Computational Biology: Biological Transport and Networks

The embryonic yolk sac provides a unique window into the emergence of blood flow and the early development of vascular networks. Using high-speed time-lapse microscopy, we extract vessel centerlines, construct attributed graphs, and infer time-resolved flow fields across developmental stages. These measurements reveal how pulsatile forcing and local hemodynamic variability shape the remodeling of the vascular plexus. By linking experimental data with physics-based models of network adaptation, we aim to uncover how mechanical and geometric cues drive coordinated vascular growth.

Access the preprint, code, and dataset.

Biological transport networks—such as blood vessels, plant vasculature, or neuronal networks—are naturally modeled as metric graphs where edges carry flow or diffusive signals and nodes enforce conservation laws. These high-density networks encode effective material and functional properties. To investigate how these properties emerge, we develop a continuum-limit framework in the dense vertex limit as edge lengths  shrink to 0. This replaces edgewise differential equations with a coarse-grained partial differential equation (PDE) defined on the continuous space occupied by the network. This framework captures how real-world, space-filling networks operate simultaneously across system-wide and local scales, using the continuum as a feature.

The derivation naturally introduces an edge-conductivity tensor, an edge-capacity function, and a vertex number density, which together describe how each microscopic patch of the graph contributes to macroscopic behavior. All macroscopic parameters are computed from first principles via a systematic discrete-to-continuous homogenization, revealing an anomalous effective embedding dimension arising from the homogenized diffusivity \(d_{eff}\).

Access the preprint “A continuum limit for dense spatial networks.”

Biological transport systems — such as neuronal and vascular networks — are remarkable in their ability to build themselves. These systems grow and reshape through the relocation and consumption of mass, often relying on the very transport pathways they are creating. However, this dependence of growth on the transport of building material is frequently overlooked in self-organizing growth models.

Our project develops a one-dimensional transport network model that links material flow to network growth and retraction. By modeling tip growth as dependent on local concentrations of transported material, we can simulate the dynamic feedback between transport and structure.

Inspired by the active processes of neuronal development, our work explores how local material delivery and recycling shape evolving networks. In collaboration with CCBx and CCB Scope, we are testing our theoretical predictions against the observed growth trajectories of real neurons.