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  • 1
    Language: English
    In: Journal of Biomechanics, Jan 3, 2012, Vol.45(1), p.107(9)
    Description: To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jbiomech.2011.09.015 Byline: Tiina Roose (a), Melody A. Swartz (b) Keywords: Interstitial flow; Tissue fluid balance; Darcy flow; Tissue architecture; Capillary Abstract: Lymphatic capillary drainage of interstitial fluid under both steady-state and inflammatory conditions is important for tissue fluid balance, cancer metastasis, and immunity. Lymphatic drainage function is critically coupled to the fluid mechanical properties of the interstitium, yet this coupling is poorly understood. Here we sought to effectively model the lymphatic-interstitial fluid coupling and ask why the lymphatic capillary network often appears with roughly a hexagonal architecture. We use homogenization method, which allows tissue-scale lymph flow to be integrated with the microstructural details of the lymphatic capillaries, thus gaining insight into the functionality of lymphatic anatomy. We first describe flow in lymphatic capillaries using the Navier-Stokes equations and flow through the interstitium using Darcy's law. We then use multiscale homogenization to derive macroscale equations describing lymphatic drainage, with the mouse tail skin as a basis. We find that the limiting resistance for fluid drainage is that from the interstitium into the capillaries rather than within the capillaries. We also find that between hexagonal, square, and parallel tube configurations of lymphatic capillary networks, the hexagonal structure is the most efficient architecture for coupled interstitial and capillary fluid transport; that is, it clears the most interstitial fluid for a given network density and baseline interstitial fluid pressure. Thus, using homogenization theory, one can assess how vessel microstructure influences the macroscale fluid drainage by the lymphatics and demonstrate why the hexagonal network of dermal lymphatic capillaries is optimal for interstitial tissue fluid clearance. Author Affiliation: (a) Bioengineering Group, School of Engineering Sciences, University Road, University of Southampton, SO17 1BJ, United Kingdom (b) Institute of Bioengineering and Swiss Institute for Experimental Cancer Research (ISREC), Ecole Polytechnique Federale de Lausanne (EPFL), 1015 Lausanne, Switzerland Article History: Accepted 28 September 2011
    Keywords: Skin -- Analysis ; Skin -- Mechanical Properties ; Skin -- Models ; Cancer Metastasis -- Analysis ; Cancer Metastasis -- Mechanical Properties ; Cancer Metastasis -- Models ; Permeability -- Analysis ; Permeability -- Mechanical Properties ; Permeability -- Models
    ISSN: 0021-9290
    Source: Cengage Learning, Inc.
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  • 2
    Language: English
    In: Plant and Soil, 2011, Vol.339(1), pp.231-245
    Description: Diversity in phosphorus (P) acquisition strategies was assessed among three species of arbuscular mycorrhizal fungi (AMF) isolated from a single field in Switzerland. Medicago truncatula was used as a test plant. It was grown in a compartmented system with root and root-free zones separated by a fine mesh. Dual radioisotope labeling ( 32 P and 33 P) was employed in the root-free zone as follows: 33 P labeling determined hyphal P uptake from different distances from roots over the entire growth period, whereas 32 P labeling investigated hyphal P uptake close to the roots over the 48 hours immediately prior to harvest. Glomus intraradices , Glomus claroideum and Gigaspora margarita were able to take up and deliver P to the plants from maximal distances of 10, 6 and 1 cm from the roots, respectively. Glomus intraradices most rapidly colonized the available substrate and transported significant amounts of P towards the roots, but provided the same growth benefit as compared to Glomus claroideum , whose mycelium was less efficient in soil exploration and in P uptake and delivery to the roots. These differences are probably related to different carbon requirements by these different Glomus species. Gigaspora margarita provided low P benefits to the plants and formed dense mycelium networks close to the roots where P was probably transiently immobilized. Numerical modeling identified possible mechanisms underlying the observed differences in patterns of mycelium growth. High external hyphal production at the root-fungus interface together with rapid hyphal turnover were pointed out as important factors governing hyphal network development by Gigaspora , whereas nonlinearity in apical branching and hyphal anastomoses were key features for G. intraradices and G. claroideum , respectively.
