Modeling blood flow around a thrombus using a hybrid particle–continuum approach

Abstract

A hybrid, multiscale, particle-continuum numerical method is developed for resolving the interaction of a realistic thrombus geometry with unsteady hemodynamics typically occurring within large arteries. The method is based on a discrete particle/element description of the thrombus, coupled to blood flow using a fictitious domain finite element method. The efficacy of the discrete element approach in representing thrombi with arbitrary aggregate morphology and microstructure is demonstrated. The various features of the method are illustrated using a series of numerical experiments with a model system consisting of an occlusion embedded in a channel. The results from these numerical experiments establish that this approach can resolve the complex macroscale flow structures emanating from unsteady hemodynamics interacting with a thrombus. Simultaneously, it can also resolve micromechanical features, and microscale intra-thrombus flow and perfusion. Using a staggering algorithm, the method can further capture hemodynamics around time-varying thrombus manifolds. This is established using a numerical simulation of lysis of an idealized clot. The hybrid particle-continuum description of thrombus-hemodynamics interaction mechanics, and the unified treatment of macroscale as well as microscale flow and transport, renders significant advantages to the proposed method in enabling further investigations of physiological interest in thrombosis within patient-specific settings.

Microstructure Aware Modeling Of Biochemical Transport In Arterial Blood Clots

“…The resultant intra-thrombus flow velocities are illustrated using thrombus cross-sectional slices taken along vessel axis (sections labelled S1 − S3) and perpendicular to the vessel axis (labelled S4 − S6) as shown in Figure 2, panel a. Intra-thrombus velocities for the heterogeneous thrombus microstructure considered here, are shown in panel d. for sections S1 − S3 and times T 1 − T 4; and in panel e. for sections S4 − S6 and times T 1 − T 4 respectively. Intra-thrombus velocities are observed to be ≥ 2 orders of magnitude smaller than extra-thrombus flow -consistent with previously demonstrated studies on microscale platelet plugs [43,27] and two-dimensional macroscale models [30,42] . Specifically, we observe a permeation region along the boundary shell of the thrombus, which draws flow into the thrombus interior through pore network pathways.…”

“…Unsteady flow around a heterogeneous thrombus aggregate is computed using a hybrid particle-continuum fictitious domain finite element approach outlined in prior work [30,42] . Briefly, we consider the total com-putational domain Ω = Ω f ⊕ Ω t , with Ω f as the fluid (blood) domain, and Ω t the thrombus domain with heterogeneous microstructure composed of a union of mesoscopic discrete particle domains such that: .…”

“…The Navier-Stokes momentum and mass balance equations are solved using a Petrov-Galerkin stabilized formulation [30,42] , with the overall weak form stated as follows: where we use the notation ( a, b ) Ω = ∫ Ω a · b d Ω; u , p are the velocity and pressure trial functions; v , q are the respective test functions; is the residual of the momentum and continuity equations; τ u and τ p are the velocity and pressure stabilization terms [9] ; and F denotes the external body force (gravity). The term denotes the interaction contribution for the fictitious domain which constrains the velocity u to be u 0 and is defined as: and κ u is a velocity penalization term over the fictitious domain modeled as [30] : where h is the element size. Efficient resolution of the fictitious particle domain requires the mesh sizing in the fictitious domain to be commensurate with particle size [41] .…”

“…A simplified model thrombus domain (Ω t ) was created in form of a hemispherical shell of radius 3.0 mm booleaned with the vessel using OpenSCAD [1] (see Figure 1). Corresponding discrete particle thrombus reconstruction was generated using tessellation based particle algorithms outlined in [30,42] . Unstructured tetrahedral mesh with target edge size 100.0 μm was created for the vessel.…”

Atomistic Molecular Dynamics Simulations of Trioleoylglycerol – Phospholipid Membrane Systems

“…The CG and UA simulations has not essentially provided details of initial TAG conformation and even not the number of TAGs according to given conformation. Considering group of atoms as single entity or bead is no doubt a big achievement and is serving as a tool to simulate larger systems (50)(51)(52). As a tradeoff, beads do not essentially represent actual volume and molecule to molecule distances.…”