Organized by: Jessica Crawshaw, Vijay Rajagopal, Michael Watson, Mitchel Colebank, Seth Weinberg
Note: this minisymposia has multiple sessions. The other session is MS04-CARD-1.

• Miguel Bernabeu The University of Edinburgh (The Bayes Centre)
  "Red blood cell dynamics in complex vascular networks: implications in development and disease"
In this talk, I will review recent progress on the application of cellular flow simulations (with the HemeLB flow solver) to characterise red blood cell (RBC) dynamics in complex vascular networks. First, I will demonstrate an intriguing association between reduced RBC flow and vascular remodelling during vascular development. Second, I will present two recently published studies relating vascular phenotypes encountered in the tumour microenvironment with anomalous RBC transport and potential tumour tissue hypoxia, a mechanism previously unreported. Finally, I will outline future research directions related to predicting vascular network function from its structure and how this can become a tool for biomedical investigation and eventually clinical translation.
• Mette Olufsen North Carolina State University (Mathematics)
  "Multiscale approach for assessment of hemodynamics in Pulmonary Hypertension"
This study discusses the use of multiscale models for the assessment of pulmonary hypertension (PH). This heterogeneous disease with multiple subtypes is categorized as pre-capillary (leading to remodeling of the pulmonary arteries), or post-capillary, also referred to as venous PH. The latter is often associated with left heart failure. Common for both types is an increase in pulmonary arterial pressure. This study will use 1D and systems-level modeling to assess changes and propose treatments for PH patients. The focus is on patient-specific predictions using a computational framework merging imaging and dynamic data with computational models. The systems-level model allows us to study the effects of high pulmonary arterial pressure on the cardiovascular system as a whole, particularly how a right heart disease can affect the left heart via ventricular-ventricular interaction. Whereas the spatial pulmonary network model can help predict lung perfusion. Both properties are essential to assess patient health. We extract pulmonary networks represented by a directed graph extracted from computed tomography images. In the large vessels, we solve the 1D Navier Stokes equations. In contrast, in the systems level model and the network of small vessels and capillaries, we solve linearized equations coupled to large vessels via outflow boundary conditions. We demonstrate the importance of sensitivity analysis and parameter inference to render the model patient-specific and show how the calibrated models can be used to predict treatment effects for patients with thromboembolic pulmonary hypertension.
• Fabian Spill University of Birmingham (Mathematics)
  "The Human Cardiac Age-OME: Multi-omics analysis and mechanistic modelling of the ageing heart"
The heart is a mechanical pump, whose function is essential to life. Reduced heart function in ageing is a key contributor to frailty, and heart diseases are among the major causes of death. An impediment to understanding age-related heart diseases is our lack of understanding of healthy cardiac ageing. This limits our ability to distinguish data from age-related diseases to data from healthily aged hearts, identifying the true causes of these diseases. A challenge to understanding healthy ageing is a lack of available data from healthy donors. Making use of the unique resources of the Sydney Heart Bank, we present an integrated mathematical modelling and bioinformatics analysis of human cardiac ageing. We performed transcriptomics, proteomics, metabolomics, and lipidomics analysis, and obtained a holistic picture of metabolic and mechanical alterations that characterize the ageing heart. In older hearts, we observed a downregulation of proteins involved in calcium signalling and of the contractile apparatus itself. In addition, we found a potential counteractive upregulation of central carbon generation of fuel, upregulation of glycolysis and increases in long-chain fatty acids. We then developed predictive mechanistic models that demonstrated how calcium signalling and oxidative phosphorylation, two key pathways regulating cardiomyocyte function, are altered in the ageing heart.

Organized by: Jessica Crawshaw, Vijay Rajagopal, Michael Watson, Mitchel Colebank, Seth Weinberg
Note: this minisymposia has multiple sessions. The other session is MS03-CARD-1.

