arXiv subjects

Aaron L. Fogelson

Publications and source records attributed to Aaron L. Fogelson.

17 recordsLinked to original sources

arXiv2026

Platelet plug microstructure and flow modulate fibrin gelation dynamics: Insights from computational simulations

During the formation of a thrombus, the architecture of the growing platelet aggregate is heterogeneous, with areas of dense and loosely packed platelets. The surface of activated platelets facilitate biochemical coagulation reactions that ultimately result in the formation of a fibrin network which stabilizes the thrombus. How platelet-plug microstructure and flow jointly govern the onset and development of fibrin is incompletely understood. We developed a novel 2D computational framework that integrates (1) a pre-adhered, discrete platelet aggregate, (2) a reduced coagulation model that generates thrombin, and (3) a fibrin polymerization model. Three platelet-plug configurations were constructed with prescribed interplatelet gaps and simulations were performed with various wall shear rates. We quantified spatiotemporal clotting metrics, including coagulation factor concentrations, fibrin evolution, and gelation onset. Across geometries, gelation initiation accelerated with increasing plug density. For more dense geometries, gelation emerged first near the plug periphery. As the platelet density increased, intraplug transport was increasingly restricted and the thrombin concentrations in between platelets increased. In contrast, the loose plug supported fibrinogen replenishment deeper into the plug core. Despite slower coagulation initiation due to reduced platelet surface area, monomer generation persisted in the interior, causing gelation to begin at the vessel wall. These results suggest a mechanistic tradeoff: rapid sealing of the injured vessel wall by early platelet contraction, i.e. plug densification, may impede the intraplug fibrin formation needed for durable stabilization. The proposed model provides a basis for studies of platelet-coagulation interactions under flow, including therapeutic developments relevant to prevention of cardiovascular disease.

q-bio.BM↗

arXiv2025

Mechanisms of thrombin inhibition by protein S and the TFPIα-fVshort-protein S complex

Protein S (PS) is a notable anticoagulant implicated in both bleeding and thrombotic disorders, making it a promising drug target. Importantly, PS enhances the anticoagulant function of TFPI$α$, likely circulating in the bloodstream together with TFPI$α$ and a truncated form of factor V (fVshort) in the trimolecular complex, TFPI$α$-fVshort-PS, which we call protein S complex (PSC). PSC has been proposed to strongly inhibit thrombin production by enhancing the ability of TFPI$α$ to inhibit clotting factor Xa up to 100-fold and by localizing to platelet membranes, limiting fXa activity shortly after coagulation starts. Yet, exactly how PS functions with TFPI$α$ as an anticoagulant remains poorly understood. To investigate, we extend an experimentally validated mathematical model of blood coagulation to include PSC and free PS (not part of PSC) in the plasma, as well as free PS and TFPI$α$ in platelets. We find that shortly after coagulation initiation, PSC strongly inhibits thrombin production. We find that the (unknown) magnitude of the enhanced affinity of PSC binding to inhibit fXa critically regulates PSC's impact on thrombin production. We find that under flow, PSC can unexpectedly accumulate on platelets to concentrations ~50 times higher than in the plasma. We also find that PSC limits thrombin production by occupying fV-specific binding sites on platelets. Our results show that changes in PSC can dramatically impact severity of pathological bleeding disorders. For the east Texas bleeding disorder, elevated PSC concentrations eliminate thrombin bursts, leading to bleeding. With fV deficiency, reducing PSC rescues thrombin production in severe fV deficiency and returns thrombin production due to mild fV deficiency to normal. Finally, thrombin production in severe hemophilia A can be substantially improved by blocking PSC's anticoagulant function.

