Advection, diffusion and delivery over a network

Many biological, geophysical and technological systems involve the transport of resource over a network. In this paper we present an algorithm for calculating the exact concentration of resource at any point in space or time, given that the resource in the network is lost or delivered out of the network at a given rate, while being subject to advection and diffusion. We consider the implications of advection, diffusion and delivery for simple models of glucose delivery through a vascular network, and conclude that in certain circumstances, increasing the volume of blood and the number of glucose transporters can actually decrease the total rate of glucose delivery. We also consider the case of empirically determined fungal networks, and analyze the distribution of resource that emerges as such networks grow over time. Fungal growth involves the expansion of fluid filled vessels, which necessarily involves the movement of fluid. In three empirically determined fungal networks we found that the minimum currents consistent with the observed growth would effectively transport resource throughout the network over the time-scale of growth. This suggests that in foraging fungi, the active transport mechanisms observed in the growing tips may not be required for long range transport.Comment: 54 pages including appendix, 10 figure

Evaluating transport in irregular pore networks

A general approach for investigating transport phenomena in porous media is presented. This approach has the capacity to represent various kinds of irregularity in porous media without the need for excessive detail or computational effort. The overall method combines a generalized effective medium approximation (EMA) with a macroscopic continuum model in order to derive a transport equation with explicit analytical expressions for the transport coefficients. The proposed form of the EMA is an anisotropic and heterogeneous extension of Kirkpatrick's EMA which allows the overall model to account for microscopic alterations in connectivity (with the locations of the pores and the orientation and length of the throat) as well as macroscopic variations in transport properties. A comparison to numerical results for randomly generated networks with different properties is given, indicating the potential for this methodology to handle cases that would pose significant difficulties to many other analytical models

Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications

Resorting to a multiphase modelling framework, tumours are described here as a mixture of tumour and host cells within a porous structure constituted by a remodelling extracellular matrix (ECM), which is wet by a physiological extracellular fluid. The model presented in this article focuses mainly on the description of mechanical interactions of the growing tumour with the host tissue, their influence on tumour growth, and the attachment/detachment mechanisms between cells and ECM. Starting from some recent experimental evidences, we propose to describe the interaction forces involving the extracellular matrix via some concepts coming from viscoplasticity. We then apply the model to the description of the growth of tumour cords and the formation of fibrosis

The role of taxonomic expertise in interpretation of metabarcoding studies

Abstract The performance of DNA metabarcoding approaches for characterizing biodiversity can be influenced by multiple factors. Here, we used morphological assessment of taxa in zooplankton samples to develop a large barcode database and to assess the congruence of taxonomic identification with metabarcoding under different conditions. We analysed taxonomic assignment of metabarcoded samples using two genetic markers (COI, 18S V1–2), two types of clustering into molecular operational taxonomic units (OTUs, ZOTUs), and three methods for taxonomic assignment (RDP Classifier, BLASTn to GenBank, BLASTn to a local barcode database). The local database includes 1042 COI and 1108 18S (SSU) barcode sequences, and we added new high-quality sequences to GenBank for both markers, including 109 contributions at the species level. The number of phyla detected and the number of taxa identified to phylum varied between a genetic marker and among the three methods used for taxonomic assignments. Blasting the metabarcodes to the local database generated multiple unique contributions to identify OTUs and ZOTUs. We argue that a multi-marker approach combined with taxonomic expertise to develop a curated, vouchered, local barcode database increases taxon detection with metabarcoding, and its potential as a tool for zooplankton biodiversity surveys

Dispersion in Rectangular Networks: Effective Diffusivity and Large-Deviation Rate Function

The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply and urban pollution. Motivated by this, we develop a large-deviation theory that predicts the evolution of the concentration of a scalar released in a rectangular network in the limit of large time $t \gg 1$. This theory provides an approximation for the concentration that remains valid for large distances from the centre of mass, specifically for distances up to $O(t)$ and thus much beyond the $O(t^{1/2})$ range where a standard Gaussian approximation holds. A byproduct of the approach is a closed-form expression for the effective diffusivity tensor that governs this Gaussian approximation. Monte Carlo simulations of Brownian particles confirm the large-deviation results and demonstrate their effectiveness in describing the scalar distribution when $t$ is only moderately large

Differential microRNA profiles of intramuscular and secreted extracellular vesicles in human tissue-engineered muscle

