CARD Subgroup Contributed Talks

Erin Zhao

Indiana University-Purdue University Indianapolis

"Mathematical modeling of arterial occlusion"

Major arterial occlusion can lead to serious health complications such as peripheral arterial disease and ischemic stroke. Pre-existing collateral vessels provide alternate routes for blood flow when a major artery is occluded, thereby supplying oxygen to tissue regions downstream of an occlusion. However, the extent to which collateral vessels are able to compensate for a major arterial occlusion is not fully understood. Mathematical modeling is used in this study to determine the role of collaterals in flow compensation following occlusion and to elucidate which vascular response mechanisms facilitate the recruitment and dilation of collateral vessels. A wall mechanics model is developed and applied to a rat hindlimb model of femoral arterial occlusion and a human brain model of middle cerebral arterial occlusion. The model incorporates both acute vascular responses (e.g., immediate vessel constriction and dilation) and chronic vascular responses (e.g., arteriogenesis and angiogenesis). In the hindlimb model, dilation of the collateral vessel and arteriogenesis were predicted to be the most significant factors leading to increased flow following occlusion. The model is adapted to a simplified geometry of the cerebral circulation to assess the role of leptomeningeal collaterals in compensating for a middle cerebral artery occlusion. This model will yield predictions of blood and tissue oxygenation in the posterior, anterior, and middle cerebral regions and will be eventually compared to data on the collateral formation and infarct volume measured during acute ischemic stroke.
Additional authors: Jared Barber, Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis; Julia Arciero, Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis

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Keshav Patel

University of Utah

"A Spatially Averaged Model for Platelet Cohesion by Von Willebrand Factor and Fibrinogen"

High shear rate conditions in arterial blood flow result from several pathologies, such as cardiovascular disorders, cholesterol buildup, and stenosis. These conditions are correlated with an increased risk of thrombosis, mediated primarily by Von Willebrand Factor (vWF), a mechanically sensitive protein found in circulating blood and released by activated platelets. At high shear rates, vWF elongates from a globular state and reveals binding sites for platelet receptors, mediating both platelet aggregation and activation. Modeling vWF’s effect on aggregation with computational fluid dynamics has allowed researchers to understand relationships between physical and chemical processes with high detail. However, computational complexity limits our ability to examine various physiological conditions that could impact aggregation, like shear rate, vessel geometry, and injury size. In this talk, we will discuss steps toward building a spatially-averaged model of platelet aggregation to inform PDE models and efficiently determine essential parameters involved in aggregate formation. This purely dynamical systems framework incorporates an averaged flow through porous media, imparting a drag force that is balanced by crosslink bonds. These bonds are formed by vWF and fibrinogen and break in a force-dependent manner. Time-dependent simulations exhibit the development of a positive feedback loop, allowing for increased activation and binding to the aggregate. We will show how vWF significantly decreases the time under which platelet aggregates develop at higher shear rates. Finally, through steady-state analysis, we will highlight model predictions regarding the biological contexts under which vWF allows for platelet aggregation.
Additional authors: Aaron L Fogelson (University of Utah)

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Michael Watson

University of New South Wales

"Journey to the Centre of the Plaque: A PDE Model of Necrotic Core Localisation in Atherosclerosis"

Atherosclerotic plaques are fatty, cellular lesions that form in major arteries. Rupture of mature plaques leads to heart attack and stroke. Plaques are initiated by lipid particles (“bad cholesterol”) that escape the bloodstream and deposit in the artery wall. Specialised immune cells called macrophages are recruited to ingest and remove these lipids. However, when lipid-loaded macrophages die in the artery wall, the plaque accumulates a dangerous necrotic core of lipid and cellular debris. Observations suggest that the necrotic core usually localises in the central or deeper regions of the plaque. This phenomenon is poorly understood because core formation depends upon a complex interplay between the macrophages and lipids in the plaque. In this talk, I will use a novel spatial PDE model to investigate necrotic core localisation in the atherosclerotic plaque. Using steady state analysis and numerical simulations, I will demonstrate the formation of a necrotic core in the model and discuss the factors that determine its profile and position. By identifying the biophysical and immunological mechanisms that lead to realistic simulations of core localisation, I aim to improve current biological understanding of plaque formation, growth, and progression.

