Analysis of the Glomerular Basement Membrane in Images of Renal Biopsies Using the Split-and-Merge Method: A Pilot Study

The Glomerular Basement Membrane

The kidney is a part of the urinary system responsible for the excretion of the body’s waste products and for maintaining the proper balance of water and electrolytes in the blood. The functional unit of the kidney, the nephron, comprises the renal corpuscle and the renal tubule. The renal corpuscle, in turn, includes Bowman’s capsule and the glomerulus, where the filtering of selected blood components occurs.^1,2 The filtering action within the glomerulus is performed by endothelial cells, the glomerular basement membrane (GBM), and the visceral epithelium (podocytes), which together prevent the passage of negatively charged molecules larger than albumin (about 3.6 nm) through the barrier.³

The GBM plays a crucial role in both structural support and functional operation of the glomerulus. The GBM is built of a meshwork of fused basal lamina mainly composed of laminin and collagen IV, and is divided into three layers: the lamina rara interna, the lamina densa, and the lamina rara externa. The typical width of the GBM is twice the thickness of most of human basement membranes, and is usually in the range of 300–350 nm.^1,2

Imaging and Analysis of the GBM for the Diagnosis of Renal Pathology

Analysis of transmission electron microscopy (TEM) images of renal biopsy samples is an important tool for the diagnosis of diseases such as essential hematuria and thin-basement-membrane nephropathy,^4–6 Alport syndrome (AS),^7,8 and diabetes mellitus.^9,10

Hematuria is defined as the presence of red blood cells in the urine, which can result from bleeding at any level of the urinary tract. Glomerular hematuria usually indicates glomerular disease, such as inflammation (glomerulonephritis), or basement membrane abnormality, such as thin membranes or AS. Pathological changes of the GBM in patients with hematuria include thinning to the range of 100–200 nm with occasional disruption and breaks.²

For patients with AS, the typical lesion is characterized by irregular thickening of the GBM to the range of 800 to 1,200 nm, with splitting and fragmentation of the lamina densa, sometimes alternating with thinning of some portions of the GBM to the range of 100–200 nm. In early or mild cases of AS, thinning may be the predominant feature.

Diabetic nephropathy is a microvascular disease of the glomerulus that affects patients with type 1 and 2 diabetes. Pathological changes in the glomerulus include diffuse thickening of the GBM accompanied by steady decline of the glomerular filtration rate. The pathogenesis of this alteration is poorly understood; it correlates with proteinuria and may be related to abnormal podocyte function.^3,11

Although quantitative analysis of the GBM is of high importance to a pathologist, only a limited number of reliable techniques have been developed. The available techniques include the manual methods developed by Osawa et al.¹² and methods relying on a sampling grid superimposed on the micrograph.^5,6 Whereas these techniques can be applied to a limited dataset of images, the general use of the existing methods is subjective, time consuming, and prone to errors. Only a few image-processing methods^13,14,15 have been proposed to detect and analyze the GBM. The method proposed by Ong et al.¹³ includes measures of smoothness, uniformity, intensity difference, and intensity continuity to track the center line of the GBM starting from a manually initialized point and direction, followed by region growing. Although Ong et al. provided the details of evaluation of the results by a pathologist, no results of clinical application were provided. Recently, we proposed methods based on morphological image processing and active contour models (ACM) for semiautomatic segmentation and analysis of the GBM.¹⁵ The procedure was tested with 34 TEM images of six patients. Comparative analysis of the results with manual measurements by an experienced renal pathologist indicated low error in the range of 36 ± 11 nm. However, weaknesses of the ACM-based method include the requirement of manual construction of walls to prevent leakage of the ACM contours, manual initialization of contours, and the complexity of the parameters affecting the deformation of the ACM contours.

In the present paper, we propose methods for semiautomatic and user-guided methods for objective, reliable, and quantitative analysis of the GBM thickness in TEM images of renal biopsy samples. The methods include steps for the split-and-merge (SAM) algorithm,¹⁶ morphological image processing,¹⁷ skeletonization,^16,18,19 and statistical analysis of the width of the GBM.^15,20

Image Acquisition

TEM²¹ is extensively used in medical applications to reveal the ultrastructure of biological samples to the order of a few nanometers.^19,22 The images used in the present study were acquired by using a Hitachi H-7000 TEM system with magnification in the range of 1,500 to 17,000, and were digitally captured by an H-7000 4.2 MP (mega pixel) charge-coupled device camera with 8 bits per pixel. The computer used to process the images is a Dell Precision 360 workstation with the following characteristics: 3.20 GHz Pentium 4 processor, 2 MB of cache memory, and 2 GB of RAM. Figure 1a shows an example of a TEM image including parts of a GBM.

The dataset used in the present study includes 34 TEM images of renal biopsy samples of six patients: one patient with abnormally thin GBM, one with abnormally variable GBM width, two with normal GBM, and two with abnormally thick GBM. Some of the details of the six patients are listed in Table 1. For each patient, one image was selected for manual segmentation and analysis, with several regions of interest (ROIs) including sections of the GBM. The images were processed independently by an experienced renal pathologist (H.B.) and the proposed methods, including segmentation of the GBM, measurement of its width, and computation of the statistics for comparative analysis. The same dataset of images and manual measurements as reported in our previous related report¹⁵ were used in the present study.

