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Quantitative morphological traits may be defined based on the 3D anatomy reconstructed from micro X-ray computed tomography (μCT) images. In this study, the heterogeneous spatial distribution of trichomes (hairs) on the adaxial leaf blade surface in Arabidopsis was evaluated in terms of 3D quantitative traits, including trichome number, average nearest-neighbour distance between trichomes, and proportion of large trichomes. The data reflect spatial heterogeneity in the radial direction, in that a greater number of trichomes were observed on the leaf blade margins relative to the non-margins, a distribution effect caused by the CAPRICE (CPC) and GLABRA3 (GL3) genes, which have previously been shown to affect trichome density. We further determined that the proportion of large trichomes on the blade mid-rib increases from the proximal end to the distal leaf tip in both wild-type plants and GL3 mutants. Our results indicate that the GL3 gene affects trichome distribution, rather than trichome growth, causing trichome initiation at the proximal base rather than the distal tip. On the other hand, CPC does affect trichome growth and developmental progression. Hence, quantitative phenotyping based on μCT enables precise phenotypic description for elucidation of gene control in morphological mutants.
Conventional phenotypic screening methods depend largely on visual observations of qualitative traits (Nakazawa et al., 2003). However, subtle trait changes may not be detected by this method. Therefore, mutant candidate lines that require difficult objective evaluation have not been studied. In order to apply a systematic approach to phenotypic analyses, we have proposed a novel method for in silico phenotypic analysis based on 3D shape measurement. This approach includes a 3D laser surface scanner measurement system (Kaminuma et al., 2004), in silico quantitative trait determination via a reconstructed 3D shape model (Kaminuma et al., 2005a), and statistical in silico mutant screening methods (Kaminuma et al., 2005b). In this report, we propose a method for in silico quantitative trait determination using a microfocus computed tomography system (μCT), which functions as a 3D shape-measuring device. Several conventional studies have obtained 2D images of plant inner structures using X-rays (e.g. Koroleva et al., 2000). Allen et al. (2006) used 2D plant root images for practical phenotypic screening. As for 3D based conventional studies, Heeraman et al. (1997) quantified rooting spatial distribution and root length with X-ray CT data in bush bean (Phaseolus vulgaris L.). Similar approaches have been used in chestnut trees (Aesculus hippocastanum L.) and maple (Acer pseudoplatanus L.) (Pierret et al., 1999, 2000). In addition, Stuppy et al. (2003) conducted a survey of high-resolution X-ray CT in plant samples. They reconstructed 3D image data based on X-ray CT; however, in silico phenotypic analysis was not performed. In other words, complete use of 3D image data to reconstruct a 3D shape model or in silico extraction of phenotype was not implemented. In this study, we used μCT-based processing for in silico phenotypic analysis of Arabidopsis thaliana. In order to demonstrate the utility of analytical in silico phenotypic analysis for μCT, 3D-specific leaf trichome traits were proposed. Trichomes are unicellular or multicellular appendages that originate from cells of the aerial epidermis. Population-level studies in plants have indicated that resistance to herbivorous insects is positively correlated with mean trichome density (Valverde et al., 2001). In Arabidopsis, trichome cells are unicellular structures with elusive functions. However, Gutierrez-Alcala et al. (2000) found evidence that biosynthesis occurs in these epidermal structures. Despite the importance of trichome density, most studies of trichome traits are limited to qualitative discussion due to the difficulty of quantification. A successful methodology to quantify trichome traits will greatly facilitate the identification of genes that are integral in trichome control. In this study, two transgenic Arabidopsis lines were evaluated with respect to trichome position, number and size. The CAPRICE (CPC) mutant (Schellmann et al., 2002) is known to possess a large number of trichomes compared with the corresponding wild-type. On the other hand, the GLABRA3 (GL3) mutant displays a reduction in trichome number (Payne et al., 2000). The wild-type, CPC and GL3 mutants were chosen to illustrate how 3D trichome traits can be investigated using both correlation analysis and hypothesis testing for two types of spatial heterogeneity, including the margin, non-margin and mid-rib. In addition, we describe the advantages and disadvantages of μCT as a means for 3D resolution of leaf trichome position. In particular, several important points regarding spatial resolution, data acquisition artefacts and measurement precision are highlighted. Trichome analyses based on μCT can therefore provide new information with regard to trichome phenotypes.
