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Fluid Dynamics in Heart Development: Effects of Hematocrit and Trabeculation

Recent \emph{in vivo} experiments have illustrated the importance of understanding the hemodynamics of heart morphogenesis. In particular, ventricular trabeculation is governed by a delicate interaction between hemodynamic forces, myocardial activity, and morphogen gradients, all of which are coupled to genetic regulatory networks. The underlying hemodynamics at the stage of development in which the trabeculae form is particularly complex, given the balance between inertial and viscous forces. Small perturbations in the geometry, scale, and steadiness of the flow can lead to changes in the overall flow structures and chemical morphogen gradients, including the local direction of flow, the transport of morphogens, and the formation of vortices. The immersed boundary method was used to solve the fluid-structure interaction problem of fluid flow moving through a two chambered heart of a zebrafish (\emph{Danio rerio}), with a trabeculated ventricle, at $96\ hpf$ (hours post fertilization). Trabeculae heights and hematocrit were varied, and simulations were conducted for two orders of magnitude of Womersley number, extending beyond the biologically relevant range ($0.2$ -- $12.0$). Both intracardial and intertrabecular vortices formed in the ventricle for biologically relevant parameter values. The bifurcation from smooth streaming flow to vortical flow depends upon the trabeculae geometry, hematocrit, and $Wo$. This work shows the importance of hematocrit and geometry in determining the bulk flow patterns in the heart at this stage of development.

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