Modeling transit time distributions in microvascular networks.

The time a red blood cell (RBC) spends in the microvasculature is of prime importance for a number of physiological processes. In this work, we present a methodology for computing an approximation of the so-called transit time distribution (TTD), i.e.

Model Microvascular Networks Can Have Many Equilibria.

We show that large microvascular networks with realistic topologies, geometries, boundary conditions, and constitutive laws can exhibit many steady-state flow configurations. This is in direct contrast to most previous studies which have assumed, implicitly or explicitly, that a given network can only possess one equilibrium state. While our techniques are general and can be applied to any network, we focus on two distinct network types that model human tissues: perturbed honeycomb networks and random networks generated from Voronoi diagrams.

Spiral and Rotor Patterns Produced by Fairy Ring Fungi.

A broad class of soil fungi form the annular patterns known as 'fairy rings' and provide one of the only means to observe spatio-temporal dynamics of otherwise cryptic fungal growth processes in natural environments. We present observations of novel spiral and rotor patterns produced by fairy ring fungi and explain these behaviors mathematically by first showing that a well known model of fairy ring fungal growth and the Gray-Scott reaction-diffusion model are mathematically equivalent. We then use bifurcation analysis and numerical simulations to identify the conditions under which spiral waves and rotors can arise.

Oscillations and Multiple Equilibria in Microvascular Blood Flow.

We investigate the existence of oscillatory dynamics and multiple steady-state flow rates in a network with a simple topology and in vivo microvascular blood flow constitutive laws. Unlike many previous analytic studies, we employ the most biologically relevant models of the physical properties of whole blood. Through a combination of analytic and numeric techniques, we predict in a series of two-parameter bifurcation diagrams a range of dynamical behaviors, including multiple equilibria flow configurations, simple oscillations in volumetric flow rate, and multiple coexistent limit cycles at physically realizable parameters.

Observations of spontaneous oscillations in simple two-fluid networks.

We investigate the laminar flow of two-fluid mixtures inside a simple network of interconnected tubes. The fluid system is composed of two miscible Newtonian fluids of different viscosity which do not mix and remain as nearly distinct phases. Downstream of a diverging network junction the two fluids do not necessarily split in equal fraction and thus heterogeneity is introduced into network.

Local behavioral rules sustain the cell allocation pattern in the combs of honey bee colonies (Apis mellifera).

In the beeswax combs of honey bees, the cells of brood, pollen, and honey have a consistent spatial pattern that is sustained throughout the life of a colony. This spatial pattern is believed to emerge from simple behavioral rules that specify how the queen moves, where foragers deposit honey/pollen and how honey/pollen is consumed from cells. Prior work has shown that a set of such rules can explain the formation of the allocation pattern starting from an empty comb.