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Phosphorus (P) is a key yield-limiting nutrient for crops, but the main source of P fertiliser is finite. Therefore, efficient fertilisation is crucial. Optimal P application requires understanding of the dynamic processes affecting P availability to plants, including fertiliser dissolution rate and soil buffer power. However, standard soil testing methods sample at fixed time points, preventing a mechanistic understanding of P uptake variability. We used image-based modelling to investigate the effects of fertiliser dissolution rate and soil buffer power on P uptake by wheat roots imaged using X-ray CT. We modelled uptake based on 1-day, 1-week, and 14-week dissolution of a fixed quantity of total P for two common soil buffer powers. We found rapid fertiliser dissolution increased short-term root uptake, but total uptake from 1-week matched 1-day dissolution. We quantified the large effects root system architecture had on P uptake, finding that there were trade-offs between total P uptake and uptake per unit root length, representing a carbon investment/phosphorus uptake balance. These results provide a starting point for predictive modelling of uptake from different P fertilisers in different soils. With the addition of further X-ray CT image datasets and a wider range of conditions, our simulation approach could be developed further for rapid trialling of fertiliser-soil combinations to inform field-scale trials or management., (© 2022. The Author(s).)

Microbial communities in agricultural soils underpin many ecosystem services including the maintenance of soil structure, food production, water purification and carbon storage. However, the impact of fertilization on the health of microbial communities is not well understood. This study investigates the spatial and temporal dynamics of nitrogen (N) transport away from a fertilizer granule with pore scale resolution. Specifically, we examined how soil structure and moisture content influence fertilizer derived N movement through the soil pore network and the subsequent impact of on soil microbial communities. We develop a mathematical model to describe N transport and reactions in soil at the pore-scale. Using X-ray Computed Tomography scans, we reconstructed a microscale description of a soil-pore geometry as a computational mesh. Solving two-phase water/air model produced pore-scale water distributions at 15, 30 and 70% water-filled pore volume. The N-speciation model considered ammonium (NH 4 + ) and dissolved organic N (DON), and included N immobilization, ammonification and nitrification processes, as well as diffusion in soil solution. We simulated the dissolution of a fertilizer pellet and a pore scale N cycle at three different water saturations. To aid interpretation of the model results, microbial activity at a range of N concentrations was measured. The model showed that the diffusion and concentration of N in water films is critically dependent upon soil moisture and N species. We predict that the maximum NH 3 - concentrations in soil solution around the pellet under dry conditions are in the order of 1 × 10 4 + and NO 3 - concentrations in soil solution around the pellet under dry conditions are in the order of 1 × 10 3 and 1 × 10 4 , respectively. Supporting experimental evidence suggests that these concentrations would be sufficient to reduce microbial activity in the short-term in the zone immediately around the fertilizer pellet (ranging from 0.9 to 3.8 mm), causing a major loss of soil biological functioning. This model demonstrates the importance of pore-scale processes in regulating N movement and their interactions with the soil microbiome.-3 respectively, and under wet conditions 2 × 10 2 and 1 × 10 3  mol m -3 , respectively. Supporting experimental evidence suggests that these concentrations would be sufficient to reduce microbial activity in the short-term in the zone immediately around the fertilizer pellet (ranging from 0.9 to 3.8 mm), causing a major loss of soil biological functioning. This model demonstrates the importance of pore-scale processes in regulating N movement and their interactions with the soil microbiome., Competing Interests: Declaration of competing interest The authors declare no conflict of interest., (Copyright © 2020 Elsevier B.V. All rights reserved.)

Rhizosphere soil has distinct physical and chemical properties from bulk soil. However, besides root-induced physical changes, chemical changes have not been extensively measured in situ on the pore scale. In this study, we couple structural information, previously obtained using synchrotron X-ray computed tomography (XCT), with synchrotron X-ray fluorescence microscopy (XRF) and X-ray absorption near-edge structure (XANES) to unravel chemical changes induced by plant roots. Our results suggest that iron (Fe) and sulfur (S) increase notably in the direct vicinity of the root via solubilization and microbial activity. XANES further shows that Fe is slightly reduced, S is increasingly transformed into sulfate (SO 4 ) and phosphorus (P) is increasingly adsorbed to humic substances in this enrichment zone. In addition, the ferrihydrite fraction decreases drastically, suggesting the preferential dissolution and the formation of more stable Fe oxides. Additionally, the increased transformation of organic S to sulfate indicates that the microbial activity in this zone is increased. These changes in soil chemistry correspond to the soil compaction zone as previously measured via XCT. The fact that these changes are colocated near the root and the compaction zone suggests that decreased permeability as a result of soil structural changes acts as a barrier creating a zone with increased rhizosphere chemical interactions via surface-mediated processes, microbial activity and acidification.2- ) and phosphorus (P) is increasingly adsorbed to humic substances in this enrichment zone. In addition, the ferrihydrite fraction decreases drastically, suggesting the preferential dissolution and the formation of more stable Fe oxides. Additionally, the increased transformation of organic S to sulfate indicates that the microbial activity in this zone is increased. These changes in soil chemistry correspond to the soil compaction zone as previously measured via XCT. The fact that these changes are colocated near the root and the compaction zone suggests that decreased permeability as a result of soil structural changes acts as a barrier creating a zone with increased rhizosphere chemical interactions via surface-mediated processes, microbial activity and acidification., (© 2019 The Authors. New Phytologist © 2019 New Phytologist Trust.)

