Variation in maturity observed along individual cotton fibers using confocal microscopy and image analysis

Abstract

A prior work describing a computer vision system for measuring maturity using longitudinal views of cotton fibers reported observing a large variation in maturity within a single fiber. This paper describes the use of confocal microscopy as an independent measuring method to validate those findings. Individual cotton fibers are imaged from end to end by a confocal microscope producing hundreds of image volumes of cotton fiber segments, each ∼150 µm in length. From these volumes, virtual fiber cross-sections are extracted, processed using the level set method, and measured according to AATCC standards. The results demonstrate with both visual and quantitative analysis that fiber maturity can exhibit large variations within a single fiber.

Keywords

cotton fiber maturity cross-section confocal microscopy level set method variation in maturity image analysis

Maturity is one of many characteristics used to evaluate cotton fiber quality. More mature fibers produce better quality yarns and have better dye affinity. However, despite the importance of this fiber property there are no measurement methods that are both fast and reliable. The current, most reliable, and direct method described by AATCC 20A-2012 section 14 calculates maturity, θ, by analyzing microscopic images of fiber cross-sections.¹ Using image analysis techniques, two features are computed for each cross-section: the perimeter, P, and the area of the secondary cell wall, A.² Maturity is then calculated according to the following formula

θ = \frac{4 π A}{P^{2}}

(1)

which is the ratio of the area A to the area of a circle having perimeter P.³ This direct method requires tedious sample preparation as bundles of fibers must be cut with a microtome and the resulting cross-sections imaged under a microscope. This process is described in greater detail by Hequet et al.⁴ Other common measurement methods include the Uster Advanced Fiber Information System (AFIS), the Cottonscope, and the Uster High Volume Instrument (HVI), which indirectly estimates maturity by combining micronaire with other measurements such as length and elongation.^5–7

While each of these indirect methods has been fully validated, research efforts continue to develop new features and techniques for evaluating fiber maturity.⁸ One such method introduced by Shahriar et al. describes a system designed to measure both length and maturity simultaneously from longitudinal images of individual fibers.⁹ Using a set of 104 reference cottons as ground truth, Shahriar et al. employ the concept of transfer learning to estimate maturity from image characteristics based on fiber width, intensity, and texture features.^4,10

One novel aspect of this system is that it not only provides an average maturity for a complete fiber, but also the variations in maturity from end to end. During processing, the image is divided into segments 150 µm long. The features described above are then extracted from each of these tiles and a maturity value, θ, is estimated from a regression equation output by the transfer learning process. The results reveal that fiber maturity can vary significantly along the length of the fiber. Figure 1 shows a graph of maturity values from one fiber taken directly from Shahriar et al.⁹ Each point in the graph represents the maturity of a segment (x-axis) versus the average maturity of its two neighboring segments (y-axis). While these maturity pairs show a strong correlation, indicating that neighboring segments exhibit very similar maturity values, maturity seems to vary significantly over the entire fiber. Hsieh and Wang show there can be variations in strength within a single fiber, which can be attributed to maturity among other factors.¹¹ However, no work has specifically examined maturity in a manner that could be used to corroborate Shahriar et al.'s findings. It is this intra-fiber variability in maturity that we wish to explore via an independent measuring method.

Figure 1.

Maturity-pair plots for a single cotton fiber. Each point shows the maturity value of a segment (x-axis) versus the average maturity of neighboring segments (y-axis). Correlation along the diagonal indicates neighboring segments have very similar maturity values, yet, overall, there is a large variation in maturity. (Reproduced with permission from Shahriar et al.⁹)

Methods

The current direct method for evaluating maturity described by Hequet et al. does not allow for easy examination of consecutive cross-sections along a single cotton fiber.⁴ The method calls for creating a bundle of fibers. Once these fibers are cut with a microtome it is practically impossible to determine which cross-section came from which fiber. Alternatively, attempting to follow this method with a single cotton fiber instead of a bundle of fibers would be equally challenging. For these reasons we have chosen to use confocal microscopy to create virtual cross-sections of a cotton fiber.

Image acquisition: confocal microscopy

A raster scanning confocal microscope acquires images point by point while its optical arrangement blocks the out-of-focus signal, thus allowing optical sectioning.¹² Three-dimensional image formation is achieved by moving the objective lens, which changes the focal plane. At each focal plane, the system acquires a standard 2D image in raster scan fashion, often referred to as a slice. Once the image is obtained, the objective is moved a very small distance and another 2D image is acquired. After the focal plane has been moved through the entire specimen (or some desired thickness), all slices are compiled into a single image volume, also known as a z-stack.

