Morphometric Methods for Virtual Endoscopy

Ronald M. Summers 1 Overview of Virtual Endoscopy 747

National institutes of Health 2 Current Problems in Virtual Endoscopy 748

3 Shape-Based Detection of Endoluminal Lesions Using Curvature Analysis 748

3.1 Clinical Application of Shape-Based Lesion Detection

4 Fractal Measures of Roughness 750

4.1 Clinical Application of Fractal Measures of Roughness

5 Conclusions 753

References 754

1 Overview of Virtual Endoscopy

Virtual endoscopy (VE) is a novel display method for three-dimensional medical imaging data. It produces endoscope-like displays of the interior of hollow anatomic structures such as airways, the gastrointestinal tract, and blood vessels [1-5]. For example, Fig. 1 shows a virtual bronchoscopy reconstruction of the air passages of a human lung with depiction of bronchi as small as fifth and sixth order. Studies have shown virtual endoscopy to be useful for the visualization of morphologic abnormalities such as aneurysms, tumors, and stenoses [6-8].

VE displays are usually produced from planar 2D computed tomography (CT) or magnetic resonance (MR) images using surface or volume rendering [9,10]. Surface rendering is generally done by taking an isosurface through the imaging volume at a specified threshold value; this generates contours in three dimensions that are analogous to the two-dimensional isocontours of temperature or pressure (isotherms, isobars) on weather maps. In the case of VE, the contours represent the wall of a hollow anatomic structure, such as airways or blood vessels. One commonly used isosurface algorithm called "marching cubes" generates a triangular tessellation of the isosurface suitable for interactive display on computers equipped with graphics accelerators [11]. Disadvantages of surface rendering are that a complex segmentation must be done as a preprocessing step and only a fraction of the data is retained in the final image.

In contrast to surface rendering, volume rendering is done by considering the imaging volume to be a translucent gelatin whose optical density and opacity are mapped to each voxel intensity through user-adjustable transfer functions. Volume rendering overcomes a disadvantage of surface rendering in that segmentation is not required. However, volume rendering is typically not interactive unless very expensive computers are used. In addition, the transfer functions can span a wide range of values; this freedom offers considerable flexibility, but it can be difficult to identify the correct choices to produce an accurate image. Some progress has been made toward defining an appropriate transfer function for virtual colonoscopy [12].

Since VE is used to visualize small structures such as airways, blood vessels, and colonic polyps whose size may be 1 cm or less, image data with small voxel dimensions, desirably 1 mm3 or less, is required to generate a VE. The smallest pathologic structure visualized on a VE will be on the order of the voxel resolution, which is as large as or larger than the voxel dimension. The voxel resolution depends on a host of adjustable parameters (e.g., for CT: helical pitch, reconstruction algorithm, section index) [13].

Presently, VE is viewed as either static images or as a movielike "fly-through" that simulates conventional endoscopy. The lack of physical feedback necessitates new tools to orient the observer. Examples of such tools include navigation aids to integrate cross-sectional images with the VE image, centerline computation for automated flight planning, unraveling of the colon to ease polyp identification, and cockpit displays to provide greater visual coverage of the wall of the lumen and reduce blind spots [14-18].

Clinical uses for VE presently include detection of many of

FIGURE 1 Images derived from CT scans of autopsy human lung specimen. (A) Coronal multiplanar reformatted image shows excellent resolution required to depict small airways. Airways are the black branching structures (arrow). The three lobes of the right lung (left side of image) and two lobes of the left lung are shown. (B) Anteroposterior view of three-dimensional surface reconstruction of airways showing exquisite depiction of branching to fifth and sixth order. (C) Virtual bronchoscopy view of bifurcation of a fifth order bronchus only 2 or 3 mm in diameter, at or near furthest point reachable by a conventional bronchoscope.

FIGURE 1 Images derived from CT scans of autopsy human lung specimen. (A) Coronal multiplanar reformatted image shows excellent resolution required to depict small airways. Airways are the black branching structures (arrow). The three lobes of the right lung (left side of image) and two lobes of the left lung are shown. (B) Anteroposterior view of three-dimensional surface reconstruction of airways showing exquisite depiction of branching to fifth and sixth order. (C) Virtual bronchoscopy view of bifurcation of a fifth order bronchus only 2 or 3 mm in diameter, at or near furthest point reachable by a conventional bronchoscope.

the same abnormalities for which conventional endoscopy is indicated, for example virtual colonoscopy to detect colonic polyps, virtual bronchoscopy to detect bronchial stenoses and to guide biopsies, and virtual angioscopy to detect vascular pathology [19-22]. Relative to conventional endoscopy, VE's main benefits are its noninvasiveness and ability to integrate information about both the lumen and extraluminal structures into a single image. Although VE seeks to emulate conventional endoscopy, which has proven to be a powerful diagnostic and therapeutic tool, VE may surpass conventional endoscopy by solving some of the problems of conventional endoscopy (underutilization due to expense and invasiveness). In this context, VE may play a role in screening a general patient population for the presence of disease and serial evaluation to detect disease recurrence in already affected individuals. Screening would greatly expand the number of VE studies performed.

2 Current Problems in Virtual Endoscopy

Important tasks of clinical diagnosis are to detect lesions and determine their significance. Although a number of studies have shown that lesions can be detected using VE, a number of roadblocks to more widespread acceptance of VE have been identified. Interpretation of a VE can be inefficient, tedious, and time consuming, which can lead to fatigue, misdiagnoses, and decreased throughput; lesion identification can be difficult in some circumstances (for example, on virtual colonoscopy, polyps can be missed if they lie behind haustral folds; retained feces can simulate masses); and the utility of VE appears to be limited to focal abnormalities such as stenoses and tumors.

There are a number of approaches to solving the problem of inefficiency. Automated lesion detection software could direct physicians to sites likely to harbor lesions, thereby facilitating interpretation. Such software may reduce the number of false negatives by identifying lesions that could be missed on an automated fly-through, such as polyps hidden behind folds. The problem of identifying more diffuse abnormalites (e.g., atherosclerosis and inflammation can present as focal or diffuse disease) can be addressed by the development of new algorithms to analyze the VE.

These problems fall into the category of morphometric analysis of VE reconstructions. We have previously described simple morphometric methods in VE (such as size measurement) and potential pitfalls (e.g., z-axis broadening, distortions due to perspective rendering) [9,13]. In this paper, we review more sophisticated morphometric approaches (curvature and fractal analyses) that address the problems described above [23-25].

3 Shape-Based Detection of Endoluminal Lesions Using Curvature Analysis

Detection of endoluminal lesions (those that distort the wall of a hollow anatomic structure or protrude into its lumen) such as polypoid masses of the airway and colon is one important task of diagnostic imaging [26]. The routine use of thin CT and MR sections allows for detection of small lesions with VE. We have found that curvature-based shape analysis can detect endobronchial lesions [23,24]. This analysis uses the principal curvatures of the VE surface to segment it into areas of different shape. Lesions that protrude into the lumen are identified as areas of the luminal surface with "elliptical curvature" of the "peak subtype." We now describe a method we have used for computing curvatures of gray-scale image data.

For a gray-scale image I(x, y, z), the local shape of an isosurface at a point is described by the Gaussian (_K) and mean (H) curvatures, which can be computed from

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