Segmentation of the GBM Using the Split-and-Merge Method

The method proposed in the present work for segmentation and analysis of the GBM includes the following steps in the SAM algorithm¹⁶ and additional morphological image-processing techniques for post-processing:¹⁷

1. Set the entire image as an initial region.

2. Split the region into a number of subregions (equal to four in the present work).

3. For each subregion, check if it satisfies a homogeneity criterion. For those that do not, go to Step (2).

4. Stop splitting when all regions satisfy the homogeneity criterion.

5. For each subregion, check the neighboring regions. If they can be merged such that the united region will satisfy the homogeneity criterion, perform merging.

6. Repeat Step (5) until all possible merges are done.

7. Reject regions based on size and shape.

8. If required, manually combine GBM segments and remove artifacts.

9. Apply morphological smoothing and opening by reconstruction.¹⁶

In the splitting procedure, to check whether a certain region is homogeneous, first, the gray-level variance of the pixels within the region is calculated; then, the result is compared with the value of the homogeneity threshold specified (set to 7 in the gray-scale range of [0, 255] in the present work). In the merging procedure, for each pixel within a region, the 8-connected neighborhood is checked to verify if there are other neighboring regions such that the absolute difference between the regions’ means is less than a second homogeneity threshold (set to 11 in the present work).

A graphical user interface (GUI) has been developed in the present work to facilitate the execution of the methods described above, as well as the subsequent steps described in the following paragraphs. The GUI and all procedures were developed in MATLAB®.

Figure 1b shows the result of application of the SAM method to the image in Figure 1a. As can be seen, most of the GBM has been recognized by the SAM algorithm as a relatively homogeneous region. In places where gray-level changes exceed the homogeneity threshold, parts of the GBM have been identified as separate segments. Such regions, if required for subsequent analysis, can be included manually by the operator. Another segmentation challenge is associated with the so-called collapsed GBM,² which is a part of the GBM corresponding to areas with lost podocytes, and should be excluded from further analysis. Due to the fact that both the collapsed and the normal GBM are of the same nature, and as a result, possess similar texture and brightness in TEM images, their separation cannot be achieved automatically. As seen from the SAM result in Figure 1b, the segmentation procedure cannot distinguish between these two types of tissue, and manual intervention of the operator is required to eliminate regions corresponding to collapsed GBM.

Due to the high complexity of TEM images of renal biopsy samples, the SAM procedure can produce a large number of segments. To limit the number of regions for further analysis, and to facilitate the operator in the recognition of the GBM, two types of filters are proposed. The part of the GUI related to the filtering step is shown in Figure 2. The first filtering technique is based on the fact that the GBM is a nearly uniform region with no abrupt discontinuities, and as a result, after application of the SAM procedure, should comprise one or a few relatively large segments. Filtering of regions by size is achieved by using a normalized threshold value τ_n that can be set in the range of [0, 1] in steps of 0.01. The default value of τ_n is set to 0.1. Then, the minimum size of the segments to be retained is calculated as

1

where M and N are numbers of rows and columns in the preprocessed image, respectively, and α is an empirical coefficient that is set to be equal to 0.05. If the procedure is to be applied to images with varying spatial resolution, an additional factor related to pixel size may be incorporated into the equation above.

The second filtering technique takes into account the shape of the GBM. The GBM is a narrow ribbon-like region, which, in comparison with other tissues present in TEM images, has higher compactness,¹⁹ defined as

2

Here, A is the area and P is the perimeter of the region being processed. The normalized definition of compactness results in a value of unity for a straight line (with the area contained being zero) and zero for a circle. The operator can set a threshold value of compactness in the range of [0, 1] in steps of 0.01: a threshold of 0 will preserve all shapes except circles, and a threshold of 1 will reject all regions. The default value for the compactness threshold is set to 0.2.

In most TEM images, the brightness of the GBM does not remain the same and can vary within the image. Therefore, after application of the SAM method, the GBM will comprise several regions of different size and shape. Manual selection of the filtering thresholds gives the user flexibility to achieve trade-off between the precision of the result and the operational time; see the GUI shown in Figure 2. If a rough estimate is adequate, the user can set high filtering thresholds, so that most of the non-GBM regions along with some of the GBM segments will be removed. To include most of the GBM regions in the analysis, the filtering thresholds should be set low; however, more subsequent manual processing may be required. Figure 1c shows the result of filtering with relatively high thresholds (equal to 0.5 for τ_n and 0.94 for cf). This way, minimal or no intervention is required from the operator to finalize the selection of the GBM to produce a result similar to that shown in Figure 1d.