In most applications of confocal microscopy, fluorescent stains, or dyes, are used to label objects of interest in the specimen being imaged. Lasers at the correct excitation wavelengths excite these stains to emit photons at a slightly longer wavelength. Initially, for our application, the stain calcofluor white was chosen, which is known to bind to cellulose.¹³ However, after some initial scans, it was determined that calcofluor was not able to uniformly penetrate the cellulose, making detection of the secondary cell wall impossible in some areas of the fiber. As an alternative, we turned to acrolein vapor fixation. Acrolein penetrates the tissue very fast, is an effective crosslinker, and is also known to induce intense autofluorescence.^14–16 Dry cotton fibers were exposed to acrolein vapors for 15 minutes before mounting to a slide for imaging. This method appears to fully penetrate the fiber's cellular structure and provides a good signal from which to detect and measure the fiber without the use of other dyes.

Figure 2 shows the difference between calcofluor and acrolein in virtual cross-sections from three different fibers. The cross-section in Figure 2(a) is taken from a mature fiber stained with calcofluor, while the mature and immature cross-sections in Figure 2(b) and (c), respectively, have been acrolein-fixed. Compared with calcofluor, acrolein produces a strong and uniform signal throughout the specimen. Another advantage for using the anhydrous vapor fixation is that staining with calcofluor or any other fluorophore may cause the fiber to swell as the fiber must be immersed in a liquid solution to apply the stain.

Figure 2.

Comparison of calcofluor white versus acrolein vapor fixation as a source of fluorescence. (a) Virtual cross-section of a mature fiber stained with calcofluor. (b) Mature and (c) Immature cross-section of fibers fixed with acrolein. Acrolein produces a more uniform signal throughout the fiber.

Once the acrolein fixative has been applied, the fiber is mounted in a coverglass bottom chamber. Two pieces of double-sided tape are placed far enough apart to which both ends of the fiber are affixed so that the fiber is held relatively straight. A piece of glass is placed on top, but spacers stop it from contacting the fiber. A mounting medium, 2,2′-thiodiethanol, is then applied to the edge of the glass, which is drawn in by capillary action and allowed to sit for several hours.¹⁷

Image volumes were acquired with an Olympus FV1000 confocal microscope using an Olympus UPLSAPO 100×/1.4 oil immersion objective. Fluorescence was excited using a 488 nm argon ion laser, and emission was detected in the 500–600 nm wavelength range. Microscope parameters were also adjusted to achieve the desired pixel size, which in our experiments, varied between 250 and 300 nm per pixel in all three dimensions. As a point of reference, at 250 nm/pixel, a fiber 10 µm in width would contain about 40 pixels across the diameter. Also, at this magnification the field of view contains a ∼150 µm fiber segment. In order to scan a complete fiber from end to end, a z-stack must be acquired for each segment resulting in 100–300 image volumes depending on the length of the fiber, a process which takes several hours. Figure 3 shows a 3D rendering of an image volume for one particular cotton fiber segment.

Figure 3.

(a) Three-dimensional rendering of a z-stack for one particular cotton fiber segment. (b) Same segment as in (a) viewed from the top. (c) Markup of (b) indicating the location and orientation of the cross-section images taken from this volume. The thick white line running through the middle of the fiber is the medial axis and the short, thin lines perpendicular to the medial axis generally show how the cross-section slices are extracted.

Extraction of cross-section volumes

Once a z-stack has been acquired, the next step is to extract virtual cross-sections similar to the physical cross-sections described by the current direct method. This process is automated using the maximum intensity projection (MIP; e.g. Figure 3(b)) as a guide to identifying the path of the fiber through the image volume. First, the medial axis of the fiber is located in this 2D projection by applying a gray level threshold followed by morphological thinning.¹⁸ Next, beginning at one end of the medial axis, a cross-section image is extracted from the image volume for each pixel along the medial axis. Figure 3(c) shows the location and orientation of the cross-sections taken from the volume shown in Figure 3(a) and (b). The thick white line running through the middle of the fiber is the medial axis, while the short thin lines perpendicular to the medial axis represent the location of the cross-sections. While cross-sections are actually taken at every point along the medial axis, for illustration purposes the cross-section lines in this figure are drawn through every 20th point just to give the observer the general idea. This particular segment generated 500 cross-section images.

All of the cross-section images for a segment are assembled to form a cross-section volume. While the cross-section volume is very similar to the original image volume, it differs in two respects. First, it is much smaller. By limiting the size of the profile just enough to span the width of the fiber, a significant amount of background is removed, which reduces processing time in later steps. Second, since the cross-sections are oriented in a perpendicular fashion with respect to the medial axis, the cross-section volume approximates the axial views of the fiber.

