in vivo experiments, as well as from clinical data, are necessary both to validate in silico efforts and to provide biological and mechanistic information as inputs into such models. The gold standard preclinical experiment is a large animal model with appropriately long timescales, however, this can be both practically challenging and expensive. Benchtop in vitro studies thus have less logistical and financial burden for implementation, thereby increasing throughput, but can encounter the same challenges discussed in 4.1 and 4.2: timescale and selection of parameters and endpoints. Both types of experiments can provide useful information to identify thrombogenic hotspots. Clinical data on the location and incidence of thrombosis in devices is ideal for validation but can be challenging to obtain. New methodologies for obtaining validation data, both in preclinical experiments and from device patients, are needed.

4.5. Incorporation of Pathologies and Blood State

Modelling is most frequently implemented with idealized parameters. Biological variability and patient pathophysiology may play key roles in the lack of translation of modelling results to the patient. Patients will likely be treated with pharmacological agents that modify hemostatic and thrombotic function, e.g. virtually all MCS patients will be anticoagulated. In addition, devices can alter the blood state, induce pathologies, and perturb the endothelial environment during implantation. This endothelial disruption can cause deleterious effects like restenosis of coronary stents and potentiate platelet activation and thrombus formation [68]. Incorporation of these clinically relevant blood states may increase the translatablitly of modelling efforts.

4.6. Conclusion

Due to the inherent complexity of the cardiovascular system, thrombosis modelling of high integrity is challenging. However, while the current tangible application is device design, computationally-guided patient care is the “science fiction” of today but will be the needed “reality” in the future.

Abbreviations

CFD

computational fluid dynamics

CV

cardiovascular

ECMO

extracorporeal membrane oxygenation

FXII

Factor XII

GPIb

glycoprotein Ib

IgG

immunoglobulin G

IVC

inferior vena cava

MCS

mechanical circulatory support

PDE

partial differential equation

REBOA

resuscitative endovascular balloon occlusion of the aorta

TAH

total artificial heart

TAVR

transcatheter aortic valve replacement

VAD

ventricular assist device

VWF

von Willebrand Factor