q-bio.MN↗

arXiv2025

Adaptive Mesh Refinement for Two-Phase Viscoelastic Fluid Mixture Models

Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases in which separate momentum equations are used for each phase along with a co-incompressibility condition on the velocity fields. The resulting system of equations poses numerical challenges due to the presence of multiple non-linear terms and the co-incompressibility condition, and the resulting fluid dynamics motivate the development of an adaptive mesh refinement (AMR) technique to accurately capture regions of high stresses and large material gradients while keeping computational costs low. We present an accurate, robust, and efficient computational method for simulating multiphase mixtures on adaptive grids, and utilize a multigrid solver to precondition the saddle-point system. We demonstrate that the AMR discretization asymptotically approaches second order accuracy in $L^1$, $L^2$ and $L^\infty$ norms. The solver can accurately resolve sharp gradients in the solution and, with the multigrid preconditioning strategy introduced herein, the linear solver iterations are independent of grid spacing. Our AMR solver offers a major cost savings benefit, providing up to ten fold speedup over a uniform grid in the numerical experiments presented here, with greater speedup possible depending on the problem set-up.

physics.flu-dyn↗

arXiv2025

Modeling Platelet P2Y$_1$/$_{12}$ Pathway to Integrin Activation

Through experimental studies, many details of the pathway of integrin $α_{\rm IIb}β_3$ activation by ADP during the platelet aggregation process have been mapped out. ADP binds to two separate G protein coupled receptors on platelet surfaces, leading to alterations in the regulation of the small GTPase RAP1. We seek to (1) gain insights into the relative contributions of both pathways to RAP1-mediated integrin activation and to (2) predict wildtype and mutated cell behavior in response to a continuous range of external agonist concentrations. To this end, we develop a dynamical systems model detailing the action of each protein in the two pathways up to the regulation of RAP1. We perform a parameter estimation using flow cytometry data to determine a number of unknown rate constants. We then validate with already published data; in particular, the model confirmed the effect of impaired P2Y$_1$ receptor desensitization or reduced RASA3 expression on RAP1 activation. We then predict the effect of protein expression levels on integrin activation and show that components of the P2Y$_{12}$ pathway are critical to the regulation of integrin. This model aids in our understanding of interindividual variability in platelet response to ADP and therapeutic P2Y$_{12}$ inhibition. It also provides a more detailed view of platelet activation in the ongoing mathematical study of platelet aggregation.

q-bio.MN↗

arXiv2024

Flagellum Pumping Efficacy in Shear-Thinning Viscoelastic Fluids

Microorganism motility often takes place within complex, viscoelastic fluid environments, e.g., sperm in cervicovaginal mucus and bacteria in biofilms. In such complex fluids, strains and stresses generated by the microorganism are stored and relax across a spectrum of length and time scales and the complex fluid can be driven out of its linear response regime. Phenomena not possible in viscous media thereby arise from feedback between the "swimmer" and the complex fluid, making swimming efficiency co-dependent on the propulsion mechanism and fluid properties. Here we parameterize a flagellar motor and filament properties together with elastic relaxation and nonlinear shear-thinning properties of the fluid in a computational immersed boundary model. We then explore swimming efficiency over this parameter space. One exemplary insight is that motor efficiency (measured by the volumetric flow rate) can be boosted vs.\ degraded by moderate vs.\ strong shear-thinning of the viscoelastic environment.

physics.flu-dyn↗

arXiv2023

A Model of Fluid-Structure and Biochemical Interactions for Applications to Subclinical Leaflet Thrombosis

Subclinical leaflet thrombosis (SLT) is a potentially serious complication of aortic valve replacement with a bioprosthetic valve in which blood clots form on the replacement valve. SLT is associated with increased risk of transient ischemic attacks and strokes and can progress to clinical leaflet thrombosis. SLT following aortic valve replacement also may be related to subsequent structural valve deterioration, which can impair the durability of the valve replacement. Because of the difficulty in clinical imaging of SLT, models are needed to determine the mechanisms of SLT and could eventually predict which patients will develop SLT. To this end, we develop methods to simulate leaflet thrombosis that combine fluid-structure interaction and a simplified thrombosis model that allows for deposition along the moving leaflets. Additionally, this model can be adapted to model deposition or absorption along other moving boundaries. We present convergence results and quantify the model's ability to realize changes in valve opening and pressures. These new approaches are an important advancement in our tools for modeling thrombosis in which they incorporate both adhesion to the surface of the moving leaflets and feedback to the fluid-structure interaction.

