Mathematical approaches to vascular biology

Thursday, June 17 at 02:15am (PDT)
Thursday, June 17 at 10:15am (BST)
Thursday, June 17 06:15pm (KST)

SMB2021 SMB2021 Follow Wednesday (Thursday) during the "MS17" time block.
Note: this minisymposia has multiple sessions. The second session is MS18-CDEV (click here).

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Jessica Crawshaw (The University of Melbourne, Australia), James Osborne (The University of Melbourne, Australia), Lowell Edgar (The University of Edinburgh, Scotland)


Mathematical models of the vascular system are a pivotal component of mathematical biology woven between many important areas of the field, including developmental biology, oncology, drug development, tissue engineering, regenerative medicine, and more. The approach one takes to model the vascular system will vary depending on the biological question at hand and the translational application of the model. This mini-symposium aims to bring together mathematicians modelling the vascular system from different areas of biology, using different modelling strategies and with different perspectives to share their important research in a lively and diverse forum. In doing so, we are encouraging the integration and dissemination of new modelling techniques, knowledge and data between the different facets of mathematical vascular biology, which ultimately promotes the translation of vascular mathematical biology to clinically applicable outcomes.

Alys Clark

(The University of Auckland, New Zealand)
"What drives vascular remodelling in the uterus in pregnancy? Vascular adaptions to elevated blood flow."
During pregnancy, the placenta transfers nutrients between the mother and the developing fetus. To do this it must establish a supply of nutrients from the mother’s circulation in the uterus, and so it adapts the maternal blood vessels of the uterus to carry increasing volumes of blood to its surface. If this process does not occur as it should, it can lead to pregnancy complications such as fetal growth restriction. Uterine vascular adaption occurs due to changes in mechanical forces acting on the blood vessel walls (with increases in blood flow), changes in the structure of the vascular walls (termed outward remodelling) and changes in the hormonal environment of the uterus. This occurs in a multi-scale manner, with adaption at each level in the circulatory network potentially impacting up and downstream function. Here we present data-driven mathematical models of uterine vascular adaption that aim to tease apart the impact of individual contributors to function in a healthy pregnancy. We show that small radial arteries that are potential rate limiters for the volume of blood that can be delivered through the uterus in pregnancy, adapt to be more compliant in rodent pregnancies, and that arteries from rodent pregnancies are more robust to increases in flow without vasoconstriction than outside of pregnancy. Finally, we demonstrate how quantitative descriptions of vascular anatomy and numerical simulations can help to translate data from rodent models to human pregnancies at the organ scale.

Richard Clarke

(The University of Auckland, New Zealand)
"Understanding the mechanical impact of the endothelial glycocalyx’s microstructure"
The Endothelial Glycocalyx Layer (EGL) is a thin, brush-like layer that coats the inside of blood vessels. It is believed to serve as a protective barrier against excessive fluid shear, as well as perform a number of other biological functions, such as mechanotransduction. The fragile nature of the EGL, however, makes it very difficult to examine experimentally, and so theoretical models can provide interesting and useful insights. In the past the EGL has been modelled as an isotropic, homogeneous porous layer. However, there is an increasing volume of evidence to suggest that the EGL has a microstructural organisation that brings in to question this assumption. In this talk I will explain some of our recent work using Homogenisation Theory to explore the connections between the EGL’s microstructure, and its bulk macroscopic properties.

Michael Watson

(The University of Sydney, Australia)
"A Multiphase Model of Cap Formation in the Atherosclerotic Plaque"
Atherosclerosis is characterised by the growth of fat-filled plaques in the artery wall. In advanced disease, vascular smooth muscle cells (SMCs) enter the plaque and deposit a cap of fibrous tissue over the fatty plaque core. The fibrous cap isolates the thrombogenic plaque material from the bloodstream and prevents the formation of blood clots that cause heart attacks or strokes. Despite the protective role of the cap, the mechanisms that regulate cap formation and maintenance remain poorly understood. In this talk, I will discuss recent work on modelling the dynamics of cap formation. We use multiphase PDEs with non-standard boundary conditions to simulate plaque SMC migration and tissue remodelling in response to endothelium-derived growth factors. The model results reproduce several observations from experiments in atherosclerosis-prone mice and provide novel insight into the relationship between fibrous cap stability and cap region SMC numbers.

Fabian Spill

(The University of Birmingham, England)
"Organisation and dynamics of the microvasculature"
The microvasculature is a highly dynamic organ. Naturally, during its formation, blood vessel cells move, divide and form networks. Interestingly, the cells maintain dynamic features after the formation of stable networks, where they move around, exert forces on neighbouring cells and extracellular matrix, and form gaps in between the cells. These gaps are critical for the passage of fluid or transmigrating cells. The latter is a critical feature for the immune system, where immune cells need to cross the vasculature into surrounding tissues to reach sites of infection. It is also a deadly process, where cancer cells cross the vasculature during metastasis. I will discuss some ongoing work on characterising 3D microvascular networks through image analysis and extracting relevant features such as transport capabilities. The analysis shows how network formation depends on conditions such as extracellular matrix. Next, I will discuss a model of blood vessel cell dynamics that can predict how gaps in between the cells form, in dependence on forces and adhesion properties. Experiments validated the model predictions and indicate that these gaps can be exploited by metastasising cancer cells that cross the vasculature to invade surrounding tissues.

Hosted by SMB2021 Follow
Virtual conference of the Society for Mathematical Biology, 2021.