Tradeoffs between energy efficiency and mechanical response in fluid flow networks

Biological systems are influenced by fluid mechanics at nearly all spatiotemporal scales. This broad relevance of fluid mechanics to biology has been increasingly appreciated by engineers and biologists alike, leading to continued expansion of research in the field of biological fluid dynamics. While this growth is exciting, it can present a barrier to researchers seeking a concise introduction to key challenges and opportunities for progress in the field. Rather than attempt...

The model by Hu and Cai [Phys. Rev. Lett., Vol. 111(13) (2013)1 ] describes the self-organization of vascular networks for transport of fluids from source to sinks. Diameters, and thereby conductances, of vessel segments evolve so as to minimize a cost functional E. The cost is the trade-off between the power required for pumping the fluid and the energy consumption for vessel maintenance. The model has been used to show emergence of cyclic structures in the presence of local...

To address the issue of computational efficiency related to the modelling of blood flow in complex networks, we derive a family of nonlinear lumped-parameter models for blood flow in compliant vessels departing from a well-established one-dimensional model. These 0D models must preserve important nonlinear properties of the original 1D model: the nonlinearity of the pressure-area relation and the pressure-dependent parameters characterizing the 0D models, the resistance $R$ a...

A central debate in biology has been the allometric scaling of metabolic rate. Kleiber's observation that animals' basal metabolic rate scales to the 3/4-power of body mass (Kleiber's rule) has been the prevailing hypothesis in the last eight decades. Increasingly, more evidences are supporting the alternative 2/3-power scaling rule, especially for smaller animals. The 2/3-rule dates back to before Kleiber's time and was thought to originate from the surface to volume relatio...

Complex distribution networks are pervasive in biology. Examples include nutrient transport in the slime mold \emph{Physarum polycephalum} as well as mammalian and plant venation. Adaptive rules are believed to guide development of these networks and lead to a reticulate, hierarchically nested topology that is both efficient and resilient against perturbations. However, as of yet no mechanism is known that can generate such networks on all scales. We show how hierarchically o...

In this paper, we study the role of boundary conditions on the optimal shape of a dyadic tree in which flows a Newtonian fluid. Our optimization problem consists in finding the shape of the tree that minimizes the viscous energy dissipated by the fluid with a constrained volume, under the assumption that the total flow of the fluid is conserved throughout the structure. These hypotheses model situations where a fluid is transported from a source towards a 3D domain into which...

Within animals, oxygen exchange occurs within networks containing potentially billions of microvessels that are distributed throughout the animal's body. Innovative imaging methods now allow for mapping of the architecture and blood flows within real microvascular networks. However, these data streams have so far yielded little new understanding of the physical principles that underlie the organization of microvascular networks, which could allow healthy networks to be quanti...

It was hypothesized that the structures of biological transport networks are the result of either energy consumption or adaptation dynamics. Although approaches based on these hypotheses can produce optimal network and form loop structures, we found that neither possesses complete ability to generate complex networks that resemble vascular network in living organisms, which motivated us to propose a hybrid approach. This approach can replicate the path dependency phenomenon o...

In this paper, a multiscale constitutive framework for one-dimensional blood flow modeling is presented and discussed. By analyzing the asymptotic limits of the proposed model, it is shown that different types of blood propagation phenomena in arteries and veins can be described through an appropriate choice of scaling parameters, which are related to distinct characterizations of the fluid-structure interaction mechanism (whether elastic or viscoelastic) that exist between v...

Recent work on self-organized remodeling of vasculature in slime-mold, leaf venation systems and vessel systems in vertebrates has put forward a plethora of potential adaptation mechanisms. All these share the underlying hypothesis of a flow-driven machinery, meant to alter rudimentary vessel networks in order to optimize the system's dissipation, flow uniformity, or more, with different versions of constraints. Nevertheless, the influence of environmental factors on the long...