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.

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.

Blood flow in microvascular networks: a study in nonlinear biology.

Plasma skimming and the Fahraeus-Lindqvist effect are well-known phenomena in blood rheology. By combining these peculiarities of blood flow in the microcirculation with simple topological models of microvascular networks, we have uncovered interesting nonlinear behavior regarding blood flow in networks. Nonlinearity manifests itself in the existence of multiple steady states.

Stability of a microvessel subject to structural adaptation of diameter and wall thickness.

Vascular adaptation--or structural changes of microvessels in response to physical and metabolic stresses--can influence physiological processes like angiogenesis and hypertension. To better understand the influence of these stresses on adaptation, Pries et al. (1998, 2001a,b, 2005) have developed a computational model for microvascular adaptation.

Multiple equilibrium states in a micro-vascular network.

We use a simple model of micro-vascular blood flow to explore conditions that give rise to multiple equilibrium states in a three-node micro-vascular network. The model accounts for two primary rheological effects: the Fåhraeus-Lindqvist effect, which describes the apparent viscosity of blood in a vessel, and the plasma skimming effect, which governs the separation of red blood cells at diverging nodes. We show that multiple equilibrium states are possible, and we use our analytical and computational tools to design an experiment for validation.

Bistability in a simple fluid network due to viscosity contrast.

We study the existence of multiple equilibrium states in a simple fluid network using Newtonian fluids and laminar flow. We demonstrate theoretically the presence of hysteresis and bistability, and we confirm these predictions in an experiment using two miscible fluids of different viscosity-sucrose solution and water. Possible applications include blood flow, microfluidics, and other network flows governed by similar principles.

Oscillations in a simple microvascular network.

We have identified the simplest topology that will permit spontaneous oscillations in a model of microvascular blood flow that includes the plasma skimming effect and the Fahraeus-Lindqvist effect and assumes that the flow can be described by a first-order wave equation in blood hematocrit. Our analysis is based on transforming the governing partial differential equations into delay differential equations and analyzing the associated linear stability problem. In doing so we have discovered three dimensionless parameters, which can be used to predict the occurrence of nonlinear oscillations.