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X-ray computed tomography to quantify tree rooting spatial distributions
Geoderma 90 Ž1999. 307–326
X-ray computed tomography to quantify tree rooting spatial distributions Alain Pierret b
a,b,)
, Yvan Capowiez b, Christopher J. Moran a , Andre´ Kretzschmar b
a CSIRO Land and Water, G.P.O. Box 1666, Canberra, ACT, Australia INRA Zoologie, AÕignon, Domaine Saint-Paul Cantarel, Site Agroparc, 84914 AÕignon Cedex 9, France
Received 18 December 1997; accepted 18 October 1998
Abstract Poor root development due to constraining soil conditions could be an important factor influencing health of urban trees. Therefore, there is a need for efficient techniques to analyze the spatial distribution of tree roots. An analytical procedure for describing tree rooting patterns from X-ray computed tomography ŽCT. data is described and illustrated. Large irregularly shaped specimens of undisturbed sandy soil were sampled from various positions around the base of trees using field impregnation with epoxy resin, to stabilize the cohesionless soil. Cores approximately 200 mm in diameter by 500 mm in height were extracted from these specimens. These large core samples were scanned with a medical X-ray CT device, and contiguous images of soil slices Ž2 mm thick. were thus produced. X-ray CT images are regarded as regularly-spaced sections through the soil although they are not actual 2D sections but matrices of voxels ; 0.5 mm = 0.5 mm = 2 mm. The images were used to generate the equivalent of horizontal root contact maps from which three-dimensional objects, assumed to be roots, were reconstructed. The resulting connected objects were used to derive indices of the spatial organization of roots, namely: root length distribution, root length density, root growth angle distribution, root spatial distribution, and branching intensity. The successive steps of the method, from sampling to generation of indices of tree root organization, are illustrated through a case study examining rooting patterns of valuable urban trees. q 1999 Elsevier Science B.V. All rights reserved. Keywords: tree roots; image analysis; morphology; spatial distribution; sample preparation
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Corresponding author. E-mail: [email protected]
0016-7061r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 6 - 7 0 6 1 Ž 9 8 . 0 0 1 3 6 - 0
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1. Introduction In the urban environment, the health of large trees is important for a variety of reasons. In many cases, the cost of replacing ailing or dead trees is significant. Observations along trenches dug for maintenance of subterranean infrastructure consistently showed that the root systems of urban trees were not fully developed compared to what would be expected under natural conditions. The spatial extent of roots of these urban trees is often restricted to the volume of the pit in which they were initially planted. This poor root development is a threat to the growth and health of the above-ground part of the tree. This aberrant root development is believed to decrease the life expectancy of urban trees by 10 to 20 years because it affects water and nutrient uptake and potentially leads to extra-sensitivity to diseases. Another problem is associated with trees whose roots spread excessively towards leaking parts of the water supply network and cause considerable damage, which is expensive to remedy. Therefore, urban management authorities are keen to develop techniques to minimize ill-health of trees and to provide a favorable growth environment. The spatial distribution of tree roots and their relationship with the surrounding environment is important information for understanding how to manage trees to meet these objectives. An additional restriction is that the value of the trees constrains the extent to which the root system of any one tree can be sampled. If the soil lacks cohesion it is not possible to take specimens to estimate root length density with any confidence. To obtain the required information, undisturbed specimens must be extracted and analyzed non-destructively. Spatial organization of plant or tree roots is most commonly assessed by mapping the contact of roots with horizontal or vertical planes Ž Tardieu, 1988a,b; Commins et al., 1991; Bruckler et al., 1991; Logsdon and Allmaras, 1991; McBratney et al., 1992; Van Rees et al., 1994; Stewart et al., 1994; Pellerin and Pages, ` 1996, Stewart, 1997.. This approach appears well suited to the analysis of the spatial patterns of roots, and several of these studies provided conclusive evidence of interaction between root distribution and soil structure. As an alternative to these manual, tedious and destructive investigations, some studies have been focused on automatic and non-destructive assessment of soil structural features. X-ray computed tomography ŽCT. with low energy medical scanners has been demonstrated as a valuable method for documenting soil macro-porosity Ž e.g., Warner et al., 1989; Peyton et al., 1992., root growth dynamics ŽTollner et al., 1994. , and earthworm burrow system development ŽJoschko et al., 1993, Capowiez et al., 1998.. Difficulty in accessing facilities and imaging limitations Že.g., limited spatial resolution of medical X-ray CT devices, low penetration capability leading to low signalrnoise ratios, or problems related to soil Fe content when using nuclear magnetic resonance ŽNMR.. has meant that efforts have seldom been put into reconstructing plant root 3D distributions using non-destructive methods Ž MacFall and Johnson,
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1994; Liu et al., 1994. . Heeraman et al. Ž 1997. recently demonstrated that a quantitative description of roots of experimentally grown plants can be achieved with high-energy industrial tomography equipment. However, X-ray CT has not been used before for looking at the in situ morphology of root-networks.
Fig. 1. Schematic maps of field sampling. Circular grey areas are trees and white squares are samples. The four samples studied in this paper are grey squares indicated by arrows. Figures reported next to the dotted lines are approximate distances in meters.
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We present here a technique for mapping roots in 3D using low-energy X-ray CT images of undisturbed soil cores. Even though X-ray CT resolution is usually only around 0.5 to 1 mm with medical equipment, this is a sufficient resolution to examine a large proportion of the population of tree roots. The drawback of using a low-energy source of X-rays Ž leading to low penetration capability and associated artifacts. was counterbalanced by using long integration times. X-ray CT images are used as the basic information to generate an equivalent of horizontal root contact maps, at regularly spaced depths, but representing the projection of a volume rather than an actual section. These maps are used to reconstruct the skeletons of three-dimensional objects assumed to be roots. The resulting connected objects are then used to derive indices of the spatial organization of roots.
2. Materials and methods 2.1. Sample collection and preparation Tree root systems were sampled in Paris from two tree species and soil type conditions in parklands: chestnut trees Ž Aesculus hippocastanum L.. growing in an homogeneous sandy soil Ž Boulogne site. , and maples Ž Acer pseudoplatanus L.. growing in a sandy to sandy clay soil ŽVincennes site.. Particle size distribution of Vincennes soil is: 8.5% gravel, 37.4% coarse sand, 30.7% fine sand, 15.6% silt and 7.8% clay. Samples were taken as shown in Fig. 1. Only the samples indicated by arrows in Fig. 1 are discussed in this study. Undisturbed cores could not be sampled by direct use of a normal coring tool because of the abundance of roots and the low cohesion of these sandy soils. To overcome this disturbance problem, a method of field impregnation adapted from Moran et al. Ž1989. was used. A flow diagram of the procedure is given Fig. 2. The method begins with in situ impregnation with an epoxy resin designed to harden in moist soil and to maintain low viscosity under cold temperatures Ž- 58C.. The resin was poured into an aluminium frame Ž 20 = 20 = 22.5 cm. pushed 2 to 3 cm into the soil. As discussed by McBratney et al. Ž1992., a drawback of this field impregnation procedure can be that resin does not infiltrate deeply into soil under certain conditions. To obtain deeper infiltration, six small PVC tubes were pushed into the soil at the periphery of each aluminium frame and the soil then removed from inside the tubes with an auger before resin was poured. Details of manufacturer references and formulation of the field mix are given in Table 1 1. At a temperature of about 108C, the resin sets after 1 to 2 h, and samples can be removed after 1 or 2 days. These times 1
Supply of information regarding this product does not constitute a product recommendation.
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Fig. 2. Flow diagram of the sampling procedure. Ž1. Setting up of the square aluminium frame Ž20 cm.. Ž2. Deep resin infiltration using the aluminium frame and the additional set of PVC tubes. Ž3. Extraction of an undisturbed specimen from which a core will be cut. Ž4. A core ready to be processed after sawing down to 20 cm in diameter.