The growth of rice in submerged soils depends on its ability to form continuous gas channels-aerenchyma-through which oxygen (O 2 ) diffuses from the shoots to aerate the roots. Less well understood is the extent to which aerenchyma permits venting of respiratory carbon dioxide (CO 2 ) in the opposite direction. Large, potentially toxic concentrations of dissolved CO 2 develop in submerged rice soils. We show using X-ray computed tomography and image-based mathematical modelling that CO 2 venting through rice roots is far greater than thought hitherto. We found rates of venting equivalent to a third of the daily CO 2 fixation in photosynthesis. Without this venting through the roots, the concentrations of CO 2 and associated bicarbonate (HCO 3 - ) in root cells would have been well above levels known to be toxic to roots. Removal of CO 2 and hence carbonic acid (H 2 ) from the soil was sufficient to increase the pH in the rhizosphere close to the roots by 0.7 units, which is sufficient to solubilize or immobilize various nutrients and toxicants. A sensitivity analysis of the model showed that such changes are expected for a wide range of plant and soil conditions.3 ) from the soil was sufficient to increase the pH in the rhizosphere close to the roots by 0.7 units, which is sufficient to solubilize or immobilize various nutrients and toxicants. A sensitivity analysis of the model showed that such changes are expected for a wide range of plant and soil conditions., (© 2019 The Authors. Plant, Cell & Environment published by John Wiley & Sons Ltd.)

In this paper, we use multiple scale homogenisation to derive a set of averaged macroscale equations that describe the movement of nutrients in partially saturated soil that contains growing potato tubers. The soil is modelled as a poroelastic material, which is deformed by the growth of the tubers, where the growth of each tuber is dependent on the uptake of nutrients via a sink term within the soil representing root nutrient uptake. Special attention is paid to the reduction in void space, resulting change in local water content and the impact on nutrient diffusion within the soil as the tubers increase in size. To validate the multiple scale homogenisation procedure, we compare the system of homogenised equations to the original set of equations and find that the solutions between the two models differ by [Formula: see text]. However, we find that the computation time between the two sets of equations differs by several orders of magnitude. This is due to the combined effects of the complex three-dimensional geometry and the implementation of a moving boundary condition to capture tuber growth.

Soil adjacent to roots has distinct structural and physical properties from bulk soil, affecting water and solute acquisition by plants. Detailed knowledge on how root activity and traits such as root hairs affect the three-dimensional pore structure at a fine scale is scarce and often contradictory. Roots of hairless barley (Hordeum vulgare L. cv Optic) mutant (NRH) and its wildtype (WT) parent were grown in tubes of sieved (<250 μm) sandy loam soil under two different water regimes. The tubes were scanned by synchrotron-based X-ray computed tomography to visualise pore structure at the soil-root interface. Pore volume fraction and pore size distribution were analysed vs distance within 1 mm of the root surface. Less dense packing of particles at the root surface was hypothesised to cause the observed increased pore volume fraction immediately next to the epidermis. The pore size distribution was narrower due to a decreased fraction of larger pores. There were no statistically significant differences in pore structure between genotypes or moisture conditions. A model is proposed that describes the variation in porosity near roots taking into account soil compaction and the surface effect at the root surface., (© 2018 The Authors. New Phytologist © 2018 New Phytologist Trust.)

Spatially averaged models of root-soil interactions are often used to calculate plant water uptake. Using a combination of X-ray computed tomography (CT) and image-based modelling, we tested the accuracy of this spatial averaging by directly calculating plant water uptake for young wheat plants in two soil types. The root system was imaged using X-ray CT at 2, 4, 6, 8 and 12 d after transplanting. The roots were segmented using semi-automated root tracking for speed and reproducibility. The segmented geometries were converted to a mesh suitable for the numerical solution of Richards' equation. Richards' equation was parameterized using existing pore scale studies of soil hydraulic properties in the rhizosphere of wheat plants. Image-based modelling allows the spatial distribution of water around the root to be visualized and the fluxes into the root to be calculated. By comparing the results obtained through image-based modelling to spatially averaged models, the impact of root architecture and geometry in water uptake was quantified. We observed that the spatially averaged models performed well in comparison to the image-based models with <2% difference in uptake. However, the spatial averaging loses important information regarding the spatial distribution of water near the root system., (© 2017 John Wiley & Sons Ltd.)