Acquisition of 3D X-ray data
μCT system and principle of X-ray imaging Our μCT system is based on the cone-beam geometry (Kalender, 2006), which irradiates X-rays in a conical form. Figure 1 shows the CT block diagram system used in this study. The X-ray CT system comprises an X-ray tube, an X-ray detector, a sample rotation stage and a control computer. The sample is placed on the rotation stage and the apparatus emits X-rays onto the sample. The stage is rotated 360°, and the detectors collect perspective image data in a 2D array. Radon transformation is used to reconstruct the image to produce 3D image data from the 2D array data (Cherry, 2004). A set of cubes represent the reconstructed 3D image data (Figure 1); the cube is generally referred to as a volumetric pixel element (abbreviated as voxel). Voxel data allow visualization of the cross-section of a 3D image based on volume rendering (a computer graphics technique) (Calhoun et al., 1999). Voxel values must be interpreted carefully. The level of attenuation is measured by X-ray detectors, which display it as a 3D image. Incident X-ray energy, sample density and the atomic number of the sample determine the voxel intensities in the 3D image, corresponding to the level of attenuation. The level of X-ray attenuation is called the X-ray value in this study.
Trade-off between spatial resolution and measured volume. The measurement volume of Arabidopsis individuals varies greatly, from microscopic germination samples to mature macroscopic individual plants. In our μCT system, the maximum measurement volume cannot exceed the volume of a cylinder with radius 3 cm and height 6 cm. As the number of vertical and horizontal pixels in the X-ray detector is fixed at 512 × 512, an inverse relationship exists between spatial resolution and measurement volume. A small measurement volume corresponds to a high spatial resolution, while large measurement volumes correspond to low spatial resolutions. Arabidopsis individuals display a wide variation in size during developmental stages. A seed is approximately 0.5 mm long, and a mature individual has a height of roughly 500 mm. Figure 2(a) shows an Arabidopsis seed cross-section at the highest spatial resolution of 1 μm. A visualization of 3D images by volume rendering is shown in Figure 2(b). Thus, when using μCT for measurements, it is important to consider the trade-off between measurement volume and spatial resolution.
Artefact noise. Imperfect shape measurement by μCT may occur. Therefore, it is important to recognize artefact noise when using μCT for data collection. Plants are particularly subject to peculiar plant artefacts originating from ‘plant self-movement’ and ‘peculiar plant shape’. For artefacts resulting from self-movement, attention must be paid to measurement time. During short 15 min intervals, self-movement causes plant shape transformations. Most notable is the movement of leaf structures. Although visual observation cannot detect plant motion, shape data differences at the μCT resolution level are so large that they inevitably lead to artefact noise. Thus, to avoid artefacts of plant movement, each measurement must be completed as quickly as possible. This requires adjustment of the μCT measurement parameters, because several parameters used simultaneously to enhance precision often require longer measurement times. Another source of artefacts is peculiar plant shape. In general, measurements of cylindrically thick objects such as human or mouse bodies do not result in artefacts. However, thin objects such as plant leaves tend to induce artefact noise due to specific incident angles from X-ray properties. Artefacts in plant shape data can be avoided by placing leaves such that they are not parallel to incident X-rays. Figure 3(a) shows an A. thaliana wild-type Columbia strain leaf cross-section exhibiting artefacts of peculiar plant shape. When compared with Figure 3(b), which lacks noise, artefact noise can be observed on the tips of leaf edges. Therefore, in μCT plant shape measurement, artefacts due to plant movement and peculiar plant shape are important considerations.
Polygon model reconstruction
Polygonal modelling is an approach for modelling objects using a representation or approximation of sample surfaces (e.g. Schroeder et al., 2004). The basic object used in mesh modelling is a point in 3D space termed a vertex. Multiple triangles or four-sided polygons can be used to create complex polygon models. To generate a polygon model from voxel data, it is essential to determine the boundary line between objects and the air, which should correspond to the surface of the polygon model. Following determination of the boundary line, triangle polygons are generated along the line.