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Table 1 Base Resin PY303-1 Reactive Diluent DY 0397 Hardener HY 2963
50% 25% 25%
All products are from Ciba-Geigy, Switzerland.
are subject to great variability. For the sampling described here, conducted under cold conditions Ž0 to 18C., samples could be extracted three weeks after field impregnation, allowing the resin to infiltrate deeply. In the laboratory, the partly impregnated samples were set to dry at room temperature for 2 months and were re-impregnated under vacuum. Even after re-impregnation, soil was not saturated with resin. Rather than a complete impregnation, the technique acts to consolidate cohesionless soil, allowing collection of large specimens. Among the twelve specimens thus obtained, only the four longest were kept for further study by X-ray CT. These four specimens were sawn using a helicoidal tungsten wire saw and a disc diamond saw to obtain cores 500 mm high and 200 mm in diameter, which is the maximum diameter that could be imaged using the medical CT scanning device available. 2.2. Image acquisition The samples were scanned using a CT Pace scanner, General Electrice, at 140 kV, 140 mA, with an exposure time of 4 s, and field-of-view of 230 mm, to image 2 mm contiguous horizontal slices. For a review of the physical principles and soil related applications of X-ray CT scanning, see Heijs et al. Ž 1995. or Anderson and Hopmans Ž1994.. Images provided by X-ray CT scanners are based on X-ray attenuation through the sample according to Lambert’s law. Intensities received by detectors are expressed on the linear Hounsfield scale for which typical values are y1000 Ž air. and 0 Ž water. . For subsequent image processing, 8-bit images were captured with a pixel size of 0.4 mm. Before conversion to 8-bit, two parameters, the window width Ž ww. and the window center Žwc., have to be defined. They are clipping values according to which the portion of the Hounsfield scale to be processed is defined. Here, these values were chosen to give optimal contrast between mineral and organic materials Žww s 1400, wc s 700.. The Hounsfield range thus defined, is subsequently converted into 8-bit data, from 0 s black to 255 s white. 2.3. Reconstruction method 2.3.1. Image segmentation and deriÕation of horizontal root maps The basic assumption considered in this work is that the part of the root system concealed in the samples is an arrangement of branching, low density,
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cylindrical segments. Depending on their angle of incidence to the horizontal plane of each image, roots appear in tomographic images as more or less elliptical areas with specific low Hounsfield values Žor grey levels. . It was difficult to separate macropores from roots because resin partly impregnates some roots, resulting in similar Hounsfield values for roots and pores filled with resin. However, on average Hounsfield values for rootrresin areas was 240 Žranging from 200–270. and 750 for soil matrix Ž ranging from 500 to 900.. Consequently, we defined root related objects Ž RRO. as every elliptical area composed of low grey levels. This may result in some misclassification errors in the cases of pores formed by roots or fauna, that were not occupied by roots at the time of sampling. Histograms of the grey levels of 3D images Ž Fig. 3. typically show two sharp peaks corresponding to low density objects Ž around 15 s rootrresin areas. and high density objects Žaround 210 s flint gravels., and a broad peak corresponding to the soil matrix density Žcentered around 140–150.. RROs were extracted from grey level images using a threshold value to segment the image into two distinct populations. Such a method implies that the range of grey levels within which the objects of interest appear is sufficiently narrow and homogeneous. With the samples studied here, bi-partitioning of the histogram was achieved by estimating the distance, d, between the rootrresin peak and the soil matrix peak, and the threshold value was chosen to be at a distance of Ž 2r3. = d from the peak corresponding to the soil matrix Žmethod described in Russ, 1995, and used in Capowiez et al., 1998. . However, by comparison with what was expected from visual inspection of X-ray CT images, it appeared that the smallest RROs could not be correctly selected using this bi-partitioning method. To overcome this problem we used a so-called top-hat filtering Ž Meyer, 1977. which results in extraction of areas of an arbitrarily chosen size, darker than
Fig. 3. Grey levels histogram for the sum of the images forming the BL3 core and method for the bi-partitioning threshold.
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their immediate neighborhood. The combination of Ž 1. a threshold value allowing extraction of low density areas and Ž2. a top-hat filter of size 5, appeared to be well suited to the selection of RROs, as has been found relevant for segmenting pore structure images Ž Moran et al., 1988. . Despite the spatial resolution of the CT-unit used being theoretically 0.5 mm, in the conditions we were using it, the smallest roots imaged were not less than approximately 1 mm in diameter. Root diameters range up to several centimeters Žfor example, presence of roots ; 30 mm in diameter in BL1 and BL3. . 2.3.2. Continuity assessment Continuity assessment was achieved using an overlapping criterion Ž McDonald et al., 1986a,b. , which implies an object in one plane is connected to any of the objects in the following plane only if there is a face-to-face voxel contact. After image segmentation, the continuous 3D objects were reconstructed in three steps. First, RROs in each 2D binary image were labelled. Then, contacts between RROs were identified using a temporary image which is the sum of two successive images Ž n and n q 1, n being the order number of an individual image in a CT series.. Voxels with values larger than the initial value in image n indicate that the faces of two RRO voxels are touching and therefore part of the same object. Because the RROs on both images n and n q 1 were previously labelled, it was possible to record the x, y, z coordinates where the i th object of image n is in contact with the k th object of image n q 1, the latter being itself in contact with the l th object of image n q 2, etc. By applying this rule to every object, at each depth successively, each 3D object Ž or more precisely its skeleton. was eventually reconstructed and identified. This algorithm runs with only two contiguous 2D images loaded at a time which is an advantage given the large computer memory requirements of operating on the entire 3D data set. Because we did not link the centroid positions of connected objects but only the first contact point encountered while scanning images, it is likely, for the largest and very elliptical RROs, that the reconstruction procedure ends up in a ‘broken trajectory’, which is an artifact. To avoid this artifact, we chose to apply a size threshold for the RROs, and not to take into account very elliptical RROs. This reconstruction method can be considered acceptable for preliminary investigations, but it suffers from several drawbacks, the most important of which are: Ž1. the loss of root diameter information; Ž2. a required upper size threshold for the RROs under consideration; and Ž 3. the loss of horizontal roots. Therefore, the method is weakest in circumstances where a significant proportion of the root system has a horizontal preferred orientation. A certain number of continuous roots can also appear discontinuous after reconstruction because segmentation can lead to artificial interruption when individual root pixel values change, according to, e.g., variations in diameter andror in orientation, or when roots grow inside any porous component of the soil.
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3. Results and discussion 3.1. Geometric characteristics inferred from Õisual inspection of 3D skeletons A visual inspection of the four specimens was attempted using the Rotate 2 v1.13 beta freeware package. The reconstructions show objects longer than 20 mm ŽFig. 4.. Important variability can be inferred from this visual inspection. The large number of objects in the upper part of BL3 is related to measurement of surficial litter, which is not present in the other cores. An interesting ‘bypass’ pattern is visible on the left middle part of BL1 Ž as indicated by the arrow in Fig. 4.. It is noticeable that the V6 root network is interrupted around 200 mm in depth. This is an example of previously discussed artifact resulting from segmentation when roots grow in or pass through macropores Žhere, a large rodent burrow. . Vincennes samples appear to show a strong vertical orientation of the root system whereas slanted roots seem more abundant in the Boulogne samples. This visual feature is confirmed by the measurement of each object’s orientation, as indicated by the star plots of directions ŽFig. 5. which show the angles from the horizontal. The length of the arms of the star are normalized against the most frequent angle for all the specimen, i.e., 668 in V6. This difference between Boulogne and Vincennes samples could be related to the sample-to-nearest-tree distance, assuming that roots are almost vertical under tree trunk and increasingly slanted as the distance to the trunk increases Ž the geotropic growth hypothesis, see Grabarnik et al., 1998. . However, it appears that BL3 is not more distant to the nearest tree than V3, and BL1 is even closer to a tree than any of the other samples. Another possible explanation is that the maples in Vincennes mainly developed horizontal and vertical axis roots but few oblique ones whereas the Boulogne chestnuts developed a wider range of oblique roots. 3.2. Root length distributions The root length distributions Ž Fig. 6. indicate that in all specimens, ) 95% of roots are - 100 mm in length. The comparison of length Žsolid line. and vertical extent Ž dotted line. distributions also shows that the vertical extent of roots is mainly - 20 mm Žvertical extent is the number of slices in which an individual segment is present multiplied by slice thickness. . This is another expression of the previously discussed slanted orientation of roots and again, the greatest proportion of long slanted segments is found in the BL3 sample. The 2
Rotateq for MSDos by Marijke vanGans, available from http:rrwww.siliconalley.comrcatr rotate.html. First developed as Rotaterq for the Mac platform by Craig Kloeden, available from http:rrraru.adelaide.edu.aurrotaterr..