• Keith Chambers University of Oxford (Wolfson Centre for Mathematical Biology, Mathematical Institute)
  "Resolution vs chronic inflammation: A lipid/phenotype dual-structured model for early atherosclerosis"
Atherosclerosis is a chronic inflammatory condition of the artery wall. Despite being the underlying cause of approximately half the deaths in westernized society, the disease remains incompletely understood due to its biological complexity. A key component of the disease is the role played by monocyte-derived macrophages, which are the primary type of immune cell recruited to the lesion in response to artery wall lipid accumulation. Macrophages accumulate lipid by clearing their local environment of low-density lipoprotein particles and cellular debris, and can offload lipid to HDL particles to ferry out of the lesion. Further, macrophages can either promote further inflammation or disease resolution by contributing to signaling pathways according to their phenotype. Macrophage phenotype is strongly influenced by microenvironmental stimuli and is commonly represented as a spectrum from pro-inflammatory M1-like cells to anti-inflammatory M2-like cells in the biological literature. The balance of M1-like and M2-like cells determines the trajectory of atherosclerosis. In this talk, I present a differential equation model of early atherosclerosis with a macrophage population that is structured by both lipid load and phenotype. We consider firstly a discrete formulation in which lipid and phenotype are represented as indices taken from a bounded set of integers. We show that this model admits a closed subsystem by summing the equations of the full model. Numerical solutions indicate that if endothelial damage is ongoing, the model artery wall may exhibit chronic inflammation or oscillatory solutions that are induced by the partial resolution of inflammation. If endothelial damage is an initial transient, the model predicts a transition from a predominantly M1-like macrophage population at early times to a resolving M2-like population at later times; this behaviour reflects an acute inflammatory response.
• Alys Clark University of Auckland, New Zealand (Auckland Bioengineering Institute)
  "The fetal circulation and its adaption to pathological placental development"
The placenta provides a critical exchange function between the mother and developing fetus. To effectively exchange nutrients and gases it develops a complex branching vasculature across pregnancy. Dysfunction in its exchange capacity impacts fetal growth trajectory, leading to a condition known as fetal growth restriction (FGR). FGR results in increased long term cardiovascular risk for the baby, compared to appropriately grown fetuses. FGR placentae exhibit impaired vascular function, increasing the resistance in this major vascular bed within the fetal circulation. In turn, this dysfunction is thought to impact cardiac development, with FGR hearts exhibiting structural changes such as hypertrophy. However, the biomechanical interactions between the heart and the placenta in pregnancy are not well-established. Computational modelling of the placenta and heart, as well as their interaction within the fetal circulation provides opportunities to better understand the contribution of pathological placental development to cardiac dysfunction in FGR pregnancies. Here we present an image and model based approach to understanding these interactions. First, we present detailed anatomical assessment of placental vascular structure, alongside model predictions of the impact of placental vascular network architecture on its haemodynamic function. We then assess the impact of placental vascular architecture embedded in a zero-dimensional fetal circulation model, that predicts the relationship between placental branching structure and clinically measurable ultrasound metrics. Finally, we show how we can extend this model and imaged based framework to animal models of placental dysfunction, where we have demonstrated a significant decrease in right ventricular cavity volume, alongside a reduction in placental vascular density.
• Joyce Lin Cal Poly State University (Mathematics)
  "Conduction reserve theory in cardiac tissue with reduced gap junction coupling"
While many cardiac pathologies have been correlated with reduced gap junctional coupling, the relationship between phenotype and functional expression of the connexin gap junctional family of proteins is unclear. These proteins are an important modulator of cardiac conduction velocity, yet a 50% reduction of gap junctional protein has been shown to have little impact on myocardial conduction. We explore the theory of conduction reserve, which can operate through two mechanisms: The first mechanism, ephaptic coupling, maintains conduction with low gap junctional coupling by increasing the electrical fields generated in the sodium channel-rich clefts between neighboring myocytes. The other mechanism allows low gap junctional coupling to increase intracellular charge accumulation within myocytes, resulting in a faster transmembrane potential rate of change during depolarization that maintains macroscopic conduction. To provide insight into the role these two mechanisms play during gap junctional remodeling, we focus on the relationship between ephaptic coupling and charge accumulation using simulations as well as perfused mouse heart experiments. Mathematical modeling of conduction in a cardiac tissue as well as corresponding experimental heart studies will be presented. With insight from simulations, the relative contributions of ephaptic coupling and charge accumulation on action potential parameters and conduction velocities will be shown. Both simulation and experimental results support a common conclusion that low gap junctional coupling decreases and narrowing perinexal width increases the rate of the action potential upstroke when sodium channels are densely expressed at the ends of myocytes, indicating that conduction reserve may be more dependent on ephaptic coupling than charge accumulation under pathological conditions.
• Nicolae Moise Ohio State University (Biomedical Engineering)
  "Emergent Pacemaking and Tissue Heterogeneity in a Calcium Feedback Regulatory Model of the Sinoatrial Node"
The sinoatrial node (SAN) is the primary pacemaker of the heart. SAN activity emerges at an early point in life, and maintains a steady rhythm for the lifetime of the organism. The ion channel composition and currents of the cells can be influenced by a variety of factors. Therefore, the emergent activity and long-term stability imply some form of dynamical feedback control of the SAN cell activity. Here, we adapt a recent neuronal model to the SAN rabbit cell. The model describes a minimal regulatory mechanism of neuronal ion channel conductance based on a feedback loop defined by an intracellular [Ca2+] level as its target. Briefly, the cell upregulates or downregulates its channel mRNA and membrane expression levels based on the difference between the intercellular Ca2+ level in the cell and a set intercellular Ca2+ target. Based on this feedback model, spontaneous electrical activity emerges in the SAN cell from a quiescent state with low initial conductances. As conductances increase, the intracellular [Ca2+] level reaches the target, and ion channel conductance reach a steady state consistent with sustained spontaneous activity. In a 2D tissue, variability in [Ca2+] target leads to heterogeneous ion channel expression and Ca2+ transients throughout the tissue. Further, dominant focal clusters appear, which interact with one another leading to a heterogeneous tissue cycle length, implying that variability in heart rate is an emergent property of the feedback model. Finally, the 2D tissue is robust to the silencing of leading cells or ion channel knock-outs. Thus, the calcium feedback regulatory model explains a number of experimental data using a minimal description of intracellular calcium and ion channel regulatory networks.