Segmentation of cross-section volumes

Once the cross-section volume is assembled, the boundaries of each cross-section are located by a process generally known as segmentation. For each slice in the cross-section volume the objective is to isolate the fiber cross-section from the background so that the current method's cross-section measurements can be directly applied.⁴ (Note that in the context of a cross-section volume, the term slice now refers to a single cross-section image.)

First, as a preprocessing step, the cross-section volume is smoothed in the direction of the fiber. This is done for each slice by averaging the current slice with 10 of its neighbors. In other words, each pixel in slice S₀ is smoothed according to

{\overset{\land}{S}}_{0} (x, y) = \frac{1}{11} \sum_{i = - 5}^{5} S_{i} (x, y)

(2)

where

{\overset{\land}{S}}_{0}

is the smoothed version of the current slice, S₀, and S_i includes the neighboring slices preceding (

i < 0

) and following (

i > 0

) the current slice. Through experimentation it was determined that smoothing only along the direction of the fiber sufficiently removes noise and improves image quality, while smoothing in all three dimensions produced too much blurring near the edges of the cross-section, which hinders the segmentation process.

With the smoothed cross-section volume, segmentation of each cross-section is carried out one slice at a time. Since by observation, the shape of the cross-section changes very little from slice to slice within a volume, the segmentation boundary can be initialized by using the result of the previous cross-section. Of course, this requires that the first slice of each volume be manually segmented in order to improve the segmentation accuracy by minimizing cumulative errors. The following is a brief discussion of the technical aspects of this method.

Segmentation of the images is carried out by implementing the level set method.¹⁹ In this method, boundaries of interest are represented as the zero level set of an implicit function, Φ, i.e. Φ( $\overset{⇀}{x}$ ) = 0. Osher and Sethian describe an iterative approach for explicitly evolving the level set function, Φ, according to some criteria, which in turn deforms the boundary of interest (i.e. the zero level set, Φ = 0) implicitly.¹⁹

Given an initial boundary Φ( $\overset{⇀}{x}$ ) = 0, Φ is often initialized to be a signed distance function. A distance function can be defined as

x_{I}^{⇀} | Φ (x_{I}^{⇀}) = 0}

(3)

then Φ(

\overset{⇀}{x}

) = −d(

\overset{⇀}{x}

) when

\overset{⇀}{x}

is inside the boundary and Φ(

\overset{⇀}{x}

) = d(

\overset{⇀}{x}

) when

\overset{⇀}{x}

is outside the boundary. In other words, the values of Φ inside the boundary are less than zero, and the values of Φ outside the boundary are greater than zero.

Following the general framework of Osher and Sethian, the following update equation was designed for Φ:

Φ_{t} + \underset{\binom{external}{\binom{velocity}{force}}}{\underset{︸}{\overset{⇀}{V} \cdot \nabla Φ}} + \underset{\binom{normal}{force}}{\underset{︸}{{β f}_{n} | \nabla Φ |}} = \underset{\binom{curvature}{force}}{\underset{︸}{{κ f}_{c} \nabla^{2} Φ}}

(4)

where

Φ_{t}

, represents the time derivative of the level set function, Φ. As indicated, Equation (4) has three distinct parts, or forces, which affect how the boundary behaves. In the discussion that follows, it is important to note that this equation was originally developed to overcome many obstacles encountered while attempting to segment calcofluor-stained fibers, which exhibit a weak fluorescent signal. The stronger signals observed in acrolein-fixed fibers greatly alleviated but did not completely eliminate many of these issues. As such, the following figures use cross-sections from fibers stained with calcofluor to better demonstrate the details of this method.

The external velocity force is composed of the gradient of the level set function, $\nabla Φ$ , and an external velocity field, $\overset{⇀}{V}$ . The external velocity field is created using gradient vector flow (GVF).^20,21 The idea of GVF is to drive the boundary towards local gradients (edges) in the image. This is the primary force in the evolution of the boundary and solves a common problem. In some cases, an edge seems to disappear over several slices. Typically, it reappears in the same general area as when it was last observed. Figure 4 shows an example of this. Humans possess the ability to observe the middle image in the sequence of images in Figure 4(a) and mentally fill in the missing edge information because of what was observed in previous slices. This external velocity term mimics that behavior by moving the segmentation boundary only in areas that have good edge information. Similarly, in areas that lack edge or other image data, the boundary remains in the same location. Figure 4(b) demonstrates the effectiveness of this force.

Figure 4.

(a) Edges may disappear and reappear over a number of slices. (b) The light gray boundary indicates the final segmentation results using only the GVF force from Equation (4).