After application of the SAM algorithm and subsequent filtering of the result, the segmented region(s) should correspond to the GBM tissue present within the image, as shown in Figure 3a for the original image and the preprocessed versions in Figure 1. However, it was observed that the regions included holes and were surrounded by a connected mesh-type network of pixels that were falsely recognized to be part of the GBM. The causes of these artifacts are the intensity variations present within the GBM and also the absence of sharp boundaries of the GBM. To eliminate these artifacts, the morphological smoothing operation is applied, which consists of the morphological opening operator followed by the closing operator.¹⁷ Figure 3a shows the result of morphological smoothing applied to the image in Figure 1d. However, this step does not fill holes of size larger than the structuring element (defined as a disk of radius 2 pixels in the present work). To overcome this limitation, opening by reconstruction¹⁷ is applied to the result of morphological smoothing. The marker for the reconstruction step is chosen to be a black square of the size of the image, placed within a white frame of unit-pixel width. The mask is set to be equal to a binary negative of the image surrounded in a similar manner by a white frame. Figure 3b gives an example of the result of application of opening by reconstruction to the result of morphological smoothing shown in Figure 3a.

Skeletonization of the GBM

After most of the GBM tissue present in the image being analyzed has been segmented, the results of segmentation are passed on to a procedure for the detection of the skeleton.^15,16,18,19 The skeleton is a binary, 1-pixel-wide representation of the given image that summarizes information related to the size, orientation, shape, and connectivity of the objects in the image. A point belongs to the skeleton of F, if, for the largest disc centered at h, expressed as D(h), there does not exist a disc D, such that .^16,18 The skeleton of the segmented GBM shown in Figure 3b is displayed in Figure 4a.

In addition to pixels corresponding to the central line of the GBM, the skeletons obtained using the procedure described above were observed to contain several short segments due to the presence of protrusions, incursions, and minor details in the GBM (see Fig. 1a and Fig. 4a). Such spurs or hair-like parts of the skeleton, if left intact, could lead to erroneous measurements of the GBM width and therefore should be removed. The technique of “skeleton shaving”¹⁷ was applied for this purpose. When applied once, the procedure removes a single pixel at each end of the skeleton. If the procedure is repeated N_s times, where N_s is called the “shaving depth”, such that N_s is larger than the length of the spurs, the remaining skeleton corresponds to the central line of the GBM. Figure 4b shows the result of “skeleton shaving” of the skeletons in Figure 4a, with a “shaving depth” N_s = 23 pixels. It is seen that most of the spurs have been trimmed or removed. This procedure results in the loss of a few points, as determined by the value of N_s used, at the ends of each GBM segment. In the present work, such a loss was considered to have negligible effect on the final results of statistical analysis.

The pixels of a given skeleton need to be linked together with the skeleton’s chains. The linking procedure starts at one of the skeleton’s ends, and is carried on using the 8-connected neighborhood until the other end is detected. If, during the linking procedure, the skeleton splits into two or more branches, the linking for the current chain is terminated, and the pixels corresponding to the beginnings of each branch are added to the list of the skeleton’s end points to form their own skeleton chains. Because a GBM image can comprise several disconnected regions, there can be many skeleton chains formed at the end of the linking procedure. The process ends when all skeleton points get linked to the skeleton chains. Upon completion of the linking procedure, the length of each skeleton chain is checked against the minimum length threshold. If a chain’s length is less than the specified minimum size (equal to 21 pixels in the present work), it is removed. The minimum-length limit was determined based upon the characteristics of the typical images in the dataset processed. The low limit set ensures that significant portions of the GBM are not deleted.

Measurement and Analysis of the Width of the GBM

The following procedure is applied for the estimation of the GBM width:¹⁵

1. Start with the first skeleton chain.

2. Denote by w the size of a sliding window and by l a chain’s length. Place the sliding window at the beginning of the chain such that the first w elements of the chain are included in the analysis.

3. Fit a straight line to all the pixels within the sliding window and calculate its slope t.

4. Estimate the slope of the normal to the composed line as n = −1/t. If t is less than a minimum slope threshold (equal to 0.2 in the present work), mark n as a vertical line.

5. Using the slope of the normal n and the pixel corresponding to the center of the sliding window, build the equation to the line perpendicular to the straight-line fit obtained in Step (3).

6. Follow the perpendicular line in both directions from the skeleton pixel until the boundary of the GBM region is reached. If, during the growth procedure, the perpendicular line touches the image boundary or intersects with another skeleton point, discard the line.

7. Calculate the Euclidean distance between the two end points, corresponding to the intersections of the perpendicular line with the GBM boundary.

8. If the position of the sliding window is less than l − w/2, advance it by 1 to the next skeleton point and go to Step (3); otherwise proceed to the next skeleton chain and go to Step (2).

Figure 4c depicts the width measurements along the GBM using the skeleton shown in Figure 4b. The histogram of all of the GBM width measurements is accumulated for the case being processed, which could include several ROIs from several images. The following steps are then applied for analysis of the GBM:¹⁵

1. conversion of the width data from pixels to nm;

2. calculation of the mean (μ) and the standard deviation (σ);

3. rejection of the width values outside the range [μ ± 2σ];

4. recalculation of μ and σ;

5. estimation of skewness, kurtosis, and coefficient of variation (CV = σ/μ);

6. plotting of the histogram of the GBM width measurements; and

7. updating the accumulated statistics.

The GUI developed for the present work facilitates the application of the methods described above.