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Fig. 4. Example of 3D skeleton representations of root patterns. Only segments longer than 20 mm are shown. Note the ‘bypass’ pattern in BL1, as indicated by the arrow.
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Fig. 5. Star plots of root growth angle to the horizontal ŽA: BL1, B: BL3, C: V3 and D: V6.. For each plot, 0 degree to the horizontal corresponds to the right end and 90 degrees to the vertical. The length of the spikes is proportional to the frequency of roots Žthe circle represents 5%.. Minimum, maximum and mean growth angle are reported beside each plot.
Fig. 6. Root length cumulative distribution functions ŽA: BL1, B: BL3, C: V3 and D: V6.. The dotted line is the vertical extent function Žvertical extent: number of slices in which an individual segment is present multiplied by slice thickness Žhere 2 mm.. and the solid line is the actual length function.
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relationship between root orientation and length showed that, on average, long roots were no more oblique than shorter ones. The shape of the length distribution functions for short roots is difficult to analyze, but it seems that there is little difference between the Vincennes and Boulogne samples. On average, for all of the samples, the cumulative distribution functions show that approximately 5% of the segments are ) 20 mm in length, 15% are ) 10 mm, 25% are ) 8 mm and 50% ) 4 mm. 3.3. Root length density (L Õ ) As noted in Section 1, it was not possible to sample cores from these trees nor to create large exposures to take root contact maps. Therefore, it was not possible to estimate root length densities other than by analysing the CT scans. Root length density was derived from the number of connected objects present at each depth and the volume of each slice. The orders of magnitude of L v for a given minimum length of roots are comparable Ž Fig. 7. for all the samples Žexcept for the 100 upper mm of BL3 due to surficial litter as mentioned above. and are of about 1 to 3 cm cmy3 Žincluding all segments more than 2 mm in length..
Fig. 7. Root length density functions ŽA: BL1, B: BL3, C: V3 and D: V6.. Null values in the upper parts of BL1, V3, and V6 are because data corresponding to the first centimeters of the profile are missing.
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The L v values obtained here are smaller than those obtained by other authors, mainly because of the limited spatial resolution of the images. The order of magnitude of our measurements are close to those derived from root contact mapping in the field ŽTardieu, 1988a,b; Van Rees et al., 1994. or mini-rhizotron counts ŽThomas et al., 1996., but smaller than those derived from polished sections, thin-sections, or X-ray microtomography measurements. As a comparison, our measurements are 100 times less than what Krebs et al. Ž 1994. , obtained on a grass Ž Poa triÕialis . and a dicotyledon plant Ž Rumex obtusifolius., 35 times less than what Heeraman et al. Ž 1997. , obtained on bush beans, and 10–20 times less than what Stewart Ž 1997. obtained on wheat, Van Noordwijk et al. Ž 1992. , obtained on maize and McBratney et al. Ž 1992. , obtained on oats. According to Thomas et al. Ž 1996. fine roots Ž- 0.5 mm in diameter. can represent up to 86% of the total root length of young pine trees Ž Pinus radiata.. In the case of maize plants Ž Kooistra et al., 1992. , the proportion of roots ) 0.5 mm in diameter was found to be even smaller. Therefore, the values of L v estimated here are not unexpected, and these preliminary results indicate that X-ray CT provides similar data to that detected visually in the field, but of course, with the additional advantages of 3D information. 3.4. Distribution analysis using nearest neighbor distances Root spatial distribution was quantified using the 3D coordinates of the reconstructed segments. Calculation of distances between neighboring roots was carried out, at each depth, by considering the x, y coordinates of connected objects as events. The event-to-nearest-event distances Ž referred to as nearest neighbor distances, d . were measured in 2D considering all segments longer than 2 mm. Once d has been computed for every event at a given depth, it is possible to derive a frequency distribution of d . This method only gives information at the smallest scales of the pattern and cannot lead to any conclusions at larger scales, because distances are measured to the closest events ŽCressie, 1991.. Frequency distributions derived from the observed data at each depth were compared with randomness as represented by an homogeneous Poisson process in 2D. The intensity of the process being known for each depth, a random number generator was used to derive simulated d . 99 Poisson process simulations were used to define an envelope representing the domain of randomness for the point processes we consider. In principle, the global significance value of this test is 1% ŽMonte Carlo test; Diggle, 1983.. If the observed distribution function falls inside the simulation envelope, the distribution is random. Departure from randomness is indicated by events falling outside the simulated envelope. At some depths, the intensity of the spatial process was too low, and the test had little actual significance. No formal method was used to account for
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edge effects, however, we did check that when random points fall within a border region of 20 mm, that the observed trends were not significantly altered. Distribution functions were not analyzed individually, but were used to derive a more global spatial arrangement index on the basis of which general trends of root distributions were investigated. Thus, for each depth, an index called the spatial arrangement index Ž S . was calculated from the nearest neighbor distances. S is defined as the mean value of the ratio Si derived following Eq. Ž 1. : Si s
do d Si
Ž1.
where do is the median of the observed nearest neighbor distances and dS i is the median of the i th simulated nearest neighbor distance, and S is the mean of the Si for each of the 99 Poisson process simulations. The lower Ž L1 s . and upper Ž L2 . 95% confidence limits about S are the boundaries of the region from s S y 1.96 = ´ S , to S q 1.96 = ´ S where ´ S is the expected standard error of S. When L 2 s - 1 the roots tend to be spatially clustered; when L1 s - 1 - L2 s, roots tend to be randomly distributed and when L1 s ) 1 roots tend to exhibit an inhibition or regular distribution. As shown in Fig. 8, there is a slight but measurable trend to clustering at depths in between 25 and 40 cm for V3, at depths more than 30 cm for BL3, and at depths more than 47 and 50 cm for V6
Fig. 8. Spatial arrangement index, S, as a function of depth for all segments longer than 2 mm. Note the slight trend to clustering ŽCl symbols on the right hand side of plots. at some depths for BL3 ŽB., V3 ŽC., and V6 ŽD.. Depths at which root segments are randomly distributed are indicated by the Rd symbol on the right hand side of plots. Plain line: median, dotted lines: 95% confidence interval.