The next term in Equation (4), the normal force, assists the GVF force in cases where a very faint edge moves outside the segmentation boundary undetected by GVF and in later slices increases in signal strength. The image sequence in Figure 5(a) demonstrates this problem. The normal force consists of three components: a constant that controls the overall magnitude of the force, β, a function that can turn the force on or off based on the underlying image data, $f_{n}$ , and the gradient magnitude of the level set function, $| \nabla Φ |$ . The design of the function, $f_{n}$ , is such that it tends to 0 for regions of the image that are background and 1 for regions that are considered to be part of the cross-section, e.g.

f_{n} (x, y) = \frac{1}{1 + \exp {- k_{n} (g (x, y) - c_{n})}}

(5)

Figure 5.

(a) Using only the GVF force, sometimes subtle edges move outside the boundary undetected. (b) GVF and normal force together can properly track the edge missed in (a). However, a new problem has been introduced: protrusions. (c) Segmentation results using all three forces: GVF, normal, and curvature.

Equation (5) is essentially a smooth thresholding function on the image slice, $g (x, y)$ , where k_n is a constant controlling the speed of the transition and c_n is the chosen threshold value. For $g (x, y) \in [0, 1]$ , we chose k_n = 30 and c_n = 0.2. This force has the effect of pushing the boundary outward when it overlays part of the cross-section. Figure 5(b) shows how the normal force alleviates this problem but simultaneously introduces unwanted protrusions.

Protrusions typically occur when weak edge boundaries move inward over several slices. From slice to slice, the GVF force is too weak to pull the boundary along with the retreating edge. What typically remains is a section of the boundary stuck in an area of the image that is essentially the background. Based on numerous observations, these protrusions exhibit high curvature and, therefore, can be eliminated by the curvature force indicated in Equation (4). This force contains three parameters: a constant, K, a function to control this force based on image data, $f_{c}$ , and the Laplacian of the level set function, $\nabla^{2} Φ$ . The control function, $f_{c}$ , works in the opposite manner of its counterpart, $f_{n}$ . It tends to 0 for regions considered to be part of the cross-section (i.e. higher intensity values) and 1 for the background, e.g.

f_{c} (x, y) = 1 - \frac{1}{1 + \exp {- k_{c} (g (x, y) - c_{c})}}

(6)

Once again, this equation is a smooth thresholding function on the image slice, g(x,y), where k_c is a constant controlling the speed of the transition and c_c is the chosen threshold value. For $g (x, y) \in [0, 1]$ , we chose k_c = 30 and c_c = 0.1. Overall, this term has the effect of forcing high curvature areas of the boundary that extend into the background to shrink. Figure 5(c) shows the effect of all three forces working in unison to properly track the edge of the cross-section.

As mentioned previously, while this technique was originally designed for use with calcofluor-stained fibers, it works quite well with the stronger fluorescent signals associated with fibers fixed with acrolein. Figure 6 shows segmentation results for six cross-sections taken from the image volume of the acrolein-fixed fiber segment in Figure 3. Slices 1 and 500 correspond to the left- and right-most cross-section lines, respectively, in Figure 3(c). In each cross-section, the outline shows the final result of the segmentation boundary after applying the method described above. Using these segmentation results for each cross-section, a 3D model of the fiber segment can be constructed. Figure 7 shows a 3D model of this same fiber segment.

Figure 6.

Six cross-sections taken from the image volume shown in Figure 3. The outline indicates the final segmentation boundary.

Figure 7.

Three-dimensional reconstruction of the fiber segment shown in Figures 3 and 6. (a) View from the top matching that shown in Figure 3(b). (b) Different view showing the fiber segment's twists and folds.

Cross-section measurements

With the cross-section boundaries identified by the segmentation process, one can proceed to directly measure the area and perimeter of each cross-section. Given a known pixel size, an intuitive approach would be to simply count the number of pixels inside the boundary for the area and the number of pixels along the boundary for the perimeter. However, for perimeter this method is prone to significant error. For example, Figure 8(a) shows the error using the pixel-counting method for these two measurements. Given an image of a circle of known, fixed diameter, as the resolution increases (i.e. as the number of pixels representing the object increases), the estimated area using pixel counting becomes more accurate. However, under the same conditions, the perimeter measurement seems to consistently underestimate the true perimeter by about 10%. Thus, a different method must be employed.

Figure 8.

Comparison of methods for calculating area and perimeter for the image of a circle of known, fixed diameter as resolution increases. (a) Using pixel-counting method works well for area but not for perimeter. (b) DSS algorithm for calculating perimeter produces much less error.

Using the theoretical framework of finite topology, the Digital Straight Segments (DSS) algorithm provides a much more accurate perimeter estimation technique.^22,23 By redefining the relations between adjacent pixels into cellular complexes, the DSS algorithm divides the boundary into a series of straight segments and estimates the perimeter by summing the Euclidean distance of each segment. Figure 8(b) shows that the error for this method appears to converge near 0% the resolution increases.

