Accuracy of 1D microvascular flow models in the limit of low Reynolds numbers.

We describe results of numerical simulations of steady flows in tubes with branch bifurcations using fully 3D and reduced 1D geometries. The intent is to delineate the range of validity of reduced models used for simulations of flows in microcapillary networks, as a function of the flow Reynolds number Re. Results from model problems indicate that for Re less than 1 and possibly as high as 10, vasculatures may be represented by strictly 1D Poiseuille flow geometries with flow variation in the axial dimensions only. In that range flow rate predictions in the different branches generated by 1D and 3D models differ by a constant factor, independent of Re. When the cross-sectional areas of the branches are constant these differences are generally small and appear to stem from an uncertainty of how the individual branch lengths are defined. This uncertainty can be accounted for by a simple geometrical correction. For non-constant cross-sections the differences can be much more significant. If additional corrections for the presence of branch junctions and flow area variations are not taken into account in 1D models of complex vasculatures, the resultant flow predictions should be interpreted with caution.

Bubble-induced acoustic micromixing.

A mixing technique based on the principle of bubble-induced acoustic microstreaming was developed. The mixer consists of a piezoelectric disk that is attached to a reaction chamber, which is designed in such a way that a set of air bubbles with desirable size is trapped in the solution. Fluidic experiments showed that air bubbles resting on a solid surface and set into vibration by the sound field generated steady circulatory flows, resulting in global convection flows and thus rapid mixing. The time to fully mix a 22 microL chamber is significantly reduced from hours (for a pure diffusion-based mixing) to tens of seconds. Numerical simulations showed that the induced flowfield and thus degree of mixing strongly depend on bubble positions. Optimal simulated mixing results were obtained for staggered bubble distribution that minimizes the number of internal flow stagnation regions. Immunomagnetic cell capture experiments showed that acoustic microstreaming provided efficient mixing of bacterial cell (Esherichia coli K12) matrix suspended in blood with magnetic capture beads, resulting in highly effective immunomagnetic cell capture. Bacterial viability assay experiments showed that acoustic microstreaming has a relatively low shear strain field since the blood cells and bacteria remained intact after mixing. Acoustic microstreaming has many advantages over most existing chamber micromixing techniques, including simple apparatus, ease of implementation, low power consumption (2 mW), and low cost.

Convected element method for simulation of angiogenesis.

We describe a novel Convected Element Method (CEM) for simulation of formation of functional blood vessels induced by tumor-generated growth factors in a process called angiogenesis. Angiogenesis is typically modeled by a convection-diffusion-reaction equation defined on a continuous domain. A difficulty arises when a continuum approach is used to represent the formation of discrete blood vessel structures. CEM solves this difficulty by using a hybrid continuous/discrete solution method allowing lattice-free tracking of blood vessel tips that trace out paths that subsequently are used to define compact vessel elements. In contrast to more conventional angiogenesis modeling, the new branches form evolving grids that are capable of simulating transport of biological and chemical factors such as nutrition and anti-angiogenic agents. The method is demonstrated on expository vessel growth and tumor response simulations for a selected set of conditions, and include effects of nutrient delivery and inhibition of vessel branching. Initial results show that CEM can predict qualitatively the development of biologically reasonable and fully functional vascular structures. Research is being carried out to generalize the approach which will allow quantitative predictions.