    Keywords: Arbuscular mycorrhiza ; Extraradical mycelium ; Functional diversity ; Hyphal growth model ; Medicago truncatula ; Phosphorus
    ISSN: 0032-079X
    E-ISSN: 1573-5036
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  • 3
    Language: English
    In: Journal of Biomechanics, 03 January 2012, Vol.45(1), pp.107-115
    Description: Lymphatic capillary drainage of interstitial fluid under both steady-state and inflammatory conditions is important for tissue fluid balance, cancer metastasis, and immunity. Lymphatic drainage function is critically coupled to the fluid mechanical properties of the interstitium, yet this coupling is poorly understood. Here we sought to effectively model the lymphatic-interstitial fluid coupling and ask why the lymphatic capillary network often appears with roughly a hexagonal architecture. We use homogenization method, which allows tissue-scale lymph flow to be integrated with the microstructural details of the lymphatic capillaries, thus gaining insight into the functionality of lymphatic anatomy. We first describe flow in lymphatic capillaries using the Navier–Stokes equations and flow through the interstitium using Darcy's law. We then use multiscale homogenization to derive macroscale equations describing lymphatic drainage, with the mouse tail skin as a basis. We find that the limiting resistance for fluid drainage is that from the interstitium into the capillaries rather than within the capillaries. We also find that between hexagonal, square, and parallel tube configurations of lymphatic capillary networks, the hexagonal structure is the most efficient architecture for coupled interstitial and capillary fluid transport; that is, it clears the most interstitial fluid for a given network density and baseline interstitial fluid pressure. Thus, using homogenization theory, one can assess how vessel microstructure influences the macroscale fluid drainage by the lymphatics and demonstrate why the hexagonal network of dermal lymphatic capillaries is optimal for interstitial tissue fluid clearance.
    Keywords: Interstitial Flow ; Tissue Fluid Balance ; Darcy Flow ; Tissue Architecture ; Capillary ; Medicine ; Engineering ; Anatomy & Physiology
    ISSN: 0021-9290
    E-ISSN: 1873-2380
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  • 4
    Language: English
    In: Journal of Biomechanics, July 2012, Vol.45, pp.S421-S421
    Keywords: Medicine ; Engineering ; Anatomy & Physiology
    ISSN: 0021-9290
    E-ISSN: 1873-2380
    Source: ScienceDirect Journals (Elsevier)
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  • 5
    In: Journal Of Experimental Botany, 2016, Vol. 67(4), pp.1059-1070
    Description: Rigorous mathematical techniques and image-based modelling were used to quantify the effect of root hairs on nutrient uptake and to investigate how uptake is influenced by growing root hairs. In this study, we developed a spatially explicit model for nutrient uptake by root hairs based on X-ray computed tomography images of the rhizosphere soil structure. This work extends our previous work to larger domains and hence is valid for longer times. Unlike the model used previously, which considered only a small region of soil about the root, we considered an effectively infinite volume of bulk soil about the rhizosphere. We asked the question: At what distance away from root surfaces do the specific structural features of root-hair and soil aggregate morphology not matter because average properties start dominating the nutrient transport? The resulting model was used to capture bulk and rhizosphere soil properties by considering representative volumes of soil far from the root and adjacent to the root, respectively. By increasing the size of the volumes that we considered, the diffusive impedance of the bulk soil and root uptake were seen to converge. We did this for two different values of water content. We found that the size of region for which the nutrient uptake properties converged to a fixed value was dependent on the water saturation. In the fully saturated case, the region of soil we needed to consider was only of radius 1.1mm for poorly soil-mobile species such as phosphate. However, in the case of a partially saturated medium (relative saturation 0.3), we found that a radius of 1.4mm was necessary. This suggests that, in addition to the geometrical properties of the rhizosphere, there is an additional effect of soil moisture properties, which extends further from the root and may relate to other chemical changes in the rhizosphere. The latter were not explicitly included in our model.
    Keywords: Phosphate ; Plant–Soil Interaction ; Rhizosphere ; Structural Imaging ; X - Ray Ct.