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Solomon Feuerwerker

University of Vermont Larner College of Medicine

"Parsing the effects of differential programmed cell death pathways on plaque stability in atherosclerosis using an agent-based model"

Introduction: Atherosclerotic plaque rupture is a critical step in the development of acute vascular events. They become unstable and prone to rupture when there is an increase in the necrotic composition of the plaque. This process involves a combination of systemic features, such as hyperlipidemia, that increase inflammation in the atheroma and accelerate necrotic core formation. While programmed cellular death pathways (PCDPs) play a critical role in the maintenance of homeostasis in living organisms, inflammation-propagating PCDPs, namely pyroptosis and necroptosis, have been implicated in the development of unstable plaques. Traditionally, these PCDPs have been primarily studied independently, but there is an increasing recognition of extensive crosstalk between pathways. We posit that modeling the differential role of PCDPs in an atherogenic environment, with an emphasis on the cell-death features of pyroptosis and necroptosis, can provide insight into the relative contribution of the respective PCDPs in the generation of unstable plaques. Methods: We created an agent-based model of an atheromatous plaque in a segment of arterial wall termed the Ruptured Unstable Plaque Programmed Cell Death Model (RUP-PCDM). The principal agents represented are endothelial cells, monocytes/macrophages and vascular smooth muscle cells. Rules for the three most commonly studied PCDPs, namely apoptosis, pyroptosis, and necroptosis, were extracted from available literature and implemented in the model. The effect of oxidated Low Density Lipoproteins (oxLDL) was simulated as the inflammatory driver in plaque development. Plaque instability was represented by the number of dead cells present within the necrotic core of plaques. The RUP-PCDM was initially calibrated by reproducing known development of unstable plaques reported in the literature. Next, variations in crosstalk rule parameters, including paracrine/autocrine signaling via Interleukin-1 (IL-1), Interleukin-18 (IL-18) and Tumor Necrosis Factor-alpha (TNFα), signaling through Toll-like Receptors (TLRs) and regulation of Nuclear Factor kappa-B (NFκB), were explored by calibrating to the differential effects of inhibition of pyroptosis and necroptosis as reported in distinct experiments. One publication reported a 69% reduction in plaque size by interrupting pyroptosis via knockouts of NLRP3 (1), and a separate publication reported a 68% reduction in the necrotic core with inhibition of necroptosis (2). Finally, the efficacy of dual-PCDP-targeting therapies was evaluated. Results: PCDPs were successfully implemented in the RUP-PCDM, with reproduction of the evolution of unstable plaques as represented by the aggregation of dead cells in the simulated necrotic core. Calibration simulations to fit independent experiments studying pyroptosis and necroptosis identified a set of parameter combinations across paracrine/autocrine PCDP signaling, control of TLR messaging, and NFκB expression which regulate crosstalk between pyroptosis and necroptosis. Inhibition of both pyroptosis and necroptosis fully mitigated plaque progression. Conclusion: The RUP-PCDM accurately replicates the evolution of an unstable atheromatous plaque, demonstrating the respective effects of different PCDPs on this process. The integrative nature of the RUP-PCDM provided the ability to reconcile distinct experiments that studied pyroptosis and necroptosis in isolation and produced a series of testable hypotheses regarding the crosstalk between these PCDPs. While interruption of pyroptosis and necroptosis individually did reduce the development of plaque instability, the redundancy between these two pathways limited the effectiveness of such interventions. Interrupting both pathways mitigated the development of the unstable plaque, suggesting the potential benefit of dual directed therapy. Future work will include expanding the representation of PCDPs to include autophagy and ferroptosis, as well as representing a larger portion of the pathogenic process of atherosclerotic plaque development. References: 1. Duewell, P., Kono, H., Rayner, K. et al. NLRP3 inflammasomes are required for atherogenesis and activated by cholesterol crystals. Nature 464, 1357–1361 (2010). https://doi.org/10.1038/nature08938 2. Karunakaran D, Geoffrion M, Wei L, Gan W, Richards L, Shangari P, DeKemp EM, Beanlands RA, Perisic L, Maegdefessel L, Hedin U, Sad S, Guo L, Kolodgie FD, Virmani R, Ruddy T, Rayner KJ. Targeting macrophage necroptosis for therapeutic and diagnostic interventions in atherosclerosis. Sci Adv. 2016 Jul 22;2(7):e1600224. doi: 10.1126/sciadv.1600224. PMID: 27532042; PMCID: PMC4985228.
Additional authors: R. Chase Cockrell, PhD, Department of Surgical Research, University of Vermont Larner College of Medicine; Gary An, MD, Department of Surgery, University of Vermont Larner College of Medicine

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