Threshold to determine the precision of object boundaries. In our system, 3D images indicate a grey-scale value with 16 bits per voxel. Each individual sample is assigned a whole voxel value, which displays a frequency distribution of X-ray value (Figure 4a). The frequency on the vertical axis is log scale. The largest peak indicates the air distribution. Values greater than the air peak are due to plant structures. In order to generate a 3D surface shape model, a threshold value must be determined to specify the boundary lines between the plant sample and the surrounding air. A polygonal surface is generated on the boundary lines. The boundary lines between objects and the air vary as threshold values are changed. Therefore, determining the threshold is one of the most significant factors for establishing precision in a generated shape model (Figure 4b). However, the threshold for distinguishing a plant sample and air is difficult to determine. Tylén et al. (2001) proposed thresholds calculated by assigning intermediate values between the air peak and unique tissue peaks in Homo sapiens. As this method is widely used in the CT research field, we similarly adopted an intermediate value between the air peak and the plant peak as the threshold.
Conversion from 3D image to polygon model. To create a polygonal model when using a laser surface scanner as the 3D measurement device (Kaminuma et al., 2004), we began with a 2D depth image. The 2D depth image pixels represent Z-values corresponding to depth. Consequently, the 2D depth image can be easily converted to polygons by connecting adjacent pixels and assigning Z-values at the vertices of the polygons. However, output data from X-ray CT form a 3D image. For conversion from 3D images to polygon models, we adapted the ‘Marching Cubes’ algorithm (Lorensen and Cline, 1987). This is the most common algorithm for reconstructing faceted isosurfaces from 3D image data. Creation of a polygonal surface within a volume that has the same value at each vertex is used to construct isosurfaces. The Marching Cubes algorithm creates an isosurface from a 3D image at a specified isovalue. As the goal is to reconstruct the plant surface, the above-mentioned threshold is used as the specific isovalue. The algorithm considers the eight corners of a cube as voxels. If several pixels of a cube have values either less or greater than the user-specified isovalue, the cube must contribute some component of the isosurface. In addition, by determining the edges of the cube intersecting the isosurface, triangular polygons are created. The polygons divide the cube into regions within and outside the isosurface. Subsequently, a surface representation is obtained by connecting all the cube polygons on the isosurface boundary. A polygon model thus generated is shown in Figure 5(a) (upper side view) and Figure 5(b) (opposite side view). An individual in its entire original shape is shown. However, due to reconstruction from a 3D image, the original polygon model contains noise generated by different sources. Figure 5(c) shows the individual with the polygon mesh corresponding to small noises removed. These noisy polygons were defined as unconnected polygon meshes. Only the largest cluster corresponding to the plant sample was retained.
Difference between CT- and laser scanner-based polygon models. The strategy defining in silico phenotypic analysis is based on polygon models generated by 3D measurements. In CT- and laser scanner-based polygons, the approach is nearly identical. In the case of laser-based polygons, the tendency of laser scanners to avoid extraction of inaccurate traits must be considered. In a previous study, Kaminuma et al. (2005a) indicated the representative 3D traits of leaf blade height, width and depth (Table 1) as XYZ lengths of a polygon model 3D bounding box. The laser scanner-based polygon models measured only the adaxial surface of the leaf blade. Therefore, the extracted depth traits were intrinsically inaccurate because the generated blade polygon did not represent thickness. On the other hand, CT-based blade polygons reproduce both adaxial and abaxial surfaces, so extraction of accurate depth traits is achieved via thickness.
Table 1. Representative macroscopic leaf blade 3D traits for gl3-7454, Col-0 and cpc-2
3D traits (mm)
Details of the 3D traits have been described previously (Kaminuma et al., 2005a). Means and standard deviations were calculated from 22 leaf blades for each phenotype.
Blade longitudinal length (X)
1.67 ± 0.38
2.22 ± 0.25
2.28 ± 0.36
Blade lateral length (Y)
1.59 ± 0.37
2.14 ± 0.25
2.16 ± 0.38
Blade depth length (Z)
0.55 ± 0.06
0.69 ± 0.07
0.79 ± 0.12
Problems with modelling inner structures. In a previous section, we discussed how to generate the boundary line polygon model between air and plant material. X-ray images represent the inner structure of a plant, which provides the opportunity to create a polygon model of the inner plant structure. However, the above-defined threshold cannot be used to determine boundary lines for inner structures. For example, an embryo inside the seed wall may need to be modelled (Figure 2a). Automatic extraction of the boundary line of the embryo is difficult as computer segmentation processing is subject to inaccuracies when the 3D image lacks high contrast. Typically, as the number of slice images increases, creation of one model from manual segmentation by visual observation becomes a time-consuming process.
