Chapter 7

Detecting and Analyzing Linear Structures

in Biomedical Images: A Case Study Using

Corneal Nerve Fibers

Mohammad A. Dabbah, James Graham, Rayaz A. Malik, and Nathan Efron

7.1 Introduction

Diabetic peripheral neuropathy (DPN) is one of the most common long-term complications of diabetes. The accurate detection and quantification of DPN are important for defining at-risk patients, anticipating deterioration, and assessing new therapies. Current methods of detecting and quantifying DPN, such as neurophysiology, lack sensitivity, require expert assessment and focus primarily on large nerve fibers. However, the earliest damage to nerve fibers in diabetic neuropathy is to the small nerve fibers. At present, small nerve fiber damage is currently assessed using skin/nerve biopsy; both are invasive technique and are not suitable for repeated investigations.

Recent research [1–3] using Corneal Confocal Microscopy (CCM) suggests that this noninvasive, and hence reiterative, test might be an ideal surrogate endpoint for human diabetic neuropathy. These studies demonstrate that measurements made by CCM accurately quantify corneal nerve fiber morphology. The measurements reflect the severity of DPN and relate to the extent of intra-epidermal nerve fiber loss seen in skin biopsy. However, the major limitation preventing extension of this technique to wider clinical practice is that analysis of the images using interactive image analysis is highly labor-intensive and requires considerable expertise to quantify nerve fiber pathology. To be clinically useful as a diagnostic tool, it is essential that the measurements be extracted automatically.

The chapter is organized as follows. Section 7.2 provides an overview of some linear structure detection methods. Section 7.3 focuses on the quantification of CCM imaging. Section 7.3.1 provides more detail on its relationship with diabetic neuropathy, while Sect. 7.3.2 discusses the characteristics of CCM images and

M.A. Dabbah ( )

The University of Manchester, Manchester, England e-mail: [e-mail]

G. Dougherty (ed.), Medical Image Processing: Techniques and Applications, Biological

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and Medical Physics, Biomedical Engineering, DOI 10.1007/978-1-4419-9779-1 7, © Springer Science+Business Media, LLC 2011

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Sect. 7.3.3 presents the metrics used to quantify the images. The dual-model detection algorithm is then presented in Sect. 7.4. The foreground and background models are described in Sect. 7.4.1 and the method for estimating local orientation is presented in Sect. 7.4.2. The final outcome of the dual-model and its postprocessing are discussed in Sects. 7.4.3 and 7.4.4, respectively. Section 7.5 describes the method and results of the comparative evaluations together with the assessment of clinical utility. The conclusion is provided in Sect. 7.6.

7.2 Linear Structure Detection Methods

The first critical stage in analysis of CCM images is the detection of nerve fibers. This is challenging as the nerve fibers often show poor contrast in the relatively noisy images. The literature on this topic is not extensive, although the problem has a superficial similarity to other, more widely investigated, applications, such as detection of blood-vessels in retinal images. Ruggeri et al. [4] describe a heuristic method that was adapted from retinal analysis. Linear structures occur in a number of imaging applications, in biomedicine and other fields. Below, we briefly review some that are particularly relevant to this application.

In [5], we conducted a preliminary comparison of methods for contrast enhancement of nerve fibers, comparing a Gabor wavelet with a well-established line detector. This method (Line Operator – LinOp), originally developed for detection of asbestos fibers [6] has also been used in other contexts, such as the detection of cracks in metal castings [7] and has been shown to be effective in detecting ducts and other linear structures in mammograms [8]. LinOp exploits the linear nature of the structures to enhance their contrast by computing the average intensity of pixels lying on a line passing through the reference pixel for multiple orientations and scales. The largest values are chosen to correspond to the line, the strength of which is determined by the difference with the average intensity of the similarly oriented square neighborhood. In the original LinOp implementation, processing was conducted at a single scale, but later versions used a multi-scale analysis.

In our comparative study [5], the 2D Gabor filter [9] was used to detect nerve fibers in CCM images. The filter is a band-pass filter that consists of a sinusoidal plane wave with a certain orientation and frequency, modulated by a Gaussian envelope. This spatial domain enhancement is based on the convolution of the image with the even-symmetric Gabor filter that is tuned to the local nerve fiber orientation. The comparison indicated that the oriented Gabor response, gave slightly improved enhancement of nerve fibers over that provided by LinOp.