math.NA↗

arXiv2021

A Hybrid Semi-Lagrangian Cut Cell Method for Advection-Diffusion Problems with Robin Boundary Conditions in Moving Domains

We present a new discretization for advection-diffusion problems with Robin boundary conditions on complex time-dependent domains. The method is based on second order cut cell finite volume methods introduced by Bochkov et al. to discretize the Laplace operator and Robin boundary condition. To overcome the small cell problem, we use a splitting scheme that uses a semi-Lagrangian method to treat advection. We demonstrate second order accuracy in the $L^1$, $L^2$, and $L^\infty$ norms for both analytic test problems and numerical convergence studies. We also demonstrate the ability of the scheme to handle conversion of one concentration field to another across a moving boundary.

math.NA↗

arXiv2021

An Efficient High-Order Meshless Method for Advection-Diffusion Equations on Time-Varying Irregular Domains

We present a high-order radial basis function finite difference (RBF-FD) framework for the solution of advection-diffusion equations on time-varying domains. Our framework is based on a generalization of the recently developed Overlapped RBF-FD method that utilizes a novel automatic procedure for computing RBF-FD weights on stencils in variable-sized regions around stencil centers. This procedure eliminates the overlap parameter $δ$, thereby enabling tuning-free assembly of RBF-FD differentiation matrices on moving domains. In addition, our framework utilizes a simple and efficient procedure for updating differentiation matrices on moving domains tiled by node sets of time-varying cardinality. Finally, advection-diffusion in time-varying domains is handled through a combination of rapid node set modification, a new high-order semi-Lagrangian method that utilizes the new tuning-free overlapped RBF-FD method, and a high-order time-integration method. The resulting framework has no tuning parameters and has $O(N \log N)$ time complexity. We demonstrate high-orders of convergence for advection-diffusion equations on time-varying 2D and 3D domains for both small and large Peclet numbers. We also present timings that verify our complexity estimates. Finally, we utilize our method to solve a coupled 3D problem motivated by models of platelet aggregation and coagulation, once again demonstrating high-order convergence rates on a moving domain.

math.NA↗

arXiv2021

Immersed boundary simulations of cell-cell interactions in whole blood

We present a new method for the geometric reconstruction of elastic surfaces simulated by the immersed boundary method with the goal of simulating the motion and interactions of cells in whole blood. Our method uses parameter-free radial basis functions for high-order meshless parametric reconstruction of point clouds and the elastic force computations required by the immersed boundary method. This numerical framework allows us to consider the effect of endothelial geometry and red blood cell motion on the motion of platelets. We find red blood cells to be crucial for understanding the motion of platelets, to the point that the geometry of the vessel wall has a negligible effect in the presence of RBCs. We describe certain interactions that force the platelets to remain near the endothelium for extended periods, including a novel platelet motion that can be seen only in 3-dimensional simulations that we term "unicycling." We also observe red blood cell-mediated interactions between platelets and the endothelium for which the platelet has reduced speed. We suggest that these behaviors serve as mechanisms that allow platelets to better maintain vascular integrity.

math.NA↗

arXiv2021

Pump efficacy in a fluid-structure interaction model of a chain of contracting lymphangions

