Flow rate of transport network controls uniform metabolite supply to tissue

Meigel, Felix J.; Alim, Karen

doi:10.1098/rsif.2018.0075

Cited by 22 publications

(31 citation statements)

References 58 publications

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“…One may also consider a direct postulation of cross-network feedback in the adaptation dynamics to account for the actual network structures. Recent studies regarding solute transport and optimization of cross-wall transport [53,54] might present a suitable basis for such an approach. Eventually, we strive toward a generalized formulation of environmental factors whose influence can be depicted in the form of local adaptation rules of complex flow networks.…”

Section: Discussionmentioning

confidence: 99%

How to pare a pair: Topology control and pruning in intertwined complex networks

Kramer

Modes

2020

Phys. Rev. Research

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Recent work on self-organized remodeling of vasculature in slime molds, 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-term adaptation dynamics as well as the network structure and function have not been fully understood. Therefore, interwoven capillary systems such as those found in the liver, kidney, and pancreas present a novel challenge and key opportunity regarding the field of coupled distribution networks. We here present an advanced version of the discrete Hu-Cai model, coupling two spatial networks in three dimensions. We show that spatial coupling of two flow-adapting networks can control the onset of topological complexity in concert with short-term flow fluctuations. We find that both fluctuation-induced and spatial coupling induced topology transitions undergo curve collapse, obeying simple functional rescaling. Further, our approach results in an alternative form of Murray's law, which incorporates local vessel interactions and flow interactions. This geometric law allows for the estimation of the model parameters in ideal Kirchhoff networks and respective experimentally acquired network skeletons.

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Section: Discussionmentioning

confidence: 99%

How to pare a pair: Topology control and pruning in intertwined complex networks

Kramer

Modes

2020

Phys. Rev. Research

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show abstract

“…One may also consider a direct postulation of cross-network feedback in the adaptation dynamics to account for the actual network structures. Recent studies regarding solute transport and op-timization of cross-wall transport [53,54] might present a suitable basis for such an approach. Eventually, we strive towards a generalized formulation of environmental factors whose influence can be depicted in the form of local adaptation rules of complex flow networks.…”

Section: Discussionmentioning

confidence: 99%

How to Pare a Pair: Topology Control and Pruning in Intertwined Complex Networks

Kramer

Modes

2019

Preprint

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Recent work on self-organized remodelling of vasculature in slimemold, 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 prune primary plexi 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-term adaptation dynamics as well as the networks structure and function have not been fully understood. Therefore, interwoven capillary systems such as found in the liver, kidney and pancreas, present a novel challenge and key opportunity regarding the field of coupled distribution networks. We here present an advanced version of the discrete Hu-Cai model, coupling two spatial networks in 3D. We show that spatial coupling of two flow-adapting networks can control the onset of topological complexity given the system is exposed to shortterm flow fluctuations. Further, our approach results in an alternative form of Murray's law, which incorporates local vessel interactions and flow interactions. This scaling law allows for the estimation of the parameters in lumped parameter models and respective experimentally acquired network skeletons.

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“…Graph theoretic perspectives have proven useful in characterising, classifying and understanding transport in various examples of biological networks [8,9,10]. The approach we take in this paper uses concepts from spectral graph theory, where a linear operator describing a particular physical property or characteristic of the network is decomposed into its eigenspectum.…”

Section: Introductionmentioning

confidence: 99%

Spectral graph theory efficiently characterises ventilation heterogeneity in lung airway networks

Whitfield

Latimer

Horsley

et al. 2020

Preprint

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AbstractThis paper introduces a linear operator for the purposes of quantifying the spectral properties of transport within resistive trees, such as airflow in lung airway networks. The operator, which we call the Maury matrix, acts only on the terminal nodes of the tree and is equivalent to the adjacency matrix of a complete graph summarising the relationships between all pairs of terminal nodes. We show that the eigenmodes of the Maury operator have a direct physical interpretation as the relaxation, or resistive, modes of the network. We apply these findings to both idealised and image-based models of ventilation in lung airway trees and show that the spectral properties of the Maury matrix characterise the flow asymmetry in these networks more concisely than the Laplacian modes, and that eigenvector centrality in the Maury spectrum is closely related to the phenomenon of ventilation heterogeneity caused by airway narrowing or obstruction. This method has applications in dimensionality reduction in simulations of lung mechanics, as well as for characterisation of models of the airway tree derived from medical images.

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Flow rate of transport network controls uniform metabolite supply to tissue

Cited by 22 publications

References 58 publications

How to pare a pair: Topology control and pruning in intertwined complex networks

How to pare a pair: Topology control and pruning in intertwined complex networks

How to Pare a Pair: Topology Control and Pruning in Intertwined Complex Networks

Spectral graph theory efficiently characterises ventilation heterogeneity in lung airway networks

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