• 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.
• 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.
• 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.
• 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.

• Elisa Serafini Houston Methodist Research Institute
  "An Agent-Based Model of Cardiac Allograft Vasculopathy: towards a Cost-Effective Platform to Better Understanding Chronic Rejection Dynamics"
Cardiac allograft vasculopathy (CAV) is a coronary artery disease affecting 50% of heart transplant recipients, and it is the major cause of chronic graft rejection. CAV is driven by the interplay of immunological and non-immunological factors with the infiltration of macrophages as one of the main pathological triggers, setting off a cascade of events promoting endothelial damage and vascular cell dysfunction. Since etiology and evolution of the pathology are still largely unknown, disease management remains challenging and re-transplantation is today the only long-term solution to CAV. A deep understanding of the pathology mechanobiology is fundamental to improve prevention, diagnosis, and treatment of CAV. So far, in vivo models, mostly mouse-based, have been widely used to study CAV, but they are resource-consuming, pose many ethical issues, and allow limited time points of investigation during experimental follow-up. Recently, agent-based models (ABMs) proved to be valid computational tools for capturing and deciphering processes at cell/tissue level, augmenting cost-effectively in vivo lab-based experiments, i.e., guaranteeing richness in observation time points while maintaining low resource consumptions. We hypothesize that integrating ABMs with lab-based experiments can aid classic pre-clinical research by overcoming its limitations. Accordingly, we present a bidimensional ABM of CAV in a mouse-like coronary artery cross-section, simulating the arterial wall response to two distinct stimuli: inflammation and hemodynamic disturbances, the latter in terms of low wall-shear stress (WSS), which together trigger macrophage response activation and exacerbate vascular cell activities. In addition, we performed an extensive analysis to investigate the ABM working mechanisms and gain insight on the driving parameters and the stimuli influences. The ABM replicates with high fidelity a 4-week CAV initiation and progression, well highlighting lumen area decreasing due to progressive intimal thickening in regions exposed to high inflammation and low WSS. The sensitivity analysis remarked that the inflammatory-related events, rather than the WSS, predominantly drive CAV, corroborating the inflammatory nature of the vasculopathy. This proof-of-concept model offers to the scientific community an agile computational platform to deepen CAV understanding and to support the in vivo analysis of CAV in a cost-effective fashion.
• Pak-Wing Fok University of Delaware
  "Shear stress regulation in cylindrical arteries through medial growth and nitric oxide release"
The mechanisms employed by blood vessels in order to adapt to their hemodynamic environment are important for our general understanding of disease and development. Changes in arterial geometry are generally induced by two effects: vasodilation and/or constriction; and growth and remodeling (“G&R”). The first can occur over short periods of a few minutes, while the second usually occurs over timescales of weeks or months. The free radical Nitric oxide (NO) is one of the few biological signaling molecules that is gaseous. When smooth muscle cells internalize NO, they lengthen and ultimately induce a relaxation of the artery. In addition, Platelet-Derived Growth Factor (PDGF) is a growth factor released by smooth muscle cells and platelets that regulates cell growth and division. In this talk, we present a single-layered, axisymmetric hyperelastic model for a deforming, growing artery in which the opening angle is regulated by NO and growth is induced by PDGF. Our model describes vasodilation and G&R in a long cylindrical artery regulated by a steady-state Poiseuille flow. The transport of NO released by the endothelium is governed by a diffusion equation with a shear-stress dependent flux boundary condition. Arterial opening angle is assumed to be a Hill function of the wall-averaged NO concentration. We find that both growth and NO help to regulate shear stress with respect to the flow rate, but regulation through growth occurs only at large times. In contrast, regulation through NO is immediate but can only occur as long as the opening angle is able to continually decrease as a function of flow rate. Our model is calibrated using experimental data from ligated, control, and anastomosed carotid arteries of adult and weanling rabbits. Our results generate shear stress/flow rate and lumen radius/flow rate curves that agree with experimental data from control and NO-inhibited rabbit carotid arteries.
• Shake Ibna Abir Western Kentucky University
  "Deep Learning Application of Long Short-Term Memory (LSTM) to predict the risk factors of etiology cardiovascular disease."
Cardiovascular disease (CVD) is presently one of the leading causes of death, with an estimated 24.1 million people expected to be affected by 2025. Therefore, the establishment of the health care industry's objective is to gather a vast amount of data on cardiovascular disease and utilize Deep Learning (DL) algorithms to analyze the information to assist doctors in early detection and identification of potential risk factors for CVD. DL algorithms can help to discover potential patterns of diseases and symptoms based on this structured and unstructured case information. In epidemiology, this is the first prospective study on cardiovascular disease in the community free movement population, and the related risk factors can be recognized. The prediction method of cardiovascular disease based on LSTM is proposed, and the connection between LSTM and unit state is tried to ensure the correct data acquisition during operation, and the prediction method based on LSTM is realized. The original medical data of 4434 participants in the data set with 11628 observations are verified by experiments. The algorithm has an accuracy of nearly 94% and a 0.96 Matthews correlation coefficient (MCC) score.