In silico phenotypic analysis using CT-based 3D polygon models
Here, we describe an example of in silico phenotypic analysis from CT-based 3D polygon models. Leaf blade trichomes were examined to test the efficacy of CT-based 3D polygon models. Previous work with laser scanner measurement methods could not digitize trichome position owing to insufficient spatial resolution. Here, 3D-based trichome traits, including trichome number, size and nearest-neighbour distances between trichomes, are defined. The difference in the traits between wild-type Col-0 and the two mutant lines cpc-2 (Kurata et al., 2005) and gl3-7454 (Ishida et al., 2007) in the Col-0 background was investigated. Correlation analysis among the three trichome traits was performed, and the spatial heterogeneity of the trichome traits was evaluated statistically.
Definitions of new 3D trichome traits. Trichomes were extracted on polygon models using a local 3D curvature calculation called the Gaussian curvature (http://mathworld.wolfram.com/GaussianCurvature.html). Gaussian curvature has been discussed with reference to leaf macroscopic curvature (e.g. Dumais and Kwiatkowska, 2001;Sharon et al., 2004). Based on visual inspection, the local curvatures at the top and base of a trichome assume positive (convex) and negative (concave) Gaussian curvatures, respectively. Surfaces without trichomes are considered flat, which corresponds to zero Gaussian curvature. Figure 6(a) illustrates colour mapped Gaussian curvature using a leaf model.
(i) Trichome number (T-NUM). Polygons indicating Gaussian curvatures over the absolute value threshold were computed to estimate trichome position. Spatially isolated spots consisting of polygons of high Gaussian curvature were extracted (Figure 6b), and averaged positions of isolated spots were identified as putative trichome positions (Figure 6c). The number of isolated spots represents the number of trichomes.
(ii) Averaged nearest-neighbour distances between trichomes (T-NND). Trichome positions (T-NUM) were used to define T-NND. Three-dimensional nearest-neighbour distances between trichome positions were calculated. The distance distribution median was calculated, and the average of distances for all blades was defined as T-NND.
(iii) Quantitative trichome large-size ratio(T-LSRATIO). As for the T-NUM definition, spatially isolated spots were detected first. The size of the isolated spots represents the quantitative trichome size. However, local 3D polygonal areas corresponding to trichome spots do not include protruding plant parts. Therefore, an accurate size representation is not generated. Consequently, the area of a spot on a projected 2D plane was quantitatively assessed as the individual trichome size. The ratio of number of large trichomes, whose area size is greater than the specified threshold, to the total number of trichomes (T-LSRATIO).
Accuracy of model-based trait extraction by photographic evaluation. The number of trichomes determined using the 3D models was compared to numbers determined from photographs. We used the results of a photographic trichome manual count as the true numbers of trichomes. Two expert operators manually marked each trichome on a photograph, and indistinct trichomes were included (or not) after subjective discussion. Figure 7 illustrates computer-detected trichome positions (Figure 7a) compared with manually determined trichome positions (Figure 7b). For 10 Col-0 leaf blades, a mean of 92% of the manually detected trichomes were identified by in silico extraction. Errors were due to sectioned noise at the blade and petiole connection. Other sources of mis-identification may derive from insufficient spatial resolution and background/margin ambiguities.
