Bifurcations in valveless pumping techniques from a coupled fluid-structure-electrophysiology model in heart development

We explore an embryonic heart model that couples electrophysiology and muscle-force generation to flow induced using a $2D$ fluid-structure interaction framework based on the immersed boundary method. The propagation of action potentials are coupled to muscular contraction and hence the overall pumping dynamics. In comparison to previous models, the electro-dynamical model does not use prescribed motion to initiate the pumping motion, but rather the pumping dynamics are fully coupled to an underlying electrophysiology model, governed by the FitzHugh-Nagumo equations. Perturbing the diffusion parameter in the FitzHugh-Nagumo model leads to a bifurcation in dynamics of action potential propagation. This bifurcation is able to capture a spectrum of different pumping regimes, with dynamic suction pumping and peristaltic-like pumping at the extremes. We find that more bulk flow is produced within the realm of peristaltic-like pumping.Comment: 11 pages, 13 figures. arXiv admin note: text overlap with arXiv:1610.0342

Pulsing corals: A story of scale and mixing

Effective methods of fluid transport vary across scale. A commonly used dimensionless number for quantifying the effective scale of fluid transport is the Reynolds number, Re, which gives the ratio of inertial to viscous forces. What may work well for one Re regime may not produce significant flows for another. These differences in scale have implications for many organisms, ranging from the mechanics of how organisms move through their fluid environment to how hearts pump at various stages in development. Some organisms, such as soft pulsing corals, actively contract their tentacles to generate mixing currents that enhance photosynthesis. Their unique morphology and intermediate scale where both viscous and inertial forces are significant make them a unique model organism for understanding fluid mixing. In this paper, 3D fluid-structure interaction simulations of a pulsing soft coral are used to quantify fluid transport and fluid mixing across a wide range of Re. The results show that net transport is negligible for $Re<10$, and continuous upward flow is produced for $Re\geq 10$.Comment: 8 pages, 8 figure

Three-dimensional low Reynolds number flows near biological filtering and protective layers

Mesoscale filtering and protective layers are replete throughout the natural world. Within the body, arrays of extracellular proteins, microvilli, and cilia can act as both protective layers and mechanosensors. For example, blood flow profiles through the endothelial surface layer determine the amount of shear stress felt by the endothelial cells and may alter the rates at which molecules enter and exit the cells. Characterizing the flow profiles through such layers is therefore critical towards understanding the function of such arrays in cell signaling and molecular filtering. External filtering layers are also important to many animals and plants. Trichomes (the hairs or fine outgrowths on plants) can drastically alter both the average wind speed and profile near the leaf's surface, affecting the rates of nutrient and heat exchange. In this paper, dynamically scaled physical models are used to study the flow profiles outside of arrays of cylinders that represent such filtering and protective layers. In addition, numerical simulations using the Immersed Boundary Method are used to resolve the 3D flows within the layers. The experimental and computational results are compared to analytical results obtained by modeling the layer as a homogeneous porous medium with free flow above the layer. The experimental results show that the bulk flow is well described by simple analytical models. The numerical results show that the spatially averaged flow within the layer is well described by the Brinkman model. The numerical results also demonstrate that the flow can be highly 3D with fluid moving into and out of the layer. These effects are not described by the Brinkman model and may be significant for biologically relevant volume fractions. The results of this paper can be used to understand how variations in density and height of such structures can alter shear stresses and bulk flows.Comment: 28 pages, 10 figure

Social and Policy Implications of Low-Level Exposures to Chemicals

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