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and V3 respectively. BL1 is random at all depths. The range of S values can vary significantly, and all the samples except V6 tend towards a clustered distribution with depth. When considering the proportion of events involved in this increasingly clustered process Ž i.e., the ratio of the number of events for which do values are falling above the envelope of simulated values dS i , to the total number of events., we find that only 10 to 30% of the segments contribute to the observed trend Ž Fig. 9. , and that the proportion tends to increase with depth for all the samples. Fig. 10 shows that this clustering trend is not constant when one considers only segments longer than a given threshold. For different segment length thresholds, S has been summed and divided by the number of slices, giving an average spatial index for each core referred to as S. Long segments tend to exhibit less clustering Ž S increases with increasing minimum segment length., and sample V3 tends towards a regular distribution when considering only segments longer than 20 mm. 3.5. Branching intensity Branching intensity was estimated by counting the number of contacts a given RRO has with other RROs in the sections above and below it. Branching intensity is variable between samples. BL1 and V6 are comparable: they show constant branching intensity with depth. V3 shows a higher maximum number of branches and an increased branching intensity at depths more than 200 mm. BL3 is atypical because of the anomaly corresponding to the 100 upper millimetres Žsurficial litter., but it seems to be regular with depth and with more branches than BL1 and V3.
Fig. 9. Proportion of events involved in the clustering of segments longer than 2 mm, as a function of depth.
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Fig. 10. S as a function of the minimum segment length considered, for each core. The clustering trend observed when short segments are included decreases when only longer segments are taken into account. The horizontal line at Ss1 indicates the limit between clustered Žbelow the line. and regular Žabove the line. distributions.
A possible explanation for the clustered patterns observed could have been that there exists a correlation between branching intensity and do . However, as
Fig. 11. Branching intensity as a function of the median NND ŽA: BL1, B: BL3, C: V3 and D: V6..
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is visible in Fig. 11, even though there seems to be a threshold above which branching is clearly related to a decrease of do , it is more likely that there is no such clear relationship for most of the objects taken into account in our reconstructions. Consequently it can be argued that some clustering actually exists and is not simply a consequence of branching intensity. 4. Conclusion A set of methods, from field sampling to spatial analysis, has been presented to describe tree root distributions in undisturbed soil. The method of field impregnation and subsequent laboratory re-impregnation successfully provided large undisturbed samples of cohesionless soil which were heavily colonized by tree roots. In addition, specimens were taken without fatal damage to the valuable trees. These specimens were well suited to extraction of cores approximately 200 mm in diameter which are successfully imaged using a medical X-ray CT scanner. The approach based on analysis of binary images was demonstrated to be capable of producing reconstructions of 3D continuous objects assumed to be roots with diameters ) 0.5 to 1 mm. Some constraints in unambiguously separating roots and resin-filled pore space have been noted. 3D reconstructions were effective for assessing the spatial organization of tree roots in undisturbed conditions. A set of tools for quantifying the 3D spatial organization of roots was developed and applied to the reconstructed systems. Although there is no statistical assessment of the measurements, this application shows that: 1. a significant part of the tree root systems of both species in both soil types grow at angles - 45 degrees to the horizontal; 2. chestnuts could develop more oblique roots than maples; 3. short root segments exhibit a slightly clustered distribution at some depths; 4. the trend towards clustering tends to increase with depth; 5. long root segments are more randomly distributed, than shorter segments. As recently stated by Clothier and Green Ž 1997. , roots are very difficult to observe in situ, ‘tightly enmeshed in the matrix of soil’, and there is an essential need for better observation and description tools of the complexity of root systems. This work is an attempt to improve our perception of such a complex system by exploring the potential of a method to obtain unique data, e.g., nearest neighbor distances and orientation, which are not easily obtained by other means. We conclude that X-ray CT, even with low energy and limited resolution offered by medical equipment, is a valuable tool to obtain an in situ view of the overall morphology of the root network. Eventually, it could contribute to improve our understanding of spatial variability of root systems in response to the physical, chemical and biological environments they experience.
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Acknowledgements Funding for this work was provided by the city of Paris Ž convention Ville de ParisrINRA for the improvement of tree health in the urban environment. . We would like to thank Herve´ Bossuat for field sampling management and critical discussions. CT scanning facilities in Avignon Hospital were used after the agreement of Drs Roumieu and Burdelle. The authors are grateful to Jacques Barthes, Jean-Marc Becard, Dominique Beslay, and Michael Krebs for help ´ during sampling and laboratory manipulation.
References Anderson, S.H., Hopmans, J.W., 1994. Tomography of Soil–Water–Root Processes. SSSA Special Publication No. 36. Madison, WI, USA, 148 pp. Bruckler, L., Lafolie, F., Tardieu, F., 1991. Modelling root water potential and soil–root water transport: II. Field comparisons. Soil Sci. Soc. Am. J. 55, 1213–1220. Capowiez, Y., Pierret, A., Daniel, O., Monestiez, P., Kretzschmar, A., 1998. 3D skeleton reconstructions of natural earthworm burrow systems using cat scan images of soil cores. Biol. Fertil. Soils 27 Ž1., 51–59. Clothier, B.E., Green, S.R., 1997. Roots: the big movers of water and chemical in soil. Soil Sci. 162 Ž8., 534–543. Commins, P.J., McBratney, A.B., Koppi, A.J., 1991. Development of a technique for the measurement of root geometry in the soil using resin-impregnated blocks and image analysis. J. Soil Sci. 42, 237–250. Cressie, N.A.C., 1991. Statistics for Spatial Data. Wiley-Interscience, New York, 900 pp. Diggle, P.J., 1983. Statistical Analysis of Spatial Point Patterns ŽMathematics in Biology.. Academic Press, London, 148 pp. Grabarnik, P., Pages, ` L., Bengough, A.G., 1998. Geometrical properties of simulated maize root systems: consequences for length density and intersection density. Plant and Soil 200, 157–167. Heeraman, D.A., Hopmans, J.W., Clausnitzer, V., 1997. Three dimensional imaging of plant roots in situ with X-ray computed tomography. Plant and Soil 189, 167–179. Heijs, A.W.J., de Lange, J., Schoute, J.F.Th., Bouma, J., 1995. Computed tomography as a tool for non-destructive analysis of flow patterns in macroporous clay soils. Geoderma 64, 183–196. Joschko, M., Muller, P.C., Kotzke, K., Dohring, W., Larink, O., 1993. Earthworm burrow system development assessed by means of X-ray computed tomography. Geoderma 56, 209–221. Kooistra, M.J., Schoonderbeek, D., Boone, F.R., Veen, B.W., Van Noordwijk, M., 1992. Root–soil contact of maize, as measured by a thin section technique: II. Effects of soil compaction. Plant and Soil 139, 119–129. Krebs M., Kretzschmar A., Babel U., Chadoeuf J., Goulard M., 1994. Investigations on distribution patterns in soil: basic and relative distributions of roots, channels and cracks. Proc. IX Int. Working Meeting on Soil Micromorphology, Townsville, Australia, July 1992. Elsevier, Amsterdam, pp. 437–449. Liu, I.-W.Y., Waldron, L.J., Wong, S.T.S., 1994. Application of nuclear magnetic resonance to study preferential water flow through root channels. In: Anderson, S.H., Hopmans, J.W. ŽEds..,