Comparison of defined trichome traits among the wild-type and mutants. Figure 8(a, b, d) shows the T-NUM, T-NND and T-LSRATIO for wild-type (Col-0) and mutant lines (gl3-7454 and cpc-2) determined using 22 leaf blades for each line (total n =66). Figure 8(c) shows the frequencies of nearest-neighbour distances in each of the wild-type and mutant lines. The T-NUM values for gl3-7454, Col-0 and cpc-2 were 30.8, 34.5 and 50.1, respectively (Figure 8a). These values indicate a reduction in trichome number for gl3-7454 and an increase in trichome number for cpc-2. Moreover, one-way anova revealed a significant difference for T-NUM between three lines (P =1.67 × 10−15). However, Scheffe’s post-hoc test for all pairwise comparisons indicated no significant difference between gl3-7454 and Col-0 (Figure 8a). The reason for this lack of significant difference might be due to the fact that variance in the trichome number for mutant line gl3-7454 is greater than that for Col-0. T-NND values were 0.155, 0.238 and 0.207 for gl3-7454, Col-0 and cpc-2, respectively (Figure 8b). The mutant line gl3-7454 should show the highest T-NND values because its average trichome number is the lowest. However, gl3-7454 demonstrated the lowest mean values for all traits. To resolve this, we plotted the relationships between the T-NUM and T-NND values and ‘AREA’ (Figure 9), where ‘AREA’ is the 3D area size of a leaf blade calculated from the total polygon area using the method described by Kaminuma et al. (2005a). Correlation coefficients were calculated between T-NUM or T-NND and AREA, and the results indicated no significant correlation between T-NUM and AREA (Figure 9a). However, T-NND showed a significant correlation with AREA for the wild-type and mutant lines (Figure 9b). The relationship between T-NND and AREA was fitted as a first-degree polynomial equation by least-squares estimation. The T-NND values fitted to an AREA of 2.0 mm2 were 0.34, 0.26 and 0.21 for gl3-7454, Col-0 and cpc-2, respectively. Therefore, the quantitative order of T-NND values adjusted for AREA was consistent with the T-NUM results. Hypothesis testing for T-LSRATIO showed significant differences between gl3-7454 and Col-0, and between gl3-7454 and cpc-2 (Figure 8d). However, no significant difference was indicated between Col-0 and cpc-2. This might be due to the low threshold required to define large trichomes. A low threshold equalizes normally large and extremely large sizes.
Correlation analysis among 3D trichome traits. In Figure 9, Pearson’s correlation coefficients were calculated for T-NUM and T-NND traits with respect to AREA. Pearson’s correlation coefficients and partial correlation coefficients between AREA and all 3D traits for the wild-type (Col-0) are summarized in Table 2. A partial correlation coefficient describes the relationship between two variables while eliminating the effects of other variables. For each coefficient, non-significant P values are included (Table 2). The Pearson’s correlation coefficients indicated a significant correlation (P <0.05) between AREA and T-NND. Moreover, partial correlation analysis indicated a significant correlation between AREA and T-NUM (P <0.05) and between AREA and T-NND (P <0.01).
Table 2. Pearson and partial correlation coefficients between extracted 3D traits for Col-0
Values above the diagonal represent Pearson correlation coefficients, and those below the diagonal represent partial correlation coefficients.
0.41 (P =0.06)
0.63 (P =0.016)
0.11 (P =0.64)
0.55 (P =0.013)
0.007 (P =0.97)
−0.27 (P =0.23)
0.68 (P =0.001)
−0.35 (P =0.14)
0.21 (P =0.38)
−0.33 (P =0.15)
−0.042 (P =0.86)
Spatial heterogeneity of 3D trichome traits. Investigation of spatial distribution variation in 3D trichome traits is of value. A conventional study of 2D spatial pattern analysis of trichome distribution has been reported (Larkin et al., 1996), which focused on clustering, regularity and complete spatial randomness (Clark and Evans, 1954; Diggle, 1983). Our Col-0 trichome distribution data from projected 2D images showed a non-random distribution, consistent with the results of the study by Larkin et al. (1996). Here, we focus on two spatially heterogeneous areas. First, the spatial heterogeneity of margin trichomes was analyzed quantitatively. Qualitative data have shown that margin trichomes are distributed differently to non-margin trichomes (Hauser et al., 2001; Marks, 1997). We defined the margin and non-margin spatial sections on a projected 2D leaf blade area. First, the center of mass for all projected 2D polygons was determined. Two leaf blade sections were divided in the ratio 9:1 from the centre of the blade to the margin. The central blade was defined as the non-margin, and the margin was the area delimiting the blade (Figure 10a). We then divided the blade into four sections to investigate the distribution of trichomes along the mid-rib because trichome initiation may be restricted to the base of leaf blades (Schnittger et al., 1999). As shown in Figure 10(b), the mid-rib from the petiole connection to the leaf tip was evenly divided into four sections (1, 2, 3 and 4) on a projected 2D leaf blade area. For the four sections, 2D and 3D areas were analyzed to generate means and standard deviation for each section of Col-0 