This study applied time lapse (four-dimensional) synchrotron X-ray computed tomography to observe micro-scale interactions between plant roots and soil. Functionally contrasting maize root tips were repeatedly imaged during ingress into soil columns of varying water content and compaction. This yielded sequences of three-dimensional densiometric data, representing time-resolved geometric soil and root configurations at the micronmetre scale. These data were used as inputs for two full-field kinematic quantification methods, which enabled the analysis of three-dimensional soil deformation around elongating roots. Discrete object tracking was used to track rigid mineral grains, while continuum digital volume correlation was used to track grey-level patterns within local sub-volumes. These techniques both allowed full-field soil displacements to be quantified at an intra-rhizosphere spatial sampling scale of less than 300 µm. Significant differences in deformation mechanisms were identified around different phenotypes under different soil conditions. A uniquely strong contrast was observed between intact and de-capped roots grown in dry, compacted soil. This provides evidence that functional traits of the root cap significantly reduce the amount of soil disturbance per unit of root elongation, with this effect being particularly significant in drier soil., (© 2017 The Author(s).)

In this paper, we provide direct evidence of the importance of root hairs on pore structure development at the root-soil interface during the early stage of crop establishment. This was achieved by use of high-resolution (c. 5 μm) synchrotron radiation computed tomography (SRCT) to visualise both the structure of root hairs and the soil pore structure in plant-soil microcosms. Two contrasting genotypes of barley (Hordeum vulgare), with and without root hairs, were grown for 8 d in microcosms packed with sandy loam soil at 1.2 g cm -3 dry bulk density. Root hairs were visualised within air-filled pore spaces, but not in the fine-textured soil regions. We found that the genotype with root hairs significantly altered the porosity and connectivity of the detectable pore space (> 5 μm) in the rhizosphere, as compared with the no-hair mutants. Both genotypes showed decreasing pore space between 0.8 and 0.1 mm from the root surface. Interestingly the root-hair-bearing genotype had a significantly greater soil pore volume-fraction at the root-soil interface. Effects of pore structure on diffusion and permeability were estimated to be functionally insignificant under saturated conditions when simulated using image-based modelling., (© 2017 The Authors. New Phytologist © 2017 New Phytologist Trust.)

The mechanical impedance of soils inhibits the growth of plant roots, often being the most significant physical limitation to root system development. Non-invasive imaging techniques have recently been used to investigate the development of root system architecture over time, but the relationship with soil deformation is usually neglected. Correlative mapping approaches parameterised using 2D and 3D image data have recently gained prominence for quantifying physical deformation in composite materials including fibre-reinforced polymers and trabecular bone. Digital Image Correlation (DIC) and Digital Volume Correlation (DVC) are computational techniques which use the inherent material texture of surfaces and volumes, captured using imaging techniques, to map full-field deformation components in samples during physical loading. Here we develop an experimental assay and methodology for four-dimensional, in vivo X-ray Computed Tomography (XCT) and apply a Digital Volume Correlation (DVC) approach to the data to quantify deformation. The method is validated for a field-derived soil under conditions of uniaxial compression, and a calibration study is used to quantify thresholds of displacement and strain measurement. The validated and calibrated approach is then demonstrated for an in vivo test case in which an extending maize root in field-derived soil was imaged hourly using XCT over a growth period of 19h. This allowed full-field soil deformation data and 3D root tip dynamics to be quantified in parallel for the first time. This fusion of methods paves the way for comparative studies of contrasting soils and plant genotypes, improving our understanding of the fundamental mechanical processes which influence root system development., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Understanding the dynamics of water distribution in soil is crucial for enhancing our knowledge of managing soil and water resources. The application of X-ray computed tomography (CT) to the plant and soil sciences is now well established. However, few studies have utilized the technique for visualizing water in soil pore spaces. Here this method is utilized to visualize the water in soil in situ and in three-dimensions at successive reductive matric potentials in bulk and rhizosphere soil. The measurements are combined with numerical modelling to determine the unsaturated hydraulic conductivity, providing a complete picture of the hydraulic properties of the soil. The technique was performed on soil cores that were sampled adjacent to established roots (rhizosphere soil) and from soil that had not been influenced by roots (bulk soil). A water release curve was obtained for the different soil types using measurements of their pore geometries derived from CT imaging and verified using conventional methods, such as pressure plates. The water, soil, and air phases from the images were segmented and quantified using image analysis. The water release characteristics obtained for the contrasting soils showed clear differences in hydraulic properties between rhizosphere and bulk soil, especially in clay soil. The data suggest that soils influenced by roots (rhizosphere soil) are less porous due to increased aggregation when compared with bulk soil. The information and insights obtained on the hydraulic properties of rhizosphere and bulk soil will enhance our understanding of rhizosphere biophysics and improve current water uptake models., (© The Author 2015. Published by Oxford University Press on behalf of the Society for Experimental Biology.)