    ISSN: 0022-0957
    E-ISSN: 1460-2431
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  • 6
    In: New Phytologist, June 2013, Vol.198(4), pp.1023-1029
    Description: Root hairs are known to be highly important for uptake of sparingly soluble nutrients, particularly in nutrient deficient soils. Development of increasingly sophisticated mathematical models has allowed uptake characteristics to be quantified. However, modelling has been constrained by a lack of methods for imaging live root hairs growing in real soils. We developed a plant growth protocol and used Synchrotron Radiation X‐ray Tomographic Microscopy (SRXTM) to uncover the three‐dimensional (3D) interactions of root hairs in real soil. We developed a model of phosphate uptake by root hairs based directly on the geometry of hairs and associated soil pores as revealed by imaging. Previous modelling studies found that root hairs dominate phosphate uptake. By contrast, our study suggests that hairs and roots contribute equally. We show that uptake by hairs is more localized than by roots and strongly dependent on root hair and aggregate orientation. The ability to image hair–soil interactions enables a step change in modelling approaches, allowing a more realistic treatment of processes at the scale of individual root hairs in soil pores.
    Keywords: 3d Reconstruction ; Imaging ; Modelling ; Phosphate ; Root Hair ; ‐Ray
    ISSN: 0028-646X
    E-ISSN: 1469-8137
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  • 7
    Language: English
    In: Plant and Soil, 2016, Vol.401(1), pp.109-123
    Description: Background and aim Recycled sources of phosphorus (P), such as struvite extracted from wastewater, have potential to substitute for more soluble manufactured fertilisers and help reduce the long-term threat to food security from dwindling finite reserves of phosphate rock (PR). This study aimed to determine whether struvite could be a component of a sustainable P fertiliser management strategy for arable crops. Methods A combination of laboratory experiments, pot trials and mathematical modelling of the root system examined the P release properties of commercial fertiliser-grade struvite and patterns of P uptake from a low-P sandy soil by two different crop types, in comparison to more soluble inorganic P fertilisers (di-ammonium phosphate (DAP) and triple super phosphate (TSP)). Results Struvite had greatly enhanced solubility in the presence of organic acid anions; buckwheat, which exudes a high level of organic acids, was more effective at mobilising struvite P than the low level exuder, spring wheat. Struvite granules placed with the seed did not provide the same rate of P supply as placed DAP granules for early growth of spring wheat, but gave equivalent rates of P uptake, yield and apparent fertiliser recovery at harvest, even though only 26 % of struvite granules completely dissolved. Fertiliser mixes containing struvite and DAP applied to spring wheat have potential to provide both optimal early and late season P uptake and improve overall P use efficiency. Conclusions We conclude that the potential resource savings and potential efficiency benefits of utilising a recycled slow release fertiliser like struvite offers a more sustainable alternative to only using conventional, high solubility, PR-based fertilisers. Electronic supplementary material The online version of this article (doi:10.1007/s11104-015-2747-3) contains supplementary material, which is available to authorized users.
    Keywords: Phosphorus ; Struvite ; Wheat ; Buckwheat ; Fertiliser ; Root system modelling ; Organic acids
    ISSN: 0032-079X
    E-ISSN: 1573-5036
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  • 8
    Language: English
    In: Bulletin of Mathematical Biology, 2013, Vol.75(1), pp.49-81
    Description: This study investigates the fluid flow through tissues where lymphatic drainage occurs. Lymphatic drainage requires the use of two valve systems, primary and secondary. Primary valves are located in the initial lymphatics. Overlapping endothelial cells around the circumferential lining of lymphatic capillaries are presumed to act as a unidirectional valve system. Secondary valves are located in the lumen of the collecting lymphatics and act as another unidirectional valve system; these are well studied in contrast to primary valves. We propose a model for the drainage of fluid by the lymphatic system that includes the primary valve system. The analysis in this work incorporates the mechanics of the primary lymphatic valves as well as the fluid flow through the interstitium and that through the walls of the blood capillaries. The model predicts a piecewise linear relation between the drainage flux and the pressure difference between the blood and lymphatic capillaries. The model describes a permeable membrane around a blood capillary, an elastic primary lymphatic valve and the interstitium lying between the two.