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Tomography of Soil–Water–Root Processes. SSSA Special Publication No. 36. Madison, WI, USA, pp. 135–148. Logsdon, S.D., Allmaras, R.R., 1991. Maize and soybean root clustering as indicated by root mapping. Plant and Soil 131, 169–176. MacFall, J.S., Johnson, G.A., 1994. Use of magnetic resonance imaging in the study of plants and soils. In: Anderson, S.H., Hopmans, J.W. ŽEds.., Tomography of Soil–Water–Root Processes. SSSA Special Publication No. 36. Madison, WI, USA, pp. 99–113. McBratney, A.B., Moran, C.J., Stewart, J.B., Cattle, S.R., Koppi, A.J., 1992. Modifications to a method of rapid assessment of soil macropore structure by image analysis. In: Mermut, A.R., Norton, L.D. ŽEds.., Digitization, Processing and Quantitative Interpretation of Image Analysis in Soil Science and Related Areas. Geoderma, 53, 255–274. McDonald, I., Kaufmann, P., Dullien, F., 1986a. Quantitative image analysis of finite porous media: I. Development of genus and pore map software. J. Microsc. 144 Ž3., 277–296. McDonald, I., Kaufmann, P., Dullien, F., 1986b. Quantitative image analysis of finite porous media: II. Specific genus of cubique lattice models and Berea sandstone. J. Microsc. 144 Ž3., 297–316. Meyer, F., 1977. Contrast features extraction. In: Chermant, J.L. ŽEd.., Quantitative Analysis of Microstructures in Material Sciences, Biology and Medicine. Riederer-Verlag, Stuttgart, pp. 374–380. Moran, C.J., Koppi, A.J., Murphy, B.W., McBratney, A.B., 1988. Comparison of the macropore structure of a sandy loam surface soil horizon subjected to two tillage treatments. Soil Use and Management 4, 96–102. Moran, C.J., McBratney, A.B., Koppi, A.J., 1989. A rapid analysis method for soil pore structure: I. Specimen preparation and digital binary image production. Soil. Sci. Soc. Am. J. 53, 921–928. Pellerin, S., Pages, ` L., 1996. Evaluation in field conditions of a three-dimensional architectural model of the maize root system: comparison of simulated and observed horizontal root maps. Plant and Soil 178, 101–112. Peyton, R.L., Haeffner, B.A., Anderson, S.H., Gantzer, C.J., 1992. Applying X-ray CAT to measure macropore diameters in undisturbed soil cores. In: Mermut, A.R., Norton, L.D., ŽEds.., Digitization, Processing and Quantitative Interpretation of Image Analysis in Soil Science and Related Areas. Geoderma, 53, 329–340. Russ, J.C., 1995. The Image Processing Handbook. CRC Press, Boca Raton, FL, 674 pp. Stewart, J.B., 1997. The spatial distribution of plant roots and their interaction with soil structure. Ph.D. Thesis. The University of Sydney, Australia. Stewart, J.B., Moran, C.J., McBratney, A.B., 1994. Measurement of root distribution from sections through undisturbed soil specimens. Proc. IX Int. Working Meeting on Soil Micromorphology, Townsville, Australia, July 1992. Elsevier, Amsterdam, pp. 507–514. Tardieu, F., 1988a. Analysis of the spatial variability of maize roots density: I. Effect of wheel compaction on the spatial arrangement of roots. Plant and Soil 107, 259–266. Tardieu, F., 1988b. Analysis of the spatial variability of maize roots density: II. Distances between roots. Plant and Soil 107, 267–272. Thomas, S.M., Whitehead, D., Adams, J.A., Reid, J.B., Sherlock, R.R., Leckie, A.C., 1996. Seasonal root distribution and soil surface carbon fluxes for one-year-old Pinus radiata trees growing at ambient and elevated carbon dioxide concentrations. Tree Physiol. 16, 1015–1021. Tollner, E.W., Murphy, C., Ramseur, E.L., 1994. Techniques and approaches for documenting plant root development with X-ray computed tomography In: Anderson, S.H., Hopmans, J.W. ŽEds.., Tomography of Soil–Water–Root Processes. SSSA Special Publication No. 36. Madison, WI, USA, pp. 115–133. Van Noordwijk, M., Kooistra, M.J., Boone, F.R., Veen, B.W., Schoonderbeek, D., 1992.
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Root–soil contact of maize, as measured by a thin section technique: I. Validity of the method. Plant and Soil 13, 109–118. Van Rees, K.C.J., Hoskins, J.A., Hoskins, W.D., 1994. Analyzing root competition with Dirichlet tessellation for wheat on three landscape positions. Soil Sci. Soc. Am. J. 58, 423–432. Warner, G.S., Nieber, J.L., Moore, I.D., Geise, R.A., 1989. Characterizing macropores in soil by computed tomography. Soil Sci. Am. J. 53, 653–660.
X-ray computed tomography to quantify tree rooting spatial distributions Alain Pierret b
a,b,)
, Yvan Capowiez b, Christopher J. Moran a , Andre´ Kretzschmar b
a CSIRO Land and Water, G.P.O. Box 1666, Canberra, ACT, Australia INRA Zoologie, AÕignon, Domaine Saint-Paul Cantarel, Site Agroparc, 84914 AÕignon Cedex 9, France
Received 18 December 1997; accepted 18 October 1998
Abstract Poor root development due to constraining soil conditions could be an important factor influencing health of urban trees. Therefore, there is a need for efficient techniques to analyze the spatial distribution of tree roots. An analytical procedure for describing tree rooting patterns from X-ray computed tomography ŽCT. data is described and illustrated. Large irregularly shaped specimens of undisturbed sandy soil were sampled from various positions around the base of trees using field impregnation with epoxy resin, to stabilize the cohesionless soil. Cores approximately 200 mm in diameter by 500 mm in height were extracted from these specimens. These large core samples were scanned with a medical X-ray CT device, and contiguous images of soil slices Ž2 mm thick. were thus produced. X-ray CT images are regarded as regularly-spaced sections through the soil although they are not actual 2D sections but matrices of voxels ; 0.5 mm = 0.5 mm = 2 mm. The images were used to generate the equivalent of horizontal root contact maps from which three-dimensional objects, assumed to be roots, were reconstructed. The resulting connected objects were used to derive indices of the spatial organization of roots, namely: root length distribution, root length density, root growth angle distribution, root spatial distribution, and branching intensity. The successive steps of the method, from sampling to generation of indices of tree root organization, are illustrated through a case study examining rooting patterns of valuable urban trees. q 1999 Elsevier Science B.V. All rights reserved. Keywords: tree roots; image analysis; morphology; spatial distribution; sample preparation
)
Corresponding author. E-mail: [email protected]
0016-7061r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 6 - 7 0 6 1 Ž 9 8 . 0 0 1 3 6 - 0
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1. Introduction In the urban environment, the health of large trees is important for a variety of reasons. In many cases, the cost of replacing ailing or dead trees is significant. Observations along trenches dug for maintenance of subterranean infrastructure consistently showed that the root systems of urban trees were not fully developed compared to what would be expected under natural conditions. The spatial extent of roots of these urban trees is often restricted to the volume of the pit in which they were initially planted. This poor root development is a threat to the growth and health of the above-ground part of the tree. This aberrant root development is believed to decrease the life expectancy of urban trees by 10 to 20 years because it affects water and nutrient uptake and potentially leads to extra-sensitivity to diseases. Another problem is associated with trees whose roots spread excessively towards leaking parts of the water supply network and cause considerable damage, which is expensive to remedy. Therefore, urban management authorities are keen to develop techniques to minimize ill-health of trees and to provide a favorable growth environment. The spatial distribution of tree roots and their relationship with the surrounding environment is important information for understanding how to manage trees to meet these objectives. An additional restriction is that the value of the trees constrains the extent to which the root system of any one tree can be sampled. If the soil lacks cohesion it is not possible to take specimens to estimate root length density with any confidence. To obtain the required information, undisturbed specimens must be extracted and analyzed non-destructively. Spatial organization of plant or tree roots is most commonly assessed by mapping the contact of roots with horizontal or vertical planes Ž Tardieu, 1988a,b; Commins et al., 1991; Bruckler et al., 1991; Logsdon and Allmaras, 1991; McBratney et al., 1992; Van Rees et al., 1994; Stewart et al., 1994; Pellerin and Pages, ` 1996, Stewart, 1997.. This approach appears well suited to the analysis of the spatial patterns of roots, and several of these studies provided conclusive evidence of interaction between root distribution and soil structure. As an alternative to these manual, tedious and destructive investigations, some studies have been focused on automatic and non-destructive assessment of soil structural features. X-ray computed tomography ŽCT. with low energy medical scanners has been demonstrated as a valuable method for documenting soil macro-porosity Ž e.g., Warner et al., 1989; Peyton et al., 1992., root growth dynamics ŽTollner et al., 1994. , and earthworm burrow system development ŽJoschko et al., 1993, Capowiez et al., 1998.. Difficulty in accessing facilities and imaging limitations Že.g., limited spatial resolution of medical X-ray CT devices, low penetration capability leading to low signalrnoise ratios, or problems related to soil Fe content when using nuclear magnetic resonance ŽNMR.. has meant that efforts have seldom been put into reconstructing plant root 3D distributions using non-destructive methods Ž MacFall and Johnson,
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1994; Liu et al., 1994. . Heeraman et al. Ž 1997. recently demonstrated that a quantitative description of roots of experimentally grown plants can be achieved with high-energy industrial tomography equipment. However, X-ray CT has not been used before for looking at the in situ morphology of root-networks.
