Session: 3.3 - Open Source CFD

Paper Number: 158086

158086 - Simulating the Steady Hemolymph Flow and Transient Perfusion in the Forewing Vein Network of Drosophila Using OpenFOAM 

Abstract: 

The wings of Drosophila contain a simple network of veins through which blood (hemolymph) flows and supplies the wings with vital resources to maintain healthy function. Understanding the hemolymph flow through the vein network and resultant perfusion can lend insights into how the design of the Drosophila wing vein network fosters the efficient dispersal of blood throughout that network.  However, the pattern of hemolymph flow through this network remains poorly understood. As to our knowledge, there is no literature on simulating steady hemolymph flow and transient perfusion through the wing vein network of the Drosophila. Using computational fluid dynamics (CFD) is an easier way to gain insight into the flow dynamics inside the small and complex wing vein network of the Drosophila, versus attempting direct observations of a live insect. In the case of using free and open-source CFD software, it is also more cost effective.

In our investigation, we studied the steady hemolymph flow and resultant transient perfusion through the Drosophila wing vein network using OpenFOAM. For mesh generation, we also made use of SALOME, another open-source software, to generate a mesh for our model of the Drosophila wing vein network. This was done through utilization of SALOME's meshing toolbox and Netgen, a mesh generation algorithm from the NGSolve finite element analysis software, which is included in SALOME. Meshes generated using SALOME were then imported to OpenFOAM for use in simulations. 

We utilized two of OpenFOAM's solvers for obtaining solutions to governing differential equations: simpleFOAM and scalarTransportFOAM. The solver simpleFOAM employs the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm to solve the Navier-Stokes equation, while scalarTransportFOAM utilizes a finite-volume method to obtain a solution to the convection-diffusion equation for a user-specified transported scalar. We first utilized the simpleFOAM solver to obtain a steady-state solution to the Navier-Stokes equation for incompressible flow. Then, the velocity field obtained from the simpleFOAM solver was used with scalarTransportFOAM to simulate the transport of dye injected at the inlet throughout the Drosophila wing vein network. The dye was represented by the scalar in the convention-diffusion equation.

We examined the results of these simulations for their validity by studying the convergence of results across increasing refinements of the mesh. Using the open-source data visualization software Paraview,  we visualized the steady velocity field and streamlines for the Drosophila wing vein network and rendered an animation of the advection of dye through the vein network using data obtained from the OpenFOAM simulations.

Our results show that hemolymph flow speed is highest along the shortest path through the Drosophila wing vein network from the inlet to the outlet. Furthermore, we found two vein segments on the Drosophila wing where the simulations report a flow speed very close to zero. In our simulations of transient perfusion, the dye did not reach the interior of these two segments even after an extended period. This suggests that not all vein segments in the Drosophila wing vein network play a vital role in hemolymph circulation. The results of our dye transport simulation show that most of the dye entering the wing vein network will take the shortest path to the outlet and exit the network. The rest of the dye takes a path following the leading edge vein before permeating in direction of the trailing edge and exiting through the outlet. Lastly, our investigation demonstrates that OpenFOAM can be used to effectively simulate steady flow and transient perfusion in insect wing vein networks.

Presenting Author: Jacob White University of Nebraska Omaha

Presenting Author Biography: Jacob White is a graduate student in mathematics at the University of Nebraska Omaha, where he works under the supervision of Dr. Mahboub Baccouch and Dr. Sangjin Ryu in numerical partial differential equations and computational fluid dynamics.