Flow and Transport in Complex Tissues, Part I

eSMB2020 eSMB2020 Follow Wednesday at 9:30am EDT
Share this


Philip Pearce, Mohit Dalwadi, Alys Clark, Igor Chernyavsky


Within complex biological systems, transport of nutrients, wastes, cells and signalling molecules is influenced by various physical mechanisms, including fluid flow, diffusion and active transport. To un- derstand the general relationships between structure and function in such systems, it is important to characterise the relative importance to transport of the dominant physical processes, as well as the sys- tem geometry. In recent work, experiments and theory have been used to delineate the effects of geometry, fluid flow, diffusion and active biological processes on transport in various idealised and realistic model systems; in growing systems, the geometry may be coupled to physical processes over certain timescales. This minisymposium brings together experimental and theoretical researchers to investigate the re- lationship between physics and geometry in several complex biological systems. In Part I we focus on bacterial biofilms, in which fluid flow is an important driver of nutrient availability, signalling via quorum sensing molecules, cell erosion, and growth-induced architecture. In Part II we focus on vascular networks and complex tissues, in which fluid flow is the primary mechanism for transport of red blood cells, oxygen and other solutes. The goal will be to discuss the state-of-the-art techniques used to characterise these different systems, including how the associated physical and biological processes interact across different spatial scales, and how to accurately parameterise models across scales. Such techniques are expected to be highly applicable between the systems. Therefore the minisymposium will promote collaboration and help advance research into the broad topic of flow and transport in biology. The minisymposium is intended for those studying specific or general complex biological systems, at any stage in their research careers. The talks will also be useful for any researcher who would like a broad introduction to the applications of fluid mechanics and transport phenomena in biology.

Alys Clark

"Emerging organ-scale function via large-scale network models of blood flow and exchange"
For healthy development and aging we must acquire sufficient oxygen from our environment to supply our metabolic demands. Before we are born we get oxygen from our mother’s blood through the pla- centa, and after birth the lungs take over the placenta’s role exchanging oxygen from the air. These two exchange organs have complex vascular branching structures with multiple generations of asymmetrically branching blood vessels which provide a large capillary surface area for exchange. Disruptions to this vascular branching and heterogeneity in blood delivery (perfusion) have been implicated in a number of diseases. Often, micro-vascular dysfunction contributes to an organ scale pathology, which can be difficult to detect in clinical imaging. We present organ-scale computational models vascular networks in lung and placenta, which take as inputs vascular anatomy derived from imaging, and simulate both haemodynamic and exchange function. This allows functional prediction of how anatomical perturbations in vascular structures contribute to organ function in health and disease, and provides steps toward determining what constitutes normal and abnormal levels of vascular heterogeneity in representative populations.

Igor Chernyavsky

"Structural and physical determinants of transport in complex microvascular networks"
Across mammalian species, solute transport takes place in complex microvascular networks. How- ever, despite recent advances in three-dimensional (3D) imaging, there has been poor understanding of geometric and physical factors that determine solute exchange and link the structure and function. Here, we use an example of the human placenta, a fetal life-support system, where the primary exchange units, terminal villi, contain disordered networks of fetal capillaries and are surrounded externally by maternal blood. We show how the irregular internal structure of a terminal villus determines its exchange capacity for a wide range of solutes, integrating 3D image-based properties into new non-dimensional parameters. We characterise the structure-function relationship of terminal villi via a simple and robust algebraic approximation, revealing transitions between flow- and diffusion-limited transport at vessel and network levels. The developed theory accommodates for nonlinear blood rheology and tissue metabolism and offers an efficient method for multi-scale modelling [2]. Our results show how physical estimates of trans- port, based on scaling arguments and carefully defined geometric statistics, provide a useful tool for understanding solute exchange in placental and other complex microvascular systems.

Felix Meigel

Max Planck Institue
"Robust increase in supply by local vessel dilation in globally coupled microvasculature"
Vascular networks pervade all organs of animals and are the paradigm of adaptive transport net- works. In the brain, neural activity induces changes in blood flow by locally dilating vessels in the brain microvasculature. How can the local dilation of a single vessel increase flow-based metabolite supply, given that flows are globally coupled within the microvasculature? Here, we build a theoretical model for flow-based transport and absorption of nutrients and determine how capillary geometry and network topology affect the control by active adaptation. On the level of an individual capillary, we derive ana- lytically how vessel parameters affect the change in supply due to dilation. Solving the supply dynamics for a rat brain microvasculature, we find one parameter regime to dominate physiologically. This regime allows for robust increase in supply independent of the position in the network, which we explain ana- lytically. We show that local coupling of vessels promotes spatially correlated increased supply by dilation.

Edwina Yeo

"Magnetically-driven Cell Aggregation in Blood"
In regenerative medicine magnetic cell targeting aims to deliver stem cells precisely to an injury site. For a safe and effective therapy, the stem cells must be delivered in large numbers under physiological flow conditions, but critically, the aggregation of cells at the target site must be controlled. Mathematical modelling offers insight into the dynamics of the system and allows efficient examination of physiological and therapeutic parameters. We adapt existing continuum models for the delivery of magnetic nanoparticles [2] to magnetic cell delivery. Cells are captured on the vessel wall closest to the magnet, this leads to the growth of a solid cell aggregate which obstructs the flow. We determine how the interplay between aggregate growth af- fects stem cell capture and identify parameter regimes in which potentially dangerous vessel blockage is predicted.

Hosted by eSMB2020 Follow
Virtual conference of the Society for Mathematical Biology, 2020.