    Keywords: Mechanics ; Fluid flow ; Lymphatic system ; Primary lymphatic valves ; Euler–Bernoulli’s beam equation ; Darcy’s law ; Schwarz Christoffel mapping
    ISSN: 0092-8240
    E-ISSN: 1522-9602
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  • 9
    Language: English
    In: Bulletin of Mathematical Biology, 2011, Vol.73(9), pp.2175-2200
    Description: Arbuscular mycorrhizas, associations between plant roots and soil fungi, are ubiquitous among land plants. Arbuscular mycorrhizas can be beneficial for plants by overcoming limitations in nutrient supply. Hyphae, which are long and thin fungal filaments extending from the root surface into the soil, increase the volume of soil accessible for plant nutrient uptake. However, no models so far specifically consider individual hyphae. We developed a mathematical model for nutrient uptake by individual fungal hyphae in order to assess suitable temporal and spatial scales for a new experimental design where fungal uptake parameters are measured on the single hyphal scale. The model was developed based on the conservation of nutrients in an artificial cylindrical soil pore (capillary tube) with adsorbing wall, and analysed based on parameter estimation and non-dimensionalisation. An approximate analytical solution was derived using matched asymptotic expansion. Results show that nutrient influx into a hypha from a small capillary tube is characterized by three phases: Firstly, uptake rapidly decreases as the hypha takes up nutrients, secondly, the depletion zone reaches the capillary wall and thus uptake is sustained by desorption of nutrients from the capillary wall, and finally, uptake goes to zero after nutrients held on the capillary wall have been completely depleted. Simulating different parameter regimes resulted in recommending the use of capillaries filled with hydrogel instead of water in order to design an experiment operating over measurable time scales.
    Keywords: Experimental design ; Fungal nutrient uptake ; Mineral weathering ; Mycorhizosphere ; Phosphorus cycling ; Simulation model
    ISSN: 0092-8240
    E-ISSN: 1522-9602
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  • 10
    In: Plant, Cell & Environment, December 2011, Vol.34(12), pp.2038-2046
    Description: Rice ( L.) secretes far smaller amounts of metal‐complexing phytosiderophores (PS) than other grasses. But there is increasing evidence that it relies on PS secretion for its zinc (Zn) uptake. After nitrogen, Zn deficiency is the most common nutrient disorder in rice, affecting up to 50% of lowland rice soils globally. We developed a mathematical model of PS secretion from roots and resulting solubilization and uptake of Zn, allowing for root growth, diurnal variation in secretion, decomposition of the PS in the soil, and the transport and interaction of the PS and Zn in the soil. A sensitivity analysis showed that with realistic parameter values for rice in submerged soil, the typically observed rates of PS secretion from rice are sufficient and necessary to explain observed rates of Zn uptake. There is little effect of diurnal variation in secretion on cumulative Zn uptake, irrespective of other model parameter values, indicating that the observed diurnal variation is not causally related to Zn uptake efficiency. Rooting density has a large effect on uptake per unit PS secretion as a result of overlap of the zones of influence of neighbouring roots. The effects of other complications in the rice rhizosphere are discussed. This follows up an earlier paper (Arnold et al., 2010, PCE , 370–381) giving evidence for phytosiderophores (PS) involvement in Zn uptake by rice, using isotope discrimination. While the role of PS in Fe uptake by grasses is well established, their involvement in Zn uptake is debated. In this paper, a complete mathematical model of PS‐mediated Zn uptake is developed, allowing for root growth, inter‐root interaction, diurnal variation in PS secretion, decomposition of the PS in the soil, and the transport and interaction of the PS and Zn in the soil. It shows that (a) measured PS secretion rates are sufficient to explain measured Zn uptake rates and differences between rice genotypes; (b) there is an important interaction with rooting density; but (c) diurnally varying PS secretion has little effect on uptake.
    Keywords: Cereal ; Micronutrient ; Mugineic Acid ; Rhizosphere ; Solubilization
    ISSN: 0140-7791
    E-ISSN: 1365-3040
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