samples (Figure 10c). As shown in Figure 10(c), the 3D area standard deviation is too great to apply data analysis. Therefore, the spatial configuration for the mid-rib was computed based on 2D areas. Hypothesis testing was subsequently applied to the two types of spatial section. To detect spatial differences in T-NUM, margin and non-margin sections were analyzed using a chi-squared test. The wild-type Col-0 and two mutant lines showed significant differences between margin and non-margin areas. The ratio of marginal to non-marginal T-NUM for both the wild-type and two mutant lines is shown in Figure 10(d). Furthermore, a significant ratio difference was detected among Col-0, gl3-7454 and cpc-2 for all variables (P =2.1 × 10−6). Subsequently, a post-hoc Ryan’s test detected ratio differences between Col-0 and the two mutant lines (Figure 10d). For sections along the mid-rib, the frequencies of large, small and all trichomes are shown in Figure 10(e) and normalized frequencies of large and small trichomes are shown in Figure 10(f). The normalized ratio of large trichomes showed a tendency to increase for all lines from the proximal base to the distal leaf tip sections. To detect a T-LSRATIO trend along the discrete mid-rib sections, the Mantel extension trend test (Schlesselman, 1982) was used. A statistically significant increase trend in T-LSRATIO was detected for Col-0 (P =3.8 × 10−6) and gl3-7454 (P =1.5 × 10−2). No significant trend was detected for cpc-2 (P =9.8 × 10−2). In order to determine the spatial heterogeneity for the T-LSRATIO with larger trichome size, we shifted the threshold from 5 to 9. The P-values for hypothesis tests at the stricter threshold parameters are shown in Figure 10(g). The results suggest that cpc-2 lacks spatial heterogeneity for large trichomes along the mid-rib compared to Col-0 and gl3-7454.
In this paper, we present an in silico phenotypic analysis based on 3D shape models using μCT for plant morphological measurements. We studied A. thaliana leaf blade trichomes on the basis of newly defined 3D-based trichome traits including T-NUM, T-NND and T-LSRATIO. The wild-type Col-0 and two mutant lines gl3-7454 and cpc-2 were used to investigate trichome traits. Correlation analysis for all traits with the blade area revealed a significant correlation with the blade area for both between T-NUM and T-NND in Col-0 wild-type. Moreover, we examined the spatial heterogeneity of T-NUM and T-LSRATIO for two spatial patterns, the blade margin versus non-margin regions and sections of the mid-rib. Trichome numbers at the margins were significantly greater than in the non-margin area for the wild-type, CPC and GL3 mutants. The result indicates the existence of specific gene controlling marginal spatial patterns of trichomes, and is consistent with qualitative observations reported by Marks (1997). Spatial heterogeneity along the mid-rib was detected in both Col-0 and the gl3-7454 line, indicating that the number of large trichomes increases from the proximal base to the distal end. Trichome initiation originates at the proximal leaf base (Schnittger et al., 1999). Consistent with the results of the study by Morohashi et al. (2007), our data indicate that GL3 affects trichome initiation rather than trichome growth. On the other hand, CPC appears to affect trichome growth and developmental progression rather than trichome initiation. With respect to the technical aspects of μCT, there are several critical issues related to the time course of data acquisition, the template and inner structure modelling to be considered. First, time-course data can be acquired by adding a function to our μCT system resulting in in silico phenotypic analysis of broader developmental stages. However, resolution adjustment over a range of developmental stages may be problematic. Second, the template model must be realized. Raw 3D shape models are not labelled with morphological data (e.g. leaf and stem parts). Therefore, segmented template model definitions for morphological plant features are required. In addition, segmentation processing from whole shape to model parts is necessary. Currently, segmentation processing is conducted manually, but semi-automation of segmentation processing is desirable. Finally, modelling inner structures can lead to a substantial increase in processing time because determining boundary lines in low-contrast images must be completed manually. The inner structures of plant parts generally appear as low-contrast CT scan images. On the other hand, plant tissues cover several plant parts, such as seeds in a mature fruit or undeveloped petals. The ability of CT to distinguish internal morphological shapes from air enabled us to apply the analytical methodology presented here to generate a 3D model of internal plant structures. These easily modelled plant structures should be targeted for the first in silico phenotyping analyses directed at evaluating internal plant structures. In conclusion, micro X-ray CT enables comprehensive quantification of various plant morphological traits using whole-shape models. Phenotyping analysis using in silico CT has distinct advantages over conventional measurement devices, such as light micrography, and the potential to contribute abundant gene dissection data.