Exercise affects the expression of microRNAs (miR/s) and muscle-derived extracellular vesicles (EVs). To evaluate sarcoplasmic and secreted miR expression in human skeletal muscle in response to exercise-mimetic contractile activity, we utilized a three-dimensional tissue-engineered model of human skeletal muscle (“myobundles”). Myobundles were subjected to three culture conditions: no electrical stimulation (CTL), chronic low frequency stimulation (CLFS), or intermittent high frequency stimulation (IHFS) for 7 days. RNA was isolated from myobundles and from extracellular vesicles (EVs) secreted by myobundles into culture media; miR abundance was analyzed by miRNA-sequencing. We used edgeR and a within-sample design to evaluate differential miR expression and Pearson correlation to evaluate correlations between myobundle and EV populations within treatments with statistical significance set at p < 0.05. Numerous miRs were differentially expressed between myobundles and EVs; 116 miRs were differentially expressed within CTL, 3 within CLFS, and 2 within IHFS. Additionally, 25 miRs were significantly correlated (18 in CTL, 5 in CLFS, 2 in IHFS) between myobundles and EVs. Electrical stimulation resulted in differential expression of 8 miRs in myobundles and only 1 miR in EVs. Several KEGG pathways, known to play a role in regulation of skeletal muscle, were enriched, with differentially overrepresented miRs between myobundle and EV populations identified using miEAA. Together, these results demonstrate that in vitro exercise-mimetic contractile activity of human engineered muscle affects both their expression of miRs and number of secreted EVs. These results also identify novel miRs of interest for future studies of the role of exercise in organ-organ interactions in vivo

Dispersive transport and symmetry of the dispersion tensor in porous media

The macroscopic laws controlling the advection and diffusion of solute at the scale of the porous continuum are derived in a general manner that does not place limitations on the geometry and time evolution of the pore space. Special focus is given to the definition and symmetry of the dispersion tensor that is controlling how a solute plume spreads out. We show that the dispersion tensor is not symmetric and that the asymmetry derives from the advective derivative in the pore-scale advection-diffusion equation. When flow is spatially variable across a voxel, such as in the presence of a permeability gradient, the amount of asymmetry can be large. As first shown by Auriault [J.-L. Auriault et al. Transp. Porous Med. 85, 771 (2010)TPMEEI0169-391310.1007/s11242-010-9591-y] in the limit of low Péclet number, we show that at any Péclet number, the dispersion tensor D_{ij} satisfies the flow-reversal symmetry D_{ij}(+q)=D_{ji}(-q) where q is the mean flow in the voxel under analysis; however, Reynold's number must be sufficiently small that the flow is reversible when the force driving the flow changes sign. We also demonstrate these symmetries using lattice-Boltzmann simulations and discuss some subtle aspects of how to measure the dispersion tensor numerically. In particular, the numerical experiments demonstrate that the off-diagonal components of the dispersion tensor are antisymmetric which is consistent with the analytical dependence on the average flow gradients that we propose for these off-diagonal components

A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone

Recommended standardized procedures for determining exhaled lower respiratory nitric oxide and nasal nitric oxide have been developed by task forces of the European Respiratory Society and the American Thoracic Society. These recommendations have paved the way for the measurement of nitric oxide to become a diagnostic tool for specific clinical applications. It would be desirable to develop similar guidelines for the sampling of other trace gases in exhaled breath, especially volatile organic compounds (VOCs) which reflect ongoing metabolism. The concentrations of water-soluble, blood-borne substances in exhaled breath are influenced by: (i) breathing patterns affecting gas exchange in the conducting airways; (ii) the concentrations in the tracheo-bronchial lining fluid; (iii) the alveolar and systemic concentrations of the compound. The classical Farhi equation takes only the alveolar concentrations into account. Real-time measurements of acetone in end-tidal breath under an ergometer challenge show characteristics which cannot be explained within the Farhi setting. Here we develop a compartment model that reliably captures these profiles and is capable of relating breath to the systemic concentrations of acetone. By comparison with experimental data it is inferred that the major part of variability in breath acetone concentrations (e.g., in response to moderate exercise or altered breathing patterns) can be attributed to airway gas exchange, with minimal changes of the underlying blood and tissue concentrations. Moreover, it is deduced that measured end-tidal breath concentrations of acetone determined during resting conditions and free breathing will be rather poor indicators for endogenous levels. Particularly, the current formulation includes the classical Farhi and the Scheid series inhomogeneity model as special limiting cases.Comment: 38 page