Fig. 1. Schematic maps of field sampling. Circular grey areas are trees and white squares are samples. The four samples studied in this paper are grey squares indicated by arrows. Figures reported next to the dotted lines are approximate distances in meters.
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We present here a technique for mapping roots in 3D using low-energy X-ray CT images of undisturbed soil cores. Even though X-ray CT resolution is usually only around 0.5 to 1 mm with medical equipment, this is a sufficient resolution to examine a large proportion of the population of tree roots. The drawback of using a low-energy source of X-rays Ž leading to low penetration capability and associated artifacts. was counterbalanced by using long integration times. X-ray CT images are used as the basic information to generate an equivalent of horizontal root contact maps, at regularly spaced depths, but representing the projection of a volume rather than an actual section. These maps are used to reconstruct the skeletons of three-dimensional objects assumed to be roots. The resulting connected objects are then used to derive indices of the spatial organization of roots.
2. Materials and methods 2.1. Sample collection and preparation Tree root systems were sampled in Paris from two tree species and soil type conditions in parklands: chestnut trees Ž Aesculus hippocastanum L.. growing in an homogeneous sandy soil Ž Boulogne site. , and maples Ž Acer pseudoplatanus L.. growing in a sandy to sandy clay soil ŽVincennes site.. Particle size distribution of Vincennes soil is: 8.5% gravel, 37.4% coarse sand, 30.7% fine sand, 15.6% silt and 7.8% clay. Samples were taken as shown in Fig. 1. Only the samples indicated by arrows in Fig. 1 are discussed in this study. Undisturbed cores could not be sampled by direct use of a normal coring tool because of the abundance of roots and the low cohesion of these sandy soils. To overcome this disturbance problem, a method of field impregnation adapted from Moran et al. Ž1989. was used. A flow diagram of the procedure is given Fig. 2. The method begins with in situ impregnation with an epoxy resin designed to harden in moist soil and to maintain low viscosity under cold temperatures Ž- 58C.. The resin was poured into an aluminium frame Ž 20 = 20 = 22.5 cm. pushed 2 to 3 cm into the soil. As discussed by McBratney et al. Ž1992., a drawback of this field impregnation procedure can be that resin does not infiltrate deeply into soil under certain conditions. To obtain deeper infiltration, six small PVC tubes were pushed into the soil at the periphery of each aluminium frame and the soil then removed from inside the tubes with an auger before resin was poured. Details of manufacturer references and formulation of the field mix are given in Table 1 1. At a temperature of about 108C, the resin sets after 1 to 2 h, and samples can be removed after 1 or 2 days. These times 1
Supply of information regarding this product does not constitute a product recommendation.
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Fig. 2. Flow diagram of the sampling procedure. Ž1. Setting up of the square aluminium frame Ž20 cm.. Ž2. Deep resin infiltration using the aluminium frame and the additional set of PVC tubes. Ž3. Extraction of an undisturbed specimen from which a core will be cut. Ž4. A core ready to be processed after sawing down to 20 cm in diameter.
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Table 1 Base Resin PY303-1 Reactive Diluent DY 0397 Hardener HY 2963
50% 25% 25%
All products are from Ciba-Geigy, Switzerland.
are subject to great variability. For the sampling described here, conducted under cold conditions Ž0 to 18C., samples could be extracted three weeks after field impregnation, allowing the resin to infiltrate deeply. In the laboratory, the partly impregnated samples were set to dry at room temperature for 2 months and were re-impregnated under vacuum. Even after re-impregnation, soil was not saturated with resin. Rather than a complete impregnation, the technique acts to consolidate cohesionless soil, allowing collection of large specimens. Among the twelve specimens thus obtained, only the four longest were kept for further study by X-ray CT. These four specimens were sawn using a helicoidal tungsten wire saw and a disc diamond saw to obtain cores 500 mm high and 200 mm in diameter, which is the maximum diameter that could be imaged using the medical CT scanning device available. 2.2. Image acquisition The samples were scanned using a CT Pace scanner, General Electrice, at 140 kV, 140 mA, with an exposure time of 4 s, and field-of-view of 230 mm, to image 2 mm contiguous horizontal slices. For a review of the physical principles and soil related applications of X-ray CT scanning, see Heijs et al. Ž 1995. or Anderson and Hopmans Ž1994.. Images provided by X-ray CT scanners are based on X-ray attenuation through the sample according to Lambert’s law. Intensities received by detectors are expressed on the linear Hounsfield scale for which typical values are y1000 Ž air. and 0 Ž water. . For subsequent image processing, 8-bit images were captured with a pixel size of 0.4 mm. Before conversion to 8-bit, two parameters, the window width Ž ww. and the window center Žwc., have to be defined. They are clipping values according to which the portion of the Hounsfield scale to be processed is defined. Here, these values were chosen to give optimal contrast between mineral and organic materials Žww s 1400, wc s 700.. The Hounsfield range thus defined, is subsequently converted into 8-bit data, from 0 s black to 255 s white. 2.3. Reconstruction method 2.3.1. Image segmentation and deriÕation of horizontal root maps The basic assumption considered in this work is that the part of the root system concealed in the samples is an arrangement of branching, low density,
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cylindrical segments. Depending on their angle of incidence to the horizontal plane of each image, roots appear in tomographic images as more or less elliptical areas with specific low Hounsfield values Žor grey levels. . It was difficult to separate macropores from roots because resin partly impregnates some roots, resulting in similar Hounsfield values for roots and pores filled with resin. However, on average Hounsfield values for rootrresin areas was 240 Žranging from 200–270. and 750 for soil matrix Ž ranging from 500 to 900.. Consequently, we defined root related objects Ž RRO. as every elliptical area composed of low grey levels. This may result in some misclassification errors in the cases of pores formed by roots or fauna, that were not occupied by roots at the time of sampling. Histograms of the grey levels of 3D images Ž Fig. 3. typically show two sharp peaks corresponding to low density objects Ž around 15 s rootrresin areas. and high density objects Žaround 210 s flint gravels., and a broad peak corresponding to the soil matrix density Žcentered around 140–150.. RROs were extracted from grey level images using a threshold value to segment the image into two distinct populations. Such a method implies that the range of grey levels within which the objects of interest appear is sufficiently narrow and homogeneous. With the samples studied here, bi-partitioning of the histogram was achieved by estimating the distance, d, between the rootrresin peak and the soil matrix peak, and the threshold value was chosen to be at a distance of Ž 2r3. = d from the peak corresponding to the soil matrix Žmethod described in Russ, 1995, and used in Capowiez et al., 1998. . However, by comparison with what was expected from visual inspection of X-ray CT images, it appeared that the smallest RROs could not be correctly selected using this bi-partitioning method. To overcome this problem we used a so-called top-hat filtering Ž Meyer, 1977. which results in extraction of areas of an arbitrarily chosen size, darker than
Fig. 3. Grey levels histogram for the sum of the images forming the BL3 core and method for the bi-partitioning threshold.