Plant materials and growth conditions
Arabidopsis thaliana wild-type Columbia-0 (Col-0) was chosen as the control line. The mutant transgenic lines, gl3-7454 (Ishida et al., 2007) and cpc-2 (Kurata et al., 2005), in the Columbia background, were selected to represent small and large numbers of trichomes, respectively. Seeds were sown in soil and incubated at 4°C for 7 days. Following an initial cold treatment, plant samples were cultivated in a growth room (16 h light white light/8 h dark at 22°C). The average light intensity was 70 μmol m−2 sec−1. Plant samples were transplanted to small microtubes prior to CT scanning. The entire above-ground plant shape was scanned at 17 days after sowing. This stage of Arabidopsis Col-0 has emergence of two cotyledon leaves and two true leaves. A small rosette subsequently develops and we chose to evaluate trichome number at this stage because it is relatively easy at this stage by photographic evaluation. For the phenotypic analysis, we used the first and second true leaves because qualitative observations indicated that these leaves were the same size. For statistical analyses, 22 leaf blades for the wild-type and both mutant lines were assessed (n =66). In addition, ten leaf blades from Col-0 were used for photographic determination of trichome number.
System configuration of 3D measurement
A Shimadzu SMX-100CT-SV3 device (Shimadzu Corporation, http://www.shimadzu.com) device was employed for μCT. Voltage and current were uniformly set at 24 kV and 75 mA, respectively, for all measurements. The X-ray detector size was set at 4.0 inch for 512 × 512 sampling points. The source-to-image distance (the distance from the X-ray tube to the X-ray detector) was 375.1 ± 0.008165 mm (mean ± SD). The source-to-object distance (the distance from the X-ray tube to the object) was 76.2 ± 8.44 mm for all individuals. During stage rotation, the number of X-ray views was 1800. Detected images were collected and processed using CT-Solver software (Shimadzu Corporation) to generate 3D X-ray images. The average individual voxel size was 512 × 512 × 191 for XYZ. The XY field-of-view was 11.2 ± 1.21 mm. The Z field-of-view was 4.16 ± 1.03 mm. The corresponding XYZ spatial resolution was 0.0219 ± 0.00237 mm pixel−1. The measurement duration for each individual was approximately 30 min, comprising time to adjust parameters, 5–15 min; scanning time, 10–15 min; reconstruction time 10–15 min.
Polygon model reconstruction
Software processing for data analysis was developed using MATLAB version 7.2 with the image processing toolbox 5.2 (MathWorks Inc., http://www.mathworks.com). Extra slice images in the depth direction were manually removed to save processing time. The slice images were visualized, and extra upper and lower slices were cut by visual manipulation. Upper slices were removed if no plant image was visible. Lower slices were removed when stems without soil were visualized. The X-ray slice image was 16 bits in grey scale (covering all values in the range 0–65 535). The threshold between the air and plant sample was determined via a series of steps. Initially, peak positions for the air and plant were determined, and mean peak positions of 34 842 ± 167 and 55 526 ± 1645, respectively, were obtained. The threshold was calculated as the mean of the air and plant mean peak positions, i.e. 45 184. This threshold was used as the isovalue for the Marching Cubes algorithm to generate 3D polygonal surfaces from the voxel data. The polygonal surfaces consisted, on average, of 1.9 × 105 vertices and 3.9 × 105 triangle faces. Noise was evident on the generated surfaces. Therefore, we separated non-connections of polygonal surface clusters using Rapidform 2002 3D modelling software (INUS Technology, http://www.rapidform.com). The number of clusters varied from 70 to 520. The largest cluster corresponding to the plant sample was retained, and Rapidform 2002 was used to manually determine the two true leaf blades.