Inspired by [10, 11], Frangi et al. [12] used a multi-scale decomposition of the Hessian matrix (matrix of second order image derivatives) to detect and measure blood vessels in Digital Subtraction Angiography images in 2D and 3D Magnetic Resonance Angiography images. Local second order structure of the image can

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be decomposed by extracting the principal directions using the eigenvalues of the Hessian. Unlike Lorenz et al. [10] and Sato et al. [11], Frangi et al. [12] simultaneously used the eigenvalues and eigenvectors of the Hessian to derive a discriminant function that has maximum response for tube-like structures. The method uses the norm of the Hessian to distinguish between background and foreground based on the observation that the magnitude of the derivatives (and thus the eigenvalues) is small at background pixels. Several other models based on second derivatives have been widely used for linear structure detection in medical image analysis [13].

The dual-tree complex wavelet transform (DTCWT) [14] is an extension of the discrete wavelet transform (DWT), which provides a sparse representation and characterization of structures and texture of the image at multiple resolutions. The DTCWT utilizes two DWT decompositions (trees) with specifically selected filters that give it the properties of approximate shift-invariance and good directionality. The key feature of the DTCWT operation lies in the differences between the filters in the two trees. DTCWT has been used in extracting and decomposing information from images to obtain rich feature descriptors of key-points [15]. It was also used to detect linear structures in retinal image [16] and mammograms [17].

The Monogenic Signal [18] (a variant of a 2D analytic signal) is an extension of the analytic signal using quaternionic algebra in an attempt to generalize the method to enable it to analyze intrinsically 2D signals, for example, structures within images. The Monogenic Signal is based on the Riesz transform, which is a 2D generalization of the Hilbert transform used in the conventional analytic signal. The Monogenic Signal is defined as the combination of the original signal and the Riesz-transformed one in the algebra of quaternions. It has been used in extracting structure information (such as edge, ridge, etc.) from images in several medical image analysis applications [19, 20].

7.3Quantification of Nerve Fibers in Corneal Confocal Microscopy Imaging

CCM imaging is a new technology based on confocal laser scanning microscopes (CLSM), which captures high-resolution images with depth selectivity from the cornea of the human eye. However, confocal microscopy itself is not new, having been first introduced in 1961 [21] and later adopted as a standard technology in the late 1980s.

Confocal microscopy provides highly improved image quality over “conventional” transmitted-light microscopy due to its highly controlled and limited depth of focus. Images are reconstructed by detecting light from the focal plane in a point-by-point fashion, with the result that light from out-of-focus parts of the sample does not contribute to image background. Confocal imaging is widely

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used for constructing three dimensional images of prepared samples. A number of instruments are available that apply the same imaging procedure to the cornea in vivo (such as Tomey Confoscan,1 Nidek,2 HRT-III.3)

7.3.1 CCM for Imaging Diabetic Peripheral Neuropathy

Diabetic neuropathy is one of the commonest long-term complications of diabetes and is the main initiating factor for foot ulceration, Charcot’s neuroarthropathy, and lower extremity amputation. As 80% of amputations are preceded by foot ulceration, an effective means of detecting and treating neuropathy would have a major medical, social, and economic impact. The development of new treatments to slow, arrest, or reverse this condition is of paramount importance but is presently limited due to difficulties with end points employed in clinical trials [22].

Recent studies suggest that small unmyelinated c-fibers may be the earliest to be damaged in diabetic neuropathy [23–25]. The only technique which allows a direct examination of unmyelinated nerve fiber damage are those of sural nerve biopsy with electron microscopy [25, 26], and the skin-punch biopsy [27–29], but both are invasive procedures. However, our previous studies in patients with diabetic neuropathy have shown that CCM can be used to quantify early small nerve fiber damage and accurately quantify the severity of diabetic neuropathy [1, 2]. These observations led us to suggest that CCM may be an ideal noninvasive surrogate marker for detecting small fiber damage in diabetic and other peripheral neuropathies [3]. Moreover, we have shown that corneal nerve damage assessed using CCM relates to the severity of intra-epidermal nerve fiber loss in foot skin biopsies [30] and the loss of corneal sensation [31] in diabetic patients. CCM also detects early nerve fiber regeneration following pancreas transplantation in diabetic patients [32]. Recently, we have also shown that CCM detects nerve fiber damage in patients with Fabry disease [33] and idiopathic small fiber neuropathy [34] in the presence of normal electrophysiology and quantitative sensory testing (QST). CCM offers considerable potential as a surrogate marker, and hence as an end-point for clinical trials in diabetic neuropathy [35].

7.3.2 CCM Image Characteristics and Noise Artifacts

CCM images are captured at different depths in the cornea by manual focusing of the CLSM. Due to different capturing conditions such as saccadic eye movements

1Tomey Corporation, http://www.tomey.com/.