The transport of lymph through the lymphatic vasculature is the mechanism for returning excess interstitial fluid to the circulatory system, and it is essential for fluid homeostasis. Collecting lymphatic vessels comprise a significant portion of the lymphatic vasculature and are divided by valves into contractile segments known as lymphangions. Despite its importance, lymphatic transport in collecting vessels is not well understood. We present a computational model to study lymph flow through chains of valved, contracting lymphangions. We used the Navier-Stokes equations to model the fluid flow and the immersed boundary method to handle the two-way, fluid-structure interaction in 2D, non-axisymmetric simulations. We used our model to evaluate the effects of chain length, contraction style, and adverse axial pressure difference (AAPD) on cycle-mean flow rates (CMFRs). In the model, longer lymphangion chains generally yield larger CMFRs, and they fail to generate positive CMFRs at higher AAPDs than shorter chains. Simultaneously contracting pumps generate the largest CMFRs at nearly every AAPD and for every chain length. Due to the contraction timing and valve dynamics, non-simultaneous pumps generate lower CMFRs than the simultaneous pumps; the discrepancy diminishes as the AAPD increases. Valve dynamics vary with the contraction style and exhibit hysteretic opening and closing behaviors. Our model provides insight into how contraction propagation affects flow rates and transport through a lymphangion chain.

physics.flu-dyn↗

arXiv2020

A Mathematical Model of Platelet Aggregation in an Extravascular Injury Under Flow

We present the first mathematical model of flow-mediated primary hemostasis in an extravascular injury, which can track the process from initial deposition to occlusion. The model consists of a system of ordinary differential equations (ODE) that describe platelet aggregation (adhesion and cohesion), soluble-agonist-dependent platelet activation, and the flow of blood through the injury. The formation of platelet aggregates increases resistance to flow through the injury, which is modeled using the Stokes-Brinkman equations. Data from analogous experimental (microfluidic flow) and partial differential equation models informed parameter values used in the ODE model description of platelet adhesion, cohesion, and activation. This model predicts injury occlusion under a range of flow and platelet activation conditions. Simulations testing the effects of shear and activation rates resulted in delayed occlusion and aggregate heterogeneity. These results validate our hypothesis that flow-mediated dilution of activating chemical ADP hinders aggregate development. This novel modeling framework can be extended to include more mechanisms of platelet activation as well as the addition of the biochemical reactions of coagulation, resulting in a computationally efficient high throughput screening tool.

q-bio.CB↗

arXiv2018

Hyperviscosity-Based Stabilization for Radial Basis Function-Finite Difference (RBF-FD) Discretizations of Advection-Diffusion Equations

We present a novel hyperviscosity formulation for stabilizing RBF-FD discretizations of the advection-diffusion equation. The amount of hyperviscosity is determined quasi-analytically for commonly-used explicit, implicit, and implicit-explicit (IMEX) time integrators by using a simple 1D semi-discrete Von Neumann analysis. The analysis is applied to an analytical model of spurious growth in RBF-FD solutions that uses auxiliary differential operators mimicking the undesirable properties of RBF-FD differentiation matrices. The resulting hyperviscosity formulation is a generalization of existing ones in the literature, but is free of any tuning parameters and can be computed efficiently. To further improve robustness, we introduce a simple new scaling law for polynomial-augmented RBF-FD that relates the degree of polyharmonic spline (PHS) RBFs to the degree of the appended polynomial. When used in a novel ghost node formulation in conjunction with the recently-developed overlapped RBF-FD method, the resulting method is robust and free of stagnation errors. We validate the high-order convergence rates of our method on 2D and 3D test cases over a wide range of Peclet numbers (1-1000). We then use our method to solve a 3D coupled problem motivated by models of platelet aggregation and coagulation, again demonstrating high-order convergence rates.

math.NA↗

arXiv2018

Robust Node Generation for Meshfree Discretizations on Irregular Domains and Surfaces

We present a new algorithm for the automatic one-shot generation of scattered node sets on irregular 2D and 3D domains using Poisson disk sampling coupled to novel parameter-free, high-order parametric Spherical Radial Basis Function (SBF)-based geometric modeling of irregular domain boundaries. Our algorithm also automatically modifies the scattered node sets locally for time-varying embedded boundaries in the domain interior. We derive complexity estimates for our node generator in 2D and 3D that establish its scalability, and verify these estimates with timing experiments. We explore the influence of Poisson disk sampling parameters on both quasi-uniformity in the node sets and errors in an RBF-FD discretization of the heat equation. In all cases, our framework requires only a small number of "seed" nodes on domain boundaries. The entire framework exhibits O(N) complexity in both 2D and 3D.