Trichome extraction for new 3D trichome traits
The reconstructed polygon models were used to extract trichomes, and the adaxial surfaces of the polygon models were manually extracted using Rapidform. Subsequently, Rapidform was used to extract and smooth upper surface models by a local smoothing method with ten iterations. Second, the Gaussian curvature for the polygon models was calculated by computation of the discrete curvature for each vertex (e.g. Dyn et al., 2001; Meyer et al., 2003). The discrete Gaussian curvature K(p) around vertex p is calculated as:
where θj is the angle of the jth face at the vertex, m is the number of faces and Aj is the area of the jth triangle Voronoi cell. Following Gaussian curvature for all vertices, values >0.34 average absolute value were assumed to be a trichome vertex. Third, polygon model vertices and Gaussian curvature maps were transformed to 3D principal axes. XY grids at even intervals on the 2D XY principal axes were generated from vertices for convenience. The grid size was divided into almost 50 steps in the longitudinal Y principal axis, and a 3D surface mesh model was generated on the XY grids. Neighbouring grids with high absolute values for Gaussian curvature were assumed to be isolated trichome spots. Consequently, the number of isolated spots indicated the number of trichomes, here defined as the T-NUM trait. The 3D position of a trichome was determined as the XYZ average position of an isolated spot in a grid outline. The T-NND trait was defined as the median of the 3D Euclidean distance between each trichome and its nearest neighbour trichome. Further, the 2D projected plane of the 3D blade model was used to identify trichome size. The total spot number and trichome size ratio over a threshold of 5 were selected, and defined here as T-LSRATIO.
Photographic evaluation of trichome number
Photographs of the entire plant body for each individual were obtained using ScanDo dynA+ and the associated software SilverFast Ai (Kaiser Fototechnik GmbH, http://www.kaiser-fototechnik.de/en). The camera was set directly above the plant, the photograph was taken and the images of each individual were saved in TIF format. The images were transferred to MS PowerPoint 2003 (Microsoft, http://www.mircosoft.com), and two independent technicians circled the trichome positions in the image using the same protocol to reduce subjective bias. The number of circled objects was counted by a macro program of MS PowerPoint. Finally, the number agreed among technicians was assumed to be the correct number of trichomes.
Comparison of defined trichome traits among wild-type and mutants
One-way anova was used to determine whether significant differences exist for T-NUM among the three lines. For T-LSRATIO, differences were investigated using a chi-squared test and subsequent post-hoc comparisons using the Ryan test (Ryan, 1960). The correlation coefficient calculations are explained in detail below. The first-degree polynomial fit for significant correlations was performed by least-squares estimation.
Correlation analysis for 3D trichome traits
Statistical correlation analysis and partial correlation analysis were performed using the MATLAB statistics toolbox 5.2. Pearson correlation coefficients among traits were calculated using the covariance matrix, denoted by C(i, j). The (i,j)th element of the correlation coefficient matrix R is:
To test the null hypothesis that no correlation existed among the variables, a t test was performed:
where N is the number of samples. A partial correlation measures the strength of the relationship between two variables, while controlling for the effect of one or more additional variables. The Pearson partial correlation for a pair of variables is defined as the error correlation after controlling variable regression.
Spatial heterogeneity of 3D trichome traits
For the margin and non-margin sectional analysis, the χ2 statistic for T-NUM was calculated as:
where N, Nm and No indicate the total leaf blade trichome, marginal trichome and non-marginal trichome numbers, respectively. The m_ratio and o_ratio represent the marginal area and non-marginal area ratios divided by the total leaf blade area. The degree of freedom was 1. The Mantel extension test (Mantel, 1963) was performed to test for a trend of T-LSRATIO in the four sections of the mid-rib.
We thank Junko Nakamura for CT data collection assistance and manual 3D modelling approaches. We also thank Naohiko Heida and Yoshikazu Hasegawa for μCT system condition adjustments. We are grateful to Masako Fukuda and Mari Suzuki for plant growth management. This work was partially supported by Ministry of Education, Science, Sports and Culture Grants-in-Aid for Young Scientists (B) (numbers 16700278 and 19770044), and also an Institute of Physical and Chemical Research grant for pregnant research staff or research staff taking care of small children.