It should be noted that the reference image of a circle varied in resolution such that on the low end, the area was represented by as few as 21 pixels and as much as 1500 pixels at the high end. In other words, those are the left and right extremes in the graphs of Figure 8. By comparison, cross-section areas vary between 500 and 3000 pixels, so the operating range in these graphs is generally in the region where the error has stabilized, i.e. resolution >12. In this region the mean error in the area calculation is 0.33%, while the mean error in the perimeter calculation using the DSS algorithm is 0.35%.

Comparison with manual segmentation

In an effort to quantify the effectiveness of the segmentation method discussed above, we present a comparison of that technique versus manual segmentation. Using the six fiber segments detailed in Figures 15, 16, 18, 19, 21, and 22 of the following section, every 60th slice was extracted, i.e. slice 1, 61, 121, 181, etc., resulting in a total of 47 slices. As will be discussed later, these segments represent a wide variety of fiber shapes and maturities. Each of these slices was manually segmented five times, and area and perimeter were measured as described above. Figure 9 shows the area and perimeter of the automated segmentation algorithm versus the average area and perimeter over the five manual segmentation results for each of the 47 slices. Both graphs in this figure show a strong linear correlation with a regression equation close to a diagonal line. For area in Figure 9(a), the slope of 1.044 (95% confidence interval [CI] 1.033–1.056) indicates that area is generally overestimated by about 4.4%. For the perimeter in Figure 9(b), while the slope of 1.006 (95% CI 1.000–1.012) indicates a slight overestimation, the error is not statistically significant.

Figure 9.

Comparison of automated segmentation technique versus manual segmentation over 47 slices of varying size, shape, and maturity. (a) Area and (b) Perimeter both show a strong linear correlation with manual segmentation.

Fiber swelling

Early experiments (not discussed in this paper) revealed that the fiber may swell either as a result of the calcofluor staining process or by being immersed in the mounting medium during imaging. As mentioned previously, acrolein vapor fixation replaced calcofluor and removed it as a potential source of swelling. With the remaining variable, the mounting medium, 2,2′-thiodiethanol, a study was devised to quantify the effects of swelling, if any.

For this experiment, two fibers, one mature and one immature, were selected by manual examination under a microscope using polarized light and each was fixed with acrolein.^24–26 Then, one at a time, each fiber was mounted onto a coverglass bottom chamber following the procedures described previously. However, rather than letting the fiber sit in the mounting medium for several hours, once the medium was applied, a time-lapse series was begun on a particular segment of the fiber using the confocal microscope. The time-lapse consisted of a z-stack acquired every 15 minutes for the same segment over a period of 4 hours. For each fiber, the first z-stack was started within 3–5 minutes of applying the medium. For the mature fiber we chose a particularly full/round segment, and for the immature fiber we chose a particularly flat/deflated segment.

Figure 10 shows images of the entire segment for each fiber. The segments are about 50 µm in length, and each represents one particular time point for that fiber. Figure 10(a) and (c) show the MIP for the mature and immature fiber segments, respectively. Figure 10(b) and (d) show the 3D reconstruction of each segment based on the results of the segmentation algorithm described above. In Figure 10(d), the outer shell is translucent to show the lumen, which has also been segmented. The lumen in the mature fiber segment was at most a few pixels when observed, so no attempt was made to segment or measure it.

Figure 10.

(a) MIP of one time point of the mature fiber segment. (b) Three-dimensional reconstruction after segmentation of mature fiber segment. (c) MIP of one time point of the immature fiber segment. (d) Three-dimensional reconstruction after segmentation of immature fiber segment. In (d), the outer shell is made translucent to show the segmented lumen inside.

Among the z-stacks for each fiber, there is virtually no visually discernible change in the fiber size or shape. The fiber did shift its position slightly over the course of the 4-hour experiment. This was due to the fiber “flowing” with the medium as it slowly reached a state of equilibrium between the two pieces of glass. This demonstrates why it is usually a good idea to let the specimen sit in the medium for several hours prior to imaging. For both fibers, a few z-stacks were excluded because the fiber moved outside of the optical sectioning window during those time points.

