Reliability of the Minkowski functionals
The systematic underestimation of root length based on the mean curvature as compared to the skeleton is highly correlated with the number of branches (Figure 2.2). This can be explained by different sensitivities to root junctions. The root length of the virtual root systems is the sum of Euclidean distances between the connected root nodes. Because lateral roots emerge at the center of the parent root, the total length corresponds to the length of the skeleton. The integral of mean curvature is a measure of the surface of the structure; therefore, at each junction a fraction of the lateral which is covered by the radius of the parent root is not seen. Hence, the loss of root length due to number of branches also depends on root radius. For simple root systems, the approach based on mean curvature can give satisfactory results, however for very densely branched root systems a correction factor might be necessary. Schladitz et al. (2012) used the porosity of an open foam as a correction factor when estimating the strut length of open foams with the same approach. This is based on the assumption that an increasing density and thickness of struts leads to an increased overlap of the struts. This cannot be directly transferred to root systems, because the branching pattern of a root system is less regular than the strut system of foams. It can, however, be argued that the length which is omitted at the junctions is actually excess root length produced by the thinning procedure during skeletonization. This is the reasoning behind the use of adjusted root length. When adjusted root length was used mean curvature estimations were more accurate than skeletonization. Still, some uncertainties remain to the use of mean curvature in length estimation. Root tips increase the mean curvature integral and should therefore lead to an overestimation of length, the same is probably true for surface roughness. The degree of both effects is unknown and should be addressed in future research. Since skeletonization also has some drawbacks (e.g. the sensitivity to surface roughness, which leads to the production of extra branches), we conclude that the approach based on Minkowski functionals is on a par with skeletonization, while being computationally much more efficient. Furthermore, estimation of volume and surface area of roots is possible without additional computational costs when a higher resolution is used (at least 5 voxels diameter, Vogel et al., 2010). This is relevant for future CT studies, given that the resolution of the newest generation of CT scanners is improving fast. On the downside, our approach yields no additional structural information like branching density and number of tips, which is possible with skeletonization.
33 Quantification of RSA
Although root length in CT images was underestimated by 9.3 % as compared to destructive sampling, the overall ability of our method to quantify root distribution in soil is consistent with previous studies. Flavel et al. (2012) found that CT underestimated root length of wheat by 8 %. They had a much higher resolution (68.23 µm) in their columns of only 30 mm diameter which enabled them to analyze finer roots than in the present study. Earlier studies showed a similar trend of underestimation of root length by up to 10 % (Gregory et al., 2003; Perret et al., 2007) but the opposite trend was also reported (Heeraman et al., 1997). In most of these studies the size of the system was considerably smaller than in our case. A general problem of CT is the trade-off between sample size and image resolution.
We specifically aimed for a large sample diameter to provide more realistic growth conditions for the roots, which necessarily leads to reduced resolution. Additionally, in order to penetrate the whole sample we needed higher energy X-rays which produce lower contrast between soil and roots. Finally, the segmentation routine involved different user based decisions that clearly affected the resulting root structure. Even with these limitations we show that X-ray CT can be used to visualize and quantify complex root systems and their development over time. Some of the discrepancy between root length estimated with X-ray CT and WinRHIZO can be explained by the loss of roots that were directly growing at the container wall, due to the cropping of the container wall itself. The smallest structures that can be safely detected should have at least double the size of the resolution if not larger (Vogel et al., 2010), in our case 490 µm, which leads to the possibility of the loss of fine roots. The length of roots with a smaller diameter than 500 µm estimated in WinRHIZO amounted to only 2.7 % of total length; thus this can only partly explain the difference between the two methods. The influence of water content on the accuracy of our measurements was not tested since we only had destructive data for the last day of sampling. Zappala et al. (2013b) reported a significant effect of water content on the success of segmenting a root system from soil showing that volumetric water contents above 25 % lead to a significantly reduced volume of segmented roots from CT as compared to WinRHIZO, probably due to the inability to segment fine roots. In spite of our relatively large sample size, the resulting root distribution was still constrained by the geometry of our container and is therefore not representative of root distributions in the field. The sample size we used was near the maximum that could be entirely penetrated by the X-ray beams without photon starvation. The resulting resolution was good enough to image RSA of Vicia faba, which is known for having coarse roots.
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Distance measurements
Direct measurement of 3D Euclidean distances to the nearest root surface was performed as a measure for soil exploration of roots. It is a straightforward method to describe travel distance from any point in the soil to the root surface.
Potential applications of the distance map include the calculation of water or nutrient uptake, root exudation, root-pathogen interactions, communication in the rhizosphere, determination of chemical or physical gradients in the rhizosphere, and competition between roots to name just a few examples. The frequency distribution of distances depends largely on root length density but can show considerable variation due to non-regular distribution of roots (Van Noordwijk et al., 1993).
Comparison with HMD calculated from root length density in two dimensions with Gardner’s formula shows that the bulk of measured distances (up to 80 %) are shorter than HMD (Figure 2.8). This is partly due to the fact that HMD is calculated in discrete layers and therefore roots in neighboring layers have no effect on HMD while they are accounted for in 3D distance transform. In our case study, the deviation of HMD from the arithmetic mean of distances derived from 3D distance transform was small, indicating a regular root distribution within each layer (Figure 2.9). Situations, where the deviation between the two methods is larger are likely to occur in larger containers with heterogeneous soil properties or in samples taken from the field (Tardieu, 1988). Since non-regular root distributions will have an influence on the actual water and nutrient uptake of the root system, the frequency distribution of distances might be a better predictor for root uptake than root length density in 1D uptake models. Distance measurements can also be used to analyze the deviation of rooting patterns from randomness (Pierret et al., 1999). The accuracy of the distance map depends primarily on image resolution, as no distances shorter than the voxel side length can be detected. Obviously, also the quality of the segmentation affects the results. Any missing root structures, misclassified macropores, and both under- and overestimation of root diameter, will change the outcome of the distance measurements.
Root age
The non-invasive nature of CT imaging allows the quantification of root age within a root system when the same sample is imaged repeatedly over time. By simple subtraction of root length per layer from subsequent dates, new root growth can be quantified and the age determined based on the temporal resolution, i.e. the time between two scans. In some cases root length decreased between two subsequent scans. When this was the case we attributed the difference to the uncertainty of our method as discussed above and therefore assumed no growth.
Estimated root age distributions are a result of the dynamics of root growth in the container. Encroachment of young roots in the deeper soil near the end of the
35 experiment might hint to preferential growth in moist soil layers but the pattern is also a consequence of the sample geometry as laterals were forced to grow downwards when they reached the cylinder walls. Since root properties can change drastically with the maturation of roots, distribution of root ages can be an important factor in root-soil interactions. So far, experimental data on root age distribution are virtually non-existent for 3D root systems growing in soil. However, studies based on root architectural models show the importance of age-related changes in root functions for water and phosphorous uptake (Doussan et al., 1998b;
Schnepf et al., 2012). Such model studies show that there is clearly a need for methods to quantify age distribution within root systems. A method for the spatially explicit assignment of root age for individual root segments using a 3D virtual reality system similar to Stingaciu et al. (2013) is currently under development.
Figure 2.9: Relationship of root length density and mean distance to root surface in each 1 cm layer for every time step. The solid line represents the theoretical relationship of half mean distance and root length density according to Gardner (1960)
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