2Nidek Inc. http://usa.nidek.com/.

3Heidelberg Engineering, Inc. http://www.heidelbergengineering.com/.

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Fig. 7.1 CCM images of nerve fibers obtained from the Bowman’s membrane. The images exhibit different varieties of artifacts due to acquisition conditions

in the eye, the degree of physical pressure on the eye, the spherical shape of the cornea, etc. images can suffer a variety of artifacts (Fig. 7.1).

One of the common artifacts seen in CCM images is uneven illumination: low frequency intensity variations across the entire CCM image with no correspondence to the feature of interest of the image (nerve fibers, cells, etc.). These illumination artifacts are caused by the physical pressure of the CLSM lens on the spherically shaped cornea. It is difficult to avoid such artifacts while capturing the images as the acquisition requires constant physical contact through a medium that matches the refractive index of the cornea. These artifacts could not be defined by a certain orientation or frequency. This makes it plausible for pass-band directional filters to eliminate them from the image. Two-dimensional wavelets are an example of such filters.

Motion artifacts arise from the fact that it is difficult for patients to keep their eyes still with the microscope lens in contact with the cornea, despite the application of an anesthetic drop. The result is blurring of the nerve fibers.

The human cornea has a diameter of about 11.5 mm and a thickness of 0.5–0.6 mm in the centre and 0.6–0.8 mm at the periphery. It is transparent, has no blood supply and gets oxygen directly from the atmosphere. It consists of five layers: Epithelium, Bowman’s membrane, Stroma, Descemet’s membrane, and Endothelium. The Bowman’s membrane is 8–12 μm thick, helps the cornea maintain its shape and is composed of nerve fibers. It is in this layer that CCM images are acquired for analysis.

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Fig. 7.2 CCM image characteristics. Nerve fibers flow in a predominant direction everywhere in the image with some minor variation in the direction and size. The size of these nerve fibers can be attributed to high-frequency components in the Fourier domain as shown in the right-hand side of the figure

These nerve fibers extend into different depths of the membrane causing them to disappear when they move out of the scanning focal plane. The spherical shape of the cornea also contributes to this depth-of-field artifact, especially around the periphery of the field of view.

Nerve fibers in CCM images display different lengths, widths, patterns, and orientations (Fig. 7.2). However, within an image they exhibit a predominant global orientation with minor variations across the image.

This predominant orientation depends on the part of the cornea the image is captured from. Across the cornea, the nerve fibers tend to converge toward the centre, in front of the pupil. The 2D Fourier Transform of the image in Fig. 7.2 shows the high frequency components (i.e., edges or nerve fibers) lying in an oriented pattern around the origin. These image characteristic can be used to detect nerve fibers and filter out noise.

7.3.3 Quantified Metrics of Nerve Fibers in CCM Images

For quantitative measurement of nerve fibers four main metrics are used: nerve fiber length (NFL), nerve fiber density (NFD), nerve-branch density (NBD), and nerve fiber tortuosity (NFT). The nerve fibers are considered as being the main trunks while braches are the secondary fibers which originate from the main nerve fibers (see Fig. 7.2).

NFL is defined as the total length of all nerve fibers visible in the CCM image per square millimeter. The total length is computed by tracing all the nerve fibers and nerve-branches in the image. This number is then divided by the area of the field- of-view provided by the microscope to produce the NFL [mm/mm2]. According to

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Fig. 7.3 An example of a CCM image with a tortuous nerve fiber

ongoing research and previously published data, this metric seems to be the most significant measure in categorizing and analyzing the diabetic neuropathy. The NFD and nerve-branch densities are the number of the major nerves per square millimeter and the number of branches emanating from those major nerve trunks per square millimeter of corneal tissue, respectively.

NFT is a metric indicating the degree of curvature or tortuousness of the main nerve fibers. There have been several attempts to quantify this property in medical image analysis such as in retinopathy [36], corneal neuropathy [2], etc. Clinical research [2] has shown that NFT (Fig. 7.3) can differentiate between differing severities of neuropathy.

7.4A Dual-Model Detector for Linear Structures in CCM Images

To quantify the CCM images, the nerve fibers have to be reliably detected. The quality of captured images is often low due to the imaging effects outlined in Sect. 7.3.2 and nerve fibers may appear faint due to either their small size or being only partly in the focus plane. Therefore, a nerve fiber contrast enhancement algorithm is needed to exploit the linear structure of the nerve fibers and distinguish them from the background noise. All of the methods described in Sect. 7.2 are capable of providing this enhancement. In the next section, we describe our approach, the dual-model [37].