Figure 11 shows the measurements from the cross-section segmentation of the mature fiber segment. In each of these graphs, the measurements for a given time point (TP) are shaded from dark to light gray, with the darker shades indicating time points earlier in the experiment and lighter shades indicating time points towards the end of the 4-hour period. For the mature fiber, TP1, TP15, and TP16 were not processed because a part of the fiber was too close or slightly outside of the optical sectioning window. Also, to visually simplify the graphs, five time points have been selected that are relatively evenly spaced over the time period of the experiment. Figure 11 shows the (a) area, (b) perimeter, and (c) maturity of each cross-section along the length of the fiber. In Figure 11(c), θ is calculated assuming that the area of the lumen is zero, which is a reasonable estimate. By inspection, amidst the variation it is difficult to observe any swelling in the graphs. In fact, analysis of the difference between TP2 and TP14 for each measurement reveals that swelling does not have a significant impact on the mature fiber. The mean difference (calculated as TP14 minus TP2) for area and perimeter are 0.380 µm² (95% CI –10.183 to 10.943 µm², s = 68.8 µm², n = 163) and 0.385 µm (95% CI –0.098 to 0.870 µm, s = 3.15 µm, n = 163), respectively, while the mean difference in maturity (θ) is –0.002 (95% CI –0.005 to 0.000, s = 0.015, n = 163).

Figure 11.

Graphs of (a) Area, (b) Perimeter, and (c) Maturity, θ, for the mature fiber segment over the 4-hour experiment. Darker gray lines represent time points (TP) earlier in the experiment, while lighter gray lines indicate time points towards the end of the 4-hour period.

Figure 12 shows the same measurements for the immature fiber. TP9–TP13 were not processed because the fiber moved outside the focal region. Also, as with the mature fiber results, five time points have been selected from the remaining data. Note that the area in Figure 12(a) takes into account the area of the lumen by subtracting it from the total area. Unlike the mature fiber, the immature fiber exhibits a clear pattern of swelling over time. The mean difference between TP1 and TP16 (calculated as TP16 minus TP1) for the area and perimeter are 703.00 µm² (95% CI 682.34–723.67 µm², s = 132.08 µm², n = 157) and 11.40 µm (95% CI 10.62–12.19 µm, s = 5.02 µm, n = 157), respectively, while the mean difference in maturity is 0.027 (95% CI 0.025–0.029, s = 0.014, n = 157).

Figure 12.

Graphs of (a) Area, (b) Perimeter, and (C) Maturity, θ, for the immature fiber segment over the 4-hour experiment. Swelling is readily apparent in all three measurements.

Based on this time-lapse experiment, swelling does not have a significant impact on maturity calculations for mature fiber segments; however, its effects are readily apparent in immature fiber segments. We suspect that the immature fiber has more room to expand, while the mature fiber is packed with cellulose. It should be noted, however, that the swelling seems to stabilize by the end of the experiment for the immature segment. The mean maturity difference between TP 14 and TP16, which represents a 30-minute time span, is 0.0029 (95% CI 0.0017–0.0040, s = 0.008, n = 162). In the experiment described in the following section, the fibers have been allowed to sit in the mounting medium for several hours prior to imaging.

Results

The primary objective of this validation study is to analyze the maturity of a fiber from end to end. For this experiment, three fibers of varying maturity were chosen by manual examination under a microscope using polarized light: one mature, one middle-maturity, and one immature fiber. Each fiber was imaged and processed using the methods described previously.

Since the lumen was difficult to detect in a vast majority of the segments for this experiment, the maturity measurements shown in the rest of this section use total cross-section area—i.e. the area of the lumen is not considered. Using the reference cottons described by Hequet et al., the mature fiber was taken from bale 3140, while the other two fibers were taken from bale 3056.⁴ Figure 13 shows the relationship between the area of the secondary cell wall (henceforth, simply referred to as “area”) and the total area for fiber cross-sections taken from these two bales using the direct measurement method.⁴ Each graph contains around 4200 cross-section measurements. Both cotton samples show a strongly correlated linear relationship between area and total area. According to Figure 13(a), for bale 3140, area is related to total area by a factor of 1.114 (95% CI 1.112–1.116). The same analysis was applied to maturity by incorporating perimeter measurements also taken from the reference study.⁴ Maturity, θ, using area is related to θ using total area by a factor of 1.111 (95% CI 1.109–1.113) with a root mean squared predictive error of 0.042. For bale 3056 in Figure 13(b), area and total area are related by a factor of 1.185 (95% CI 1.182–1.187), while the maturity measurements are related by a factor of 1.170 (95% CI 1.167–1.173) with a root mean squared predictive error of 0.044.

Figure 13.

Relationship between area and total area for cross-sections measured using the direct method described by Hequet et al.⁴ (a) The mature fiber was drawn from bale 3140. (b) Both the middle-maturity and the immature fibers were drawn from bale 3056. The linear relationship indicated in each graph justifies the use of total area to calculate θ for the purpose of making comparisons between cross-sections.