cs.DS↗

arXiv2015

A Radial Basis Function (RBF)-Finite Difference Method for the Simulation of Reaction-Diffusion Equations on Stationary Platelets within the Augmented Forcing Method

We present a computational method for solving the coupled problem of chemical transport in a fluid (blood) with binding/unbinding of the chemical to/from cellular (platelet) surfaces in contact with the fluid, and with transport of the chemical on the cellular surfaces. The overall framework is the Augmented Forcing Point Method (AFM) (\emph{L. Yao and A.L. Fogelson, Simulations of chemical transport and reaction in a suspension of cells I: An augmented forcing point method for the stationary case, IJNMF (2012) 69, 1736-52.}) for solving fluid-phase transport in a region outside of a collection of cells suspended in the fluid. We introduce a novel Radial Basis Function-Finite Difference (RBF-FD) method to solve reaction-diffusion equations on the surface of each of a collection of 2D stationary platelets suspended in blood. Parametric RBFs are used to represent the geometry of the platelets and give accurate geometric information needed for the RBF-FD method. Symmetric Hermite-RBF interpolants are used for enforcing the boundary conditions on the fluid-phase chemical concentration, and their use removes a significant limitation of the original AFM. The efficacy of the new methods are shown through a series of numerical experiments; in particular, second order convergence for the coupled problem is demonstrated.

math.NA↗

arXiv2015

Augmenting the Immersed Boundary Method with Radial Basis Functions (RBFs) for the Modeling of Platelets in Hemodynamic Flows

We present a new computational method by extending the Immersed Boundary (IB) method with a spectrally-accurate geometric model based on Radial Basis Function (RBF) interpolation of the Lagrangian structures. Our specific motivation is the modeling of platelets in hemodynamic flows, though we anticipate that our method will be useful in other applications as well. The efficacy of our new RBF-IB method is shown through a series of numerical experiments. Specifically, we compare our method with the traditional IB method in terms of convergence and accuracy, computational cost, maximum stable time-step size and volume loss. We conclude that the RBF-IB method has advantages over the traditional Immersed Boundary method, and is well-suited for modeling of platelets in hemodynamic flows.

math.NA↗

arXiv2014

A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction-Diffusion Equations on Surfaces

In this paper, we present a method based on Radial Basis Function (RBF)-generated Finite Differences (FD) for numerically solving diffusion and reaction-diffusion equations (PDEs) on closed surfaces embedded in $\mathbb{R}^d$. Our method uses a method-of-lines formulation, in which surface derivatives that appear in the PDEs are approximated locally using RBF interpolation. The method requires only scattered nodes representing the surface and normal vectors at those scattered nodes. All computations use only extrinsic coordinates, thereby avoiding coordinate distortions and singularities. We also present an optimization procedure that allows for the stabilization of the discrete differential operators generated by our RBF-FD method by selecting shape parameters for each stencil that correspond to a global target condition number. We show the convergence of our method on two surfaces for different stencil sizes, and present applications to nonlinear PDEs simulated both on implicit/parametric surfaces and more general surfaces represented by point clouds.

math.NA↗

arXiv2012

A Study of Different Modeling Choices For Simulating Platelets Within the Immersed Boundary Method

The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid-structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmitting information (forces and velocities) between these two representations. Most IB simulations represent their structures with piecewise-linear approximations and utilize Hookean spring models to approximate structural forces. Our specific motivation is the modeling of platelets in hemodynamic flows. In this paper, we study two alternative representations - radial basis functions (RBFs) and Fourier-based (trigonometric polynomials and spherical harmonics) representations - for the modeling of platelets in two and three dimensions within the IB framework, and compare our results with the traditional piecewise-linear approximation methodology. For different representative shapes, we examine the geometric modeling errors (position and normal vectors), force computation errors, and computational cost and provide an engineering trade-off strategy for when and why one might select to employ these different representations.

math.NA↗