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their immediate neighborhood. The combination of Ž 1. a threshold value allowing extraction of low density areas and Ž2. a top-hat filter of size 5, appeared to be well suited to the selection of RROs, as has been found relevant for segmenting pore structure images Ž Moran et al., 1988. . Despite the spatial resolution of the CT-unit used being theoretically 0.5 mm, in the conditions we were using it, the smallest roots imaged were not less than approximately 1 mm in diameter. Root diameters range up to several centimeters Žfor example, presence of roots ; 30 mm in diameter in BL1 and BL3. . 2.3.2. Continuity assessment Continuity assessment was achieved using an overlapping criterion Ž McDonald et al., 1986a,b. , which implies an object in one plane is connected to any of the objects in the following plane only if there is a face-to-face voxel contact. After image segmentation, the continuous 3D objects were reconstructed in three steps. First, RROs in each 2D binary image were labelled. Then, contacts between RROs were identified using a temporary image which is the sum of two successive images Ž n and n q 1, n being the order number of an individual image in a CT series.. Voxels with values larger than the initial value in image n indicate that the faces of two RRO voxels are touching and therefore part of the same object. Because the RROs on both images n and n q 1 were previously labelled, it was possible to record the x, y, z coordinates where the i th object of image n is in contact with the k th object of image n q 1, the latter being itself in contact with the l th object of image n q 2, etc. By applying this rule to every object, at each depth successively, each 3D object Ž or more precisely its skeleton. was eventually reconstructed and identified. This algorithm runs with only two contiguous 2D images loaded at a time which is an advantage given the large computer memory requirements of operating on the entire 3D data set. Because we did not link the centroid positions of connected objects but only the first contact point encountered while scanning images, it is likely, for the largest and very elliptical RROs, that the reconstruction procedure ends up in a ‘broken trajectory’, which is an artifact. To avoid this artifact, we chose to apply a size threshold for the RROs, and not to take into account very elliptical RROs. This reconstruction method can be considered acceptable for preliminary investigations, but it suffers from several drawbacks, the most important of which are: Ž1. the loss of root diameter information; Ž2. a required upper size threshold for the RROs under consideration; and Ž 3. the loss of horizontal roots. Therefore, the method is weakest in circumstances where a significant proportion of the root system has a horizontal preferred orientation. A certain number of continuous roots can also appear discontinuous after reconstruction because segmentation can lead to artificial interruption when individual root pixel values change, according to, e.g., variations in diameter andror in orientation, or when roots grow inside any porous component of the soil.
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3. Results and discussion 3.1. Geometric characteristics inferred from Õisual inspection of 3D skeletons A visual inspection of the four specimens was attempted using the Rotate 2 v1.13 beta freeware package. The reconstructions show objects longer than 20 mm ŽFig. 4.. Important variability can be inferred from this visual inspection. The large number of objects in the upper part of BL3 is related to measurement of surficial litter, which is not present in the other cores. An interesting ‘bypass’ pattern is visible on the left middle part of BL1 Ž as indicated by the arrow in Fig. 4.. It is noticeable that the V6 root network is interrupted around 200 mm in depth. This is an example of previously discussed artifact resulting from segmentation when roots grow in or pass through macropores Žhere, a large rodent burrow. . Vincennes samples appear to show a strong vertical orientation of the root system whereas slanted roots seem more abundant in the Boulogne samples. This visual feature is confirmed by the measurement of each object’s orientation, as indicated by the star plots of directions ŽFig. 5. which show the angles from the horizontal. The length of the arms of the star are normalized against the most frequent angle for all the specimen, i.e., 668 in V6. This difference between Boulogne and Vincennes samples could be related to the sample-to-nearest-tree distance, assuming that roots are almost vertical under tree trunk and increasingly slanted as the distance to the trunk increases Ž the geotropic growth hypothesis, see Grabarnik et al., 1998. . However, it appears that BL3 is not more distant to the nearest tree than V3, and BL1 is even closer to a tree than any of the other samples. Another possible explanation is that the maples in Vincennes mainly developed horizontal and vertical axis roots but few oblique ones whereas the Boulogne chestnuts developed a wider range of oblique roots. 3.2. Root length distributions The root length distributions Ž Fig. 6. indicate that in all specimens, ) 95% of roots are - 100 mm in length. The comparison of length Žsolid line. and vertical extent Ž dotted line. distributions also shows that the vertical extent of roots is mainly - 20 mm Žvertical extent is the number of slices in which an individual segment is present multiplied by slice thickness. . This is another expression of the previously discussed slanted orientation of roots and again, the greatest proportion of long slanted segments is found in the BL3 sample. The 2
Rotateq for MSDos by Marijke vanGans, available from http:rrwww.siliconalley.comrcatr rotate.html. First developed as Rotaterq for the Mac platform by Craig Kloeden, available from http:rrraru.adelaide.edu.aurrotaterr..
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Fig. 4. Example of 3D skeleton representations of root patterns. Only segments longer than 20 mm are shown. Note the ‘bypass’ pattern in BL1, as indicated by the arrow.
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Fig. 5. Star plots of root growth angle to the horizontal ŽA: BL1, B: BL3, C: V3 and D: V6.. For each plot, 0 degree to the horizontal corresponds to the right end and 90 degrees to the vertical. The length of the spikes is proportional to the frequency of roots Žthe circle represents 5%.. Minimum, maximum and mean growth angle are reported beside each plot.
Fig. 6. Root length cumulative distribution functions ŽA: BL1, B: BL3, C: V3 and D: V6.. The dotted line is the vertical extent function Žvertical extent: number of slices in which an individual segment is present multiplied by slice thickness Žhere 2 mm.. and the solid line is the actual length function.
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relationship between root orientation and length showed that, on average, long roots were no more oblique than shorter ones. The shape of the length distribution functions for short roots is difficult to analyze, but it seems that there is little difference between the Vincennes and Boulogne samples. On average, for all of the samples, the cumulative distribution functions show that approximately 5% of the segments are ) 20 mm in length, 15% are ) 10 mm, 25% are ) 8 mm and 50% ) 4 mm. 3.3. Root length density (L Õ ) As noted in Section 1, it was not possible to sample cores from these trees nor to create large exposures to take root contact maps. Therefore, it was not possible to estimate root length densities other than by analysing the CT scans. Root length density was derived from the number of connected objects present at each depth and the volume of each slice. The orders of magnitude of L v for a given minimum length of roots are comparable Ž Fig. 7. for all the samples Žexcept for the 100 upper mm of BL3 due to surficial litter as mentioned above. and are of about 1 to 3 cm cmy3 Žincluding all segments more than 2 mm in length..
Fig. 7. Root length density functions ŽA: BL1, B: BL3, C: V3 and D: V6.. Null values in the upper parts of BL1, V3, and V6 are because data corresponding to the first centimeters of the profile are missing.