Consequently, although strictly speaking, using total area to calculate θ in Equation (1) is not appropriate, it does provide an adequate estimate. More importantly, the linear relationship indicated in the graphs in Figure 13 justifies the use of total area for our purpose, which is making maturity comparisons between cross-sections that are quite different. In the following results, for the mature fiber, note that the reported maturity values are about 11.4% above the true maturity and that values within ±0.042 are not significantly different. Similarly, for the middle maturity and immature fibers, reported maturity values are about 11.1% above the true value, and values within ±0.044 are not significantly different.

The mature fiber generated 221 confocal volumes. Of those, 73 volumes were discarded for various reasons. In most of these cases the fiber was not fully contained within the optical sectioning field of view. Other cases included trash or optical artifacts which would skew measurements. Of the remaining 148 volumes, 32 volumes were selected as having exemplary segmentation results determined by manual examination. Figure 14 shows the (a) area, (b) perimeter, and (c) maturity measurements for these 32 volumes. Each point along the line in each graph is a measurement for one slice, i.e. one cross-section approximately 280 nm thick, totaling 11,356 cross-sections. Vertical lines indicate the boundaries between cross-section volumes. The shaded segments are examined in more detail below. It is important to note that while these cross-section volumes are in order from one end of the fiber to the other, because some data was discarded, they are not necessarily consecutive. Because of this, there will be some disjointedness in the measurements at the boundaries of each segment.

Figure 14.

(a) Area, (b) Perimeter, and (c) Maturity measurements of 32 image volumes from the mature fiber. Note that maturity in (c) is calculated using total area. The shaded sections, the 5th and 19th segments, are examined in detail in Figures 15 and 16, respectively.

Overall the measurements for these 32 volumes indicate that this fiber is quite mature; although, there are a few segments that show some variation. The first shaded segment in the graphs in Figure 14 (5th segment from the left) is examined in Figure 15. Cross-section images associated with the lowest and highest maturity measurements are shown in Figures 20(a) and (b), respectively. The locations of these two cross-sections within this segment are indicated by the solid vertical lines in the graphs in Figure 15(c). These two images offer visual evidence that confirms the validity of their maturity measurements taking into consideration the aforementioned error. Also, the lumen is visible as a bright area in the center of the images, which, as stated previously, is not often observed. By visual inspection it is reasonable to estimate that area of the lumen is equal in both of these cross-sections. Even though the maturity calculation is performed using the total area, excluding the lumen from this measurement would not notably change the difference in maturity between these two cross-sections. Also, note that because of very small inaccuracies in the digital measurements (e.g. see Figure 8 and related discussion), some maturity values for this segment are slightly above 1. This is particularly likely for cross-sections that are very close to a circle such as Figure 15(b). Figure 16 shows a closer look at the second shaded segment from Figure 14 (19th segment from the left). This particular segment shows consistently lower maturity values.

Figure 15.

Detailed view of the 5th segment in Figure 14. (a) Cross-section corresponding to the location indicated by the left solid vertical line in the graphs. (b) Cross-section corresponding to the right solid vertical line. (c) Plots of area, perimeter, and maturity for this segment. Note that maturity is calculated using total cross-section area. (d) Three-dimensional reconstruction for this segment.

Figure 16.

Detailed view of the 19th segment in Figure 14. (a) Cross-section corresponding to the location indicated by the left solid vertical line in the graphs. (b) Cross-section corresponding to the right solid vertical line. (c) Plots of area, perimeter, and maturity for this segment. Note that maturity is calculated using total cross-section area. (d) Three-dimensional reconstruction for this segment.

Measurements for the middle-maturity fiber are shown in Figure 17. There were a total of 187 volumes for this fiber. Of those, 74 were thrown out for the same reasons discussed previously, but also many of the more immature segments' cross-sections were tightly folded making them extremely difficult to segment properly. Out of the remaining 113 segments, 22 segments were chosen as having extremely good segmentation outputs, resulting in 9473 cross-section measurements. This particular fiber was initially chosen because it seemed to have widely varying maturity when viewed under a microscope using polarized light. Figure 17(c) shows that maturity ranges from 0.4 to almost 1. Figure 18 shows details of the 5th segment from the graphs in Figure 17. The 5th segment is one of the more mature segments for this fiber. The cross-section shown in Figure 18(a) appears quite mature. Then the maturity drops by ∼0.15 in the twisted region of the segment. On the other end of the spectrum, Figure 19 shows the 21st segment, which is a very immature segment. (This is the same segment shown in Figures 3, 6, and 7.) These two segments show that fiber maturity can, indeed, exhibit large variations within a single fiber.

Figure 17.

(a) Area, (b) Perimeter, and (c) Maturity measurements of 22 image volumes from the middle-maturity fiber. Note that maturity is calculated using total area. The shaded sections, the 5th and 21st segments, are examined in detail in Figures 18 and 19, respectively.

Figure 18.

