Mathematical approaches to vascular biology

Thursday, June 17 at 04:15am (PDT)
Thursday, June 17 at 12:15pm (BST)
Thursday, June 17 08:15pm (KST)

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

Jessica Crawshaw

(The University of Melbourne, Australia)
"To collapse or not to collapse: how do mechanical forces drive vascular regression?"
Vascular regression is a critical process concluding the maturation of developing capillary networks, in which redundant blood vessels are removed. Recent research suggests that forces from the local blood flow (haemodynamic forces) trigger polarized endothelial cell migration against the flow, resulting in capillary collapse and regression. However, vascular regression is also driven by several additional pathways including local adhesion forces and cellular signalling factors. Due to the delicate nature of these microvessels, it is difficult to experimentally untangle the roles of each pathway during vascular development. As such, the development of computational models to analyse the relationship between the local haemodynamic forces and the surrounding vasculature during regression are invaluable. In this talk, we will present a novel computational framework to mathematically study and isolate the role of haemodynamic in vessel deformation and collapse during vascular regression. To model regression, we describe the capillary wall as a discretised hyperelastic membrane, coupled with a lattice-Boltzmann model of blood flow in an iterative manner. This discrete approach provides a natural framework to consider the relationship between the capillary wall and the local blood flow, and allows for the easy inclusion of structural heterogeneities across the capillary wall. Using this model we are able to examine the role of the haemodynamic forces during vascular regression, as well as the network level ramifications of local regression.

Daria Stepanova

(CRM Centre for Mathematical Research, Spain)
"Multiscale approach to understanding cell rearrangements in early angiogenesis"
Angiogenesis is the process whereby endothelial cells (ECs) migrate from a pre-existing vascular bed guided by local environmental cues and interacting with each other to eventually create a new vascular network. We introduce a multiscale model of migration-driven angiogenic sprouting which accounts for the individual phenotype selection of ECs, cell-cell and cell-extracellular matrix interactions. The model, calibrated and validated against various experimental data, captures the characteristic behavior of ECs: branching, cell mixing and, chemotactic sensitivity. These properties, rather than being hard-wired into the model, emerge naturally due to accounting for heterogeneous behavior of ECs depending on their gene expression pattern. This allows us to use the model to investigate the role of cell rearrangements during angiogenic sprouting on the vascular network structure. In particular, we show how cells with impaired gene expression of a specific receptor are characterised by reduced levels of cell rearrangement which influences the branching pattern of vascular networks. Overall, our results support the hypothesis that cell rearrangements play a central role in angiogenesis.

Katie Bentley

(The Crick Institute, England)
"Filopodia speed up Notch selection of endothelial tip cells: in silico predictions confirmed in vivo"
I will describe our recent proof of concept in silica/in vivo study demonstrating that filopodia (actin-rich, dynamic, finger-like cell membrane protrusions) play an unexpected role in speeding up collective endothelial decisions during the time-constrained process of 'tip cell' selection during blood vessel formation (angiogenesis). We first validate simulation predictions in vivo with live imaging of zebrafish intersegmental vessel growth. Further simulation studies then indicate the effect is due to the coupled positive feedback between movement and sensing on filopodia conferring a bistable switch-like property to Notch lateral inhibition, ensuring tip selection is a rapid and robust process. We then employ measures from computational neuroscience to assess whether filopodia function as a primitive (basal) form of active perception due to the sensorimotor coordination apparent in filopodia and find evidence in support. By viewing cell behaviour through the 'basal cognitive lens' we acquire a fresh perspective on the tip cell selection process, revealing a hidden, yet vital time-keeping role for filopodia. Finally, I’ll discuss a myriad of new and exciting research directions stemming from our conceptual approach to interpreting cell behaviour.

Lowell Edgar

(The University of Edinburgh, U.K)
"Force transmission between migrating endothelial agents regulates functional shunting during angiogenic remodelling"
During angiogenic remodelling endothelial cells (ECs) composing blood vessels polarise and migrate against the direction of flow. The cellular mechanisms which prevent functional shunting during this process remain poorly understood despite being relevant to arteriovenous malformations and dysfunctional microcirculation and local hypoxia in cancer. We hypothesise that force transmission between migrating ECs plays a crucial role in shunt formation and have designed a model based on force-transmitting agents to investigate. EC agents consisted of nested ellipses polarised against flow. Force transmission between neighbouring agents, based on overlap, consists of extrusive (pushing) forces which maintain spacing and cohesive (pulling) forces which maintain the collective. We simulated migration within an idealised capillary plexus in which agents either split apart or combined at bifurcations based on the convergence/divergence of flow. Extrusion forces stabilise the vasculature and allow cells to intercalate to reduce stress. Excessive amounts of cohesion disrupted this intercalation, creating tension and prolonged flow reversals. Flow reversals switch convergence/divergence at bifurcations, which aggregates cells and leads to shunting and perfusion loss. Our results implicate dysfunctional junctional remodelling and/or force transmission as a possible mechanism vascular malformation and implicate new targets for investigation in future experimental studies.

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Virtual conference of the Society for Mathematical Biology, 2021.