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The L v values obtained here are smaller than those obtained by other authors, mainly because of the limited spatial resolution of the images. The order of magnitude of our measurements are close to those derived from root contact mapping in the field ŽTardieu, 1988a,b; Van Rees et al., 1994. or mini-rhizotron counts ŽThomas et al., 1996., but smaller than those derived from polished sections, thin-sections, or X-ray microtomography measurements. As a comparison, our measurements are 100 times less than what Krebs et al. Ž 1994. , obtained on a grass Ž Poa triÕialis . and a dicotyledon plant Ž Rumex obtusifolius., 35 times less than what Heeraman et al. Ž 1997. , obtained on bush beans, and 10–20 times less than what Stewart Ž 1997. obtained on wheat, Van Noordwijk et al. Ž 1992. , obtained on maize and McBratney et al. Ž 1992. , obtained on oats. According to Thomas et al. Ž 1996. fine roots Ž- 0.5 mm in diameter. can represent up to 86% of the total root length of young pine trees Ž Pinus radiata.. In the case of maize plants Ž Kooistra et al., 1992. , the proportion of roots ) 0.5 mm in diameter was found to be even smaller. Therefore, the values of L v estimated here are not unexpected, and these preliminary results indicate that X-ray CT provides similar data to that detected visually in the field, but of course, with the additional advantages of 3D information. 3.4. Distribution analysis using nearest neighbor distances Root spatial distribution was quantified using the 3D coordinates of the reconstructed segments. Calculation of distances between neighboring roots was carried out, at each depth, by considering the x, y coordinates of connected objects as events. The event-to-nearest-event distances Ž referred to as nearest neighbor distances, d . were measured in 2D considering all segments longer than 2 mm. Once d has been computed for every event at a given depth, it is possible to derive a frequency distribution of d . This method only gives information at the smallest scales of the pattern and cannot lead to any conclusions at larger scales, because distances are measured to the closest events ŽCressie, 1991.. Frequency distributions derived from the observed data at each depth were compared with randomness as represented by an homogeneous Poisson process in 2D. The intensity of the process being known for each depth, a random number generator was used to derive simulated d . 99 Poisson process simulations were used to define an envelope representing the domain of randomness for the point processes we consider. In principle, the global significance value of this test is 1% ŽMonte Carlo test; Diggle, 1983.. If the observed distribution function falls inside the simulation envelope, the distribution is random. Departure from randomness is indicated by events falling outside the simulated envelope. At some depths, the intensity of the spatial process was too low, and the test had little actual significance. No formal method was used to account for
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edge effects, however, we did check that when random points fall within a border region of 20 mm, that the observed trends were not significantly altered. Distribution functions were not analyzed individually, but were used to derive a more global spatial arrangement index on the basis of which general trends of root distributions were investigated. Thus, for each depth, an index called the spatial arrangement index Ž S . was calculated from the nearest neighbor distances. S is defined as the mean value of the ratio Si derived following Eq. Ž 1. : Si s
do d Si
Ž1.
where do is the median of the observed nearest neighbor distances and dS i is the median of the i th simulated nearest neighbor distance, and S is the mean of the Si for each of the 99 Poisson process simulations. The lower Ž L1 s . and upper Ž L2 . 95% confidence limits about S are the boundaries of the region from s S y 1.96 = ´ S , to S q 1.96 = ´ S where ´ S is the expected standard error of S. When L 2 s - 1 the roots tend to be spatially clustered; when L1 s - 1 - L2 s, roots tend to be randomly distributed and when L1 s ) 1 roots tend to exhibit an inhibition or regular distribution. As shown in Fig. 8, there is a slight but measurable trend to clustering at depths in between 25 and 40 cm for V3, at depths more than 30 cm for BL3, and at depths more than 47 and 50 cm for V6
Fig. 8. Spatial arrangement index, S, as a function of depth for all segments longer than 2 mm. Note the slight trend to clustering ŽCl symbols on the right hand side of plots. at some depths for BL3 ŽB., V3 ŽC., and V6 ŽD.. Depths at which root segments are randomly distributed are indicated by the Rd symbol on the right hand side of plots. Plain line: median, dotted lines: 95% confidence interval.
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and V3 respectively. BL1 is random at all depths. The range of S values can vary significantly, and all the samples except V6 tend towards a clustered distribution with depth. When considering the proportion of events involved in this increasingly clustered process Ž i.e., the ratio of the number of events for which do values are falling above the envelope of simulated values dS i , to the total number of events., we find that only 10 to 30% of the segments contribute to the observed trend Ž Fig. 9. , and that the proportion tends to increase with depth for all the samples. Fig. 10 shows that this clustering trend is not constant when one considers only segments longer than a given threshold. For different segment length thresholds, S has been summed and divided by the number of slices, giving an average spatial index for each core referred to as S. Long segments tend to exhibit less clustering Ž S increases with increasing minimum segment length., and sample V3 tends towards a regular distribution when considering only segments longer than 20 mm. 3.5. Branching intensity Branching intensity was estimated by counting the number of contacts a given RRO has with other RROs in the sections above and below it. Branching intensity is variable between samples. BL1 and V6 are comparable: they show constant branching intensity with depth. V3 shows a higher maximum number of branches and an increased branching intensity at depths more than 200 mm. BL3 is atypical because of the anomaly corresponding to the 100 upper millimetres Žsurficial litter., but it seems to be regular with depth and with more branches than BL1 and V3.
Fig. 9. Proportion of events involved in the clustering of segments longer than 2 mm, as a function of depth.
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Fig. 10. S as a function of the minimum segment length considered, for each core. The clustering trend observed when short segments are included decreases when only longer segments are taken into account. The horizontal line at Ss1 indicates the limit between clustered Žbelow the line. and regular Žabove the line. distributions.
A possible explanation for the clustered patterns observed could have been that there exists a correlation between branching intensity and do . However, as
Fig. 11. Branching intensity as a function of the median NND ŽA: BL1, B: BL3, C: V3 and D: V6..
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is visible in Fig. 11, even though there seems to be a threshold above which branching is clearly related to a decrease of do , it is more likely that there is no such clear relationship for most of the objects taken into account in our reconstructions. Consequently it can be argued that some clustering actually exists and is not simply a consequence of branching intensity. 4. Conclusion A set of methods, from field sampling to spatial analysis, has been presented to describe tree root distributions in undisturbed soil. The method of field impregnation and subsequent laboratory re-impregnation successfully provided large undisturbed samples of cohesionless soil which were heavily colonized by tree roots. In addition, specimens were taken without fatal damage to the valuable trees. These specimens were well suited to extraction of cores approximately 200 mm in diameter which are successfully imaged using a medical X-ray CT scanner. The approach based on analysis of binary images was demonstrated to be capable of producing reconstructions of 3D continuous objects assumed to be roots with diameters ) 0.5 to 1 mm. Some constraints in unambiguously separating roots and resin-filled pore space have been noted. 3D reconstructions were effective for assessing the spatial organization of tree roots in undisturbed conditions. A set of tools for quantifying the 3D spatial organization of roots was developed and applied to the reconstructed systems. Although there is no statistical assessment of the measurements, this application shows that: 1. a significant part of the tree root systems of both species in both soil types grow at angles - 45 degrees to the horizontal; 2. chestnuts could develop more oblique roots than maples; 3. short root segments exhibit a slightly clustered distribution at some depths; 4. the trend towards clustering tends to increase with depth; 5. long root segments are more randomly distributed, than shorter segments. As recently stated by Clothier and Green Ž 1997. , roots are very difficult to observe in situ, ‘tightly enmeshed in the matrix of soil’, and there is an essential need for better observation and description tools of the complexity of root systems. This work is an attempt to improve our perception of such a complex system by exploring the potential of a method to obtain unique data, e.g., nearest neighbor distances and orientation, which are not easily obtained by other means. We conclude that X-ray CT, even with low energy and limited resolution offered by medical equipment, is a valuable tool to obtain an in situ view of the overall morphology of the root network. Eventually, it could contribute to improve our understanding of spatial variability of root systems in response to the physical, chemical and biological environments they experience.
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Acknowledgements Funding for this work was provided by the city of Paris Ž convention Ville de ParisrINRA for the improvement of tree health in the urban environment. . We would like to thank Herve´ Bossuat for field sampling management and critical discussions. CT scanning facilities in Avignon Hospital were used after the agreement of Drs Roumieu and Burdelle. The authors are grateful to Jacques Barthes, Jean-Marc Becard, Dominique Beslay, and Michael Krebs for help ´ during sampling and laboratory manipulation.
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