Detailed view of the 5th segment in Figure 17. (a) Cross-section corresponding to the location indicated by the left solid vertical line in the graphs. (b) Cross-section corresponding to the right solid vertical line. (c) Plots of area, perimeter, and maturity for this segment. Note that maturity is calculated using total cross-section area. (d) Three-dimensional reconstruction for this segment.

Figure 19.

Detailed view of the 21st segment in Figure 17. (a) Cross-section corresponding to the location indicated by the left solid vertical line in the graphs. (b) Cross-section corresponding to the right solid vertical line. (c) Plots of area, perimeter, and maturity for this segment. Note that maturity is calculated using total cross-section area. (d) Three-dimensional reconstruction for this segment.

Finally, measurements for the immature fiber are shown in Figure 20. This fiber generated 196 confocal volumes, of which 121 were discarded. Due to its immature nature and the propensity for the fiber to fold over on itself, many segments were impossible to accurately segment and measure. From the remaining 75 volumes, we selected 15 that exhibited very accurate segmentation results totaling 5831 cross-sections. It is clear from the maturity calculations in Figure 20(c) that this fiber was, overall, much less mature than the previous two fibers. Figure 21 shows more details on the 9th segment from Figure 20. The maturity for the cross-section shown in Figure 21(a) is around 0.26. This was the most immature segment observed out of the three fibers. Also, in Figure 21(b), the lumen is apparent as a dark area, which causes the maturity calculation based on the total area to be overestimated in this location of the segment. Despite this, however, the maturity remains much lower for this cross-section than any other segment discussed in these results. Finally, Figure 22 shows details from the 14th segment from the graphs of the immature fiber. This particular segment occurs towards the end of the fiber where the cross-section area and perimeter have tapered considerably: note the downward trend of the area and perimeter in Figures 20(a) and (b). Due to the small diameter of the fiber at this end, the deposition of even a small amount of cellulose causes it to appear slightly more mature than the rest of the fiber, hence the upward trend in maturity in that region.

Figure 20.

(a) Area, (b) Perimeter, and (c) Maturity measurements of 15 image volumes from the immature fiber. Note that maturity is calculated using total area. The shaded sections, the 9th and 14th segments, are examined in detail in Figures 21 and 22, respectively.

Figure 21.

Detailed view of the 9th segment in Figure 20. (a) Cross-section corresponding to the location indicated by the left solid vertical line in the graphs. (b) Cross-section corresponding to the right solid vertical line. (c) Plots of area, perimeter, and maturity for this segment. Note that maturity is calculated using total cross-section area. (d) Three-dimensional reconstruction for this segment.

Figure 22.

Detailed view of the 14th segment in Figure 20. (a) Cross-section corresponding to the location indicated by the left solid vertical line in the graphs. (b) Cross-section corresponding to the right solid vertical line. (c) Plots of area, perimeter, and maturity for this segment. Note that maturity is calculated using total cross-section area. (d) Three-dimensional reconstruction for this segment.

Summary

While the results discussed above represent a relatively small percentage of the total length of each fiber, overall it presents an analysis for more than 26,000 cross-sections taken from only three fibers. The variation in area, perimeter, and maturity is clearly shown for each fiber as a whole as well as for selected segments. Furthermore, each figure containing a detailed analysis of a segment is accompanied by a 3D reconstruction of that segment as well as selected cross-section images that, together, lend visual evidence to the presented measurements. The mature fiber generally shows a consistent level of high maturity (near 1) throughout its length with the exception of a few segments where the maturity drops to 0.8 or slightly less. The middle maturity fiber exhibits the largest variation with some segments appearing quite mature (0.9 to 1) and other segments more immature (near 0.4). Finally, the immature fiber contains maturity values ranging from 0.2 up to 0.7 near the tip of the fiber.

Conclusion

A protocol for imaging cotton fibers with a confocal microscope has been presented as well as methods for processing image volumes for the purpose of measuring cross-sections according to the current direct method. Also, it has been shown that fiber swelling slightly alters observable fiber properties but only for immature fiber segments. However, this does not diminish the validity of comparisons made between segments that exhibit significantly different maturities. Finally, the variability in maturity has been investigated for three different cotton fibers. Both visual and quantitative evidence show that it is possible for maturity to exhibit large variations within a single cotton fiber (e.g. between 0.4 and 1 for the middle-maturity fiber), which seems to corroborate the findings reported by Shahriar et al.⁹ (shown in Figure 1).

Footnotes

Acknowledgements

The use of the Microscopy and Imaging Center facility at Texas A&M University is gratefully acknowledged. The Olympus FV1000 confocal microscope acquisition was supported by the Office of the Vice President for Research at Texas A&M University.

Funding

This research was supported by Cotton Incorporated [agreement number 12-256].

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