· 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., (© 2013 The Authors. New Phytologist © 2013 New Phytologist Trust.)

In this paper, we set out to illustrate and discuss how mathematical modelling could and should be applied to aid our understanding of plants and, in particular, plant-soil interactions. Our aim is to persuade members of both the biological and mathematical communities of the need to collaborate in developing quantitative mechanistic models. We believe that such models will lead to a more profound understanding of the fundamental science of plants and may help us with managing real-world problems such as food shortages and global warming. We start the paper by reviewing mathematical models that have been developed to describe nutrient and water uptake by a single root. We discuss briefly the mathematical techniques involved in analysing these models and present some of the analytical results of these models. Then, we describe how the information gained from the single-root scale models can be translated to root system and field scales. We discuss the advantages and disadvantages of different mathematical approaches and make a case that mechanistic rather than phenomenological models will in the end be more trustworthy. We also discuss the need for a considerable amount of effort on the fundamental mathematics of upscaling and homogenization methods specialized for branched networks such as roots. Finally, we discuss different future avenues of research and how we believe these should be approached so that in the long term it will be possible to develop a valid, quantitative whole-plant model.

We present a model for water uptake by plant roots from unsaturated soil. The model includes the simultaneous flow of water inside the root network and in the soil. It is constructed by considering first the water uptake by a single root, and then using the parameterized results thereby obtained to build a model for water uptake by the developing root network. We focus our model on annual plants, in particular the model will be applicable to commercial monocultures like maize, wheat, etc. The model is solved numerically, and the results are compared with approximate analytic solutions. The model predicts that as a result of water uptake by plant roots, dry and wet zones will develop in the soil. The wet zone is located near the surface of the soil and the depth of it is determined by a balance between rainfall and the rate of water uptake. The dry zone develops directly beneath the wet zone because the influence of the rainfall at the soil surface does not reach this region, due to the nonlinear nature of the water flow in the partially saturated soil. We develop approximate analytic expressions for the depth of the wet zone and discuss briefly its ecological significance for the plant. Using this model we also address the question of where water uptake sites are concentrated in the root system. The model indicates that the regions near the base of the root system (i.e. close to the ground surface) and near the root tips will take up more water than the middle region of the root system, again due to the highly nonlinear nature of water flow in the soil. [Copyright &y& Elsevier]

Root-secreted mucilage and microbially produced extracellular polymeric substances (EPS) modify soil physical and biogeochemical processes. Most studies infer the effects of these polymeric substances from soil bulk behaviour rather than investigating the pore scale. This investigation quantified the isolated physical behaviour of mucilage in a simplified pore-scale setup. We placed drops of mucilage of different concentrations between two flat surfaces to form liquid bridges and monitored their drying using optical imaging and magnetic resonance imaging (MRI). We used our observations to validate a polymer-based multi-phase model that characterises the gel-water-air interactions. In the experiments, while pure water liquid bridges rupture, the mucilage buckled under drying, but maintained connection between the surfaces. MRI showed more water was lost from the central region in the middle of the two plates. In the model, mucilage gel accumulated near the boundaries where surface adhesion occurs. The modelled accumulation times overlapped with monitored bridge buckling for the different concentrations, showing the model can predict the observed transition at which the mixture no longer behaves like a pure liquid. Results suggest that the earlier phase transitions observed for higher mucilage concentrations show a potential mechanism for the greater drought tolerance for plant roots and increase the soil water holding capacity. Furthermore, we discuss potential applications of our model for describing the impacts that microbial biofilms may have on soil structure along with impacts of soil fauna on soil physical functions. • Roots and microbes exude a gel-like substances that modify water flow in soil. • Soil pore scale, gel properties were characterised via experiments and modelling. • Gel alone was shown to store water and reduce evaporation. • Changes in drying gel were captured e.g. localised polymer accumulation. • Results outlined how gel might assist plants with drought tolerance and soil aggregation. [ABSTRACT FROM AUTHOR]