MS04 - CARD-1
Barbie Tootle Room (#3156) in The Ohio Union

Integrating Mathematics Across the Cardiovascular System: A Mini-Symposium on Multilevel Modelling of Cardiovascular Biology

Tuesday, July 18 at 04:00pm

SMB2023 SMB2023 Follow Tuesday during the "MS04" time block.
Room assignment: Barbie Tootle Room (#3156) in The Ohio Union.
Note: this minisymposia has multiple sessions. The other session is MS03-CARD-1 (click here).

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Jessica Crawshaw, Vijay Rajagopal, Michael Watson, Mitchel Colebank, Seth Weinberg


Cardiovascular biology is a complex and multifaceted field that encompasses a wide range of physical and biological processes occurring across multiple levels, including the cardiac, vascular, and microvascular systems. At each level of the cardiovascular system, mathematical modelling plays a critical role in integrating data and understanding the underlying mechanisms governing these processes. While there has been significant progress in mathematical and computational cardiovascular biology over the past decade, mathematicians and engineers at each level have tended to work in isolated silos, which risks producing a fragmented understanding of the cardiovascular system and threatens to slow scientific progress. This issue carries significant implications for the broader field of mathematical biology, as cardiovascular models frequently serve as building blocks for larger models of other systems, such as developmental biology, oncology, drug development, tissue engineering, and regenerative medicine. To address this challenge, this mini-symposium seeks to provide a forum for collaboration between mathematicians and engineers from each level of the cardiovascular system. The aim is to facilitate the exchange of ideas, foster new collaborations, and promote a more comprehensive understanding of cardiovascular biology through mathematical modelling. The mini-symposium will feature talks by leading researchers in the field covering various topics, including cardiac physiology modelling, vascular disease, microvascular development, and blood flow dynamics. Each talk will showcase innovative mathematical models and computational tools used to understand the complex processes underlying cardiovascular development, function, and dysfunction. This mini-symposium provides a unique opportunity for mathematicians and engineers interested in cardiovascular biology to exchange ideas, discuss recent developments, and foster new collaborations.

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.
Additional authors: Prof. Mary R Myerscough, School of Mathematics and Statistics, University of Sydney; Prof. Helen M Byrne, Mathematical Institute, University of Oxford

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.
Additional authors: Anandita Umapathy, Department of Obstetrics and Gynaecology, Faculty of Medical and Health Sciences, University of Auckland; Sophie Shamailov, Department of Physics, Faculty of Sciences, University of Auckland; Toby Jackson, Auckland Bioengineering Institute, University of Auckland; Jo James, Department of Obstetrics and Gynaecology, Faculty of Medical and Health Sciences, University of Auckland

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.
Additional authors: Sarah Ellwein (Cal Poly State University) Steve Poelzing (Virginia Tech Carilion School of Medicine) Anand Abraham (Virginia Tech Carilion School of Medicine) Sharon A. George (Virginia Tech Carilion School of Medicine) Amara Greer-Short (Virginia Tech Carilion School of Medicine) Grace A. Blair (Virginia Tech Carilion School of Medicine) Angel Moreno (The George Washington University) Bridget R. Alber (The George Washington University) Matthew W. Kay (The George Washington University)

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.
Additional authors: Seth Weinberg, Ohio State University, Department of Biomedical Engineering.

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